Computational Internal Dosimetry Methods as Applied to the University of Florida Series of Hybrid Phantoms

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Title:
Computational Internal Dosimetry Methods as Applied to the University of Florida Series of Hybrid Phantoms
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1 online resource (488 p.)
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english
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Wayson, Michael B
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University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
Bolch, Wesley E
Committee Members:
Gilland, David R
Hintenlang, David E
Hagen, Stephen J
Sgouros, George
Lee, Choonsik

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Subjects / Keywords:
beta -- cancer -- computational -- dosimetry -- electron -- imaging -- internal -- medicine -- morphometry -- nuclear -- phantom -- photon -- radiopharmaceutical -- saf -- sensitivity
Biomedical Engineering -- Dissertations, Academic -- UF
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Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
Two primary areas of consideration for dosimetry of nuclear medicine imaging and therapy procedures are (1) the organ absorbed dose calculations, taking into account size, shape, and proximity of all internal organs as well as the energy and type of radiation emitted, and (2) the biokinetic models, taking into account how the radiopharmaceutical distributes throughout the body as a function of time.  This study focuses on methods used to estimate radiation absorbed dose to organs of the human body from internal radiation emitting nuclides.  Estimating absorbed dose to human tissues from radiations emitted from inside the body is known as internal dosimetry and is an integral part of performing risk assessment for the induction of secondary cancers, nuclear medicine image optimization, and limitation of dose to non-targeted organs in radiopharmaceutical therapy. This study developed a new system of blood vessels and blood dosimetry model, and the subsequent iteration of phantoms represents the latest University of Florida (UF) hybrid computational phantom (computerized representation of the human body) family.  Skeletal photon fluence-to-dose response functions were computed for the pediatric and adolescent series of UF phantoms to allow for the determination of absorbed dose to the skeletal tissues at risk for radiogenic leukemia and osteosarcoma. A complete set of photon and electron specific absorbed fractions (SAFs)were computed for the entire family of UF phantoms.  SAFs are used with radiopharmaceutical biokinetic data to determine individual organ doses.  Variations in radiation absorbed dose with changes in source and target organ masses, and source and target organ separation, and body habitus were investigated. These dosimetric sensitivity studies led to useful dose scaling methods for individual patients when patient-specific imaging-based methods of internal dosimetry are not available.  Results of the SAF calculations and scaling methodologies can be incorporated into software, thus facilitating their ease of use. Improvements in the accuracy of internal dose estimates allows for optimization of nuclear medicine imaging procedures and assessment of dose to normal tissues at risk during molecular radiotherapy procedures. In all cases, effectively balancing radiation dose with adequacy of clinical outcomes can be better achieved with more accurate patient dose estimates.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Michael B Wayson.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
Local:
Adviser: Bolch, Wesley E.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-08-31

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lcc - LD1780 2012
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UFE0044569:00001


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1 COMPUTATIONAL INTERNAL DOSIMETRY METHODS AS APPLIED TO THE UNIVERSITY OF FLORIDA SERIES OF HYBRID PHANTOMS By MICHAEL B WAYSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFI LLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 20 12

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2 20 12 Michael B Wayson

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3 To Leslie

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4 ACKNOWLEDGMENTS I would like to thank my doctoral dissertation chair, Dr. Wesley Bolch, for his extensive he lp, guidance, and mentoring throughout my time here at the University of Florida. My project needed a question answered or an idea critically assessed, and I was always able to talk out issues with him to make breakthroughs throughout my doctoral research. I will forever be grateful for the support he gave me during my time here. I would like to thank the members of my committee (not in order of importance) Dr. David Hintenlang, Dr. David Gilland, Dr. Stephen Hagen Dr. George Sgouros, and Dr. Choonsik Lee. They were all instrumental in provided input and critically assessing my methods and approaches. I appreciate all they have done to maximize the effecti veness of my project. I would like to thank Dr. Choonsik Lee for his instruction in the use of MCNPX v2.6. Ever since 2006, he has helped me understand the intricacies and avoid the pitfalls of MCNPX v2.6. I would like to thank all of my colleagues who h ave given me help along the way. The collaborative nature of our department truly facilitates progress. In no particular order I would like to thank Laura Padilla, Dr. Deanna Pafundi, Matthew Maynard, Dr. Perry Johnson, Dr. Justin Hanlon, Amir Bahadori, Daniel Long, Andres Abadia, Badal Juneja, and Lindsay Sinclair. There are others who have helped me, and if I left your name off this list, know that I am still appreciative. Finally, I would like to thank my family for all of the support they have given me throughout the years, my loving wife who has always supported me in my academic endeavors, and my Lord and Savior Jesus Christ who has blessed me with many opportunities to pursue my goals.

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5 TABLE OF CONTENTS P age ACKN OWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ......................... 10 LIST OF FIGURES ................................ ................................ ................................ ....................... 15 LIST OF ABBREVIATIO NS ................................ ................................ ................................ ........ 21 ABSTRACT ................................ ................................ ................................ ................................ ... 26 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 28 Specific Aims ................................ ................................ ................................ .......................... 29 Hypothesis ................................ ................................ ................................ .............................. 29 Background ................................ ................................ ................................ ............................. 30 Overview of Nuclear Medicine Imaging Procedures and Dosimetry Concepts ..................... 32 History of Computational Dosimetry Phantoms ................................ ................................ ..... 35 Stylized Phantoms ................................ ................................ ................................ ........... 36 Voxel Phantoms ................................ ................................ ................................ ............... 38 Hybrid Phantoms ................................ ................................ ................................ ............. 39 Development of the UF Hybrid Computational Phantoms ................................ ..................... 40 Phantom Specificity ................................ ................................ ................................ ................ 44 Relevant Radiological Physics ................................ ................................ ............................... 46 Photon Energy Deposition ................................ ................................ ............................... 47 Electron Energy Deposition ................................ ................................ ............................ 49 Photon Electron Cascades ................................ ................................ ............................... 51 Absorbed Fraction of Energy ................................ ................................ .......................... 52 Effective Dose ................................ ................................ ................................ ................. 53 Relevant Studies and Current Limitations ................................ ................................ .............. 55 Phantom Blood Vessel Systems ................................ ................................ ...................... 56 MCAT to XCAT: the evolution of 4 D computerized phantoms for imaging research (Segars et al. 2009) ................................ ................................ ................. 56 The virtual family development of surface based anatomical models of two adults and two children for dosimetric simulations (Christ et al. 2010) ............... 57 Skeletal Photon Fluence to Dose Resp onse Functions ................................ ................... 58 Evolution and status of bone and marrow dose models (Stabin et al. 2002) ........... 58 Specific absorbed fractions of energy at various ages from internal photon sources. I. methods et al. 1987) ................................ ............................ 60 Photon Specific Absorbed Fractions ................................ ................................ ............... 62 Specific a bsorbed fractions of energy at various ages from internal photon sources. I. methods (Cristy et al. 1987) ................................ .............................. 62 ICRP 110: adult reference computational phantoms (ICRP 2009) .......................... 65

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6 Electron Specific Absorbed Fractions ................................ ................................ ............. 67 Specific absorbed fractions of energy at various ages from internal photon sources. I. methods (Cristy et al. 1987) ................................ .............................. 67 ICRP 110: adult reference computational phantoms (ICRP 2009) .......................... 68 Dosimetric Sensitivity Analysis for Internal Sources ................................ ..................... 68 Patient specific scaling of reference S values for cross organ radionuclide S values: what is appropriate? (Petoussi Henss et al. 2007) ................................ .... 68 Changes in radiation dose with variations in human anatomy: larger and smaller normal stature adults (Marine et al. 2010) ................................ ............... 70 Changes in radiation dose with variations in human anatomy: mode rately and severely obese adults (Clark et al. 2010) ................................ .............................. 71 Internal Dosimetry Software ................................ ................................ ........................... 73 OLINDA/EXM: the second generation personal co mputer software for internal dose assessment in nuclear medicine (Stabin et al. 2005) ................................ .... 73 2 MATERIALS AND METHODS ................................ ................................ ........................... 95 Blood Vessel Sys tem for the UF Hybrid Phantom Family ................................ ..................... 95 Non Uniform Rational B Splines Model ................................ ................................ ........ 95 Vascular Dosimetry for Blood Sources ................................ ................................ ........... 98 Skeletal Photon Fluence to Dose Response Functions ................................ ........................ 102 Sub Segmented Skeleton Development ................................ ................................ ........ 102 Skeletal Photon Fluence to Dose Response Function Development ............................ 104 15 year old and newborn phantoms ................................ ................................ ....... 104 1 year old, 5 ye ar old, and 10 year old phantoms ................................ ................. 107 Photon Specific Absorbed Fractions ................................ ................................ .................... 113 Overview ................................ ................................ ................................ ....................... 113 Radiation Transport Code ................................ ................................ .............................. 114 Phantom Physical Characteristics ................................ ................................ .................. 115 Blood Inclusive Elemental Compositions ................................ ................................ ..... 116 Phantom Preparation ................................ ................................ ................................ ..... 125 Voxel Resolution ................................ ................................ ................................ ........... 126 Initial Energies and Particle Histories ................................ ................................ ........... 130 Tally Types ................................ ................................ ................................ .................... 131 Miscellaneous Transport Details ................................ ................................ ................... 133 Ene rgy cutoff ................................ ................................ ................................ .......... 133 Electron energy indexing algorithm ................................ ................................ ....... 134 Source Tissues ................................ ................................ ................................ ............... 137 Uniform source sampling ................................ ................................ ....................... 139 Non uniform source sampling ................................ ................................ ................ 140 Target Tissues ................................ ................................ ................................ ................ 142 Photon Specific Absorbed Fraction Calculation ................................ ........................... 143 Variance Reduction Techniques ................................ ................................ .................... 145 Overview ................................ ................................ ................................ ................ 145 Reciprocity ................................ ................................ ................................ ............. 146 Log linear back extrapolation ................................ ................................ ................ 147 Three point smoothing ................................ ................................ ........................... 149

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7 Electron Specific Absorbed Fractions ................................ ................................ .................. 149 Similarities to Photon Transport Methods ................................ ................................ ..... 149 G eneral Transport Methodology ................................ ................................ ................... 150 Collisional Energy Loss Contribution to Dose ................................ .............................. 152 Tally types ................................ ................................ ................................ .............. 152 Miscellaneous transport details ................................ ................................ .............. 153 Collisional specific absorbed fraction calculation ................................ ................. 153 Radiative Ene rgy Loss Contribution to Dose ................................ ................................ 155 Methodology ................................ ................................ ................................ .......... 155 Particle tracking ................................ ................................ ................................ ...... 155 Particle histories ................................ ................................ ................................ ..... 156 Radiative energy loss specific absorbed fraction calculation ................................ 158 Total Electron Specific Absorbed Fraction ................................ ................................ ... 159 Extra skeletal sources ................................ ................................ ............................. 159 Intra skeletal sources ................................ ................................ .............................. 160 Variance Red uction Techniques ................................ ................................ .................... 161 Computing Resources and Runtimes ................................ ................................ .................... 162 Radionuclide S Values ................................ ................................ ................................ .......... 163 Biokinetics ................................ ................................ ................................ ............................ 166 Dosimetric Sensitivity Studies ................................ ................................ .............................. 168 Variation in Source and Target Size and Separation ................................ ..................... 170 Sphere studies ................................ ................................ ................................ ......... 170 Validation studies ................................ ................................ ................................ ... 173 Variation in Anthropometric Characteris tics ................................ ................................ 181 Sitting height ................................ ................................ ................................ .......... 183 Weight ................................ ................................ ................................ .................... 185 Constant weight with morphometr y variation ................................ ........................ 186 Validation studies ................................ ................................ ................................ ... 189 Internal Dosimetry Software ................................ ................................ ................................ 193 3 RESULTS ................................ ................................ ................................ ............................. 239 UF Hybrid Phantom Blood Vessel System ................................ ................................ .......... 239 Adult Male ................................ ................................ ................................ ..................... 239 Neck and clavicles ................................ ................................ ................................ .. 239 Arms ................................ ................................ ................................ ....................... 239 Thoracic and abdominal region ................................ ................................ .............. 240 Le gs ................................ ................................ ................................ ........................ 241 Whole body ................................ ................................ ................................ ............ 241 Remainder of Phantom Family ................................ ................................ ...................... 242 Vascular Dosimet ry ................................ ................................ ................................ ....... 243 Skeletal Photon Fluence to Dose Response Functions ................................ ........................ 244 Single Image Radiation Transport Simulations ................................ ............................ 244 Response Functions ................................ ................................ ................................ ....... 245 Photon Specific Absorbed Fractions ................................ ................................ .................... 250 Electron Specific Absorbed Fr actions ................................ ................................ .................. 254 Dosimetric Sensitivity Studies ................................ ................................ .............................. 259

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8 Variation in Source and Target Size and Separation ................................ ..................... 259 Photon self dose ................................ ................................ ................................ ..... 259 Electron self dose ................................ ................................ ................................ ... 261 Photon cross dose ................................ ................................ ................................ ... 262 Electron cross dose ................................ ................................ ................................ 265 Variation in Anthropometric Characteristics ................................ ................................ 266 Sitting height ................................ ................................ ................................ .......... 266 Weight ................................ ................................ ................................ .................... 267 Constant weight with morphometry variation ................................ ........................ 269 Internal Dosimetry Softwa re ................................ ................................ ................................ 270 4 DISCUSSION ................................ ................................ ................................ ....................... 320 UF Hybrid Phantom Blood Vessel System ................................ ................................ .......... 320 Vasc ular Dosimetry ................................ ................................ ................................ .............. 322 Skeletal Photon Fluence to Dose Response Functions ................................ ........................ 325 Photon Specific Absorbed Fractions ................................ ................................ .................... 326 Electron Specific Absorbed Fractions ................................ ................................ .................. 329 Dosimetric Sensitivity Studies ................................ ................................ .............................. 332 Variation in Source and Target Size and Separation ................................ ..................... 332 Photons ................................ ................................ ................................ ................... 332 Electrons ................................ ................................ ................................ ................. 339 Va riation in Anthropometric Characteristics ................................ ................................ 343 Sitting height dose scaling application ................................ ................................ ... 343 Sitting height dose scaling validation ................................ ................................ ..... 345 Weight dose scaling application ................................ ................................ ............. 347 Weight dose scaling validation ................................ ................................ .............. 349 Combined dose scaling application ................................ ................................ ........ 350 Combined dose scaling validation ................................ ................................ .......... 351 Final morphometric dose scaling factors ................................ ................................ 353 Internal Dosimetry Software ................................ ................................ ................................ 357 Case Studies ................................ ................................ ................................ .......................... 359 Radiopharmaceuticals ................................ ................................ ................................ .... 359 Tc 99m labeled red blood cells ................................ ................................ .............. 359 Ga 67 citrate ................................ ................................ ................................ ........... 360 Biokinetics ................................ ................................ ................................ ..................... 360 Dosimetry ................................ ................................ ................................ ...................... 360 Results ................................ ................................ ................................ ........................... 361 Clinical Application ................................ ................................ ................................ .............. 364 5 CONCLUSIONS ................................ ................................ ................................ .................. 409 Blood Vessel Model ................................ ................................ ................................ ............. 4 09 Specific Absorbed Fractions and Skeletal Dosimetry ................................ .......................... 410 Internal Dose Scaling ................................ ................................ ................................ ............ 414 Deliverables ................................ ................................ ................................ .......................... 415 Future Work ................................ ................................ ................................ .......................... 416

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9 APPENDIX A LARGE TABLES ................................ ................................ ................................ ................. 419 B SAMPLE FILES ................................ ................................ ................................ ................... 466 Lattice File ................................ ................................ ................................ ............................ 467 Uniform Source File ................................ ................................ ................................ ............. 469 Non Uniform Source File ................................ ................................ ................................ ..... 471 Input File ................................ ................................ ................................ ............................... 473 LIST OF REFERENCES ................................ ................................ ................................ ............. 480 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 488

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10 LIST OF TABLES Table P age 1 1 Image set sources and voxel resolutions for the construction of the UF hybrid phantom family ................................ ................................ ................................ .................. 76 2 1 Blood vessel wall thicknesses for the newborn to 1 year old and adult reference individuals for the arterial, venous, and pulmonary systems ................................ ........... 196 2 2 Width, height, and depth measurements and isotropic voxel resolutions for all bone sites in the UFH01MF, UFH05 MF, and UFH10MF phantoms ................................ ....... 197 2 3 Total matrix sizes and voxel numbers by width, depth, and height for all bone sites in the UFH01MF UFH05MF, and UFH10MF phantoms ................................ ................... 198 2 4 Percent regional blood distribution in the ICRP reference adult male and female ......... 199 2 5 Total blood volumes in the ICRP reference human series ................................ .............. 200 2 6 Derived vascular growth scaling factors for the brain, kidneys, trabecular bone, and cortical bone for the ICRP reference human series ................................ ......................... 200 2 7 Derived regional blood distributions for the ICRP reference pediatric human series and ICRP reference adult regional blood distributions ................................ ................... 201 2 8 Derived regional blood volumes for the ICR P reference pediatric human series and ICRP reference adult regional blood volumes ................................ ................................ 202 2 9 Derived regional blood distribution in volume percent for the UF series of hybrid computational phantom s ................................ ................................ ................................ .. 203 2 10 Derived regional blood masses for the UF series of hybrid computational phantoms .... 204 2 11 Voxel resolutions applied to th e UF hybrid phantom family and resulting matrix sizes ................................ ................................ ................................ ................................ .. 205 2 12 Voxel resolution study showing doses calculated for a fine and course resolution phantom ................................ ................................ ................................ ............................ 205 2 13 Variance of energy deposition with changes in lower bound electron energy cutoff values ................................ ................................ ................................ ............................... 206 2 14 Comparison of dosimetry results obtained using the MCNP style bin ce ntered and ITS style nearest bin electron energy indexing algorithms ................................ ............. 207 2 15 Source tissues explicitly simulated in the UF hybrid computational phantom series ...... 208 2 16 Source tissues mathematically assembled in the UF hybrid computational phantom ..... 211

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11 2 17 Target tissues explicitly simulated in the UF hybrid computational ph antom series ...... 212 2 18 Target tissues mathematically assembled in the UF hybrid computational phantom series ................................ ................................ ................................ ................................ 214 2 19 Biokinetic para meters for 99m for the newborn patient .............................. 215 2 20 Morphometric measurements for the phantoms created to assess dosimetric sensitivity as a function of sitting height ................................ ................................ ......... 216 2 21 Voxel resolutions and total matrix sizes for the phantoms created to assess dosimetric sensitivity as a function of sitting height ................................ ....................... 217 2 22 Morphometric measurements for the phantoms created to assess dosimetric sens itivity as a function of weight ................................ ................................ ................... 218 2 23 Voxel resolutions and total matrix sizes for the phantoms created to assess d osimetric sensitivity as a function of weight ................................ ................................ .. 219 2 24 Morphometric measurements for the phantoms created to assess dosimetric sensitivity for patients of similar weight but different body morph ometry ..................... 220 2 25 Voxel resolutions and total matrix sizes for the phantoms created to assess dosimetric sensitivity for patients of similar weight but different body morphometry ... 220 3 1 Volumes of the blood v essels in the UF phantom family ................................ ................ 273 3 2 Superior (sup) and inferior (inf) diameters of the blood vessels in the U F phan tom family ................................ ................................ ................................ ............................... 274 3 3 Photon SAFs (excerpt) for the UFH00MF pituitary gland source ................................ ... 275 3 4 Radiation absorbed dose per unit AA and comp arison for two patients at the same weight but different body morphometry for 99m ................................ ........... 276 3 5 Radiation absorbed dose and effective dose per unit AA and comparison for two patients at t he same weight but different body morphometry ................................ .......... 277 3 6 SAF and S value subroutine verification study for the liver source in the UFH00MF phantoms ................................ ................................ ................................ .......................... 278 4 1 Anterio posterior (AP), lateral (LAT), and axial dimensions and prism volumes for blood vessel wall scaling methodology ................................ ................................ ........... 367 4 2 SAFs to the blood vessel walls for a uniforml y distributed blood s ource for the UF phantom family ................................ ................................ ................................ ................ 367 4 3 Percent difference between the UFH00MF phantom and the ORNL adult stylized phantom skeletal fluence to dose response functions for se lected bone sites ................. 368

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12 4 4 Energy averaged percent differences between the UF hybrid phantom and ORNL stylized ph antom monoenergetic photon SAFs ................................ ............................... 369 4 5 Absolute energy averaged percent differences between the UF hybrid phantom and ORNL stylized ph antom monoenergetic photon SAFs ................................ ................... 369 4 6 Excerpt of the 3 D mass ratio scaling p ower matrix used to scaled photon self dose ..... 370 4 7 Photon self dose scaling validation study for the photon spectrum of 99m .................. 371 4 8 Photon self dose scaling validation study for photons ................................ ........ 372 4 9 Photon self dose scaling validation study for photons ................................ ...... 372 4 10 Patient specific photon self dose scaling validation study using all UF mass ratio scaling powers for 131 photons ................................ ................................ ........................ 373 4 11 Excerpt of the photon cross dose sphere SAFs showing a subset of the source masses, target masses, photon energies, a nd center to center separations ...................... 374 4 12 Photon cross dose validation study using an arbitrary reference and non reference set of spheres and liver and pancreas ad justed reference UFHADM phantom ................... 375 4 13 Photon cross dose scaling validation study showi ng predictive quality of UF scaling method as applied to patient specific phantoms for 131 photons ................................ .... 376 4 14 Excerpt of the 3 D mass ratio scaling power matrix used to scaled electron self dose showing results for electrons ................................ ................................ ............... 377 4 15 Electron self dose scaling validation study for the electron spectrum of 99m .............. 378 4 16 Electron self dose scaling validation study for electrons ................................ .... 379 4 17 Electron self dose scaling validation study for electrons ................................ .. 379 4 18 Patient specific electron self dose scaling validation study using all UF mass ratio scaling powers for 90 beta particles ................................ ................................ ................ 380 4 19 Electron cross dose validation s tudy using the liver and brain ad justed reference UFHADM phantom ................................ ................................ ................................ ......... 381 4 20 Electron cross dose validation study using the liver and brain adjusted reference UFHADM phantom ................................ ................................ ................................ ......... 382 4 21 Percentage point gain in accuracy over reference values using dose scaling factors based on sitting height for the UFH00M based phantom for 131 photons ...................... 383 4 22 Percentage point gain in accuracy over reference values using dose scaling factors based on sitting height for the UFH00M based phantom for 90 beta particles .............. 384

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13 4 23 Average percentage point gain in accuracy using dose scaling factors based on sitting height for all non reference phantoms for 131 photons ................................ ................... 385 4 24 Average percentage point gain in accuracy using dose scaling factors based on sitting height for all non reference phantoms for 90 beta particles ................................ ........... 385 4 25 Percentage point gain i n accuracy using dose scaling factors based on waist circumference for 131 photons ................................ ................................ ......................... 386 4 26 Percentage point gain in accuracy using dose scaling factors based on waist circumference for 90 b eta particles ................................ ................................ ................. 387 4 27 Average percentage point gain in accuracy using dose scaling factors based on waist circumference for all non reference phantoms for 131 photons ................................ ...... 388 4 28 Average percentage point gain in accuracy using dose scaling factors based on waist circumference for all non reference phantoms for 90 beta particles .............................. 388 4 29 Percentage point gain in accuracy using dose scaling factors based on sitting height and waist circumference for the UFH00M based phantom for 131 photons ................... 389 4 30 Percentage poi nt gain in accuracy using dose scaling factors based on sitting height and waist circumference for the UFH00M based phantom for 90 beta particles ........... 390 4 31 Average percentage point gain in accu racy using dose scaling factors based on sitting height and waist circumference for all non reference phantoms for 131 photons ........... 391 4 32 Average percentage point gain in accuracy using dose sca ling factors based on sitting height and waist circumference for all non reference phantoms for 90 beta particles ... 392 4 33 Photon internal dosimetry scaling factors (excerpt) for the shortest UFH00M based phantom of the sitting height dosimetric sensitivity study ................................ .............. 393 4 34 Photon internal dosimetry scaling factors (excerpt) for the tallest UFH00M based phantom of the sitting heig ht do simetric sensitivity study ................................ .............. 394 4 35 Percentage point gains in accuracy for interpolated sitting height and waist circumference based target average dose scaling factors ................................ ................ 395 4 36 Biokinetic data for 99m ................................ ................................ .................. 396 A 1 All tissue names, tag identification numbers, and densities for all phantoms in the UF hybrid phantom family ................................ ................................ ................................ ..... 420 A 2 Tissue masses in grams for all phantoms in the UF hybrid ph antom family after voxelization ................................ ................................ ................................ ...................... 427

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14 A 3 Blood inclusive el emental compositions in mass percent for all tissues in the UFH00MF phantoms ................................ ................................ ................................ ....... 434 A 4 Blood inclusive elemental compositions in mass percent for all tissues in t he UFH01MF phantoms ................................ ................................ ................................ ....... 437 A 5 Blood inclusive elemental compositions in mass percent for all tissues in t he UFH05MF phantoms ................................ ................................ ................................ ....... 440 A 6 Blood inclusive elemental compositi ons in mass percent for all tissues in t he UFH10MF phantoms ................................ ................................ ................................ ....... 443 A 7 Blood inclusive elemental compositions in mass percent for all tissues in the UFH15M phantom ................................ ................................ ................................ ........... 446 A 8 Blood inclusive elemental compositions in mass percent for all tissues in the UFH15F phantom ................................ ................................ ................................ ............ 449 A 9 Blood inclusive elemental compositions in mass percent f or all tissues in the UFHADM phantom ................................ ................................ ................................ ......... 452 A 10 Blood inclusive elemental compositions in mass percent for all tissues in the UFHADF phantom ................................ ................................ ................................ ........... 455 A 11 Non uniform source sampling probabilities for the UFH00MF phantoms ..................... 458 A 12 Non uniform source sampling probabilities for the UFH01MF phantoms ..................... 459 A 13 Non uniform source sampling probabilities for the UFH05MF phantoms ..................... 460 A 14 Non uniform source sampling probabilities for the UFH10MF phantoms ..................... 461 A 15 Non uniform source sampling probabilities for th e UFH15M phantom ......................... 462 A 16 Non uniform source sampling probabilities for th e UFH15F phantom ........................... 463 A 17 Non uniform source sampling probabilities for the UFHADM phantom ....................... 464 A 18 Non uniform source sampling probabilities for th e UFHADF phantom ......................... 465

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15 LIST OF FIGURES Figure P age 1 1 Artistic example of radiopharmaceutical biodistribution ................................ .................. 77 1 2 Front and side views of the UF newborn physical phantom ................................ .............. 78 1 3 The first stylized model of the trunk of an adult human ................................ .................... 79 1 4 The MIRD Pamphlet No. 5 revised stylized computational dosimetry phantom .............. 80 1 5 The complete current ORNL stylized computational dosimetry phantoms series ............ 80 1 6 The VIP Man voxel phantom ................................ ................................ ............................ 81 1 7 Visual representation of the process by which patient images are used t o create a hybrid NURBS phantom ................................ ................................ ................................ .... 82 1 8 The UF newborn hybrid female phantom as viewed in Rhinoceros TM ............................ 83 1 9 The UF NURBS /PM based hybrid phantom family ................................ .......................... 84 1 10 The continuum of phantom anatomic specificity ................................ ............................... 85 1 11 XCAT phantoms of the adult male, adult female, and newbor n ................................ ....... 86 1 12 Photon SAFs for the ICRP Publication 110 adult male voxel phantom ............................ 87 1 13 Electron SAFs f or the ICRP Publication 110 adult male voxel phantom .......................... 88 1 14 Ratios of SAFs for a thyroid source of the original mass to SAFs for thyroid of the reference mass in each GSF voxel phantom to a kidney target ................................ ......... 89 1 15 Ratios of SAFs for a liver source irradiating the red bone marrow to SAFs for the red bone marrow irradiating the liver for the family of GSF voxel phantoms ........................ 89 1 16 Ratios of SAFs for a self irradiating thyroid source to SAFs for a self irradiating thyroid source of reference mass for the family of GSF voxel phantoms ......................... 90 1 17 SAFs for selected source and target organs in the adult male phantom for varying weight percentiles ................................ ................................ ................................ .............. 91 1 18. Cross sections of the adult male and female voxelized NURBS phantoms at different levels of obesity ................................ ................................ ................................ ................. 91 1 19 Input forms f or OLINDA/EXM 1.0 ................................ ................................ ................... 92

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16 2 1 Three dimensional stylistic model showing different views for an excerpt of the ir radiation geometries for the vascula r dosimetry computational study .......................... 221 2 2 Sample heterogeneous skeletal sites of the UF newborn hy brid phantom showing the hand, right humer us, pelvis, and L spine ................................ ................................ ......... 222 2 3 Polygon mesh and voxel versions of the UFH01MF femur ................................ ............ 223 2 4 Photon simulation flowchart used to gen erate monoenergetic photon SAFs .................. 224 2 5 Illustration of artifa ct correction in ImageJ TM ................................ ................................ 225 2 6 UFH00F phantom voxelized at an isotropic resolution of ............................ 226 2 7 Number of particle histories simulated as a function of initial photon energy ................ 226 2 8 Vi sual representation of uniform and non uniform source sampling .............................. 227 2 9 Variance reduction technique flowchart used to improve the reliability of the monoene rgetic photon and electron SAFs ................................ ................................ ....... 228 2 10 Reverse Monte Carlo method demonstrating the reciprocity principl e ........................... 229 2 11 Low energy photon back extrapolation method ................................ .............................. 230 2 12 Three point smoothing method ................................ ................................ ........................ 231 2 13 Electron simulation flowchart used to gener ate monoenergetic electron SAFs .............. 232 2 14 Photon energy spectrum generated from simulating monoenergetic electrons in the liver of the UFH00M phantom ................................ ................................ ........................ 233 2 15 Graphical depiction of the systematic approach to studying dosimetric sensitivity with changes in source and target tissue size and separation ................................ ........... 233 2 16 Patient specific voxel phantom used for internal dosimetric mass scaling analysis ....... 234 2 17 Irradiation geometry for the photon cross dose scaling validation study ........................ 234 2 18 Standing height as a function of total body mass for the NHANES III pediatric male population ................................ ................................ ................................ ........................ 235 2 19 Sample set of NURBS/PM phantoms created for the internal dosimetric standing height sensitivity study ................................ ................................ ................................ .... 236 2 20 Sample set of NURBS/PM phantoms created for the internal dosimetric weight sensitivity study ................................ ................................ ................................ ............... 237 2 21 Phantoms created for the internal dosimetric body morphometry sensitivity study ........ 238

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17 3 1 Perspective views in Rhinoceros TM of the arteries and veins in the neck and clavicles, arms, thoracic and abdominal regions, and legs of the UFHADM phantom .. 279 3 2 Blood vessel systems as implemented in the entire UF hybrid phantom family ............. 280 3 3 Absorbed dose to the blood vessel wall from photons for vessels with wall thickness as a function of vessel length and photon energy ................................ ............ 281 3 4 Absorbed dose to the blood vessel wall from electrons for vessels with wall thickness as a function of vessel length and electron energ y ................................ ........... 281 3 5 AFs as a function of initial electron energy for a uniform electron source in the spongiosa of the cranium in the UFH01MF phantom ................................ ..................... 282 3 6 Spongiosa/MC self dose AFs as a function of initial electron energy for all bone sites in the UFH01MF phantom ................................ ................................ ............................... 282 3 7 AFs for spongiosa/MC irradiating cortical bone as a function of initial electron energy for all bone sites in the UFH01MF phantom ................................ ....................... 283 3 8 EFs for spongiosa/MC sources as a function of initial electron energy for all bone sites in the UFH01MF phantom ................................ ................................ ....................... 283 3 9 Skeletal fluence to dose response functions and skeletal fluence to kerma response functions for AM and TM 50 targets in the mandible of the UFH00MF phantom .......... 284 3 10 Skeletal fluence to dose response functions for all bone sites in the UFH00MF phantom for the AM target ................................ ................................ .............................. 285 3 11 Skeletal fluence to dose response functions for all bone sites in the UFH00MF phantom for the TM 50 target ................................ ................................ ........................... 286 3 12 Skeletal fluence to dose response functions for the AM target in the cervical vertebra of all pe diatric and adolescent phantoms ................................ ................................ ......... 287 3 13 Skeletal fluence to dose response functions for the TM 50 target in the cervical vertebra of all pe diatric and adolescent phantoms ................................ ........................... 288 3 14 Excerpt of the photon SAF curves for a large (liver) and small (thyroid) source tissue in the UFH00MF phantoms ................................ ................................ ............................. 289 3 15 Photon mass attenuation coefficients as a function of initial photon energy ................... 290 3 16 Photon SAFs showing for all ph antoms in the UF phantom family ........ 291 3 17 Photon SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ................ 291

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18 3 18 Photon SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ............................... 292 3 19 Photon SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ............................... 292 3 20 Photon SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ................ 293 3 21 Electron SAFs for a uniform electron source in the liver of the UFH00M phantom using full transport techniques ................................ ................................ ......................... 293 3 22 A subset of the electron SAF curves for a large (liver) and small (thyroid) source tissue in the UFH00MF phantoms ................................ ................................ ................... 294 3 23 Electron SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ............................... 295 3 24 Electron SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ 295 3 25 Electron SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ............................... 296 3 26 Electron SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ............................... 296 3 27 Electron SAFs showing for all ph antoms in the UF phantom family ................................ ................................ ................................ ................ 297 3 28 Sphere self dose SAFs as a function of initial photon energy and sphere size for the photon self dose scaling study ................................ ................................ ......................... 298 3 29 Mass scaling powers for photon self dose showing the minimum, maximum, and average values at each photon energy ................................ ................................ .............. 299 3 30 Mass scaling powers for photon self dose as a function of both reference sphere mass and initial photon energy ................................ ................................ ................................ 299 3 31 Sphere self dose SAFs as a function of initial electron energy and sphere size for the e lectron self dose scaling study ................................ ................................ ....................... 300 3 32 Mass scaling powers for electron self dose showing the minimum, maximum, and average values at each electron energy ................................ ................................ ............ 301 3 33 Mass scaling powers for electron self dose as a function of both reference sphere m ass and initial electron energy ................................ ................................ ....................... 301

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19 3 34 Photon specific absorbed fractions for different source spheres and photons as a function of sphere separation and target sphere mass ................................ ............... 302 3 35 Photon specific absorbed fractions for the source spheres and different photon energies as a function of sphere separation and t arget sphere mass ................................ 304 3 36 Photon specific absorbed fractions for the different source spheres and photons as a function of sphere separation and target sphere mass ................................ 305 3 37 Photon specific absorbed fractions for the source spheres and different photon energies as a function of sphere separation and target sphere mass ................................ 307 3 38 Electron specific absorbed fractions for the different source spheres and electrons as a function of sphere separation and target sphere mass ............................... 308 3 39 Electron specific absorbed fractions for the source spheres and different electron energies as a function of sphere separation and target sphere mass .................. 31 0 3 40 Electron cross dose SAFs for differing target sphere sizes for the center to center separation and source sphere ................................ ................................ ... 311 3 41 Variations in SAF with changes in sitting height for uniform photon sources in the liver of the UFH00M based phantoms ................................ ................................ ............ 312 3 42 Variations in SAF with changes in sitting height for uniform electron sources in the liver of the UFH00M based phantoms ................................ ................................ ............ 313 3 43 Variations in whole body SAF with changes in sitting height for uniform photon and electron sources in the liver of the study phantoms ................................ ...... 314 3 44 Variations in SAF with changes in weight for uniform photon sources in the liver of the UFH00M based phantoms ................................ ................................ ......................... 315 3 45 Variations in SAF with changes in weight for uniform electron sources in the liver of the UFH00M based phantoms ................................ ................................ ......................... 316 3 46 Variations in whole body SAF with changes in weightfor uniform photon and electron sources in the liver of the study phantoms ................................ ......................... 317 3 47 Radionuclide S values calculated using a summary of the radionuclide spectra compared to those calculated using the entire radionuclide spectra ................................ 318 3 48 Radionuclide S values calculated using direct spectrum sampling as compared to those calculated using an assembling of monoenergetic SAFs ................................ ....... 318 3 49 Ratios of S values calculated using the internal dosimetry software S value subroutin e to those calculated from direct spectrum sampling ................................ ........ 319

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20 4 1 Monoenergetic photon SAFs for a uniform blo od source in the UFH00M phant om ...... 401 4 2 Monoenergetic electron SAFs for a uniform blo od source in the UFH00M phantom .... 401 4 3 Monoenergetic photon SAFs for a uniformly distributed blood source in all pediatric and adolescent phantoms in the UF hybrid phantom family ................................ ........... 402 4 4 Average absorbed doses to the blood vessel wall of interest for the blood vessel wall dosimetry study ................................ ................................ ................................ ................ 403 4 5 Top and perspective views of the final irradiation geometry designed to provide estimates of radiation absorbed dose to the walls of blood vessels in the human body .. 404 4 6 Monoenergetic photon SAFs to the blood vessel walls for a uni formly distributed blood source ................................ ................................ ................................ ..................... 404 4 7 Monoenergetic electron SAFs to the blood vessel walls for a uni formly distributed blood source ................................ ................................ ................................ ..................... 405 4 8 UF newborn hybrid phantom and ORNL adult male stylized phantom fluence to dose response functions for the cervical vertebra for the AM tar ge t ............................... 405 4 9 Comparison of specific absorbed fractions for photons sources in the liver and thyroid between UF, ORNL, and GSF phantoms ................................ ........................... 406 4 10 Two simulation validation study for the UFH00M phantom ................................ .......... 407 4 11 Internal anatomy comparison between the ORNL stylized 10 year old and UFH10F phantoms ................................ ................................ ................................ .......................... 408

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21 LIST OF ABBREVIATION S 1 D one dimensional 2 D two dimensional 3 D three dimensional 4 D four dimensional AA administered activity ACD annihilation coin cidence detection AF absorbed fraction ALRADS Advanced Laboratory for Radiation Dosimetry Studies AM active marrow ANS American Nuclear Society AP anterio posterior BMI body mass index BPR blood perfusion rate BS bone surface BVF bone volume fraction CAP c hest abdomen pelvis CB cortical bone CBIST chord based infinites spongiosa transport CBV cortical bone volume CDC Centers for Disease Control and Prevention CEL collisional energy loss CF cellularity factor CHO channelized Hotelling observer CMA cortical m arrow

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22 CPE charged particle equilibrium CSDA continuous slowing down approximation CT computed tomography CV coefficient of variation DCF dose conversion factor DF dose factor DMSA dimercaptosuccinic acid DNA deoxyribonucleic acid DOCAL dose calculations DO D Department of Defense DRF dose response function EC electron capture EF escape fraction EGS4 Electron Gamma Shower version 4 EGSnrc Electron Gamma Shower National Research Council EXM Exponential Modeling FDA Food and Drug Administration FDG fluorodeoxyg lucose FTM full transport method GSF German Research Center for Environmental Health GUI graphical user interface HCP heavy charged particle IC internal conversion ICRP International Commission on Radiological Protection ICRU International Commission on Ra diation Units and Measurements

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23 IDL Interactive Data Language IM inactive marrow ITS integrated TIGER series KERMA kinetic energy released per unit mass LAT lateral LAR lifetime attributable risk LET linear energy transfer LUT look up table MATLAB TM Matrix Laboratory MC medullary cavity mCBF mean global cerebral blood flow MCNPX Monte Carlo N Particle Extended MIRD Medical Internal Radiation Dose committee MIRDOSE MIRD dosimetry method based internal dosimetry software MR magnetic resonance MRI magnetic reso nance imaging NCAT NURBS cardiac torso phantom NCI National Cancer Institute NHANES National Health and Nutrition Examination Surveys NIBIB National Institute of Biomedical Imaging and Bioengineering NIH National Institutes of Health NLM National Library o f Medicine NURBS non uniform rational b splines OLINDA Organ Level Internal Dose Assessment OLINDA/EXM Organ Level Internal Dose Assessment/Exponential Modeling

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24 ORISE Oak Ridge Institute for Science and Education ORNL Oak Ridge National Laboratory PET posi tron emission tomography PIRT paired image radiation transport PM polygon mesh PTRAC particle tracking RADAR Radiation Dose Assessment Resource RBC red blood cells RBE relative biological effectiveness rCBF regional cerebral blood flow REL radiative energy loss RIDIC Radiation Internal Dose Information Center ROC receiver operating characteristic ROI region of interest SAF specific absorbed fraction SIRT single image radiation transport SNM Society of Nuclear Medicine Sp spongiosa SPECT single photon emissi on computed tomography TB trabecular bone TBS trabecular bone surface TBV trabecular bone volume TLD thermoluminescent dosimeter TM total marrow TM 50 total shallow marrow

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25 TMA trabecular marrow TSM two simulation method UF University of Florida UFH00MF UF n ewborn hybrid male and female computational phantoms (UFH00M UFH01MF UF 1 year old hybrid male and female computational phantoms (UFH01M UFH05MF UF 5 year old hybrid male and female computational phantoms (UFH05M UFH10MF UF 10 year old hybrid male and female computational phantoms UFH15M UF 15 year old hybrid male computational phantom UFH15F UF 15 year old hybrid female computational phantom UFHADM UF adult hybrid male computational phantom UFHADF UF adult hybrid female computational phantom VB Visual Basic XCAT Extended Cardiac Torso Phantom

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26 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy COMPUTATIONAL INTER NAL DOSIMETRY METHODS AS APPLIED TO THE UNIVERSITY OF FLORIDA SERIES OF HYBRID PHANTOMS By Michael B Wayson August 20 12 Chair: Wesley Bolch Major: Biomedical Engineering Two primary areas of consideration for dosimetry of nuclear medicine imaging an d therapy procedures are (1) the organ absorbed dose calculations, taking into account size, shape, and proximity of all internal organs as well as the energy and type of radiation emitted and (2) biokinetic models taking into account how the radiopharma ceutical distributes throughout the body as a function of time. This study focuses on methods used to estimate radiation absorbed dose to organs of the human body from internal radiation emitting nuclides Estimating absorbed dose to human tissues from r adiations emitted from inside the body is known as internal dosimetry and is an integral part of performing risk assessment for the induction of secondary cancers, nuclear medicine imag e optimization, and limit ation of dose to non targeted organs in radiop harmaceutical therapy This study developed a new system of blood vessels, and the subsequent iteration of phantoms represents the latest University of Florida (UF) hybrid computational phantom (computerized representation of the human body) family. Skele tal photon fluence to dose response functions were computed for the pediatric and adolescent series of UF phantoms to allow for the determination of absorbed dose to the skeletal tissues at risk for radiogenic leukemia and osteosarcoma A complete set of photon and electron specific absorbed fractions

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27 (SAFs) were computed for the entire family of UF phantoms. SAFs are used with radiopharmaceutical biokinetic data to determine individual organ dose s V ariation s in radiation absorbed dose with changes in s ource and target organ masses, and source and target organ separation and body habitus were investigated The se dosimetric sensitivity studies led to useful dose scaling methods for individual patients when patient specific imaging based methods of inter nal dosimetry are not available R esults of the SAF calculations and scaling methodologies can be incorporated into software thus facilitating their ease of use. Improvements in the accuracy of internal dose estimates allows for optimization of nuclear m edicine imaging procedures and assessment of dose to normal tissues at risk during molecular radio therapy procedures. In all cases, effectively balancing radiation dose with adequacy of clinical outcomes can be better achieved with more accurate patient d ose estimates.

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28 CHAPTER 1 INTRODUCTION (American College of Radiology 2009) This statement was made by Marilyn Goske, MD, chair of the Al liance for Radiation Safety in Pediatric Imaging in a press release honoring the Alliance for their Image Gently campaign initiative The Alliance was founded by a society consortium including the Society for Pediatric Radiology, the American Society of R adiologic Technologists, the American College of Radiology, and the American Association of Physicists in Medicine The Image Gently campaign was created to educate radiologic technologists, medical physicists, radiologists, pediatricians, and parents abo ut the radiation dose to children during computed tomography (CT) exams (American College of Radiology 2009) Recently, the Alliance has created a new campaign that emphasizes radiation dose awareness during fluoroscopic procedures called Step Lightly (Th e Alliance for Radiation Safety in Pediatric Imaging 2009) It has been shown that children are at a higher risk of expressing radiation induced effects later in life than adults from medical procedures involving radiation (Harrison et al. 2007) This is explained by the fact that children are inherently more sensitive to radiation because their bodies are still developing along with the fact that children have a much longer time to express radiation induced effects Although intuitive, t hese observation s further emphasize that radiation dose to children must be minimized for any given medical diagnostic procedure While the Image Gently and Step Lightly campaigns highlight the practice of minimizing radiation dose in CT and fluoroscopic imaging, they un derscore the fact that radiation dose must be minimized for any medical procedure that involves ionizing radiation, including the imaging method of focus in this study: nuclear medicine. Very recently,

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29 by publishing consensus guidelines for calculating patient specific administered activities (AAs) for pediatric patients (SNM 2011). The scientific studies described in the current document work to improve the way nuclear medicine dosimetry is performed to help attain the ultimate goal of reducing radiation exposure to patients undergoing nuclear medicine procedures. The following numbered s pecific aims were performed to achieve this goal Specific Aims 1. Final impr ovements were made to the UF hybrid computational phantoms with the addition of large arteries and large veins as well as the development of a model of organ distribution of blood by both age and gender. 2. Skeletal photon fluence to dose response functions were generated for the newborn (UFH00MF), one year old (UFH01MF), five year old (UFH05MF), ten year old (UFH10MF), fifteen year old male (UFH15M), and fifteen year old female (UFH15F) computational phantoms. 3. Photon specific absorbed fractions ( SAFs ) were c omputed for a variety of source target energy combinations for the UFH00MF, UFH01MF, UFH05MF, UFH10MF, UFH15M F and UFH ADM F computational phantoms. 4. Electron SAFs were computed for a variety of source target energy combinations for the UFH00MF, UFH01MF, UFH 05MF, UFH10MF, UFH15M F and UFH ADM F computational phantoms. 5. Dosimetric sensitivity studies were performed to identify possible SAF scaling methodologies with respect to (1) variations in combinations of source and target size and separation and (2) variati ons in anthropometric characteristics. 6. MATLAB TM (The MathWorks, Inc., Natick, MA) based subroutines were developed to implement the results of Aims 3 6 into a future internal dosimetry software package Hypothesis The work that has tak en place over the p ast several years within the Advanced Laboratory for Radiation Dosimetry Studies (ALRADS) has been focused on advanced techniques for modeling human anatomy and using these models to simulate the transport of ionizing radiation from medical imaging and the rapy procedures. These advancements include updates to both the internal and external anatomy of human computational models used for dosimetry studies.

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30 Because of these many improvements, the computational models and methods used in this study are arguab ly some of the most advanced in the field. As a result, the dosimetry performed in the current study is predicted to improve upon existing data, from the skeletal dosimetry models derived from actual human skeletal samples to the internal dose measures ca lculated for a complete set of source target energy combinations. The dosimetric sensitivity studies can be performed with powerful computing resources that allow for hundreds of simulations in parallel and so promise to reveal statistically reliable scal ing techniques. Previous studies have shown that some scaling endpoints are difficult to achieve (e.g., photon and electron cross dose), but predictable self dose and human morphometric measurement based scaling techniques are thought to be achievable bas ed on the systematic nature of the studies and a posteriori knowledge of general dosimetric trends. Background Occupational dosimetry in the clinical environment is typically assessed by way of physical dosimeters Usually, thermoluminescent dosimeters (T LDs) and more recently optically stimulated luminescent dosimeters (OSLDs) are used to record an integral dose for medical workers whose duties include working with ionizing radiation sources The dosimeters are then analyzed and the integral radiation do se is recorded for that worker While this works well for determining occupational exposures, the patient undergoing a medical procedure involving ionizing radiation is rarely given physical dosimetry (e.g., select research investigations). This is due i n large part to the difficult logistics and cost of patient physical dosimetry Resultantly alternative methods of determining patient organ and effective dose have been investigated extensively over the years Accurately calculating both organ absorbed dose and patient effective dose are an important step s in managing the risks associated with medi cal imaging of the patient

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31 Quantifying radiation dose is essential for the purpose of radiation risk management Retrospective s tudies performed on the Japa nese atomic bomb survivors show that an increase in radiation dose le ads to roughly proportional increase s in excess cancer incidence for the study population (Hall et al. 2006) The result of that radiation risk study made it clear that excessive exposur e to radiation is detrimental While comprehensive studies of cancer risk s associated with low doses of ionizing radiation are not feasible due to statistical reasons the mechanisms for increased cancer risk from any exposure to radiation can be rational ized As a basic example, the mechanism for increased cancer risk from the absorption of electromagnetic radiation ( a photon) is given below The incident photon interacts with molecules within a cell in human tissue Through either photoelectric absorpt ion or Compton scattering interactions, electron s are liberated by the se photon interactions A free radical is thus formed defined as an atom or molecule that possesses an unpaired orbital electron (Hall et al. 2006) For example, an interaction with a water molecule can produce the reaction H 2 O H 2 O + + e where the water molecule is ionized and an electron is liberated The water ion radical then interacts with a second water molecule, producing the reaction H 2 O + + H 2 O H 3 O + species called th e hydroxyl radical (Hall et al. 2006) The hydroxyl radical then may interact with deoxyribonucleic acid ( DNA ) to create a DNA radical which in turn may lead to a DNA single strand break If the st rand breaks are not repaired, DNA mutation can occur and lead to the induction of cancer This is one example of how incident radiation, in this case, photons, may initiate cancer at the molecular level It would follow that any incident ionizing radiati on particle may initiate a similar cascade of da maging events

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32 The pertinent application to medical imaging is that one must always attempt to minimize the radiation dose to the patient Obviously, medical imaging aims to procure a view of patient anato my and/or physiology that can assist in an accurate diagnosis Consequently, image quality is a priority when administering an imaging exam There is a constant balance between radiation dose and image quality that medical professionals must always keep in mind when ordering and performing these patient exam s. However, this is not always possible due to insufficient quantitative relationships between radiation dose and image quality It is important for the dose estimates for these procedures involving radiation to be optimal in accuracy (i.e., the greatest accuracy should be achieved with reasonable runtimes), but uncertainties the in risk estimates themselves probably always outweigh those of the dose estimates. In addition, uncertainties in biokineti c modeling usually outweigh those of the internal S value estimates. Ov erview of Nuclear Medicine Imaging Procedures and Dosimetry Concepts Nuclear medicine (or molecular) imaging is a powerful tool available to physicians for the diagnosis of many disease s. What sets nuclear medicine apart from other imaging modalities is that other modalities such as x ray projection imaging, fluoroscopy, computed tomography (CT) and magnetic resonance imaging (MRI) are mostly useful for anatomic imaging, detailing the physical anatomy within a patient while nuclear medicine is based fundamentally on imaging of patient metabolic processes characterizing cell metabolism within the body (Cherry et al. 2003) Imaging modalities such as x ray projection, fluoroscopy, and CT use a technique known as rays are created outside of the body, transmitted through the body and detected on the other side of the body by radiation detectors (Cherry et al. 2003) Nuclear medicine imaging us because photons are created (emitted) inside the body, travel through the body, and are detected outside of the body by radiation detectors (Cherry et al. 2003)

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33 Two main modes of decay are utilized to create the nuclear medicine images: gamma emission and positron decay. Gamma emission is the mode used for single photon emission computed tomography (SPECT) and planar imaging (Cherry et al. 2003) SPECT uses position sensitive gamma cameras to detect g amma rays at various angles around the body. A three dimensional image is formed when the information collected from a subset of angles is assembled through reconstruction algorithms (Cherry et al. 2003) Planar images are formed when a single projection image is taken at one angle (Cherry et al. 2003) Positron decay is utilized for positron emission tomography (PET) imaging. Positrons annihilate 1 in human tissue and two photons are emitted in opposite directions and detected by radiation detectors. U sing annihilation coincidence detection (ACD), PET system radiation detectors are able to localize where the annihilation even t took place (Cherry et al. 2003) A fundamental difference b etween nuclear medicine imaging/ therapy procedures and structural ima ging procedures such as x ray projection imaging or CT scans is the location of the radiation source. For nuclear medicine imaging, a radiopharmaceutical is injected into the bloodstream of the patient and subsequently travels throughout the body to vario us organs/tissues of interest (Treves 1995) A typical radiopharmaceutical used for PET imaging is 18 flurodeoxyglucose ( 18 ), and the radionuclide, 18 is produced using a cyclotron and the process 18 18 (Cherry et al. 2003) The 18 is finally substituted into a glucose molecule for the purpose of assessing glucose metabolism (Ch erry et al. 2003) Glucose is used by cells in the body in a process called glycolysis where the end product is adenosine triphosphate (ATP). ATP is subsequently used as energy for the cell (Cherry et al. 2003) 18 is an analog of glucose, and as such goes through phosphorylation step of glycolysis 1 Positrons interact with electrons in tissue, and thei r rest mass energies are converted into two photons directly at approximately from each other (Attix 2004)

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34 (Joensuu et al. 1987) However, once phosphorylized, 18 cannot proceed along the normal gylcolysis pathway and it is not released from the cell (Joensuu et al. 1987) A s a result, accumulat ion of 18 in areas of the body is proportional to true levels of glucose metaboli sm (Joensuu et al. 1987) Energy requirements for diseased cells vary from healthy cells, so the accumulation of 18 in a particular tissue of the body can b e used to diagnose diseases or disorders (Cherry et al. 2003) For radiation dosimetry purposes, the tissues in the body to which the radiopharmaceutical localizes are of great interest When a radiopharmaceutical is injected into the bloodstream, it dist ributes throughout the body to various tissues, and these tissues in turn become sources of Figure 1 1 2 Radiation is emitted from within the source tissues and deposits its energy in itself. Internal dosimetry refers to the process of estimating the amount of energy deposited in any target tissue per unit mass of that target tissue from radiation emitted from any source tissue. Once the energy deposited in all target tissues of interest from all source tissues of interest is determined, individual organ doses are estimated by combining absorbed doses from all source tissues according to the relative amount of radiopharmaceutical that localizes in the source tissues of interest. Finally, the individual organ doses may be mass weighted to estimate whole body dose. This description of estimating absorbed dose to individual organs and the whole body is presented in the way that internal dosimetry is approached in the current study but may not be the most utilized approach in the field. Those in the field think of dose to a certain tissue 2 For reference modeling purposes, radiation emissions may be modeled as uniformly distributed throughout the tissues in which the radiopharmaceutical localizes. Non uniform source distributions within a particular tissue can only be modeled if nuclear medicine images are available to determine voxel by voxel radiopharmaceutical uptake.

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35 as a sum of dose contribu tions from a variety of source tissues, and the whole body dose is calculated based on a whole body S value. The mass weighting is not explicit to them. History of Computational Dosimetry Phantoms As previously discussed, it would not be feasible to use p hysical dosimeters to estimate organ doses for patients undergoing nuclear medical imaging procedures Therefore, a quicker, more feasible method was developed in which computational dosimetry phantoms are used to determine organ doses in a virtual enviro nment Computational dosimetry phantoms are virtual /computerized representations of humans which are then input into radiation transport codes to calculate radiation dose from any number of radiation sources, both internal and external This is in contra st to ano ther type of phantom used for dosimetry the physical dosimetry phantom Physical dosimetry phantoms are actual constructs made to model human anatomy, based on the segmentation of tissue regions from CT or magnetic resonance ( MR ) image sets th at are imbedded with physical dosimeters to determine radiation absorbed doses to various points within the phantom (for nuclear medicine applications, cavities would be constructed that would be subsequently filled with radioactivity) An example of a ph ysical phantom can be seen in Figure 1 2 ( Jones et al. 2006) However, it is usually not optimal to utilize physical dosimetry phantoms for on the fly dosimetry because the construction process is time consuming and difficult, and physical phantoms cannot be easily modified once built Additionally, for nuclear medicine applications, biokinetics cannot be sufficiently modeled due to the immense complexity of constructing an activity transfer system (if even possible) and because any dose measuring devices inserted into the activity region must not displace any of the activity. C omputational dosimetry phantoms may be used to assess the radiation absorbed dose from a variety of radiation sources Radiation sources from radiography, CT, or fluoroscopy are

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36 known as external sources since the radiation is emitted from the machine and travels through the body while radiation sources from nuclear medicine imaging modalities such as PET and SPECT are known as internal sources since the radiation is emitted from within the body and travels out of the body The emphasis of this study was the analysis of internal sources for the purpose of performing dosimetry for nuclear medicine imaging procedures Stylized Phantoms Computational dosimetry phantoms composed of si mple mathematical shapes are referred to as stylized phantoms These phantoms are obviously not anatomically realistic in nature since internal and external structures of the human body can rarely, if ever, be accurately represented by simple shapes. How ever, the scalability of stylized phantoms makes it easy to change the body habitus or organ sizes of the phantoms. An early attempt at creating a virtual representation of humans was described in the diation Dose (MIRD) committee P amphlet No 3 in 1968 (Brownell et al. 1968) The MIRD committee tabulated a set of photon absorbed fractions (AF s ) for an adult phantom with internal and external structures represented by a combination of simple mathematic al shapes such as spheres, ellipsoids, and elliptical and right circular cylinders (Brownell et al. 1968) Body t issues in this phantom were homogeneous in nature and elemental compositions included the elements hydrogen carbon nitrogen oxygen chlorin e and sodium (Brownell et al. 1968) Another early model was developed by Oak Ridge National Laboratory (ORNL) in the early 1960s and was a whole body model created for the purpose of external beam dosimetry (NCRP 1971) This model attempted to represent only the trunk of an adult and was a simple right circular cylinder 30 cm in diameter and 60 cm in height (NCRP 1971) While this model seems inordinately simple by modern standards it was an effective way to obtain rough

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37 estimates of whole body radiati on absorbed doses from a variety of medical procedures. This early generation phantom can be seen in Figure 1 3 (NCRP 1971) In the mid 1960s, ORNL developed a new stylized adult phantom called the Fisher Snyder Phantom (Snyder et al. 1969) This model consisted of three distinct regions: the head and neck, the trunk including arms, and the legs (Snyder et al. 1969) The head neck trunk, and arms were descr ibed by an elliptical cylinder and the legs were represented by truncated elliptical cones (Sn yder et al. 1969) Some structures left out of this model include hands, feet, ears, nose, lungs, and skeleton (Snyder et al. 1969) All tissues were assumed to be homogeneous (Snyder et al. 1969) The MIRD committee published in 1969 an advancement of t he Fisher Snyder adult phantom in their 5 th pamphlet (Snyder et al. 1969) The Fisher Snyder phantom was a heterogeneous model of the adult and was officially called the MIRD P hantom (Snyder et al. 1969) In this phantom, 22 internal organs were modeled by way of three dimensional surface equations (Snyder et al. 1969) Three body tissues were modeled: skeletal tissue, lung tissue, and soft tissue (Snyder et al. 1969) Photon AFs were calculated for 12 energies and particle histories between 25,000 and 50,000 were run for each simulation (Snyder et al. 1969) The MIRD P hantom was later revised in 1978 with improvements in the organ models and statistical reliability of the AFs The number of photon histories was increased to 60,000 for each source org an (Snyder et al. 1978) The revised MIRD Pamphlet No. 5 adult phantom can be seen in Figure 1 4 ( Snyder et al. 1978) Development of pediatric models also took place in the 1970s at ORNL Early attempts at pediatric models involved non uniform down scal ing of the adult MIRD Phantom (Cristy et al. 1987) A newborn phantom along with 1 y ear old 5 y ear old 10 y ear old and 15 y ear old

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38 phantoms were created in this fashion (Cristy et al. 1987) Currently, the international standard for computational dosi metry phantoms is the phantom model series created in 1980 by Mark Cristy and Keith Ec kerma n ( Cristy 1980, Cristy et al. 1987) These phantoms were a revision to the ORNL pediatric series of models and can be seen in Figure 1 5 ( Cristy et al. 1987) The key improvements of these models were new models of the heart, breasts, and thyroid and a new model for skeletal dosimetry using skeletal fluence to dose response functions (Cristy et al. 1987) A complete set of SAFs were calculated for each of these pha ntoms Voxel Phantoms In contrast to stylized phantoms where the internal and external structures of the human body are represented by mathematical equations and shapes, voxel phantoms are almost exactly representative of actual patient anatomy. Voxel pha ntoms are three dimensional (3 D) matrices of rectangular prisms (voxels) where each voxel is assigned a unique identification number that indicates the type of tissue associated with the voxel of interest. This is accomplished by using image sets of actu al patients and segmenting a variety of tissue volumes. Segmentation is performed by manually (and sometimes automatically) tracing the periphery of an organ of interest across all image slices containing the organ of interest. Once this is done for all pertinent image slices, the image segmentation software combines the image slice thickness and traced peripheries of the organ to create a three dimensional volume. Once all tissues of interest are segmented, these volumes are then voxelized (converted in to a three dimensional matrix of rectangular prisms) for use in radiation transport codes Frequently, but not always, the rectangular prisms are defined to have equal length sides, thereby forming a set of cubes known as isotropic voxels If these cubes are created at a fine enough resolution, the original shape can be faithfully represented It can be thought of as taking a photograph whereby a pixilated representation of a continuous object is created, and the higher the resolution of the image, the

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39 m ore faithfully the person is represented. Voxelization is like taking a 3 D picture of a set of continuous objects, and the pixels, formerly in two dimensions (2 D), are now voxels in 3 D. Voxel phantoms are very anatomically realistic, but they are unabl e to be extended to a variety of patient morphometries due to their patient specific nature A phantom created from the image set of a specific patient can only be appropriately used for dosimetry on that patient or on patients with very similar body shap es and internal organ structure I t is very difficult to a djust the size and position of tissues within a voxel phantom to model changes in patient size since voxel phantoms are rigid in nature Because the process of segmentation is time consuming indi vidual voxel phantoms cannot be created for every patient who undergoes an imaging procedure In addition, some structures in the body such as the large and small intestines are difficult to accurately segment on a CT or MR image set One previous voxel p hantom was the VIP Man, created using transverse color photographic images from the Visible Human Project of the National Library of Medicine (NLM) ; t he sub ject was a recently executed 38 year old male from Texas (Xu et al. 2000) The resulting voxel mode l can be seen in Figure 1 6 ( Xu et al. 2000) Another example of previous voxel phantoms is the GSF voxel phantom family (Petoussi Henss et al. 2002) This set of phantoms includes females of 8 weeks, 7 years, 26 years, and 40 years, males of 38 years, a second 38 year old, 48 years, and an unknown age phantom two physical phantoms representing a torso and head and the thorax, and one female standardized gastrointestinal tract (Petoussi Henss et al. 2002) This family of voxel phantoms can be seen in Pe toussi Henss et al. ( 2002) Hybrid Phantoms Both voxel phantoms and stylized phantoms have positive and negative attributes Stylized phantoms have unrealistic anatomy but are easily deformable while voxel phantoms have realistic anatomy but are difficult to modify. The drawbacks of these respective options for

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40 computational radiation dosimetry necessitate d a bridge between the stylized and voxel phantoms which would allow for anatomic realism as well as deformability This study addresses that void and describes the recent addition of a new type of computational phantom : the hybrid phantom The hybrid phantom combines elements of both stylized and voxel phantoms to create a phantom with anatomic realism and deformability. Development of the UF Hybrid Co mputational Phantoms The computational dosimetry phantoms discussed previously represent the 1 st and 2 nd generation phantoms The simple stylized phantoms based on mathematical functions are 1 st generation phantoms The medical image based voxel phantoms are 2 nd generation phantoms A 3 rd generation phantom has recently emerged and has progressed extensively at UF This 3 rd generation phantom combines the concepts of the 1 st and 2 nd generation phantoms to yield a new type of phantom that is anatomically realistic and easily deformable. NURBS modeling A n on uniform ra tional b spline (NURBS) surface is a mathematical modeling technique commonly used in computer animation whereby 3 D continuous surfaces are defined by a series of control points NURBS su rfaces can model virtually any free form shape, and thus they are very useful in modeling complicated volumes such as human organs and body regions The mathematics of NURBS surfaces can be explained by addressing the mathematics behind NURBS curves. Inst ead of using explicit equations (such as a sine or cosine function, for example) to define curves in 3 D modeling software, parametric equations are used to allow curves to move back over themselves (Schneider 1996). As an example, the equation could be defined by and giving the equation of a circle (Schneider 1996). A simple equation could not achieve shapes looping back on

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41 themselves b ecause two different values of would not be allowed for As previously mentioned, a NURBS surface, and hence a NURBS curve, is defined by a series of control points that define the shape of the surface or curve. Imagine a moving point that defines a NURBS curve. The position of this point at any time could be defined by Equation 1 1 (Schneider 1996). (1 1) where is the position of the point for any time is the position of control point is the influence of each control point on the point defining the curve at time (otherwise known is the number of control points. controls the strength with which the control point coordinates influence the position of the curve. At any point in time, the sum of all basis functions is equal to unity (Schneider 1996). An example given in Schneider (1996) is a series of bell curves at subsequent arbitrary time points 0 4 with widths at of 3. These are equally sized overlapping bell curves. The width of the basis functions can be modified to affect the overall area the function has influence on the curve position (i.e., the positions along the curve that the basis function of the control point has influence over) and the height of the basis functions can be modified to affect the magnitude of this influence (Schneider 1996). This weight can be assigned to each control point to change the amount the curve is pulled toward the control point (Schneider 1996). NURBS surfaces are both flexible and easily modifiable and thus NURBS technology was selected as the primary method to create a new generation of phantoms that are both anatomically realistic as well as easily deformable Since this 3 rd generation phantom combines

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42 elements of stylized and voxel phantoms (as will be discussed later), the 3 rd generation phantom computational dosimetry phantom UF phantom family construction To illustrate the process of creating the UF family of hybrid computational phantoms, construction of the newborn phantom will be described. The UF newborn hybrid phantom is an adva ncement of the previous UF newborn voxel phantom (Lee et al. 2007) that was constructed from a CT scan of a 6 day old female (Nipper et al. 2002) This scan was saved as a data array with a slice thickness of At this slice thickness and data array size, the UF newborn voxel model was the highest resolution model at the time (Nipper et al. 2002) Delineation of organs was then performed using an in house Interactive Data Language (IDL) (ITT Visualizati on Solutions, Boulder, CO) code, and 66 different anatomic regions were defined (Nipper et al. 2002) The UF newborn voxel model can be seen in Nipper et al. ( 2002) The computer software 3D DOCTOR TM (Able Software Corp., Lexington, MA) was used to conver t the UF newborn voxel phantom into polygon mesh (PM) geometry The vox el phantom was imported into 3D DOCTOR TM and individual organs were segmented using interactive segmentation tools (Lee et al. 2007) Once all organs of interest were segmented, the PM model was imported to Rhinoceros TM (McNeel North America, Seattle, WA), a NURBS modeling software, to transform the PM geometry into NURBS geometry Seven distinct anatomic groups were defined and imported separately into Rhinoceros TM the exterior bo dy contour, the respiratory system, the alimentary system, the circulatory system, the urogenital system, other soft tissue organs, and the skeleton (Lee et al. 2007) The organs of interest were then converted to NURBS surfaces NURBS surface s are easie r to manipulate than PM volume s because NURBS surfaces are defined by a series of control points which can be individually

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43 manipulated in 3 D Volumes bounded by NURBS surfaces can easily be scaled in one dimension (1 D) 2 D or 3 D Because of this, th e majority of internal organs were modeled with NURBS surfaces rather than PM volumes Conversion from polygon mesh geometry originating from segmented images to NURBS geometry was relatively straightforward for most tissues but several small organs and o rgans that were difficult to segment from the original CT data necessitated a different approach Small organs such as the eyes, lenses, ovaries, urinary bladder, breasts, pituitary gland, and tonsils were modeled using stylistic NURBS based models (Lee e t al. 2007) The original shapes and positions of these organs were referenced from the CT data and faithfully followed in the construction of stylistic representative shapes The contents of walled organs such as the heart, gall bladder, and urinary bla dder were modeled by replicating the organ wall and scaling inward (Lee et al. 2007) The esophagus, small intestine, colon, and rectum were unable to be segmented from the original CT data, so a 3 D trace of the lumen centroid was approximated from the s egmented UF newborn voxel phantom (Lee et al. 2007) This was not feasible for the small intestine due to CT slice discontinuity, so a stylistic model was created and approved by a pediatric radiologist (Lee et al. 2007) A visual representation of the p rocess by which patient images are used to create a hybrid phantom is in Figure 1 7 At this point, a non reference newborn hybrid computational dosimetry phantom was completed, but the model only represented the patient from which the original CT data was obtained This patient was not necessarily representative of reference 3 values defined by the International Commission on Radiological Protection (ICRP) for the newborn Therefore, ICRP 3 average individual. Do simetry for this reference individual can be used to estimate radiation dose to a population of people but not typically for a single person undergoing a nuclear medicine procedure. Further consideration must be given when using reference individuals to r epresent an actual individual.

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44 Publication 89 was utilized to adjust the UF newborn hybrid phantom to reflect the reference values for most organ masses detailed in the publication (Lee et al. 2007) Once the finalized ICRP reference UF newborn hybrid phantom was created, it was voxelized for use in a radiation transport code as will be discussed late r The completed NURBS/PM based UF hybrid newborn female phantom can be seen in Figure 1 8 The methodology used to construct the remainder of the UF hybrid phantom family was mostly consistent with that used to construct the UFH00MF phantoms. Subject a ges and voxel resolutions used to construct the UF family of hybrid phantoms are in Table 1 1 (Lee et al. 2010) The final UF NURBS/PM hybrid phantom family can be seen in Figure 1 9 Phantom Specificity Ideally, one would like to have a computational pha ntom that was constructed directly from images taken of the patient of interest to perform dosimetry. However, current standards of technology are not sophisticated enough to automatically generate phantoms specific to the patient of interest in the amoun t of detail desired in a timely manner Current methods do allow for real time patient specific dosimetry, and are very good for high dose radionuclide therapy applications (Kolbert et al. 1997, Prideaux et al. 2007, Hobbs et al. 2009). However, even the methods used in the referenced studies required user defined region of interest (ROI) definitions and were limited by scan coverage. B ecause of radiation dose concerns, most CT scans do not cover the entire body, and without a whole body scan, whole body models cannot be constructed. The referenced studies did not require whole body patient specific models because only certain tissues were identified as dose limiting, and the focus was given to those tissues. Due to the inability to construct whole body phantoms closely representative of the patient of interest on the fly, other levels of patient specificity had to be explored for the purpose of whole body internal dosimetry

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45 externa l and internal anatomy of the patient. Three major levels of patient specificity can be defined as follows (in order of specificity): Patient specific These phantoms are almost exactly specific to the patient for which the dosimetry is being performed. Patient specific phantoms are constructed from actual CT or MR image sets taken of the patient by manual (and sometimes automated) segmentation of organ volumes. To a certain extent, even these phantoms segmented directly from the patient cannot currentl y be considered truly patient specific since the detailed microstructure within the skeleton cannot be segmented from ex vivo CT or MR images. In addition, CT and MR images are not perfect and not all organs of interest can be effectively segmented. Furt hermore, segmentation is a subjective human driven process for the most part, so human error comes into effect. Despite these limitations organ dose estimates for most organs in these phantoms will always be more accurate than in other phantom types. Pat ient dependent These phantoms are initially created as a library of phantoms covering a range of physical characteristics. Based upon a series of reference phantoms, statistical analysis of morphometric measurements of thousands of individuals is perfor med, and a grid of measurements is determined that covers the majority of patient morphometries that would be seen in the clinic. For example, a grid could be created for adult males where phantoms are created for the 10 th 25 th 50 th 75 th and 90 th perc entiles by height, and at each height phantoms are created for the 10 th 25 th 50 th 75 th and 90 th percentiles by weight 4 Then, when an adult male patient walks through the door for a procedure, the phantom in the grid that most closely matches the meas urements taken for the patient would be selected for dosimetry. 4 This is just an example. Recent developments in patient dependent phantom library construction have made it clear that a grid of equal height and weight increments is more effective than percentiles because percentiles cha nge over time.

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46 The dosimetry for the selected patient dependent phantom would have already been performed ahead of time, so dose estimates could be obtained immediately. Patient dependent phantoms more clo sely approximate the true anatomy of an arbitrary patient than reference phantoms, but uncertainty still lies in the internal anatomy since the internal organs were segmented from images for a different patient. Reference These phantoms are defined by t he ICRP and represent the average person by height and weight. They were originally developed to be applied to prospective radiation protection where radiation environments are investigated to see if the average worker or member of the general population would incur radiation doses above recommended limits or action levels. irradiated. While this application is strictly for prospective radiation protection, reference phantom s were not intended to be applied to individual dosimetry for medical procedures or occupational radiation accidents Since most patients are not average dosimetry calculations performed on reference phantoms can only be taken as rough estimates for the actual absorbed doses for the patient of interest. These three classes of phantom specificity cover the spectrum of phantom detail, but within each class there are further distinctions between phantom sub types and their level of specificity as depicted in Figure 1 10 Relevant Radiological Physics The underlying physical occurrence important for radiation dosimetry is energy deposition in human tissue. An example was given earlier that described the process by which DNA strand breaks can occur from radiat ion energy deposition so understanding energy deposition from radiation sources is crucial Since a primary purpose of the current study was to determine

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47 radiation dose measures from photons and electrons some basic mechanisms by which photons and elect rons deposit their energy will be discussed. Photon Energy Deposition Two types of ionizing radiation are currently defined (1) indirectly ionizing radiation and (2) directly ionizing radiation (Attix 2004) Indirectly ionizing radiation first transfers its kinetic energy to another particle, and the particle to which the energy was transferred directly deposits its energy to the medium. Photons are considered indirectly ionizing since they give up their energy to electrons in tissue, and the electrons subsequently deposit their energy in the tissue For the purpose of this study, the three most frequently encountered photon interactions will be discussed, and they are as follows: Photoelectric effect The kinetic energy of the incident photon is absor bed by an orbital electron that is then ejected from the atom (Attix 2004) The energy of the incoming photon must be greater than the binding energy of the electron, and the resulting kinetic energy of the electron is given by Equation 1 2 (Attix 2004) (1 2 ) where is the initial kinetic energy of the electron, is the kinetic energy of the incoming photon, and is the binding energy of the electron. The vacancy left by the electron may be filled by electrons in other orbitals, leading to x ray emission or Auger electrons. The probability of this interaction occurring is given by Equation 1 3 (Attix 2004) (1 3 ) where a is the interaction cross section per atom (effectively the interaction probability) for the photoelectric eff ect, is the atomic number of the atom, and is the kinetic energy of the

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48 incoming photon. The powers on the atomic number and photon energy vary as a function of photon energy, but Equation 1 3 gives a useful relationship for and below where the photoelectric effect is most important. From this relationship, it can be seen that the photoelectric effect is highly probably for high Z elements at low photon energies. As applied to the phantoms, one would expect higher interaction rates in bone than in soft tissue since the effective atomic number for bone is higher. Compton scattering An incoming photon scatters off of a bound electron (kinematically, the electron can be treated as free and stationary) and some of the photon energy is transferred to the electron and some is retained by the photon (Attix 2004) The photon changes direction, and the electron is ejected from the atom, depositing its newly attained kinetic energy along its path. The initial kinetic energy of the electron is given by Equation 1 4 (Attix 2004) (1 4 ) where is the initial kinetic energy of the electron, is the kinetic energy of the incoming photon, is the rest mass energy of the electron ( ), and is the scattering angle of the photon relative to the path of travel of the incom ing photon. The probability of this interaction occurring is given by Equation 1 5 (Attix 2004) (1 5 ) w here is the Compton mass attenuation coefficient and is the atomic number of the atom It can be seen that the Compto n mass attenuation coefficient, another form of interaction probability, is mostly independent of the atomic number of the material. Compton interaction probability depends more on electron density of the material.

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49 Pair production A photon disappears in a nuclear Coulomb field, and its energy is converted into an electron positron pair (Attix 2004) The nucleus is required for this type of photon interaction to occur in order to conserve momentum. Some of the energy of the photon is used to create the electron and positron rest mass equaling or The remainder of the kinetic energy is transferred as kinetic energy to the electron and positron, not necessarily in equal quantity (Attix 2004) In the threshold situation where t he photon has just enough energy to create the electron positron pair, the electron and positron will have no momentum. Since the incoming photon had momentum, another body has to absorb that momentum. The average kinetic energy attained by the electron or positron in a pair production interaction is given by Equation 1 6 (Attix 2004) (1 6 ) where is the average initial kinetic energy of the electron or positron and is the kinetic energy of the incoming photon. The probability of this interaction occurring is given by Equation 1 7 (Attix 2004) (1 7 ) where a is the interaction cross section per atom for pair production, is the atomic number of the atom, and is the P value and is a function of the incoming photon energy and atomic number of the atom. The interaction cross section increases roughly logarithmi cally with photon energy. Electron Energy Deposition While each photon interaction removes a large fraction of the initial energy of the photon, either by total absorption (photoelectric effect and pair production) or by hard scattering collisions with ele ctrons, electrons lose their energy in a large number of very small interactions

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50 (Attix 2004) Due to its Coulomb electric field, a free electron interacts with the valence electrons with every atom it passes (Attix 2004) Since electrons lose their ener gy in small increments over the entire path it travels, it can be considered to continuously slow down, a (Attix 2004) Electrons lose energy in the following two ways: Radiative energy l oss This type of energy loss can be attributed to Coulomb force inelastic interactions with the external nuclear field (Attix 2004) The electron passes near the nucleus and is deflected, transferring its energy to a photon, or bremsstrahlung radiation (Attix 2004) As electrons travel through a material, a continuous spectrum of photon radiation is emitted, resulting from the electron interactions with the nucleus (Attix 2004) This interaction is proportional to so radiative emission is more likely in bone than in soft tissue. Radiative energy does not account for energy deposition in the medium since the kinetic energy of the electron is converted into photons only energy transfer has occurred in this case. Collisional energy loss Two ty pes of collisional energy loss are prevalent in electron physics (1) soft collisions and (2) hard collisions (Attix 2004) Soft electron collisions are the most common type of interaction, and they transfer energy to the medium of interest (Attix 2004) The Coulomb field of the electron affects the atom and either excites it to a higher level or ejects a valence shell electron (Attix 2004) Hard collisions are a result of the electron interacting directly with a valence shell electron and ejecting it f rom the atom (Attix 2004) The electron liberated from the atom is known as a delta ( ) ray, and it continues on its own path of ionization and excitation (Attix 2004)

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51 Photon Electron Cascades A combination of all of the previously discussed photon and e lectron interactions are of different interaction events occur. For example, a monoenergetic photon source could be started within a radiation transport code, and the following sequence could be one possible interaction path for a single photon The photon could scatter and eject an inner shell electron from an atom. The photon loses some energy and changes direction. T he liberated electron transfers energy to the medium and simultaneously creates bremsstrahlung photons that then proceed to experience their own interactions. The vacancy left by the ejected electron is filled by an outer shell electron, and an x ray is emitted 5 and the x ray proceeds to experi ence its own interactions. The scattered primary photon experiences the photoelectric effect and is absorbed by an atom. The energy is transferred to an inner shell electron which is subsequently ejected from the atom. The liberated electron transfers e nergy to the medium and simultaneously creates bremsstrahlung photons that then proceed to experience their own interactions. The vacancy left by the ejected electron is filled by an outer shell electron, and an x ray is emitted, and the x ray proceeds to experience its own interactions. Again, this is only one example of the interaction path a photon could take and is not an exclusive list. This series of processes continues until all energy has been expended into the medium. When computing radiation do se to tissues in the human body with computational phantoms and radiation transport codes, these types of interactions showers are occurring, and the amount of energy deposited to the tissues of interest is modeled. 5 The vacancy could also lead to energy transfer to another electron that is subsequently ejected from the atom.

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52 Absorbed Fraction of Energy Having consi dered how radiation deposits energy in tissues of the body, the dose measure important to this study and to nuclear medicine dosimetry in general will be discussed. In nuclear medicine dosimetry, the final dose measure of interest is the radionuclide S va lue a measure that gives absorbed dose to a target tissue from a source tissue per nuclear transformation in the source tissue for a particular radionuclide in units of milligray per megabecquerel second ( ) Along with the radionuclide S value, biokinetic models are needed but development of detailed biokinetic models are beyond the scope of this study Within the S value only one measure must be determined by means of radiation transport the AF and SAF of energy given in Equation s 1 8 and 1 9 (1 8 ) (1 9 ) where and are both the absorbed fraction of energy to target volume from source volume for radiation of energy is the amount of en ergy deposited in target volume from source volume for radiation of energy is the total amount of energy emitted from source volume for radiation of energy and are both the specific absorbed fraction of energy to target volume from source volume for radiation of energy and is the mass of target volume The process by which a radiop harmaceutical distributes throughout the body was previously discussed. When a radiopharmaceutical distributes to a particular organ or tissue, that tissue becomes a source of radiation and is indicated in Equation 1 8 by All tissues in the

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53 body including become target tissues, indicated in Equation 1 8 by potential points in the body where radiation energy may be deposited. The point of simulating radiation with a radiation transport code is to determine the fraction of energ y emitted from the source tissue that is deposited in each target tissue, the AF. The AF includes both information about the geometry of the problem as well as the initial energy of the radiation of interest. All other factors that compose the S value ca n be determined from outside sources without simulation, so the AF, and ultimately the SAF, is the dosimetric measure of interest for this study. The SAF is usually preferred over the AF because the mass of the target tissue is already considered, elimina ting the need to obtain that information separately Effective Dose At the most basic level, the quantity most relevant to radiation dosimetry is the absorbed dose. Absorbed dose refers to the amount of energy imparted to a material per unit mass of the m aterial with units of joules per kilogram ( ) or grays ( ) (Attix 2004) This is a good metric to compare dose information about a certain nuclear medicine imaging study, but the absorbed dose does not take into account differences in radiation or tissue types. Photons, electrons, proton s, neutrons, etc. have different properties and are thus predicted (and observed) to have different effects on body tissues for the same amount of energy deposition (Attix 2004) The radiation weighting factor was introduced to account for the impact each radiation type has on materials and is based on the linear energy transfer (LET) characteristics of the radiation type High LET particles (e.g., protons, neutrons, heavy charged particles (HCPs) recoil atoms, etc. ) deliver more energy per unit penetrati on distance into a material than low LET radiations (e.g., photons and electrons) (Attix 2004) Since biological damage toward an arbitrary biological endpoint depends partially on the spatial distribution of the ionizing events, high LET particles are mo re biologically damaging than low LET particles (Hall et al. 2006)

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54 Relative biological effectiveness (RBE) is a direct measure by which the relative contribution of a particular radiation type has toward a particular biological endpoint, either stochasti c or deterministic 6 (Hall et al. 2006) For an example where photons are the reference radiation (the reference radiation could be any radiation type), RBE is measured by selecting a biological endpoint and determining the amount of absorbed dose needed f rom a type of radiation to produce the same endpoint as photons (Hall et al. 2006) The RBE is then calculated by dividing the dose needed by photons by the dose needed by the arbitrary radiation type. RBE increases with decreasing absorbed dose because ionization tracks become more spatially dense, so the radiation weighting factor s were assigned the maximum RBE ( RBE m ) (ICRP 2007) When multiplied by the radiation weighting factor, an absorbed dose to any tissue in the body is then referred to as the eq uivalent dose to that tissue and is given in units of sieverts ( ) The tissue weighting factor was introduced to account for differences in the way different body tissues react to energy deposition from radiation, otherwise known as their radiosensitivity (Attix 2004) Tissue weighting factors are based on radia tion stochastic risk data and takes into account lifetime cancer incidence, dose and dose rate effectiveness, lethality, quality of life for non fatal cancers, and years of life lost (ICRP 2007) The unit of measure used for effective dose is also the sie vert, an issue that can cause confusion. It is important to judge based on the context whether the unit sievert refers to individual organ equivalent doses or whole body effective dose. Typically, authors should include the organ name if referring to the equivalent dose. Individual organ equivalent doses are calculated using Equation 1 10 and the whole body effective dose is calculated using Equation 1 1 1 (ICRP, 2007) : 6 Tissue weighting factors as defined by ICRP Publication 103 are based on stochastic biological endpoints (ICRP 2007).

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55 (1 10 ) (1 11 ) w here is the ra diation weighting factor for r adiation type is the tissue weighting factor for target organ is the absorbed dose to target organ from radiation type in units of is the organ s pecific equivalent dose in units of and is the whole body effective dose in units of The units of dose in these equations may also be in and but nuclear medicine dose are generally generated normalized to th e administered activity (AA) so that the final dose estimates may be simply scaled by the AA. Relevant Studies and Current Limitations Each of the specific aims in this study addresses an area of work that could be improved in some way. Prior to exploring the methods used to improve these areas of study, previous investigations by other researchers will be discussed to illuminate other approaches and identify areas of improvement. Some of the studies discussed in the upcoming sections have valid approache s that work for the particular application of the research group from which the study originated. In these cases, the approach used by the research group was not ideal for the UF phantom family, so other approaches were developed to improve the UF phantom family, not necessarily to improve the area of study as a whole. In other cases, room for improvement of general methodology was identified, and results from the current study could potentially be used by the nuclear medicine community as a whole. Each specific aim was addressed individually and by summarizing relevant studies. References were omitted from each summary section because, unless otherwise indicated, the quoted article serves as the reference.

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56 Phantom Blood Vessel System s MCAT to XCAT: t he e volution of 4 D c omputerized p hantoms for i maging r esearch (Segars et al. 2009) The four dimensional (4 D) NURBS CArdiac Torso ( NCAT ) phantom was first developed by Dr. Paul Segars as part of his dissertation at the University of North Carolina, Chapel Hi ll (Segars 2001) This phantom was created primarily to model cardiac and respiratory motion in the NURBS environment as applied to different medical imaging techniques. The internal anatomy was taken from the Visible Human project of the NLM (Segars 200 1) The dataset was described by axial matrix elements at a slice resolution and a pixel width of over the entire body. Initially, this phantom was only a torso phantom, lacking any arms or legs. The eXtended CArdiac Torso ( XCAT ) phantom was an improvement on the NCAT phantom and extended the NCA T to include arms, legs, and a much more detailed internal anatomy. The XCAT phantom was based on the high resolution Visible Male and Female of the N LM This was done to extend the phantom to high resolution applications such as CT or MRI In this iter ation of the original NCAT phantom, a circulatory system was included from direct segmentation. It was then desired that the XCAT phantom be extended to other ages and was done by obtaining several CT datasets covering a range of ages from newborn to adul t. The datasets were first manually segmented to include the easily observable anatomy. Then, the organs which were n o t able to be directly segmented from the datasets were scaled down from the adult XCAT phantom to match the existing framework of the pe diatric XCAT phantoms. All organs were scaled to match ICRP Publication 89 volumes. However, the study did not quote blood vessel volumes or masses and did not explicitly state that the blood vessels were scaled to match ICRP Publication 89 reference vol umes.

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57 Figure 1 11 shows the current XCAT blood vessel model for the adult male and female and newborn phantom. While there are limitations with some of the other aspects of the XCAT phantom series, the circulatory system is well modeled. This model is de scribed by approximately one artery and one vein (with some branching) in the legs and arms and two arteries and two veins in the neck. However, there is fairly detailed vasculature in the heart and lungs. The present proposal does not aim to create a mor e detailed circulatory system, only to provide a circulatory system for the UF series of hybrid phantoms. The level of detail used in the lungs of the XCAT phantom is not critical since blood can be apportioned uniformly throughout the lung volume. The v i rtual f amily d evelopment of s urface based a natomical m odels of t wo a dults and t wo c hildren for d osimetric s imulations (Christ et al. 2010) The blood vessel models in this study were derived from a volunteer study. Two adults and two children were subjec ted to whole body MR scans. The subjects were scanned on a Siemens Magnetom Avanto T otal Imaging Matrix whole body scanner. A contrast agent was used to facilitate imaging of the blood vessels. After the contrast agent was administered, a first p ass scan was performed to capture only the arteries. Then, after the agent reached equilibrium, a second pass scan was performed to capture all the blood vessels. From these two scans, the arteries and veins could be distinguished and subsequently segmen ted, creating a realistic whole body blood vessel system. Vessels less than in diameter were excluded du e to difficulty in segmenting. These models were of a 34 year old male, 26 year old female, 11 year old female, and 6 year old male. The models were not scaled to ICRP Publication 89 reference values and represent a set of patient specific phantoms. Smoothing was done to the PM models using the

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58 software Amira 4.0 by reducing the number of surface triangles. This blood vessel model closely resembles the model by Segars et al. (2009) with the exception that no pulmonary v essel system was modeled. The location and number of the arteries and veins is essentially the same as the XCAT phantom series. However, there is no mention of blood vessel masses or volumes and their comparison to ICRP Publication 89 reference volumes. Despite this, the blood vessel model provides an effective vehicle for the simulation of a distributed blood source Skeletal Photon Fluence to Dose Response Functions Evolution and s tatus of b one and m arrow d ose m odels (Stabin et al. 2002) Radiation abso rbed dose to hematopoietically active marrow ( AM ) and bone endosteum (TM 50 ) (Hough et al. 2011) ) has been of interest for quite some time due to concerns over marrow toxicity as a possible side effect of radiopharmaceutical therapy as well as the risk for genesis of leukemia or osteosarcoma from irradiation of the AM or TM 50 respectively The trabecular microstructure of the skeleton is so small and intricate that it presently cannot be explicitly integ rated into a computational phantom for use in radiation transport codes. F. W. Spiers was one of the first to attempt to develop a method for determining skeletal dose based on actual microstructure of bone Spiers created a model for the calculation of r adiation absorbed dose to marrow from the volume of trabecular bone ( TB ) 7 First, optical scanning was performed on TB samples from several cadavers, and chord length distributions were produced for TB and marrow cavities from the acquired images. Chord length distributions describe the frequency of lengths of straight lines which intersect two surfaces (Jokisch et al. 7 Each b one in the human body is surrounded by a hard mineral bone shell called cortical bone (CB). For most bone sites, this CB shell is filled with a material called spongiosa, which includes both trabecular bone (TB) and total marrow (TM). Trabecular bone is a complicated network of hard mineral bone spicules, the cavities of which are filled with TM. TM is made up of both active marrow (AM) and inactive marrow (IM). TB is generally not present in the shafts of the long bones. These long bone shafts are kno wn as medullary cavities (MCs).

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59 2001) Then, transport was performed stochastically by basing the electron paths on the resultant chord length frequency distributions. The average energy deposition to marrow was then calculated from electron sources in the TB volume (TBV). Snyder et al. (1975) subsequently derived AFs for sources in TBV and marrow. The results of these derivations were incorporated into Monte Carlo rad iation transport simulations to determine S values in the Fisher Snyder computational phantom for use in MIRD Pamphlet No. 11. However, these simulations were known to show conservatively high doses for initial monoenergetic photon energies below because it was assumed that marrow absorbs energy per gram as efficiently as mineral bone. length distributions and electron transport methods, Ec kerma n later calculated electron AFs for 7 bone types for a range of energies. The AFs for these bone types were distributed to the 15 skeletal regions of the Cristy/Ec kerma n phantoms, weighted by the mass fraction of each bone type within each skeletal region. Fairly recently, Bouchet et al. (2000) calculated AFs for 7 adult TB si tes treating the trabecular marrow space and bone volume all as sources and targets. They did this using length distributions and the Electron Gamma Shower version 4 (EGS4) radiation transport code. Three major differences exist between the Ec kerma n and Bouchet models. The first difference is that the Ec kerma n model assumes that the AF for red marrow (AM) irradiating red marrow is equal to the AF for the total marrow (TM) space irradiating the TM space multiplied by the cellularity the fra ction of TM occupied by red marrow. The Bouchet model assumes that the AF for red marrow irradiating red marrow is equal to the AF for the TM space irradiating the TM space with no correction. Because of this, the Bouchet model predicts doses approximate ly

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60 twice as large as the Ec kerma n model. A second difference between the two models stems from the definition of the bone endosteum, or TM 50 The Ec kerma n model treats TM 50 as a 2 D planar surface at the interface between the marrow space and trabecular bone while the Bouc h et model simulates the endosteum as a bone surface (BS) source a deep layer of tissue within the marrow space adjacent to the TB Accordingly, the Bouchet dose conversion factors (DCFs) (mathematically equivalent to S values) for bone surface sources are up to 2 times as great as the Ec kerma n model Specific a b sorbed f ractions of e nergy at v arious a ges from i nternal p hoton s ources. I. m ethods (Cristy et al. 1987) With this report came the introduction of skeletal photon fluence to dose response functions for the determination of absorbed dose to AM and BS. T he BS was used as a surrogate for osteoprogenitor cells (cells at risk for osteosarcoma) and at that point was defined as the volume of TM that was deep from the TB of the spongiosa and deep from the cortical shell in the shafts of the long bones (ICRP 1979) The following equations were used to develop the skeletal photon fluence to dose response functions in Cristy et al. (1987). (1 12 ) (1 13 ) where for electrons of energy for electrons of energy is the and denotes the mass attenuation coefficients in medium for the photoelectric, Compton, and pair production interactions,

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61 number of electrons of energy between and liberated in region per interaction length distributions. Integration over the energy dependent AFs, photon mass interaction coeffi cients, secondary electron spectrum, and electron energy over the whole secondary electron spectrum gives the energy deposited in either the AM or BS per unit photon fluence per unit source mass. This integration was performed for the three dominant photo n interaction processes (photoelectric absorption, Compton scattering, and pair production) and summed. To obtain the absorbed dose per unit photon fluence to the target region, the integrations were performed for each source region and weighted by the ma ss ratio of the source region to the target region. These are the formulations that are used in the current study, but full 3 D electron transport will be completed for the determination of skeletal AFs rather than chord based calculations. Skeletal photo n fluence to dose response functions were computed for 7 bone sites, but Cristy and Ec kerma n recommended the use of skeletal photon fluence to dose response functions from only two bone sites to apply to the whole skeleton. The authors noted that the pari etal bone skeletal photon fluence to dose response function seemed to differ noticeably from the other bone sites, and the lumbar vertebra appeared to faithfully represent the other bone sites. Also, the age dependence of the trabecular microstructure did not show appreciable influence on the skeletal photon fluence to dose response functions for the AM target Based on these discoveries, the authors recommended that the parietal fluence to dose response functions be used to calculate the dose to AM and B S in the cranium and the lumber vertebra fluence to dose response functions be used to calculate the dose to all other bone sites. They also recommended that the same fluence to dose response functions be used across all ages.

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62 Photon Specific Absorbed Fra ctions Specific a bsorbed f ractions of e nergy at v arious a ges from i nternal p hoton s ources. I. m ethods (Cristy et al. 1987) The SAFs calculated by Cristy and Ec kerma n at Oak Ridge National Laboratory (ORNL) in 1987 for the computational phantoms developed by the MIRD committee or MIRD type phantoms, represents the current standard for internal dosimetry. The ICRP has recently migrated to new voxel phantoms as the reference for the adults, but the work by Cristy and Ec kerma n is still the standard for the pediatric series of phantoms. Stylized computational phantoms based on the adult phantom of Snyder et al. (1975) were used for the calculation of SAFs. Pediatric phantoms were constructed with the same general body shape but slightly different proportions as described by Cristy ( 1 980) However, the 15 year old phantom was modified to represent the adult female. Though having the same body dimensions, breast tissue, ovaries, and a uterus were added. Three materials were used to describe the structures of the phantom s : soft tissue, lung, and bone. Correspondingly, three tissue densities and compositions were used, and these material descriptors were only unique for the newborn phantom T he 1 year old, 5 year old, 10 year old 15 year old, and adult phant oms all had the same tissue densities and compositions. The Cristy Ec kerma n pha ntoms can be seen in Cristy et al. (1987) I t is obvious that these phantoms are not anatomically realistic and t his is one immediate drawback to using these phantoms for int ernal dosimetry. The radiation transport techniques used in the development of these SAFs were similar to those used by Snyder et al. (1975) with the primary deviation being the treatment of skeletal tissues. For non skeletal target organs, it was assumed that all liberated electron energy was locally deposited an assumption known as the kerma approximation which refers to the phrase The kerma approximation is generally only valid for

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63 situations in which charged p article equilibrium (CPE) is established. In this situation, electrons leaving the volume of interest are compensated by electrons entering the volume of interest. This assumption was considered valid for any organs which were not on an interface with di fferent tissue compositions. The report did not explicitly state the number of histories used in the models but only discussed acceptable statistical errors. Snyder et al. (1975) simulated up to 60,000 particle histories, but it is unclear to what degree the number of particles was increased for the ORNL calculations. lung and non skeletal organs, the kerma approximation was justified to a degree. However, for internal dosimetry, CPE is not definite ly established for every target organ. In the case of self dose, the dose to the source could be over estimated using the kerma approximation since secondary electron escape is not considered. The total energy deposited in each target organ was recorde d and divided by the mass of the target organ and the initial energy of the photon to obtain the SAF. Skeletal photon fluence to dose response functions were used to calculate the SAFs to AM and BS. The reliability of an SAF was assessed based on the coef ficient of variation (CV), which is the ratio of the standard deviation to the mean, multiplied by It was known previous to these calculations that Monte Carlo techniques alone would not be sufficient to provide reliable SAFs. The point source kern el method was used in cases where the CV was greater than The point kernel equation can be seen in Equation 1 13 (1 14 ) where is the point isotropic SAF at is the linear energy absorption coefficient at the source energy, is the linear attenuation coefficient at the source energy, is the density of the medium, and r representing the contribution of the scattered

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64 This equation was integrated over the volume of the source and target organ. Numerically, this was performed by randomly sampling a point in the source organ and a poin t in the target organ to obtain the point pair distance, in the equation. The process was repeated many times to produce statistically reliable results (all point kernel CVs were less than ). The drawback of the use of this equation is that it assumes a homogenous water phantom embedded in an infinite water medium. Obviously, with the incorporation of bone and lung tissue in the phantoms, the point kernel method will be an approximation. The authors compensate for this with the introduction of correction factors for certain so urce target combinations. Since the computing power at the time was far inferior to what is available today, a variety tes that the reciprocity theorem was invoked. That is, the Monte Carlo simulation was performed for the target irradiating the source. The reciprocity theorem states that the SAF for the source irradiating the target is equal to the SAF for the target ir radiating the source. The following were techniques used by Cristy and Ec kerma n to smooth the SAF curves. If the CV for the direct and inverse Monte Carlo estimate and point kernel estimate were greater than the SAF was rejected. For all SAF estimat es, an average was taken of the direct and reverse Monte Carlo estimates with each SAF weighted by the inverse of its variance. If the reverse Monte Carlo estimate was not available, the direct Monte Carlo estimate was taken as the weighted average. If t he CV for the weighted average was greater than an average was taken of the weighted average and the corrected point kernel estimate with each SAF weighted by the inverse of its variance. Once the first three conditions were assessed and

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65 appropriate a ctions taken, a cubic spline technique was used to smooth the data on a log log plot of the final weighted average versus initial photon energy. If the spline did not fit well at low energies, more weight was given to the first two values. If the CV at was greater than and the results appeared poor, the weighted average of the uncorrected and corrected point kernel estimate was taken at The spline technique was then reapplied. After all smoothing techniques were applied, if the S AF curve still appeared unreliable, the smoothing was done subjectively by hand. If no acceptable Monte Carlo estimates were available, the corrected point kernel estimate was taken as the recommended value. If neither organ was simulated as a source org an, no recommendation was made. There are many limitations to the approaches in the Cristy Ec kerma n series of SAFs. While this work is dated, until the ICRP officially adopts a new full series of pediatric phantoms, the Cristy Ec kerma n work is still the s tandard dataset for a broad range of radiation dose coefficients The phantoms used were stylized/mathematical phantoms, and while easily deformable, these phantoms lack the anatomic realism of voxel or hybrid phantoms. Also, only 3 material types were u sed, a simplistic tissue characterization compared to the information and computing abilities today. The data smoothing techniques were convoluted and unduly complicated, but this was necessitated by the poor statistical uncertainties resulting from only being able to simulate approximately particle histories. In the present study, to particle histories were simulated. Resultantly much improved precision is achieved, and complicated variance reduction techniques will be unnecessar y. ICRP 110: a dult r eference c omputational p hantoms (ICRP 2009) This publication of the ICRP lays out the groundwork for SAF calculations in the future. Work has been done by other groups to calculate some photon SAFs for certain source target

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66 combinatio ns in the ICRP Publication 1 1 0 voxel phantom s However, full scale, complete internal dosimetric characterization is presently underway at the time of this writing It is important to note that complete tables of SAFs are currently unavailable. The ICRP recently adopted new reference adult male and female voxel phantoms. These phantoms were developed from whole body CT data sets. The adult male was segmented from images of a 38 year old at a height of and a weight of the same as the ICRP Publication 89 reference adult male. The adult female was segmented from a 43 year old at a height of and a weight of ; the reference adult female detailed in ICRP Publication 89 has a height of and a weight of All segmented organs were scaled to match ICRP Publication 89 reference values. A noted limitation was that the surface shapes of the organs were unique to the individual that they were segmented from. The vox el resolutions used were and for the male and female, respectively. Some complications were noted by the ICRP and included skin thicknesses that were not equal to the reference value and the inability to accurately model the gall bladder. Utilizing the resolutions quoted, the skin masses were and greater than the reference values for the male and female, respectively. The gall bladder was difficult to model due to the voxel resolutions T he wall mass was greater than the reference value, but the total gall bladder mass (including the contents) was matched to the ICRP Publication 89 reference value. Since the trabecular microstructure in the skeleton was too small to segment from the CT images, th ree regions of bone were explicitly modeled: CB spongiosa, and medullary cavities ( MCs ) Masses of skeletal constituents were apportioned based on ICRP Publication 70 and ICRP Publication 89. For source simulations, cortical bone will be simulated unifo rmly since the

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67 volume is explicitly defined. The marrow and TB sources will be created by assigning bone site specific sampling probabilities based on the relative distribution of marrow. SAFs to AM and TM 50 will be calculated using either correction fac tors as described by Zankl et al. (2002) and Schlattl et al. (2007) or the skeletal photon fluence to dose response functions developed by Cristy and Ec kerma n (1987) The publication does not go into detail about skeletal dosimetry methods to be used. The ICRP Task Group on DOse CALculations (DOCAL) produced a set of photon SAFs for the liver, lungs, and thyroid as source regions and the colon, lungs, stomach wall, and breasts as target tissues using two radiation transport codes: Electron Gamma Shower of the National Research Council Canada (EGSnrc) and Monte Carlo N Particle eXtended ( MCNPX ) (Los Alamos National Laboratory, Los Alamos, NM) The results from two irradiation geometries are displayed in Figure 1 1 2 The two radiation transport codes used s howed good agreement for most of the combinations of sources and targets. Electron Specific Absorbed Fractions Specific a bsorbed f ractions of e nergy at v arious a ges from i nternal p hoton s ources. I. m ethods (Cristy et al. 1987) Electron absorbed fractions were assumed to be equal to unity in the case of self irradiation of non walled organs and equal to zero for cross fire (Snyder et al. 1975) Consequently to calculate any given SAF for non walled organs, one would simply take the inverse of the target mass. To calculate the SAF for a walled organ being irradiated by its contents, one would take the inverse of twice the target mass (this would assume an absorbed fraction of 0.5) (Snyder et al. 1975) These were clearly approximations, but no simulation s were performed to verify their validity.

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68 ICRP 110: a dult r eference c omputational p hantoms (ICRP 2009) The DOCAL task group performed full electron transport in both EGSnrc and MCNPX to calculate a small set of electron SAFs for the ICRP Publication 110 a dult male and female voxel phantoms. The source and target regions simulated in the development of the photon SAFs were used for the electron SAFs. Results from two irradiation scenarios can be seen in Figure 1 13 It is clear from these curves that the assumption of complete electron energy absorption for self irradiation and insignificant electron energy absorption for cross fire was a poor one. At high energies, electron escape was found to be appreciable and electron cross fire, significant. Some m inor disagreements between EGSnrc and MCNPX and poor statistical uncertainties were seen at electron energies less than Dosimetric Sensitivity Analysis for Internal Sources Patient specific s caling of r eference S values for c ross organ r adionuclide S values: w hat is a ppropriate? (Petoussi Henss et al. 2007) MIRD Pamphlet No. 11 was one of the first to give any g uidelines on SAF scaling methodology, and the Petoussi Hens et al. (2007) study aimed to verify the MIRD Pamphlet No. 11 recommendations The authors attempt ed to uncover any further information on patient specific SAF scaling. This investigation was per formed solely with computational phantoms, and for the most part, validation was the focus. The German Research Center for Environmental Health ( GSF ) voxel phantoms (Petoussi Henss et al. 2002) and ORNL MIRD type stylized phantoms (Cristy et al. 1987) wer e used for comparison. First, photon cross fire dose variation with changes in source organ mass was examined by comparing the photon SAFs for a particular source organ from the GSF voxel phantoms as originally segmented to the SAFs for the same source org an when scaled to the ICRP Publication 89 reference mass. and

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69 were shown (note: target source). Ratios of the SAFs for source organs of the original mass to the SAFs for the source organs of the ICRP Publication 89 matched mass were close to 1.00, so the authors claim that no corrections are necessary for changes in source organ mass, even for distributed target organs such as red bone marrow. However, Figure 1 14 show ed that there can be some variab ility up to around Next, the reciprocity principle was investigated for a distributed organ, the red bone marrow. The reciprocity theorem states that the SAF from a particular source/target combination is equal to the SAF if the source and target are reversed. However, this had not yet been proven for distributed organs, so this study simulated the liver and red bone marrow as sources and targets, and the results can be seen in Figure 1 15 No mass correction was recommended for initial photon energi es or greater since deviations were only seen from about to Finally, the authors sought to verify the photon self dose mass scaling recommendation of MIRD Pamphlet No. 11 that the SAFs for photon energies greater than should scale as the inverse power of the organ mass. That is, to scale an SAF for the self irradiation scenario, one must multiply the original SAF by the factor To verify that the scaling was perfo rmed correctly, the SAF should decrease for a larger source organ. Results were shown for photon self irradiation of the thyroid in the GSF family of voxel phantoms and can be seen in Figure 1 16 The SAFs for the thyroid irradiating the thyroid at the o riginal segmented mass were divided by the SAFs for the thyroid irradiating the thyroid at the reference mass. The results were found to be in good agreement with the MIRD Pamphlet No. 11 recommendation. Red bone marrow self irradiation was also examined but no conclusions could be drawn.

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70 While some previously recommended methods of SAF scaling for a variety of scenarios were explored, the results seemed to be in fairly good agreement but with some variation. No mass scaling was recommended for distant organs, but variation s w ere seen up to Also, the MIRD Pamphlet No. 11 SAF scaling methodology for photon self irradiation was claimed to be valid, but graphical, and no numerical verification was offered. There seemed to be deviations from the inver se power recommendation which were not taken into account. It is possible to develop energy dependent scaling methodologies which could scale the SAFs in an even more accurate manner as was investigated in this study. Changes in r adiation d ose with v ariations in h uman a natomy: l arger and s maller n ormal s tature a dults (Marine et al. 2010) This study sought to examine the general trends of changes in dose with variations in stature. The 50 th percentile NURBS phantoms were constructed according to ICRP Publication 89 reference data. Anthropometric data from Dekaban (1978) Grandmaison et al. (2001) the U.S. Department of Defense (DOD), and the Centers for Disease Control (CDC) were used to construct 25 th and 75 th percentile by height adults. Organ mas ses for which autopsy data was unavailable were approximated by a increase or decrease. The 10 th and 90 th percentile s by height adults were constructed using data from the DOD HDBK 743A (anthropometry of U.S. military personnel) and total body masses w ere calculated from assumed body mass indices (BMIs). Scaling factors were the used to adjust organ masses until the constructed total body mass matched the calculated total body mass. The radiation transport code Geant 4 was used to calculate SAFs for a variety of source target combinations. The results were compared to both the 50 th percentile Cristy Ec kerma n phantom and 50 th percentile NURBS ICRP reference phantom SAFs.

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71 The SAFs were found to decrease with increases in percentile size because the effe ct of increases in organ mass dominates the effect of increases in organ separation. The percent differences between the SAFs of the 50 th percentile and non 50 th percentile phantom s were averaged over all photon energies and absolute differences were repo rted. For self irradiation, SAFs vary from to variation in organ mass. Organs outside of the main trunk area showed SAF differences which were within the uncertainty of the SAFs themselves. Organs inside the main trunk area showed SAFs with difference between and target organ mass. Absolute percent differences were seen between about ( adult female) and ( adult male), comparing the 10 th percentile to the 90 th percentile by height phantoms. Res ults from selected source organs in the adult male can be seen in Figure 1 17 While this study presented a systematic method for examining variations in SAFs based on and could help understand how the dose varies from patient to patient. In addition, the analysis was only performed for adults, and the differences in SAFs were averaged over all photon energies. The current study aim ed to generate empirical e quations or look up table (LUT) type scaling factors which would allow for the scaling of SAFs at all photon energies, based on the or 50 th percentile heights. Changes in r adiation d ose with v ariations in h uman a natomy : m oderately and s everely o bese a dults (Clark et al. 2010) This study sought to examine the general trends of changes in dose for individuals of varying levels of obesity. The 50 th percentile NURBS phantoms were constructed according to ICRP Publication 8 9 reference data. First two adult male and two adult female phantoms were created at larger BMIs than the reference phantom by adjusting the outer body contours and

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72 scal ing to match typical body circumferences. Visceral fat deposits were modeled for the kidneys and the intestines. The small and large intestines were scaled in an elliptical fashion to model mesenteric fat deposits, and the kidneys were moved in the anterior direction to model pararenal and perirenal fat deposits. Cross sections of the p hantoms simulated are displayed in Figure 1 18 The radiation transport code Geant 4 was used to calculate SAFs for a variety of source target combinations. The results were compared to the 50 th percentile NURBS ICRP reference phantom SAFs. The SAFs were found to decrease with increases in percentile size, because the effect of increases in organ mass dominates the effect of increases in organ separation. The percent differences between the SAFs of the 50 th percentile non 50 th percentile phantoms were av eraged over all photon energies but only a few examples were discussed For the most part, the SAFs showed about a maximum of a few percent difference overall, but target organs in the abdominal area were up to 1.6 times lower in the moderately obese pha ntom and up to 2 times lower in the severely obese phantom than in the 50 th percentile phantom. The large intestines irradiating the liver showed the greatest differences while the lungs and large intestines showed little differences in the moderately obe se case up to a difference of a factor of 1.3 for the severely obese case due to mesenteric adipose deposits While this study presented a systematic method for examining variations in SAFs based on s that there is not much SAF variation with patient obesity with the exception of a few organ pairs. However, the analysis was only performed for adults, the differences in SAFs were averaged over all photon energies, and BMIs less than the reference BMI were not examined. The current study aim ed to generate empirical equations or LUT type scaling factors which would allow for the scaling of SAFs for all photon

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73 oth below and above the 50 th percentile. Internal Dosimetry Software OLINDA/EXM: t he s econd g eneration p ersonal c omputer s oftware for i nternal d ose a ssessment in n uclear m edicine (Stabin et al. 2005) One of the first widely distributed internal dose calcul ation software packages was the Radiation Internal Dose Information Center (RIDIC) at the Oak Ridge Institute for Science and MIRD dosimetry method based internal dosimetry personal computer software (MIRDOSE) However, the code was wr itten in Visual Basic (VB) and did not translate very well to Windows 2000. In addition, the U.S. Food and Drug Administration rewrite was needed since MIRDOSE was in unstructured VB, and it was subsequently translate d to Java. The converted software was named Organ Level INternal Dose Assessment (OLINDA). Also, exponential fitting to biokinetic data was made available, so a naming extension of EXponential Mod eling (EXM) was added. The final product was called OLINDA/EXM 1.0, and the FDA subsequently approved it for worldwide marketing. OLINDA/EXM 2.0 has recently been released, but not much is currently known about the phantoms or methods used in the softwar e. The input screens for OLINDA/EXM can be seen in Figure 1 19 Figure 1 19 ( A ) shows the main input form. This form can be used to either produce dose factors (DFs) or final doses calculated from the DFs and kinetic data. DFs are mathematically equival ent to S values, but OLINDA/EXM includes the radiation weighting factors in the calculation of DFs. While this is insignificant for radionuclides whose radiation emission consist only of photons and electrons, the inclusion of radiation weighting factors becomes important when considering alpha emission.

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74 Figure 1 19 ( B ) shows the nuclide input form. The user simply selects the element of interest, then the isotope. The decay data comes from the RAdiation Dose Assessment Resource (RADAR), a group who mai ntains a web site useful for internal and external radiation dose assessment (Stabin et al. 2003) Figure 1 19 ( C ) shows the model input form. The user selects from a list of computational phantoms or individual region models. The Fisher Snyder (MIRD ty pe) stylized phantom is used for the adult male and female phantoms, and the Cristy Ec kerma n stylized pediatric phantoms are used for the pediatric series. Figure 1 19 ( D ) shows the bio kinetics input form. The user enters the total number of nuclear tran sformations per unit AA which is mathematically equivalent to the old unit of residence time, in the desired source ed it too confusing Figure 1 23 ( E ) shows the final output window. Absorbed doses per unit AA to individual organs are listed by radiation type, and the total radiation absorbed dose is listed by organ. Effective dose equivalents per unit AA as defined by ICRP Publication 30 and equivalent doses per unit AA as defined by ICRP Publication 60 are listed by organ (Stabin 2005) Finally, the whole body effective dose equivalent and effective dose per unit activity are given. The OLINDA/E XM 1 .0 software program is intuitive to use and delivers results in an easy to understand format. Some improvements have been introduced with the creation of OLINDA/EXM 2.0. Decay data for over 1200 radionuclides from ICRP Publication 107 has been includ ed. New realistic NURBS based phantoms have been introduced (Stabin et al. 2006) The NURBS phantoms in version 2.0 were scaled from the existing models to match reference values given in ICRP Publication 89. However, there is little documentation on the phantoms used in this version of the code and it is unclear exactly how the phantom series was created or what they look like.

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75 Also, tissue weighting factors from ICRP Publication 103 were included in this version (Stabin et al. 2010) The old weightin g factors and phantoms were retained for comparison purposes.

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76 Table 1 1 Image set sources and voxel resolutions for the construction of the UF hybrid phantom family Adapted from Lee et al. ( 2010) Body region Phantom Head Torso C vertebrae Arms and Legs UFH00MF 6 day F 0.586 x 0.586 x 1 mm 3 UFH01MF 2 year F 1 year F 0.379 x 0.379 x 4.5 mm 3 0.406 x 0.406 x 3 mm 3 UFH05MF 4 year F 0.451 x 0.451 x 5 mm 3 UFH10MF 12 year M 11 year M 0.469 x 0.469 x 6 mm 3 0.469 x 0.469 x 6 mm 3 UFH15M 18 year M a 14 year M 15 year M 18 year M c 1 mm 0.625 x 0.625 x 6 mm 3 0.21 x 0.21 x 0.75 mm 3 1 mm UFH15F 15 year F 14 year F (all ages except newborn) (all ages except newborn) 0.449 x 0.449 x 4.5 mm 3 0.742 x 0.742 x 6 mm 3 UFHA DM 18 year M 36 year M 1 mm 1.97 x 1.97 x 3 mm 3 UFHADF 15 year F b 25 year F 0.449 x 0.449 x 4.5 mm 3 0.66 x 0.66 x 5 mm 3 a Head model of UFHADM was downscaled to create the UFH15M model. b Head model of UFH15F was upscaled to cr eate the UFHADF head model. c High resolution (1 mm slice thickness) CT images of arms and legs were obtained from an 18 year male cadaver.

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77 (A) (B) (C) (D) Figure 1 1 Artistic example of radiopharmaceutical biodistribution including (A) injection of radiopharmaceutical, (B) distribution through the bloodstream, (C) u ptake in various organs in the body, and (D) excretion of radiopharmaceutical from the organs receiving uptake.

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78 (A) (B) Figure 1 2. (A) Front and (B) side views of the UF newborn physical phantom (Jones et al 2006) Reproduced with permission ( 2006 American Association of Physicists in Medicine).

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79 Figure 1 3. The first stylized model of the trunk of an adult human A right circular cylinder 30 cm in diameter and 60 cm in height (NCRP 1971) Reproduced with permission ( 1971 National Commission on Radiological Protection).

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80 (A) ( B ) Figure 1 4. The MIRD Pamphlet No 5 revised stylized computational dosimetry phantom (Snyder et al 1978) ( A) Outer b ody contour and ( B) a nterior view of principle organs in head and trunk. Reproduced with permission ( 1978 Society of Nuclear Medicine) Figure 1 5. The complete current ORNL stylized computational dosimetry phantoms series Adapted from Cristy et al. (1987).

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81 (A) ( B ) Figure 1 6. The VIP Man voxel phantom (Xu et al 2000) ( A) Original image used for segmentation and ( B) f inal VIP Man voxel model. Reproduced with permission ( 2000 Health Physics Society).

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82 Figure 1 7 Vis ual representation of the process by which patient images are used to create a hybrid NURBS phantom

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83 ( A ) ( B ) ( C ) Figure 1 8 The UF newborn hybrid female phantom as viewed in Rhin oceros TM showing the ( A) c oronal (B) sagittal, and (C) p erspective view s

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84 UFH00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Figure 1 9 T he UF NURBS/PM based hybrid phantom family

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85 Figure 1 10 The continuum of phantom anatomic specificity showing the progression from population averaged reference phantoms to phantoms almost exactly representative of the patient of interest

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86 (A) (B) (C) Figure 1 11 XCAT phantoms of the (A) adult male, (B) adult female, and (C) newborn (S egars et al 2009) Reproduced with permission ( 2009 IEEE).

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87 (A) (B) Figure 1 12 Photon SAFs for the ICRP Publication 110 adult male voxel phantom for (A) the lungs irradiating the lungs and (B) the lungs irradiating the colon using the EGSnrc and MCNPX radiation transport codes (ICRP 2009) Reproduced with permission ( 2009 ICRP).

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88 (A) (B) Figure 1 13 Electron SAFs for the I CRP Publication 110 adult male voxel phantom for (A) the lungs irradiating the lungs and (B) the liver irradiating the colon using the EGSnrc and MCNPX radiation transport codes (ICRP 2009) Reproduced with permission ( 2009 ICRP).

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89 Figure 1 14 Ratio s of SAFs for a thyroid source of the original mass to SAFs for thyroid of the reference mass in each GSF voxel phantom to a kidney target (Petoussi Henss et al 2007) Reproduced with permission ( 2007 Petoussi Henss). Figure 1 15 Ratios of SAFs for a liver source of the original mass irradiating the red bone marrow to SAFs for the red bone marrow irradiating the liver for the family of GSF voxel phantoms (Petoussi Henss et al 2007) Reproduced with permission ( 2007 Petoussi Henss).

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90 Figure 1 1 6 Ratios of SAFs for a self irradiating thyroid source of the original mass to SAFs for a self irradiating thyroid source of reference mass for the family of GSF voxel phantoms (Petoussi Henss et al 2007) Reproduced with permission ( 2007 Petoussi Hen ss).

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91 Figure 1 17 SAFs for selected source and target organs in the adult male phantom for varying weight percentiles (Marine et al 2010) Reproduced with permission ( 2010 Society of Nuclear Medicine). Figure 1 18 Cross sections of the adult ma le and female voxelized NURBS phantoms at different levels of obesity (not to scale) (Clark et al 2010) Reproduced with permission ( 2010 Society of Nuclear Medicine).

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92 (A) (B) Figure 1 19 The (A) main input form, (B) radionuclide input form, (C) phantom models input form (following pages) (D) biokinetics input form (following pages) and (E) output window (following pages) for OLINDA/EXM 1.0 (Stabin 2005)

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93 (C) (D) Figure 1 19 Continued.

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94 (E) Figure 1 19 Continued.

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95 CHAPTER 2 MATERIALS A ND METHODS Blood Vessel System for the UF Hybrid Phantom Family Non Uniform Rational B Splines Model The previous iteration of the UF hybrid phantom family was described by 64 unique structures including a separat ion of CB and spongiosa/ MC The final desi red improvements to the phantoms included the addition of separate delineation of skeletal muscle, subcutaneous fat, lymph atic node s and major blood vessels. A blood vessel model was needed for the simulation of distributed blood sources as well as compl eteness of t he computational model itself. Currently, a distributed blood source would be apportioned to the heart chambers, to the lungs, and to the remaining tissues (the compartment is broken down further in Tables 2.1 3 and 2.14 of ICRP Publication 89 for the adult male, for which newborn values can be approximated ) (ICRP 2002) It was desired that a higher level of detail be achieved with the addition of a system of blood vessels. Upon examining the list of documente d reference vessels, it was determined that the pulmonary vessels could be appropriately modeled by uniformly apportioning of the total blood volume to the lungs. Consequently the available vessels to consider were the systemic vessels: aorta and l arge arteries, small arteries, capillaries, small veins, and large veins. Capillaries typically have diameters less than in the adult male (ICRP 2002) so those structures were ruled out. Small arteries have diameters less than and small veins have diameters less than Due to the se small dimensions and the lack of space between organs in the phantoms, it was determined that small arteries and veins would not be modeled explicitly Large arteries have diameters between and and large veins have diameters between and in the adult male (ICRP 2002) These dimensions could be modeled effectively in the NURBS

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96 environment for the adult male so it was determined that the explicit blood vessel system would cons ist of large arteries and veins only Values for the distribution of blood volume by organ and vessel system are only given for the adult male and female in ICRP Publication 89. While it is noted that there may be age dependent variations in blood volume distribution, no reference values have been adopted Based on the adult distribution information in ICRP Publication 89 the ratio of large vein volume to large artery volume is In this study, t his same volume ratio was matched consistently across a ll phantom ages. Reference blood vessel diameter information is only available for the adult male, so the adult male blood vessel system was constructed with the available reference information. The blood vessel systems of the newborn and adult female we re then constructed artistically due to lack of imaging data. The one year old, five year old, ten year old, and fifteen year old male systems were subsequently created by interpolating vessel diameters between those in the newborn and adult male systems. The fifteen year old female system was constructed by interpolation of blood vessel diameter between the newborn and adult female systems. The vessels were then adjusted to match the vein to artery volume ratio. Since the major blood vessels were no t directly segmented from CT or MR scans, they were artistically created. It was not necessary to match the total blood volume since the purpose of designing the blood vessel system was to provide a vehicle for the apportionment of blood volume rather tha n create an anatomically exact representation of the human systemic blood vessel system. Furthermore the modeling space available for placing blood vessels is very limited in the torso of the se phantoms and thus compromise s had to be made. It is a poss ibility that the aortic arch and other vessels in the torso may not appear visually accurate due to lack to space. Again, the purpose of these vessel models is to provide a dosimetric source region in the

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97 phantoms for radiopharmaceutical decays occurring in circulation, and not necessarily to provide for realistic imaging of these tissue structures. The major arteries roughly represented in the blood vessel model include the common carotid arteries and subclavian artery in the neck and clavicles regions, t he brachial, radial, and ulnar arteries in the arms, the aortic arch and thoracic and abdominal aortas in the thoracic and abdominal regions, and the femoral, popliteal, interior tibial, and posterior tibial arteries in the legs. Each vessel mentioned was not necessarily explicitly modeled, but the position s of these vessels were occupied by the constructed surrogate vessels. The major veins roughly represented in the blood vessel model include the external and internal jugular vein and subclavian vein in the neck and clavicles regions, the axillary, cephalic, brachial, basilica, radial, and ulnar veins in the arms, the superior and inferior vena cava in the thoracic and abdominal regions, and the f emoral vein in the legs. Each vessel mentioned was not nec essarily explicitly modeled, but the position s of these vessels were occupied by the constructed surrogate vessels. It was decided that the blood vessels would be modeled by pipe structures within Rhinoceros TM NURBS modeling software. The foundation of a pipe structure in the 3 D software package is a curve which is created by user defined control points. For this purpose, the free form method of curve creation was used, wherein the curve itself was not connected directly from control point to control poi nt but by spline fitting from the addition of each subsequent control point. Consequently the blood vessel systems were created stylistically, based on the placement of series of control points. The control points were adjusted independently in 3 D to p roduce the desired shapes.

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98 Vascular Dosimetry for Blood Sources Blood vessel systems in computational phantoms serve a purpose in that they both assist in the simulation of a distributed blood source and move the computational phantoms towards a higher lev el of anatomic realism. The construction methodology detailed in the previous section pertains exclusively to the blood vessel lumen, the volume in the blood vessel through which blood flows. Neglected in this blood vessel construction was consideration for blood vessel walls. Blood vessel wall toxicity is an issue that should be considered in some radionuclide therapy applications, including myeloablative therapy, a high dose procedure where AA is determined by dose limitations to normal organs other th an bone marrow, and possibly some other standard dose radioimmunotherapy procedures (Hobbs et al. 2010) Hobbs et al. (2010) found that arterial wall absorbed doses for standard radioimmunotherapy ranged from approximately to and from ap proximately to for myeloablative therapy (one patient had a dose of ) (Hobbs et al. 2010) Early studies had placed the dose limit for arterial toxicity in the neighborhood of (Brosius et al. 1981) but more recent stud ies have shown that long term complications can present at doses as low as about (Hull et al. 2003) Certain nuclear medicine therapy procedures approach these limits, but blood vessel toxicity does not seem to be as much of a concern for nuclear medicine imaging although one should always be cognizant of it. It was clear from the outset that blood vessel walls could not be effectively modeled in the voxel environment due to the small dimensions. NURBS versions of blood vessel walls could have be en constructed, but they would all but disappear from the voxel model since the limiting voxel resolutions are generally larger than blood vessel wall thicknesses Table 2 1 shows typical blood vessel wall thicknesses for the newborn to 1 year old and adu lt arterial, venous,

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99 and pulmonary systems (ICRP 1975) Minimum, maximum, and average values for this set of blood vessel wall thicknesses are and respectively (ICRP 1975) The minimum voxel resolution used in the UF hybrid computational phantom family in this study is for the UFH00MF phantoms ( see section of the ). While the walls of some vessel types could have been modeled, many of the wall thicknesses are smaller than the voxel resolutions used in the phantoms. In addition, only a select set of blood vessels were able to be modeled at all, so assigning a wall thickness to those vessels would be difficult. Instead of explicitly mod eling blood vessel walls within the NURBS phantoms, a computational dosimetry study was designed to develop an estimation model for determining radiation absorbed dose to blood vessel walls. Simple coaxial cylinders were selected as the geometry to repres ent both blood vessels and blood vessel walls. For a blood source, the blood vessel lumen would act as the source of radiation, so the inner cylinder in this model was assigned a uniform distribution of radiation emissions. B lood vessels with varying lum inal areas, wall thickness, and lengths were designed based on luminal diameters determined from the blood vessel systems developed for the UF hybrid phantom family (discussed in the previous section), minimum, maximum, and average wall thicknesses calcula ted from ICRP Publication 23 ( Table 2 1 ) (ICRP 1975) and typical lengths of vessels measured from the UFHADM phantom. Varying these parameters allowed investigation into the dependence of blood vessel wall dose on overall size of the blood vessel. Then, depending on the results, certain dosimetric trends could be eliminated from consideration. Two radiation types, photons and electrons, and three energies, and were simulated to assess dose dependence on particle type and particle energy.

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100 For each blood vessel modeled, a second, identical blood vessel was created with its center located at a distance equal to the radius of t he original blood vessel plus the wall thickness of the blood vessel. In a similar simulation the newly created blood vessel was moved from its current position further f rom the original blood vessel. Relative contributions from blood located in v essels near the blood vessel of interest to blood vessel wall absorbed dose were determined in this way. If relative contributions were low, adjacent vessels could be ignored, and a one vessel model cou ld be adopted. In contrast, if relative contribution s from adjacent vessels were significant, a model could be developed to give a best estimate of absorbed dose to the blood vessel walls. Absorbed dose to the first blood vessel wall from its contents will be referred to as dose in this context even though the source and target are not the same tissue. Absorbed dose to the second blood vessel from the source blood vessel will be referred to as cross dose in this context. Single blood vessels imbedded in an infinite soft tissue medium were also simu lated for verification purposes, ensuring differences between blood vessel wall, blood, and soft tissue elemental compositions would not perturb dose estimates. MCNPX v2.6 was used for radiation transport, and the energy deposited in both the blood vessel wall surrounding the source and the adjacent blood vessel wall was recorded. Particle histories were set to and for radiation energies of and respectively. Secondary electrons were followed, and t he Integrated Tiger Series (ITS) style electron energy b in indexing algorithm was used 1 Elemental compositions for blood, heart wall, and adult soft tissue from ICRP Publication 89 were used for the blood vessel contents, 1 The ITS Fracti

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101 blood vessel walls, and soft tis sue, respectively (ICRP 2002) The geometry for this study can be seen in Figure 2 1 In this simulation environment, a true blood source would fill both blood vessel contents and cross irradiate both blood vessel walls. However, relative contributions t o dose (self dose versus cross dose) could not be deciphered if both blood vessel contents were treated as the radiation source. Both blood vessels in each simulation scenario were geometrically identical, so the absorbed dose from one blood vessel conten ts to its own wall and the wall of the other blood vessel wall was considered to be unchanged when the blood vessel contents source was located in the other blood vessel. The true absorbed dose to both walls was mathematically derived using Equation 2 1 (2 1) where is the absorbed dose to the wall of the first blood vessel from the contents of both blood vessels, is the absorbed dose to the wall of the second blood vessel from th e contents of both blood vessels is the absorbed dose to the wall of the first blood vessel from its own contents, is the absorbed dose to the wall of the second blood vessel from the contents of the first blood vessel, is the volume of the contents of the first blood vessel, and is the volume of the contents of the second blood vessel. Equation 2 1 reduces to a simple linear average of and since and are equal for each irradiation scenario.

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102 Skeletal Photon Fluence to D ose Response Function s Sub S egmented Skeleton Development In the first iteration s of the UF hybrid computatio nal phantom s the skeleton s in the phantoms w ere homogeneous, a uniform mixture of all relevant sub regions of the skeleton AM IM TB and CB The homogeneous skeletal model was created by segmenting the skeleton in actual patient images and importing the segmented volumes into Rhinoceros TM Once imported into Rhinoceros TM the skeletal sites were left in the default polygon mesh (PM) format ( the PM format defines a volume by a series of polygons connected at their vertices) Since many bone sites cou ld not be effectively modeled with NURBS surfaces, they were left in the PM format However, the ribs were sometimes distorted due t o the slice thickness of the original CT imaging and so they were built stylistically by creating pipe shapes based on cen tral tracks taken from the original PM rib cage model (Pafundi et al. 2009) While the homogeneous model provided adequate information to compute reasonable dose estimates to the skeleton, a considerable amount of anatomic detail was lost. Further anatom ic detail was needed for the human skeleton, so a sub segmented skeletal model was developed. The process of creating a multiple region skeletal model began with the segmentation of all bone sites from a set of whole body cadaver CT data (Pafundi et al. 20 09) This was done automatically by adjusting the lower bound of the thresholding window in 3D DOCTOR TM to exclude cartilage (Pafundi et al. 2009) Application of this thresholding window allowed for automatic segmentation of the whole skeleton from ever y CT slice, creating a whole body homogeneous skeletal model in one action step This initial segmentation provided the outer contour of the skeleton Next, the cartilage was manually segmented and two distinct cartilage regions were identified: bone ass ociated cartilage and non bone associated cartilage (Pafundi et al. 2009) The spongiosa region and associated sub regions were then delineated by the analysis

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103 of microCT images of selected bone sites (Pafundi et al. 2009) The sternum, occipital bone, 2 nd right rib, 2 nd left rib, L 2 L 5 vertebrae, T 9 T 12 vertebrae, C 3 C 7 vertebrae, T 1 T 5 vertebrae, T 10 T 12 vertebrae, L 1 L 5 vertebrae, 4 th right rib, 4 th left rib, and a portion of the right iliac crest obtained from two specimens were imaged using microCT a t an isotropic resolution of (Pafundi et al. 2009) The T M and TB within each bone site were automatically segmented by applying a filter based on visual inspection of the image gradient magnitude (Rajon et al. 2006) This technique separated the T M and TB and created a new binary image file with all gray scale values attributed to TM converted to black pixels and all gray scale values attributed to TB converted to whi t e pixels These files were then used to calculate the fraction of spongiosa occupied by trabeculae and the fraction occupied by T M This was performed for every bone site and s keletal tissue masses were then obtained using methods detailed in Pafundi et al. (2009) and Hough et al. (2011) A detailed model of the human skeleton including the marrow cavities of the spongiosa cannot be effectively represented in voxel models because voxel resolutions required to preserve the detail of the skeletal microstructure would create voxel models too large to efficiently simulate with radiation transport codes For examp le, if all the phantoms in the UF phantom family were voxelized at an isotropic resolution of the average binary file size would be well over Consequently while the previously discussed advancements in skeletal tissue modeling for the purpose of computational radiation dosimetry produced extensive data characterizing the distribu tion of skeletal tissues, the results were not directly applicable to the corresponding whole body NURBS phantom However, the results did lay the groundwork for the development of skeletal dosimetry methods that would be incorporated in steps separate fr om the primary dosimetry simulations While the AM and TB sub regions of the spongiosa could

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104 not be explicitly modeled in Rhinoceros TM the spongiosa itself was able to be modeled Resultantly the final heterogeneous skeletal model was visualized in Rhi noceros TM as a three region model with the regions being the cartilage, cortical bone and trabecular spongiosa Examples of heterogeneous bone sites in Rhinoceros TM can be seen in Figure 2 2 The orange wireframe regions are cartilage The black wirefr ame reg ions indicate cortical bone spongiosa and medullary cavities Examining the long bone in Figure 2 2 (B), outer and inner black wireframe regions can be seen, the outer region representing cortical bone and the inner region representing the medull ary cavities in the shaft and spongiosa in the proximal and distal ends A similar situation is seen in non long bones where the inner black wireframe region is spongiosa Skeletal Photon Fluence to Dose Response Function Development 15 year old and n ewbo rn p hantoms Since the intricacies of the spongiosa could not be explicitly modeled in the NURBS/ PM environment, another technique was used to incorporate the lost spongiosa detail into the phantom the skeletal photon fluence to dose response function A dose response function (DRF) allows for the pre calculation of the absorbed dose of a particular region per arbitrary unit of measure in this case photon fluence in regions of the skeleton In other words, separate simulations were performed which were able to model much smaller volumes The results of these simulations were then used in conjunction with the NURBS based computational phantom so that the skeletal microstructure did not have to be explicitly modeled in Rhinoceros TM First, the radiosensit ive cells in skeletal tissue had to be identified Much research has been done to determine this, and the radiosensitive cells were found to be hematopoietic stem cells, osteoprogenitor cells, and chondrocytes (Pafundi et al. 2010) The surrogate tissues for these radiosensitive cells were determined to be active marrow (AM) for hematopoietic stem cells, endosteum or total shallow marrow ( TM 50 ) for osteoprogenitor cells, and unossified

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105 cartilage for chondrocytes (Pafundi et al. 2010) The endosteal regio n of the spongiosa was defined as all bone marrow that is within of either the trabecular bone surfaces or the inner cortical bone surfaces of the long bone shafts (Bolch et al. 2007) For the newborn, only AM is present within the skeleton and s o total shallow marrow TM 50 and active shallow marrow AM 50 are equivalent. Photons that interact with human tissue liberate electrons, and those electrons then directly ionize the medium The energy deposited in this process, divided by the total mass of the medium irradiated results in the calculated radiation absorbed dose Consequently while it is of great interest where the emitted photons are transported, the electrons liberated by those photons must also be taken into account Because of the small dimensions of the skeletal microstructure, secondary electron transport is a concern within whole body phantom radiation transport This is due to the fact that electrons liberated by high energy photons have ranges which are relatively large compared to the spacing of the trabeculae in the spongiosa To properly characterize the behavior of secondary electrons liberated in the skeleton, the AFs for different skeletal source target combinations were calculated The paired image radiation transport (PIRT) model was used in conjunction with the EGSnrc radiation transport code to calculate the skeletal AFs (Pafundi et al. 2010) The combined model allows for tracking of electrons within the microstructure of the spongiosa simultaneously with the macrostruct ure of the hybrid phantom heterogeneous skeletal sites (Shah et al. 2005) The microstructure was described with voxels of isotropic resolution, and the macrostructure was described with voxels ranging from isotropic resolutions of to (Pafundi et al. 2010) Skeletal AFs were calculated for photons incident on the spongiosa with energies ranging from to (Pafundi et al. 2010) Tissue regions of

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106 AM, TBV and CB volume (CBV) were all simulated as source tissues, and AM and TM 50 were simulated as target tissues. An in house MATLAB TM code was used to calculate the skeletal photon fluence to dose response functions based on the AFs of the two target tissues, AM and TM 50 the elemental compositions of mineral bone (trabecular and cortical), AM and cartilage, and the masses of both source and target regions The code uses the formulation i n Equation 2 2 (Cristy et al. 1987 Johnson et al. 2011) : (2 2) w here and are the masses of the source and target tissues, respectively, is the AF in target tissue from source tissue for electrons of energy are the mass attenuation coeffici ents for source tissue where and is the number of electrons with energies between and liberated in sour ce tissue for interaction type and is the skeletal photon fluence to dose response function relating the absorbed dose to target tissue to the incident fluence of photons with energy on the spongiosa C alculations w ere also performed setting the AF to unity for self irradiation and to zero for cross fire for every bone site thereby modeling the kerma approximation The kerma approximation assumes that all of the energy of the liberated secondary electrons is locall y deposited; none of the energy escapes into any adjacent regions Thus, for a source region emitting electrons liberated by the incident photons, all of the electrons will be absorbed by that source region, resulting in an AF of approximately unity for t he self dose irradiation scenario Alternately, no electrons emitted from the source region will penetrate into adjacent regions, so

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107 the AF for the irradiation geometry of the source and target regions not being the same is approximately zero The reason for this will be explained in greater detail later, but to summarize, the skeletal fluence to dose response functions were assumed to conform to the kerma approximation for energies greater than 1 year old, 5 year old, and 10 year old p hantoms Methodology Skeletal photon fluence to dose response functions as developed for the UFH00MF and UFH15MF phantoms were derived based on electron AFs that were calculated using the PIRT algorithm (Pafundi et al. 2010) C adaver bone samples were used to generate the detailed geometries within spongiosa and the medullary cavities for these phantoms However, even though the macroscopic images of all bone sites with CB, homogeneous spongiosa and h omogeneous MCs were used to generate the skeletal models for the UFH01MF, UFH05MF, and UFH10MF phantoms, cadavers were not available to create detailed microstructure models for these phantoms. Therefore, a different approach was used to calculate skeleta l electron AFs for sources in spongiosa and MCs and these results were used in the skeletal fluence to dose response function equation (Equation 2 2 ). A combination of c h ord based infinite spongiosa transport (CBIST) and single image radiation transport ( SIRT) was used to generate the set of electron AFs for the UFH01MF, UFH05MF, and UFH10MF phantoms. CBIST refers to the simulation of electrons traversing spongiosa by way of measured c h ord length distributions. Most current skeletal fluence to dose respo nse functions are based on the c h ord length distributions measured by Spiers and his colleagues at the University of Leeds in the 1970s ( Spiers 1969 Whitwell 1973 Beddoe 1976 ) In those studies, linear path lengths were measured through alternating regi ons of trabecular bone and bone marrow (Stabin et al. 2002) By generating frequency distributions of varying chord

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108 lengths, the complicated microarchitecture was represented without having to generate explicit computer models ( computer models were not an option at the time). Bouchet et al. (2000) used these c h ord length distributions in combination with the EGS radiation transport code to calculate electro n AFs in 7 different bone sites. Electron AFs were determined by randomly sampling c h ord lengths o f trabecular bone and marrow cavities alternately. Once a c h ord length was chosen, electron range energy relationships were used to determine the residual kinetic energy of the electron. From this, the energy deposited in each region of spongiosa could b e determined. Electrons were transported until all of their energy was expended which effectively created an infinite region of spongiosa hence the name c h ord based infinite spongiosa transport. Since only 7 bone sites were analyzed, the AFs calculated in the Bouchet et al. (2000) study were assigned to all other bone sites based on their similarity to the microstructure of each respective bone site. However, this infinite transport did not take into account electron escape into cortical bone or any oth er surrounding tissues. So, in the current study, the macro scopic images of each bone site were used to calculate electron escape fractions (EFs) using the SIRT transport methodology. SIRT uses the macroscopic bone models that include the CB, homogeneous spongiosa and homogeneous MCs in each bone site. These models were converted into voxel models, and electrons were transported. Energy deposition in spongiosa and MC regions was tracked, and the electron AF was calculated. The complement of the electr on AF gives the fraction of electron energy that escapes spongiosa and MC regions. By multiplying the electron AFs obtained from the CBIST simulations by the spongiosa/MC AFs calculated in the SIRT simulations, complete electron AFs were obtained for use in the skeletal photon fluence to dose response function formulation (Pafundi 2009) Equation 2 3 was used to calculate the CBIST electron AFs for the

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109 TBV, AM, and IM sources, and Equation 2 4 (derived from Pafundi (2009)) was used to calculate the CBIST electron AFs for the CBV source (Pafundi 2009). ( 2 3 ) ( 2 4 ) where is the electron AF for source tissue irradiating target tissue (either AM or TM 50 ) for electr ons of energy for bone site is the electron AF obtained during the CBIST simulations for the same source target energy combination, is the electron AF obtain ed during the SIRT simulations for the same source tissue and electron energy irradiating the spongiosa or medullary cavity sites of bone site is the electron AF for the CBV irradiating target tissue at electron energy for bone site is the electron AF obtained during the SIRT simulations for the CBV irradiating the spongiosa or medullary cavity sites of the same bone site for the same electron energy, and are all the electron AFs obtained during the CBIST simulations for the various source tissues in the spongiosa and medullary cavities of each bone site irradiating the target tissues for the same electron energy, is the cellularity factor indicating the fraction of TM occupied by AM, and is the bone volume fraction indicating the fraction of spongiosa occupied by TBV (Pafundi 2009). S ingle i mage r adiation t ransport s imulations The purpose of the SIRT simulations was to obtain electron AFs/EFs for all macroscopic bone models in the UFH01MF UFH05MF, and UFH10MF phantoms. Escape of electrons created in spongiosa and MCs into surround ing

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110 CB and subsequently into tissues beyond was modeled. Recalling concepts described in the development of the skeletal fluence to dose response functions, photons interact with tissues in the spongiosa and medullary cavities and create secondary electro ns. These electrons then deposit their energy through ionization and excitation. Since explicit bone trabeculae models cannot be efficiently simulated in the NURBS/PM format mathematical methods were developed to virtually represent the physical model. Weighting electron AFs in spongiosa/MC by corresponding AFs obtained from CBIST modeling is a good approximation for electron energy deposition physics in spongiosa and MCs First, all 20 bone sites in the three phantoms of interest were isolated in the N URBS/PM model and voxelized for insertion into the ra diation transport code MCNPX v2 Based on previous experience, the computing resources were able to efficiently simulate voxel models with a total matrix size of approximately Therefore, t his total matrix size was targeted when selecting the voxel resolutions for each bone site. Since the three dimensional matrix dimensions in the and directions depend on the total extent of the width, depth, and height of the object of interest, Rhinoceros TM the 3 D modeling software used to create the UF hybrid phantoms, was utilized to take measurements of these same dimensions for all 20 bone sites in the three phantoms of interest. Each individual bone site (including spongiosa, MCs and CB ) was isolated and, using the multiple view option in Rhinoceros TM a linear measurement was taken from the leftmost point to the rightmost poi nt in the front view window, which represented the width of the bone site. A linear measurement was taken from the leftmost point to the rightmost point in the side view window which represented the depth of the bone site. Finally, a linear measurement was taken from the bottommost point to the topmost

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111 point in the front view window, which represented the height of the bone site. Then, an isotropic voxel resolution was calculated for each bone site using Equation 2 5 (2 5 ) where is the measured width of the bone site in is the measured depth of the bone site in is the measured height of the bone site in is the total targeted matrix size in number of voxel elements, and is the i sotropic voxel resolution for the bone site of interest. The final width, depth, and height measurements along with the final voxel resolutions and total matrix sizes are in Table s 2 2 and 2 3 An example of a bone site the femur of the UFH01MF phantoms in NURBS/PM format and post voxelization is in Figure 2 3 Due to human measurement of dimensions and some oddities in the software package Rhinoceros TM not all bone sites achieved a total matrix size close to the targeted matrix size. However, all bo ne sites were individually inspected after voxelization using the image processing software package ImageJ TM (National Institutes of Health, Bethesda, MD) and all regions of interest in all bone sites for the three phantoms were faithfully represented. I n addition, any artifacts introduced during the voxelization process were corrected using ImageJ TM All voxels in the voxelized bone models not associated with spongiosa/ MC or CB a material composition and density published in ICRP Publication 89 (ICRP 2002) A sphere of exclusion (interface at which radiation is no longer transported) was placed around the entire voxel model for each bone site and was also tissue located within the voxel model itself.

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112 Once all bone sites were voxelized and any resulting artifacts were corrected, input files and all associated files were asse mbled for electron transport. Lattice files were generated for the 20 voxelized bone models for each phantom files that indicate to the radiation transport code tissue tag identification numbers associated with all voxels in the simulation. Skeletal ph oton fluence to dose response functions are applied to energy dependent photon fluence incident upon regions of spongiosa and MCs in the skeleton, so the source of electrons in these cases would be those same regions. It followed that, for each bone site, all sub regions of spongiosa and medullary cavities were simulated as source regions for the SIRT simulations. CBV was also simulated as a source region to generate electron AFs for CBV sources. Source files were created for each sub region files that indicate to the radiation transport code the location of all voxels associated with the source region of interest. A total of 34 source regions were simulated per phantom. The number of source regions was greater than the number of bone sites because so me bones (the long bones) were divided up into several sub regions. Long bones in the phantoms consisted of a separate proximal end, shaft, and distal end with the humerus and femur having shafts separated into upper and lower regions. Twenty eight monoen ergetic electron energies, mirroring those of Pafundi et al. (2010) were simulated per source region, giving a total of 952 simulations per phantom and a n overall total of 2856 simulations. Following all photons and electrons produced during the simulati ons, energy deposition was tracked in spongiosa/ MCs CB and soft tissue located in the voxel model. Any energy deposited beyond these tissues was calculated as the total energy emitted less the energy deposited in the three tissues just mentioned. Elect ron EFs were calculated using Equation 2 6

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113 (2 6 ) where is the escape fraction for bone site at initial electron energy for source region is the electron absorbed fraction for bone site for source region target regi on and electron energy and is the energy deposited in target region from source region at electron energy Ten million particle histories were simulated at each initial ele ctron energy, ensuring that all statistical uncertainties would be well below Since the lowest electron energy was and the default cutoff energy in MCNPX is the lower bound energy cutoff for both photons and electrons was lowered to The ITS style electron energy bin indexing algorithm was used (described later). Photon Specific Absorbed Fractions Overview The purpose of the photon SAF calculations was to generate a complete set of monoenergetic SAFs that would later be inc orporated into a n internal dosimetry software package. These SAF values were considered to be a complete set because all source target combinations of importance were modeled. The software package would take information about radiation emission spectra f rom radionuclides of interest and use the monoenergetic photon SAFs to calculate radionuclide specific S values. With biokinetics of the radiopharmaceutical known, final absorbed dose estimates would be obtained. To generate monoenergetic photon SAFs, the UF hybrid computational phantom family was used with a radiation transport code to model the transmission of photons throughout the body from internal sources. The physical characteristics all tissues in the phantoms (densities, volumes, elemental compos itions) were incorporated into the models to ensure maximum

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114 accuracy from the available information Photons were transported throughout each phantom for a variety of source tissues. The energy deposited in a number of target tissues was recorded. From the energy deposited, the AFs, and subsequently the SAF, were calculated. This process was repeated for many monoenergetic photon energies. Aft er wards, several variance reduction techniques were used to ensure quality of the data. A flowchart schematic of the photon dosimetry scheme is in Figure 2 4 All aspects of the flowchart will be described in greater detail in the following sections but the flowchart can be referred to as a visual aid. Radiation Transport Code The radiation transport code MCNPX v 2.6 was used for the calculation of the SAFs in this work MCNPX is a three dimensional computational environment that models the movement of radiation through geometries specified by the user (LANL 2005) These geometries can be created by combinations of simple surfaces (planes or cylindrical shells) or macrobodies (cubes, spheres, ellipsoids, etc.) (LANL 2005) However, to utilize the complicated geometries of NURBS based computational dosimetry phantoms, the phantoms had to be reformed into voxel arr ays because MCNPX cannot currently handle NURBS surfaces or PM geometries Usually, the user must define a set of surfaces and construct cells of interest by combining the defined surfaces. While some of this is retained in the simulation of voxel phanto ms, the phantoms called by the main MCNPX input file defines the organ/tissue tag identification number associated with each voxel in the model. Then, a universe is defined by grouping all voxels with the same identification number. From this, MCNPX can know where any particular tissue is in the phantom. MCNPX stochastically model s the transport of radiation through any geometry by way of random number generation Since statistical processes are utilized in MCNPX, larger numbers

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115 of parti cle histories simulated produce lower uncertainty results. Incoherent and coherent scattering, fluorescent emission after photoelectric absorption, and absorption in electron pos itron pair production are all accounted for during photon transport (LANL 2005) Angular deflection through multiple scattering events, collisional energy loss, and production of secondary particles are all accounted for during electron transport (LANL 20 05) Unfortunately, phantoms at this time must be voxelized prior to use within most radiation transport codes. The voxelization process decreases some of the detail attained using NURBS/PM surfaces. Progress has been made in the radiation transport co de GEANT4 that allows for direct input of PM surfaces, but researchers comment that simulation runtimes increase drastically, up to 10 times the normal runtime for a voxel model (Jeong et al. 2011). Considering that some voxel based runtimes reach 24 hour s, this was abandoned as an option. However, the MCNP development team is currently working on this problem, and direct simulation of NURBS/PM surfaces may be feasible in the near future. Phantom Physical Characteristics MCNPX requires input of several ph ysical parameters to assist in completely defining the phantom model. Tissue density, elemental composition, and volumes were required for MCNPX to both calculate tissue masses and perform accurate radiation transport. Since radiation interaction process es depend heavily on the atomic number of tissues, thorough analysis of the elemental composition of each material/tissue was necessary and will be addressed later. Methods used for the construction of the UF hybrid phantom family were detailed earlier, bu t it is necessary to give some pertinent physical information about the phantoms here. Detailed characteristics and morphometric measurements of the entire phantom family can be found in Lee et al. (2010) but some information was reproduced since some in formation changed slightly during voxelization. All tissues modeled in all phantoms along with the

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116 associated tissue ta g identification numbers and tissue densities are given in Table A 1 in Appendix A and tissue masses for all phantoms are given in Tabl e A 2 in Appendix A Elemental compositions will be addressed in the next section. Blood I nclusive Elemental Composition s The elemental compositions of the various materials used in the phantoms were initially taken from ICRP Publication 89 (ICRP 2002) However, these elemental compositions were only relevant to the organ parenchyma and did not include the elemental composition of the organ blood content (ICRP 2009) Therefore, the Equation 2 7 was used to apportion the elemen tal composition of blood to the overall elemental composition of the organ (ICRP 2009) An example of adjust ment of the relative abundance of hydrogen in the liver is shown. (2 7 ) where is the final adjusted w eight percent of hydrogen in the liver, is the reference weight percent of the liver parenchyma, is the reference mass of the liver, inclusive of blood, is the mass of blood located in the liver, and is the reference weight percent of hydrogen in blood. This methodology was used for all elements documented for all blood containing organs as listed in ICRP Publication 89 (I CRP 2002) Before Equation 2 7 could be applied to account for the material composition of blood in all blood containing organs, regional blood masses had to be calculated. Unfortunately, ICRP Publication 89 only defines regional blood distribution for th e adult male and female and this distribution can be seen in Table 2 4 (ICRP 2002)

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117 Since only adult male and female regional blood distributions were officially defined and no large scale detailed measurements had been performed, in lieu of embarking on a multiple year data collection project, a mathematical method was developed to attempt to predict the regional blood distributions in the newborn, 1 year old, 5 year old, 10 year old, and 15 year old male and female. First, it generally assumed that the v olume of blood per unit volume organ did not vary by age. If this was indeed the case, one could simply perform volume scaling to predict the regional distribution of blood at different ages. Following this theory, the volume of blood within a particular organ in the adult male or female (depending on the gender of interest) was scaled by the ratio of volumes of organ of interest ( Equation 2 8 ). (2 8 ) where is the volume of blood located in the organ of i nterest, is the age of interest, is the gender of interest, and is the volume of the organ itself. The volume of blood in any organ in the adult male or female was obtained using Equation 2 9 (2 9 ) where is the fraction of whole body blood located in the organ of interest (taken from Table 2 4 ), is the gender of interest and is the reference volume of whole body blood (taken from ICRP Publication 89) Whole body blood volumes can be seen in Table 2 5 (ICRP 2002) Once the volume of blood in each organ had been calculated, the regional distribution was determined by applying Equation 2 10

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118 (2 10 ) where i s the fraction of whole body blood located in the organ of interest, is the age of interest, is the gender of interest, and is the volume of blood located in the organ of interest, obtained from Equation 2 8 It is importa nt to note that the sum of all organ specific calculated blood volumes was not necessarily equal to the reference whole body blood volume. This is because assumptions were made in the development of this model which, while reasonable in theory, may not be exactly accurate for everyone Additionally, the reference values themselves were averaged over a population of people (ICRP 2002) However, fractional blood distribution values obtained from this procedure were applied to the reference total blood volu mes to obtain final organ dependent regional blood volumes. In essence, the volume scaling was performed to develop a regional blood distribution, which could then be used to appropriately apportion blood volumes to the tissues listed in Table 2 4 After further investigation, it was determined that some organs did not behave as predicted by the previously mentioned theory that the volume of blood in any organ per unit volume of that organ ( ) was independent of age. ICRP Publication 89 indicates that, in children, the kidneys may receive more cardiac output than adults, the brain have a higher blood perfusion rate (BPR) ( ) than ad ults, and the skeletal tissues may have BPRs and blood content up to 2 to 3 times more than adults (based on animal studies) (ICRP 2002) These three organs were investigated further to determine if scaling factors could be developed to effectively correct for the regional changes in blood volume per unit organ volume. When direct information on blood volume per unit organ volume was not available, i t was

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119 assumed that relative BPRs were direct indicators of regional changes in vascular growth From the ou tset, it was decided that a ratio of either BPR or blood volume per unit organ volume would be used as a scaling factor. In other words, the volume scaling methodology would be retained, but a scaling factor would be introduced to further adjust the calcu lated regional blood volumes for the kidneys, brain, and skeletal tissues. Rubin et al. (1949) provided renal plasma flow normalized to the adult body surface area ( ) for 5 ages between 0 and 3 years. The renal plasma flow rate reached the adult value at 3 years of age (Rubin et al. 1949) At the referenc e ages of the newborn (100 d ays old) and the 1 year old, Figure s 2 A and 2B from Rubin et al. (1949) w ere used to assign an average renal plasma flow rate The age specific values were then divided by the adult value to obtain the scaling factor However, s ince dramatic growth was not seen between the ICRP refe rence newborn and the 1 year old and the values themselves were variable, the renal plasma flow rate for the 1 year old was assigned to the newborn Data from Chiron et al. (1992) were used to calculate blood volume scaling factors for the brain. This study provided mean global cereb ral blood flow (mCBF) in for 22 ages between 0 and 22 years. Forty two children between the ages of 2 days and 19 years (Chiron et al. 1992) were imaged using 133 SPECT The adult value was taken as the average obtaine d over 32 patients between the ages of 19 and 29 years (Chiron et al. 1992) The authors used an algorithm described in Celsis et al. (1981) to calculate the regional cerebral blood flow (rCBF) for 25 regions of interest (ROIs) covering the cortical ribbo n, thalamus, and both hemispheres as a whole (Chiron et al. 1992) mCBF was calculated as the average of all hemisphere ROIs on the upper 4 image slices and whole brain on the bottom image slice (Chiron et al. 1992) The adult mCBF was taken to be (22 year old value).

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120 Scaling factors for all reference ages were calculated as the ratio of the mCBF at the age of interest to the adult mCBF. Simonet et al. (1988) reported direct measurements of vascular volume per uni t volume organ ( ) for mineral bone in dogs for a pup, adolescent, and adult dog. The value reported for the pup was assigned to the reference newborn and 1 year old human, and the value reported for the adolescent was assigned to the r eference 15 year old human. Vascular volumes per unit volume organ for the reference 5 year old and 10 year old humans were linearly interpolated between the 1 year old and 15 year old measures. The scaling factor was calculated as the ratio of the age d ependent vascular volumes to the adult vascular volume. From other literature searches, it could not be proven that bone marrow vascular volume per unit volume organ changes as a function of age. Therefore, scaling factors were applied to CB and TB but n (see Table 2 4 ). As a result, total skeletal blood volume was taken to be the sum of the derived blood volumes of the skeletal constituents. A table of age dependent scaling factors for the kidneys, brain, and skelet on can be seen in Table 2 6 Since regional changes in vascular growth were accounted for using scaling factors, Equation 2 8 was amended to include these changes, resulting in Equation 2 11 (2 11 ) where is the scaling factor used to correct for regional changes in vascular growth (for organs other than kidneys, brain, and mineral bone, this factor was set to unity) Equation 2 1 2 is the aggregate equation used to calculate regional blood distribution fractions for the whole reference human series. Reference regional blood volumes were finally obtained by multiplying the regional blood fractions by the reference whole body blood volume.

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121 (2 1 2 ) ICRP Publication 89 gi ves reference organ masses in its Table 8.2 but, for various organs, no reference volumes or tissue densities are given (e.g. density of lung) (ICRP 2002) Resultantly, when available, ICRP reference organ masses and densities were used to calculate refe rence organ volumes. When reference masses or densities were unavailable, either surrogate tissues were assigned or the tissue properties detailed in Lee et al. (2010) were used. Lung density was taken from Lee et al. (2010) and includes relative contrib utions from parenchyma, blood, and air. These densities were calculated based on the ICRP Publication 89 reference mass and segmented lung volume of the various phantoms. No reference mass for bronchi was found, the bronchial tree probably grows at roughly the same rate as the trachea. Whole skeleton average density was taken from Lee et al. (2010) calculated as the whole skeleton mass and volume less the AM, TB, and CB masses and P Publication 89 reference whole body mass less the mass of the listed tissues and organ contents. A density of pediatric values of mass or volume were found for aorta and large arteries or large veins, so the adult regional blood portion values of (aorta and large arteries) and (large veins) were used to calculate the reference masses for all other ages. Combining elements of the ICRP reference models and the UF ph antom models to develop the regional blood distribution model

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122 did not pose a problem because the important measure was the age dependent organ volumes relative to the adult organ volumes. Consequently the actual volumes themselves were somewhat irrelevan t. Regional blood distributions and blood volumes for the entire ICRP reference family can be seen in Tables 2 7 and 2 8 respectively. These regional distributions were initially developed for the intent of ICRP adoption as reference values. However, the regional distributions of Tables 2 7 and 2 8 do not directly translate to the UF hybrid phantom family. Specifically, while the UF phantoms are ICRP reference they do not necessarily have explicit compartments for all of the listed organs. For example, regional blood volumes were apportioned according to the available structures in the UF hybrid phantom family. First, the regional blood volumes were multiplied by the IC RP reference blood density of to obtain regional blood masses for implementation in Equation 2 7 (ICRP 2002) T he blood volumes in all organs explicitly defined in the UF hybrid phantom family were retained, which included the fat, brain, small intestine, large intest ine, coronary tissue, kidneys, liver, pulmonary, bronchial tissue, skeletal muscle, pancreas, cortical bone, skin, spleen, thyroid, lymph nodes, gonads, and adrenals. The large intestine, kidneys, and bronchial tissue blood volumes were not apportioned to their constituent organs (i.e. large intestine into left colon, right colon, and rectosigmoid walls) because their constituents share the same material composition. es ophagus separately by volume weighting since they do not share the same material composition ( Equations 2 1 3 and 2 1 4 ).

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123 (2 1 3 ) (2 1 4 ) where is the mass of blood in the stomach wa ll, is the age of interest, is the gender of interest, is the combined mass of blood in the stomach wall and esophagus, is the volume of the stomach wall, is the volume of the esophagus, and is the mass of blood in the esophagus. Blood volumes in the right and left heart chambers were added together and assigned to the of the U F phanto defined to be all tissues not specifically documented in the regional blood distribution less air in the body as well as walled organ contents. These tissues were found to be the breasts, ears, external nose, gall bladder wall, larynx, nasal layers, oral cavity layer, pharynx, pituitary gland, salivary glands, spinal cord, thymus, tongue, tonsils, penis, prostate, scrotum, and uterus. individual constituents The aorta, large arteries, and large veins were not considered since they consist entirely of blood. AM, TB and "other skeleton" were more complicated to appropriately distribute since these compartments were not explicitly modeled in NURBS/PM format (Lee et al. 2010) AM IM and TB are homogeneously combined in the UF phantom models, and material compositions are calculated as site specific homogeneous mixtures of these materials. These homogenous volumes are known as either spongiosa or MCs As a result, blood volumes for the 34 delineated spongiosa/ MC sites were necessarily a fractional combination of AM, TB and some portion of AM, TB, and CB were explicitly defi ned in the

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124 regional blood distribution "other skeleton" consists of bone associated cartilage and IM The volume of blood attributed to each skeletal spongiosa/ MC site was calculated as the fraction of total AM, TB, and IM located in each site multiplied by the total AM, TB, and IM volume as described in Equation 2 1 5 The volume of blood located in the bone associated cartilage was calculated using Equation 2 1 6 (2 1 5 ) where is the volume of blood loca ted in either spongiosa or a medullary cavity, is the age of interest, is the gender of interest, is the bone site of interest, is the total volume of blood located in whole body AM is the volume of AM is the total volume of blood located in whole body IM is the volume of IM is the volume of blood located in whole body TB is volume of TB is the volume of blood located in the skeleton" compartment, and is the total volume of whole body cartilage. (2 1 6 ) where is the volume of blood located in whole body bone associated cartilage. Once the mass of blood in each tissue of interest was determined, Equation 2 7 was used to adjust the material composition of those tissues to include the blood content. After calculating the blood inclusive compositions the UF hybrid phantom family consisted of 88 unique

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125 material s. Regional blood distributions and blood masses as applied to the UF hybrid phantom family are in Tables 2 9 and 2 1 0 (with gender differences averaged for the UFH00MF, UFH01MF, UFH05MF, and UFH10MF phantoms) and t he final blood inclus ive material compositions (with gender differences averaged for the UFH00MF, UFH01MF, UFH05MF, and UFH10MF phantoms) for the UF hybrid phantom family can be found in Tables A 3 through A 1 0 in Appendix A Phantom Preparation The UF hybrid phantom s are NURB S /PM based in their original, but since MCNPX cannot currently utilize continuous 3 D surfaces, the phantom was reconstituted into a voxel model a 3 D array of rectangular prisms Once a phantom was finalized in its NURBS/PM form in Rhinoceros TM it w as exported as a raw triangles ( .raw ) file. This raw triangles file approximates the continous and PM surfaces with millions of triangles. The hundreds of contours in the phantom was represented by defining the coordinates of the vertices of all the trian gles in the model An in house MATLAB TM code was used to convert the raw triangles model into a voxel model at the voxel resolution defined for the specific phantom (selection of voxel resolutions will be addressed later). An illustration of the process by which an object was taken from the original segmented image data, imported into Rhinoceros TM in PM format, converted into NURBS format, and voxelized was previously illustrated in Figure 1 9 The skin of the phantom was not modeled explicitly in the NUR BS /PM format because there was a chance that the skin could be lost during the voxelization procedure due to the thinness of the structure. Consequently a MATLAB TM code was written to insert skin in the voxel phantom, which wa s accomplished by replacing the outermost layer of non air voxels with skin voxels all while avoiding the eye balls After the skin was placed on the phantom, the phantom was examined using ImageJ TM an image processing software package, and any

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126 artifacts introduced during voxeliza tion were manually corrected. An example of a voxelization artifact and the correction of the artifact can be seen in Figure 2 5 Streaking artifacts occur in the rare case where two surfaces touch each other in Rhinoceros TM and the MATLAB TM code cannot resolve the conflict. An example of a voxelized UF hybrid phantom (UFH00F) is shown in Figure 2 6 Using t he binary file output from ImageJ TM a MATLAB TM code was written to create the lattice ( lat ) file. The lattice file for each phantom communicates to MCNPX the number of voxel elements in the and directions and defines, in raster fashion a tissue identification number to each voxel For example, the header of the lattice file contains a definition of the number of voxels in the and directions and the body of the fil e contains a single array of tissue tag identification numbers. MCNPX will read through the tag numbers until the number of tag numbers read is equal to the number of voxels in the direction. Then MCNPX will move to the next row of voxels and conti nue reading the tag numbers. Once the number of voxels in the and directions are filled, MCNPX moves to the next layer of voxels. In this way, the 3 D phantom is virtually represented. Once these steps were completed, the phantom is ready to b e integrated into the MCNPX input file structure. A sample lattice file and detailed description can be found in Appendix B Voxel Resolution Ideally, isotropic voxel resolutions for the entire phantom family would be set equal to the skin thickness at e a ch age. Selecting resolutions at these thicknesses would ensure that the skin and almost all other structures would be effectively represented during particle transport. This follows since the skin in every phantom is the thinnest structure (expect for s ome CB sites in some phantoms). However, voxelizing all phantoms at isotropic skin thickness resolution creates

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127 unreasonably large matrix sizes for all but the newborn phantom as the thickness of the skin does not grow as quickly as the overall phantom di mensions. Resultantly isotropic skin thickness resolution had to be abandoned and replaced by a different methodology for defining the final voxel resolutions. It was found that simulation times for the UFH00MF phantoms voxelized at an isotropic resoluti on equal to the skin thickness were reasonable, and so a total matrix size of for the UFH00MF phantoms was selected as the target total matrix size. Initially, the in plane voxel resolutions (width and depth) were set equal to the skin thickn ess, and the axis resolution was derived so that the total matrix size of the phantom of interest was equal to the total matrix size of the UFH00MF phantoms using Equation s 2 1 7 through 2 1 9 (2 1 7 ) (2 1 8 ) (2 1 9 ) where is the total number of voxel elements in the UFH00MF phantom, is the total width of the phantom, is the total depth of the phantom, is the total height of the phantom, is the voxel resolution in t he direction (width), is the voxel resolution in the direction (depth), and is the voxel resolution in the direction (height) and were obtained by measuring the total extent from the nearest point to the most distant p oint as viewed from the front and side of the phantoms (e.g., the height was measured by viewing the phantoms from the front and measuring from the bottom of the feet to the top of the head).

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128 This calculation was performed for the entire phantom family I n so doing, it was discovered that by setting the in plane resolution equal to the skin thickness and deriving the axis resolution based on the total matrix size of the UFH00MF phantom, the number of voxels in the direction was unsatisfactory. That is, th ere were too few voxels in the direction. While determining total matrix sizes for voxel phantoms is a so mewhat subjective dimensions. Since the inherent approximation in voxelization is the representation of continuous surfaces by a 3 D matrix of voxels, voxels with resolutions close to isotropic are optimal. In light of this, the in plane voxel resolutions were slightly increased, and the resolution was again derived to match the total matrix size of the UFH00MF phantom. Resulting voxel dimensions and matrix sizes are in Table 2 11 It is important to note that for a single voxel matrix, all voxels must be the same shape and size, othe rwise gaps and overlaps may occur. Optimization of voxel resolutions led to some concerns, primarily that by somewhat subjectively changing the voxel dimensions, dose estimates may change correspondingly If dose to the target tissue of interest was highl y dependent on the voxel dimension, selection of the appropriate voxel dimensions would necessarily need to be a more rigorous process. To examine this possible phenomenon, the UFH15F phantom was voxelized at resolutions of and resulting in total matrix sizes of and respectively. The fine resolution voxel produced a total matrix size that was about 2.7 times greater than the coarse resolution voxel. Annihilation photons from 18 were simulated as uniformly distributed throughout the liver, and energy deposition events (following secondary electrons) w ere recorded in various target tissues. Comparison of the results can be seen in Table 2 12 It was found that of the target tissues examined, there was a

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129 range of differences from (gall bladder wall) to (ovaries) with an average deviation of (indicating how well a course resolution approximates a fine resolution with regards to total dose over all organs) and an absolute average deviation of ( indicating how well a course resolution approximates a fine resolution with regards to individual organ doses). In addition to comparing differences in absorbed doses, it was of interest to examine how much the mass of all tissues change with changes in voxel resolution. The masses of all tissues in both versions of the voxelized phantom were compared, and the largest deviation in mass was seen for the skin at This made sense since the skin was defined as a single layer of voxels on the outside surface of the phantom. Any changes in voxel resolution will affect the skin mass the most. Interestingly, while the difference in skin mass was the greatest, the difference in calculated absorbed dose was only A conclusion could be drawn from this observation: the amount of energy deposited in tissues tends to change proportionally with changes in tissue mass resulting from changes in voxel resolutio n. As the skin voxels increased in size from the fine resolution to the coarse resolution, more energy was deposited in the voxels. Acting in opposition to the increase in energy deposition, the mass of the skin also increased. Since absorbed dose is eq ual to energy absorbed in the tissue divided by its mass, these two occurrences offset. From this analysis, it was determined that voxel resolution, while having some influence on recorded doses as applied to internal dosimetry, does not affect the outcom e of the simulations in such a way that rigorous testing is needed to determine the voxel resolutions of all the phantoms in the UF hybrid phantom family.

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130 Initial Energies and Particle Histories A range of starting monoenergetic photon energies was selecte d for simulation. The list of a maximum photon energy cutoff (ICRP 2008) The maximum photon energy (between x rays and gamma rays) was found to be and of all 25,256 photon emissions were below Therefore, a maximum energy of was selected, and the remaining energies for simulation were modeled after the simulations of the ORNL stylized phantoms (Cristy et al. 1987) The electron energy grid was set equal to the photon energy grid to promote symmetry. While the results from the current work will be applicable to nuclear medicine imaging and therapy procedures as well as radiation protection purposes, nuclear medicine imaging was the focus. Photon energies up to in nuclear medicine imaging are rarely seen but certain radionuclides used in nuclear medicine imaging to have emission energies approaching that limit. Several commonly used nuclear medicine imaging radionuclides were referenced for examples, a nd these radionuclides were 11 13 15 18 67 81m 82 99m 111 123 131 133 178 191m 195m and 201 (Treves 1995). Average photon emission energies were calculated for each radionuclide and the av erage of these average energies was ( ) (ICRP 2008) These are the typical average energies of emission for nuclear medicine imaging procedures in the range of hundreds of The mid energy range allows for adequate escape from the body but optimal detection quality (Cherry et al. 2003) However, the average maximum energy of emission for these same radionuclides was found to be ( ) (ICRP 2008) Consequently while primary emission energies for nuclear medicine image studies may be in the range of hundreds of energies up to are observed and should be taken into account.

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131 Next, the number of particle histories was determined. As the initial energy of the photons incre ases, the simulation runtimes increase. From previous trial simulations in the UFH00MF phantoms particles are generally sufficient to give satisfactory statistical uncertainties (other specific dosimetry studies were performed with other phantoms, and particles gave satisfactory results) However, lower initial photon energies lead to higher statistical uncertainties. Consequently, a range of particle histories, dependent upon the initial energies of the photons was developed with a maximu m of particle histories at a photon energy of and a minimum of particle histories at a photon energy of An anchor value of was set for the photon energy to control runtimes for energies of a nd greater. Numbers of particle histories for starting energies between and were log linearly interpolated, and the resulting photon energies and associated numbers of particle histories are given in Figure 2 7 Tally Types MCNPX refers to the measure that is being tracked. Tally types available for use in MCNPX are current integrated over a surface (units of particles or ), flux averaged over a surface (units of or ), flux averaged over a cell (units of or ), flux at a point or ring detector (units of or ), energy deposition averaged over a cell (units of or ), coll ision heating (units of ), fission energy deposition averaged over a cell (units of or ), energy distribution of pulses created in a detector by radiation (units of pulses or ), and deposition (units of charge) (LANL 2 005) After selecting the tally type, the user must indicate a tally type for all cells of interest (in this case, cells are equivalent to tissue tag identification number s ), and multiple tally types are allowed.

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132 Two primary tally types were used for the calculation of photon SAFs for the UF hybrid phantom family. The first tally type was energy distribution of pulses created in a detector by radiation in units of (* tally in MCNPX syntax (LANL 2005) ) and this tally was selected to track the total energy deposition in non skeletal target tissues of interest. When coupled with the MCNPX photon electron mode, this tally accounts for contributions from all secondary particles. The photon electron mode indicates to MCNPX that both photons and electrons should be followed throughout the entire geometry until they either reach a particle killing boundary or fall below the energy threshold of the problem (LANL 2005) Since no dose enhancement takes place for general ( non skeletal ) organs, only the total energy deposition needed to be recorded to eventually calculate the absorbed dose (or SAF) to the organ. Secondary electrons incident upon spongiosa were accou nted for through application of the skeletal photon fluence to dose response functions as these functions include electrons born in surrounding soft tissue and cortical bone. (F4 tally in MCNPX syntax (LANL 2005) ) The vol ume averaged fluence tally was selected for application to the skeletal photon fluence to dose response functions. Energy dependent photon fluences throughout regions of spongiosa and MCs were needed to eventually calculate the SAF to AM and TM 50 within each bone site (Johnson et al. 2011) The SAFs for each bone site would then be weighted by the mass fraction of the skeletal tissue of interested to obtain whole skeleton SAFs to AM an d TM 50 Resultantly, the volume average d fluence tallies were divided into energy bins reflective of the energies at which the skeletal photon fluence to dose response functions were assembled The MCNPX output files would then contain the number of pho tons per square centimeter per starting source particle incident on spongiosa or medullary cavities

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133 between the upper and lower energy bounds of each energy bin. After extraction from the output files, the energy dependent photon fluences were multiplied by their corresponding energy dependent photon fluence to dose response function, and the results were summed to obtain the dose to radiosensitive skeletal tissues in each bone site. A MATLAB TM code was written to extract all output data from the photon do simetry simulations, and t he code performed all data extraction and post processing. During each post processing phase, the resulting SAFs were recorded into separate Microsoft Excel (Microsoft Corporation, Redmond, WA) files to isolate any errors in pro cessing if present. The code handled all tally information discussed here and all variance reduction techniques subsequently discussed. Miscellaneous Transport Details Energy cutoff The default cutoff for all particle types in MCNPX is the energy at which the particle is no longer followed and assumed to be locally deposited (LANL 2005) This means that any particle falling below this energy threshold during the course of radiation transport is terminated. The lower bound ene rgy threshold feature can be used in some cases to decrease overall simulation times. For example, if high energy (in the case of this study, ) photons were simulated with a lowered electron energy cutoff of the simulation time would inc rease quite drastically in order to follow secondary electrons down to that energy. In turn, the true physics of the model would be more accurately represent ed However, while the physics would be more accurately modeled, the actual recorded energy depos ition may not change at all due to the short range of electrons A different scenario occurs when the lower bound energy threshold is increased from to In this case, simulation time would decrease since secondary electrons would be terminated once they achieve an energy of

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134 but the true physics would be inadequately modeled since electrons at could escape the region of interest Given that simulation time could be saved if dosimetry results did not vary drastically with changes in the lower bound energy thr eshold, this issue was further pursued. A uniform photon source of energy was simulated for the UFH00M phantom with lower bound electron energy thresholds of and and the energy deposition was recorded i n various target tissues of interest. The results were examined for many target tissues, and several of them are displayed in Table 2 13 It was found that for some tissues, the recorded energy deposition did not vary drastically across the different ele ctron cutoff energies. However, for others, the variation was seen to be significant. In the interest of adequately modeling the true physics, the lower bound electron cutoff energy of was selected. Ranges in soft tissue for electrons of energy are on the order of micrometers, so electron escape from target tissues of interest was not of great concern. E lectron energy indexing algorithm The default electron energy inde xing algorithm used in MCNPX is the MCNP style bin centered algorithm (LANL 2005) Another option available for use is the ITS style nearest bin algorithm. According to the 2005 American Nuclear Society (ANS) Topical Meeting in Mathematics and Computatio ns in Avignon, France, the ITS style nearest bin algorithm can be evidenced as the consistently more accurate of the two and the reasons will be described here (Hughes 2005) Electron physics within MCNPX are handled using energy bins. Under the MCNP sty le bin centered algorithm, an electron with energy would be assigned to the energy group and the energy group structure would be (Hughes 2005) Within this energy group,

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135 a range ( which will be called an energy group ran ge here ) is calculated so that if an electron with initial energy travels a distance it will attain an energy of giving a mean energy loss of (Hughes 2005) This assumes that the electron actually has an e nergy of an obvious approximation. Once is selected, the number of angular sub steps taken within is defined as (dependent on the elemental composition of the material), and the sub step range is calculated as (Hughes 2005) The sub step range is the distance traveled after each angular deflection. The energy group straggled energy loss is sampled from the Landau straggling distribution based on and (Hughes 2005) The observed after a certain path length of tissue has been traversed. The sub step straggled energy loss is calculated as (Hughes 2005) MCNPX attempts to transpor t the electron through sub steps, and if all sub steps are successfully completed, the electron is reassigned to a new energy group (Hughes 2005) If the electron crosses a cell boundary or attains an energy below it is assigned to a new ene rgy group (Hughes 2005) While the MCNP style bin centered algorithm assigns electrons of energy to a bin so that the ITS style nearest bin algorithm assigns electrons of energy to a bin so that (Hughes 2005) Using the ITS style method, the electron will be assigned to the energy group whose upper limit is closest to the energy of the electron. For example, if and the electron would be assigned to using the MCNP style method since the energy of the electron is between and However, this same electron would be assigned to using the ITS style method since its energy fal ls between and

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136 The MCNP calculating predicted energy loss are pre computed at the center of each bin (Hughes 2005) The bin centered algorithm presents problems because the electron will likely not achieve the predicted range due to the fact that the electron will typically have an energy less than the upper limit of the energy bin and hence a lower range (Hughes 2005) This leads to linear interpolatio n of energy loss in a process which is non linear (Hughes 2005) In addition, the final energy loss sub step within the energy group usually carries over into the next energy bin, resulting in systematic error (Hughes 2005) These problems are not encoun tered in the ITS style algorithm because the electron is assigned to the energy bin whose upper limit is closest to the energy of the electron, and the electron is not assigned to a new energy bin if it attains an energy below the current energy bin (Hughe s 2005) These factors minimize the negative effects introduced by linear interpolation of non linear processes. To investigate the effect these electron energy indexing algorithms have on computational internal dosimetry, test cases were simulated using both algorithms and the results were compared. Uniform photon sources of energies and were simulated in the adipose tissue of the UFH00M phantom, and the energy deposited in a variety of target tissues of interest was recorded using bo th the MCNP style and ITS style algorithms. Results can be seen in Table 2 14 Differences in energy deposition estimates were seen between and for the simulations and between and for the simulations Disagreemen t between the MCNP style and ITS style algorithms increased over all target tissues from the simulations to the simulations with pronounced effect for smaller target tissues. Resultantly it was decided that the recommendation of the M CNP development team would be

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137 taken and the ITS style nearest bin electron energy indexing algorithm was selected for the photon and electron SAF simulations. Source Tissues The UF series of pediatric hybrid computational phantoms has recently been in cons ideration for adoption by the ICRP as the new reference series of pediatric computational phantoms. While the UF adult phantoms will not be adopted by the ICRP, the UF adult phantoms were included in the current study for in house use. In anticipation of the UF pediatric series being adopted by the ICRP, it was prudent to model both the photon and electron simulations and any relevant details after the latest ICRP document, ICRP Publication 110. In this publication, the ICRP introduced a reference adult male and female voxel phantom and laid out detailed plans about the future calculation of monoenergetic photon and electron SAFs (ICRP 2009) In an effort to model the UF work after the ICRP intentions all source tissues listed in ICRP Publication 110 wer e simulated as source tissues in the UF phantoms. Since the ICRP and UF phantoms were developed separately, several structures were not consistent between the two models, so approximations were made in these cases. For example, the ICRP has explicitly mo deled intrapulmonary bronchi (ICRP 2009) while the UF phantoms have a homogenous lung model. In this case, the ICRP models a bronchiole source explicitly while the lungs were assigned as the surrogate tissue for the UF phantoms. In addition, several extr a source tissues were simulated in the UF phantoms that were not included in the ICRP phantoms. Some source tissues were not explicitly simulated since their components were simulated individually, as in the case of the colon. The right colon wall, left c olon wall, and rectosigmoid wall were all simulated as source tissues, so simulating a combined colon source would only duplicate efforts. Because of this, volume weighting was used to calculate the SAF to target

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138 tissues from composite sources, and Equati on 2 20 was used to calculate the volume weighted SAFs. (2 20 ) where is total SAF for source tissue irradiating target tissue at an initial photon energy of with all contributions from individual components of included, is the SAF for source component irradiating target tissue at an initial photon energy of and is the volume of source component A MATLAB TM code was written to perform all composite source tissue calculations. A final list of all explicitly simulated source tissues and all mathematically assembled source tissues in the UF hybrid computational phantom seri es are in Tables 2 15 and 2 16 respectively For use in MCNPX, source tissues were represented in the form of source files. Source files define the and coordinates of voxels located in the source tissue along with the sampling distribution t ype and sampling probabilities MCNPX accesses the source file to randomly select a voxel within the source tissue of interest Once a voxel is selected, a point within the voxel is randomly selected to start a particle history. Source files were either uniform or non uniform in nature, but the sampling algorithm assigned to the voxel level remained unchanged regardless of the type of source. Essentially, any non uniformity in the source was handled by adjusting the probability of selecting a certain se t of voxels, but once the voxel was selected, all source points within the voxel were equally likely to be selected. Uniform source sampling at the voxel level was accomplished by defining three dimension bins one in the direction, one in the dire ction, and one in the direction. Each bin was assigned a sampling probability of unity across its entire extent. In this way, all points along its length had

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139 an equal probability of being selected as a starting source point. With equal probabilities of source point selection for all points along the and directions, all points within the voxel volume were equally likely to be selected as a starting source point. Uniform source sampling For most source tissues, specifically those whose enti re physical structure was explicitly represented within the hybrid phantom s uniform source sampling was used to sample points of radiation emission. Two sampling steps were required to select a starting emission point for the photons (1) selecting a vo xel and (2) selecting a point within the voxel (s electing a point within the chosen voxel was described in the previous section ) A distribution of source voxels was defined for MCNPX to sample. Many uniform sources only consisted of one tissue element (e.g., the spleen with tissue tag identification number 45) while some uniform sources were composed of several elements (e.g., the salivary glands with tissue tag identification numbers 39, 60, and 61). For both cases, only one source distribution was de fined even though different numbers of tis sues were involved simply because it was the most efficient way to compose the source file. Separate distributions could have been defined for each sub component, but the distributions would be fundamentally equal All voxels in the phantom that had tissue tag identification numbers equal to those in the source tissue(s) of interest were recorded into a source file along with the coordinates (in numbers of voxels) of each voxel. The discrete source variable flag Next a probability of selection of unity was assigned to all voxels in the source file. This ensured that all voxels would be equally likely to be selected for sour ce sampling. A sample uniform source file and detailed description can be found in Appendix B

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140 To visually represent uniform source sampling, a simulation was performed, and the and coordinates of the starting source particle were recorded. A small subset of these points was chosen, and a red sphere was created at each point. Visual modeling was done in Rhinoceros TM and a subset of points was chosen so that the distribution could be more easily visualized. The lungs of the UFH00M phantom were chosen as the source tissue, and the resulting source points can be seen in Figure 2 8 (A) It should be noted that the concentration of source points appears to be uniform, indicating that uniform source sampling was correctly executed. Non uniform source sampling Uniform source tissues were defined to be uniform because all structures of interest were present in the voxel model. In the case of several skeletal source tissues, the tissues of interest were unable to be explicitly represented in the S keletal P hoton F luence to D ose R esponse F unction s of Chapter 2 bone trabeculae and marrow cavities were too small to be effectively modeled in voxel format. If the structures that could not be explicitly mode led in the voxel model were distributed proportional to the volume of their parent tissues (e.g., bone marrow throughout spongiosa and medullary cavities), non uniform source sampling would not be necessary because the amount of source tissue per unit volu me parent tissue would be equal across the entire sampling volume. However, skeletal source tissues such as TBV are unevenly distributed throughout the spongiosa and MCs (Pafundi et al. 2009) and thus were sampled non uniformly with respect to phantom reg ions volumes (e.g., spongiosa for an active marrow source) Similar to the method used to accomplish uniform source sampling, the and coordinates of all voxels in the parent tissues of interest were defined. For example, if total

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141 marrow was s imulated as the source, the parent tissues were identified as all spongiosa and medullary cavities since bone marrow is found in all of these sites. Thus spongiosa of the cranium with tissue tag identification number 201 was found in the voxel phantom, a nd the coordinates of all those voxels were recorded and assigned a sampling probability of unity. Next, in a separate distribution but in the same file, spongiosa of the mandible with tissue tag identification number 202 was found in the voxel phantom, a nd the same information was recorded. For the total marrow example, this process was completed for tissue tag numbers 201 through 234. If the example source file for TM were left in this condition, a uniform source distribution throughout whole body spong iosa and MCs would have been defined. Since a non uniform source distribution was desired a final step was added. The purpose of creating separate uniform distributions for each spongiosa and medullary cavity site was to separate the sites for which sam pling probabilities would be defined. Each separate site specific voxel distribution was given a distribution number and a sampling probability was assigned to that distribution number. The sampling probability where is the fraction ( either volume or surface fraction) of tissue located in spongiosa or MC site was set equal to the volume (whole body AM TM in spongiosa, TM in medullary cavities, TBV and CBV ) or surface ( TBS ) fraction of the tissue. In this way, a non uniform sourc e was created. A sample non uniform source file and detailed description can be found in Appendix B All sampling probabilities for the UF hybrid phantom family are in Tables A 11 through A 18 in Appendix A The fractional source distributions for the U FH00MF, UFH01MF, UFH05MF, UFH10MF, and UFH15MF phantoms were taken from the doctoral dissertation of Deanna Pafundi (Pafundi 2009) F raction al source distributions for the UFHADM phantom were taken from Hough et al. (2011) Fractional source distribution s for

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142 the UFHADF phantom were recently developed by Lindsay Sinclair at UF (Sinclair et al. 2009) To visually represent non uniform source sampling, a simulation was performed, and the and coordinates of the starting so urce particle were recorded. A small subset of these points was chosen, and a red sphere was created at each point. Visual modeling was done in Rhinoceros TM and a subset of points was chosen so that the distribution could be more easily visualized. The lungs of the UFH00M phantom were again chosen as the source tissue, but this time the sampling probability of the right lung was set to 0.9 and the sampling probability of the left lung was set to 0.1. The resulting source points can be seen in Figure 2 8 (B) It should be noted that the concentration of source points no longer appears to be uniform with the right lung being sampled more heavily than the left lung, indicating that non uniform source sampling was correctly executed. Target Tissues Like th e source tissues simulated in this study, the list of target tissues w as also modeled after those given in ICRP Pub lication 110. Again, since the ICRP and UF phantoms were developed separately, several target tissues were not consistent between the two mo dels, so approximations were made in these cases as they were with the source tissue definitions. For example, the ICRP has explicitly modeled both adipose and glandular tissue in the breasts (ICRP 2009) while the UF phantoms have a homogenous breast mode l. In this case, the ICRP models left and right adipose and glandular breast tissue sources explicitly while the left and right homogeneous breast tissue were assigned as the surrogate tissues for the UF phantoms. In addition, several extra target tissue s were simulated in the UF phantoms that were not included in the ICRP phantoms.

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143 Some target tissues comprised of several sub components were not explicitly simulated since their sub components were simulated individually, as in the case of the kidneys. T he left and right kidney cortex, medulla, and pelvis were all considered as separate target tissues, so tallying energy deposition in all regions simultaneously would simply replicate efforts. Consequently mass weighting was used to calculate the SAF to the composite target tissue and Equation 2 21 was used to calculate the mass weighted SAFs. (2 21 ) where is total SAF for source tissue irradiating target tissue at an initial photon energy of with all contributions from individual components of included, is the SAF for source irradiating target tissue componenet at an initial photon energy of and is the volume of target component A MATLAB TM code was written to perform all composite target tissue calculations. A final list of all explicitly simulated target tissues and all mathematically assembled target tissues in th e UF hybrid computational phantom series are in Tables 2 17 and 2 18 respectively Photon Specific Absorbed Fraction Calculation The primary goal of the photon simulations was to use t he UF hybrid phantoms to calculate a set of SAFs at various photon ener gies The SAF is an important measure which reflects the geometry of the irradiation scenario as well as the radiation energy It is ultimately used to calculate either individual organ absorbed doses, individual organ equivalent doses, or whole body eff ective dose Dosimetry of internal emitters is derived from the emission of radiation from any source tissue and the absorption of that radiation in target tissu e For any target tissue, the time independent formulation of radiation absor bed dose from a set of

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144 arbitrary source tissues emitting radiation is described by Equations 2 22 and 2 2 3 ( Bolch et al. 2009 ) : (2 22 ) (2 2 3 ) w here is the time integrated activity or the total n umber of nuclear transformations occurring in source tissue is the radionuclide S value, defined as the mean absorbed dose rate to target tissue per unit activity in source tissu e is the energy of the radiation, i s the yield of the radiation, is the AF, defined as the fraction of radiation energy emitted in source tissue that is absorbed in target tissue at radiation energy is the mass of the target tissu e is the delta value for the radiation, defined as the product of the energy and the yield of the radiation, and is the SAF, defined as the ratio of the AF to the target tissue mass. As discussed previously, the tally type used for non skeletal target tissues recorded energy deposition over a cell (target tissue) in units of per photon. T o obtain the SAF for any target tissue, the tally result s w ere divided by the initial photon energy and the mass of the target tissue This equation was validated conceptually because the tally described the amount of energy deposited in the target tissue by a single photon emitted in the source tissue The deposite d energy divided by the emitted energy determined the fraction of that emitted energy that was deposited in the target tissue which is, by definition, the AF The SAF is defined as the AF divided by the mass of the target tissue When multiplied by the a ppropriate conversion factors, the SAF was expressed in units of

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145 A different method was used to convert the volume averaged fluence tallies in the spongiosa and medullary cavity regions to SAFs for the AM and TM 50 target tissues because the skel etal photon fluence to dose response functions were used instead of direct dose or energy tallying Equation 2 24 was used to calculate the SAFs for both AM and T M 50 target regions for the whole skeleton. (2 24 ) where is a unit conversion constant, i s the initial photon energy, i s the mass fraction of target tissue in bone site x i s the skeletal photon fluence to dose response function for target tissue ( AM or T M 50 ) at photon energy is the photon fluence emitted from source tissue incident on the spongiosa or medullary cavity of bone site x for photons of energ y and is the SAF for target tissue from any source tissu e Unfortunately, the symbol used to indicate the SAF and photon fluence are the same, so the reader will have to discern which measure is referred to based on the context. SAFs were calculated for e very source target energy combination for the entire UF hybrid phantom family This was considered to be a complete set of photon SAFs and thus a complete internal photon dosimetry characterization of the UF hybrid phantom family These SAFs can be used to perform dosimetry calculations for any nuclear medicine procedure, provided the radiopharmaceutical biokinetics are known. Variance Reduction Techniques Overview While the majority of SAFs obtained from the radiation transport simulations had relative u ncertainties around and were thus considered to be statistically reliable, a small subset of

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146 source target energy combinations had relative errors that were less than satisfactory. In the interest of providing the most reliable data possible, steps wer e taken to make educated adjustments of the data to improve the reliability of some of the less reliable data These steps included application of (1) the reciprocity principle, (2) log linear back extrapolation, and (3) three point data smoothing. A f lowchart schematic of the variance reduction scheme is in Figure 2 9 All aspects of the flowchart will be described in greater detail in the following sections but the flowchart can be referred to as a visual aid to this discussion. Reciprocity Most sour ce target energy combinations for the photon simulations gave SAFs with satisfactory statistical uncertainties. The MCNP manual gives the recommendation that values with uncertainties above should be disregarded, values with uncertainties between and can be believed to within a factor of a few, values with uncertainties between and are questionable, and values with uncertainties less than are generally reliable (X 5 Monte Carlo Team 2003) However, some source target energy combina tions had unsatisfactory uncertainties, and methods to correct this undesirable behavior were explored. The reciprocity theorem states that the SAF from a source organ irradiating a target organ is equivalent to the SAF when the source target designations are reversed as given in Equation 2 25 (Loevinger 1969) (2 25 ) where is the SAF for source tissue irradiating target tissue for radiation energy and is the SAF for target tissue irradiating source tissue for radiation energy The theorem is rigorously valid for an infinite uniform homogenous media but it has also been shown to be approximately true for heterogeneous media (Petous si Henss et

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147 al. 2007) When applied in heterogeneous media, this methodology is referred to as the reciproci (Cristy et al. 1987) However, the principle is not valid when one of the organs is a skeletal tissue for initial energies between and (owing to photon dose enhancements), and it is not valid when one of the organs is the left or right lung for initial energies between and (due to differences in density and elemental composition) (Petoussi Hen ss et al. 2007) Reverse (adjoint) Monte Carlo was performed for most source target combinations by reversing the source and target designations and retaining the SAF with the lowest statistical uncertainty. T he reciprocity principle was not applied for s keletal target tissues at initial energies less than or equal to or for the lungs at initial energies less than or equal to The uncertainties were seen to improve for the larger organ targets as more energy ab sorption events were recorded. An example of an application of the reciprocity principl e is given in Figure 2 1 0 Log linear back extrapolation For some SAFs at low initial photon energies, no energy deposition was recorded. However, due to the penetrating nature of electromagnetic radiation, it was determined to be an unphysical artifact o f the Monte Carlo radiation transport methodology. If sufficient source points were sampled, some, albeit insignificant, energy deposition would take place. Additionally, it was indicated from other more statistically reliable curves that photon SAFs whe re the source and target are not the same tissue tend to decrease in a log linear fashion with respect to decreases in initial photon energy. Therefore, it was not unreasonable to log linearly back extrapolate from adjacent SAFs to estimate low energy pho ton SAFs, and a MATLAB TM code was written to perform this operation on the data via Equation 2 26 :

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148 (2 26 ) where is the SAF for target tissue and energy index and is the initial energy of the photon at energy index An example of low energy photon back extra polation is shown in Figure 2 11 A potential argument against this method is that the SAFs were created using equations rather than data generated by explicit radiation transport simulation. There are three reasons why the low energy photon back extrapolation method is reasonable within this study (1) an SAF of zero is unphysica l since at a certain radiation level, energy deposition will occur, no matter how low the photon energy (based on the exponential attenuation equation), (2) a log linear trend was indicated by other reliable SAF curves at low initial photon energies, (3) a best guess estimate is better than no estimate for the purpose of conservativeness In addition, the impact of any errors introduced by the back extrapolation method was minimized by the fact that if no energy deposition was recorded, no particles reache d the target tissue. That meant that if there had been enough particles simulated to give an adequate number of photon interactions in the target tissue, the dose would have been very low in the first place Interestingly, the photon SAF simulations disp layed a good characteristic in that target tissues of the highest importance (those receiving the greatest dose) displayed the most favorable statistical uncertainties while those of lower importance (those receiving the least dose) displayed the most unfa vorable statistical uncertainties. Essentially, when the dose estimate mattered, the dose estimate was good; when the dose estimate matter ed less the dose estimate was not as good. A follow up argument to this point would question why the back extrapola tion was necessary at all if the results did not

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149 impact final radionuclide S values No matter what the circumstance, it is always the goal to give the best dose estimates possible, regardless of the perceived importance. Three point smoothing For some source target combinations, invoking the reciprocity principle was not sufficient to improve the statistical uncertainties of the SAFs. These cases were seen when both the source and target tissues were small in size. Distant organs display ed reasonable statistical uncertainties if they were moderate to large in size. When poor statistical uncertainties were seen across all energies of a particular target organ, they almost always (if not always) manifested themselves as an un smooth curve that seemed to behave erratically around a perceived central tendency Since curves of similar general shape were observed for o ther source target combinations, it was concluded that the true shape of the erratic curve could be approximated by applying a three point sm oothing algorithm to the range of energies where the curve was seen to be the most erratic. In cases where the initial energy of the photon was equal to or (the lower and upper energy limits), two point smoothing was applied. An exampl e of the three point smoothing technique is in Figure 2 1 2 Electron Specific Absorbed Fractions Similarities to Photon Transport Methods Many of the details used to generate the input files and all associated files for the photon simulations were identica l to those used to generate the files for the electron source simulations. The phantom physical characteristics were all the same since the electron dosimetry was performed for the same phantoms. Lattice files, source files, voxel resolutions, total matr ix sizes, tissue densities, material compositions, tissue masses, s ource tissues, target tissues, and radiation emission energies were identical in both the photon and electron dosimetry simulations.

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150 General Transport Methodology A significant difference o bserved between photon and electron computational dosimetry was that the uncertainties associated with any tally for electron dosimetry in cross dose scenarios were typically higher than those for photon dosimetry 2 In fact, many estimates of electron cro ss dose (especially for low initial electron energies) for several test simulations had uncertainties of or no energy deposition at all. This characteristic was mostly seen when the source tissue and target tissue were separated by a distance greater than the CSDA range of the electrons. When this was the case, energy deposition to target tissues was a result of electrons created by photons that were themselves created by the initial electrons. Uncertainties were high because the number of photons c reated during the course of a single source electron losing energy was lower than the number of particle histories. In addition, since the photons were mostly bremsstrahlung photons, the photon spectrum was more heavily weighted toward energies lower than the initial energies of the monoenergetic electrons The combination of low yield and low energy photons expectedly produced high uncertainties in the electron SAFs When target tissues received energy deposition from collisional energy losses of the pr imary electrons (electrons started in the simulation), the statistical uncertainties were much lower. To combat the undesirable characteristic of high uncertainties, a novel method was created to produce lower uncertainty electron SAFs. This method consis ts of two simulations separately modeling the two mechanisms of electron energy loss (1) a collisional energy loss (CEL) simulation and (2) radiative energy loss (REL) simulation When an arbitrary electron (primary electron) was started in any particul ar source tissue, it deposited energy in the target tissues through excitation and ionization from the primary electron and its secondary electrons 2 This is observed when electron dosimetry is performed in the traditional way by simply starting monoenergetic electrons and following all photons and electrons created during the course of simulation.

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151 (collisional energy loss) and through excitation and ionization from electrons created by photons generated during the course of the primary electron traversal through tissue (radiative energy loss). The photons were mostly created in the source tissue itself due to comparatively short electron ranges. If sufficient electrons were simulated, the photons create d during particle transport could be approximated as uniformly distributed throughout the source tissue and isotropic in their angular emissions In light of this, the connection was made that this very scenario had already been modeled with reliable resu lts in the previous photon simulations. Since the photon simulations had relatively low uncertainties and variance reduction techniques had already been applied it was a natural extension to somehow replace the radiative energy loss component of the ele ctron simulations with the already completed photon simulations. To accomplish this separation of the electron energy loss components a feature within MCNPX was utilized to record the initial energies of all photons created during the electron simulations 3 Next the pre computed, low uncertainty, monoenergetic photon SAFs could be used to calculate a photon spectrum weighted SAF that would represent the radiative energy loss contribution to absorbed dose in the target tissue of interest. The collisional energy loss simulation accounted for the removal of energy from bremsstrahlung photon creation but did not follow those photons, thus saving simulation time. Collisional energy loss from primary electrons was thus simulated entirely separately from the r adiative energy loss component. Since the photon SAF simulations followed all secondary electrons and any subsequent photon electron showers the physics of a full electron dosimetry simulation (following all photons and electrons created during simulatio n) was accurately modeled with the added effect of virtually simulating many more particle histories through application of the previously constructed 3 Bremsstrahlung photons are prima rily created in these simulations, but characteristic x rays are also observed.

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152 monoenergetic photon SAF dataset A flowchart schematic of the electron dosimetry scheme is given in Fig ure 2 1 3 All aspects of the flowchart will be described in greater detail in the following sections but the flowchart is given here as a visual aid to the discussion It was of slight concern that the lack of an explicit blood vessel wall model could pe rturb the bremsstrahlung spectrum of a source within the blood vessels. In addition, possible shielding effects could be introduced when considering electron emitters in the blood vessels. However, in the end, distributed blood sources were of primary in terest, not blood vessel only sources. Any slight perturbations in the results from a lack of blood vessel wall model were considered to be compensated by the averaging of the results from all blood containing organs. Collisional Energy Loss Contribution to Dose Tally types Energy deposition over a cell was used for all target tissues for the CEL electron simulations. Regions of spongiosa and MCs in the skeleton were tallied separately, giving a total of 34 tallies for these regions. Fluence tallies were not needed for application of the skeletal photon fluence to dose response functions because the dose resulting from photons created during electron transport to AM and TM 50 from extra skeletal sources were handled in the REL simulations. Skeletal photon fluence to dose response functions were needed for photon simulations to account for the dose enhancement effect of electrons created in TB of the skeleton (Pafundi et al. 2010) However, when considering ionization and excitation from primary electrons in AM and TM 50 there is no dose enhancement effect, indicating that energy is not preferentially deposited in one tissue over another per unit mass. As a result absorbed dose to homogeneous spongiosa and the marrow within medullary cavities can be used as a surrogate for the absorbed dose to AM and TM 50 in those same tissue regions Total dose to AM and TM 50 was calculated as a weighted average over the whole skeleton.

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153 Miscellaneous transport details The initial monoenergetic electron energies and numbe r of particle histories simulated at each energy for the CEL simulations was the same as was used for the photon simulations and can be seen in Figure 2 7 The default electron energy cutoff of was used, and the ITS style nearest bin algorithm was selected for electron energy indexing. Collisional specific absorbed fraction calculation Energy deposition over a cell was tallied for all non skeletal target tissues in the CEL simulations. Equation 2 27 was used to calculate the SAFs for all non skeletal target tissues. (2 27 ) where is the SAF due to collisional energy loss of the primary electrons for source tissue irradiating target tissue at initial electron energy for non skeletal target tissues, is the energy deposited in target tissue and is the mass of the target tissue. For extra skeletal sources, e nergy deposition o ver a cell was tallied for all regions of spongiosa and MCs For reasons previously detailed, the SAFs to AM and TM 50 were approximated by the SAF to whole body spongiosa or medullary marrow A weighted average of energy deposited in all spongiosa and MC s was used to calculate the SAFs to AM and TM 50 and is detailed in Equation 2 28 : (2 28 ) where is the SAF due to collisional energy loss of the primary electrons for source tissue irradiating target tissue at initial electron energy for skeletal target tissues and extra skeletal sou rces is the energy deposited in spongiosa or MC region is the

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154 mass of spongiosa or MC region and is the mass fraction of target tissue in spongiosa or MC region Since the skeletal target tissues for extra skeletal sources each had an associated uncertainty, an uncertainty was calculated for the whole skeleton estimates for variance reduction purposes. Whole skeleton uncertainties for AM and TM 50 for extra skeletal sources were calculated using Equat ion 2 33 and was derived using Equations 2 29 through 2 32 (2 29 ) (2 30 ) (2 31 ) (2 32 ) (2 33 ) where is the SAF due to collisional energy loss of the primary electrons for source tissue irradiating target tissue at initial electron energy for skeletal target tissues and extra skeletal sou rces is the SAF due to collisional energy loss of the primary electrons for source tissue irradiating spongiosa or MC region at initial electron energy is the mass fraction of target tissue in spongiosa or MC region is the absolute uncertainty for the whole skeleton SAF, is the absolute uncertainty associated with the SAF for spongiosa or MC region and is the relative uncertainty associated w ith the SAF for spongiosa or MC region as given in the output of the MCNPX simulations. The

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155 relative uncertainty for the whole skeleton was obtained by dividing the absolute uncertainty for the whole skeleton by Radiative Energy Loss Contribution to Dose Methodology sub portion of Chapter 2 but the important points will be restated here. For each source tissue and initial electron energy, instead of tracking energy deposition over a cell, the initial energies of all photons created during the simulation were recorded. As previously noted, photons generated during transp ort include both bremsstrahlung and characteristic x rays, but large fraction of photon intensity can be attributed to bremsstrahlung radiation. By simulating a number of particle histories, a photon spectrum was created. This photon spectrum was then we ighted by the previously generated set of monoenergetic photon SAFs for the source tissue of interest to obtain the SAF to all target tissues of interest due exclusively to contributions from radiative energy loss by the primary electrons. Particle trackin g The particle tracking (PTRAC) file feature within MCNPX was utilized to record the initial energies of all photons (bremsstrahlung and characteristic x rays, in particular) created during the transport of the primary electrons in the source tissue Rele vant i nput parameters available for use and values used in the simulations were as follows (LANL 2005) FILE This input parameter determines the type of output file generated, and the value process ing with MATLAB TM

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156 MAX This input parameter specifies the maximum number of events to write to the output file, and the value was set to to ensure that all events would be recorded to the output file. This number was arbitrary but equal to the gr eatest number of particles simulated. WRITE This input parameter details what measures are to be written to the output file, reported when all parameters are wri tten. EVENT This input parameter determines what physical occurrence should be recorded by banking them for later transport. TYPE This input parameter filters e vents based on the selected particle type, and the Particle histories Unlike the photon and CEL electron simulations, minimizing uncertainties associated with energy deposition tallie s was not considered A different endpoint was defined for the REL electron simulations: a reliable photon energy spectrum. Two factors were considered when determining the number of particle histories to be used for the REL simulations. The first consi deration was file size. During the course of several test simulations, it was found that simulating particle histories produced PTRAC files that were too large to be efficiently process ed Additionally, SAF values for the REL simulations showed li ttle variation between particle histories of and The second consideration was the desire to model the photon spectra as accurately as possible. Photon spectra accuracy increases with increasing number of particle histories, but at a certai n point, further technical accuracy did not significantly change the SAF estimates.

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157 After considering the tradeoff between simulation time, file size, and photon spectrum accuracy, the number of particle histories was set to Photon energy spectr a were generated for a uniform electron source in the liver of the UFH00M phantom, and the results are in Figure 2 1 4 The photon spectra match the predicted bremsstrahlung spectra fairly well and seem to indicate that the number of particle histories cho sen was reasonable. At the chosen number of particle histories, t he MATLAB TM code written to process the REL simulation output took approximately 8 hours to process all output for each phantom. If many more particle histories had been simulated, the time required to process the output would be unreasonable and would push the memory limits of MATLAB TM It is important to remember that a REL photon spectrum was generated for each monoenergetic electron energy for every source organ. If the resulting spectr a were not heavily dependent on the source organ, perhaps a single spectrum could be used and applied for each source organ. To investigate this possibility, photon spectra were generated for all 21 electron energies for the adipose tissue, left and right 1 4 were compared to the spectrum obtained by averaging the results of all the modeled source organs. Differences up to abou t were observed for the statistically reliable energy bins across the different source organs. In addition, the left and right adrenals showed about deviation from each other, even given the equivalent elemental compositions. This is due to th e inherent approximation that all photon created outside of the source organ are treated as a photon emission in the source organ. Because of these differences in photon spectra, each source tissue was individually simulated instead of using an average ph oton spectrum.

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158 Radiative energy loss specific absorbed fraction calculation Once all REL simulations were complete for all source tissue in all phantoms, the resulting photon energy spectra were converted into REL SAFs using Equation 2 37 derived from Equa tions 2 34 through 2 36 Equation 2 35 gives the equation that would be used if a continuous photon and electron energy spectrum were available. However, since only a certain number of photon energies were recorded, the continuous equation was discretize d. The important concept in these equations is that the absorbed fraction of energy in any target tissue of interest due to radiative energy losses by the primary electrons is equal to the energy deposited in the target tissue from electrons created by ph oton interactions divided by the total electron energy emitted from the source tissue. (2 34 ) (2 35 ) (2 36 ) (2 37 ) where is the SAF to target tissue from source tissue at initial electron energy due to radiative energy losses of the primary electrons, is the AF to tar get tissue from source tissue at initial electron energy due to radiative energy losses of the primary electrons, is the mass of target tissue

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159 is the energy deposited in target tissue that can be attributed to the photons created during simulation (photons are indirectly ionizing), is the total primary electron energy emitted from source tissue is the maximum photon energy in an arbitrary continuous photon energy spectrum, is the photon AF to target tissue from source tissue at photon energy is the maximum electron energy in an arbitrary electron energy spectrum, is the energy of an electron in an arbitrary electron energy spectrum, is the photon AF to target tissue from source tissue at energy of the photon, is the total number of primary electrons simulated, and is the photon S AF to target tissue from source tissue at energy of the photon. While the REL simulations were effectively performed in all source tissues in all phantoms, the REL simulations were not physically performed in se veral instances. The UFH00MF, UFH01MF, UFH05MF, and UFH10MF phantoms share the same internal structure between genders with the only difference being the gender specific organs (Lee et al. 2010) Since the structures and tissue elemental compositions wer e the same between genders, REL simulations were only performed for the gender specific organs in the UFH00F, UFH01F, UFH05F, and UFH10F phantoms. The photon spectra generated for the common organs in the male phantoms were used for the common organs in t he female phantoms. Total Electron Specific Absorbed Fraction Extra skeletal sources The CEL simulations were performed to model dose contributions due to collisional energy loss, and the REL simulations were performed to model dose contributions due to ra diative energy loss. Since these simulations modeled two separate processes that did not

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160 included any overlap in dose contributions, the final total electron specific absorbed fraction for extra skeletal source tissues was determined from Equation 2 38 (2 38 ) where is the total electron SAF for source tissue irradiating target tissue at initial electron energy is the SAF obtained from the CEL s imulation for source tissue irradiating target tissue at initial electron energy and is the SAF obtained from the REL simulation for source tissue irradiating target tissue at ini tial electron energy This equation was applied when the source tissue was not located within the skeleton and the target tissue was either a non skeletal tissue or a skeletal tissue. Intra skeletal sources When the source tissue was located wit hin the skeleton and the target tissue was a non skeletal target tissue, Equation 2 38 was applied to calculate the total electron SAF. However, a special case arose when calculating the total electron SAF for intra skeletal target tissues from intra skel etal source tissues as in the case of TBV irradiating AM. In these cases, the trabecular microstructure must be taken into account since electrons were being transported with starting points in the complicated geometries of spongiosa (all regions with bon e trabeculae and marrow cavities) and the medullary cavities of the long bones To account for the complicated microstructure, previous work was used in addition to methods described in this study. Intra skeletal electron SAFs had already been computed by Pafundi et al. (2010) for the UFH00MF and UFH15MF (Pafundi 2009) phantoms and by Hough et al. (2011) for the UFHADM phantom. The following SAFs were taken from those studies: and The following SAFs were mathematically derived:

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161 and CMA refers to total bone marrow associated with the shafts of the long bones, and TMA refers to total bone marrow associated with all other skeletal sites. As this is the case, the CMA and TMA SAFs will be computed by taking a volume weight ed average of the SAFs across all relevant skeletal sites Intra skeletal electron SAFs assembled from the CBIST SIRT calculations were used in this study for the UFH01MF, UFH05MF, UFH10MF, and work by Sinclair et al. (2009) was utilized in this study for the UFHADF. Varia nce Reduction Techniques Variance reduction had already been performed for the SAFs from the REL simulations since they were derived from the photon SAFs. Therefore, no further variance reduction techniques were applied to the REL simulation SAFs. Howeve r, the CEL simulation SAFs had not been post processed, so variance reduction techniques were considered for this subset of the electron SAFs. Log linear back extrapolation was not an option because the physics behind the argument that photon dose will n ot be zero at low energies does not apply as rigorously to electron physics. Electrons have a definite range, so if no energy deposition was recorded, the SAF was taken to be zero. Occasionally, energy deposition with high uncertainty was seen at a parti cular energy or one or more SAFs at greater energies were zero. In these cases, the positive, high uncertainty SAF was set to zero. of Chapter 2 was used for the CEL simulation SAFs. Cristy and Ec kerma n detailed the use of the reciprocity principle and explained that the principle applies to all radiation types (Cristy et al. 1987) and thus the application of th e principle for dose due to electron collisional energy loss was considered valid.

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162 Computing Resources and Runtimes The ALRADS research group in the Department of Biomedical Engineering at UF has four computing clusters available for use. Most of the MATL AB TM simulations were performed on a 6 node cluster built with Dell, Inc. (Round Rock, TX) computers. Each node in the Dell cluster has 8 processors per node with a CPU speed of per processor. Each processor has of memory, and the whole c luster has of hard disk space. All of the MCNPX simulations were performed on the other three clusters. The first cluster was built with PSSC Labs (Lake Forest, CA) computers and has 4 nodes with 8 processors per node and 9 nodes with 4 process ors per node. Each processor has a CPU speed of and of memory The whole cluster has of hard disk space. The second cluster was built with Dell ( Round Rock TX ) computers and has 4 nodes with 16 processors per node and 1 node wi th 24 processors per node. Each processor has a CPU speed of and of memory The whole cluster has of hard disk space. The third cluster was built independently by another research group and has 17 nodes with 4 processors per node. Each processor has a CPU speed of and of memory The whol e cluster has of hard disk space. The vast computing resources available were needed to simulate the large of input files needed for the current study. Average r untimes for the photon, CEL, and REL simulations were approximately and respectively. An approximate total runtime for all simulations was calculated as However, running on an average of 5 0 processors (due to cluste r down time and shared usage ) gave an approximate real time runtime of or about A myriad other simulations were performed across the span of this entire

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163 study that required the v ast computing resources as well, and i t is estimated that well over 50,000 simulations were performe d Radionuclide S Values Monoenergetic photon and electron SAFs may be useful in and of themselves for academic purposes, but radionuclide S values are needed to perform relevant clinical dosimetry studies. S AFs provide necessary information about the internal geometry of the patient phantom and radiation energy, but they do not directly estimate the radiation absorbed dose to radiosensitive organs. Radionuclide S values give the radiation absorbed dose to a target organ of interest from a source organ of interest for a particular radionuclide of interest per nuclear disintegration in the source tissue the formulation of which is given in Equation 2 39 When combined with the total number of disintegrations in the source tissue, repeated and summed over all source tissues, the final absorbed dose estimate to the target tissue of interest is determined (Equation 2 36) (2 39 ) where is the S value to target tissue from source tissue in units of is the SAF to target tissue from source tissue for radiation of energy and is t he yield of the radiation. This equation is summed over all radiation emission types A MATLAB TM code was written to calculate radionuclide S values for all source target combinations detailed in the monoenergetic photon and electron models based on provided radionuclide emission energies and yields. Monoenergetic photons (gamma rays and x rays ), monoenergetic electrons (Aug er and internal conversion (IC) electrons), and beta particles were considered for contributions to the S value. ICRP Publi cation 107 was used for radionuclide spectra information (energies and yields) (ICRP 2008) The methodology for implementing

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164 Equation 2 39 for monoenergetic photon and electrons emissions was relatively straightforward since each photon and electron emiss ion had an associated absolute yield. Absolute yield refers to the number of particles emitted per nuclear disintegration at the energy of interest (Attix 2004) The code cycles through each radiation energy and yield, and at each energy the SAF for all source target combinations is calculated by log linear interpolation between the two nearest energy points for which the SAFs were evaluated. For both monoenergetic photons and electrons if the energy is less than and the pre computed monoenergetic SAF at is greater than zero, the energy specific SAF is log linearly back extrapolated. Beta particle yields were given in units of number of beta particles per nuclear transformation per so th e methodology for monoenergetic photons and electrons could only be applied once the beta spectra were converted into absolute yields. This was done by reconstituting the beta spectra into absolute yield spectra by breaking up the spectra into energy bins and calculating the absolute yield at each energy bin. For the continuous spectra, absolute yield at each energy would be calculated using Equation 2 40 (2 40 ) where is the absolute beta yield at energy and is the beta yield density However, Equation 2 40 was reduced to Equation 2 41 for practical implementation. (2 41 ) where is the absolute beta yi eld at energy is the beta yield density, and is an arbitrary energy bin width for which was evaluated. When approximating a continuous function with discrete bins, care must be taken in selecting the bin width. A sensi tivity study was performed to determine the point at which the approximately SAFs

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165 from the UFH00MF phantoms were used to calculate the S value beta contributions for 90 The beta spectrum was taken from ICRP Publication 107 (ICRP 2008) An energy bin width of was chosen as the finest energy bin width that would be selected and was considered the energy bin width that would give the most accurate S value estimate for reaso nable computation times S values were calculated using additional energy bin widths of and for comparison. 99m and 90 radionuclide beta component of the S values were computed at these energy bin widths and compared to the beta component of the S values computed when using a bin width of Differences in results were seen for 90 at the bin width of up to about (as compared to results from the reference bin width of ) and differ ences in results were seen for 99m at the bin width of up to about Statistically insignificant ( ) differences were seen for 90 at an energy bin width of It was quickly determined that the difference between the 90 and 99m results was due to the difference in overall number of bins. At the energy bin width, with a maximum beta particle energy of the 90 beta spectrum had 4561 bins while for the same energy bin width, 99m had 873 bins due to the maximum beta particle energy of 99m was reevaluated using an energy bin width of an energy bin width that would yield 4561 total bins. The difference between the bin width results and the bin width re sults for 99m were statistically insignificant ( ). Since computation time was reasonable for 4561 energy bins, a round number of 5000 energy bins was selected for all radionuclides. This number of energy bins should ensure that the accuracy of t he beta component of the S values will not depend on the numerical methods in the code.

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166 Biokinetics Radionuclide S values give the dosimetric information regarding the radionuclide and phantom of interest. Biokinetic information information regarding how the radiopharmaceutical distributes throughout the body, is needed to determine the source tissues in which the radiopharmaceutical localizes and to calculate the number of radioactive decays in those source tissues using both physical and biologic al half lives As an example, the radiopharmaceutical 99m dimercaptosuccinic acid (DMSA) was selected for demonstration of biokinetic analysis. The total number of radioactive decays must be calculated for each organ that retains the radiopharmaceutical a s described by in Equation 2 22 This was defined as the AA multiplied by the total number of nuclear transformations per unit AA for each source tissue An alternative approach, one that was used in the current study, is to simply multiply the radionuclide S value for the source tissue of interest by the total number of nuclear transformations in that source tissue to obtain an absorbed dose per unit AA. Then, the dose for a variety of AAs may be calculated. The total number of nuclear tr ansformations in each source tissue takes into account both the physical and biological half lives. The source tissues for 99m were determined to be the left and right kidneys (the kidney cortex was assumed to receive all of the kidney activity), liver, spleen, urinary bladder contents, heart contents, lungs, and rest of body (Arnold et al. 1975, Evans et al. 1996, Smi th et al. 1996) For illustration purposes, t he biodistribution parameters for the newborn patient can be seen in Table 2 19 (Arnold et al. 1975, Smith et al. 1996) Blood kinetics were a nalyzed separately to obtain the total number of nuclear transforma tions in the lung and heart contents.

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167 From the information in Table 2 19 as well as additional information not reported here, the total number of nuclear transformations were calculated based on Equations 2 22 and 2 42 (Faw et al. 1999) : (2 42 ) w here is the fractional maximum uptake, is the fractional initial uptake, is the uptake rate in units of is the clearance rate in units of is the effective clearance rate in an d is the time dependent fractional injected activity. Equation 2 42 was integrated over all time to obtain the tissue specific radiopharmaceutical number of nuclear transformations as detailed in Equation 2 22 In depth biokinetic analysis was be yond the scope of this study, so the biokinetic calculations were simply patterned after a previous completion of the 99m biokinetic analysis (Evans et al. 1996) For any subsequent studies requiring dose calculations using biokinetics of a r adiopharmaceutical, the methodology outlined in this section was used. It is important to note that uncertainties associated with the biokinetic models generally greatly outweigh those associated with the internal dose parameters obtained through radiation transport. Uncertainties in the radiation transport simulations arise from three main contributions (1) uncertainties in the modeling algorithm, (2) uncertainties in the internal anatomic structure of the phantoms, and (3) uncertainties in the tissue c ompositions and densities of the phantoms. Uncertainties in the modeling algorithm are probably the least of all uncertainty contributions between the biokinetic models and internal dose parameter calculations due to relatively well understood physical ph enomena and modeling methods. Uncertainties in the internal structure and tissue compositions and densities are reduced through definitions with regard to actual patient data. The internal anatomy in the UF phantoms was based on actual patient images, an d

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168 tissue elemental compositions and densities were based on population averages of actual measurements (ICRP 2002). Uncertainties in biokinetic model could potentially arise from 4 main contributions (1) uncertainties in the structure of the biokinetic m odels, (2) uncertainties in applications of human data, (3) uncertainties in inter element extrapolations of biokinetics, and (4) uncertainties in inter species extrapolations of biokinetic data (Leggett 2001). For most relevant radionuclides, human data is available and is the preferred method for developing biokinetic models (Leggett 2001). However, even when biokinetic data is available, a quote on page 201 of Leggett (2001) ith potentially large inter subject variability in the biokinetics of an element; short observation periods, coupled with potentially large intra subject variability; use of unhealthy subjects whose diseases may alter the biokinetics of the element; paucit y of observations for women and children; collection of small, potentially non representative samples of tissue; inaccuracies in measurement techniques; uncertainty in the pattern of level of intake of the element; atypical study conditions; and inconsiste It is evident from this quote that there are many ways uncertainty is introduced in the development of biokinetic models. It is important to keep this in perspective because it is always attempted to minimize the uncertainties in the internal dose factors developed in the current study, but in reality the final internal dose factor uncertainties will probably always be less than those of the biokinetic modeling. Dosimetric Sensitivity Studies The analyses up to this point have bee n directed at developing internal dosimetry models applicable to phantoms that are ICRP reference That is, the phantoms are a reference set of phantoms that apply to the average individual by height and weight (ICRP 2002) These phantoms may be applied as an estimate for patient dosimetry, but there is a high probability that

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169 the patient for whom the dosimetry is being performed is not 50 th percentile in either height and /or weight. In these cases, dose estimates based on the ICRP reference phantoms is more desirable than crude estimates using outdated or simplified models, but they may not truly represent the individual undergoing the nuclear medicine exam. To further personalize dose estimates provided by this work, dosimetric sensitivity studies were performed to attempt to characterize changes in radiation absorbed dose with changes in a variety of measureable parameters. The goal was to develop equations that could be implemented within the internal dosimetry software or to generate sets of LUT sty le scaling factors These equations or scaling factors would require the input of known organ masses, known organ separations, and p atient sitting height and weight Other parameters were introduced as they were found relevant. Based on these inputs, th e reference dose measure could be scaled to better predict the actual dose to CNPX would be created. T he final implementation of this section of the dissertation will be based on user selection of either explicit definition of either organ volumes or morphometric characteristics. Presumably, one would not typically be able to readily extract organ volumes for every single scan in a clinic, so morphometry based internal dosimetry scaling will probably be used more frequently. If organ volumes are available, the user will select the organ specific dose scaling would be applied based on the entered organ volumes. If organ volumes are not available, the user will select the morphometry in Anthropometri sitting height and waist circumference.

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170 Variation in Source and Target Size and Separation Sphere studies Self dose A computational study in MCNPX was designed t o examine the r elationship between radiation absorbed dose and source / target region size and separation For the self dose study, t wenty one spheres were constructed with masses ranging from to The spheres were assigned a density of and a tissue composition of average adult male soft tissue, as defined in Report 46 of the International Commission on Radiation Units and Measurements (ICRU) (ICRU 1992) The surrou nding medium consist ed of ICRU Report 46 average adult male soft tissue and represented an surrounding medi a. Photons were simulated first to both investigate the validity of the MIRD Pamphlet No. 11 recommendation to us e a mass ratio scaling f actor of for photon self dose scaling and attempt to predict dose scaling algorithms for photon cross dose (Snyder et al. 1975) Uniform photon sources were simulated within each source sphere, and the energy deposited in the source sphere was recorded. Based on MIRD Pamphlet No. 11, it was cl ear that changes in photon self dose with changes in tissue size could be predicted to assume some power of the ratio of masses of the reference tissue size and non reference tissue size (Snyder et al. 1975) However, MI RD Pamphlet No. 11 simplified the power to a single number that could be applied for a select range of energies (Snyder et al. 1975) although the scaling power is actually applied across all energies in OLINDA/EXM 1.0 This study used the general formula provided by MIRD Pamphlet No. 11 to develop energy and mass dependent scaling powers, and the formula is given in Equation 2 43 (Snyder et al. 1975) Additionally, the scaling power is given in Equation 2 44

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171 (2 43 ) (2 44 ) where is the SAF from source tissue to target tissue where and are the same tissue at initial photon energy for non reference tissue mass is the SAF from source tissue to target tissue where and are the same tissue at initial photon energy for the reference tissue mass and is the scaling power as a function of initial photon energy reference tissue mass and non reference tissue mass The primary difference between this study and the MIRD Pamphlet No. 11 recommendation was that the MIRD recommendation treated the scaling power, as a constant while this study treated it as a function of three variables (Snyder et al. 1975) In this study, it was predicted that the scaling power was not only dependent upon the energy of the photons emi tted, but it was also dependent upon the s ize of the tissue in question (e.g ., scaling photon self dose for the pituitary gland could be different than scaling photon self dose for the brain due to differences in original organ size ). SAFs for all combina tions of tissue masses and photon energies were computed by dividing the energy deposited in the source/target tissue and the initia l photon energy, and the resulting value of was computed using Equation 2 44

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172 MIRD Pamphlet No. 11 also recommended that the electron self dose SAFs scaled as the inverse of the ratio of reference to non reference masses (Snyder et al. 1975) The same anal ysis was completed for monoenergetic electrons at the energies equal to those simulated for photons to further examine this recommendation All photons and electrons created during transport were tracked, and energy deposition in the target tissues of int erest was recorded. The same methodology for determining scaling factors used for the photon simulations was additionally applied to the electron simulations. Cross dose For the cross dose study, seventeen spheres were constructed with masses of to since was the upper limit for discrete (non distributed) organ masses in the adult male phantom (Lee et al. 2010) The spheres were assigned a density of and a tissue composition of average adult male soft tissue, as defined by ICRU Report 46 (ICRU 1992) The surrounding medium consisted of ICRU Report 46 average adult male soft tissue and Each sphere mass was simulated as a source tissue with every sphere included as a ta rget tissue The set of target spheres was incrementally placed away from the source sphere with an initial center to center separation of approximately equal to the diameter of the largest sphere, and a final center to center separation of greater than the largest discrete organ to organ separation seen in the UF hybrid phantom family (~ from the urinary bladder wal l to the brain) with a total of five equal increments. P hoton energies and particle histories used for the photon SAF simulations were used for these simulations as well Energy deposition accounting for all photons and electrons created during the simul ation was recorded in all target spheres. The default photon and electron cutoff energy of was used, and the ITS style nearest bin algorithm was selected for electron energy indexing. A visual representation of the

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173 simulation geometry is in Figure 2 1 5 Previous studies have determined radiation absorbed cross dose from a source tissu e to a target tissue to be relatively insensitive of changes in source and target tissue masses (Petoussi Henss et al. 2007) However, these studies did not investigate this issue in a rigorous fashion, and this study aimed to further test this matter. I n addition, the current study investigated changes in absorbed dose with variations in separation. The SAFs for all source target energy combinations were calculated as the energy deposited in the target tissue of interested divided by the mass of the targ et tissue and the initial energy of the photons No scaling equations were predicted beforehand, so results were examined upon completion for any trends or need for further analysis. The cross dose study was not immediately repeated for electrons because it was hypothesized that results for electrons would be insufficient for two reasons (1) poor statistical uncertainties at the defined center to center separations and (2) no primary electron dose contributions at any of the center to center separations. Because of this, photon cross dose was first analyzed, and electron cross dose was addressed after the photon results were processed The electron cross dose computational experiment is described in Chapter 3. Validation studies The MCNPX sphere studies were designed to attempt to predict dosimetric sensitivity trends by somewhat eliminating the dependen ce on the shape of the tissue of interest. It was hypothesized that by simulating objects of the same shape but different sizes, the dose to non reference size organs could be predicted since the general shape of the organ would be similar to that in the reference case. Obviously, individual variability will introduce error in the predictions since organ shapes in the actual patient will most likely vary to some degree from the shape of

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174 the reference organs Despite this the sphere approach was determin ed to be the most However, before any scaling methods could be applied to the monoenergetic SAFs, the results of the dosimetric sensitivity studies required validation so actual hybrid phantoms were used to test th e self dose scaling powers and any cross dose trends that were discovered To assist the investigation into the efficacy of any discovered photon or electron dose scaling techniques, patient specific phantoms constructed by Johnson et al. (2011) were uti lized. Patient specific phantoms were generated by segmenting CT image sets of each patient to create three dimensional organ and body volumes. The phantom resulting from the segmentation was a very good physical model of the patient of interest but d ue to human error from subjective visual examination of the images, patient specific models should not be considered perfect. CT image sets of 14 adult male patients and 13 adult female patients covering broad ranges of height and weight were segmented to cr eate patient specific phantoms (Johnson et al. 2011) These CT image sets were chest abdomen pelvis (CAP) scans, so tissues in the head and legs were not present (Johnson et al. 2011) Several organs were difficult to visualize in the scans, so only the pericardium, liver, spleen, stomach wall, stomach contents, pancreas, kidneys, urinary bladder wall, urinary bladder contents, skeleton, subcutaneous fat, and outer body contour were segmented (Johnson et al. 2011 ). All phantoms were voxelized at an isotr opic resolution of (Johnson et al. 2011) BEXXAR ( 131 Tositumomab) and Zevalin ( 90 ibritumomab tiuxetan) were selected as the radiolabled antibodies for analysis ICRP Publication 107 was consulted for radionuclide spectra for 131 and 90 (ICRP 2008) Photons were simulated for 131 and beta particles were simulated for 90 The package inserts for BEXXAR and Zevalin were

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175 consulted (as well as a case study for BEXXAR) to determine possible source tissues for simulation (GlaxoSmithKl ine 2005, Spect rum Pharmaceuticals, Inc. 2011, Hong et al. 2010) The liver and spleen were selected as the source tissues, and all tissues segmented in the patient specific phantoms were treated as target tissues Liver and spleen self dose were of inte rest for the self dose validation studies, and liver to pancreas cross dose was of interest for the cross dose validation studies. Radionuclide spectra were directly sampled and uniformly distributed throughout each source tissue. All photons and electron s created during transport were followed until reaching the lower bound energy cutoff where the remaining energy was assumed to be locally deposited. Energy deposition in all target tissues was recorded, and the radionuclide S value was calculated using E quation 2 45 (2 45 ) where is the radionuclide S value from source tissue to target tissue is a unit conversion coefficient, is the energy deposited in target tissue from source tissue is t he yield of the radiation, and is the mass of target tissue Tissue densities and material compositions were taken from ICRP Publication 89 (ICRP 2002) Ten million particle histories were simulated to ensure adequate uncertainti es. A particle energy cutoff of was used as well as the ITS style nearest bin electron energy indexing algorithm. The applications of these patient specific simulations will be discussed in the next section. Photon self dose To demonstrate t he effectiveness of the scaling powers obtained in the self dose study, the masses of the liver and thyroid of the UFH00M phantom were both increased and decreased by isotropically scaling both tissues in Rhinoceros TM The liver was scaled from

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176 the refere nce voxelized mass of to both and smaller and larger than the reference mass respectively. The thyroid was scaled from the reference voxelized mass of to both and smaller and larger, respectively. Each o rgan was voxelized separately at the resolution used for the SAF calculations, Instead of 131 or 90 99m was selected as the radionuclide of interest for these validation studies. The photon spectrum of 99m was simulated separate ly in each source tissue as uniformly distributed throughout the organ. ICRP Publication 107 was consulted for the photon energy spectrum (ICRP 2008) Energy deposition was recorded in both organs, and the photon component of the radionuclide S value was calculated using Equation 2 23 Then, the SAFs from both source tissues calculated in the reference UFH00M phantom were used in conjunction with the scaling powers developed in the photon self dose scaling study to calculate the non reference photon comp onent of the 99m S value. In addition, the MIRD Pamphlet No. 11 recommendation of a mass ratio scaling power of was also used with the 99m S value, and the result s was compared with those found using the scaling powers calculated in the current study. To ascertain any energy dependent phenomena, the same liver and thyroid self dose irradiation scenario was repeated using monoenergetic and photon s. Energy deposition accounting for all photons and electrons created during the simulation was recorded in all target tissues. The default photon and electron cutoff energy of was used, and the ITS style nearest bin algorithm was selected for e lectron energy indexing. Ten million particle histories were simulated to ensure reasonable statistical uncertainties. While the previous validation study looked at applying the sphere studies to isotropic scaling of the UF hybrid phantom organs, a seco nd validation study was performed to test the

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177 results on an actual patient. A patient specific phantom of the torso for an adult fe male constructed in Johnson et al. (2011) (discussed ealier) was used to calculate the self dose photon component of the 99m radionuclide S value for the liver and spleen To discover any energy dependent phenomena, the same irradiation geometry was simulated using monoenergetic and photons. The patient chosen for the study had a voxelized liver mass of and a voxelized spleen mass of as compared to the UFHADF liver and spleen masses of and respectively. T he patient specific phantom representing this patient can be seen in Fig ure 2 1 6 The 99m photon spect rum was taken from ICRP Publication 107 (ICRP 2008) Energy deposition was recorded in the target tissues of interest, and the S value was calculated using Equation 2 39 Like the previous isotropic scaling validation study, reference photon SAFs for the UFHAD F phantom were scaled using both the mass ratio scaling powers developed in the current study and the MIRD Pamphlet No. 11 recommendation, and the results were compared The default photon and electron cutoff energy of was used, and the ITS style nearest bin algorithm was selected for electron energy indexing. Ten million particle histories were simulated to ensure reasonable statistical uncertainties. To further investigate the accuracy of the photon self dos e scaling methodology, results from the patient specific internal dose simulations were analyzed Uniform 131 photon sources were simulated in the liver and spleen of all the patient specific phantoms. Both UF and MIRD photon self dose scaling methodol ogies were applied to the UFHADM and UFHADF liver and spleen self dose S values based on the reference masses of the liver and spleen and non reference masses from each patient specific phantom. The UF and MIRD results were compared and analyzed to determ ine the more appropriate scaling approach.

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178 Electron self dose Electron self dose was validated using the same processes described for the photon self dose validation study comparing self dose scaling as applied to the UFH00M hybrid phantom and as appli ed to a patient specific adult female phantom However, the 99m monoenergetic electron spectrum was used instead of the 99m photon spectrum, according to data in ICRP Publication 107 (ICRP 2008) Additionally, the dosimetry results from the serie s of patient specific adult male and adult female phantoms were utilized to compare electron self dose scaling approaches. Uniform 90 beta sources were simulated in the liver and spleen of all the patient specific phantoms. Mirroring the approach in th e photon self dose study, the reference UFH00M UFHADM, and UFHADF SAF s w ere scaled using the MIRD Pamphlet No. 11 recommendation and the mass ratio scaling powers calculated in the present study and combined to yield the electron component of the radionuc lide S value s and the results were compared. Photon cross dose From the outset, it was unclear what scaling methodology (if any) would materialize upon examination of the cross dose simulation results. Despite this, two validation studies were created to check any scaling techniques that may have developed. A sphere study was first conducted to validate the results. Mimicking the geometry stated in the cross dose sphere study 4 and the target sphere was with a separation of sphere set was constructed so that the source sphere was the target sphere was and the separation was A visual representation of the dif fering irradiation geometries may be seen in Figure 2 1 7 Monoenergetic photons at were simulated, and energy deposition was recorded in the target tissues. Energy deposition was then divided by the initial energy of 4 Unit density spheres in an infinite soft tissue medium with the elemental composition set to that of the adult in ICRP Publication 89 (ICRP 2002)

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179 the photons and the mass o f the target to obtain the SAF. This study was repeated using the photon spectrum of 99m obtained from ICRP Publication 107 (ICRP 2008) Since the reference and non reference SAF s were known, any scaling factors developed in the photon cross dose st udy could be applied to the reference SAF and the result compared to the actual n o n reference SAF. Scaling factors were also applied to all reference SAFs needed to compute the 99m radionuclide S value. The default photon and electron cutoff energy o f was used, and the ITS style nearest bin algorithm was selected for electron energy indexing. Ten million particle histories were simulated to ensure reasonable statistical uncertainties. A second phantom based validation study was performed in which the liver and pancreas of the UFHADM phantom were scaled to smaller volumes and translated slightly The reference masses of the liver and pancreas for the UFHADM phantom were and respectively, and the non reference masses o f the liver and pancreas for the UFHADM phantom were and respectively. Reference and non reference center to center separations were determined using the volume centroid feature in Rhinoceros TM Centroids of the liver and pancreas wer e recorded, and the separation was calculated using basic vector mathematics. The reference and non reference separations were and respectively. A uniform photon source was simulated in the pancreas and the liver was tr eated as the target tissue. This was then repeated for the 99m photon spectrum, as defined in ICRP Publication 107 (ICRP 2008) All photons and electrons were tracked during simulation, and energy deposition was recorded in the liver The reference UFHADM SAF for the pancreas liver irradiation combination was then scaled using any scaling methodologies discovered during the cross dose sphere study and compared to the actual non reference SAF for the photons Reference SAFs were scaled in the same way for the 99m photon spectrum and

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180 combined to yield the photon component of the radionuclide S value. The default photon and electron cutoff energy of was used, and the ITS style nearest bin algorithm was selected for electron ener gy indexing. Ten million particle histories were simulated to ensure reasonable statistical uncertainties. To further investigate the accuracy of the photon cross dose scaling methodology, results from the patient specific internal dosimetry simulations were used. Uniform 131 photon sources were simulated in the liver of all patient specific phantoms, and the cross dose S values to the pancreas were calculated. The volume centroid feature in Rhinoceros TM was utilized to measure the center to center non reference distances f or each patient specific phantom. Liver and pancreas masses for all patient specific phantoms were calculated and used for dose scaling. Electron cross dose Electron cross dose was difficult to assess before the SAF scaling analysis was performed becaus e cross dose for electrons behaves quite differently than for photons. S ince primary electron dose contributions depend heavily on the surface shape and surface to surface distance of the source and target tissues, the primary electron dose contribution w ould probably not be able to be scaled since defining these parameters in the clinic is very difficult. It was predicted that the radiative contribution to dose could be effectively scaled to non reference conditions but not the primary electron contribut ion to dose. Bearing this in mind, a validation study was designed to address the radiative dose component alone. A phantom based validation study was performed in which the liver and brain of the UFHADM phantom were scaled to smaller volumes and translat ed slightly The reference masses of the liver and brain for the UFHADM phantom were and respectively, and the non reference masses of the liver and brain for the UFHADM phantom were and respectively. A uniform electron source was simulated

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181 in the liver, and the brain was treated as the target tissue. The 82 beta spectrum 5 was also simulated in the liver according to data in ICRP Publication 107 (ICRP 2008) The reference UFHADM SAF for the brai n liver irradiation combination was then scaled using any scaling methodologies discovered during the cross dose sphere study and compared to the actual non reference SAF for the electrons. Reference SAFs were scaled in the same way for the 82 beta spectrum and combined to yield the beta component of the radionuclide S value. The non reference beta component of the 82 radionuclide S value was subsequently compared to the predicted S value. Reflecting the validation approach to photon c ross dose scaling, results from the patient specific internal dosimetry simulations were utilized to assess the efficacy of the electron cross dose scaling method Uniform 90 beta sources were simulated in the liver of all patient specific phantoms, and the SAF to the pancreas was calculated. The volume centroid feature in Rhinoceros TM was utilized to measure the center to center non reference distances for each patient specific phantom. Liver and pancreas masses for all patient specific phantoms were calculated and used for dose scaling. Variation in Anthropometric Characteristics Reference phantoms are ideally suited to act as computation dosimetry models for an average population but are inadequately suited to serve the role of patient specific mode ls because reference phantoms are average in height and weight (ICRP 2002) Chances are that patients undergoing nuclear medicine procedures are not average in height and weight. Therefore, steps were taken to address this issue. 5 The 82 beta spectrum was used in lieu of 99m monoenergetic electron spectrum because the 82 beta spectrum had a higher average beta particle energy than the average 99m monoenergetic electron energy and was thus expected to give more statistically reliable results.

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182 The UF ALRADS research g roup developed a library of phantoms that covered a large percentage of patient morphometries seen on a day to day basis (Johnson et al. 2009) Primary target parameters were defined as standing height, sitting height, and total body mass, and secondary t arget parameters were defined as waist, buttocks, arm, and thigh circumferences (Johnson et al. 2009) A set of phantoms were created with each of these parameters derived from the National Health and Nutrition Examination Surveys (NHANES) conducted by th e National Center for Health Statistics of the CDC (Johnson et al. 2009) The NHANES III database covering 33,994 individuals between 2 months and 90 years of age from years 1988 to 1994 was consulted when deriving the previously mentioned morphometric pa rameters (Johnson et al. 2009) Statistical analysis was performed to create 25 adult male and 25 adult female phantoms at standing height percentiles of 10 th 25 th 50 th 75 th and 90 th with weight percentiles of 10 th 25 th 50 th 75 th and 90 th at each standing height (Johnson et al. 2009) Average values of sitting height were calculated at each standing height, average values of waist, buttocks, arm, and thigh circumferences were calculated at each standing height/weight combination (Johnson et al. 20 09) The same analysis was performed for pediatric ages but standing height bins were created rather than standing height percentiles for a total of 100 pediatric phantoms (Johnson et al. 2009) Morphometric parameterization for standing height as a fun ction of total body mass for the pediatric male population can be seen in Fig ure 2 1 8 (Johnson et al. 2009) This figure demonstrates the grid of phantoms that was created to represent a population of patients. The library of phantoms was created by modi fying one of the ICRP reference phantoms (known in this case as an anchor phantoms) by scaling the upper body in 3 D to match sitting height and then the legs to match standing height (Johnson et al. 2009) Next, the secondary parameters

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183 were matched by b oth uniformly and non uniformly scaling arm, thigh, waist, and buttocks circumferences (Johnson et al. 2009) If a patient came for a nuclear medicine procedure, the phantom that mostly closely matched the morphometric characteristics of the patient would be selected to perform dosimetry. The computational phantom library published by Johnson et al. (2009) is currently undergoing an update in the UF ALRADS research group with up to date data, but the concept of a phantom library remains the same. Despite the advantage of having a library of computational phantoms, performing Monte simulation times needed for reasonable results. The monoenergetic photon and electron SAFs previously developed were incorporated into a MATLAB TM computer code so that on the fly dose estimates could be provided for the average individual. Instead of performing the same immensely time consuming task of generating monoenergetic pho ton and electron SAFs for all of the phantoms in the library, several studies were done to attempt to develop patient specific scaling relationships based on in clinic measureable morphometric characteristics such as sitting height, body circumferences, an d weight. These scaling relationships would be applied to the ICRP reference set of phantoms for which the detailed simulations were already completed. Sitting height While organ sizes have been shown to correlate fairly well with standing height (Grandma ison et al. 2001) s itting height was isolated as a possible metric by which reference dose estimates could be scaled because it is intuitive that the size of important internal organs would correlate more closely with changes in the trunk of the body rath er than the length of the legs This is because standing height is heavily influenced by leg length. Because the chest cavity expands or contracts with increases or decreases in sitting height relative to the reference sitting height of the anchor phanto ms from which the library of phantoms was derived, it was

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184 expected that radiation absorbed doses to tissues of interest would be affected by the change in position and size of organs within the chest cavity. Therefore, a computational study was designed t o attempt to derive a correlation between changes in dose from internal emitters and changes in sitting height. Two phantoms of shorter stature and two phantoms of taller stature were created using the UFH00M, UFH10M, and UFHADM as the anchor phantoms for a total of 12 scaled phantoms. All tissues except those located in the legs of the phantoms were scaled in 3 D consistent with the methodology described in Johnson et al. ( 2009 ) to achieve these different statures. NURBS/PM models of the UFH00M phantom s created for the sitting height study are in Fig ure 2 1 9 The phantoms were all voxelized at the resolutions used for the monoenergetic photon and electron simulations. P hantom morphometric measurements are in Table 2 20 and voxel resolutions and total matrix sizes are in Table 2 21 Uniform monoenergetic photon and electron sources were simulated in the brain, liver, lungs, and spleen. A whole body AM source was simulated based on the AM mass distributions of the UFH00M, UFH10M, and UFHADM phantoms (e .g., the tallest scaled UFHADM based phantom was assigned an AM distribution of the UFHADM reference phantom). Tissues simulated as targets in the monoenergetic photon and electron SAF simulations were used in this sitting height study. Fifteen monoenerg etic photon and electron energies were simulated based on the energies used in the monoenergetic SAF simulations. Each energy selected was assigned a particle history value consistent with those given in the monoenergetic SAF simulations. The tally struc ture was identical to that used in the monoenergetic SAF simulations except that full transport was run for the electron simulations rather than the separate CEL/REL simulations A

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185 particle energy cutoff of was used as well as the ITS style neare st bin electron energy indexing algorithm. Weight Previous studies had shown that radiation absorbed doses do not heavily depend on increases in subcutaneous fat (Clark et al. 2010) but dose dependencies for underweight individuals were not examined. It would be expected that internal doses would not change much, if at all, for increases in subcutaneous fat because the internal structure of the patient remains fairly constant 6 Only the absorbed dose to subcutaneous fat and possibly the skin would be exp ected to change noticeably. However, when underweight individuals were modeled in the UF patient dependent computational phantom library, some were scaled in 2 D to match the waist and buttocks circumferences (Johnson et al. 2009) According to a French autopsy study correlating changes in organ size with changes in anthropometric characteristics, the 2 D scaling technique created reasonably accurate organ sizes (Johnson et al. 2009) However, individual variability is unavoidable, and a range of organ s izes was noted. As a result of two dimensional scaling for underweight individuals, organ volumes decrease, and the separation between the organs decreases. Dose variation for underweight individuals was therefore expected, and a dosimetric sensitivity s tudy was created similar to that created for variations in sitting height. Two underweight phantoms and one overweight phantom were created using the UFH00M, UFH10M, and UFHADM as the anchor phantoms for a total of 9 scaled phantoms. The underweight phant oms were created by decreasing the a rm, thigh, waist, and buttocks circumferences through 2 D scaling in the transverse plane The overweight phantom was 6 Clark et al. (2010) showed that some dose variations could occur depending on intra abdominal fat deposits. However, the current study does not consider any fat deposits aside from the subcutaneous fat layer.

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186 created by increasing the arm, thigh, waist, and buttocks circumferences in addition to adding subcut aneous fat elsewhere in the body. NURBS/PM models of the UFH00M phantoms created for the weight study are in Figure 2 20 The phantoms were all voxelized at the resolutions used for the monoenergetic photon and electron simulations. Phantom morphometric measurements are in Table 2 22 and v oxel resolutions and total m atrix sizes are in Table 2 23 Uniform monoenergetic photon and electron sources were simulated in the brain, liver, lungs, and spleen. A whole body AM source was simulated based on the AM mass distributions of the UFH00M, UFH10M, and UFHADM phantoms (e.g., the thinnest scaled UFHADM based phantom was assigned an AM distribution of the UFHADM reference phantom). Tissues simulated as targets in the monoenergetic photon and electron SAF simul ations were used in this weight study. Fifteen monoenergetic photon and electron energies were simulated based on the energies used in the monoenergetic SAF simulations. Each energy selected was assigned a particle history value consistent with those giv en in the monoenergetic SAF simulations. The tally structure was identical to that used in the monoenergetic SAF simulations except that full transport was run for the electron simulations rather than the separate CEL/REL simulations A particle energy c utoff of was used as well as the ITS style nearest bin electron energy indexing algorithm. Constant weight with morphometry variation When pediatric patients undergo nuclear medicine imaging procedures, one of several AA scaling equations may be u sed to adjust the amount of radiopharmaceutical given to the patient ( Equation 2 46 Equation 2 47 Equation 2 48 Rule ( Equation 2 49 ) (Radi o pharmacy, Inc. 2004) weight and age.

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187 (2 46 ) (2 47 ) (2 48 ) (2 49 ) where is the scaled administered activity for the pediatric patient, is the administered activity that would be given to an adult patient for the exam of interest, is the weight of the pediatric patient in pounds, is the age of the pediatric patient in years, and is the age of the pediatric patient in months. More recently, pediatric radiopharmaceutical dose guidelines were released that are based on weight only (Gelfand et al. 2011) These equations attempt to adjust the AA because pediatric patients have less attenuating material between the source of radiation emission and the detectors in the imaging system. As a result, less AA is needed to create an image with diagnostic value equal to that achieved when giving a higher AA to an adult patient. The decreased AA ensures good diagnostic quality while reducing the radiation exposure to the child. However, even though the described scaling equations are a first attempt at personaliz ing the AA to the patient they do not account for body morphometry. Two pediatric patients at the same weight but different statures could be given a diagnostic nuclear medicine exam with the same AA. In this c ase, one patient could be short and heavy while the other is tall and thin. The tall patient has less attenuation than the short patient,

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188 so better diagnostic quality would result for the tall patient. One of two situations would then present itself (1 ) the tall patient could be given less AA if the diagnostic quality for the short patient was adequate or (2) the short patient could be given more AA if the diagnostic quality for the short patient was inadequate. In the first case, the radiation absorbe d dose to the tall patient would be reduced while in the second case, the diagnostic quality of the image generated for the short patient would be improved. The AA scaling equations do not account for this scenario, so a dosimetric sensitivity study was d esigned to examine this further. This particular body morphometry study has been looked at recently but a second study was performed to uncover any possible dosimetric trends. Two phantoms were constructed at the same weight but different heights The l atest UF patient dependent phantom library was consulted when selecting the weight at which the phantoms would be constructed, and the common weight was set to The short, heavy phantom was constructed based on the UFH10F phantom, and the tall, thin phantom was constructed based on the UFH15F phantom. N URBS/PM models of the phantoms created for the body morphometry study are in Fig ure 2 2 1 Both phanto ms were voxelized at the resolutions used for the monoenergetic photon and electron simulations. Phantom morphometric measurements are in Table 2 24 and v oxel resolutions and total matrix sizes are in Table 2 25 Instead of simulating monoenergetic photo ns and electrons, the photon and monoenergetic electron (Auger and IC electrons) spectra for 99m were directly sampled and simulated u niform ly in the heart chambers, kidney cortex, liver, lungs, muscle, spleen, and urinary bladder contents, consistent with the source tissues of interest for 99m the same radiopharmaceutical modeled i n the study by Sgouros et al. (2011) Radionuclide spectra were obtained from ICRP Publication 107 (ICRP 2008) and only photons (both x rays and gamma

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189 rays) and Auger and IC electrons were simulated since the delta value, a measure in units of indicating the contribution of a particular radiation type to dose, for the 99m beta particles was on the order of while the delta values for photons and monoenergetic electrons were on the order of and respectively (IC RP 2008) Tissues that were simulated as targets in the monoenergetic photon and electron SAF simulations were used in this body morphometry study. Ten million particle histories were simulated, and t he tally structure was identical to that used in the m onoenergetic SAF simulations except that full transport was run for the electron simulations rather than the separate CEL/REL simulations A particle energy cutoff of was used as well as the ITS style nearest bin electron energy indexing algorithm. Validation studies Dose scaling based on anthropometric characteristics was the goal of the phantom based dosimetric sensitivity study, so ultimately the results wou ld be applied to the UF reference hybrid phantom monoenergetic SAFs. To verify the efficacy of this method, a series of validation studies were performed, and the general process was as follows: 1. Create a unique non reference phantom based on one of the re ference phantoms that was scaled in the dosimetric sensitivity study. 2. Separately simulate a photon and electron spectrum in one source tissue within the reference phantom using MCNPX v2.6 and determine the radionuclide S values to all target tissues of int erest. 3. Calculate the radionuclide S values to all target tissues of interest for the reference phantom upon which the unique non reference phantom is based, applying scaling factors estimated in the phantom based dosimetric sensitivity study. 4. Compare the a ctual non reference S values to the scaled reference S values for both photons and electrons. Scaling the reference SAFs should yield more accurate estimates of radionuclide S values for a non reference phantom than radionuclide S values for the reference phantom. If this is the case, the dosimetric sensitivity studies will improve dose estimates for individual dosimetry.

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190 improved for an imaginary patient dependent p hantom, not a patient specific phantom, since the scaling methodology was developed based on the original reference hybrid phantoms. Sitting height Conditions of the sitting height dose variation study were such that dose variations were valid for unifor m 3 D scaling of the torso of the UF hybrid phantoms with no additional weight adjustments. As this is the case, three non reference phantoms were scaled from the reference UFH00M, UFH10M, and UFHADM phantoms (one scaled phantom per anchor phantom), and u niform photon and electron sources were separately simulated within the liver of each phantom. The 131 photon spectrum and 90 beta spectrum were selected, and the radiation energies and yields were obtained from ICRP Publication 107 (ICRP 2008) Any dose scaling techniques derived from the anthropometric variation sitting height dose sensitivity study were applied to the reference SAFs at each radiation energy and combined to yield the photon component of the 131 radionuclide S value and the beta component of the 90 radionuclide S value. Scaling techniques for the UFH00M phantom were applied to pr ovide estimates for the UFH00M based non reference phantom, scaling techniques for the UFH10M phantom were applied to provide estimates for the UFH10M based non reference phantom, and scaling techniques for the UFHADM phantom were applied to provide estima tes for the UFHADM based non reference phantom. These scaled results were compared to the actual radionuclide S values obtained for the three non reference phantoms through simulation in MCNPX v2.6 to determine the efficacy of dose scaling based on sittin g height. In both the photon and electron simulations, all particles created during transport were tracked. Ten million particle histories were simulated, and the tally structure was identical to that used in the monoenergetic SAF simulations except that full transport was run for the electron simulations rather than the separate

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191 CEL/REL simulations A particle energy cutoff of was used as well as the ITS style nearest bin electron energy indexing algorithm. The physical characteristics of the sitting height based validation phantoms were as follows: UFH00M based non reference phantom with a sitting height of and a weight of UFH10M based non reference phantom with a sitting height of and a weight of UFHADM based non reference phantom with a sitting height of and a weight of Weight The patient dependent phantoms based on the UFHADM reference phantom described at the beginning of this section were simulated with uniform photon ( 131 spectrum) and electron ( 131 monoenergetic electron and beta spectra and 90 beta spectrum) sources in the liver of each phantom The 50 th percentile by height phantoms were used for the weight dose variation validation study because several phantoms were available at a constant sitting height but varying weights. Scaling factors developed in the weight dose variation stud y were applied to reference UFHADM monoenergetic SAFs to calculate the photon component of the radionuclide S value for 131 and the beta component of the radionuclide S value for 90 for the non reference 50 th percentile by height phantoms. These results were compared to the actual radionuclide S values found using MCNPX v2.6 for each of the non reference 50 th percentile b y height phantoms All explicitly simulated patient dependent phantoms at the 50 th height percentile were selected for comparison. Two additional phantoms were created for comparison purposes one based on the UFH00M phantom and one based on the UFH10M p hantom. One scaled phantom was created for each reference phantom, holding the height constant and varying the weight. The weight for the UFH00M phantom was decreased, and the weight for the UFH10M phantom was increased

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192 to capture trends in both circumst ances. Photons and electrons were simulated in the liver of these phantoms via the 131 photon spectrum and 90 beta spectrum using MCNPX v2.6. Scaling methods discovered in the weight dose variation study were applied to reference UFH00M and UFH10M mo noenergetic SAFs to calculate the photon and electron components of the radionuclide S value s for 131 and 90 respectively, for the non reference 50 th percentile by height phantoms. These results were compared to the actual radionuclide S values found using MCNPX v2.6. The physical characteristics of the weight based validation phantoms were as follows (excluding the previously defined UFHADM based phantoms) : UFH00M based non reference phantom with a sitting height of a weight of and a waist circumference of UFH10M based non reference phantom with a sitting height of a weight of and a waist circumference of Arbitrary morphometry The approach used for validating dose dependencies o n variations in patient weight was used to validate the combination of the sitting height and weight scaling factors. Previously constructed patient dependent phantoms described earlier were used to simulate 131 and 90 sources in the liver of each pha ntom The key difference for analyzing a combinatorial approach to dose scaling is that phantoms at non 50 th percentile height were used. Radionuclide S values for 131 and 90 were calculated for phantoms of various weights at non 50 th percentile heig hts by applying scaling factors derived from the sitting height and weight dose variation studies to the UFHADM reference monoenergetic SAFs. These results were compared to the actual radionuclide S values found using MCNPX v2.6. All explicitly simulated non 50 th percentile by height / non 50 th percentile by weight patient dependent phantoms were selected for comparison.

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193 Two additional phantoms were created for comparison purposes one based on the UFH00M phantom and one based on the UFH10M phantom. One scaled phantom was created for each reference phantom, varying both the height and weight. Height was increased, and weight was decreased for the UFH00M phantom. Height was decreased, and weight was increased for the UFH10M phantom. Photons and electron s were simulated in the liver of these phantoms via the 131 photon spectrum and 90 beta spectrum using MCNPX v2.6. Scaling methods discovered in the height and weight dose variation studies were combined and applied to reference UFH00M and UFH10M monoenergetic SAFs to calculate the photon and electron compone nts of the radionuclide S values for 131 and 90 respectively for the non reference phantoms. These results were compared to the actual radionuclide S values found using MCNPX v2.6. The physical characteristics of the combined height and weight vali dation phantoms were as follows (excluding the previously defined UFHADM based phantoms) : UFH00M based non reference phantom with a sitting height of a weight of and a waist circumference of UFH10M based non reference pha ntom with a sitting height of a weight of and a waist circumference of Internal Dosimetry Software Development of the internal dosimetry software is a collaborative effort between researchers at UF and the National Cance r Institute (NCI) of the National Institutes of Health (NIH). Initial software development was completed at UF in the MATLAB TM coding language and will be migrated to a more easily deployable format at NCI. Therefore, all graphical user interfaces (GUIs) will be developed at NCI while the core coding originated at UF. Development of the internal dosimetry code is an ongoing process. The dosimetry code was primar il y written by Laura Padilla of the ALRADS research group at UF to include her work towards in ternal dosimetry fo r arbitrarily inserted tumors.

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194 However, radionuclide spectrum generation and the S value algorithm were developed by both researchers and cross verified. Radionuclide spectra were taken from ICRP Publication 107 (ICRP 2008) Methodolo gy behind the S value algorithm was previously discussed in the Chapter 2 Non reference dose scaling will be addressed in Chapters 3 and 4 Any apparent dose trends were applied in the dosimetry code with simple scaling mechanisms. For instance, if waist circumference was identified as a dose nent organs based on the identified scaling equation. In this software, the user is able to select the radionuclide (and multiple radionuclides) and phantom (and multiple phantoms). The user is then able to enter the total number of nuclear transformation s for all relevant source tissues, non reference tissue masses and body measures, and total AA. Based on these inputs, the software extracts pre calculated radionuclide S values (to save computation time, S values were pre calculated for all phantoms in t he UF series) performs any necessary dose scaling, and applies the total number of nuclear transformations to calculate absorbed doses to all target tissues per unit AA in addition to total absorbed doses based on the given AA. Effective dose is also pro vided using the tissue weighting factors (radiation weighting factors for both photons and electrons are unity) from ICRP Publication 103 (ICRP 2007) In addition to these necessities Laura Padilla developed a tumor insertion feature which allows the user to define an ellipsoidal tumor from definition of the and axes. Using a ray trace algorithm, the code uses a point kernel method to determine the dose from

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195 source tissues to the tumor and vice versa. This feature will be more fully described in Laura D dissertation.

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196 Table 2 1 B lood vessel wall thicknesses for the newborn to 1 year old and adult reference individuals for the arterial, venous, and pulmonary systems Adapted from ICRP Publication 23 (I CRP 1975) Wall Thickness Age / system Blood vessel Gender (mm) N ewborn to one year of age Aorta M/F 0.830 Pulmonary artery M/F 0.790 Carotis communis artery M/F 0.550 Superior vena cava M/F -Inferior vena cava M/F -Adult arterial system Aorta Ascending M 1.630 F 1.480 Descendin g M 1.200 F 1.110 Abdominalis M 1.140 F 1.080 Arteries Common iliac M 0.930 F 0.890 Common carotid M 0.910 F 0.810 Small arteries M/F 0.800 Arterioles M/F 0.020 Capillaries M/F 0.001 Adult v enous system Venae cavae Superior M/F 1.500 Inferior M/F 1.500 Veins M/F 0.500 Venules M/F 0.002 Adult pulmonary system Arteries M 1.270 F 0.960 Veins M/F -Capillaries M/F -Maximum M/F 1.630 Minimum M/F 0.001 Average M/F 0.905

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197 Table 2 2 Width, height, and depth measurements and isotropic voxel resolutions for all bone sites in the UFH01MF, UFH05MF, and UFH10MF phantoms. Bone size (cm) Voxel resolution (cm) UFH01MF UFH05MF UFH10MF Site Width Depth Height Width Depth Height Width Depth Height UFH01MF UFH05MF UFH10MF Cranium 12.74 15.25 13.32 14.08 16.69 14.91 14.69 17.20 15.57 0.0363 0.0401 0.0417 Mandible 7.50 5.75 4.35 10.06 7.23 5.69 10.4 6 7.69 5.83 0.0151 0.0197 0.0205 Scapulae 15.01 3.33 6.19 24.40 4.77 8.93 28.66 6.88 12.53 0.0179 0.0268 0.0357 Clavicles 14.09 3.41 1.19 21.01 4.65 1.32 24.99 4.10 3.91 0.0102 0.0133 0.0195 Sternum 1.89 3.07 5.75 3.26 3.24 8.05 4.39 5.21 10.38 0.0085 0.0116 0.0164 Ribs 15.36 9.20 15.99 20.53 11.94 23.44 23.71 15.32 29.06 0.0347 0.0473 0.0580 Vertebrae C 3.86 3.63 5.82 4.23 4.25 6.03 6.63 6.17 7.82 0.0115 0.0126 0.0181 Vertebrae T 4.33 3.64 14.56 4.44 5.31 19.77 6.79 7.54 26.03 0.0162 0.0205 0.0291 Vertebrae L 3.79 3.94 10.59 5.45 5.94 10.61 6.87 7.38 14.29 0.0143 0.0185 0.0237 Sacrum 4.56 3.75 5.61 6.66 5.56 7.35 7.03 6.47 10.06 0.0121 0.0171 0.0204 Os Coxae 11.92 5.32 9.19 19.63 6.88 12.41 22.75 10.12 18.36 0.0221 0.0314 0.0427 Femora 3.23 2.51 15.85 4.99 4.00 26.84 8.62 5.92 34.89 0.0133 0.0215 0.0320 Ti biae 2.76 2.16 13.53 4.05 3.10 22.34 6.71 4.80 29.00 0.0114 0.0173 0.0258 Fibulae 1.56 1.33 13.30 2.10 2.32 21.94 2.55 2.93 28.50 0.0080 0.0126 0.0158 Patellae 1.26 0.58 0.91 2.50 1.16 2.64 3.59 1.62 2.95 0.0023 0.0052 0.0068 Ankle s and feet 3.42 8.34 3.23 4.86 13.00 5.27 6.79 18.36 7.35 0.0119 0.0183 0.0257 Humera 5.57 2.97 14.10 5.76 3.69 20.95 8.78 5.41 27.54 0.0163 0.0202 0.0289 Radii 1.34 2.22 10.58 1.73 2.83 15.47 2.63 4.60 20.44 0.0084 0.0112 0.0166 Ulnae 2. 01 2.72 11.22 3.33 2.93 16.85 3.83 4.30 22.04 0.0104 0.0145 0.0189 Wrists and hands 2.91 5.63 7.24 2.50 5.77 11.17 4.15 8.60 14.61 0.0130 0.0144 0.0213

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198 Table 2 3 T otal matrix sizes and voxel numbers by width, depth, and height for all bone sites in the UFH01MF, UFH05MF, and UFH10MF phantoms. Number of voxels Matrix size ( x 10 6 ) UFH01MF UFH05MF UFH10MF Site Width Depth Height Width Depth Height Width Depth Height UFH01MF UFH05MF UFH10MF Cranium 360 426 37 4 352 447 384 346 438 376 57.36 60.42 56.98 Mandible 501 391 297 517 378 298 508 383 290 58.18 58.24 56.42 Scapulae 822 304 337 900 169 320 804 194 354 84.21 48.67 55.22 Clavicles 1356 327 137 1562 371 110 1272 219 212 60.75 63.75 59.06 Sternum 209 380 673 282 270 678 261 310 635 53.45 51.62 51.38 Ribs 452 267 462 436 254 499 418 265 503 55.76 55.26 55.72 Vertebrae C 331 332 511 398 406 468 359 451 444 56.15 75.62 71.89 Vertebrae T 263 269 894 226 348 947 227 456 891 63.25 74.48 92.23 Vertebrae L 321 327 579 282 327 572 296 516 601 60.78 52.75 91.79 Sacrum 3 58 309 466 395 502 422 336 315 478 51.55 83.68 50.59 Os Coxae 544 246 413 624 219 401 531 237 419 55.27 54.80 52.73 Femora 276 200 1178 255 239 1246 264 285 1099 65.03 75.94 82.69 Tibiae 270 194 1166 209 325 1264 142 220 851 61.08 85.86 26.59 Fibulae 193 238 1623 141 151 1711 213 188 1787 74.55 36.43 71.56 Patellae 575 225 441 457 293 453 495 216 453 57.05 60.66 48.43 Ankles and feet 287 700 269 268 708 286 267 711 280 54.04 54.27 53.15 Humer a 340 187 860 285 194 1031 296 189 946 54.68 57.00 52.92 Radii 153 274 1236 163 264 1381 146 272 1219 51.82 59.43 48.41 Ulnae 216 274 1073 226 194 1146 202 226 1159 63.50 50.25 52.91 Wrists and hands 168 394 516 169 399 761 174 405 672 34. 16 51.31 47.36

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199 Table 2 4 Percent regional blood distribution in the ICRP reference adult male and female Adapted from ICRP Publication 89 (ICRP 2002) Blood content (% total blood volume) Organ / t issue Male Female Fat 5.00 8.50 Brain 1.20 1. 20 Stomach and esophagus 1.00 1.00 Small intestine 3.80 3.80 Large intestine 2.20 2.20 Right heart 4.50 4.50 Left heart 4.50 4.50 Coronary tissue 1.00 1.00 Kidneys 2.00 2.00 Liver 10.00 10.00 Pulmonary 10.50 10.50 Bronchial tissue 2.00 2.00 Skel etal muscle 14.00 10.50 Pancreas 0.60 0.60 Skeleton 7.00 7.00 Red marrow 4.00 4.00 Trabecular bone 1.20 1.20 Cortical bone 0.80 0.80 Other skeleton 1.00 1.00 Skin 3.00 3.00 Spleen 1.40 1.40 Thyroid 0.06 0.06 Lymph nodes 0.20 0 .20 Gonads 0.04 0.02 Adrenals 0.06 0.06 Urinary bladder 0.02 0.02 All other tissues 1.92 1.92 Aorta and large arteries 6.00 6.00 Large veins 18.00 18.00

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200 Table 2 5 Total blood volumes in the ICRP reference human series Adapted from ICRP Publi cation 89 (ICRP 2002) Blood volume (L) Age Male Female Newborn 0.27 0.27 1 year 0.50 0.50 5 years 1.40 1.40 10 years 2.40 2.40 15 years 4.50 3.30 Adult 5.30 3.90 Table 2 6 Derived vascular growth scaling factors for the brain, kidneys, trabe cular bone, and cortical bone for the ICRP reference human series. Skeleton Trabecular Cortical Age Brain Kidneys b one b one Newborn 1.04 0.67 4.7 2.6 1 year old 1.16 0.67 4.7 2.6 5 year old 1.39 1.00 4.4 2.4 10 year old 1.33 1.00 4.0 2.2 15 year old 1.13 1.00 3.7 1.9 Adult 1.00 1.00 1.0 1.0

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201 Table 2 7 Derived regional blood distributions for the ICRP reference pediatric human series and ICRP reference adult regional blood distributions (ICRP 2002) Blood distribution (%) Newbor n 1 year old 5 year old 10 year old 15 year old Adult Organ/Tissue Male Female Male Female Male Female Male Female Male Female Male Female Fat 5.73 5.78 9.32 9.47 5.94 6.04 5.35 5.43 3.90 7.68 5.00 8.50 Brain 6.42 5.57 6.97 6.09 5.31 4.18 3.25 2.47 1.59 1.47 1.20 1.20 Stomach and esophagus 0.92 0.78 1.00 0.85 1.10 0.94 1.13 0.96 0.95 0.93 1.00 1.00 Small intestine 3.41 2.88 3.77 3.20 4.48 3.80 4.53 3.83 3.65 3.57 3.80 3.80 Large intestine 1.97 1.57 2.26 1.82 2.48 2.00 2.61 2.10 2.14 1.99 2.20 2.20 Ri ght heart 4.42 4.74 3.21 3.47 4.15 4.48 4.25 4.57 4.56 4.22 4.50 4.50 Left heart 4.42 4.74 3.21 3.47 4.15 4.48 4.25 4.57 4.56 4.22 4.50 4.50 Coronary tissue 1.19 1.22 1.16 1.20 0.91 0.94 0.90 0.92 0.85 0.96 1.00 1.00 Kidneys 2.13 1.87 2.31 2.04 2.49 2.2 0 2.45 2.16 1.96 1.91 2.00 2.00 Liver 14.31 14.33 14.04 14.14 11.13 11.21 9.74 9.79 8.76 10.16 10.00 10.00 Pulmonary 5.52 5.59 8.22 8.37 7.73 7.89 9.15 9.31 9.76 9.85 10.50 10.50 Bronchial tissue 1.06 1.04 1.58 1.56 1.51 1.50 1.73 1.72 1.85 1.88 2.00 2. 00 Skeletal muscle 7.58 7.33 7.03 6.84 9.50 9.25 11.22 10.90 14.06 11.16 14.00 10.50 Pancreas 0.50 0.45 0.65 0.59 0.52 0.47 0.54 0.49 0.57 0.54 0.60 0.60 Skeleton 9.38 9.83 11.84 12.50 11.06 11.66 11.52 12.10 10.86 12.04 7.00 7.00 Red marrow 3.32 3.36 3.89 3.96 4.05 4.12 4.51 4.58 4.44 4.82 4.00 4.00 Trabecular bone 4.02 4.30 5.34 5.75 4.67 5.03 4.56 4.90 4.15 4.70 1.20 1.20 Cortical bone 1.43 1.53 1.93 2.08 1.72 1.85 1.67 1.80 1.42 1.61 0.80 0.80 Other skeleton 0.61 0.64 0.68 0.7 1 0.63 0.66 0.79 0.82 0.85 0.92 1.00 1.00 Skin 3.09 3.46 2.41 2.71 1.80 2.03 1.56 1.75 2.19 2.40 3.00 3.00 Spleen 1.76 1.58 2.05 1.86 1.62 1.47 1.56 1.41 1.46 1.52 1.40 1.40 Thyroid 0.08 0.07 0.04 0.04 0.04 0.03 0.05 0.05 0.04 0.05 0.06 0.06 Lymph node s 0.19 0.17 0.21 0.20 0.18 0.17 0.18 0.17 0.18 0.19 0.20 0.20 Gonads 0.02 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.02 0.01 0.04 0.02 Adrenals 0.50 0.42 0.13 0.11 0.07 0.06 0.06 0.05 0.05 0.05 0.06 0.06 Urinary bladder 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 All other tissues 1.52 1.29 1.38 1.17 1.47 1.40 1.60 1.48 1.38 1.17 1.92 1.92 Aorta and large arteries 5.97 6.31 4.29 4.57 5.58 5.94 5.59 5.93 6.16 5.51 6.00 6.00 Large veins 17.90 18.93 12.88 13.71 16.73 17.82 16.76 17.80 18.48 16. 52 18.00 18.00

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202 Table 2 8 Derived regional blood volumes for the ICRP reference pediatric human series and ICRP reference adult regional blood volumes (ICRP 2002) Blood volume (cm 3 ) Newborn 1 year old 5 year old 10 year old 15 year old Adult Orga n/Tissue Male Female Male Female Male Female Male Female Male Female Male Female Fat 15.67 15.82 46.60 47.35 84.06 85.46 126.28 128.07 176.43 253.51 264.15 328.77 Brain 17.55 15.24 34.84 30.43 75.08 59.11 76.59 58.19 72.11 48.42 63.40 46.42 Stomach and esophagus 2.52 2.13 4.99 4.24 15.56 13.24 26.75 22.70 42.97 30.68 52.83 38.68 Small intestine 9.33 7.87 18.85 15.99 63.37 53.79 106.73 90.38 165.45 117.87 200.75 146.98 Large intestine 5.38 4.30 11.28 9.08 35.15 28.31 61.61 49.50 97.08 65.61 116.23 85.09 Right heart 12.09 12.97 16.07 17.34 58.69 63.39 100.13 107.89 206.49 139.29 237.74 174.06 Left heart 12.09 12.97 16.07 17.34 58.69 63.39 100.13 107.89 206.49 139.29 237.74 174.06 Coronary tissue 3.25 3.34 5.80 6.00 12.81 13.25 21.13 21.81 38.30 31.80 5 2.83 38.68 Kidneys 5.83 5.12 11.53 10.18 35.30 31.18 57.85 50.98 88.62 63.07 105.66 77.36 Liver 39.16 39.19 70.21 70.70 157.51 158.68 229.68 230.85 396.81 335.50 528.30 386.79 Pulmonary 15.11 15.31 41.08 41.87 109.44 111.60 215.87 219.61 441.98 325.39 5 54.72 406.13 Bronchial tissue 2.89 2.85 7.88 7.82 21.40 21.24 40.88 40.48 83.70 61.93 105.66 77.36 Skeletal muscle 20.74 20.07 35.13 34.19 134.47 130.95 264.51 256.99 636.57 368.53 739.62 406.13 Pancreas 1.37 1.23 3.25 2.94 7.39 6.69 12.69 11.46 25.66 1 7.89 31.70 23.21 Skeleton 25.67 26.90 59.21 62.52 156.56 165.05 271.75 285.33 491.55 397.56 369.81 270.75 Red marrow 9.09 9.20 19.45 19.81 57.27 58.34 106.27 108.00 200.95 159.06 211.32 154.72 Trabecular bone 10.99 11.77 26.71 28.77 66.08 71.2 0 107.53 115.58 187.82 155.15 63.40 46.42 Cortical bone 3.91 4.18 9.65 10.39 24.27 26.15 39.43 42.38 64.30 53.12 42.26 30.94 Other skeleton 1.68 1.75 3.39 3.56 8.93 9.37 18.51 19.37 38.48 30.22 52.83 38.68 Skin 8.46 9.45 12.07 13.56 25.53 28.7 0 36.78 41.25 98.95 79.36 158.49 116.04 Spleen 4.81 4.32 10.27 9.28 22.99 20.79 36.84 33.23 66.03 50.11 73.96 54.15 Thyroid 0.21 0.19 0.20 0.19 0.50 0.46 1.17 1.08 1.96 1.52 3.17 2.32 Lymph nodes 0.51 0.47 1.04 0.98 2.56 2.42 4.33 4.06 8.35 6.25 10.57 7 .74 Gonads 0.05 0.02 0.07 0.04 0.10 0.14 0.11 0.25 1.00 0.39 2.11 0.77 Adrenals 1.37 1.14 0.65 0.54 1.05 0.87 1.47 1.22 2.33 1.49 3.17 2.32 Urinary bladder 0.09 0.08 0.14 0.13 0.32 0.31 0.49 0.48 0.87 0.63 1.06 0.77 All other tissues 4.16 3.52 6.90 5.8 6 20.84 19.87 37.77 34.98 62.60 38.61 101.43 74.26 Aorta and large arteries 16.32 17.27 21.47 22.85 78.93 84.05 131.74 139.95 279.00 181.80 316.98 232.08 Large veins 48.96 51.80 64.42 68.56 236.79 252.15 395.22 419.86 837.00 545.41 950.94 696.23

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203 Table 2 9 Derived regional blood distribution in volume percent for the UF series of hybrid computational phantoms. Phantom Tissue UFH00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Adipose tissue (separable) 8.68 12.43 8.77 7.91 5.88 11.04 7.46 12.69 Adrenals 0.69 0.16 0.10 0.08 0.08 0.06 0.09 0.09 Brain 9.03 8.63 6.93 4.19 2.40 2.11 1.79 1.79 Cartilage 0.94 0.65 0.29 0.24 0.13 0.14 0.08 0.06 Cortical bone 2.23 2.65 2.61 2.55 2.14 2.31 1.19 1.19 Ears 0.16 0.10 0.14 0.08 0.09 0.07 0.23 0.16 Esophagus 0.28 0.24 0.25 0.27 0.29 0.27 0.31 0.30 External nose 0.05 0.06 0.09 0.12 0.06 0.04 0.14 0.25 Extrapulm. bronch. + trachea 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 Heart 1.82 1.56 1.35 1.34 1.28 1.38 1.49 1.49 Kidneys 3.02 2.87 3.44 3.38 2.95 2.75 2.98 2.99 Large intestine 2.66 2.69 3.28 3.45 3.24 2.86 3.28 3.28 Liver 21.60 18.64 16.35 14.33 13.23 14.61 14.92 14.93 Lung 9.95 13.03 13.59 16.06 17.49 16.84 18.62 18.63 Lymph nodes 0.27 0.27 0.26 0.26 0.28 0.27 0.30 0.30 Muscle 11.25 9.17 13.7 2 16.22 21.22 16.05 20.88 15.67 Nasal layers 0.09 0.06 0.18 0.14 0.12 0.10 0.22 0.19 Oral cavity layer 0.08 0.01 0.03 0.02 0.05 0.09 0.02 0.03 Ovaries 0.02 0.01 0.01 0.01 0.03 0.02 0.06 0.03 Pancreas 0.72 0.82 0.73 0.75 0.86 0.78 0.89 0.90 Penis 0.09 0.10 0.17 0.12 0.29 0.00 0.26 0.00 Pharynx 0.03 0.02 0.04 0.03 0.03 0.03 0.02 0.03 Salivary glands 0.68 0.62 0.73 0.68 0.71 0.73 0.81 1.31 Scrotum 0.19 0.08 0.07 0.03 0.24 0.00 0.47 0.00 Skin 4.94 3.39 2.81 2.43 3.30 3.46 4.47 4.48 Small intestine 4.7 4 4.61 6.05 6.13 5.51 5.13 5.67 5.67 Spinal cord 0.73 0.64 0.67 1.05 0.49 0.62 0.69 0.89 Spleen 2.51 2.58 2.26 2.18 2.20 2.18 2.09 2.09 Spongiosa and medullary cavities 11.32 12.81 13.74 14.56 14.12 14.86 9.17 9.19 Stomach 1.00 0.98 1.24 1.27 1.15 1.07 1.18 1.19 Testes 0.02 0.01 0.01 0.01 0.03 0.02 0.06 0.03 Thyroid 0.11 0.05 0.05 0.07 0.07 0.07 0.09 0.09 Urinary bladder wall 0.05 0.04 0.03 0.03 0.03 0.03 0.03 0.03

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204 Table 2 10. Derived regional blood masses for the UF series of hybrid computational phantoms. Phantom Tissue UFH00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Adipose tissue (separable) 16.17 67.45 93.68 140.52 182.12 292.83 280.90 351.39 Adrenals 1.29 0.86 1.06 1.49 2.41 1.72 3.37 2.48 Brain 16.88 46.97 74.46 74.79 74.44 55.93 67.42 49.61 Cartilage 1.76 3.51 3.07 4.19 3.87 3.72 2.87 1.71 Cortical bone 4.15 14.37 27.84 45.16 66.37 61.35 44.94 33.07 Ears 0.30 0.52 1.46 1.42 2.78 1.91 8.64 4.54 Esophagus 0.53 1.33 2.66 4.79 8.88 7.11 11.79 8.27 External nose 0.09 0.34 1. 02 2.09 1.84 0.97 5.36 6.80 Extrapulm. bronch. + trachea 0.03 0.11 0.23 0.45 0.86 0.72 1.12 0.83 Heart 3.39 8.47 14.40 23.72 39.53 36.73 56.18 41.34 Kidneys 5.63 15.62 36.82 60.25 91.48 72.85 112.36 82.68 Large intestine 4.99 14.67 35.20 61.60 100.21 7 5.79 123.60 90.95 Liver 40.24 101.17 174.76 254.47 409.61 387.53 561.80 413.40 Lung 18.54 70.71 145.25 285.10 541.78 446.67 701.13 515.92 Lymph nodes 0.50 1.45 2.76 4.64 8.62 7.22 11.24 8.27 Muscle 20.97 49.80 146.78 288.31 657.11 425.68 786.52 434.07 Nasal layers 0.18 0.30 1.97 2.46 3.80 2.65 8.24 5.37 Oral cavity layer 0.16 0.08 0.27 0.30 1.63 2.31 0.73 0.92 Ovaries 0.04 0.08 0.13 0.20 1.03 0.45 2.25 0.83 Pancreas 1.34 4.45 7.80 13.36 26.48 20.67 33.71 24.80 Penis 0.17 0.54 1.84 2.21 8.98 0.00 9. 92 0.00 Pharynx 0.06 0.12 0.43 0.55 0.93 0.81 0.82 0.80 Salivary glands 1.28 3.40 7.77 12.02 21.99 19.39 30.65 36.20 Scrotum 0.35 0.41 0.72 0.54 7.35 0.00 17.65 0.00 Skin 9.19 18.37 29.92 43.05 102.15 91.67 168.54 124.02 Small intestine 8.85 25.09 64. 93 109.20 170.79 136.15 213.48 157.09 Spinal cord 1.36 3.47 7.12 18.65 15.32 16.56 25.86 24.75 Spleen 4.69 14.06 24.24 38.78 68.17 57.88 78.65 57.88 Spongiosa and medullary cavities 21.07 69.46 146.71 258.27 437.16 394.13 345.45 254.59 Stomach 1.86 5.3 2 13.30 22.61 35.47 28.32 44.39 33.07 Testes 0.04 0.08 0.13 0.20 1.03 0.45 2.25 0.83 Thyroid 0.20 0.28 0.53 1.24 2.02 1.75 3.37 2.48 Urinary bladder wall 0.09 0.19 0.35 0.54 0.90 0.72 1.12 0.83

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205 Table 2 11 Voxel resolutions applied to the UF hybrid p hantom family and resulting matrix sizes. Voxel Resolution (cm) Number of Voxels Total Matrix Phantom X direction Y direction Z direction X direction Y direction Z direction Size ( x 10 6 ) UFH00MF 0.0663 0.0663 0.0663 350 215 720 54.18 UFH 01MF 0.0663 0.0663 0.1400 396 253 550 55.10 UFH05MF 0.0850 0.0850 0.1928 416 235 576 56.31 UFH10MF 0.0990 0.0990 0.2425 428 226 580 56.10 UFH15M 0.1250 0.1250 0.2832 414 226 590 55.20 UFH15F 0.1200 0.1200 0.2828 410 238 574 56.01 U FHADM 0.1579 0.1579 0.2207 362 195 796 56.19 UFHADF 0.1260 0.1260 0.2700 390 241 610 57.33 Table 2 12 Voxel resolution study showing doses calculated for a fine and course resolution phantom. Uniform photon source in the liver of the UFH15F phantom. S value (mGy/MBq s) Target Tissue Fine Resolution Coarse Resolution Difference Brain 4.78E 08 4.76E 08 0.39% Breast 2.16E 06 2.17E 06 0.44% Esophagus 2.30E 06 2.30E 06 0.22% Gall bladder wall 1.26E 05 1.27E 05 0.68% Kidneys 2.25E 06 2 .26E 06 0.22% Liver 1.80E 05 1.81E 05 0.30% Lungs 1.91E 06 1.92E 06 0.50% Oral cavity layer 1.63E 07 1.60E 07 1.81% Ovaries 2.64E 07 2.55E 07 3.34% Pancreas 3.16E 06 3.17E 06 0.48% Skin 4.03E 07 4.06E 07 0.68% Stomach wall 3.75E 06 3.77E 06 0. 54% Thyroid 3.40E 07 3.40E 07 0.08% Urinary bladder wall 1.88E 07 1.84E 07 1.96% Uterus 2.27E 07 2.28E 07 0.47%

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206 Table 2 13 Variance of energy deposition with changes in lower bound electron energy cutoff values. Uniform photon source in t he UFH00M liver. Energy Deposition (MeV) Difference (%) Electron Cutoff Energy Electron Cutoff Energy Target 1 keV 10 keV 50 keV 100 keV 10 keV 50 keV 100 keV Adipose tissue 7.175E 02 7.183E 02 7.177E 02 7.174E 02 0.11% 0.03% 0.01% Adrena l glands 2.409E 03 2.406E 03 2.389E 03 2.387E 03 0.13% 0.83% 0.91% Brain 5.429E 03 5.432E 03 5.423E 03 5.432E 03 0.06% 0.11% 0.06% Breasts 1.250E 05 1.115E 05 1.300E 05 1.316E 05 10.81% 3.99% 5.27% Lungs, bronchi, and trachea 1.602E 02 1.597E 02 1.607E 02 1.603E 02 0.28% 0.34% 0.09% Esophagus 5.503E 04 5.425E 04 5.447E 04 5.457E 04 1.42% 1.00% 0.84% Lens 3.567E 06 3.320E 06 2.961E 06 3.184E 06 6.92% 16.99% 10.74%

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207 Table 2 14 Comparison of dosimetry results obtained using the MC NP style bin centered and ITS style nearest bin electron energy indexing algorithms. Uniform photon source in the adipose tissue of the UFH00M phantom. MCNP style ITS style Difference (%) Initial Energy (MeV) Initial Energy (MeV) Initial Energy ( MeV) Target 0.15 4.00 0.15 4.00 0.15 4.00 Adipose tissue 5.85E 03 8.51E 02 5.85E 03 8.57E 02 0.01% 0.63% Adrenals 2.77E 05 5.67E 04 2.78E 05 5.79E 04 0.00% 2.12% Brain 5.24E 04 1.21E 02 5.24E 04 1.21E 02 0.00% 0.07% Breasts 5.33E 07 8.77E 06 5.36E 07 9.74E 06 0.46% 9.99% Cartilage 4.87E 04 9.55E 03 4.87E 04 9.54E 03 0.03% 0.12% Esophagus 7.73E 06 1.48E 04 7.72E 06 1.47E 04 0.06% 1.06% ET1 2.18E 07 4.12E 06 2.17E 07 3.74E 06 0.59% 10.21% Extrathoracic lymph nodes 2.18E 07 3.11E 06 2.13E 07 3.01E 06 1.97% 3.34% Heart Wall 1.06E 04 2.03E 03 1.05E 04 2.02E 03 0.04% 0.64% Kidneys Cortex 9.94E 05 1.94E 03 9.94E 05 1.95E 03 0.02% 0.34% Kidneys Medulla 3.49E 05 6.70E 04 3.49E 05 6.82E 04 0.01% 1.70% Left colon wall 5 .75E 05 1.06E 03 5.75E 05 1.06E 03 0.02% 0.08% Lens 2.71E 07 5.51E 06 2.72E 07 6.21E 06 0.21% 11.27% Liver 7.31E 04 1.43E 02 7.31E 04 1.43E 02 0.00% 0.06% Lungs 2.73E 04 5.54E 03 2.73E 04 5.51E 03 0.01% 0.60% Muscle 7.55E 03 1.46E 01 7.55E 0 3 1.46E 01 0.00% 0.16% Pituitary gland 1.49E 07 3.76E 06 1.48E 07 3.16E 06 0.85% 19.15% Prostate 4.20E 06 8.02E 05 4.20E 06 8.41E 05 0.00% 4.64% Right colon wall 5.75E 05 1.05E 03 5.76E 05 1.06E 03 0.15% 0.36% Salivary glands 1.87E 05 3.87E 04 1.87E 05 3.98E 04 0.04% 2.74% Skin 6.03E 04 8.50E 03 6.03E 04 8.55E 03 0.01% 0.60% Stomach wall 3.97E 05 7.72E 04 3.97E 05 7.70E 04 0.01% 0.36% Testes 3.21E 06 6.67E 05 3.22E 06 6.73E 05 0.25% 0.88% Thoracic lymph nodes 1.36E 06 3.15E 05 1.36E 06 2.92E 05 0.02% 8.02% Thymus 6.07E 05 1.24E 03 6.07E 05 1.23E 03 0.01% 0.34% Thyroid 4.86E 06 1.01E 04 4.86E 06 1.02E 04 0.02% 0.89% Trachea 1.86E 06 3.56E 05 1.86E 06 3.79E 05 0.00% 6.11% Urinary bladder wall 2.35E 05 4.61E 04 2. 36E 05 4.56E 04 0.03% 0.92%

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208 Table 2 15 Source tissues explicitly simulated in the UF hybrid computational phantom series (ICRP 2009) UF ID number (s) Simulated Source Region Acronym 30 Oral cavity O cavity 30 Oral mucosa O mucosa 185 Teeth sur face activity Teeth S 185 Teeth volume activity Teeth V 51 Tongue Tongue 52 Tonsils Tonsils 10 Oesophagus fast Oesophagus f 10 Oesophagus slow Oesophagus s 10 Oesophagus wall Oesophagus 47 Stomach contents St cont 46 Stomach wall St wall 42 Small intestine contents SI cont 41 Small intestine wall SI wall 8 Right colon contents RC cont 7 Right colon wall RC wall 59 Left colon contents LC cont 58 Left colon wall LC wall 38 Rectosigmoid colon contents RSig cont 37 Rectosigmoid colon wall RSig w all 28 Surface of anterior nasal passages ET1 sur 23, 29, 34 Surface of posterior nasal passages + pharynx ( excluding OCL) ET2 sur 23, 29, 34 Sequestered ET2 region (excluding OCL) ET2 seq 71 Lymph nodes in ET region LN ET 6, 53 Bronchi fast Bronchi f 6, 53 Bronchi slow Bronchi s 6, 53 Bronchi bound Bronchi b 6, 53 Bronchi sequestered Bronchi q 26, 27 Bronchioles fast Brchiole f 26, 27 Bronchioles slow Brchiole s 26, 27 Bronchioles bound Brchiole b 26, 27 Bronchioles sequestered Brchiole q 26, 27 Alveolar interstitium AI

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209 Table 2 15. Continued. UF ID number (s) Simulated Source Region Acronym 73, 74 Lymph nodes in thoracic region LN Th 27 Right lung lobe RLung 26 Left lung lobe LLung 3 Right adrenal gland RAdrenal 2 Left adrenal gland L Adrenal 65 Blood vessels of head HBlood 66 Blood vessels of trunk TBlood 67 Blood vessels of arms ABlood 68 Blood vessels of legs LBlood 16 Blood in heart Ht cont a Cortical bone mineral surface C bone S a Cortical bone mineral volume C bone V b Tr abecular bone mineral surface T bone S c Trabecular bone mineral volume T bone V d Cortical bone marrow C marrow e Trabecular bone marrow T marrow f Active bone marrow A marrow 4 Brain Brain 62 RBreast a + RBreast g RBreast 5 LBreast a + LBreast g L Breast 24 Lenses of eye Eye lens 13 Gall bladder wall GB wall 14 Gall bladder contents GB cont 15 Heart wall Ht wall 18 Right kidney cortex RKidney C 20 Right kidney medulla RKidney M 22 Right kidney pelvis RKidney P 17 Left kidney cortex LKidney C 19 Left kidney medulla LKidney M 21 Left kidney pelvis LKidney P 25 Liver Liver 72, 75 86 Lymph nodes, except LN ET + LN TH Lymph

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210 Table 2 15. Continued. UF ID number (s) Simulated Source Region Acronym 64 Muscle Muscle 63 Right ovary ROvary 31 Left ovary LOvary 32 Pancreas Pancreas 35 Pituitary gland P gland 36 Prostate Prostate 39, 60, 61 Salivary glands S glands 43 Skin Skin 44 Spinal cord Sp cord 45 Spleen Spleen 48 Testes Testes 49 Thymus Thymus 50 Thyroid Thyroid 54 Urinary blad der wall UB wall 55 Urinary bladder contents UB cont 56 Uterus/cervix Uterus 1 Adipose/residual tissue Adipose g Rest of body (for blood source simulation) ROB a Cortical bone volume distribution applied to tissue tag ID numbers 151 184. b Trab ecular bone surface distribution applied to tissue tag ID numbers 201 234. c Trabecular bone volume distribution applied to tissue tag ID numbers 201 234. d Total marrow volume distribution in medullary cavities of bone applied to tissue tag ID numbers 213, 214, 217, 220, 225, 226, 229, and 232. e Total marrow volume distribution in spongiosa of bone applied to tissue tag ID numbers 201 212, 215, 216, 218, 219, 221 224, 227, 228, 230, 231, 233 and 234. f Active marro w volume distribution applied to tissue tag ID numbers 201 234. g Ears, external nose, nasal layers, oral cavity layer, pharynx, salivary glands, spinal cord, penis, scrotum, tongue, gall bladder wall, pituitary gland, larynx, thymus, tonsils, breas ts, prostate, and uterus.

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211 Table 2 16 Source tissues mathematically assembled in the UF hybrid computational phantom series (ICRP 2009) UF ID number (s) Calculated Source Region Acronym 23, 29, 30, 34 Surface of posterior nasal passages + pharynx (including OCL region) ET2 sur 23, 29, 30, 34 Sequestered ET2 region (including OCL region) ET2 seq 26, 27 RLung + LLung Lungs 2, 3 RAdrenal + LAdrenal Adrenals 18, 20, 22 Right kidney C+M+P RKidney 17, 19, 21 Left kidney C+M+P LKidney 17 22 RKidney + LKidney Kidneys 31, 65 ROvary + LOvary Ovaries 5, 62 RBreast + LBreast Breast 7, 37, 58 Colon Colon a Total body tissues (total body minus contents of walled organs) T body b Soft tissue (T body mineral bone) S tissue c HBlood + TBlood + ABlood + LBlood + Ht cont + Lung left, blood + Lung, right, blood + blood in organs Blood a All tissues except ROB, RC cont, GB cont, RSig cont, SI cont, St cont, UB cont, LC cont, HBlood, TBlood, ABlood, LBlood, T bone S, and A marrow. b All tissues excep t ROB, RC cont, GB cont, RSig cont, SI cont, St cont, UB cont, LC cont, HBlood, TBlood, ABlood, LBlood, T bone S, A marrow, T bone V, and C bone V. c Blood distribution applied to T marrow, C marrow, T bone V, ROB, HBlood, TBlood, ABlood, LBlood, Mus cle, Adrenals, Oesophagus, St wall, SI wall, Colon, Liver, Pancreas, Ht cont, Brain, Ht wall, Adipose, Skin, Trachea, Bronchi, Lungs, Spleen, Thyroid, Kidneys, UB wall, Testes, Ovaries, Cartilage, C bone V, LN ET, LN Th, and Lymph.

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212 Table 2 17 Targ et tissues explicitly simulated in the UF hybrid computational phantom series (ICRP 2009) UF ID number (s) Target Region Acronym a Active (red) marrow R marrow 46 Stomach wall St wall 47 Stomach contents St cont 48 Testes Testes 54 Urinary bladder wa ll UB wall 55 Urinary bladder contents UB cont 10 Oesophagus wall Oesophagus 25 Liver Liver 50 Thyroid Thyroid b 50 um endosteal region Endost BS 4 Brain Brain 39, 60, 61 Salivary glands S glands 43 Skin Skin 13 Gall bladder wall GB wall 14 Gall bladder contents GB cont 15 Heart wall Ht wall 72, 75 86 Lymph nodes, except LN ET + LN TH Lymph 64 Muscle Muscle 30 Oral mucosa O mucosa 32 Pancreas Pancreas 36 Prostate Prostate 41 Small intestine wall SI wall 42 Small intestine contents SI cont 45 Spleen Spleen 49 Thymus Thymus 56 Uterus/cervix Uterus 51 Tongue Tongue 52 Tonsils Tonsils 7 Right colon wall (ascending + right transverse) RC wall 8 Right colon contents (ascending + right transverse) RC cont 58 Left colon wall (left transvers e + descending) LC wall 59 Left colon contents (left transverse + descending) LC cont

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213 Table 2 17. Continued. UF ID number (s) Target Region Acronym 37 Sigmoid colon wall + rectum wall RSig wall 38 Sigmoid colon contents + rectum contents RSig cont 28 Basal cells of anterior nasal passages ET1 bas 23, 29, 34 Basal cells of posterior nasal passages + pharynx (exluding OCL) ET2 bas 71 Lymph nodes of ET region LN ET 6 Basal cells of bronchi Bronchi bas 6 Secretory cells of bronchi Bronchi sec 26, 27 Secretory cells of bronchioles Brchiol sec 26, 27 Alveolar interstitium AI 73, 74 Lymph nodes in thoracic region LN Th 27 Right lung lobe RLung 26 Left lung lobe LLung 3 Right adrenal gland RAdrenal 2 Left adrenal gland LAdrenal 70 RBreast a + RB reast g RBreast 5 LBreast a + LBreast g LBreast 24 Lenses of eye Eye lens 18 Right kidney cortex RKidney C 20 Right kidney medulla RKidney M 22 Right kidney pelvis RKidney P 17 Left kidney cortex LKidney C 19 Left kidney medulla LKidney M 21 Left k idney pelvis LKidney P 31 Right ovary ROvary 65 Left ovary LOvary 35 Pituitary gland P gland 44 Spinal cord Sp cord 1 Adipose/residual tissue Adipose c Whole body WBody d Rest of body (for blood source simulation) ROB

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214 Table 2 17. Continued. UF ID number (s) Target Region Acronym 65 Blood vessels of head HBlood 66 Blood vessels of trunk TBlood 67 Blood vessels of arms ABlood 68 Blood vessels of legs LBlood a Active marrow skeletal photon fluence to dose response function applied to tissue t ag numbers 201 234. b Total shallow marrow skeletal photon fluence to dose response function applied to tissue tag numbers 201 234. c All tissues except ROB, RC cont, GB cont, RSig cont, SI cont, St cont, UB cont, LC cont, HBlood, TBlood, ABlo od, LBlood, T bone S, R marrow, and Endost BS. d Ears, external nose, nasal layers, oral cavity layer, pharynx, salivary glands, spinal cord, penis, scrotum, tongue, gall bladder wall, pituitary gland, larynx, thymus, tonsils, breasts, prostate, and uterus. Table 2 18 Target tissues mathematically assembled in the UF hybrid computational phantom series (ICRP 2009) UF ID number (s) Calculated Target Region Acronym 7, 37, 58 Colon Colon 17 22 RKidney + LKidney Kidneys 26, 27 RLung + LLung Lungs 2, 3 RAdrenal + LAdrenal Adrenals 23, 28, 29, 30, 34 ET region (including OCL) ET 23, 29, 30, 34 Basal cells of posterior nasal passages + pharynx (including OCL) ET2 bas 5, 70 Breast a + Breast g Breast 31, 65 ROvary + LOvary Ovaries 23, 28, 29, 34 ET region ( excluding OCL) ET 18, 20, 22 Right kidney C+M+P R K idney 17, 19, 21 Left kidney C+M+P L K idney

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215 Table 2 19 Biokinetic parameters for 99m for the newborn patient (Evans et al. 1996) is fractional maximum uptake, is fractional initial uptake, is the uptake rate, is the clearance rate, and is the effective clearance rate. Fraction Excreted Source Tissue A m A o + (h 1 ) (h 1 ) eff (h 1 ) 6 h 24 h Left kidney corte x 0.21 -0.72 0.009 ---Right kidney cortex 0.21 -0.64 0.008 ---Liver -0.057 --0.14 --Spleen -0.016 --0.16 --Urinary bladder contents -----0.066 0.13 Whole body ------

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216 Table 2 20 Morphometric measurements for the phantoms created to assess dosimetric sensitivity as a function of sitting height. Standing Sitting Arm Thigh Waist Buttocks Mass Height Height Circumference Circumference Circumference Circumference Phantom (kg) (cm) (cm) (cm) (cm) (cm) (cm) UFH00M Shortest 1.28 38.95 25.41 9.39 16.46 27.78 27.04 Short 2.38 43.35 29.72 11.61 16.44 32.41 31.63 Reference 3.45 47.37 33.92 13.72 16.96 37.04 36.04 Tall 4.54 51.70 38.16 15.67 16.7 2 41.67 40.53 Tallest 6.07 55.92 42.29 17.38 16.82 46.29 44.91 UFH10M Shortest 17.73 121.25 56.93 14.96 31.27 53.25 54.05 Short 23.77 130.42 66.09 17.46 30.96 62.41 62.59 Reference 32.42 139.86 75.50 19.89 31.23 71.04 71.84 Tall 42.30 149.24 85.39 22.29 31.23 79.89 80.74 Tallest 55.42 158.24 95.20 24.88 31.41 88.69 89.75 UFHADM Shortest 40.35 151.69 70.57 19.86 41.69 73.37 72.88 Short 53.47 162.84 81.71 22.90 42.21 85.57 83.37 Reference 73.08 174.90 92.91 26.17 41.70 97.79 93.97 Tall 93.99 185.88 104.89 29.68 42.20 110.07 107.02 Tallest 122.82 198.23 117.79 32.83 41.65 122.36 114.19

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217 Table 2 21 Voxel resolutions and total matrix sizes for the phantoms created to assess dosimetric sensitivity as a function of sitting height. Voxel Resolution (cm) Number of Voxels Matrix Size Phantom Width Depth Height Width Depth Height ( x 10 6 ) UFH00M Shortest 0.0663 0.0663 0.0663 350 189 593 39.23 Short 0.0663 0.0663 0.0663 350 202 656 46.38 Reference 0.0663 0.0663 0.0663 350 215 720 54.18 Tall 0.0663 0.0663 0.0663 350 228 784 62.56 Tallest 0.0663 0.0663 0.0663 353 242 847 72.36 UFH10M Shortest 0.0990 0.0990 0.0990 322 201 503 32.56 Short 0.0990 0.0990 0.0990 374 211 542 42.77 Reference 0.0990 0.0990 0.0990 428 226 580 56.10 Tall 0.0990 0.0990 0.0990 480 248 619 73.69 Tallest 0.0990 0. 0990 0.0990 533 275 658 96.45 UFHADM Shortest 0.1579 0.1579 0.2207 272 181 690 33.97 Short 0.1579 0.1579 0.2207 317 184 743 43.34 Reference 0.1579 0.1579 0.2207 362 195 796 56.19 Tall 0.1579 0.1579 0.2207 406 206 849 71.01 Tallest 0.1579 0.1579 0.2207 451 220 902 89.50

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218 Table 2 22 Morphometric measurements for the phantoms created to assess dosimetric sensitivity as a function of weight. Standing Sitting Arm Thigh Waist Buttocks Mass Height Height Circumference Circumference Circumference Circumference Phantom (kg) (cm) (cm) (cm) (cm) (cm) (cm) UFH00M Lightest 1.62 47.50 33.84 10.23 11.91 25.24 24.29 Light 2.21 47.50 33.93 11.83 13.64 29.45 28.16 Reference 3.45 47.37 33.92 13.72 16.96 37.04 36.04 Heavy 5.21 47.76 36.04 15.09 22.81 48.73 47.91 UFH10M Lightest 16.37 139.66 75.30 11.81 19.84 52.59 52.52 Light 22.29 140.43 75.56 13.84 23.14 60.66 60.90 Referen ce 32.42 139.86 75.50 19.89 31.23 71.04 71.84 Heavy 53.58 139.92 76.32 30.78 42.50 92.69 94.86 UFHADM Lightest 36.08 175.11 94.04 18.42 27.93 69.64 67.03 Light 49.14 175.69 93.68 21.01 32.32 81.21 77.80 Reference 73.0 8 174.90 92.91 26.17 41.70 97.79 93.97 Heavy 124.85 175.10 94.36 41.84 62.85 126.97 126.79

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219 Table 2 23 Voxel resolutions and total matrix sizes for the phantoms created to assess dosimetric sensitivity as a function of weight. Voxel Resolution ( cm) Number of Voxels Matrix Size Phantom Width Depth Height Width Depth Height ( x 10 6 ) UFH00M Lightest 0.0663 0.0663 0.0663 264 160 720 30.41 Light 0.0663 0.0663 0.0663 306 185 720 40.76 Reference 0.06 63 0.0663 0.0663 350 215 720 54.18 Heavy 0.0663 0.0663 0.0663 350 242 720 60.98 UFH10M Lightest 0.0990 0.0990 0.0990 316 171 580 31.34 Light 0.0990 0.0990 0.0990 368 198 580 42.26 Reference 0.0990 0.0990 0.0990 428 226 580 56.10 Heavy 0.0990 0.0990 0.0990 452 289 580 75.76 UFHADM Lightest 0.1579 0.1579 0.2207 268 145 796 30.93 Light 0.1579 0.1579 0.2207 312 169 795 41.92 Reference 0.1579 0.1 579 0.2207 362 195 796 56.19 Heavy 0.1579 0.1579 0.2207 386 245 796 75.28

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220 Table 2 24 Morphometric measurements for the phantoms created to assess dosimetric sensitivity for patients of similar weight but different body morphometry. St anding Sitting Arm Thigh Waist Buttocks Mass Height Height Circumference Circumference Circumference Circumference Phantom (kg) (cm) (cm) (cm) (cm) (cm) (cm) UFH10F Reference 32.41 139.86 75.50 19.89 31.23 71.04 71.84 Short/h eavy 49.60 135.01 69.74 28.48 50.18 85.33 87.88 UFH15F Reference 52.99 161.33 84.07 28.07 43.47 76.87 80.21 Tall/thin 49.67 174.95 89.25 23.03 42.72 69.20 82.36 Table 2 25 Voxel resolutions and total matrix sizes for the phan toms created to assess dosimetric sensitivity for patients of similar weight but different body morphometry. Voxel Resolution (cm) Number of Voxels Matrix Size Phantom Width Depth Height Width Depth Height ( x 10 6 ) UFH10F Reference 0.0990 0.0990 0.0990 428 226 580 56.10 Short/heavy 0.0990 0.0990 0.0990 286 209 933 55.77 UFH15F Reference 0.1200 0.1200 0.2828 410 238 574 56.01 Tall/thin 0.1200 0.1200 0.2828 296 189 1103 6 1.71

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221 Figure 2 1 Three dimensional stylistic model showing the (A) top, (B) side, and (C) perspective views for an excerpt of the irradiation geometries for the vascular dosimetry computational study.

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222 ( A ) ( B ) ( C ) ( D ) Figure 2 2 Sample heterogeneous skeletal sites of the UF newborn hybrid phantom showing the ( A) h and ( B) r ight h umerus ( C) p elvis and ( D) L spine.

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223 (A) (B) Figure 2 3 (A) Polygon mesh and (B) voxel versions of the UFH01MF femur for use in the SIRT simulations. In the voxel version, dark gray regions are cortical bone and light gray regions are both spongiosa and medullary cavities. Spongiosa Medullary cavity Spongiosa Cortical shell

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224 Figure 2 4 Photon simulation flowchart used to generate monoenergetic photon SAFs.

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225 (A) (B) Figure 2 5 Illustration of artifact correction in ImageJ TM (A) Streaking artifacts in the UF H00M phantom and (B) artifacts corrected. Streaking artifacts

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226 ( A ) ( B ) ( C ) Figure 2 6 UFH00F phantom voxelized at a n isotropic resolution of showing the ( A) axial, ( B) coronal, and ( C) sagittal views Figure 2 7 Number of particle histories simulated as a function of initial photon energy.

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227 (A) (B) Figure 2 8 Visual representation o f (A) uniform and (B) non uniform source sampling. Points of emission were recorded and represented as red spheres in the UFH00M phantom. Arbitrary radiation source in the lungs of the UFH00M phantom.

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228 Figure 2 9 Variance reduction technique flowchart used to improve the reliability of the monoenergetic photon and electron SAFs.

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229 (A) (B) Figure 2 1 0 Reverse Monte Carlo method demonstrating the reciprocity principle showing both (A) raw SAF data and (B) reciprocal data. Uniform photon source in the muscle of the UFH00M phantom.

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230 (A) (B) Figure 2 1 1 Low energy photon back extrapolation method showing both (A) raw SAF data and (B) extrapolated data. Uniform photon source in the anterior nasal layer (ET 1 ) of the UFH00M phantom.

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231 (A) (B) F igure 2 1 2 Three point smoothing method showing both (A) raw SAF data and (B) smoothed data. Uniform photon source in the breasts of the UFH00M phantom.

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232 Figure 2 1 3 Electron simulation flowchart used to generate monoenergetic electron SAFs.

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233 Figu re 2 1 4 Photon energy spectrum generate d from simulating monoenergetic electrons in the liver of the UFH00M phantom. Energy bins were created at intervals from to Photon energies on the horizontal axis represent the upper limit of the energy bin, so the number of photons at a photon energy of represents the number of photons generate d at energies between and The energies in the legend are the initial monoenergetic electron energies. Figure 2 1 5 Graphical depiction of the systematic approach to studying dosimetric sensitivity with changes in source and target tissue size and separation Uniform spherical sources are indicated by the red set of spheres, and targets are indicated by gray sph eres. Sources were also simulated as targets.

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234 Figure 2 16 Patient specific voxel phantom used for internal dosimetric mass scaling analysis adult female at and (Johnson et al. 2011) Figure 2 1 7 Irradiation geometry for the photon cross dose scaling validation study. The red spheres are the source tissues, and the gray spheres are the target tissues. The solid spheres represent the reference geometry, and the transparent spheres represent the non reference geometry.

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235 Figure 2 1 8 Standing height as a function of total body mass for the NHANES III pediatric male population. Grey dots represent actual patients, and black dots with crosshairs represent the library of phantoms (Johnson et al. 2009) Reproduced with permission ( 2009 IEEE).

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236 Figure 2 1 9 Sample set of NURBS/PM phantoms created for the internal dosimetric standing height sensitivity study. UFH00M phantoms shown a t standing heights of (ICRP reference), and

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237 Figure 2 20 Sample set of NURBS/PM phantoms created for the internal dosimetric weight sensitivity study. UFH00M phantoms shown at weights of (ICRP reference), and

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238 (A) (B) Figure 2 2 1 Phantoms created for the internal dosimetric body morphometry sensitivity study. Two phantoms at but at heights of and

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239 CHAPTER 3 RESULTS UF Hybrid Phantom Blood Vessel System Adult Male Neck and c la vicles The arteries modeled in the neck and clavicles represent the common carotid arteries and subclavian artery. The veins modeled in the neck and clavicles represent the external and internal jugular vein and subclavian vein. One artery and one vein w ere placed on either side of the neck with the veins being located anteriorly and the arteries posteriorly. The decision to place the veins in front of the arteries was arbitrary but not critically important to the simulation of a blood source. Both veins and arteries were modeled as tube structures with the initial tube diameter equal to the final tube diameter. The artery diameters were set to which is the average large artery diameter reported in ICRP Publication 89 (ICRP 2002) The initial vein diameters were set to the average large vein diameter reported by ICRP Publication 89 (ICRP 2002) and the terminal vein diameters were set to at the distal end of the vessel. The arteries originate just below the base of the sk ull and terminate just above the thoracic spine. The veins originate just below the base of the skull, curve over the first rib, and terminate in the space adjacent to the junction of the clavicles and scapulae. The artery and vein volumes in the neck an d clavicles for the adult male were and respectively. The NURBS blood vessel model of the neck and c lavicles can be seen in Fig ure 3 1 (A) Arms The arteries modeled in the arms represent the brachial, radial, and ulnar arteries. The veins modeled in the arms re present the axillary, cephalic, brachial, basilica, radial, and ulnar

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240 veins. One artery was placed on the anterior of the arms and one vein was placed on the posterior. Only one vessel was used on either side due to space constraints and difficulty of mo deling. Both the artery and the vein originate just below the distal humerus and terminate just above the carpal bones. The artery diameter was set to the average of the large artery and vein diameters reported in ICRP Publication 89 (ICRP 2002) and the vein diameter was set to the maximum vein diameter reported in ICRP Publication 89 (ICRP 2002) These diameters were chosen to sta y within the bounds of the vessel diameters reported in ICRP Publication 89 but were defined according to the space available The artery and vein volumes in the arms for the adult male were and respectively. The NURBS blood vessel model of the arms can be seen in Figure 3 1 (B) Thoracic and abdominal region The arteries modeled in the thoracic and abdominal regions represent the aortic arch and thoracic and abdominal aortas. The veins modeled in the thoracic and abdominal r egions represent the superior and inferior vena cava. Due to space constraints, only two vessels were placed in the thoracic region and only two were placed in the abdominal region. Because of this, the actual form of the aortic arch could not be modeled The artery and vein in the thoracic region were placed just anterior to the thoracic spine, originating inferior to the larynx and terminating just superior to the bronchi. Both vessel diameters were set to the average of the large artery an d vein diameters reported in ICRP Publication 89 (ICRP 2002) The artery and vein in the abdominal region were placed just anterior to the thoracic spine, originating just inferior to the bronchi and terminating just superior to the small intestine. The initial (superior end) vessel diameters for the abdominal vessels were set to the average of the large artery and vein diameters reported in ICRP Publication 89 (ICRP 2002) and the terminal

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241 (inferior end) vessel diameters were set to due to space constraints. The artery and vein volumes in the thoracic and abd ominal regions for the adult male were both The NURBS blood vessel model of the thoracic and abdominal regions can be seen in Figure 3 1 (C) Legs The arteries modeled in the legs represent the femoral, popliteal, interior tibial, and poster ior tibial arteries. The veins modeled in the legs represent the left and right femoral veins. One artery was placed on the anterior of the arms and one vein was placed on the posterior. Only one vessel was used on either side due to space constraints a nd difficulty of modeling. Both vessels originate just below the distal femur and terminate just above the talus bone. The vein diameter was set to the maximum vein diameter reported in ICRP Publication 89 (ICRP 2002) The artery diameter was set to the average of the large artery and vein diameters reported in ICRP Publication 89 (ICRP 2002) The artery and vein volumes in the legs for the adult male were and respectively. The NURBS blood vessel model of the legs can be seen in Figure 3 1 (D) Whole body The total large artery and vein volume was not matched because of space constraints. As previo usly discussed, this was not considered critical because the remainder of the volume would be apportioned uniformly to the rest of the body for the simulation of a whole body blood source. The total reference blood volume in the adult male is and large arteries and veins account for of the total blood volume (ICRP 2002) Therefore the targeted large artery and vein volume was The actual total artery and vein blood volume modeled in the adult male phantom was less than t he targeted value.

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242 Remainder of Phantom Family The anatomy of the blood vessel systems for the rest of the UF hybrid phantom family was held constant from the UFHADM phantom model. The same large arteries and veins were represented in each region of the b ody, and the same method of creating blood vessels in Rhinoceros TM was used in each phantom. The blood vessel system for the UFHADF phantom was created by slightly scaling down the vessel diameters from the adult male. The total reference blood volume in the adult female is and large arteries and veins account for of the total blood volume (ICRP 2002) Consequently the targeted large artery and vein volume was The actual total artery and vein blood volume modeled in the adult fe male phantom was less than the targeted value. The blood vessel system for the UFH00MF phantom was then created by scaling down the vessel diameters from the adult male to proportionally fit the newborn phantom. It was assumed that the regional p ercent volume distribution of blood in the large arteries and veins relative to total blood volume, was independent of age. The total reference blood volume in the newborn is and large arteries and veins account for of the total blood volume (ICRP 2002) As a result the targeted large artery and vein volume was The actual total artery and vein blood volume modeled in the newborn phantom was less than the targeted value. The blood vessels in the UFH01MF UFH05MF UFH 10MF and UFH15M male phantoms were created by linearly interpolating between the vessel diameters in the UFH00MF and UFHADM phantoms. Next the diameters of the veins in the legs were adjusted to preserve the desired total vein to artery volume ratio of The final NURBS models of the UF hybrid phantom family blood vessel systems can be seen in Figure 3 2 The blood vessel volumes and

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243 comparisons to reference values as a function of age can be seen in Table 3 1 and t he blood vessel diameters as a fu ncti on of age can be seen in Table 3 2 Vascular Dosimetry Since blood vessel walls could not be explicitly modeled in the UF phantom family and the existing blood vessel system is not comprehensive, calculating absorbed dose to the blood vessel walls pres ented a challenge. A systematic methodology was used to ascertain a reasonable approach for providing absorbed dose estimates to blood vessel walls by varying the size of the blood vessel lumen, wall thickness, vessel length, and vessel separation and sim ulating photons and electrons of varying energies. An abbreviated set of simulations was executed to investigate any possible perturbation of the dosimetry results due to variations in elemental composition in the surrounding tissue. For example, how doe s the absorbed dose to the blood vessel wall from photon and electron sources in its own lumen change if soft tissue surrounds the vessel rather than more blood vessel s ? The answer to this question would determine if backscatter contributions from surroun ding tissue change significantly depending on the tissue adjacent to the blood vessel. A average absolute variation was observed for this study, indicating that the results of the extensive simulation set could be taken at face value and not subject ed to further criticism based on elemental composition variations surround the vessel. Figures 3 3 and 3 4 show some initial dosimetric trends from the comprehensive simulation study. These figures show absorbed dose to the blood vessel wall from its cont ents but does not include any cross dose from the adjacent blood vessel. As expected, absorbed dose to the blood vessel walls is highly dependent on source particle energy. According to Figures 3 3 and 3 4 absorbed dose estimates are also influenced by the physical size of the vessel (lumen diameter and vessel length). Absorbed dose to the vessel wall decreases with increases in lumen diameter and vessel length More attenuating material is present when lumen diameter increases,

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244 so the dose to the vess el walls would be expected to decrease due to more interactions in the blood. Additionally, increases in lumen diameter also presents more attenuating material along the axis of the blood vessel in addition to an increase in the overall mass of the vessel wall, leading to a decrease in the vessel wall dose. In keeping with the average dose approach used in the monoenergetic photon and electron SAF studies, an approach to estimate the average whole body SAF for the blood vessel walls was investigated. It w as beyond the scope of this study to estimate local absorbed dose to vessel walls for non uniform irradiation scenarios. Therefore, for a distributed blood source, it was assumed that the radiation source was actually uniformly distributed throughout all blood vessels in the body. A dose averaging methodology for estimating vessel wall dose is presented in Chapter 4 Skeletal Photon Fluence to Dose Response Functions S ingle I mage R adiation T ransport Simulations As detailed earlier, electrons were simulate d as uniform sources in voxel models of the spongiosa and MCs in whole bone sites of the UFH01MF, UFH05MF, and UFH10MF skeletons to calculate AFs and their complement, EFs Results for the uniform electron source in the spongiosa of the cranium of the UFH 01MF phantom are shown in Figure 3 5 According to the figure, remained close to 1.00 until approximately due to the short range of low to mid energy electrons and the large volume of the source tissue. At energies greater than the AF for spong iosa self dose decreased as the electrons attained sufficient energy to escape the spongiosa. was approximately zero until an energy of The AF then increased to a peak at around and decreased at energies greater than Initially, the electrons did not attain enough kinetic energy to deposit energy in the surrounding cortical bone. Then, as the initial

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2 45 energy increased, electrons began to deposit an increasing amount of energy in the cortical bone until the electrons had sufficient energy to penetrate through the cortical bone and deposit energy in tissues outside of the whole cranium. Finally, remained close to zero until an e nergy of about and increased with increasing energ y as the high energy electrons began to penetrate through the cortical bone and deposit energy in tissues outside of the whole cranium. Spongiosa/MC self dose AFs for all bone sites in the UFH01M F phantom are depicted in Figure 3 6 and AFs for the spongiosa/MC irradiating cortical bone for all bone sites in the UFH01MF phantom are in Figure 3 7 Spongiosa/MC EFs for all bone sites in the UFH01MF phantom can be seen in Figure 3 8 Due to the lar ge number of bone sites, a legend was omitted so that the general shape of the various curves could be observed. All bone site s exhibit the same general behavior for spongiosa /MC self dose and spongiosa/MC irradiating cortical bone but to varying degrees MCs tended to have the greatest EFs due to very little or no trabecular bone present in addition to their overall dimensions. Electrons have greater ranges in bone marrow than homogeneous spongiosa due to the high atomic number of mi neral bone, and so they escape into cortical bone and beyond at lower energies than other bone sites. The shape of and are all driven by the geometry and elemental composition of the bone sites themselves. Res ponse Functions Described in Chapter 2, skeletal fluence to dose response functions were developed to allow the assessment of absorbed dose to radiosensitive skeletal tissues given tallied values of photon fluence incident upon the spongiosa or medullary c avity regions of the

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246 skeleton. The mandible was chosen as a representative bone site to display the skeletal photon fluence to dose response function results Values of both fluence to dose and fluence to kerma response functions for photon int eractions in the mandible can be seen in Figure 3 9 The results were shown with units of absorb ed dose or kerma per unit photon fluence ( ) As shown in Equation 2 24 a unit conversion factor is needed to convert the original skel etal photon fluence to dose response function units to the final desired SAF units in units of Examining first the skeletal photon fluence to dose response function calculated for the AM target, it should be noted that the source was total spong iosa which was comprised of both TM (in the case of the UFH00MF phantom, TM and AM are equal) and TB and thus t he dose response was assessed for a fluence of photons incident on the spongiosa In turn, the source term was defined as electrons liberated i n both T M and TB The skeletal photon fluence to dose response function for the AM target originates at a value just below for a photon energy of This was due to the fact that the resultant secondary electrons, initiated at a comparable low energy, had very short ranges and primarily deposited most of their energy at the site in which they were born Consequently, secondary electrons born to photon interaction s in bone trabeculae were unlikely to exit and irradiat e the adjacent marrow cavities. As the incident photon energy increased to about the skeletal photon fluence to dose response function decline d due to the sharp decline in the photon mass interaction coefficient As the incident photon energy increased past the skeletal photon fluence to dose response function increased because the secondary electrons ha d enough energy to penetrate completely through the trabeculae and into adjacent regions of AM At energies greater than the skeletal photon fluence to dose response function began to decline because those response function calculations were bas ed on AF data which assumed that all initiated electrons

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247 attain ed enough energy to mostly escape from the spongiosa into the cortical bone (Pafundi et al. 2010) However, as will be discussed later, the escape of electrons into cortical bone is actually c ompensated by electrons born in cortical bone and entering spongiosa The shape of the skeletal photon fluence to dose response function for the TM 50 target can be explained in the same way as the skeletal photon fluence to dose response function for the A M target However, it was evident that at intermediate incident photon energies, the response function for the TM 50 target was slightly greater than the response function for the AM target This is because as incident photon energy increase d, the first l ayer of tissue that the secondary electrons escaping from TB regions encounters is the T M 50 layer. While some AM is also included in the TM 50 layer, the TM 50 is much smaller, so energy deposition drives the absorbed dose for TM 50 more drastically as elect rons begin to escape the TB regions. While this discussion addresses the general shape of the skeletal photon fluence to dose response functions in light of physical processes taking place, the shape and dose enhancement characteristics were heavily depend ent upon the photon interaction cross sections (probabilities of photons undergoing interactions in the various materials of interest). For example, dose enhancement takes place because photons are more likely to interact with high atomic number materials such as mineral bone at lower energies than low atomic number materials such as bone marrow (Attix 2004) Electrons created in marrow begin to escape into adjacent regions of trabeculae while electrons created in trabeculae begin to escape into adjacent marrow cavities. However, since photons preferentially interact in trabeculae, more electrons are escaping into marrow cavities at lower ( to energy ranges than into trabeculae. As previously noted, the skeletal photon fluence to dose response functions were calculated based on AF data which assumed secondary electron escape from the spongiosa into

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248 surrounding cortical bo ne (Pafundi et al. 2010) However, this model did not take into account secondary electrons born in the surrounding cortical bone entering the spongiosa At high incident photon energies ( and greater) electrons born in cortical bone entering spongiosa compensate for electrons born in spongiosa entering cortical bone, creating CPE conditions Physically, this process can be represented by assuming the secondary electrons created in the spongiosa as d epositing all of their initial energy at the site of interaction a model known as the kerma approximation Therefore, the final skeletal photon fluence to dose response functions were constructed as a forced convergence between the skeletal photon fluence to dose response functions based on the or iginal AF data and response functions based on the kerma approximation At the point where the skeletal photon fluence to dose response functions began to deviate from the skeletal photon fluence to kerma response functions, the dose response functions we re replaced by the kerma response functions. This divergence point was generally around It can be seen that there was a slight difference between the kerma response for spongiosa and the kerma response for the AM target The kerma response for spongiosa was chosen to develop the final the skeletal photon fluence to dose response functions because no skeletal microstructure is present in the UF computational phantoms The spongiosa /MC region s w ere the only region s that w ere able to be tallied for photon fluence C omplete skeletal photon fluence to dose response functions for the AM and TM 50 targets in the UFH00MF phantom can be seen in Figure s 3 10 and 3 11, respectively Due to the large number of bone sites, a legend was omitted so that the general shape of the various curves could be observed. Age related variations in the re sponse functions for the AM and TM 50 targets are shown in Figures 3 12 and 3 13 respectively, and the cervical vertebra was chosen as the bone site for

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249 demonstration. For the AM target in Figure 3 12 the response functions are mostly equal at high and l ow incident photon energies where dose enhancement is not a driving factor. At low energies, most of the liberated electrons are absorbed in the vicinity of where they are created while at high energies CPE conditions eliminate dose enhancement effects. In the mid range energies, from about to about dose enhancement becomes important, and a noticeable separation of response function values materializes. A systematic age dependence is observed for the AM target in this case where the younger phantoms experience higher doses per unit photon fluence incident upon the spongiosa of the cervical vertebra. Higher dose to AM at younger ages probably occurs because of the smaller thicknesses of bone trabeculae. Electrons escape the trabecul ae quicker at younger ages than for older ages when the bone trabeculae are thicker. Relative to the UFH00MF response functions, absolute percent differences for the rest of the pediatric and adolescent response functions across all energies were on avera ge with minimum and maximum differences of and respectively. As was the case for the AM target, Figure 3 13 shows that all response functions are approximately equal at higher energies for the TM 50 from about to due to CPE conditions Age related differences are evident from to about The differences do not appear to be systematic, but this is plausible because the irradiation geometry is different than that for the AM target AM is distributed throu ghout the marrow cavities in different concentrations depending on cellularity (fraction of marrow space occupied by AM) while TM 50 is always the deep tissue layer directly adjacent to trabecular bone, containing both AM and IM. Since this tissue is a thin layer adjacent to the enhanced source of electrons (trabecular bone), it is more greatly affected by dose enhancement at lower energies than the AM target. Relative to the UFH00MF response functions, absolute percent differences

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250 for the rest of the pediatric and adolescent response functions across all energies were on average with minimum and maximum differences of and respectively. Photon Specific Absorbed Fractions Photon SAFs were computed for the entire UF hybrid phantom family (12 phantoms) using Chapter 2 One large organ and one small organ, the liver and thyroid, in the UFH00MF phantoms were chosen as two representat ive source tissues to display the photon SAF results. A small subset of the p hoton SAF curves for these source tissues can be seen in Figure 3 14 Since the liver is a large organ, the reverse Monte Carlo method of variance reduction was very effective a nd is evident in the smoothness of the SAF curves. A verage statistical uncertainties for initial photon energies greater than or equal to for the liver and thyroid sources w ere and respectively T he final SAF values for both the liv er and thyroid source s were considered to be very reliable since most statistical uncertainties were well below In fact, over the energy range of the greatest average statistical uncertainty was for the pituitary gland target Th e SAFs will be made available in table format with the variance reduction techniques specified for each target organ an is used to indicate log linear back extrapolation, an was used to indicate reverse Monte Carlo, and an was used to indicate 3 point smoothing These tables will be made available as electronic appendices in upcoming publications. An abbreviated excerpt of the SAFs for the UFH00MF pituitary gland source is in Table 3 3 While these extensive tables will be available for direct usage, they will be incorporated into the internal dosimetry software for ease of use Most applications will not directly access the SAFs, but they are integral to the establishment of a final set of radionuclide S values for the dosimetry software

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251 The different shapes of the photon SAF curves can be explained by a combination of organ shapes, separation, and photon interaction coefficients (Figure 3 15) (NIST 2011, ICRP 2002) Most photon SAFs curves had the same approximate shape as seen in Figure 3 14 An initial increase is seen as the photon fluence incident on the target tissues increases. At this energy range between approximately to just less than the total photon mass attenuation coefficient is about an order of magnitude greater than at higher energies. Photon interaction effects begin to take over at energies just less than and are visualized by a sharp decrease in the SAF until photon energies increase to just greater than At this point, the SAF remains somewhat constant, rising and falling slightly between and due to the interplay between the penetrability of h igh energy photons, the energy of those photons and the slightly decreasing total photon interaction coefficient. As photon energy increases, interaction probabilities in the target tissues of interest decrease slightly, but the energy imparted when unde rgoing an interaction is generally greater, so these two processes work against each other. The only photon SAF curves that begin at a maximum and subsequently assume the general curve shape for any source tissue are the curves for the source tissue as a target (self dose) and for cases when the whole body is the target tissue This is because both target tissues include the source tissue as part of the target, and the source tissue experiences photon interactions at high fluences for the photon s As the photons increase in energy, they increasingly escape from the source tissue seen as an immediate decline in the SAF. While most curves have the same general shape, most are slightly different in curve grade and location of the peak. This char acteristic may be due to both the 3 D shape of the target tissue and the distance from the source. Some anomalies also arise from the log linear back extrapolation variance reduction technique. For example, a curve may bend much sharper than

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252 usual or may flatten out at lower energies. These artifacts were seen to occur at low SAF magnitudes. Age dependent SAF curves were generated to demonstrate the range of values and similarity of curve shapes for certain source target combinations Five irradiation s cenarios were chosen to include most possible types of irradiation geometries: large and small organ self dose, a large organ irradiating a large organ, a small organ irradiating a large organ 1 and a small organ irradiating a small organ. SAFs chosen to display age related trends were and and the se results are s hown in Figures 3 16 through 3 20 Figure 3 16 This irradiation geometry examines the age and energy dependent trends for large organ self dose. It was expected that as the phantom age increased, the liver self dose SAF at each initial photon energy would decrease due to reasons discussed in the photon self dose mass scaling sections of this document As organ size increases photon self dose decreases due mainly to increasing organ mass and this is observed in Figure 3 16 and thus In addition, the general shape of all the curve s as a function of energy followed the description previously discussed. The SAFs originate at a peak at decrease through the mid range energies, and form a gentle rise over the higher energies. 1 A large organ irradiating a small organ w as omitted from this demonstration because the reciprocity principle renders that irradiation scenario approximately equal to a small organ irradiating a large organ.

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253 Figure 3 17 This irradiation geometry examines the age and energy dependent trends for small organ self dose. The same dose trend as was observed for and this was expected. The adrenal self dose SA Fs were in reverse order from the order of their masses. Energy dependen t trends for photon self dose were also observed for this irradiation scenario. Figure 3 18 This irradiation geometry examines the age and energy depe ndent trends for a large organ irradiating a large organ. Muscle is distributed throughout the phantoms, so statistical uncertainties were very low as evidenced by the smoothness of the SAF curves. Age dependent trends follow what one would expect, in g eneral. As phantom size increases (with increases in subject age), separation between the lungs and muscle increase, causing a decrease in SAF. In addition, the lungs and muscle are both increasing in size, causing more self attenuation in the lungs. In creases in muscle mass increase the denominator in the SAF equation, and in combination with the increases in attenuation, cause the muscle SAF to decrease. Energy d ependent trends for photon cross dose as discussed previously are also observed in this cr oss dose example. Figure 3 19 This irradiation geometry examines the age and energy dependent trends for a small organ irradiating a large organ. Although a small organ is included in this cross dose irradiation scenario, the target organ is large, ensuring low statistical uncertainties. Age dependent trends follow those observed for Energy dependen t trends are a little different for this irradiation geometry. When the target organ is very distant from the so urce organ, curve shapes such as those for the UFHADM phantom in this example are observed. No peak around to is seen because most photons have experience multiple interactions before reaching the target tissue. A peak is present for the

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254 UFH00MF phantom in this example and remains to an increasingly lesser degree for the UFH01MF and UFH05MF phantoms as the separation between the brain and the thyroid for the these phantoms is much less than seen in the older phantoms T he separation b etween brain and thyroid for the UFH00MF phantom is less than that for the UFH01MF which is in turn less than that for the UFH05MF phantom. Figure 3 20 This irradiation geometry examines the age and energy dependent trends for a small organ irradiating a small organ. Since both organs in this example are small, statistical uncertainties could pose prob lem s in establishing a reference set of SAF values However, all three variance reduction techniques were applied in this situation, and the results, while not perfect, still give reasonable SAF curves. The same trends explained in the example apply here. Comparison of the SAF curves for the UFH00MF and UFH01MF phantoms may give one pause since the UFH00MF curve would be expected to be greater than the UFH01MF curve but the reference masses of the adrenal s in the UFH00MF phan tom are actually larger than those in the UFH01MF phantom. Electron Specific Absorbed Fractions Electron SAFs were computed for the entire UF hybrid phantom family (12 phantoms) Specific Absorbed Chapter 2 For comparison purposes, all SAFs generated in the validation study described later (uniform electron source in the UFH00M liver) were shown in Figure 3 21 2 Due to the large number of target tissues, a legend was omitted so that the general shape of the various SAF curves could be observed. Clearly, many target tissues suffer from poor statistical uncertainties, visualized as erratic and sometimes non existent curve shapes. 2 the validation simulation. Also, see Figure 4 10 for graphical results of the validation study.

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255 To display the final electr on SAF results, o ne large organ and one small organ, the liver and thyroid, in the UFH00MF phantoms were chosen as representative source tissues A small subset of the e lectron SAF curves for these source tissues can be seen in Figure 3 22 Since the liv er is a large organ, the reverse Monte Carlo method of variance reduction was very effective and is evident in the smoothness of the SAF curves. Additionally, the spectrum weighting method of calculating radiative energy loss contributions to dose is mani fested in the smooth curves for those target tissues who do not receive primary electron dose. Average statistical uncertainties for initial electron energies greater than or equal to for the liver and thyroid sources were and r espectively. The final SAF values for both the liver and thyroid sources were considered to be very reliable since most statistical uncertainties were below O ver the energy range of the greatest average statistical uncertainty was for the testes source Some statistical uncertainties associated with the electron SAFs exceed ed However, while electron transport methods have been improved in this study, statis tical uncertainties for computational electron dosimetry remain an area for improvement. The electron SAF tables are formatted in the same manner as the photon SAF tables (see Table 3 3 for reference) Again, w hile these extensive tables will be availabl e for direct usage, they will be incorporated into the internal dosimetry software for ease of use. Most applications will not directly access the SAFs, but they will be integral to the establishment of the final set of radionuclide S values for direct us e in the internal dosimetry software. A representative table of electron SAFs was not displayed because the electron SAF tables are exactly like the photon SAF tables in format. The different shapes of the electron SAF curves can be explained by a combina tion of source/target organ separation and electron interaction mechanisms. Four distinct groups of

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256 electron SAF curves may be defined with the following arbitrary terms (1) self dose, (2) full collisional, (3) partial collisional, and (4) full radiativ e. Self dose curves are identified as relatively flat curves with slight downturns at the highest energies. For any given source tissue, the self dose curves belong to the source tissue itself and the whole body as a target. Since electron ranges are so small, no appreciable electron energy escapes either the source tissue itself or the body as a whole. Only at the highest energies do bremsstrahlung losses begin to account for increasingly reduced energy deposition in these target tissues. The target ti ssues exhibiting self dose SAF curve behavior in Figure 3 22 ( A ) are the liver and whole body. the lowest electron energies, the target tissue receives energy depos ition from collisional energy losses. These curves can be identified as relatively log linearly 3 increasing over the energy range to due to CSDA. Electrons experience many small interactions along their path rather than several catastrophic interactions as in the case of photons (Attix 2004) As the initial electron energy increases, a proportional amount of ener gy is deposited into the target material with no appreciable increase in target tissue escape. One tissue exhibiting full collisional SAF curve behavior in Figure 3 22 (A) are the adrenal target s Full collisional electron SAF curves are generally charac teristic of tissues directly adjacent to the source tissue. words, primary electrons are not incident upon the target until a certain energy threshold is reached. Unti l that point, dose contributions to the target are solely from radiative losses by the primary electrons. Partial collisional curves can be recognized by two distinct curve regions, 3 Appearing linear on a log log scale.

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257 where the first region assumes a shape similar to many photon SAF curves for distant target tissues, and the second region demonstrated a sharp increas e once primary electrons have CSDA ranges allowing them to reach the target tissue. One would expect the low energy region curve shapes to resemble photon SAF curve shapes since the low energy regions of electron SAFs for partial collisional curves reflect only photon contributions. The thoracic lymph node target tissue is an example of a partial collisional electron SAF curve in Figure 3 22 (A). The final electron SAF curve typ to indicate that dose contributions to the target tissue of interest could be entirely attributed to radiative losses of the primary electrons. Absorbed dose to these target tissues are a result of bremsstrahlung and character istic x ray energy deposition and so the expected curve shape would be along the lines of what is seen for photon SAFs, and this is indeed observed. Note that the full radiative curves are a spectrum weighting of many different monoenergetic photon SAFs, not a single photon SAF. Full radiative curve behavior is seen for the brain target in Figure 3 22 (A). Age dependent SAF curves were generated to demonstrate the range of values and similarity of curve shapes for certain source target combinations. Fiv e irradiation scenarios were chosen to include most possible types of irradiation geometries: large and small organ self dose, a large organ irradiating a large organ, a small organ irradiating a large organ 4 and a small organ irradiating a small organ. SAFs chosen to display age related trends were and and the results are shown in Figures 3 23 through 3 27 Figure 3 23 This irradiation geometry examines the age and energy dependent trends for large organ self dose. It was expected that as the phantom age 4 A large organ irradiating a small organ was omitted from this demonstration because the reciprocity principle renders that irradiation scenario approximately equal to a small organ irradiating a large organ.

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258 increased, the liver self dose SAF at each initial electron energy would de crease due to reasons discussed in the electron self dose mass scaling sections. As organ size increases, electron self dose decreases, and this is observed in Figure 3 23 In addition, the general shape of all the curves as a function of energy followed the description previously discussed. The SAFs originate at a peak at and slowly decrease as electron escape increases, accelerating at higher energies The downturn s of the electron self dose SAFs are more pronounced for the younger phantoms because electron escape increases with decreases in organ size. Figure 3 24 This irradiation geometry examines the age and energy dependent trends for small organ self dose. The same dose trend as was observed for and this was expected. Electron escape at higher energies is even more pronounced in this example because of the small size of the organ The distinct electron escape region demonstrates that the MIRD Pamphlet No. 11 recommendation of self dose absorbed fractions of unity for electrons cannot be considered valid at higher energies, in this case at energies greater than Figure 3 25 This irradiation geometry examines the age and energy dependen t trends for a large organ cross irradiating a large organ. Muscle is distributed throughout the phantoms, so statistical uncertainties were very good, as evidenced by the smoothness of the SAF curves. Age dependent trends follow those seen for the photon example Energy d ependent trends for electron cross dose for this irradiation scenario are indicative of the full collisional electron SAF curve type The SAFs continue to increase as the electrons attain more and more energy escaping into adjacent regions. Figure 3 26 This irradiation geometry examines the age and energy dependent trends for a small organ cross irradiating a large organ. Although a small

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259 organ is included in this cross dos e irradiation scenario, the target organ is large, ensuring low statistical uncertainties. These SAF curves are indicative of full radiative electron SAF curves and were calculated as spectrum weighted photon SAFs. As a result, age dependent and energy d ependent trends would be expected to follow those seen for large separation photon cross dose SAF curves, and this is indeed the case. These SAFs decrease with increasing age/organ size and separation and increase gradually with electron energy. Figure 3 27 This irradiation geometry examines the age and energy dependent trends for a small organ cross irradiating a small organ. Since both organs in this example are small, statistical uncertaint ies could pose a problem. However, reciprocity and spectrum weighting were performed for this source target combination and the results give reasonable SAF cur ves. Both partial collisional and full radiative electron SAF curve types are observed in this example Partial collisional curves are seen for phantoms at a younger age due to decreased organ separation. Organ separations in these cases are approximately less than or equal to the electron range at the energy of interest, so primary electron inte ractions are taking place in the target tissue. Dosimetric Sensitivity Studies Variation in Source and Target Size and Separation Photon self dose The largest absorbed doses are observed when the source and target are the same tissue, so non reference dos e scaling techniques for self irradiation is important Since any dose scaling will be accomplished with computer codes simplistic empirical equations were not a priority The data was processed to reveal the most accurate technique for scaling referenc e doses to non reference doses. Statistical uncertainties were less than for all sphere sizes due to the large number of interactions in the source tissue Results for photon self dose SAFs at all sphere

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260 masses and photon energies are shown in Figur e 3 28 Variable scaling parameters were expected due to the variations in curve shapes as a function of energy and sphere mass (e.g., it can be seen that the shape of the curve for the sphere is markedly different that for the sphere). The analysis was first performed for photon self dose. At each photon energy, the SAF of the original sphere mass was divided by the SAFs of all other sphe re masses ) For example, This approach was used beca use any dependence on the size of the original sphere would be illuminated, revealing any possibility that scaling the SAF of a small organ would require a different methodology than for a large organ. The variable in Equation 3 1 was computed fo r ever y sphere mass combination. (3 1) where is the SAF for the non reference sphere, is the SAF for the reference sphere is the mass of the reference sphere, and is the mass of the non reference sphere. First, an overall average of the scaling power was taken at each initial photon energy to examine possible energy dependence of the scaling powers independent of the mass dependence The results can be seen in Figure 3 29 al ong with the maximum, minimum, and MIRD Pamphlet No. 11 recommendation for the scaling power (Snyder et al. 1975) The mass scaling power was very much dependent on the initial photon energy with widely varying values

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261 for energies less than and greater than After examining these scaling power curves the recommendation to apply a scaling power of seems only appropriate for a relatively narrow photon energy range, and not extendable to low and high energies (Snyder et al. 1975) Perhaps the recommendation was made for ease of use, but more rigorous approaches are possible with application of computer codes Wide variations of the mass scaling powers at high and low photon energies seemed to indicate that energy was only one of pos sibly several parameters upon which the mass scaling power depended. To investigate any possible mass dependence, the mass scaling powers were averaged over all non reference sphere sizes at each energy and reference sphere size. The results can be seen in Figure 3 30 An percent difference between the mass scaling powers of the and spheres was observed at and a difference was observed at between the same reference sphere sizes Because of the apparent energy and mass dependence of the mass scaling powers significant improvement over the MIRD 11 recommendation can be achieved by acknowledging and applying an energy and mass dependence on the photon self dose scaling parameter Electron self dose Analysis methods used for the photon self dose mass scaling study were repeated for electrons. Electron self dose SAFs can be seen in Figure 3 31 and the results suggest from the outset that energy and mass independent scaling methodologies for electron self dose may n ot be sufficient to accurately account for electron escape and photon production at higher electron energies (e.g., energy dependence is evident for the sphere by the downward tilt of the SAF curve beginning at around and the curve shapes of the and spheres are markedly different). Electron self dose mass scaling powers are shown in Figure 3 32 along

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262 with the MIRD Pamphlet No. 11 recommendation (Snyder et al. 1975) The MIRD recommendation of a scaling power of 1.00 relies o n the assumption that the AF for electron self dose is unity at all tissue masses and electron energies. However, results shown in Figure 3 32 indicate that energy dependence becomes important at electron energies around as electron escape begi ns to become significant. In addition, Figure 3 33 suggests that electron self dose scaling powers should vary as a function of mass as well. A percent difference between the mass scaling powers of the and spheres was observed at Electron self dose AFs do not appear to remain close to unity at high energies and small sphere sizes. Photon cross dose Next, dosimetric trends were investigated for photon cross dose recalling the irradiation geometry of varying sizes of concentric spheres. Reverse Monte Carlo was performed for all sphere combinations, and the SAF of the source target combination with the lowest statistical uncertainty was retained. Seventeen sphere masses were simulated at 21 initial photon energies and 7 center to center separations. A representative cross section of the results is displayed in Figures 3 34 and 3 35 Figure 3 34 illustrates variations of SAFs as a function of both distance from the source and target sphere mass with sub figures (A), (B), and (C ) showing the change in these relationships with varying source sphere mass es From Figure 3 34 (A), it is unclear at first glance whether the difference in SAFs at the largest separation is due to real differences in dose or to statistical uncertainties at that particular irradiation geometry ( photon energy and source mass). The average statistical uncertainty for that irradiation geometry is ( ), which is considered to be unreliable. However, the statistical uncertainties at the first two (and possibly third) s eparations were considered reliable at average uncertainties of and

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263 respectively. Predictably, as the source mass increased, the variations in the SAF were minimized, a result of the statistical uncertainty effects of reverse Monte C arlo techniques As the source sphere increased in size, more interactions occurred in the target sphere for the reverse Monte Carlo designation (e.g., SAFs for the sphere irradiating the sphere were actually the SAFs for the sphere irradiating the sphere). At the largest source mass, it is clear that no appreciable trends exist for dose differences with variations in target mass size at large distances. In l ooking at variations in target sphere dose with changes in source sphere size, very little deviation is seen between the minimum and maximum SAFs across all photon energies at each target sphere size and separation (see Figure 3 35 for and photons) Across the first six source target separation distances and all target spheres, an average of difference was seen between the maximum and minimum SAFs at each source target separation distance and target sphere size. Q ualitatively, it is clear that no appreciable trend exists for variations in target dose as a function of source size. However, SAFs certainly decrease with increases in center to center separation, and an attempt to predict this trend will be made later. If the center to center distance could be determined from an imaging procedure, perhaps the reference dose could be scaled to account for this geometry variation. For the first pass investigation of dosimetry sensitivity for photon cross dose, it appeare d that previous recommendations that dose to target tissues distant from source tissues was constant with changes in source and/or target size could be implemented without further investigation (Petoussi Henss et al. 2007) However, some results for the l ow statistical uncertainty irradiation geometry seemed to indicate that this recommendation breaks down at source target separations less than separations considered to be medium distan ce Differences between the maximum and minimum SAFs for the

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264 irradiation geometry from the 5 th ( ) separation to the 1 st ( ) separation were and respectively. Since the statistical uncertainties associated with this irradiation geometry were all less than the marke d increase from to difference between the maximum and minimum SAFs from the 2 nd to the 1 st separation was more than likely due to actual differences in SAFs rather than to statistical uncertainties. To further explore the possibility of cross dose scaling at medium to close distance separations, a similar cross dose computational experiment was designed allowing for center to center separations less than The experiment shared all important characteristics to the original cross dose experiment except that only separations of and and sphere masses of and were used. The number of sphere masses was limited due to overlap when larger spheres were located at these center to center distances (e.g., the sphere radius of would cause the spheres to overlap when their center to center distance was ). Figure 3 36 shows photon SAFs as a function of sphere separation, target mass, and source mass for photons in the close to mid range distance simulations Additionally, Figure 3 37 shows photon SAFs as a function of separation, target m ass, and photon energy for the source sphere. It can be perceived from these figures that for higher energies, even at these close separations, the SAF does not vary considerable as a function of source or target mass. However, Figure 3 37 gives ev idence that dose scaling may be necessary for low energies, even for larger source masses. At each photon energy, separation, and source size, the minimum and maximum SAFs were compared across all target sizes On average, the maximum SAF was great er than the minimum SAF for energies or greater but greater for energies less than These results supported findings by others in this topic that dose to

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265 distant targets need not be scaled with changes in the size of either the source or target organ (Petoussi Henss et al. 2007) but trends observed at low energies and close separations demanded the possibility of mass based dose scaling methods for photon cross dose under these more limiting conditions. Electron cross dose The close to mid separation simulation set was also performed for electrons. Distant separations were not simulated for electrons because it was assumed that statistical uncertainties would be too poor to generate meaningful results. Results similar in format to those displayed for the photon cro ss dose analysis are shown in Figures 3 38 and 3 39 Figure 3 38 shows that differences in electron SAFs at more distant center to center separations mimic those seen in the photon cross dose simulations. However, at the closest separation of differences by orders of magnitude appears between the minimum and maximum SAFs, presumably due varying levels of primary electron dose contributions. Figure 3 39 seems to corroborate this presumption as most SAFs follow the photon trend for the and electron energies with the one exception being the target tissue at separation for electrons. To further investigate the nature of electron SAF variations with changes in source and target tissues, SAFs as a fu nction of initial electron energy and target tissue size are shown for the source tissue and separation in Figure 3 40 As noted when discussing the monoenergetic electron SAFs, these curves all show partial collisional characteristics. The surface of each target sphere is located at a different distance from the source sphere despite the constant center to center separation. Primary electrons interact with the largest target sphere first, so the dose to the largest target sphere is grea ter than each subsequently smaller target sphere. This trend can be observed in Figure 3 40 at electron energies and greater.

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266 Primary electron cross dose scaling may be impractical to address since surface shape and surface separation affect the dose estimate much more than they do for photons. Electron cross dose contributions from radiative losses, on the other, can be handled in the same way as the photon cross dose simulations, and results show that distance scaling may be an option. Development of actual scaling methodologies will be addressed in the C hapter 4 of this dissertation Variation in Anthrop ometric Characteristics Sitting height The sitting heights of three anchor phantoms, the UFH00M, UFH10M, and UFHADM phantoms, were systematically adjusted, consistent with methods outlined in Johnson et al. ( 2009) and simulated with both monoenergetic pho tons and electrons uniformly distributed throughout the AM brain, lungs, liver, and spleen of those phantoms. Absorbed dose in the form of the SAF was calculated for all source target energy combinations, and the results were examined to uncover any pote ntial dose scaling methods. An excerpt of the r esults for the and photon simulations in the liver of the UFH00M based phantoms are in Figure 3 41 and an excerpt of the results for the and electrons simulations in the liver of the UFH00M based phantoms are given in Figure 3 42 These graphs show the extent to which the monoenergetic SAFs change as a function of sitting height of the UFH00M based phantoms. An overall gradual decrease in SAF is observed across almost all target tissues for both photons and electrons Increasing organ to organ separations and organ sizes with increases in sitting height both contribute to the overall decrease in SAFs. Target tissues with increasing SAFs as a function of sitting height were assumed to display poorer statistical uncertainties, and this was found to be the case. Some of the target

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267 tissues in the electron simulations had poor statistical uncertainties and were therefore no t useful in developing dose scaling factors. Figure 3 43 shows whole body dose for uniform 4 MeV phot on and electron sources in the liver of all phantoms in the sitting height dose variation study. The whole body SAF appears to be log linear ly 5 decreasing with increases in sitting height for both photons and electrons. Another feature of interest is the dependence of the whole body SAF on the anchor phantom. One would not be able to simply scale absorbed doses according to relative sitting height because the anthropometric structure of each phantom age is different. For any dose scaling to occur, the a nchor phantom must be specified. Then, a sitting height measurement could be taken and compared to the sitting height of the anchor phantom. Actual scaling methodologies will be discussed in the next chapter. Weight The weights of the same three anchor p hantoms used for the sitting height dose sensitivity study the UFH00M, UFH10M, and UFHADM phantoms, were systematically adjusted, consistent with methods outlined in Johnson et al. (2009) and monoenergetic photons and electrons were simulated as uniforml y distributed throughout the AM brain, lungs, liver, and spleen of the weight adjusted phantoms SAF s w ere calculated for all source target energy combinations, and the results were examined to ascertain any dose scaling methods. An excerpt of the r esult s for the and photon simulations in the liver of the UFH00M based weight scaled phantoms are in Figure 3 44 and an excerpt of the results for the and electrons simulations in the liver of the UFH00M based weight scaled phanto ms are in Figure 3 45 These graphs show changes in monoenergetic SAFs as a function 5 Appearing linear on a log linear scale.

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268 of weight of the UFH00M based phantoms. However, instead of comparing the SAFs against weight, waist circumference is given as the parameter by which dose variations are analyzed as waist circumference potentially gives more information about the stature of the phantom than overall weight. In addition, this parameter is also easily obtained in the clinic. An overall gradual decrease in SAF is observed across most target tissues for both photons and electrons for the underweight phantoms However, no appreciable decrease in organ doses is observed for the severely overweight phantom, as predicted by a previous study (Clark et al. 2010) Decreasing organ to organ separat ions and organ sizes in the underweight phantoms explains the increase in dose with decrease s in waist circumference It is intuitive that the overweight patient does not experience any dramatic changes in absorbed dose because the internal structure is t he same as that of the anchor phantom. Only adipose tissue is added to the outer contour of the phantom, causing only limited increases in photon backscatter 6 Poor statistical uncertainties were considered the culprit for t arget tissues displaying incre asing SAFs as a function of waist circumference and this was found to be a reasonable explanation Some of the target tissues in the electron simulations had poor statistical uncertainties and were difficult to correct, proving these target tissues to have limited application in determining scaling protocols Figure 3 46 shows whole body dose for uniform photon and e lectron sources in the liver of all phantoms in the weight dose variation study. The whole body SAF appears to be almost (but not exactly) log linearly decreasing with increases in waist circumference for both photons and electrons Scaling methodologies could potentially be developed by interpolat ing between the given data points. Like the sitting height study, absorbed dose appears to depend on 6 Again, intra abdominal fat deposits were not considered in the current study, but would be worthwhile to investigate in future work.

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269 the anchor phantom, and this should be taken into account when developing scaling methodologies. Actual scal ing mechanisms will be discussed next in the C hapter 4 Constant weight with morphometry variation A previous study had looked at the issue of constant weight with morphometry variation by performing computational internal dosimetry and had found that the effective dose per unit AA to a tall, thin patient is approximately greater than the effective dose per unit AA to a short, fat patient for 99m (Sgouros et al. 2011) In the current study, the analysis performed for the patient was repeated for two female p atients at Absorbed dose r esults for a select number o f target tissues are in Table 3 4 and whole body effective dose estimates are in Table 3 5 It can be seen from Table 3 4 that absorbed doses to all selected target tissues for the short, fat patient were greater than for the tall, thin patient. The dose to each tissue for the short, fat patient was on average greater than the dose to the tissues of the tall, thin patient with no tissues of the tall thin patient having a higher dose. Tab le 3 5 shows that the effective dose to the short, fat patient was greater than the effective dose to the tall, thin patient. It was expecte d based on the study of Sgouros et al. (2011) that the dose to the short patient would be greater than the dose to the tall patient, and this trend was indeed observed. The dose differences are due to the relative proximity of all organs in the body. Less separation between organs in the short, fat patient causes more energy deposition from source to target tissu es. In addition, the organs in the short, fat patient were almost all smaller than those in the tall, thin patient with the one exception being adipose tissue, and smaller tissues have higher self dose than larger tissues. In addition, the increase of th e effective dose difference from to between the patient study and the patient study was probably due to the degree to which the body morphometries differed. On

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270 average, the organs of the tall, thin patient were larger than thos e of the short, fat patient for the Sgouros et al. (2011) study while the organs of the tall, thin patient were greater than those of the short, fat patient for the 50 kg patients in the current study. This difference seemed to explain the increase i n dose difference s between the two studies. Internal Dosimetry Software The actual subroutines of the internal dosimetry code were written in MATLAB TM and several demonstrations will be given in this section to prove the accuracy of the code. Before any demonstrations are given, two small topics of interest when performing computational dosimetry relating to the way radionuclides are modeled will be addressed. First, when performing computational internal dosimetry, one must decide the level of spectral d etail required to give adequate dosimetry results. Spectrum summaries are available that list only the most prevalent radiation emissions for each radionuclide, allowing for more simplistic simulations. For example, 99m has four primary photon emissions, three x rays and one gamma ray at and at yields of 0.0214, 0.0406, 0.00653, and 0.891 respectively (ICRP 2008) While t hese four emissions only make up about of of the total yield of 86 different photon emissions, they dominate the delta value ( product of energy and yield) at (ICRP 2008) The delta value is a much better metric than yield to evaluate relative contribution to dose. To assess the exten t that detailed spectra should be used, a small study was performed wherein a point source was imbedded in human tissue spheres (tissue elemental compositions given for the adult in ICRP Publication 89 were used with a tissue density of ) of various masses, and self dose S values were calculated using the spectra summary and detailed spectra of photons, monoenergetic electrons,

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271 and beta particles for 99m and 82 as given by ICRP Publication 107 (ICRP 2002, ICRP 2008 ) MCNPX v2.6 was use d for radiation transport, and particle histories were simulated. The results of this study are shown in Figure 3 47 All statistical uncertainties were less than It is clear that dose estimates can be considered adequate if the spectrum summary is used for on the fly simulations. However, since the internal dosimetry software uses S value LUTs for dosimetry calculations, the entire detailed spectra were used for all radionuclides. A second issue for consideration is the validity of direct spectrum sampling as an adequate simulation technique instead of weighted monoenergetic SAF calculations. For many on the fly computational dosimetry studies for non reference individuals, it is beneficial to directly input the radiatio n emission spectrum for the radionuclide of interest into the radiation transport code. In this way, the spectrum will be sampled based on the relative yields of the emission energies. Alternatively, one could mirror the data generation component of the current study and compute monoenergetic photon and electron SAFs for the individual and weight them by the relative yields at each emission energy, clearly an impractical task. A small computational experiment was performed using the same setup as the exp eriment designed to investigate using summarized radiation spectra versus detailed radiation spectra. However, only 99m was simulated, and the results are in Figure 3 48 All statistical uncertainties were less than The results prove that spectrum sampling is a viable option for on the fly computational internal dosimetry. Again, the internal dosimetry software uses monoenergetic SAFs for reference individuals. The S value calculator subroutine of the internal dosimetry code was validated by comparing S values assembled from direct spectrum sampling of both 99m photons and 90 beta particles and S values cal culated by interpolation and weighting of the monoenergetic photon and electron SAFs for the liver source in the UFH00MF phantoms. The photon spectrum

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272 for 99m and the beta spectrum for 90 were taken from ICRP Publication 107 (ICRP 2008) MCNPX v2.6 was used as the radiation transport code for the direct spectrum simulation with particles simulated. The results of this study are in Table 3 6 and Figure 3 49 Good agreement is seen across most target tissues but greater disagreements occur w hen the target tissue is small. In addition, greater disagreement s are seen for the beta spectrum than the photon spectrum. Both instances where disagreement is greater can be attributed almost entirely to less than satisfactory statistical uncertainties in the direct spectrum sampling simulation (e.g., the statistical uncertainty for the pituitary gland target and the 90 beta spectrum was about and the S value ratio was 40.69). Greater uncertainties are usually observed for small target tissues a nd beta particles, so these trends were expected. However, considering that the S values using both techniques for many of the distant and smaller sized target tissues were almost identical, the S value calculator was considered to be adequately validated Similar results were seen for the monoenergetic electron spectra of 204 and 122m (data not shown).

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273 Table 3 1 Volumes of the blood vessels in the UF phantom family. Volume (cm 3 ) Blood Vessel UFH00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Large Arteries Neck 0.21 0.32 0.56 1.12 1.58 1.68 2.46 2.03 Thoracic 0.23 0.40 1.01 2.26 4.04 2.65 5.71 2.77 Arms 0.98 1.95 5.24 12.07 22.82 20.22 29.90 27.08 Legs 1.35 3.31 8.81 17.79 33.50 31.95 45.22 37.61 Large Veins Neck 1.06 2.05 4.53 8.39 17.25 16 .27 20.02 16.87 Thoracic 0.23 0.40 1.01 2.25 4.04 2.65 5.71 2.74 Arms 3.31 6.91 17.39 36.99 67.67 60.17 91.49 78.92 Legs 3.75 8.61 23.92 52.09 96.69 90.39 133.00 109.81 Total Arteries 2.77 5.99 15.62 33.23 61.93 56.50 83.29 69.49 Total Veins 8.34 17.97 46.86 99.73 185.64 169.49 250.22 208.33 Ratio (Veins/Arteries) 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 Total Vessel Volume 11.11 23.96 62.48 132.96 247.58 226.00 333.50 277.81 Target Vessel Volume 64.80 120.00 336.00 576.00 1080.00 792. 00 1272.00 936.00 Difference (Total/Target) 83% 80% 81% 77% 77% 71% 74% 70%

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274 Table 3 2 Superior (sup) and inferior (inf) diameters of the blood vessels in the UF phantom family. Vessel Diameter (cm) UFH00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Blood Vessel Sup Inf Sup Inf Sup Inf Sup Inf Sup Inf Sup Inf Sup Inf Sup Inf Arteries Neck 0.20 0.20 0.21 0.21 0.26 0.26 0.31 0.31 0.37 0.37 0.35 0.35 0.40 0.40 0.38 0.38 Thoracic sup 0. 20 0.20 0.22 0.22 0.31 0.31 0.41 0.41 0.52 0.52 0.37 0.37 0.58 0.58 0.40 0.40 Thoracic inf 0.20 0.15 0.22 0.16 0.31 0.22 0.41 0.29 0.52 0.36 0.50 0.34 0.58 0.40 0.56 0.38 Arms 0.21 0.21 0.23 0.23 0.31 0.31 0.42 0.42 0.52 0.52 0.50 0.50 0.58 0 .58 0.56 0.56 Legs 0.22 0.22 0.27 0.27 0.34 0.34 0.44 0.44 0.54 0.54 0.53 0.53 0.58 0.58 0.58 0.58 Veins Neck 0.30 0.40 0.33 0.43 0.43 0.53 0.55 0.65 0.68 0.78 0.66 0.76 0.75 0.85 0.73 0.83 Thoracic sup 0.20 0.20 0.22 0.22 0.31 0.31 0.41 0.41 0.52 0.52 0.37 0.37 0.58 0.58 0.40 0.40 Thoracic inf 0.20 0.15 0.22 0.16 0.31 0.22 0.41 0.29 0.52 0.36 0.50 0.34 0.58 0.40 0.56 0.38 Arms 0.40 0.40 0.43 0.43 0.57 0.57 0.73 0.73 0.90 0.90 0.88 0.88 1.00 1.00 0.98 0.98 Legs 0.40 0.40 0.43 0.43 0.57 0.57 0.73 0.73 0.90 0.90 0.88 0.88 1.00 1.00 0.98 0.98

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275 Table 3 3 Photon SAFs (excerpt) for the UFH00MF pituitary gland source in units of Variance Energy (MeV) Organ / t issue Reduction 0 .010 0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100 Adipose E 3.03E 07 4.91E 05 1.81E 03 9.99E 03 1.27E 02 1.23E 02 1.15E 02 1.07E 02 1.05E 02 Adrenals E 3.31E 07 3.84E 06 2.18E 05 2.53E 04 1.44E 03 2.43E 03 2.87E 03 3.14E 03 3.23E 03 AI 2.55E 09 4.86E 07 2.02E 05 3.85E 03 1.15E 02 1.45E 02 1.49E 02 1.40E 02 1.35E 02 Brain 1.02E+00 1.64E+00 1.75E+00 1.24E+00 7.85E 01 5.41E 01 4.18E 01 3.19E 01 2.90E 01 Breast (F) E S 7.01E 09 9.63E 07 3.16E 05 4.35E 03 1.02E 02 1.20E 02 1.17E 02 1.15E 02 1.18E 02 Breast (M) E R S 9.15E 09 1.21E 06 3.86E 05 5.10E 03 1.15E 02 1.31E 02 1.28E 02 1.22E 02 1.21E 02 Bronchial E 3.99E 09 6.54E 07 2.44E 05 3.99E 03 1.17E 02 1.48E 02 1.51E 02 1.43E 02 1.37E 02 Brchiol sec 2.55E 09 4.86E 07 2.02 E 05 3.85E 03 1.15E 02 1.45E 02 1.49E 02 1.40E 02 1.35E 02 Cartilage 1.36E 01 2.61E 01 2.71E 01 2.59E 01 2.01E 01 1.53E 01 1.22E 01 9.40E 02 8.44E 02 Colon 2.46E 10 1.20E 08 3.55E 07 9.97E 05 6.15E 04 1.08E 03 1.32E 03 1.47E 03 1.51E 03 Endo st BS 1.03E 02 8.11E 02 1.73E 01 2.64E 01 2.49E 01 2.17E 01 1.90E 01 1.56E 01 1.38E 01 ET 5.22E 05 4.97E 02 1.74E 01 2.90E 01 2.85E 01 2.42E 01 2.07E 01 1.71E 01 1.58E 01 ET1 bas E 3.82E 04 8.67E 03 7.93E 02 1.81E 01 1.66E 01 1.39E 01 1.2 0E 01 1.03E 01 9.92E 02 ET2 bas 4.26E 05 5.09E 02 1.77E 01 2.93E 01 2.88E 01 2.45E 01 2.09E 01 1.72E 01 1.60E 01 Eye lens E 2.05E 04 1.05E 02 1.70E 01 3.90E 01 3.28E 01 2.57E 01 2.13E 01 1.75E 01 1.65E 01 GB wall E S 2.38E 07 3.00E 06 1.81E 05 2.28E 04 1.37E 03 2.29E 03 2.69E 03 2.95E 03 2.99E 03 Ht wall E 4.53E 10 1.60E 07 1.03E 05 3.64E 03 1.14E 02 1.47E 02 1.50E 02 1.41E 02 1.35E 02 Kidney C E 6.76E 08 1.03E 06 7.15E 06 1.09E 04 7.57E 04 1.38E 03 1.71E 03 1.88E 03 1.92E 03 Kidne y M E 3.68E 08 6.65E 07 5.19E 06 9.38E 05 7.32E 04 1.35E 03 1.67E 03 1.83E 03 1.88E 03 Kidneys 5.95E 08 9.37E 07 6.64E 06 1.05E 04 7.50E 04 1.38E 03 1.70E 03 1.86E 03 1.91E 03 LC wall E 4.45E 11 1.05E 08 5.08E 07 1.20E 04 7.40E 04 1.28E 03 1.54E 03 1.68E 03 1.73E 03 Liver E 4.71E 12 4.96E 09 6.91E 07 7.26E 04 3.23E 03 4.77E 03 5.29E 03 5.30E 03 5.20E 03 LN ET (F) E 4.88E 04 1.16E 02 1.10E 01 2.57E 01 2.42E 01 2.01E 01 1.72E 01 1.47E 01 1.40E 01 LN ET (M) E 7.09E 03 7.63E 02 4. 12E 01 5.82E 01 4.44E 01 3.38E 01 2.75E 01 2.23E 01 2.09E 01 LN Th (F) E S 5.01E 06 3.49E 05 1.39E 04 9.67E 04 3.84E 03 5.52E 03 6.14E 03 6.25E 03 6.41E 03 LN Th (M) E S 4.63E 10 1.29E 07 7.01E 06 1.95E 03 6.48E 03 8.75E 03 9.37E 03 9.25E 03 9.20E 03 Lymph (F) E 6.47E 09 3.61E 06 3.21E 04 5.03E 03 9.40E 03 1.04E 02 1.01E 02 9.47E 03 9.26E 03 Lymph (M) E 2.14E 09 2.23E 06 3.08E 04 6.06E 03 1.12E 02 1.22E 02 1.18E 02 1.08E 02 1.04E 02 LN Total (F) 1.71E 06 4.18E 05 6.69E 04 5.72E 03 9.9 9E 03 1.08E 02 1.06E 02 9.82E 03 9.61E 03 LN Total (M) 4.43E 05 4.79E 04 2.87E 03 9.53E 03 1.38E 02 1.41E 02 1.33E 02 1.21E 02 1.16E 02

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276 Table 3 4 Radiation absorbed dose per unit AA and comparison for two patients at the same weight but differ ent body morphometry The radiopharmaceutical is 99m Dose (mGy/MBq) Difference Target Tissue Tall Thin Short Fat Short Fat/Tall Thin WBody 1.66E 06 2.04E 06 22.72% Adipose 6.01E 07 8.39E 07 39.58% LAdrenal 6.61E 06 1 .06E 05 60.24% RAdrenal 6.37E 06 1.09E 05 71.43% Brain 1.58E 07 3.27E 07 106.53% LBreast 5.17E 07 5.77E 07 11.76% Bronchi bas 1.30E 06 2.43E 06 86.15% RC wall 1.16E 06 3.15E 06 170.67% Oesophagus 1.56E 06 2.90E 06 85.24% GB wall 3.22E 06 5.56E 06 72.67% Ht wall 1.45E 06 3.09E 06 113.27% Kidney C 6.65E 05 1.10E 04 65.30% Kidney M 1.56E 05 2.52E 05 61.74% ET2 bas 5.00E 07 1.12E 06 123.90% Eye lens 2.16E 07 2.88E 07 33.41% Liver 3.59E 06 7.04E 06 96.42% LLung 1.88E 06 3.81E 06 102.29% RLung 1.80E 06 3.75E 06 108.43% ET1 bas 1.59E 07 2.55E 07 60.05% O mucosa 4.91E 07 1.01E 06 105.08% Pancreas 5.24E 06 7.88E 06 50.30% P gland 1.86E 07 5.69E 07 206.76% RSig wall 1.57E 06 3.00E 06 91.63% SI wall 2.29E 0 6 3.99E 06 74.57% Skin 4.94E 07 5.30E 07 7.36% Spleen 9.75E 06 1.95E 05 100.27% St wall 2.36E 06 4.95E 06 109.75% Thymus 8.18E 07 1.94E 06 137.14% Thyroid 5.92E 07 1.44E 06 143.24% Trachea 9.80E 07 1.93E 06 96.85% UB wall 3.06E 06 5.11 E 06 67.00% LC wall 1.07E 06 2.97E 06 176.11% Muscle 1.77E 06 3.48E 06 96.21% R B reast 5.10E 07 5.71E 07 12.10% Cartilage 1.77E 06 4.06E 06 129.54% C bone V 1.38E 06 2.35E 06 71.07% LOvary 2.04E 06 3.74E 06 83.48% ROvary 2.08E 06 3.81E 06 83.27% Uterus 2.22E 06 4.09E 06 83.72% AM 1.61E 06 2.93E 06 82.19% TM50 1.46E 06 2.54E 06 74.24%

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277 Table 3 5 Radiation absorbed dose and effective dose per unit AA and comparison for two patients at the same weight but different body morph ometry for the radiopharmaceutical 99m Tissue Dose Weighted Dose Effective Dose Weighting (mGy/MBq) (mSv/MBq) (mSv/MBq) Difference Target Tissue Factor Tall Thin Short Fat Tall Thin Short Fat Tall Thin Short Fat Short Fa t/Tall Thin Colon 0.12 1.20E 06 3.05E 06 1.44E 07 3.66E 07 2.18E 06 4.10E 06 1.88 Lungs 0.12 1.84E 06 3.78E 06 2.21E 07 4.53E 07 Stomach W 0.12 2.36E 06 4.95E 06 2.83E 07 5.94E 07 Ovaries 0.08 2.06E 06 3.78E 06 1.65E 07 3.02E 07 Uri nary Bladder W 0.04 3.06E 06 5.11E 06 1.22E 07 2.04E 07 Esophagus 0.04 1.56E 06 2.90E 06 6.26E 08 1.16E 07 Liver 0.04 3.59E 06 7.04E 06 1.43E 07 2.82E 07 Thyroid 0.04 5.92E 07 1.44E 06 2.37E 08 5.76E 08 Brain 0.01 1.58E 07 3.27E 07 1.58E 09 3.27E 09 Salivary Glands (parotid) 0.01 4.47E 07 9.59E 07 4.47E 09 9.59E 09 Breast 0.12 5.13E 07 5.74E 07 6.16E 08 6.89E 08 Skin 0.01 4.94E 07 5.30E 07 4.94E 09 5.30E 09 Remainder 0.12 6.09E 06 1.05E 05 7.31E 07 1.26E 06 Red Bone Marrow 0.12 1.61E 06 2.93E 06 1.93E 07 3.52E 07 Bone Surface 0.01 1.46E 06 2.54E 06 1.46E 08 2.54E 08 Remainder Adrenals 6.49E 06 1.08E 05 ET Region 4.94E 07 1.10 E 06 GB wall 3.22E 06 5.56E 06 Heart wall 1.45E 06 3.09E 06 Kidneys 5.11E 05 8.43E 05 Lymph nodes 0.00E+00 0.00E+00 Muscle 1.77E 06 3.48E 06 Oral mucosa 4.91E 07 1.01 E 06 Pancreas 5.24E 06 7.88E 06 Prostate 0.00E+00 0.00E+00 SI wall 2.29E 06 3.99E 06 Spleen 9.75E 06 1.95E 05 Thymus 8.18E 07 1.94E 06 Uterus 2.22E 06 4.09E 06

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278 Table 3 6 SAF and S value subroutine verification study for the liver source in the UFH00MF phantoms Ratio of the S values obtained from previously developed monenergetic SAFs to the S values obtained from dir ect simulation of the spectra. Rati o S(Calculator) / S(Direct) Radionuclide and Emission Type Tc 99m Y 90 Target Tissue Photons Betas Adipose 1.01 1.15 Adrenals 1.02 1.00 Brain 1.00 1.00 Breast (F) 0.96 1.75 Bronchial 1.01 1.01 Cartilage 1.01 1.02 ET1 sur 1.28 1.42 ET2 sur 0.9 8 0.95 Eye lens 1.28 1.02 GB wall 1.04 0.99 Ht wall 1.01 1.01 Kidney C 1.00 1.00 Kidney M 1.01 1.30 LC wall 1.03 1.04 Liver 1.01 1.00 LN ET (F) 1.24 -LN Th (F) 1.04 0.68 Lungs 1.01 1.00 Lymph (F) 1.04 1.00 Muscle 1.01 1.00 Oesophagus 1.04 1. 04 Ovaries 1.06 0.98 Pancreas 1.02 1.00 Pit gland 1.02 40.69 RC wall 1.02 0.99 RSig wall 1.03 1.15 S glands 1.06 1.31 SI wall 1.02 1.01 Skin 1.02 1.04 Sp cord 1.02 0.94 Spleen 1.00 1.01 St wall 1.02 1.00 Thymus 1.04 0.99 Thyroid 1.00 1.40 Tra chea 1.08 1.05 UB wall (F) 1.00 1.13 Uterus 1.03 1.05

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279 Figure 3 1 Perspective views in Rhinoceros TM of the arteries and veins in the (A) neck and clavicles (B) arms, (C) thoracic and abdominal regions, and (D) legs of the UFHADM phantom.

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280 UFH 00MF UFH01MF UFH05MF UFH10MF UFH15M UFH15F UFHADM UFHADF Figure 3 2 Blood vessel systems as implemented in the entire UF hybr id phantom family.

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281 Figure 3 3 Absorbed dose to the blood vessel wall from photons for vessels with wall thickness as a function of vessel length and photon energy. Figure 3 4 Absorbed dose to the blood vessel wall from electrons for vessels with wall thickness as a function of vessel length and electron energy.

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282 Figure 3 5 AFs as a function of initial electron energy for a uniform electron source in the spongiosa of the cranium in the UFH01MF phantom with spongiosa, cortical bone, and all other tissues as targets. Figure 3 6 Spongiosa /MC self dose AFs as a function of initial electron energy for all bone sites in the UFH01MF phantom. A legend was not given because the intent of the figure was to show general trends of the AFs.

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283 Figure 3 7 AFs for spongiosa /MC irradiating cortical bone as a function of initial electron energy for all bone sites in the UFH01MF phantom. A legend was not given because the intent of the figure was to show general trends of the AFs. Figure 3 8 EFs for spongiosa /MC sources as a function of initial electron energy for all bone sites in the UFH01MF phantom. A legend was not given because the intent of the figure was to show general trends of the EFs.

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284 Figure 3 9 Skeletal fluence to d ose respo nse functions and skeletal fluence to kerma response functions for AM and TM 50 targets in the mandible of the UFH00MF phantom

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285 Figure 3 10 Skeletal fluence to dose response functions for all bone sites in the UFH00MF phantom for the AM targ et. A legend was not given because the intent of the figure was to show general trends of the response functions.

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286 Figure 3 11 Skeletal fluence to dose response functions for all bone sites in the UFH00MF phantom for the TM 50 target. A legend was not given because the intent of the figure was to show general trends of the response functions.

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287 (A) (B) Figure 3 12 Skeletal fluence to d ose response functions for the AM target in the cervical vertebra of all pediatric and adolesce nt phantoms

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288 (A) (B) Figure 3 13 Skeletal fluence to d ose response functions for the TM 50 target in the cervical vertebra of all pediatric and adolescent phantoms

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289 (A) (B) Figure 3 14 Excerpt of the p hoton SAF curves for a (A) large (liver) a nd (B) small (thyroid) source tissue in the UFH00MF phantoms

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290 Figure 3 15 Photon mass attenuation coefficients in units of as a function of initial photon energy for photoelectric absorption, incoherent (Compton) scattering, pair production in a nuclear field, and total attenuation (NIST 2011)

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291 Figure 3 16 Photon SAFs showing for all phantoms in the UF phantom family Figure 3 17 Photon SAFs showing for all phantoms in the UF phantom family

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292 Figure 3 18 Photon SAFs showing for all phantoms in the UF phantom family Figure 3 19 Photon SAFs showing for all phantoms in the UF phantom family

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293 Figure 3 20 Photon SAFs showing for all phantoms in the UF phantom family Figure 3 21 Electron SAFs for a uniform electron source in the liver of the UFH00M phantom using full transport techniques (i.e., no two simulation improvement)

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294 (A) (B) Figure 3 22 A subset of the e lectron SAF curves for a (A) large (liver) and (B) small (thyroid) source tiss ue in the UFH00MF phantoms

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295 Figure 3 23 Electron SAFs showing for all phantoms in the UF phantom family Figure 3 24 Electron SAFs showing for all phantoms in the UF phantom family

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296 Figure 3 25 Electron SAFs showing for all phantoms in the UF phantom family Figure 3 26 Electron SAFs showing for all phantoms in the UF phantom family

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297 Figure 3 27 Electron SAFs showing for all phantoms in the UF phantom family

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298 Figure 3 28 Sphere self dose SAFs as a function of initial photon energy and sphere size for the photon self dose scaling study

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299 Figure 3 29 Mass scaling powers for photon self dose showing the mini mum, maximum, and average values at each photon energy and the corresponding recommendation from MIRD Pamphlet No. 11 (Snyder et al. 1975) Figure 3 30 Mass scaling powers for photon self dose as a function of both reference sphere mass and initial pho ton energy

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300 Figure 3 31 Sphere self dose SAFs as a function of initial electron energy and sphere size for the electron self dose scaling study.

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301 Figure 3 32 Mass scaling powers for electron self dose showing the minimum, maximum, and average valu es at each electron energy and the corresponding recommendation from MIRD Pamphlet No. 11 (Snyder et al. 1975) Figure 3 33 Mass scaling powers for electron self dose as a function of both reference sphere mass and initial electron energy

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302 (A) (B) Figure 3 34. Photon specific absorbed fractions for the (A) (B) and (C) (following page) source spheres and photons as a function of sphere separation and target sphere mass

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303 (C) Figure 3 34. Continued.

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304 (A) (B) Figur e 3 35 Photon specific absorbed fractions for the source spheres and (A) and (B) photons as a function of sphere separation and target sphere mass (the irradiation geometry can be seen in Figure 3 34 for compar ison)

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305 (A) (B) Figure 3 36. Photon specific absorbed fractions for the (A) (B) and (C) (following page) source spheres and photons as a function of sphere separation and target sphere mass

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306 (C) Figure 3 36. Continued.

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307 (A) (B) Figure 3 37 Photon specific absorbed fractions for the source spheres and (A) and (B) photons as a function of sphere separation and target sphere mass

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308 (A) (B) Figure 3 38. Electron specific absorbed fractions for the (A) (B) and (C) (following page) source spheres and electrons as a function of sphere separation and target sphere mass

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309 (C) Figure 3 38. Continued.

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310 (A) (B) Figure 3 39 Electron specific absorbed fractions for the source spheres and (A) and (B) electrons as a function of sphere separation and target sphere mass

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311 Figure 3 40 Electron cross dose SAFs for differing target sphere sizes for the center to center separation and source sphere.

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312 (A) (B) Figure 3 41 Variations in SAF with changes in sitting height for uniform (A) and (B) photon sources in the liver of the UFH00M based phantoms for a limited number of target tissues

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313 (A) (B) Figu re 3 42 Variations in SAF with changes in sitting height for uniform (A) and (B) electron sources in the liver of the UFH00M based phantoms for a limited number of target tissues

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314 (A) (B) Figure 3 43 Variations in whole body SAF with changes in sitting height for uniform (A) photon and (B) electron sources in the liver of the UFH00M UFH10M and UFHADM based phantoms

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315 (A) (B) Figure 3 44 Variations in SAF with changes in weight (waist circumference is used as an analog) for uniform (A) and (B) photon sources in the liver of the UFH00M based phantoms for a limited number of target tissues

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316 (A) (B) Figure 3 45 Variations in SAF with changes in weight (waist circumference is used as an analo g ue ) for uniform (A) and (B) electron sources in the liver of the UFH00M based phantoms for a limited number of target tissues

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317 (A) (B) Figure 3 46 Variations in whole body SAF with changes in weight (waist circumference is used a s an analog) for uniform (A) photon and (B) electron sources in the liver of the UFH00M UFH10M and UFHADM based phantoms.

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318 Figure 3 47 Radionuclide S values calculated using a summary of the radionuclide spectra compared to those calculated using the entire radionuclide spectra as given by ICRP Publication 10 7 (ICRP 2008) for 99m and 82 for a point source located at the center of spheres of different masses. Figure 3 48 Radionuclide S values calculated using direct spectrum sampl ing as compared to those calculated using an assembling of monoenergetic SAFs. Spectra from ICRP Publication 10 7 (ICRP 2008) for 99m for a point source located at the center of spheres of different masses.

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319 Figure 3 49 Ratios of S values calculated using the internal dosimetry software S value subroutine to those calculated from direct spectrum sampling within the radiation transport code MCNPX v2.6 as a function of target tissue mass

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320 CHAPTER 4 DISCUSSION UF Hybrid Phantom Blood Vessel System Cons truction of the blood vessel system for all phantoms in the UF hybrid phantom family provided the update needed for the latest generation of the phantoms. W ith the introduction of separable adipose tissue and a voxel based lymphatic node model, the phanto ms resulting from the addition of the blood vessel system s represented the most up to date version of the phantoms. Despite the low percentage of total vessel volume that was modeled, the blood vessels improved the overall anatomic picture of the phantoms making them visually more anatomically accurate as well as providing a vehicle to simulate short lived radionuclide blood borne sources. Even if the total targeted large artery and large vein blood volume was modeled, there was a certain arbitrary compon ent to the construction process. Construction was stylistic in nature, as was the case for several other tissues in the phantoms including the small intestine wall and contents (Lee et al. 2010) Miniscule, intricate cylindrical structures would have to be forced into every available space to approach the targeted vessel blood volume in addition to placing an inordinate number of vessels into the extremities of the phantoms. If total blood volume was valued over anatomic realism, this may have been a rea sonable approach. However, matching total blood volume was not set as a high priority. When distributed blood sources were simulated, t he missing blood volume was simply apportioned to the muscle of the phantom, where many of the major blood vessels resi de. This still gave a good approximation of the true distribution of blood vessels throughout the body. A distributed blood source was provided in the SAF and S value results from the current study, but any arbitrary blood distribution could be applied to the monoenergetic SAFs by calculating relative contributions of the SAF of each blood containing tissue. The following

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321 generalized equation (Equation 4 1 ) was used to calculate the SAF to each target tissue for a distributed blood source: (4 1) where is the SAF to target tissue from blood distributed throughout the body, is the fraction of total blood volume located in source tissue and is the SAF to target tissue from source tissue Ph oton and electron SAFs for the whole body blood source for the UFH00M phantom are shown in Figures 4 1 and 4 2 respectively. The photon SAF curves follow the general shape of SAF curves of most other sources because the shape of the curves is very simila r for self and cross dose at energies exceeding Since blood is distributed throughout many organs, self dose and cross dose are competing processes and this is manifested in many of the SAF curve shape s This competitive process is most evident in Figure 4 2 for the electron SAFs. Some SA F curves decline at higher energies while others increase. If a curve decreases with energy at higher energies, electron escape is dominating the influx of electrons from surrounding tissue. If a curve increases with energy at higher energies, electron c ross fire is overriding the effect of electron escape. This particular circumstance is evident for the heart wall target due to a high concentration of blood in the heart chambers. To show the effect the newly developed age dependent regional blood distri butions have on distributed blood dosimetry, monoenergetic photon SAFs were calculated with both the new distributions and adult distributions for each phantom ; these are then plotted in Figure 4 3 The viewing window was purposefully narrowed to emphasiz e the higher energy SAFs (the effects at lower energies are at least as great as at higher energies). The overall average absolute percent difference between the blood SAFs calculated with the new distributions and those calculated

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322 with the adult distribu tions was ( ) The only phantom that did not demonstrate the benefit of age dependent regional blood distributions was the UFH15F at an average absolute percent difference of However, all other phantoms (especially the UFH00M and UFH01M p hantoms) showed marked difference when the adult blood distributions were applied, suggesting that age dependent regional blood distributions are beneficial to performing internal dosimetry for distributed blood sources. The differences were due to chang es in blood vessel concentration in the brain, kidneys, and mineral bone as well as varying rates of growth of organs as a function of age. Vascular Dosimetry A dose averaging methodology was developed to estimate absorbed dose to blood vessel walls from w hole body, distributed blood sources. The body is full of blood vessels that cross irradiate when the blood is infused with a radioactive source, so the dose to blood vessel walls would be overestimated if the whole body model was reduced to a single vess el model. In other words, one possible approach to estimating vessel wall dose would be to model the entire blood vessel system as a single blood vessel for the sake of simplicity In doing so the radioactivity would be completely confined to a single v essel, while in reality the amount of radioactivity confined to the single vessel would actually be distributed through all blood vessels in the body. It follows then that the absorbed dose from radiation to a blood vessel wall of interest would decrease according to the number of blood vessels in the model. Bearing this in mind, a reasonable blood vessel wall dose estimate requires that the number of blood vessels in the body to be approximated in the dosimetry model. To illustrate the effect blood vesse l distribution has on dose to the blood vessel wall, the blood vessel wall simulation results were modified to account for dose averaging effects when other blood vessels are

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323 dose 1 cross dose to an adjacent blood vessel, and cross dose to a distant blood vessel were all calculated during the simulations. The single vessel model predicts that the absorbed dose to all vessel walls in the body is equal to the self dose. If the cross dose from the adjacent vessel we re included in the estimate, the absorbed dose to all vessels in the body would be equal to the linear average of the vessel self dose and the adjacent vessel cross dose. If the distant vessel were included in the model, the absorbed dose estimate would b e equal to the linear average of the vessel self dose, the adjacent vessel cross dose, and the distant vessel cross dose. Cross doses could then be extrapolated for any number of imaginary vessels distant from the vessel of interest and averaged to create a model with a higher concentration of blood vessels. That same set of blood vessels could then be superimposed on the other side of the blood vessel of interest and averaged, creating a two direction vessel arrangement. This process could be repeated f or as many directions as desired and is illustrated in Figure 4 4 Figure 4 4 shows that average dose to the blood vessel wall decreases with increasing number of adjacent vessels and increasing number of directions of inclusion keeping in mind that all blood vessels are treated as straight and parallel to one another Absorbed dose to the blood vessel wall was observed to increase with decreasing vessel length, so it would be reasonable to assume that an age (stature) dependent model is needed B lood ve ssel wall dose for the newborn patient will be greater than blood vessel wall dose for an adult patient for the same AA. In addition, a conservative approach is favored due to the admittedly approximate nature of this vascular dosimetry study. With this in mind, r ectangular prism s approximating the s ize of the torsos of the newborn, adult male and adult female were 1 was changed in this instance to distinguish it from the irradiation scenario where the blood vessel contents of one vessel is irradiating

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324 defined to represent the volume to which all bl ood vessels would be restricted. Contributions from the extremities and head to total blood v essel wall dose would only lower the whole body average vessel wall dose and so were neglected to maintain conservatism. Dimensions for the rectangular prisms in the anterio posterior, lateral, and axial directions were for the UFH00MF phantom for the UFHADM phantom and for the UFHADF phantom R esults for the vessel length were assigned to the UFH00MF phantom and results for the vessel length were assigned to both the UFHADM and UFHADF phantoms Since the number of vessels with a particular lumen diameter and wall thickness could not be confidently assumed, SAFs were averaged over all vessel sizes at the two vessel lengths. Additionally, results were averaged at each radiation energy and Two vessel directions were used, and SAFs were calculated as the average of the blood vessel wall self dose and cross doses at the anterio posterior and l ateral extremes. An illustration of the final irradiation geometry can be seen in Figure 4 5 The SAF estimate for the central blood vessel was used as the whole body estimate, again to maintain conservatism. Blood vessel wall SAFs for the UFH01MF UFH0 5MF UFH10MF and UFH15F phantoms were interpolated between those for the UFH00MF and UFHADF phantoms (the UFHADF phantom was used instead of the UFHADM phantom because the SAFs were slightly higher and conservatism was maintained ) based on similarly deve loped rectangular prisms at all ages as shown in Table 4 1 SAFs for the UFH15M phantom were interpolated between those for the UFH00MF phantom and UFHADM phantom Interpolation with respect to rectangular prism volume accounts for changes in both vessel radial distribution and vessel length. Final blood

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325 vessel wall SAF estimates are shown in Table 4 2 and the photon and electron SAF curves are displayed in Figure s 4 6 and 4 7 respectively Skeletal Photon Fluence to Dose Response Functions During the development of the ORNL series of phantoms, skeletal photon fluence to dose response functions were developed based on Equation 2 2 (Cristy et al. 1987) There were two distinct differences between the UF and ORNL skeletal photon fluence to dose response function calculation methods First, ORNL used chord length distributions of trabeculae and marrow cavities to obtain electron AFs (Cristy et al. 1987) while UF performed detailed 3 D radiation transport using the microstructure and macrostructure of all bone sites using PIRT with EGSnrc for the UFH00MF, UFH15MF, and UFHADMF phantoms 2 ( Hough et al. 2011, Pafundi et al. 2010) Second, the UF skeletal photon fluence to dose response functions were calculated based on image sets specific to each phantom of i nterest 3 while the ORNL data was based on a 44 year old male and applied to phantoms of all ages (Pafundi et al. 2010, Cristy et al. 1987) One immediately noticeable difference between newborn and adult skeletal microstructure is that the newborn has alm ost no IM while the adult has many bone sites with no AM This difference leads to different radiation interaction probabilities and marrow volume fractions so age dependent skeletal photon fluence to dose response functions are potentially needed Thre e bone sites the cervical vertebra, lumbar vertebra, and ribs from the ORNL skeletal photon fluence to dose response function data were selected for comparison, and t he skeletal target tissue was chosen to be AM The UF newborn and ORNL adult skeletal p hoton fluence 2 Chord length distributions were used for the CBIST simulations for the UFH01MF, UFH05MF, and UFH10MF phantoms. 3 The UFH01MF, UFH05MF, and UFH10MF skeletal photon fluence to dose response functions were developed based on macroscopic models specific to the phantom of interest, but weighted averages of electron AFs obtained from chord length distributions of certain bone sites were used for the microscopic models.

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326 to dose response function s for those bone sites and the AM targ et al. ong with the percent difference between them can be seen in Table 4 3 The average absolute percent difference across all photon energies was found to be approximately ( ) At intermediate incident photon energies, the response functions were found to be in relatively good agreement, but they tended to diverge at higher energies and at those energies where the response function ceased to decline and began to incre ase A graphical depiction of this comparison can be seen in Figure 4 8 The difference between the UF and ORNL response functions can be attributed to reasons previously discussed superior physic al modeling and anatomic specificity utilized in the dev elopment of the UF response functions Photon Specific Absorbed Fractions The UFH00MF phantom s w ere selected to highlight the differences between the UF photon SAFs and other available models. The current standard for monoenergetic photon SAFs for the ICR P reference newborn phantom is the ORNL/TM 8381/V6 report (Cristy et al. 1987) Therefore, results from the current study were compared to the ORNL/TM 8381/V6 report in addition to a more recent model, the GSF BABY phantom (Petoussi Henss et al. 2002) T wo source tissues, the liver and thyroid, were chosen for comparison to illuminate differences with organ size. The adrenals, brain, liver, and thyroid were chosen as target tissues for the liver source, and the adrenals, thymus, and thyroid were chosen a s target tissues for the thyroid source. Results of the comparison for the liver and thyroid sources are shown in Figures 4 9 (A) and 4 9 (B) respectively. Variations in SAFs were calculated as the ratio of the UF SAFs to the ORNL and GSF SAFs. Consider ing the chosen source target combinations, differences between monoenergetic photon SAFs ranged from for to a factor of 90 times

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327 greater for Some SAF variations can be explained by examining differences between physical characteristics of t he phantoms themselves, but some differences may be due to different simulation techniques. For example, liver masses in the UF, ORNL, and GSF phantoms are and respectively (Cristy et al. 1987, Petoussi Henss et al. 2002) Across all energies, the UF self dose SAFs for a uniform photon source in the liver was, on average, less than the ORNL SAFs and greater than the GSF SAFs for the same irradiation geometry. It is well documented that increases in tissue mass result in dec reases in self dose SAFs and vice versa (Petoussi Henss et al. 2007) so the overall differences between SAFs for this irradiation scenario can be explained by the variations in liver size. However, there is a noticeable downturn in the UF SAF curve compa red to the ORNL and GSF SAF curves at higher photon energies, which is also apparent when looking at thyroid self dose. Physical characteristics of the phantom models alone do not seem sufficient to explain this difference in curve behavior. An energy ba lance was used for the UF SAFs wherein secondary electrons were tracked while the kerma approximation was used for the ORNL and GSF calculations (Cristy et al. 1987, Petoussi Henss et al. 1998) An accentuated downward turn of the UF SAFs for photon self dose was observed because secondary electrons created within the volume of interest escape into adjacent regions while the other models assume the secondary electrons to be locally deposited Despite the inability to completely account for differences betw een the UF, ORNL, and GSF monoenergetic photon SAFs, noticeable, but not unusually large, differences were seen. In looking at the liver source for all energies and 23 target tissues in the ORNL phantom, of the UF SAFs differed from the ORNL SAFs by or more while of the UF SAFs differed from the ORNL SAFs by or more for the thyroid source. The same analysis was

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328 done for the GSF BABY phantom, and and of the UF SAFs differed from the GSF SAFs by or more for the liver and thyroid sources, respectively. Monoenergetic photon SAFs for the remainder of the UF hybrid phantom family were then compared to the ORNL stylized phantom family SAFs to illustrate differences present across the phantom size spectrum. Differences similar to those seen for the UFH00MF phantom were expected, so a cursory comparison was performed. SAFs for the following cross irradiation scenarios were analyzed to cover different source target size combinations: 4 a nd Self irradiation was examined for and The SAFs selected for comparison were and Overall and absolute percent differences between the photon SAFs of the UF and ORNL phantoms are shown in Table s 4 4 and 4 5 respectively The overall percent differences take into account whe ther the UF values are less than or greater than the ORNL values while the absolute percent differences indicate the extent to which the UF values deviate from the ORNL values. For example, if two photon energies were considered, and the percent differenc es associated with these energies were and the overall average percent difference would be while the average absolute percent difference would be If the yield of these two photon energies were the same for a given radionuclide, then the deviation of the UF SAFs from t he ORNL SAFs would not show any difference in the final radionuclide S value. However, since non uniform irradiation and varying spectra are characteristic of nuclear medicine dosimetry, the absolute percent difference is the measure of greatest interest. 4 was omitted from analysis because the reciprocity principle renders it approximately equal to

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329 Immediately, an outlier irradiation scenario can be identified as because of the absolute percent differences on the order of thousands of percent. These large percent differences are mostly due to those at low energies where statistical uncertainties are larger. For example, the SAFs for the UFH10MF and 10 year ORNL phantom at are and respectively, leading to an absolute percent difference of (four orders of magnitude difference). The UF photon SAFs are mostly within the same order of magnitude as the ORNL photon SAFs and range from about to difference, excluding the example. These comparisons show that using the new UF hybrid phantoms and simulation techniques produce monoenerget ic photon SAFs that vary significantly (but not unreasonably) from the widely used ORNL values. More detailed and physically accurate human anatomy in the UF hybrid phantoms should give reason to consider these dosimetric differences real and an indicatio n that standard SAFs should be migrated to those generated in the present study, after rigorous beta testing and checking by external researchers. Electron Specific Absorbed Fractions It is of interest to explore the impact of using transport generated ele ctron SAFs as opposed to the ICRP Publication 30 method whereby when the source and target are the same and when the source and target are different or t he approach used in the OLINDA /EXM code whereby previously calculated electron self dose AFs to spheres of various sizes are implemented for estimates of tumor and organ self dose (ICRP 1979, Stabin 2005) Consequently, S values were generated for the mon oenergetic electron (Auger and IC ) and beta components of the 90 decay scheme for a uniform 90 source in the liver of the UFH00MF phantoms using each of these three methods.

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33 0 The UF liver self dose S value for the combined monoenergetic electron and beta contributions was greater than that calculated using the I CRP Publication 30 method and about greater than that calculated using the sphere AF approach. This seems to indicate that the ICRP Publication 30 method was improved upon with the introduction of the two simulation electron dosimetry method. However, even though the OLINDA/EXM approach of using electron AFs to spheres of various sizes gave results similar to the two simulation method, electron cross dose is not accounted for with the OLINDA /EXM tissue sphere approach. In this particular comparison st udy, cross dose S values were as significant as about of the self dose S value. Cross dose could be potentially significant in other circumstances. I t is thus proposed in this study that patient dosimetry in nuclear medicine should employ the most cur rent patient anatomic model and transport techniques as they become available for deployment in the clinic. Beyond comparing the UF electron transport methods and those of the ICRP and OLINDA /EXM research group s the novel two simulation electron transport technique was validated. A validation study was performed to show the efficacy of the novel two simulation method for computational internal electron dosimetry. A uniform electron source was simulated in the liver of the UFH00M phantom using the traditi onal full transport method (FTM), and the resulting SAFs were compared to those generated using the two simulation method (TSM). Four target tissues were selected for comparison, and the results for those target tissues are in Figure 4 10 Poor statistic al uncertainties for the FTM manifested in unreliable, and sometimes non existent, curve shapes at low electron energies. The TSM showed considerable improvement over the FTM at these energies as seemingly reliable curve shapes gave reasonable values at a ll electron energies.

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331 Despite this, validation could only be performed when the FTM showed good statistical uncertainties. In this example, all four target tissues displayed reliable statistical uncertainties at energies of and greater. Average uncertainties over this energy range for the gall bladder wall, esophagus, brain, and ET 2 region were and respectively. SAFs for the ET 2 region were still considered fairly reliable since the unce rtainties were right around Figure 4 10 shows good agreement between the FTM and TSM for this energy range, indicating that the TSM is a good method to closely match what would be calculated using the FTM. Of particular interest are the brain and ET 2 target tissues since no primary electrons reach these target tissues, ensuring that all absorbed dose can be attributed to radiative losses. Comparing the TSM to the FTM for these target tissues over this energy range allows for a direct comparison of t he spectrum weighting technique utilized in the TSM. Most importantly, the assumptions made in the development of the TSM model were tested particularly the assumptions that any recorded photon is uniformly distributed throughout the source tissue and t hat all photons created outside of the source tissue originate from within the source tissue. The results seem to suggest that the spectrum weighting technique, along with its assumptions, is a valid approach to computational electron dosimetry The valid ation results show that the TSM gives good results at high energies where statistical uncertainties for the FTM may be acceptable but greatly improves the reliability of the electron SAFs at low to mid energy ranges. ermined based on what curve was expected and how closely the TSM results displayed the expected results. The TSM curves in Figure 4 10 assume the shapes that were expected for the each target tissue. Both partial collisional and full radiative electron S AF curves were identified in this analysis, the curve types that most clearly communicate the importance of the TSM. Full collisional

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332 curves are dominated by the collisional contributions, so the radiative contributions (the contributions that utilize the benefit of the TSM) are not apparent. An important fact that necessitates the work in the current study is that n o standardized set of monoenergetic electron SAFs has yet been developed. OLINDA/EXM 1.0 assumes the electron AF to be unity when the source and target are equal and zero if the source and target are different (except in the case of tumor dosimetry) (Stabin 2005) It has been shown in the current study that these assumptions are only valid for a very small subset of circumstances. Electron es cape becomes significant at higher energies and for smaller organs. Since the simulation techniques and phantoms used in this study are state of the art, migration from simple assumptions to these full dosimetry simulations is recommended upon extensive b eta testing and spot checking. Dosimetric Sensitivity Studies Variation in Source and Target Size and Separation Photons Since all dose scaling techniques will be applied within the internal dosimetry software in development, empirical scaling equations we re not necessary. Improved accuracy could be gained by simply utilizing all SAFs generated over the course of these dose variation simulations. If an empirical equation was applied, further uncertainty could be introduced at the points for which actual d ata is available. It would be relatively straightforward to use the previously generated data within the internal dosimetry software to adjust reference doses to non reference conditions. The benefit of using all generated data as opposed to averaged dat a is explored in this section. Self dose application Mass ratios were used as the basis for dose scaling for photon self dose. As previously discussed, a scaling power was calculated for each source target energy

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333 combination based on the ratio of masses of the source and target and the ratio of the SAFs of both. A 3 D matrix of scaling power ratios was developed as a function of photon energy, source size, and target size. A sample of this 3 D matrix showing scaling power ratios for photons ca n be seen in Table 4 6 As an example, if the reference tissue mass was and the non reference tissue mass was the non reference SAF would be calculated using Equation 4 2 (based on Equation 2 39). (4 2) In this example the SAF for the non reference, larger sphere is obtained by multiplying the reference SAF by a factor of 0.854. This is expected because previously studied dosimetric trends predict that the photon self dose SAF decreases with increasing tissue mass (Pe toussi Henss et al. 2007) For practical application within the internal dosimetry software, 3 D interpolation is performed to obtain mass ratio scaling powers unique to the reference mass, non reference mass, and photon energy of interest. Self dose vali dation The first validation study for photon self dose was the uniform scaling of the UFH00MF liver and thyroid and the patient specific example of the liver and spleen. Uniform 99m photon sources were simulated in all of these tissues. At each emi ssion energy, the monoenergetic photon SAFs for the UFH00MF and UFHADF phantoms were interpolated and scaled according to the reference organ masses for the UFH00MF and UFHADF phantoms and the non reference organ masses of the scaled liver and thyroid and patient specific liver and spleen. Mass ratio scaling powers in the form of a 3 D matrix were interpolated as detailed in the previous section, and a mass ratio scaling power of was also applied to all mass ratios to simulate the m ethod suggested in MIRD Pamphlet No. 11 To assess

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334 the benefit of using the entire mass ratio scaling power dataset instead of averaged values, the mass ratio scaling powers were averaged over all source target size combinations at each energy, resulting in a solely energy dependent dataset. Reference values were scaled using this averaged dataset and compared to the MIRD method as well. Absolute percent differences were compared to determine how closely the scaling method predicted the actual S values, giving no regard to whether the predicted S values were less than or greater than the actual S values Results of this validation study are in Table 4 7 When the entire dataset was used, the UF m ethod gave better results in three of the six irradiation scenarios. The MIRD method tended to do a better job predicting the non reference S value when the non reference organ mass was less than that of the reference organ mass, and the UF method tended to be more accurate when the non reference mass was greater than the reference mass. When the averaged dataset was used, the only irradiation scenario for which the UF method transitioned from the less accurate method to the more accurate method was for t he smaller UFH00MF liver self irradiation Despite this, the UF method using the entire dataset was generally more accurate that using the averaged dataset. When the entire dataset was used, the greatest deviation from the actual S value in this study wa s for either the MIRD or UF method, and the greatest percentage gain in accuracy was The average percent gain in accuracy was less than a percent when the entire dataset was used. These results indicate that the UF method is more correctly a pplied when the whole dataset is utilized rather than an averaged dataset. However, no clear conclusions about the superiority of the UF method over the MIRD method could be drawn since each method was more accurate in different circumstances. Another val idation study was performed on the liver and thyroid self dose models using monoenergetic photons. Energy dependence was a point of interest in the dose scaling

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335 studies, and the previous validation study may have not proven conclusively that the UF method should be adopted over the MIRD method because of the emission energies of 99m The comparisons performed in the previous validation study were performed for the monoenerget ic photons, and the results are in Table 4 8 The UF method proved to be more accurate by up to than the MIRD method for every irradiation sc UF method proved to be less accurate than when the entire dataset was utilized. The UF method was also compared to the MIRD method for the same irradiation geometries but for photons and only mass and energy de pendent scaling powers, and the results are in Table 4 9. The UF method was better at predicting the actual dose for all irradiation geometries by up to about It became clear that the UF method was not unequivocally more accurate than the MIRD metho d for the 99m photon application because the MIRD method do es not appreciably deviate from the UF method over the important emission energies of 99m Specifically, the principle photon emission energy for 99m is about and the MIRD and UF mass r atio scaling powers at that energy are 0.667 and about 0.644, respectively. The MIRD method may be effectively utilized from about to However, at high ( ) and low ( ) energies, the UF method becomes the preferred method. One possible source of error and reason why the UF method does not predict changes in dose more accurately than the MIRD method in every circumstance is the assumption that using volumes with the same surface shape and taking ratios of SAFs elimin ates surface dependence. This assumption may not be entirely true, and may explain why the MIRD method can predict dose changes marginally better in some cases. Finally, the set of patient specific phantoms were used to compare the UF and MIRD photon se lf dose scaling methods. Uniform 131 photon sources were simulated in the liver and

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336 spleen of 14 male and 13 female patient specific phantoms. All mass ratio scaling powers were used for the UF scaling method, and t he results of this validation study a re in Table 4 10 The MIRD and UF self dose scaling methods are both very good at predicting dose changes for the given set of patient specific phantoms There does not seem to be a firm distinction between the two methods. However, for the 131 photon spectrum, the average gain in accuracy between the two methods is well below The principle photon emission energy for 131 is so the MIRD and UF method tend to converge for this application. Even when the MIRD method gave more accurate d ose scaling results than the UF method, it was never by a significant amount. In these validation studies, the maximum accuracy gain over the UF method by the MIRD method was when all UF mass ratio scaling powers were used. Alternatively, for the h igh energy validation study, the UF scaling method gained up to in accuracy over the MIRD method. In addition, up to gains in accuracy were observed for the low energy applications. Since the UF method showed such noticeable improvements over the MIRD method for the high and low energy application s and closely approximated the MIRD method for the mid range energy application, it is proposed in this study that the UF photon self dose scaling methodology should be utilized in the UF internal dosimet ry software code in lieu of the MIRD method. It is also proposed that the entire mass ratio scaling power dataset should be used instead of the averaged dataset because, on average, the UF self dose scaling method gives better results when the entire data set is used. Cross dose application Instead of using mass ratio scaling powers for the cross dose scaling methodology, simple SAF ratios were used to scale reference cross dose SAFs based on inputs of reference and non reference center to center separati ons, reference source and target masses, non reference source and target masses and radionuclide emission energies. An excerpt

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337 of the photon cross dose tables can be seen in Table 4 11 To illustrate how the photon cross dose sphere SAFs were utilized, consider an arbitrary reference irradiation geometry where the source tissue is the target tissue is the center to center separation is and the photon energy is The non reference source tissue mass, target tissue m ass, center to center separation, and photon energy are and respectively. The equivalent reference sphere SAF is and the equivalent non reference sphere SAF is To ob tain the predicted non reference SAF, the reference SAF would be multiplied by the ratio of the equivalent non reference SAF to the equivalent reference SAF, which comes to 0.2088. The table only shows an excerpt of the photon cross dose sphere SAFs. The full dataset contains 17 source sizes, 17 target sizes, 7 center to center separations, and 21 photon energies. The equivalent reference and non reference sphere SAFs are interpolated between the available data points. Cross dose validation First, vali dation was performed using two sets of spheres where one was defined to be the reference configuration, and the other was defined to be the non reference configuration. Monoenergetic photons and the 99m photon spectrum were simulated, and t he reference configuration S value was scaled using the photon cross dose sphere SAF ratios. The scaled reference S value was compared to the actual S value to assess efficacy of the cross dose scaling method. Results of these validation studies are give n in Table 4 12 Currently, no cross dose scaling is performed in OLINDA/EXM, so the conventional approach is to only scale self dose and leave cross dose unadjusted. This validation study shows that, for this irradiation scenario, the UF photon cross do se scaling methodology would be and more accurate for photons and the 99m photon spectrum, respectively, than if one were to simply use the reference S values The UF method predicted the true non reference

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338 S value to within a nd for photons and the 99m photon spectrum, respectively. Since the average 99m photon energy is considerably lower than it was expected that the UF cross dose scaling method would be more effective for the ph otons because of statistical uncertainty issues. However, even at the lower energies of the 99m photon spectrum, the UF scaling method proved to be reasonably accurate. Actual anatomic configurations would rarely exhibit instances in which source tar get center to center separations changed from to However, this validation study was done at distance extremes to test the photon cross dose scaling method itself. A similarly formatted validation study was performed using the UFHADM phant om by scaling and moving both the liver and pancreas and simulating uniformly distributed and 99m photons in the pancreas of the non reference irradiation geometry (pancreas is the source and liver is the target) Previously calculated refe rence monoenergetic photon SAFs were scaled according to interpolated photon cross dose SAF ratios and the resulting scaled non reference S values were compared to the actual non reference S values obtained through direct simulation and t hese results may also be seen in Table 4 12 Cross dose scaling accounted for an and percentage point gain in accuracy for the monoenergetic and 99m photons, respectively. This is a real application example and one that shows the probable magnitude of gains in accuracy. A gain in accuracy is significant, and this validation study makes an argument for the use of the newly c alculated sphere cross dose SAFs for cross dose scaling. Finally, reference UFHADM and UFHADF monoenergetic SAFs were scaled with the UF photon cross dose scaling technique to attempt to predict actual S values observed in the patient specific phantoms. U niformly distributed 131 photons were simulated in the liver of each of the

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339 phantoms, and SAFs were calculated to a pancreas target in each phantom. Results from this validation study are in Table 4 13 The percentage point gain in this situation is always relative to the UF scaling method. Scaling cross dose photon SAFs for actual clinical application shows improvement for most of the patient specific phantoms. A limiting factor for photon cross dose scaling is the fact that most non reference organs will not have the same shape as the reference models. Because of this, one can only hope to scale doses in as reasonable a way as possible to push the reference values closer to the actual values. Using the methods developed in this study will never guarantee complete accuracy but the methods do seem to more accurately predict non reference scenarios than the reference values. Again, it is recommended that the photon cross dose scaling procedure detailed in this section be applied in the UF internal dosimetry software program since non reference doses have been shown to b e effectively predicted using the procedure. Electrons Self dose application Mass ratios were again used as the basis for dose scaling for electron self dose. A scaling power was calculated for each source target energy combination based on the ratio of masses of the source and target and the ratio of the SAFs of both. A 3 D matrix of scaling power ratios was developed as a function of electron energy, source size, and target size. A sample of this 3 D mat rix showing scaling power ratios for electrons can be seen in Table 4 14 As an example, if the reference tissue mass was and the non reference tissue mass was the non reference SAF would be calculated using Equation 4 3 (based on Equation 2 39). (4 3)

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340 In this example, the SAF for the non reference, larger sphere is obtained by multiplying the reference SAF by a factor of 0. 571 This is expected because previously studied dosimetric trends predict that the electron self dose SAF decreases with in creasing tissue mass (ICRP 1979) Interestingly, for this reference/non reference sphere combination, traditional electron self dose scaling algorithms would assign a mass ratio scaling power of 1 when that is not the case according to present study. Fo r practical application within the internal dosimetry software, 3 D interpolation is performed to obtain mass ratio scaling powers unique to the reference mass, non reference mass, and electron energy of interest. Self dose validation The same self dose validation studies performed for photons were also performed for electrons with the exception that monoenergetic electrons were used instead of monoenergetic photons for the UFH00MF and patient specific based studies, the 99m monoenergetic electron spectrum was used instead of the 99m photon spectrum for the UFH00MF and UFHADF based studies, and the 90 beta spectrum was used instead of the 99m photon spectrum for the 14 adult male and 13 adult female patient spe cific phantoms study. Results for 99m electrons in the scaled liver and thyroid of the UFH00MF and the scaled liver and spleen of the patient specific phantom are in Table 4 15 Results for the monoenergetic electrons for the same irradiatio n geometries are in Table 4 16 Results for the monoenergetic electrons for the same irradiation geometries are in Table 4 17. Results for the uniform 90 beta sources in the liver and spleen of the 14 adult male and 13 adult female patient sp ecific phantoms are in Table 4 18 Upon investigation, electron self dose scaling results mirrored those of photons. Mid range to low electron energies did not spotlight the benefit of using t he UF mass ratio scaling powers because electron AFs are close to unity at the electron energies seen for 99m and 90

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341 In some instances, the MIRD method (scaling power of 1) had a slightly better predictive quality than the UF method. However, the electrons in the UFH00MF scaled organs demonstrated the scenario in which the MIRD method begins to break down. At high enough electron energies and for smaller source sizes, the electron AF deviates significantly from unity due to increased electron range. This concept is evidenced by the average percentage point gain in accuracy of about with th e maximum gain in accuracy of for the smaller UFH00MF thyroid. It is recommended that the UF electron self dose scaling approach should be utilized in the internal dosimetry software instead of the MIRD method. Electron self dose does scale linearly 5 with changes in source mass for large source masses and intermediate to low electron energies since the electrons in that irradiation scenario are typically absorbed within the emitting tissue. However, at higher electron energies and for smaller source t issues, the assumption that the electron AFs are unity breaks down as electrons attain enough energy to escape into surrounding regions. To capture this effect, the UF electron self dose scaling method will be implemented in the internal dosimetry softwar e package. Cross dose application Surface shape and surface to surface distance heavily impact perturbations in electron cross dose with changes in source and target size. A target tissue may be out of the range of primary electrons in the reference mod el, but in the range of primary electrons in the non reference model. When this is the case, electron dose differences between the two models may be orders of magnitude. Segmenting individual organs in the clinic is impractical, so defining surface shape on a case by case basis was abandoned as a possible 5 The same scaling may be done by setting the mass ratio scaling power to unity.

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342 concept to assist in electron cross dose scaling. Instead, the radiative component of the electron dose was selected as the scalable part of electron dose. The radiative component of electron dose can b e attributed entirely to photons generate d during the course of electron energy loss. Photon cross dose scaling techniques could be applied in this case since the radiative component of electron simulations is effectively accomplished by photon transport. Collisional contributions to dose (primary dose) were not scaled and were subject to the uncertainties associated with changes in source target shape and surface to surface distance. Principal gains in dosimetric accuracy were con fined to the radiative componen t and therefore more distant organ pairs. Cross dose validation The UFHADM brain and liver were scaled and slightly translated to create a non reference irradiation geometry, and electrons were uniformly simulated in the liver. Absorbed dose was recorded in the brain and compared to scaled reference values. Collisional contributions to dose were excluded due to the large center to center distance between the brain and the liver. Photon cross dose scaling techniques were applied to the radiative component of electron dose and compared to actual simulation estimates, and the results are in Table 4 19 There is a gain in accuracy using the UF scaling method for monoen ergetic electrons, but there is a loss in accuracy for the 82 beta spectrum. Poor statistical uncertaint ies (~ ) could be the reason for the loss in accuracy for the 82 beta spectrum test. Patient specific phantoms were also utilized for v alidation purposes. A validation technique similar to that used for the patient specific phantom study for photon cross dose scaling was used to investigate the electron cross dose scaling method. Instead of uniform 131 photon sources in the liver of t he phantoms, 90 beta sources were simulated, and dose was

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343 recorded in the pancreas. Results from this study are given in Table 4 20 Most phantoms displayed the beneficial nature of the UF electron cross dose scaling method. Gains in accuracy were obs erved in most cases with a maximum gain of about and average gain of about This is admittedly not a drastic gain in accuracy, but the overwhelming number of cases indicates that photon cross dose scaling can be applied to the radiative component of electron dose. It is therefore recommended that this scaling technique should be applied in the internal dosimetry code in development. Variation in Anth ropometric Characteristics Sitting height dose scaling application Patient measurement based internal dose scaling techniques could not be finalized until several methods were applied to the validation studies. However, the general approach was the same for each method. Non reference SAFs obtained by scaling reference SAFs was the final goal, so natural ly a scaling factor or set of scaling factors could be envisioned as the general approach. Monoenergetic SAFs for all target tissues in reference and non reference hybrid phantoms for five source tissues were available for analysis. Sitting height inform ation was available for all phantoms systematically created for the sitting height dose scaling study. As a result, for a given photon or electron energy, monoenergetic SAFs could be interpolated for a given phantom and subsequently interpolated between t he two nearest phantoms based on the initial energy of the radiation and sitting height of the patient, defined by user input. The non reference SAF would then be obtained using Equations 4 4 and 4 5 (4 4) ( 4 5)

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344 where is the SAF for source tissue irradiating target tissue at radiation energy for a patient with sitting height is the same measure for the reference phantom with sitting height and is the dose scaling factor for source tissue irradiating target tissue at radiation energy for a patient with sitting height based on the reference phantom with sitting height The scaling factor may initially seem unnecessary since the two equations together imply that the non reference SAF could be obtained by simpl y interpolating between the av ailable SAFs. However, only the UFH00M, UFH10M, and UFHADM phantoms were simulated in this study, so it was clear that scaling factors for other phantoms would have to be interpolated between scaling factors calculated for th ese few reference phantoms. To accomplish this, sitting height ratios could be correlated with SAF ratios for the UFH00M, UFH10M, and UFHADM phantoms. Then, to obtain scaling factors for the UFH01MF, UFH05MF, UFH15MF, and UFHADF phantoms 6 scaling factor s would be interpolated for the UFH00M, UFH10M, and UFHADM phantoms based on the ratio of the patient sitting height to the reference phantom (one of the non simulated phantoms) sitting height. It was shown in Figure 3 43 that scaling factors probably var y depending on which reference phantom was used as the base phantom for the sitting height application (e.g., dose seemed to vary more for phantoms based on the UFH00M phantom than the UFHADM phantom). As a result, final scaling factors for the non simula ted phantoms would be interpolated between the sitting height ratio interpolated scaling factors of the UFH00M, UFH10M, and UFHADM phantoms based on the sitting height of the actual base reference phantom 6 Scaling factors for the UFH0 0F and UFH10F phantoms would be equal to those of the UFH00M and UFH10M phantoms due to almost identical internal anatomy.

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345 It was unclear prior to the validation studies how the scaling factors would be developed. Five source tissues were simulated to perform the sitting height dose scaling computational experiment. If the dose scaling factors for each target tissue were found to vary drastically by source tissue, then inte rnal dose scaling could prove to be too complicated to effectively implement in an internal dosimetry software package. However, if the target tissue dependent dose scaling factors were found to minimally vary with source tissue, then dose scaling would b e feasible, and target tissue average and overall average dose scaling factors could be developed. To investigate this, different levels of dose scaling factor averaging were compared in the validation studies. Since variance reduction techniques were not used in the systematic sitting height dose scaling study, many SAFs were found to be zero or had large statistical uncertainties. SAFs from the systematic study with large uncertainties could lead to unacceptably large errors in predicted changes in dose so all SAFs with uncertainties greater than were set to zero. If either the non reference SAF or the reference SAF in the SAF ratio were zero, both non reference and reference SAFs were set to zero. After these actions were performed, if a target t issue had an SAF of zero, the dose scaling factor was set to the overall target average scaling factor. Trends observed in Figure 3 41 indicated that dose scales fairly consistently for all target tissues with changes in sitting height. Sitting height dos e scaling validation Uniform 131 photon and 90 electron sources were simulated in the liver of a UFH00M based phantom with decreased sitting height, a UFH10M based phantom with decreased sitting height, and a UFHADM based phantom with increased sitting height. Radionuclide S values were predicted for all target tissues by applying dose scaling factors to each target tissue according to the sitting height of the scaled phantom and the reference phantom upon which the

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346 scaled phantom was based. The predicted S values were then compared to those obtained through direct simulation. S values determined using overall average and target average dose scaling factors were compared to S values determined using dose scaling factors that were calculated from the AM brain, liver, lungs, and sple en simulations. Complete results for the 131 and 90 study for the UFH00M based phantom are given in Tables 4 21 and 4 22, respectively Overall results for the 131 and 90 studies for all phantoms are given in Tables 4 23 and 4 24, respectively Target tissues with greater than uncertainty in the direct simulations were excluded from comparison because the predictive quality of the scaling factors cannot be assessed with a reasonable amount of certainty when the standard values themselves have larger uncertainties. While S value estimates with uncertainties greater than uncertainty can still provide useful estimates, they were considered detrimental to this investigation It was found that fairly significant increases in accuracy could be attained when using dose scaling factors based on sitting height for both photons and electrons The gains in accuracy for the UFH00M and UFH10M based phantoms were on the order of while the gains in accuracy for the UFHADM based phantom were on the order of for both photons and electrons It was foreseen that problems may arise for electron dose scaling since electrons do not penetrate as deeply as photons into tissue As a result, surface to surface distances between organ pairs can cause dose scaling factors to vary widely between phantoms of differing sitting heights. For example, the thyroid and salivary glands of the reference phantom may be oriented such that primary electrons emitted from the thyroid reach the salivary glands but may not reach for a non reference phantom, leading to an orders of magnitude difference in dose. Dose scaling factors cannot always accurately predict these anatomical changes in source/target tissues.

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347 For all three irradiation scenarios, photon and electron dose scaling factors proved to increase the accuracy of dose estimates for non reference internal photon and electron dosimetry. All scaling factor types showed increased accuracy, and no strong source dependence was observed. Because of this, it is proposed that target average photon and electron dose scaling factors should be used to calculated non reference doses based on sitting height alone It would be beneficial to use average values so that no one source tissue must be selected as the source tissue u pon which all dose scaling is based. Target average dose scaling factors seemed to predict doses as accurately as overall average dose scaling factors, so target average dose scaling factors were adopted as those that would be used in the internal dosimet ry software package since not all target tissue doses scale by the same amount Weight dose scaling application An approach similar to that used for the sitting height dose scaling study was used for the weight dose scaling study. Reference SAFs were scal ed by factors calculated as the ratio of an interpolated non reference SAF to the reference SAF. This process was adapted from Equations 4 4 and 4 5 and is given in Equations 4 6 and 4 7 (4 6) (4 7) where is the SAF for source tissue irradiating target tissue at radiation energy for a patient with waist circumference is the s ame measure for the reference phantom with waist circumference and is the dose scaling factor for source tissue irradiating target tissue

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348 at radiation energy for a patient with waist circumference based on the reference phantom with waist circumference In a fashion similar to that utilized in the sitting height study, waist circumference ratios could be correlated with SAF ratios for the UFH00M, UFH10M, and UFHADM phantoms. Then, to obtain scaling factors for the UFH01MF, UFH05MF, UFH15MF, and UFHADF phantoms 7 interpolat ion would be performed for the UFH00M, UFH10M, and UFHADM phantoms based on the ratio of the patient waist circumference to the reference phantom (one of the non simulated phantoms) waist circumference It was shown in Figure 3 46 that scaling factors probably vary depending on which reference phantom was used as the base phantom for the weight/waist ci rcumference application (e.g., dose seemed to vary more for phantoms based on the UFH00M phantom than the UFHADM phantom). As a result, final scaling factors for the non simulated phantoms would be interpolated between the waist circumference ratio interp olated scaling factors of the UFH00M, UFH10M, and UFHADM phantoms based on the waist circumference of the actual base reference phantom. Since variance reduction techniques were not used in the systematic weight dose scaling study, many SAFs were found to be zero or had large statistical uncertainties. SAFs from the systematic study with large uncertainties could lead to unacceptably large errors in predicted changes in dose, so all SAFs with uncertainties greater than were set to zero. If either the non reference SAF or the reference SAF in the SAF ratio were zero, both non reference and reference SAFs were set to zero. After these actions were performed, if a target tissue had an SAF of zero, the dose scaling factor was set to the overall target ave rage scaling factor. Trends 7 Scaling factors for the UFH00F and UFH10F phantoms would be equal to those of the UFH00M and UFH10M phantoms due to almost identica l internal anatomy.

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349 observed in Figure 3 44 and 3 45 indicated that dose scales fairly consistently for all target tissues with changes in waist circumference Weight dose scaling validation Uniform 131 photon and 90 electron sources were simu lated in the liver of a UFH00M based phantom with decreased weight/waist circumference a UFH10M based phantom with increased weight/waist circumference and a series of UFHADM based phantom s with increased and decreased weight/waist circumference Radion uclide S values were predicted for all target tissues by applying dose scaling factors to each target tissue according to the waist circumference of the scaled phantom and the reference phantom upon which the scaled phantom was based. The predicted S valu es were then compared to those obtained through direct simulation. S values determined using overall average and target average dose scaling factors were compared to S values determined using dose scaling factors that were calculated from the AM brain, l iver, lungs, and spleen simulations. Complete results for the 131 and 90 studies for the UFH00M based phantom are in Tables 4 25 and 4 26, respectively Overall results for the 131 and 90 studies for all phantoms are in Tables 4 27 and 4 28, respectively Target tissues with greater than uncertainty in the direct simulations were excluded from comparison because the predictive quality of the scaling factors cannot be assessed with a reasonable amount of certainty when the standard values themselves have larger uncertainties It was found that increases in a ccuracy (approximately ) could be attained when using dose scaling factors based on waist circumference when simulating photons for underweight phantoms, but no significant gains were seen for overweight phantoms This was expected because overweight ph antoms are constructed by simply adding adipose tissue around the body, but no significant changes in internal anatomy are made. However, considering electron

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350 dosimetry, no appreciable gains in accuracy for overweight or underweight phantoms were found wh en scaling based on waist circumference was performed. An overall average gain in accuracy of only was found It is recommended that the target average dose scaling factors should be used for underweight patients in the internal dosimetry software pack age because waist circumference based dose scaling factors were effective in adjusting reference doses to non reference doses for photon dosimetry in underweight phantoms. No gain in accuracy was seen for overweight phantoms, so reference values should be used in those cases. It is not recommended to use electron dose scaling factors to predict non reference electron dose for either overweight or underweight phantoms as no benefit was observed in the waist circumference scaling study. Electron range consi derations 8 prevent any general methodology for electron dose scaling. However, some amount of patient specificity may obtained by using electron self dose scaling methods previously discussed. Combined dose scaling application For the combined sitting hei ght and weight dose scaling procedure, the methods described in the sitting height and weight dose scaling sections were simply mathematically combine d as given in Equations 4 8 and 4 9 (4 8) 8 Any given source target combination may have very different levels of primary electron contribution, depending on the body habitus of the phantom. In one instance, primary electrons may deposit dose in the target tissue while in anot her, no primary dose may be present. These dose differences can be order of magnitude and are very difficult to predict.

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351 (4 9) where is the SAF for source tissue irradiating target tissue at radiation energy for a patient with sitting height and waist circumference is the same measure for the reference phantom with sitting height and waist circumference and is the dose scaling factor for source tissue irradiating target tissue at radiation energy for a patient with sitting height and waist circumference based on the reference phantom with sitting height and waist circumference Combined dose scaling validation Uniform 131 photon and 90 electron sources were simulated in the liver of a UFH00M based phantom with increased sitting height and decrea sed weight/waist circumference a UFH10M based phantom with decreased sitting height and increased weight/waist circumference and a series of UFHADM based phantom with various combinations of increased and decreased sitting height and weight/waist circumf erence Radionuclide S values were predicted for all target tissues by applying two dose scaling factors to each target tissue according to the sitting height and waist circumference of the scaled phantom and the reference phantom upon which the scaled ph antom was based. The predicted S values were then compared to those obtained through direct simulation. S values determined using overall average and target average dose scaling factors were compared to S values determined using dose scaling factors that were calculated from the AM brain, liver, lungs, and spleen simulations. Complete

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352 results for the 131 and 90 study for the UFH00M based phantom are in Tables 4 29 and 4 30, respectively Overall results for the 131 and 90 studies for all phantoms are in Tables 4 31 and 4 32, respectively Target tissues with greater than uncertainty in the d irect simulations were excluded from comparison because the predictive quality of the scaling factors cannot be assessed with a reasonable amount of certainty when the standard values themselves have larger uncertainties. It was found that increases in a ccuracy could be attained when using dose scaling factors based on the combination of sitting height and waist circumference for photons. The gains in accuracy for the UFH00M based phantom were on the order of and gains for the UFH10M based phantoms w ere on the order of G ains in accuracy for the UFHADM based phantom set varied between almost no gains in accuracy to about The greatest gains in accuracy for the photon simulations were seen for the shorter, underweight phantoms. The three lar gest target average scaling factor based gains in accuracy were and these belonged to the m5010 phantom (50 th percentile by height and 10 th percentile by weight), the scaled UFH10M phantom (decreased height and increased waist circumference) and the m1010 patient dependent phantom (10 th percentile by height and 10 th percentile by weight), respectively. In contrast, dose scaling factors proved to be largely unhelpful for predicting non reference dose across all phantoms for the electron simu lations Percentage point gains varied quite a bit across all target tissues, but most phantoms did not show appreciable increase s in dose prediction accuracy. Again, this is probably due to the complexity of primary versus radiative electron dose. Orde rs of magnitude variations in electron dose depending on body morphometry render predictions of internal electron dose subject to very large uncertainties

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353 Upon examination of the percentage point gains in accuracy for both photon and electron dose scaling, it is recommended that only sitting height based scaling factors should be utilized in the internal dosimetry software package for both photon and electron components of internal dose Photon and electron internal dose scaling seems plausible based on the validation simulations that were performed for the sitting height only scaling. Up to an overall average of about gain in accuracy was observed with greater gains in accuracy seen at the organ level. Changes in dose seem to be dominated by changes in sitting height rather than changes in waist circumference. Final morphometric dose scaling factors LUT type data was needed for the internal dosimetry software, so sitting height and waist circumference based internal dose scaling factors were calculated for the data generated for the UFH00M, UFH10M, and UFHADM. T arget tissue specific scaling factors were first calculated for each source target energy combination simulated in the morphometry based dosimetric sensitivity study. Fi nal scaling factors were averaged over all source tissues for each target tissue. Several pre processing conditions were set before the scaling factors were calculated (1) any SAF with uncertainty greater than was set to zero, (2) both reference and non reference SAFs were required to be greater than zero for a unique scaling factor to be calculated 9 and (3) if either reference or non reference SAF was zero, the scaling factor was set to the average of all other scaling factors 10 9 Scaling factors in this step (Condition 2) that did not meet the required conditions were temporarily set to zero, an action necessa ry to execute Condition 3. 10 Before this step (Condition 3) was performed, an overall average scaling factor was calculated at each initial radiation energy including all non zero scaling factors. These energy dependent overall average scaling factors wer e used for target tissues meeting the requirements of Condition 3.

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354 An excerpt of the p hoton dosimetry sitting height based results for the shortest and tallest UFH00M based phantoms are in Tables 4 33 and 4 34 respectively, and were selected to show both ends of the scaling spectrum Expected trends in dose scaling factors were observed i n both examples. Absorbed doses were expected to increase in general for the shortest phantom, resulting in scaling factors greater than unity, and most scaling factors in Table 4 33 are greater than unity. Alternatively, the tallest phantom was expected to have scaling factors less than unity, and this is manifested in Table 4 34 In both cases, the scaling factors tended to flatten out at energies greater than or equal to while they tended to shift away from unity at lower energies, increasing for the shortest phantom and decreasing for the tallest phantom. Absorbed dose scales more radically with changes in body morphometry at lower initial radiation energies du e to the less penetrating nature of the radiation of interest. S imilar tables were generated for both sitting height and waist circumference based photon dosimetry for the UFH00M UFH10M and UFHADM based phantom series. Scaling factors for UFH00F and UFH10F based non reference phantoms were inherently calculated because the internal structure of the UFH00F and UFH10F reference phantoms is almost identical to that of the UFH00M and UFH10M phantoms, respectively. Gender specific organs were assigned the energy dependent overall average scaling factors. However, no surrogate set of data could be assigned to the UFH01MF UFH05MF UFH15M UFH15F or UFHADF based non reference phantoms. Scaling factors for these phantoms were interpolated between the e xisting datasets based on sitting height and waist circumference ratios. As was observed in Figure s 3 43 and 3 46 morphometric dependence changed according to the anchor phantom upo n which the non re ference phantom was constructed.

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355 To accommodate this conclusion, scaling factors for the phantoms for which surrogate data could not be assigned were calculated by interpolating between scaling factors of the UFH00M UFH10M and UFHADM based phantoms according to the sitting height and waist circumference of the phantom of interest. Interpolated scaling factors could only be so calculated if a sitting height and waist circumference ratio was assigned to each virtual phantom in the non UFH15F, and UFHADF reference phantoms. The sitting height and waist circumference ratios of the UFH00M based phantoms were assigned to the imaginary UFH01MF ba sed phantoms. The sitting height and waist circumference ratios of the UFH10M based phantoms were assigned to the imaginary UFH05MF based phantoms. The sitting height and waist circumference ratios of the UFHADM based phantoms were assigned to the imagin ary UFH15M UFH15F and UFHADF based phantoms. New scaling factors were calculated for the UFH00M UFH10M and UFHADM based phantom series so that the sitting height and waist circumference ratios (ratio of non reference to reference) were constant an d equal to the imaginary phantom series (e.g., UFH01MF based phantoms of variable height and waist circumference ) of interest. Finally, scaling factors specific to the imaginary phantom series of interest were interpolated between the appropriate scaling factor sets for which actual data was available according to reference sitting height. The UFH01MF phantom was chosen as an example to explain the scaling factor interpolation method. Consider photons, the whole body as the target tissue, and t he shortest non reference phantom for which scaling factors were calculated. One would expect dose trends for the UFH01MF phantom to fall somewhere between the UFH00M and UFH10M

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356 phantoms, and the original scaling factors for this scenario and the UFH00M and UFH10M based phantoms are 1.525 and 1.399 respectively. The ratios of the sitting height of the shortest UFH00M and UFH10M based phantoms to the reference UFH00M and UFH10M phantoms are 0.749 and 0.754, respectively. The shortest imaginary UFH01MF based phantom was assigned a sitting height ratio of 0.749, so to interpolate between the UFH00M and UFH10M based scaling factors, the scaling factors for the shortest UFH10M based phantom had to be extrapolated to represent a UFH10M based phantom with a sitting height ratio of 0.749. The new scaling factors for the shortest UFH10M based phantom with a sitting height ratio of 0.749 for photons and the whole body target increased from 1.399 to 1.406. The final UFH01MF scaling factor was obtained by interpolating between the reference sitting heights of the UFH00M and UFH10M phantoms ( and respectively) acco rding to the reference UFH01MF sitting height of In this example, the final scaling factor was calculated to be 1.484. Despite the large quantities of interpolation, this approach was considered reasonable given the trends observed in Figure s 3 43 and 3 46 Absorbed dose scaled more dramatically with changes in sitting height for the UFH00M based phantoms than for the UFHADM based phantoms, and the UFH10M based phantoms were somewhere in between in terms of dosimetric sensitivity. Therefore, it is not unreasonable to assume that dosimetric sensitivity for the UFH01MF and UFH05MF would fall between trends seen for the UFH00M and UFH10M based phantoms or that dosimetric sensitivity for the UFH15M, UFH15F, and UFHADF would fall between trends se en for the UFH10M and UFHADM based phantoms. To prove this, one phantom was constructed at heights less than the reference for the UFH01MF, UFH05MF,

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357 UFH15M 11 and UFHADF phantoms, and the 99m photon spectrum was simulated in the liver of each phantom using MCNPX. Radionuclide S values were calculated for all target tissues, and S values for target tissues displaying statistical uncertainties less than were compared to those scaled from reference values. Percentage point gains in accuracy for indiv idual target tissues and overall averages for this validation study are shown in Table 4 35. All four phantom validation studies showed the benefit of sitting height and waist circumference based internal dose scaling and the validity of the interpolatio n methods used to assign dose scaling factors to phantoms that were not explicitly simulated. An overall average gain in accuracy range of approximately to was observed with the UFH15M phantom showing the highest gains in accuracy at about Th e theoretical basis for the interpolation techniques used to assign scaling factors to the UFH01MF, UFH05MF, UFH15M, UFH15F, and UFHADF appeared sound based on the validation study and implications from earlier studies and the evidence suggests that inter polation is a reasonable approach. These derived scaling factors are recommended for use in the internal dosimetry software package upon further beta testing. Internal Dosimetry Software Internal dosimetry software allows the user to quickly perform radia tion dosimetry studies for patients undergoing a variety of nuclear medicine procedures including those that are diagnostic or therapeutic in nature This is in stark contrast to the approach one would use to obtain patient specific dose estimates. Segm ented patient images and full radiation transport would be needed to perform accurate internal dosimetry on a case by case basis. Since this approach is time consuming pre simulated internal dosimetry for reference individuals scaled to 11 The UFH15F phantom was not included in this validation because of its similarities to the UFH15M and UFHADF phantoms.

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358 non reference par ameters (e.g., organ sizes, body morphometry, etc.) is the optimized method of choice for whole body dosimetry All of the time consuming radiation transport simulations and even the relatively time consuming S value construction algorithms are completed prior to software release, allowing for direct LUT type actions. Current patient specific methods, such as 3D RD (Kolbert 1997), are necessary for high dose radionuclide therapy procedures, but whole body models to assess absorbed dose to all tissues in t he body cannot be readily constructed with those methods. Currently, OLINDA/EXM 1.0 is one of the most widely used internal dosimetry software programs in the world. Combining many input screens with LUT type algorithms, OLINDA/EXM 1.0 gives a somewhat us er friendly, albeit not optimized, software environment. In addition, older phantoms and simulation techniques are utilized A more optimized software experience is being developed at UF and NCI of the NIH that will have less input screens and a more str eamlined visual layout for the user. The blood vessel model, skeletal photon fluence to dose response functions, photon and electron SAFs, and dose scaling techniques based on user input of organ size and separation or patient morphometric characteristics will all be included in the software. In addition, the NCI hosted software package will include a CT component that will allow for dual PET/CT or SPECT/CT dose estimates (Lee et al. 2011) Although the GUIs were not developed at UF, the core concepts use d in the nuclear medicine portion of the future software were developed in this work and in the dissertation studies of fellow UF student Laura Padilla. The collaboration between UF and NCI will benefit the worldwide exposure of the software upon release and will facilitate further dosimetry investigations between the two organizations

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359 Case Stud ies In its entirety, the current body of works aimed to improve the methods and approaches used to determine radiation absorbed dose to radiosensitive tissues in t he human body. Many validations and checks have been performed to ensure the validity of the data, but real examples will show the usefulness of the data in the clinic. Two radiopharmaceuticals were selected to perform dosimetric analysis (1) 99m (RBC) and (2) 67 The first was selected to showcase the blood models developed in the current study while the second was chosen to force examination of a more complicated biokinetic model. Dosimetry w as performed for all phantoms in the UF hybrid phantom family, and dosimetric results were compared to dose estimates from other sources. Radiopharmaceuticals Tc 99m labeled red blood cells 99m is produced using a 99 99m radionuclide generator, and 99m has a physical half life of 6 hours through isomeric transition decay (Cherry et al. 2003) The primary photon decay energy is with an absolute yield of 0.89 (ICR P 2008) 99m also produces IC and Auger electrons at a relativ e delta value contribution of about with gamma rays and x rays accounting for the remaining (ICRP 2008) Beta particles are also emitted, but at an insignificant relative delta value contribution of only (ICRP 2008) 99m is tagged to R BCs for the purpose of 99m scintigraphy to diagnose gastrointestinal bleeding (Treves 1995) Since the 99m is tagged to RBCs, it remains in the blood pool for a longer time than most other radiopharmaceuticals, necessitating a distributed b lood source for internal dosimetry. Average absorbed dose to blood vessel walls was also determined in this example.

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360 Ga 67 citrate 67 is a cyclotron produced radi onuclide with a physical half life of 3.3 days and d ecays through electron capture (EC) ( Treves 1995) Primary photon decay energies are and with corresponding absolute yields of 0. 39 0. 21 and 0.1 7 (ICRP 2008) 67 also produces IC and Auger electrons with a relative delta value contribution of about with gamma rays and x ray s accounting for the remaining (ICRP 2008) 67 can be used for various clinical applications of SPECT for diagnosis of abnormalities including infection and inflammation Biokinetics Biokinetic data for 9 9m was taken from ICRP Publication 106 (ICRP 2007) and biokinetic data for 67 was taken from ICRP Publication 53 (ICRP 1988) Values from important biokinetic equations for 99m and 67 are given in Tables 4 3 6 and 4 3 7 respectively (ICRP 2007, ICRP 1988) The important parameter for these case studies is which is the time integrated activity coefficient (or total number of decays per unit administered activity). Time integrated activity coefficients are multiplied by the radionuclide S value for each relevant source tissue to determine the absorbed dose to all target tissues of interest per unit AA. Time integrated activity coefficients take into account the distribution of the radiopharmaceutical throughout the body, considering physical/radioactive decay and the half life of the radiopharmaceutical in each source tissue. Dosimetry Do simetry for both radiopharmaceuticals was performed using Equation 4 10 (4 10)

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361 where is the absorbed dose to target tissue per unit AA is the radionuclide S value to target tissue from source tissue and is the time integra ted activity coefficient for source tissue Radionuclide S values were calculated by energy interpolating the monoenergetic photon and electron SAFs developed in the current study for application in Equation 4 10 Effective doses for the UFH00MF, UFH01MF UFH05MF UFH10MF UFH15MF and UFHADMF phantoms were calculated using tissue weighting factors from ICRP Publication 103 (ICRP 2007) in addition to absorbed dose to all target tissues. Results for the UFH00MF phantom were provided even though do se estimates from the selected sources were unavailable for the newborn. A secondary reason for selecting 99m as a radiopharmaceutical of interest was to provide blood vessel wall dose estimates. Twenty four percent of the total number of nuclear transformations in blood was apportioned to the large arteries and veins, as these were the vessels under consideration for blood vessel wall dose. The derived monoenergetic photon and electron SAFs for the blood vessel walls were separately interpolated and applied in the S value formulation. Results Equivalent dose per unit AA estimated for the UF phantom f amily for a variety of target tissue s relevant to the ICRP Publication 103 (ICRP 2007) tissue weighting factors for 99m and 67 as compared to estimates given in ICRP Publication 80 (ICRP 1998) as seen in Tables 4 38 and 4 39, respectively. Whole body effective dose was also calculated for both radiopharmaceuticals using maximum typical AAs fo r adults and scaled AAs for pediatric and adolescents. Maximum typical AAs for adults for 99m and 67 were found to be and respectively ( gemiddelstyrelsen 2008 Medi Physics,

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362 Inc. 1994 ). Maximum AAs w ere considered over average AAs to estimate some of the highest doses expected in the clinic for these procedures. Four AA scaling rules (defined earlier), to th e pediatric and adolescent ages, and the average of the four results at each age was taken as the AA for that age. Whole body effective dose estimates for the UF phantom family for 99m and 67 as compared to two other sources can be seen in Tables 4 40 and 4 41, respectively. First looking at the whole body effective dose estimates, the UF estimates are very close to the estimates of ICRP Publication 80 (ICR P 1998). An average absolute percent difference of ( ) was observed across all age groups except the newborn (no estimate was provided for the newborn by the data sources) for 99m Slightly greater differences were seen for 67 with an average absolute percent difference of ( ). In every case, the UF effective dose estimates were greater than the ICRP 80 estimates, and this was expected due to the phantom differences used for dosimetry. ICRP Publication 80 used SAFs from Cristy and Ec kerma n (1987) that are based on the ORNL stylized phantom family (ICRP 1998). One key difference between the UF hybrid phantoms and ORNL stylized phantom is the relative orientation of the internal organs. Figure 4 11 shows th at the separation between organs for the UFH10F phantom is less than that of the ORNL 10 year old phantom. The UFH10F models more closely what is observed in reality human organs are pressed up together, not spaced apart as mathematical shapes necessita te. Resultantly it was expected that UF dose estimates would be slightly higher in general than the ICRP Publication 80 estimates due to increased cross dose contributions This was not always the case as position of the organs themselves could vary bet ween the UF and ORNL phantoms. Tables 4 38 and 4 39 show that in

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363 many (but not the majority of) instances, the ICRP Publication 80 dose estimates are greater than the UF estimates. Even though the whole body effective dose estimates were fairly similar b etween the two estimation sources, UF estimates of equivalent doses to individual organs deviated from the ICRP estimates by an average absolute percent difference of ( ). Differences in individual organ equivalent doses can be just as important as estimates of whole body effective dose 12 because individual organ doses can influence procedural details based on known organ toxicity dose thresholds. In addition, accurate individual organ doses are still needed to estimate individual cancer risk. T he range of effective doses ( ) compared well with current estimates of typical nuclear medicine imaging effective doses ( ) (Health Physics Society 2010). Another area of focus in this section was the determination of a whole body average blood v essel wall dose for the 99m procedure. Patient specific AAs from the internal dosimetry analysis was used again for the blood vessel wall dose estimates. Blood vessel wall dose in for 99m for the entire UF phantom family can be seen in Table 4 42. The maximum (average of four AA scaling methods) wall dose was found to be about well below the threshold for blood vessel wall toxicity ( (Hull et al. 2003)) However, 99m is primarily a photon emitter, and wall doses are expected to be at a maximum for short range particle emitters such as 18 To investigate wall dose for a short range particle emitter, 18 was simulated with the AAs as recommended by the 2010 North American Consensus Guidelines ( Gelfand et al. 2010). 18 clears the blood vessels quite quickly with a biological half life of about 1 minute (ICRP 2008), so no complications were expected. 12 The importance of whole body effective dose as related to patients undergoing nuclear medicine procedures is currently under debate in the field. Optimization and procedure inter comparison for a single patient are probably the two most useful applications of whole body effective dose.

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364 However, to illustrate the effect of short range particles, 18 was assumed to have the same number of nuclear transformations in the blood vessels as 99m This is conservative because both the physical and biological half lives of 99m are greater than 18 (ICRP 2008, ICRP 2008). Results for this analysis are in Tab le 4 43. A maximum wall dose of about was observed for 18 across all phantoms, still well below the threshold for wall toxicity. In fact, most nuclear medicine imaging procedures would probably not garner enough radiation dose to the blood vessel walls to cause concern. Clinical Application The work from the current study can be immediately applied to optimize nuclear medicine procedures, as detailed in Sgouros et al. (2011). Methods utilized in the current study were used in Sgouros et al. (2011) to calculate absorbed dose to variation tissues in the body. The study attempted to optimize the administered activity ( AA ) given to two patients undergoing a 99m SPECT study for renal imaging (Sgouros et al. 2011). Two 10 year old females of equal weight but different statures were addressed in the study, and the tradeoff between cancer risk and diagnostic quality was examined based on several factor s (Sgouros et al. 2011). Currently, AA for these two girls would be calculated as a fraction of the adult AA based on the weight of each, so the same AA would be given for both girls, regardless of their difference in stature one was tall and thin, and one was short and stout (Sgouros et al. 2011). However, the same AA should probably not be given to both patients because differences in body morphometry will lead to differences in image quality. Biokinetic information for 99m was taken from Evans et al. (1996) and Smith et al. (1996), and the whole body clearance rate was calculated by fitting a monoexponential function to the complement of the urine data (Sgouros et al. 2011). Biokinetic data was

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365 necessary to ca lculate internal doses as well as simulate SPECT images. Cancer risk was estimated as age and gender specific lifetime attributable risk (LAR) (cancer incidence risk), as il 2005). Internal dose estimates were obtained with consideration for the source tissues of interest for 99m and the total number of nuclear transformations in each source tissue calculated from the biokinetic models using general radiation transport methodology very similar to that used in the current study with the primary difference being that th e 99m spectra were directly sampled during simulation. Projection images were created using an analytic projection code modeling random variations in tissue uptake (Sgouros et al. 2011). A defect was placed in three different positions with varying l evels of uptake reduction (Sgouros et al. 2011). The images were then scaled to represent and of the count level that would be observed if a low energy, high resolution dual camera system were used with a acquisit ion time (Sgouros et al. 2011). These increases and decreases in count level corresponded to a proportional change in AA. Coronal images of pixel dimensions were extracted and subjected to a channelized Hotelling observer (CHO) study whereby diagno stic quality was assessed through the production of receiver operating characteristic (ROC) curves (Sgouros et al. 2011). The CHO has been shown to accurately predict responses of real radiologists, and the ROC curves indicate diagnostic quality. The stu dy showed that the same diagnostic quality could be obtained for the tall, thin patient if the AA was reduced by about If this new AA was administered rather than the original weight based AA, less than half of the cancer incidence could be expected for the tall, thin patient than the short, stout patient (based on an exposed population) (Sgouros et al. 2011).

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366 This is one example of how the methods used in the current study could be used to optimize nuclear medicine procedures, and in this case, a nuc lear me dicine imaging procedure Accurate internal dose estimates are necessary for comparing cancer risks associated with the use of radionuclides in medicine to investigate the tradeoff between cancer risk and diagnostic quality. The results of the cur rent study are important to this end and may be used in the future to optimize more protocols. In fact, a grant awarded to researchers at Johns Hopkins University and the University of Florida by the National Institute of Biomedical Imaging and Bioenginee ring (NIBIB) of the National Institutes of Health (NIH) will address optimization of 99m and 99m protocols (extensions may be made to 18 in the future).

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367 Table 4 1 Anterio posterior (AP), lateral (LAT), and axial dimensi ons and prism volumes for blood vessel wall scaling methodology. Phantom AP (cm) LAT (cm) Axial (cm) Prism Volume (cm 3 ) UFH00MF 10 14 14 1960 UFH01MF 15 15 29 6525 UFH05MF 15 21 39 12285 UFH10MF 18 26 51 23868 UFH15M 23 30 59 40710 UFH15F 20 28 55 30 800 UFHADM 25 38 67 63650 UFHADF 20 32 60 38400 Table 4 2 SAFs to the blood vessel walls for a uniformly distributed blood source for the UF phantom family. Photon Energy (MeV) Electron Energy (MeV) Phantom 0.01 0.50 4.00 0.01 0.50 4.00 UFH00 MF 3.67E+01 9.27E 01 2.60E 01 1.44E+01 4.89E+01 1.28E+01 UFH01MF 3.37E+01 8.52E 01 2.40E 01 1.32E+01 4.49E+01 1.18E+01 UFH05MF 2.99E+01 7.58E 01 2.14E 01 1.17E+01 3.98E+01 1.05E+01 UFH10MF 2.23E+01 5.68E 01 1.61E 01 8.73E+00 2.97E+01 7.81E+00 U FH15M 2.16E+01 5.51E 01 1.56E 01 8.48E+00 2.88E+01 7.59E+00 UFH15F 1.77E+01 4.54E 01 1.30E 01 6.94E+00 2.36E+01 6.23E+00 UFHADM 1.27E+01 3.28E 01 9.51E 02 4.97E+00 1.69E+01 4.50E+00 UFHADF 1.27E+01 3.29E 01 9.57E 02 4.97E+00 1.69E+01 4.50E+00

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368 Table 4 3 Percent difference between the UFH00MF phantom and the ORNL adult stylized phantom skeletal fluence to dose response functions for selected bone sites (Cristy et al. 1987) Fluence to dose Response Function (Gy m 2 ) Photon UFH00MF O RNL Adult Male Difference Energy Cervical Lumbar Cervical Lumbar Cervical Lumbar (MeV) vertebrae vertebrae Ribs vertebrae vertebrae Ribs vertebrae vertebrae Ribs 0.010 6.32E 16 6.32E 16 6.33E 16 6.16E 16 6.14E 16 6.12E 16 3% 3% 3% 0 .015 2.76E 16 2.75E 16 2.76E 16 2.62E 16 2.61E 16 2.59E 16 5% 6% 7% 0.020 1.55E 16 1.55E 16 1.55E 16 1.45E 16 1.43E 16 1.41E 16 7% 8% 10% 0.030 7.44E 17 7.42E 17 7.45E 17 6.60E 17 6.44E 17 6.29E 17 13% 15% 19% 0.040 4.98E 17 4.95E 17 4.99E 1 7 4.27E 17 4.11E 17 3.99E 17 17% 21% 25% 0.050 4.07E 17 4.05E 17 4.08E 17 3.45E 17 3.31E 17 3.20E 17 18% 22% 27% 0.060 3.77E 17 3.76E 17 3.79E 17 3.26E 17 3.11E 17 3.01E 17 16% 21% 26% 0.080 3.97E 17 3.96E 17 3.97E 17 3.58E 17 3.45E 17 3.3 6E 17 11% 15% 18% 0.100 4.61E 17 4.61E 17 4.61E 17 4.33E 17 4.22E 17 4.14E 17 6% 9% 11% 0.150 6.90E 17 6.91E 17 6.88E 17 6.83E 17 6.74E 17 6.68E 17 1% 3% 3% 0.200 9.61E 17 9.63E 17 9.56E 17 9.63E 17 9.57E 17 9.52E 17 0% 1% 0% 0.300 1.48E 16 1.48E 16 1.49E 16 1.54E 16 1.54E 16 1.53E 16 4% 4% 3% 0.400 2.01E 16 2.02E 16 2.03E 16 2.12E 16 2.10E 16 2.10E 16 5% 4% 3% 0.500 2.53E 16 2.54E 16 2.56E 16 2.67E 16 2.66E 16 2.65E 16 5% 5% 4% 0.600 3.02E 16 3.03E 16 3.05E 16 3. 20E 16 3.19E 16 3.17E 16 6% 5% 4% 0.800 3.94E 16 3.95E 16 3.97E 16 4.17E 16 4.15E 16 4.14E 16 6% 5% 4% 1.000 4.76E 16 4.78E 16 4.81E 16 5.06E 16 5.03E 16 5.01E 16 6% 5% 4% 1.500 6.52E 16 6.54E 16 6.59E 16 6.95E 16 6.91E 16 6.89E 16 6% 5% 4% 2.000 7.97E 16 7.99E 16 8.05E 16 8.56E 16 8.50E 16 8.47E 16 7% 6% 5% 3.000 1.02E 15 1.03E 15 1.03E 15 1.13E 15 1.12E 15 1.11E 15 9% 8% 7% 4.000 1.20E 15 1.20E 15 1.21E 15 1.37E 15 1.37E 15 1.35E 15 13% 12% 10% 5.000 1 .34E 15 1.34E 15 1.35E 15 1.60E 15 1.59E 15 1.57E 15 16% 15% 14% 6.000 1.46E 15 1.47E 15 1.47E 15 1.82E 15 1.80E 15 1.78E 15 20% 19% 17% 8.000 1.66E 15 1.66E 15 1.67E 15 2.27E 15 2.23E 15 2.20E 15 27% 26% 24% 10.000 1.82E 15 1.82E 1 5 1.83E 15 2.71E 15 2.66E 15 2.62E 15 33% 31% 30%

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369 Table 4 4 Energy averaged percent differences between the UF hybrid phantom and ORNL stylized phantom monoenergetic photon SAFs. Phantom liv) adr) lun) trd) trd) Newborn 10% 15% 13% 56% 2152% 1 year 9% 20% 8% 8% 603% 5 year 3% 9% 18% 20% 376% 10 year 1% 4% 21% 21% 19569% 15 year male 7% 0% 4% 59% 227% 15 year female 6% 4% 4% 50% 954% Adult male 9% 7% 7% 59% 73% Adult female 1% 2% 7% 18% 575% Table 4 5 Absolute energy averaged percent differences between the UF hybrid phantom and ORNL stylized phantom monoenergetic photon SAFs. Phantom liv) adr) lun) bra trd) trd) Newborn 10% 15% 19% 56% 2157% 1 year 10% 20% 8% 11% 603% 5 year 6% 15% 18% 20% 376% 10 year 6% 14% 21% 21% 19569% 15 year male 8% 16% 6% 59% 227% 15 year female 7% 17% 4% 50% 954% Adult male 9% 17% 9% 59% 73% Adult female 4% 15% 7% 19% 575%

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370 Table 4 6 Excerpt of the 3 D mass ratio scaling power matrix used to scaled photon self dose showing results for photons Sphere Mass (g) Sphere Mass (g) 1 4 8 10 40 80 100 400 800 1000 1 -0.365 0.379 0.384 0.421 0. 440 0.446 0.478 0.493 0.498 2 0.360 0.371 0.389 0.394 0.435 0.455 0.461 0.494 0.509 0.513 4 0.365 -0.406 0.411 0.455 0.474 0.480 0.513 0.527 0.531 6 0.373 0.398 0.417 0.422 0.467 0.486 0.492 0.524 0.537 0.541 8 0.379 0.406 -0.429 0.476 0.495 0.500 0.531 0.545 0.549 10 0.384 0.411 0.429 -0.483 0.502 0.507 0.538 0.551 0.555 20 0.402 0.433 0.453 0.461 0.506 0.522 0.528 0.555 0.567 0.571 40 0.421 0.455 0.476 0.483 -0.539 0.544 0. 570 0.582 0.585 60 0.432 0.466 0.487 0.494 0.532 0.548 0.553 0.579 0.589 0.593 80 0.440 0.474 0.495 0.502 0.539 -0.559 0.584 0.595 0.598 100 0.446 0.480 0.500 0.507 0.544 0.559 -0.588 0.598 0.602 200 0.463 0.497 0.5 17 0.524 0.559 0.573 0.578 0.598 0.609 0.612 400 0.478 0.513 0.531 0.538 0.570 0.584 0.588 -0.619 0.623 600 0.487 0.521 0.539 0.545 0.577 0.590 0.594 0.613 0.629 0.631 800 0.493 0.527 0.545 0.551 0.582 0.595 0.598 0.6 19 -0.635 1000 0.498 0.531 0.549 0.555 0.585 0.598 0.602 0.623 0.635 -2000 0.511 0.543 0.560 0.566 0.595 0.607 0.611 0.630 0.639 0.640 4000 0.523 0.554 0.571 0.576 0.604 0.615 0.619 0.637 0.645 0.647 6000 0.529 0.560 0.577 0.582 0.609 0.620 0.624 0.642 0.649 0.651 8000 0.534 0.564 0.580 0.585 0.612 0.623 0.627 0.644 0.652 0.654 10000 0.537 0.568 0.583 0.588 0.615 0.626 0.629 0.646 0.654 0.656

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371 Table 4 7 Photon self dose scaling valid ation study analyzing the benefit of using all mass ratio scaling powers as compared to using mass averaged mass ratio scaling powers for the photon spectrum of 99m 175 136 designation for the patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tissue (g) (mGy/MBq s) (%) (%) Method (%) All powers UFH00MF Liver 54.44 2.04E 05 2.56% 3.19% MIRD 0.63% 252.12 7.45E 06 3.82% 3.21% UF 0.61% Thyroid 0.55 3.73E 04 2.67% 4.16% MIRD 1.49% 2.51 1.35E 04 2.80% 1.95% UF 0.86% f 175 136 Liver 2176.34 1.74E 06 1.66% 2.11% MIRD 0.45% Spleen 256.75 7.40E 06 6.25% 5.63% UF 0.62% Average powers UFH00MF Liver 54.44 2.04E 05 2.56% 2.39% UF 0.17% 252.12 7.45E 06 3.82% 3.69% UF 0.14% Thyroid 0.55 3.73E 04 2.67% 5.36% MIRD 2.69% 2.51 1.35E 04 2.80% 1.29% UF 1.51% f 175 136 Liver 2176.34 1.74E 06 1.66% 2.25% MIRD 0.59% Spleen 256.75 7.40E 06 6.25% 6.11% UF 0.15%

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372 Table 4 8 Photon self dose scaling validation study analyzing the benefit of using all mass ratio scaling powers as compared to using mass averaged mass ratio scaling powers for photons 175 the shorthand designation for the patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tissue (g) (mGy/MBq s) (%) (%) Method (% ) All powers UFH00MF Liver 54.44 2.62E 04 9.80% 0.18% UF 9.62% 252.12 1.09E 04 5.28% 0.05% UF 5.23% Thyroid 0.55 1.57E 03 27.24% 2.50% UF 24.74% 2.51 8.65E 04 15.86% 2.94% UF 12.92% f 175 136 Liver 2176.34 2.80E 05 1.36% 2.39% MIRD 1 .03% Spleen 256.75 1.12E 04 12.10% 7.04% UF 5.05% Average powers UFH00MF Liver 54.44 2.62E 04 9.80% 0.48% UF 9.32% 252.12 1.09E 04 5.28% 2.25% UF 3.04% Thyroid 0.55 1.57E 03 27.24% 15.45% UF 11.79% 2.51 8.65E 04 15.86% 9.23% UF 6.6 4% f 175 136 Liver 2176.34 2.80E 05 1.36% 6.66% MIRD 5.30% Spleen 256.75 1.12E 04 12.10% 4.94% UF 7.16% Table 4 9 Photon self dose scaling validation study analyzing photons 175 patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tissue (g) (mGy/MBq s) (%) (%) Method (%) All powers UFH00MF Liver 54.44 2.71E 05 23.21% 0.51% UF 22.69% 252.12 6.04E 06 23.75% 0.05% UF 23.70% Thyroid 0.55 1.78E 03 15.60% 3.34% UF 12.26% 2.51 4.68E 04 16.72% 1.33% UF 15.39% f 175 136 Liver 2176.34 7.14E 07 15.98% 0.27% UF 15.70% Spleen 256.75 5.92E 06 23.51 % 0.65% UF 22.86%

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373 Table 4 1 0 Patient specific p hoton self dose scaling validation study using all UF mass ratio scaling powers for 131 photons The patient specific naming convention is [gender][height in centimeters ][weight in kilograms ] (e.g., m 193 132 is a tall, male). UF deviation MIRD deviation Preferred Percentage point Self S value (mGy/MBq s) (%) (% ) method gain (%) Phantom Liver Spleen Liver Spleen Liver Spleen Liver Spleen Liver Spleen Male m 193 132 3.90E 06 1.38E 05 1.93% 0.63% 2.76% 0.88% UF UF 0.84% 0.25% m 183 120 4.56E 06 1.07E 05 0.57% 0.71% 0.07% 0.56% MIRD MIRD 0.50% 0.15% m 183 112 5.14E 06 1.85E 05 1.56% 1.89% 1.75% 1.67% UF MIRD 0.20% 0.22% m 183 86 5.50E 06 8.58E 06 5.31% 1.32% 5.30% 1.34% MIRD UF 0.00% 0.03% m 180 82 4.90E 06 2.66E 05 1.43% 0.05% 1.73% 0.12% UF UF 0.30% 0.07% m 178 100 5.06E 06 8.03E 06 0.94% 0.06% 1.18% 0.17% UF UF 0.24% 0.11% m 178 73 5.60E 06 1.50E 05 6.53% 0.19% 6.47% 0.46% MIRD UF 0.06% 0.27% m 175 81 5.47E 06 2.34E 05 2.15% 5.67% 2.22% 5.82% UF UF 0.06% 0.15% m 175 66 5.80E 06 1.74E 05 5.1 5% 1.66% 5.05% 1.91% MIRD UF 0.10% 0.25% m 173 98 5.72E 06 2.13E 05 2.86% 2.12% 2.79% 1.95% MIRD MIRD 0.07% 0.17% m 173 74 6.42E 06 4.37E 05 0.79% 0.71% 0.96% 0.46% UF MIRD 0.17% 0.26% m 168 78 7.86E 06 2.46E 05 1.90% 4.85% 1.41% 4.76% MI RD MIRD 0.49% 0.09% m 165 74 6.03E 06 2.27E 05 0.58% 0.53% 0.49% 0.67% MIRD UF 0.09% 0.14% m 157 44 9.60E 06 1.02E 05 3.76% 4.67% 3.06% 4.52% MIRD MIRD 0.70% 0.15% Female f 164 59 5.79E 06 4.49E 05 5.12% 13.30% 4.84% 13.16% MIRD MIRD 0.28% 0.14% f 175 136 4.90E 06 2.16E 05 0.71% 8.57% 0.18% 8.78% MIRD UF 0.53% 0.21% f 173 82 5.63E 06 2.60E 05 4.50% 11.37% 4.18% 11.51% MIRD UF 0.32% 0.14% f 165 63 8.16E 06 5.35E 05 0.42% 10.13% 0.70% 9.84% UF MIRD 0.28 % 0.29% f 163 117 3.79E 06 1.32E 05 3.18% 7.34% 2.01% 7.61% MIRD UF 1.17% 0.27% f 163 80 5.23E 06 2.64E 05 2.01% 6.86% 1.60% 6.98% MIRD UF 0.42% 0.12% f 160 61 6.56E 06 4.52E 05 2.28% 10.92% 2.24% 10.74% MIRD MIRD 0.04% 0.17% f 160 52 8.44E 06 4.06E 05 0.87% 5.19% 0.54% 5.04% MIRD MIRD 0.33% 0.14% f 160 51 6.81E 06 2.44E 05 4.55% 5.60% 4.43% 5.75% MIRD UF 0.12% 0.15% f 155 98 6.66E 06 3.71E 05 3.85% 7.40% 3.81% 7.34% MIRD MIRD 0.04% 0.06% f 155 70 5.75E 06 1.96E 05 0.70% 0.42% 0.48% 0.65% MIRD UF 0.23% 0.23% f 155 48 6.37E 06 3.08E 05 2.22% 6.18% 2.14% 6.22% MIRD UF 0.08% 0.04% f 152 66 6.04E 06 2.21E 05 3.18% 6.44% 3.27% 6.63% UF UF 0.09% 0.19%

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374 Table 4 1 1 Excerpt of the photon cross dose sphere SAFs s howing a subset of the source masses, target masses, photon energies, and center to center separations. Source Target 15.632 cm separation 31.264 cm separation mass mass Photon energy (MeV) Photon energy (MeV) (g) (g) 1.000 1.500 2.000 3.000 4.000 1.000 1.500 2.000 3.000 4.000 1.00 1.00 7.51E 03 7.13E 03 6.51E 03 5.30E 03 5.29E 03 1.19E 03 1.20E 03 9.97E 04 1.09E 03 1.01E 03 2.00 7.44E 03 6.78E 03 6.17E 03 5.39E 03 5.22E 03 1.19E 03 1.29E 03 1.07E 03 1.14E 03 1.04E 03 4.00 7.46E 03 6.61E 03 6.20E 03 5.48E 03 5.14E 03 1.10E 03 1.14E 03 1.07E 03 1.10E 03 1.05E 03 6.00 7.32E 03 6.55E 03 6.25E 03 5.59E 03 5.15E 03 1.09E 03 1.10E 03 1.10E 03 1.04E 03 1.05E 03 8.00 7.27E 03 6.57E 03 6.27E 03 5.65E 03 5.11E 03 1.09E 03 1.11E 03 1.10E 03 1.03E 03 1.04E 03 10.00 7.36E 03 6.66E 03 6.32E 03 5.69E 03 5.10E 03 1.11E 03 1.12E 03 1.12E 03 1.05E 03 1.02E 03 2.00 1.00 7.44E 03 6.78E 03 6.17E 03 5.39E 03 5.22E 03 1.19E 03 1.29E 03 1.07E 03 1.14E 03 1.04E 03 2.00 7.36E 03 6.69E 03 6.17E 03 5.74E 03 5.38E 03 1.16E 03 1.17E 03 1.05E 03 1.01E 03 1.04E 03 4.00 7.28E 03 6.50E 03 6.15E 03 5.76E 03 5.19E 03 1.12E 03 1.14E 03 1.10E 03 1.10E 03 1.09E 03 6.00 7.20E 03 6.43E 03 6.24E 03 5.79E 03 5.18E 03 1.12E 03 1.11E 03 1.13E 03 1.08E 03 1.08E 03 8.00 7.22E 03 6.49E 03 6.30E 03 5.78E 03 5.22E 03 1.10E 03 1.09E 03 1.10E 03 1.09E 03 1.04E 03 10.00 7.26E 03 6.59E 03 6.30E 03 5.74E 03 5.22E 03 1.10E 03 1.10E 03 1.09E 03 1.10E 03 1.03E 03 4.00 1.00 7.46E 03 6.61E 03 6.20E 03 5.48 E 03 5.14E 03 1.10E 03 1.14E 03 1.07E 03 1.10E 03 1.05E 03 2.00 7.28E 03 6.50E 03 6.15E 03 5.76E 03 5.19E 03 1.12E 03 1.14E 03 1.10E 03 1.10E 03 1.09E 03 4.00 7.29E 03 6.69E 03 6.22E 03 5.61E 03 5.11E 03 1.14E 03 1.15E 03 1.15E 03 1.03E 03 1.02 E 03 6.00 7.31E 03 6.69E 03 6.30E 03 5.78E 03 5.16E 03 1.13E 03 1.14E 03 1.13E 03 1.01E 03 1.03E 03 8.00 7.27E 03 6.69E 03 6.39E 03 5.79E 03 5.15E 03 1.11E 03 1.11E 03 1.13E 03 1.02E 03 1.03E 03 10.00 7.34E 03 6.74E 03 6.44E 03 5.80E 03 5.18E 03 1.14E 03 1.10E 03 1.11E 03 1.01E 03 1.03E 03

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375 Table 4 1 2 Photon cross dose validation study using an arbitrary reference and non reference set of spheres and liver and pancreas adjusted reference UFHADM phantom Percent difference Percent d ifference Percentage Reference Non reference Predicted (Predicted to (Reference to point S value S value non reference S value non reference) non reference) gain Energy (MeV) (mGy/MBq s) (mGy/MBq s) (mGy/MBq s) (%) (%) (%) Spheres Monoenergetic 3.5 MeV 3.05E 06 6.46E 07 7.58E 07 17% 372% 354% Tc 99m photon spectrum 2.04E 07 2.40E 08 3.40E 08 41% 748% 706% Phantom Monoenergetic 3.5 MeV 4.35E 06 3.20E 06 3.78E 06 18% 36% 18% Tc 99m photon spectrum 2.74E 07 1.90E 07 2.34E 07 23% 44% 21%

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376 Table 4 1 3 Photon cross dose scaling validation study showing predictive quality of UF scaling method as applied to patient specific phantoms for 131 photons The patient specific naming convention is [gender][height in centimeters][weight in kilograms] (e.g., m 193 132 is a tall, male ). Reference Actual Predicted Reference Predicted Percentage cross S value cross S value cross S value difference difference point gain Phantom (mGy/MBq s) (mGy/M Bq s) (mGy/MBq s) (%) (%) (%) Male m 193 132 6.91E 07 8.95E 07 7.18E 07 23% 20% 3.02% m 183 120 6.91E 07 8.46E 07 7.27E 07 18% 14% 4.23% m 183 112 6.91E 07 8.92E 07 7.19E 07 23% 19% 3.04% m 183 86 6.91E 07 9.23E 07 7.31 E 07 25% 21% 4.31% m 180 82 6.91E 07 1.37E 06 8.14E 07 49% 40% 8.96% m 178 100 6.91E 07 9.67E 07 7.15E 07 28% 26% 2.48% m 178 73 6.91E 07 7.01E 07 6.81E 07 1% 3% 1.42% m 175 81 6.91E 07 1.19E 06 7.44E 07 42% 38% 4.38% m 175 6 6 6.91E 07 1.22E 06 7.55E 07 43% 38% 5.22% m 173 98 6.91E 07 7.39E 07 6.50E 07 6% 12% 5.62% m 173 74 6.91E 07 1.12E 06 7.54E 07 38% 33% 5.53% m 168 78 6.91E 07 1.37E 06 7.42E 07 50% 46% 3.65% m 165 74 6.91E 07 1.83E 06 8.26E 07 62% 55% 7.35% m 157 44 6.91E 07 3.82E 06 9.66E 07 82% 75% 7.20% Female f 164 59 1.12E 06 1.20E 06 1.09E 06 7% 10% 2.75% f 175 136 1.12E 06 1.48E 06 1.20E 06 24% 19% 5.54% f 173 82 1.12E 06 1.39E 06 1.14E 06 19% 18% 1.34% f 165 63 1.12E 06 1.37E 06 1.11E 06 18% 19% 0.87% f 163 117 1.12E 06 8.43E 07 1.06E 06 33% 25% 7.70% f 163 80 1.12E 06 1.28E 06 1.15E 06 12% 10% 2.42% f 160 61 1.12E 06 1.60E 06 1.13E 06 30% 29% 0.67% f 160 52 1.12E 06 1.99E 06 1.14E 06 44% 43% 0.77% f 160 51 1.12E 06 2.39E 06 1.22E 06 53% 49% 4.03% f 155 98 1.12E 06 1.96E 06 1.17E 06 43% 40% 2.77% f 155 70 1.12E 06 1.62E 06 1.16E 06 31% 29% 2.28% f 155 48 1.12E 06 1.90E 06 1.21E 06 41% 36% 4.92% f 152 66 1.12E 06 1.07E 06 1.15E 06 5% 7% 2.60%

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377 Table 4 14. Excerpt of the 3 D mass ratio scaling power matrix used to scaled electron self dose showing results for electrons Sphere Mass (g) Sphere Mass (g) 1 4 8 10 40 80 100 400 800 10 00 1 -0.626 0.633 0.640 0.691 0.717 0.725 0.769 0.787 0.792 2 0.632 0.620 0.634 0.643 0.705 0.734 0.742 0.787 0.805 0.810 4 0.626 -0.649 0.660 0.731 0.760 0.768 0.812 0.829 0.834 6 0.628 0.636 0.667 0.680 0.751 0.7 79 0.787 0.829 0.845 0.849 8 0.633 0.649 -0.696 0.766 0.793 0.801 0.841 0.856 0.860 10 0.640 0.660 0.696 -0.777 0.804 0.811 0.849 0.864 0.868 20 0.664 0.697 0.733 0.745 0.809 0.833 0.840 0.874 0.886 0.890 40 0.691 0.731 0.766 0.777 -0.857 0.863 0.893 0.904 0.908 60 0.707 0.748 0.782 0.793 0.848 0.869 0.874 0.903 0.913 0.916 80 0.717 0.760 0.793 0.804 0.857 -0.881 0.909 0.919 0.922 100 0.725 0.768 0.801 0.811 0.863 0.881 -0.9 13 0.923 0.925 200 0.748 0.792 0.823 0.832 0.879 0.897 0.902 0.925 0.933 0.936 400 0.769 0.812 0.841 0.849 0.893 0.909 0.913 -0.942 0.944 600 0.780 0.822 0.850 0.858 0.900 0.915 0.919 0.939 0.946 0.948 800 0.787 0.829 0.856 0.864 0.904 0.919 0.923 0.942 -0.951 1000 0.792 0.834 0.860 0.868 0.908 0.922 0.925 0.944 0.951 -2000 0.807 0.848 0.873 0.880 0.917 0.930 0.933 0.950 0.957 0.959 4000 0.821 0.860 0.883 0.890 0.924 0.936 0.940 0.956 0.961 0.963 6000 0.828 0.866 0.889 0.895 0.928 0.940 0.943 0.958 0.964 0.965 8000 0.832 0.870 0.892 0.899 0.931 0.942 0.945 0.960 0.965 0.967 10000 0.836 0.873 0.895 0.901 0.933 0.944 0.947 0.961 0.966 0.968

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378 T able 4 15 Electron self dose scaling validation study analyzing the benefit of using all mass ratio scaling powers as compared to using mass averaged mass ratio scaling powers for the electron spectrum of 99m 175 designatio n for the patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tissue (g) (mGy/MBq s) (%) (%) Method (%) All powers UFH00MF Li ver 54.44 4.63E 05 2.79% 2.70% UF 0.08% 252.12 1.00E 05 2.58% 2.63% MIRD 0.05% Thyroid 0.55 4.48E 03 3.54% 3.19% UF 0.34% 2.51 9.90E 04 2.60% 2.83% MIRD 0.22% f 175 136 Liver 2176.34 1.16E 06 2.45% 2.46% MIRD 0.02% Spleen 256.75 9.84E 06 2.24% 2.30% MIRD 0.05% Average powers UFH00MF Liver 54.44 4.63E 05 2.79% 2.69% UF 0.09% 252.12 1.00E 05 2.58% 2.65% MIRD 0.07% Thyroid 0.55 4.48E 03 3.54% 3.45% UF 0.09% 2.51 9.90E 04 2.60% 2.68% MIRD 0.07% f 175 136 Liver 2 176.34 1.16E 06 2.45% 2.49% MIRD 0.05% Spleen 256.75 9.84E 06 2.24% 2.32% MIRD 0.07%

PAGE 379

379 Table 4 16 Electron self dose scaling validation study analyzing the benefit of using all mass ratio scaling powers as compared to using mass averaged mass rati o scaling powers for electrons. 175 patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tiss ue (g) (mGy/MBq s) (%) (%) Method (%) All powers UFH00MF Liver 54.44 7.44E 03 14.69% 3.19% UF 11.51% 252.12 1.94E 03 4.96% 0.98% UF 3.98% Thyroid 0.55 1.57E 01 38.78% 1.88% UF 36.90% 2.51 5.72E 02 16.43% 7.08% UF 9.36% f 175 136 Liv er 2176.34 2.54E 04 0.65% 2.41% MIRD 1.76% Spleen 256.75 1.91E 03 7.69% 1.81% UF 5.88% Average powers UFH00MF Liver 54.44 7.44E 03 14.69% 1.41% UF 13.29% 252.12 1.94E 03 4.96% 4.59% UF 0.36% Thyroid 0.55 1.57E 01 38.78% 22.87% UF 15.91% 2.51 5.72E 02 16.43% 8.10% UF 8.33% f 175 136 Liver 2176.34 2.54E 04 0.65% 7.28% MIRD 6.63% Spleen 256.75 1.91E 03 7.69% 1.81% UF 5.88% Table 4 17 Electron self dose scaling validation study analyzing the benefit of using all mass ratio scaling powers as compared to using mass averaged mass ratio scaling powers for electrons 175 patient specific female at in height and in weight. Actual MIRD UF Percent Mass S value deviation deviation Preferred Gain Method Phantom Target Tis sue (g) (mGy/MBq s) (%) (%) Method (%) All powers UFH00MF Liver 54.44 2.94E 05 0.19% 0.19% UF 0.00% 252.12 6.35E 06 95.90% 95.90% MIRD 0.00% Thyroid 0.55 2.92E 03 0.45% 0.44% UF 0.00% 2.51 6.38E 04 0.76% 0.76% MIRD 0.00% f 175 136 L iver 2176.34 7.36E 07 0.03% 0.03% UF 0.00% Spleen 256.75 6.24E 06 0.04% 0.05% MIRD 0.00%

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380 Table 4 18 Patient specific electron self dose scaling validation study using all UF mass ratio scaling powers for 90 beta particles. The patient specific naming convention is [gender][height in centimeters][weight in kilograms] (e.g., m 193 132 is a tall, male). UF deviation MIRD deviation Preferred Percentage point Self S value (mGy/MBq s) (%) (%) method gain (%) Phantom Liver Spleen Liver Spleen Liver Spleen Liver Spleen Liver Spleen Male m 193 132 4.66E 05 2.87E 04 0.79% 0.38% 0.28% 1.88% MIRD UF 0.51% 1.50% m 183 120 5.62E 05 2.02E 04 0.78% 0.48% 0.44% 2 .29% MIRD UF 0.34% 1.81% m 183 112 6.90E 05 4.56E 04 0.93% 0.96% 0.78% 0.52% MIRD MIRD 0.15% 0.44% m 183 86 7.99E 05 1.47E 04 1.30% 0.23% 1.30% 2.95% UF UF 0.00% 2.72% m 180 82 6.42E 05 7.54E 04 0.93% 1.33% 0.72% 0.88% MIRD MIRD 0.22% 0.4 5% m 178 100 6.70E 05 1.31E 04 0.76% 0.15% 0.59% 3.17% MIRD UF 0.18% 3.02% m 178 73 8.36E 05 3.27E 04 1.29% 0.40% 1.34% 1.66% UF UF 0.05% 1.26% m 175 81 7.62E 05 5.82E 04 0.77% 0.14% 0.72% 0.88% MIRD UF 0.05% 0.74% m 175 66 8.63E 05 3.97E 04 1.35% 0.46% 1.44% 1.27% UF UF 0.08% 0.81% m 173 98 7.58E 05 5.63E 04 0.59% 1.05% 0.53% 0.03% MIRD MIRD 0.06% 1.01% m 173 74 9.25E 05 1.55E 03 0.78% 1.48% 0.93% 2.91% UF UF 0.15% 1.43% m 168 78 1.29E 04 7.20E 04 1.16% 1.85% 1.69% 1.30% UF MIRD 0.53% 0.54% m 165 74 8.59E 05 5.98E 04 0.87% 0.75% 0.94% 0.21% UF MIRD 0.07% 0.53% m 157 44 1.77E 04 1.97E 04 1.26% 1.63% 2.20% 1.20% UF MIRD 0.94% 0.44% Female f 164 59 7.90E 05 1.48E 03 0.52% 1.14% 0. 24% 0.26% MIRD MIRD 0.28% 0.87% f 175 136 6.59E 05 5.40E 04 0.82% 0.55% 0.36% 2.03% MIRD UF 0.46% 1.48% f 173 82 7.65E 05 6.85E 04 0.45% 1.12% 0.14% 2.13% MIRD UF 0.31% 1.01% f 165 63 1.39E 04 2.00E 03 1.27% 0.30% 1.63% 1.53% UF UF 0.36% 1.23% f 163 117 4.40E 05 2.68E 04 0.54% 1.08% 0.28% 3.75% MIRD UF 0.26% 2.66% f 163 80 7.12E 05 7.46E 04 0.64% 0.32% 0.26% 1.13% MIRD UF 0.38% 0.81% f 160 61 9.87E 05 1.55E 03 0.72% 0.70% 0.68% 0.32% MIRD MIRD 0.04% 0.38% f 160 52 1 .49E 04 1.44E 03 1.26% 0.60% 1.70% 1.44% UF UF 0.44% 0.84% f 160 51 1.15E 04 6.77E 04 1.12% 0.02% 1.24% 1.00% UF UF 0.13% 0.98% f 155 98 9.82E 05 1.22E 03 0.94% 0.23% 0.89% 0.61% MIRD UF 0.05% 0.38% f 155 70 8.33E 05 5.22E 04 0.75% 1.05% 0.53% 0.49% MIRD MIRD 0.22% 0.57% f 155 48 9.45E 05 9.47E 04 0.73% 0.01% 0.65% 0.27% MIRD UF 0.09% 0.26% f 152 66 9.40E 05 5.80E 04 1.39% 0.35% 1.31% 1.69% MIRD UF 0.09% 1.34%

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381 Table 4 19 Electron cross dose validation study using the liver and brain adjusted reference UFHADM phantom. Percent difference Percent difference Percentage Reference Non reference Predicted (Predicted to (Reference to point S value S value non reference S value non reference) non reference) gain Energy (Me V) (mGy/MBq s) (mGy/MBq s) (mGy/MBq s) (%) (%) (%) Phantom Monoenergetic 3.5 MeV 2.40E 06 2.34E 06 2.34E 06 0% 2% 2% Rb 82 beta spectrum 8.64E 07 8.65E 07 8.50E 07 2% 0% 2%

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382 Table 4 20 Electron cross dose scaling validation stu dy showing predictive quality of UF scaling method as applied to patient specific phantoms for 90 Y beta particles. The patient specific naming convention is [gender][height in centimeters][weight in kilograms] (e.g., m 193 132 is a tall, male). Reference Actual Predicted Reference Predicted Percentage cross S value cross S value cross S value difference difference point gain Phantom (mGy/MBq s) (mGy/MBq s) (mGy/MBq s) (%) (%) (%) Male m 193 132 7.30E 09 1.07E 08 7.58E 09 32% 29% 2.65% m 183 120 7.30E 09 9.30E 09 7.66E 09 22% 18% 3.92% m 183 112 7.30E 09 9.79E 09 7.58E 09 25% 23% 2.86% m 183 86 7.30E 09 1.05E 08 7.71E 09 31% 27% 3.86% m 180 82 7.30E 09 1.53E 08 8.55E 09 52% 44% 8.17% m 178 100 7.30E 09 1.03E 08 7.54E 09 29% 27% 2.38% m 178 73 7.30E 09 6.91E 09 7.20E 09 6% 4% 1.45% m 175 81 7.30E 09 1.69E 07 7.83E 09 96% 95% 0.32% m 175 66 7.30E 09 1.48E 08 7.95E 09 51% 46% 4.41% m 173 98 7.3 0E 09 7.17E 09 6.88E 09 2% 4% 2.22% m 173 74 7.30E 09 1.41E 08 7.94E 09 48% 44% 4.52% m 168 78 7.30E 09 5.02E 08 7.82E 09 85% 84% 1.03% m 165 74 7.30E 09 2.13E 07 8.68E 09 97% 96% 0.65% m 157 44 7.30E 09 4.92E 08 1.01E 08 85% 79% 5 .72% Female f 164 59 1.23E 08 1.38E 08 1.18E 08 11% 15% 3.60% f 175 136 1.23E 08 3.05E 08 1.30E 08 60% 57% 2.31% f 173 82 1.23E 08 1.57E 08 1.23E 08 22% 21% 0.34% f 165 63 1.23E 08 1.67E 08 1.20E 08 26% 28% 1.50% f 163 117 1.23E 08 9.00E 09 1.14E 08 36% 27% 9.08% f 163 80 1.23E 08 1.38E 08 1.24E 08 11% 10% 1.31% f 160 61 1.23E 08 4.97E 08 1.22E 08 75% 75% 0.04% f 160 52 1.23E 08 4.28E 07 1.23E 08 97% 97% 0.01% f 160 51 1.23E 08 5.55E 08 1 .31E 08 78% 76% 1.55% f 155 98 1.23E 08 3.94E 08 1.27E 08 69% 68% 1.11% f 155 70 1.23E 08 2.60E 08 1.25E 08 53% 52% 0.97% f 155 48 1.23E 08 2.20E 08 1.31E 08 44% 40% 3.87% f 152 66 1.23E 08 1.06E 08 1.24E 08 16% 17% 1.46%

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383 Table 4 21 Percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height for the UFH00M based phantom for 131 photons (e.g., ng height dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (%) (%) (%) (%) WBody 14% 15% 14% 15% 15% 15% 15% Adipose 15% 14% 14% 14% 14% 14% 14% LAdrenal 15 % 15% 15% 13% 16% 16% 16% RAdrenal 11% 8% 10% 2% 10% 10% 9% Brain 14% 19% 17% 16% 16% 19% 16% ROB 15% 12% 13% 12% 12% 13% 11% Bronchi bas 15% 18% 17% 16% 17% 15% 17% RC wall 13% 9% 11% 1% 12% 11% 10% Oesophagus 13% 10% 13% 5% 12% 12% 10% Eye balls 15% 9% 12% 13% 10% 8% 2% GB wall 11% 13% 10% 2% 11% 10% 9% Ht wall 15% 12% 12% 8% 13% 13% 13% LKidney C 15% 14% 13% 14% 14% 14% 14% RKidney C 14% 14% 13% 14% 14% 14% 14% LKidney M 15% 14% 13% 14% 14% 14% 14% RKidney M 12% 11% 10% 11% 12% 11% 11% LKi dney P 14% 13% 12% 13% 14% 13% 13% RKidney P 15% 16% 16% 15% 15% 15% 15% ET2 bas OCL 12% 11% 10% 11% 11% 11% 11% Liver 13% 10% 11% 4% 12% 12% 11% LLung 15% 13% 13% 9% 13% 14% 14% RLung 14% 11% 12% 8% 12% 13% 12% O mucosa 14% 11% 11% 13% 11% 11% 10% Pancreas 14% 9% 11% 1% 11% 11% 13% RSig wall 15% 14% 14% 2% 16% 15% 15% S glands 15% 12% 12% 13% 10% 12% 11% SI wall 13% 8% 11% 1% 12% 10% 11% Skin 15% 13% 13% 12% 14% 14% 14% Sp cord 13% 10% 11% 8% 10% 11% 9% Spleen 13% 10% 12% 3% 11% 12% 12% St w all 12% 9% 11% 2% 11% 10% 11% Thymus 15% 13% 14% 10% 13% 14% 12% Thyroid 11% 6% 7% 4% 5% 8% 7% Tongue 6% 2% 3% 3% 2% 3% 1% Trachea 14% 17% 17% 18% 15% 16% 17% UB wall 14% 14% 12% 5% 15% 15% 12% LC wall 15% 13% 15% 3% 16% 14% 16% Muscle 15% 11% 12% 1 2% 11% 11% 11% Cartilage 15% 14% 15% 13% 14% 14% 14% C bone V 12% 11% 12% 9% 10% 10% 12% Prostate 15% 13% 14% 54% 11% 34% 15%

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384 Table 4 22 Percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height for the UFH00M based phantom for 90 beta particles height dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (%) (%) (%) (%) WBody 12% 19% 19% 19% 19% 19% 19% Adipose 26% 3% 30% 10% 0% 2% 21% LAdrenal 2% 4% 21% 1% 8% 8% 18% RAdrenal 25% 31% 5% 22% 24% 18% 15% Brain 21% 22% 6% 23% 24% 21% 21% ROB 25% 31% 26% 27% 27% 29% 18% RC wall 26% 10% 90% 24 % 23% 12% 17% Oesophagus 24% 24% 29% 21% 27% 35% 25% GB wall 25% 22% 14% 22% 29% 20% 19% Ht wall 26% 28% 11% 16% 21% 21% 16% LKidney C 9% 15% 16% 12% 12% 14% 15% RKidney C 26% 20% 14% 23% 23% 21% 20% RKidney M 25% 19% 13% 21% 21% 19% 18% Liver 10% 0% 6% 17% 15% 9% 18% LLung 26% 29% 24% 20% 19% 19% 23% RLung 26% 26% 29% 22% 20% 19% 17% Pancreas 22% 25% 46% 18% 7% 14% 40% SI wall 26% 22% 16% 24% 22% 17% 18% Skin 0% 11% 9% 43% 1% 15% 8% Sp cord 29% 28% 52% 28% 19% 24% 18% Sp leen 12% 16% 37% 8% 3% 27% 3% St wall 26% 28% 23% 23% 23% 23% 21% Thymus 9% 12% 2% 18% 15% 2% 18% LC wall 1% 1% 22% 4% 11% 8% 10% Muscle 23% 23% 25% 22% 23% 23% 23% Cartilage 25% 25% 19% 23% 30% 25% 24% C bone V 20% 23% 15% 21% 24% 23% 16%

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385 Table 4 23 Average percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height for all the non reference phantoms used for the sitting height dose scaling validation study for 131 photons indicates that scaling factors based on the brain source from the sitting height dose sensitivity study were used). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 14% 12% 12% 7% 12% 11% 12% Scaled UFH10M 15% 16% 18% 7% 18% 17% 17% Scaled UFHADM 5% 5% 4% 3% 5% 4% 5% Average 11% 11% 11% 6% 12% 11% 11% Table 4 24 Average percentage point gain in accuracy over reference values us ing different dose scaling factors based on sitting height for all the non reference phantoms used for the sitting height dose scaling validation study for 90 indicates that scaling factors based on the brain source from the sitting height dose sensitivity study were used). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 15% 13% 2% 11% 16% 11% 9% Scaled UFH10M 16% 17% 7% 16% 2 2% 14% 15% Scaled UFHADM 5% 7% 5% 6% 6% 4% 4% Average 12% 12% 5% 11% 15% 7% 9%

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386 Table 4 25 Percentage point gain in accuracy over reference values using different dose scaling factors based on waist circumference for the UFH00M based phan tom for 131 from the weight dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (%) (%) (%) (%) WBody 2% 7% 6% 4% 6% 6% 6% Adipose 2% 5% 8% 21% 5% 7% 10% LAdrenal 2% 2% 3% 3% 6% 1% 5% RAdrenal 2% 2% 3% 2% 5% 0% 7% Brain 2% 1% 4% 5% 0% 1% 0% ROB 2% 3% 1% 2% 2% 1% 2% Bronchi bas 2% 2% 4% 1% 1% 5% 0% RC wall 2% 2% 3% 3% 3% 0% 5% Oesophagus 2% 4% 4% 0% 5% 5% 4% Eye balls 2% 3% 5% 5% 1% 2% 1% GB wall 2% 2% 2% 25% 4% 0% 6% Ht wall 2% 3% 4% 0% 3% 4% 2% ET2 bas OCL 2% 4% 5% 4% 3% 4% 4% Liver 2% 3% 3% 1% 5% 3% 6% LLung 2% 3% 4% 0% 4% 5% 1% RLung 2% 3 % 4% 1% 3% 5% 4% Pancreas 2% 2% 3% 2% 4% 0% 2% RSig wall 2% 1% 4% 1% 0% 1% 1% S glands 2% 1% 5% 1% 1% 1% 1% SI wall 2% 1% 4% 2% 2% 0% 2% Skin 2% 8% 7% 5% 7% 7% 7% Sp cord 2% 3% 4% 0% 5% 4% 5% Spleen 2% 3% 3% 1% 6% 2% 4% St wall 2% 3% 3% 1% 4% 1% 5% Thymus 2% 2% 1% 1% 0% 1% 1% Thyroid 2% 1% 2% 1% 1% 0% 1% Tongue 2% 1% 5% 2% 0% 2% 1% Trachea 2% 1% 3% 1% 1% 4% 0% UB wall 1% 2% 5% 11% 1% 2% 1% LC wall 2% 2% 4% 2% 3% 0% 3% Muscle 2% 4% 4% 3% 4% 4% 3% Cartilage 2% 4 % 4% 4% 4% 4% 4% C bone V 2% 3% 4% 4% 3% 4% 3%

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387 Table 4 26 Percentage point gain in accuracy over reference values using different dose scaling factors based on waist circumference for the UFH00M based phantom for 90 beta ndicates that scaling factors based on the brain source from the weight dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (%) (%) (%) (%) WBody 9% 8% 8% 8% 8% 8% 8% Adipose 14% 9% 14% 65% 8% 11% 12% LAdrenal 7% 9% 3% 8% 8% 0% 5% RAdrenal 13% 9% 17% 7% 12% 0% 7% Brain 4% 4% 4% 3% 1% 1% 1% ROB 10% 10% 10% 8% 12% 11% 2% RC wall 13% 11% 50% 8% 11% 10% 4% Oesophagus 14% 10% 12% 8% 9% 14% 7% GB wa ll 14% 7% 4% 8% 13% 4% 6% Ht wall 7% 7% 4% 7% 7% 8% 3% Liver 8% 7% 5% 4% 7% 9% 7% LLung 9% 7% 10% 3% 10% 6% 7% RLung 8% 6% 11% 1% 9% 6% 4% Pancreas 7% 0% 9% 1% 2% 1% 1% SI wall 13% 5% 4% 6% 11% 1% 3% Skin 3% 333% 29% 11% 630% 470% 52 6% Sp cord 6% 0% 10% 2% 4% 2% 3% Spleen 1% 5% 0% 6% 6% 7% 6% St wall 13% 7% 2% 8% 10% 1% 13% Thymus 15% 4% 13% 5% 2% 16% 0% LC wall 13% 11% 20% 8% 4% 10% 3% Muscle 13% 10% 11% 9% 10% 10% 10% RBreast 2% 1% 1% 1% 1% 1% 1% Cartilage 13% 10% 7% 8% 13% 9% 13% C bone V 13% 9% 6% 8% 10% 10% 12%

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388 Table 4 27 Average percentage point gain in accuracy over reference values using different dose scaling factors based on waist circumference for all the non reference phantoms used for the weight do se scaling validation study for 131 indicates that scaling factors based on the brain source from the sitting height dose sensitivity study were used). The patient dependent naming convention is [gender][height percentile][weight percentile] (e.g., m5090 is a 50 th percentile height, 90 th percentile weight male). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 1% 2% 2% 2% 2% 1% 2% Scaled UFH10M 0% 0% 0% 4% 0% 0% 1% m5090 1% 0% 1% 6% 0% 3% 1% m5075 0% 0% 0% 0% 0% 1% 0% m5010 6% 12% 12% 2% 13% 11% 12% Overweight average 0% 0% 0% 3% 0% 1% 0% Underweight average 4% 7% 7% 0% 8% 6% 7% Overall average 1% 3% 3% 2% 3% 2% 3% Table 4 28 Average perc entage point gain in accuracy over reference values using different dose scaling factors based on waist circumference for all the non reference phantoms used for the sitting height dose scaling validation study for 90 beta particles (e.g., tes that scaling factors based on the brain source from the weight dose sensitivity study were used). The patient dependent naming convention is [gender][height percentile][weight percentile] (e.g., m5090 is a 50 th percentile height, 90 th percentile weigh t male). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 7% 7% 1% 1% 19% 17% 17% Scaled UFH10M 0% 0% 1% 1% 1% 1% 2% m5090 1% 4% 3% 0% 0% 13% 0 % m5075 0% 2% 1% 0% 0% 6% 0% m5010 1% 10% 7% 1% 3% 64% 1% Overweight average 1% 2% 2% 0% 0% 3% 1% Underweight average 4% 1% 4% 0% 11% 40% 9% Overall average 1% 2% 3% 0% 4% 18% 4%

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389 Table 4 29 Percentage point gain in acc uracy over reference values using different dose scaling factors based on sitting height and waist circumference for the UFH00M based phantom for 131 brain source from the combined dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (%) (%) ( %) (%) WBody 6% 2% 2% 3% 2% 3% 2% Adipose 7% 3% 2% 4% 5% 5% 6% LAdrenal 14% 13% 11% 20% 11% 12% 10% RAdrenal 7% 7% 5% 14% 4% 6% 4% Brain 24% 24% 21% 19% 28% 25% 28% ROB 9% 11% 12% 10% 11% 13% 11% Bronchi bas 22% 20% 19% 19% 20% 17% 17% RC wall 4% 4% 2% 11% 2% 4% 3% Oesophagus 7% 5% 4% 8% 4% 5% 5% Eye balls 24% 23% 20% 21% 26% 26% 24% GB wall 5% 9% 6% 30% 2% 3% 3% Ht wall 2% 4% 5% 0% 5% 6% 4% ET2 bas OCL 22% 19% 18% 19% 20% 19% 19% Liver 9% 8% 7% 13 % 6% 7% 6% LLung 7% 5% 4% 8% 4% 4% 5% RLung 1% 3% 4% 0% 4% 5% 3% O mucosa 23% 22% 19% 21% 26% 22% 21% Pancreas 7% 7% 6% 14% 5% 6% 5% RSig wall 21% 20% 18% 15% 21% 18% 21% S glands 23% 22% 19% 22% 24% 21% 25% SI wall 2% 3% 5% 4% 5% 2% 4% Skin 7% 2% 1% 4% 1% 1% 1% Sp cord 7% 5% 4% 7% 4% 4% 4% Spleen 16% 15% 15% 19% 13% 14% 13% St wall 10% 9% 9% 13% 7% 8% 7% Thymus 17% 19% 19% 16% 19% 17% 18% Thyroid 10% 12% 15% 12% 9% 13% 12% Tongue 23% 22% 20% 21% 2 5% 21% 24% Trachea 14% 15% 15% 12% 15% 17% 14% UB wall 23% 24% 14% 23% 23% 26% 22% LC wall 7% 8% 6% 15% 5% 8% 5% Muscle 4% 2% 2% 2% 2% 3% 2% Cartilage 6% 1% 2% 1% 1% 1% 1% C bone V 1% 8% 8% 7% 7% 9% 9%

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390 Table 4 30 Percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height and waist circumference for the UFH00M based phantom for 90 the brain source from the combined dose sensitivity study were used). Overall Target Active average average marrow Brain Liver Lungs Spleen Target tissue (%) (%) (%) (% ) (%) (%) (%) WBody 7% 2% 2% 2% 2% 2% 2% Adipose 11% 1% 9% 9% 10% 12% 3% LAdrenal 9% 13% 22% 10% 6% 7% 19% RAdrenal 5% 1% 12% 4% 6% 8% 12% Brain 29% 33% 44% 30% 33% 28% 31% ROB 4% 4% 9% 3% 7% 5% 6% RC wall 8% 5% 1% 9% 16 % 7% 3% Oesophagus 11% 22% 28% 13% 24% 23% 22% GB wall 6% 5% 13% 5% 5% 5% 7% Ht wall 23% 17% 11% 20% 12% 11% 20% ET2 bas OCL 0% 1% 7% 1% 1% 0% 1% Liver 8% 10% 17% 8% 8% 19% 1% LLung 18% 13% 10% 21% 7% 19% 7% RLung 22% 19% 14% 23% 10% 23% 20% Pancreas 19% 22% 31% 20% 15% 16% 31% SI wall 9% 8% 4% 11% 15% 7% 5% Skin 13% 43% 15% 15% 119% 77% 99% Sp cord 20% 22% 33% 27% 15% 15% 19% Spleen 20% 22% 30% 21% 13% 28% 19% St wall 4% 2% 10% 2% 4% 7% 6 % Thymus 26% 27% 19% 22% 26% 20% 24% LC wall 5% 8% 6% 4% 14% 8% 8% Muscle 4% 6% 7% 5% 6% 6% 6% Cartilage 9% 12% 9% 13% 14% 13% 13% C bone V 12% 17% 8% 21% 18% 16% 21%

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391 Table 4 31 Average percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height and waist circumference for all the non reference phantoms used for the sitting height dose scaling validation study for 131 ors based on the brain source from the combined dose sensitivity study were used). The patient dependent naming convention is [gender][height percentile][weight percentile] (e.g., m5090 is a 50 th percentile height, 90 th percentile weight male). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 4% 5% 5% 2% 6% 6% 6% Scaled UFH10M 13% 15% 15% 5% 17% 16% 15% m9090 2% 3% 1% 1% 2% 0% 4% m9050 4% 5% 5% 3% 5% 4% 5 % m7590 2% 0% 1% 4% 0% 3% 2% m7550 1% 1% 1% 1% 0% 1% 0% m7525 1% 4% 4% 5% 3% 2% 4% m7510 1% 8% 7% 4% 10% 9% 8% m5090 2% 1% 1% 3% 0% 1% 1% m5075 0% 0% 0% 1% 0% 0% 0% m5010 5% 11% 11% 0% 13% 12% 11% m2575 4% 5% 4% 1% 5% 5% 5% m2550 2% 2% 0% 8% 1% 4% 1% m1050 8% 6% 8% 1% 7% 4% 8% m1010 22% 22% 21% 17% 20% 19% 18% Overweight average 2% 4% 3% 0% 4% 3% 5% Underweight average 7% 10% 10% 2% 10% 10% 9% Tall average 1% 4% 3% 1% 4% 2% 4% Short average 10% 9% 10% 3% 10% 8% 10% Ov erall average 4% 6% 5% 1% 6% 4% 6%

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392 Table 4 32 Average percentage point gain in accuracy over reference values using different dose scaling factors based on sitting height and waist circumference for all the non reference phantoms used for the sittin g height dose scaling validation study for 90 from the combined dose sensitivity study were used). The patient dependent naming convention is [gender][height percentile][weight percentile] (e.g., m5090 is a 50 th percentile height, 90 th percentile weight male). Overall Target Active Non reference average average marrow Brain Liver Lungs Spleen phantom (%) (%) (%) (%) (%) (%) (%) Scaled UFH00M 0% 3% 3% 2% 8% 5% 5% Scaled UFH10M 16% 19% 5% 18% 2 4% 16% 16% m9090 3% 4% 1% 3% 4% 46% 4% m9050 6% 5% 4% 7% 7% 4% 7% m7590 0% 5% 2% 0% 1% 35% 0% m7550 1% 3% 3% 1% 0% 17% 0% m7525 0% 4% 8% 1% 4% 43% 3% m7510 6% 0% 5% 3% 9% 68% 8% m5090 0% 5% 2% 1% 1% 28% 0% m5075 0% 2% 1% 0% 0% 8% 0% m5010 9% 4% 4% 5% 12% 41% 11% m2575 3% 2% 1% 2% 5% 23% 4% m2550 14% 26% 31% 15% 4% 107% 5% m1050 2% 12% 18% 3% 6% 83% 4% m1010 1% 13% 46% 12% 19% 215% 15% Overweight average 4% 0% 0% 3% 6% 21% 4% Underweight av erage 3% 3% 13% 4% 7% 74% 6% Tall average 2% 2% 3% 2% 2% 31% 2% Short average 1% 7% 18% 2% 10% 83% 7% Overall average 2% 3% 8% 2% 5% 47% 4%

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393 Table 4 33 Photon internal dosimetry scaling factors (excerpt) for the shortest UFH00M based ph antom of the sitting height dosimetric sensitivity study Photon Energy (MeV) Target Tissue 0.010 0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100 0.200 0.500 0.800 1.000 2.000 4.000 WBody 2.019 1.998 1.936 1.761 1.632 1.557 1.519 1.502 1.512 1.561 1.58 5 1.585 1.582 1.564 1.525 LAdrenal 4.504 4.165 3.181 2.904 2.196 1.915 1.837 1.822 1.846 1.873 1.899 1.909 1.892 1.846 1.750 Brain 4.624 4.085 8.351 3.950 2.744 2.330 2.147 2.016 1.993 2.008 1.986 1.958 1.944 1.893 1.837 ROB 4.249 4.053 3.095 2.305 1.96 5 1.818 1.754 1.730 1.750 1.818 1.852 1.856 1.846 1.837 1.800 RC wall 4.614 4.351 5.113 3.451 2.506 2.211 2.071 1.946 1.906 1.979 1.943 1.936 1.910 1.885 1.864 Oesophagus 5.897 3.437 2.940 2.192 1.865 1.732 1.696 1.684 1.705 1.778 1.805 1.813 1.822 1.804 1.744 GB wall 4.680 5.384 4.229 2.675 2.104 1.946 1.777 1.827 1.819 1.875 1.856 1.855 1.867 1.820 1.830 Ht wall 4.438 4.436 5.024 2.632 2.108 1.906 1.811 1.769 1.775 1.839 1.875 1.867 1.875 1.838 1.821 Kidney C 4.499 3.828 3.762 3.371 2.517 2.171 2.039 1.948 1.927 1.947 1.935 1.919 1.900 1.878 1.816 Kidney P 7.503 4.769 4.157 2.786 2.606 2.221 1.979 1.972 1.929 2.013 1.932 1.931 1.889 1.868 1.834 Eye lens 4.932 4.379 3.655 2.363 2.135 1.846 1.780 1.810 1.819 1.804 1.861 1.879 1.891 1.851 1.768 LLung 3.452 3.039 4.080 2.432 2.035 1.873 1.797 1.760 1.769 1.824 1.845 1.841 1.836 1.800 1.742 ET1 bas 4.932 4.290 3.781 2.429 1.958 1.853 1.820 1.786 1.745 1.862 1.892 1.927 1.899 1.788 1.730 Pancreas 4.548 4.601 3.892 3.228 2.393 2.085 1.936 1.863 1.850 1.9 16 1.921 1.888 1.904 1.845 1.803 RSig wall 5.226 5.596 4.749 3.202 2.425 2.363 2.259 2.119 2.011 2.042 1.995 1.980 1.935 1.920 1.837 S glands 5.126 5.802 5.182 2.617 2.046 1.855 1.770 1.754 1.763 1.839 1.859 1.863 1.866 1.832 1.811 Sp cord 4.959 5.291 3 .308 2.380 2.042 1.879 1.797 1.757 1.762 1.820 1.849 1.854 1.847 1.851 1.798 St wall 6.549 4.022 3.283 2.919 2.252 1.992 1.907 1.808 1.823 1.874 1.916 1.891 1.880 1.837 1.807 Thymus 4.454 6.843 4.350 2.446 1.971 1.797 1.728 1.714 1.726 1.820 1.854 1.861 1.845 1.843 1.781 Tongue 6.121 6.585 6.018 2.786 2.168 1.941 1.831 1.779 1.790 1.855 1.868 1.864 1.863 1.867 1.789 Trachea 4.935 5.035 3.814 2.337 1.916 1.765 1.685 1.697 1.686 1.831 1.934 1.875 1.865 1.843 1.796 RBreast 4.932 4.704 3.867 2.697 2.038 1. 890 1.745 1.860 1.831 1.855 1.947 1.902 1.970 1.838 1.747 C bone V 2.404 2.188 2.008 1.719 1.551 1.454 1.396 1.340 1.326 1.394 1.444 1.439 1.458 1.456 1.363 Testes 4.932 4.502 3.853 3.026 2.590 2.157 2.119 2.028 1.988 1.966 1.971 1.906 1.918 1.908 1.688

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394 Table 4 34 Photon internal dosimetry scaling factors (excerpt) for the tallest UFH00M based phantom of the sitting height dosimetric sensitivity study Photon Energy (MeV) Target Tissue 0.010 0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100 0.200 0 .500 0.800 1.000 2.000 4.000 WBody 0.568 0.571 0.581 0.620 0.660 0.689 0.706 0.718 0.717 0.698 0.688 0.688 0.688 0.695 0.707 LAdrenal 0.351 0.321 0.392 0.480 0.511 0.547 0.578 0.599 0.606 0.606 0.601 0.614 0.609 0.622 0.629 Brain 0.364 0.375 0.361 0.359 0.443 0.497 0.532 0.562 0.572 0.573 0.577 0.584 0.587 0.601 0.615 ROB 0.311 0.333 0.384 0.472 0.537 0.580 0.605 0.628 0.633 0.623 0.616 0.616 0.616 0.620 0.626 RC wall 0.357 0.334 0.287 0.410 0.469 0.521 0.559 0.588 0.595 0.588 0.584 0.584 0.588 0.591 0 .614 Oesophagus 0.291 0.346 0.408 0.475 0.540 0.582 0.605 0.631 0.633 0.626 0.613 0.610 0.614 0.620 0.622 GB wall 0.341 0.350 0.311 0.426 0.501 0.549 0.580 0.612 0.604 0.615 0.624 0.618 0.617 0.600 0.615 Ht wall 0.345 0.336 0.402 0.472 0.552 0.599 0.625 0.643 0.644 0.625 0.615 0.615 0.617 0.617 0.626 Kidney C 0.341 0.362 0.382 0.477 0.510 0.558 0.586 0.617 0.617 0.599 0.595 0.598 0.599 0.613 0.613 Kidney P 0.347 0.290 0.331 0.469 0.533 0.582 0.592 0.613 0.615 0.601 0.598 0.609 0.582 0.598 0.615 Eye le ns 0.347 0.310 0.361 0.460 0.510 0.532 0.534 0.575 0.567 0.596 0.617 0.610 0.631 0.625 0.648 LLung 0.383 0.429 0.467 0.505 0.567 0.605 0.625 0.641 0.642 0.629 0.621 0.623 0.624 0.630 0.647 ET1 bas 0.347 0.343 0.376 0.443 0.460 0.512 0.566 0.576 0.530 0.6 09 0.618 0.616 0.605 0.623 0.600 Pancreas 0.341 0.309 0.345 0.459 0.503 0.554 0.583 0.611 0.615 0.604 0.601 0.600 0.603 0.603 0.617 RSig wall 0.318 0.341 0.306 0.382 0.467 0.527 0.562 0.553 0.579 0.585 0.565 0.587 0.581 0.598 0.610 S glands 0.329 0.258 0.287 0.386 0.469 0.522 0.552 0.590 0.596 0.604 0.601 0.603 0.605 0.612 0.618 Sp cord 0.296 0.271 0.371 0.475 0.537 0.580 0.605 0.628 0.631 0.621 0.617 0.618 0.619 0.620 0.630 St wall 0.357 0.345 0.402 0.488 0.523 0.575 0.603 0.623 0.631 0.612 0.604 0.60 5 0.606 0.606 0.621 Thymus 0.340 0.320 0.300 0.434 0.516 0.565 0.593 0.621 0.624 0.620 0.612 0.610 0.610 0.620 0.620 Tongue 0.347 0.334 0.323 0.397 0.489 0.547 0.577 0.608 0.615 0.610 0.614 0.613 0.613 0.615 0.627 Trachea 0.316 0.332 0.327 0.423 0.500 0 .547 0.589 0.609 0.613 0.623 0.621 0.613 0.621 0.617 0.605 RBreast 0.347 0.345 0.356 0.450 0.490 0.537 0.549 0.559 0.577 0.604 0.605 0.594 0.613 0.585 0.595 C bone V 0.422 0.472 0.512 0.580 0.633 0.672 0.699 0.732 0.743 0.719 0.679 0.669 0.678 0.686 0.66 9 Testes 0.347 0.345 0.458 0.464 0.464 0.459 0.496 0.539 0.560 0.582 0.588 0.604 0.619 0.651 0.636

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395 Table 4 35. Percentage point gains in accuracy for interpolated sitting height and waist circumference based target average dose scaling factors. Compa rison between actual simulations and doses predicted using reference SAFs and the dose scaling factors. Uniform 99m photon source in the liver of each phantom. T average percentage point gain (%) Target tissue ufh01f ufh05f ufh15m ufhadf WBody 9.24% 16.45% 32.31% 15.51% Adipose 10.39% 22.91% 39.52% 7.57% LAdrenal 12.70% 1.68% 51.19% 13.63% RAdrenal 1.49% 3.59% 49.40% 4.44% Brain 27.69% 24.24% 33.71% 25.76% ROB 16.09% 13.76% 45.26% 54.65% Bronchi bas 17.78% 24.31% 36.69% 8.81% RC wall 0.29% 3.42% 54.52% 19.00% Oesophagus 20.65% 8.79% 44.06% 5.23% Eye balls 2.78% 2.69% 42.18% 43.10% GB wall 7.08% 10.32% 55.47% 29.18% Ht wall 4.96% 2.02% 52.15% 28.52% ET2 bas 13.10% 12.70% 35.52% 22.63% LLung 19.80% 16.92% 42.45% 15.40% RLung 11.75% 8.73% 44.39% 0.66% O mucosa 39.40% 28.53% 40.06% 17.35% Pancreas 8.08% 8.63% 48.11% 7.19% RSig wall 19.40% 14.28% 46.16% 3.11% S glands 39.20% 32.34% 34.62% 26.11% SI wall 4.22% 4.46% 50.26% 13.58% Skin 7.25% 16.59% 41.25% 7.16% Sp cord 11.77% 10.40% 43.01% 4.47% Spleen 9.18% 6.33% 52.87% 11.60% St wall 3.78% 0.86% 54.35% 24.07% Thymus 30.65% 18.22% 43.60% 8.71% Thyroid 27.59% 10.89% 47.48% 2.04% Tongue 31.65% 32.47% 42.75% 10.31% Trachea 23.44% 22.97% 40.06% 9.58% UB wall 15.14% 10.93% 50.92% 2.84% LC wall 8.05% 7.77% 52.86% 15.05% Muscle 30.23% 31.62% 25.18% 29.68% Cartilage 4.83% 2.05% 5 2.49% 20.56% C bone V 33.99% 34.80% 24.61% 34.94% Prostate ----Testes --33.03% -LOvary 24.68% 37.15% -13.49% ROvary 20.47% 18.69% -32.12% Uterus -12.97% -21.87% Average 14.32% 13.06% 43.60% 3.61%

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396 Table 4 36 Biokin etic data for 99m (ICRP 2007) indicates the source tissue, indicates the fractional distribution of the radiopharmaceutical to source tissue is the biological half life, is the fraction of with biological half life and is the total number of nuclear transformations per unit AA Organ (S) F s T (h) a A s /A o Blood 1.0 60 1.0 7.89 h Kidneys 1.0 2.60 min Bladder Contents 1.0 9.00 min Table 4 37 Biokinetic data for 67 (ICRP 1988) indicates the source tissue, indicates the fractional distribution of the radiopharmaceutical to source tissue is the biological half life, is the fraction of with biological half life and is the total number of nuclear transformations per unit AA Organ (S) F s T (d) a A s /A o Total body 1.0 1.25 0.17 3.69 d (excluding GIT and 0.83 bladder contents) Adrenals 0.00053 1.25 0.17 2.8 min 25.5 0.83 Bone 0.13 1.25 0.17 11.5 h 25.5 0.83 GI tract contents SI 0.09 20.9 min ULI 0.09 1.01 h LLI 0.09 1.54 h Kidneys 0.0084 1.25 0.17 44.6 min 25.5 0.83 Liver 0.05 1.25 0.17 4.42 h 25.5 0.83 Red marrow 0.054 1.25 0.1 7 4.78 h 25.5 0.83 Spleen 0.0074 1.25 0.17 39.3 min 25.5 0.83 Bladder contents 0.91 20.8 min

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397 Table 4 38. Comparison between UF and ICRP Publication 80 estimated values of e quivalent dose per unit AA ( ) for 99m for radiosensitive tissues of the human body (ICRP 1998). Age group / Data source 1 year old 5 years old 10 years old 15 years old Adult Target tissue ICRP 80 UF ICRP 80 UF ICRP 80 UF ICRP 80 UF ICRP 80 UF Adrenals 0.056 0.050 0.030 0.027 0.020 0.017 0.012 0.012 0.010 0.011 Bladder 0.031 0.032 0.017 0.014 0.014 0.009 0.011 0.007 0.009 0.006 Bone surfaces 0.074 0.018 0.036 0.008 0.019 0.005 0.012 0.006 0.007 0.003 Brain 0.022 0.014 0.012 0.008 0.00 8 0.005 0.005 0.003 0.004 0.002 Breasts 0.019 0.016 0.011 0.011 0.007 0.008 0.004 0.005 0.004 0.005 Gall bladder 0.030 0.041 0.020 0.025 0.013 0.017 0.008 0.012 0.007 0.011 Gastrointestinal tract Sto mach 0.025 0.056 0.014 0.028 0.010 0.019 0.006 0.012 0.005 0.011 Small intestine 0.021 0.054 0.012 0.029 0.008 0.017 0.005 0.012 0.004 0.010 Colon 0.020 0.049 0.012 0.025 0.008 0.016 0.005 0.010 0.004 0.009 Heart 0.110 0.063 0.066 0.036 0.043 0.026 0.029 0.017 0.023 0.016 Kidneys 0.110 0.057 0.057 0.038 0.036 0.023 0.022 0.016 0.018 0.014 Liver 0.072 0.070 0.040 0.037 0.026 0.024 0.017 0.016 0.013 0.015 Lungs 0.110 0.079 0.056 0.040 0.035 0 .029 0.022 0.020 0.018 0.017 Muscles 0.017 0.018 0.009 0.011 0.006 0.006 0.004 0.004 0.003 0.004 Oesophagus 0.023 0.056 0.015 0.031 0.010 0.020 0.007 0.014 0.006 0.013 Gonads 0.016 0.017 0.009 0.011 0.006 0.006 0.004 0.005 0. 003 0.004 Pancreas 0.033 0.049 0.019 0.027 0.013 0.018 0.008 0.012 0.006 0.011 Red marrow 0.037 0.017 0.020 0.007 0.012 0.005 0.008 0.007 0.002 0.004 Skin 0.012 0.013 0.006 0.006 0.004 0.003 0.002 0.003 0.014 0.002 Spleen 0.081 0.083 0.043 0.042 0.027 0.026 0.017 0.017 0.002 0.016 Thymus 0.023 0.037 0.015 0.023 0.010 0.017 0.007 0.010 0.006 0.010 Thyroid 0.036 0.034 0.019 0.016 0.012 0.010 0.007 0.007 0.006 0.006 Uterus 0.019 0.032 0.011 0.019 0.007 0.013 0.005 0.008 0.004 0.008

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398 Table 4 39. Comparison between UF and ICRP Publication 80 estimated values of equivalent dose per unit AA ( ) for 67 for radiosensitive tissues of the human body (ICRP 1998). Age group / Data source 1 year old 5 years old 10 years old 15 years old Adult Target tissue ICRP 80 UF ICRP 80 UF ICRP 80 UF ICRP 80 UF ICRP 80 UF Adrenals 0.570 0.727 0.360 0.499 0.260 0.335 0.180 0.235 0.130 0.195 Bladder 0.370 0.452 0.200 0.247 0.150 0.155 0.110 0.104 0.081 0.095 Bone surfaces 5.200 0.735 2.200 0.337 1.300 0.177 0.810 0.145 0.630 0.139 Brai n 0.340 0.313 0.190 0.203 0.120 0.114 0.072 0.068 0.057 0.062 Breasts 0.290 0.373 0.150 0.224 0.093 0.131 0.061 0.083 0.047 0.078 Gall bladder 0.380 0.614 0.250 0.375 0.170 0.229 0.110 0.152 0.082 0.141 Gastrointestinal tract Stomach 0.390 0.441 0.210 0.248 0.140 0.160 0.090 0.099 0.069 0.092 Small intestine 0.280 0.434 0.160 0.258 0.110 0.160 0.074 0.106 0.059 0.098 Colon 1.000 0.472 0.540 0.269 0.330 0.172 0.200 0.111 0.160 0.104 Heart 0.380 0.404 0.210 0.241 0.140 0.152 0.089 0.091 0.069 0.088 Kidneys 0.510 0.700 0.290 0.436 0.200 0.263 0.140 0.181 0.120 0.160 Liver 0.610 0.811 0.330 0.491 0.230 0.323 0.150 0.213 0.120 0.189 Lungs 0 .360 0.656 0.190 0.385 0.130 0.254 0.083 0.156 0.063 0.135 Muscles 0.350 0.353 0.180 0.206 0.120 0.123 0.076 0.075 0.060 0.068 Oesophagus 0.350 0.405 0.190 0.248 0.120 0.153 0.079 0.097 0.061 0.093 Gonads 0.390 0.357 0.210 0.22 2 0.135 0.135 0.091 0.089 0.069 0.079 Pancreas 0.430 0.428 0.240 0.261 0.160 0.169 0.100 0.108 0.081 0.101 Red marrow 1.500 1.302 0.710 0.341 0.380 0.194 0.230 0.178 0.210 0.151 Skin 0.290 0.251 0.150 0.144 0.092 0.084 0.057 0.050 0.045 0.045 Spleen 0.860 0.990 0.480 0.584 0.310 0.368 0.200 0.232 0.140 0.221 Thymus 0.350 0.550 0.190 0.316 0.120 0.192 0.079 0.115 0.061 0.108 Thyroid 0.380 0.372 0.200 0.203 0.130 0.115 0.080 0.073 0.062 0.066 Uterus 0.420 0.574 0.230 0.333 0.150 0.200 0.097 0.124 0.076 0.121

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399 Table 4 40. Comparison between whole body effective dose estimates ( ) for the UF phantom family and two other sources for 99m (ICRP 1998). Patient age Data source Newborn 1 year old 5 years old 10 years old 15 years old Adult ICRP Publication 80 (1998) -4.0 5.6 6.1 5.4 4.7 UF (2012) 4.2 4.1 5.7 6.3 6.1 6.0 Table 4 41. Comparison between whole body effective dose estimates ( ) for the UF phantom family and two other sources for 67 (ICRP 1998). Patient age Data source Newborn 1 year old 5 years old 10 years old 15 years o ld Adult ICRP Publication 80 (1998) -16.2 22.1 21.9 19.7 16.8 UF (2012) 21.6 17.7 23.9 24.1 22.4 22.3 Table 4 42. Estimated absorbed dose to the walls of the large blood vessels for 99m for the UF phantom family based on different AA scal ing rules. Dose (mGy) Dose Clark's Young's Webster's Fried's Phantom (mGy/MBq) Rule Rule Rule Rule Average UFH00MF 2.33 20 9 73 9 28 UFH01MF 2.14 54 29 95 30 52 UFH05MF 1.90 85 99 169 135 122 UFH10MF 1.42 117 115 164 202 150 UFH15M 1.38 201 136 179 295 203 UFH15F 1.14 153 112 147 242 163 UFHADM 0.82 146 146 146 146 146 UFHADF 0.82 120 120 120 120 120

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400 Table 4 37. Estimated absorbed dose to the walls of the large blood vessels for 18 for the UF phantom family. Dose (mGy) Dose 2010 North American Consensus Phantom (mGy/MBq) Guidelines UFH00MF 4.39 162 UFH01MF 4.03 208 UFH05MF 3.58 329 UFH10MF 2.68 452 UFH15M 2.60 775 UFH15F 2.14 589 UFHADM 1.54 586 UFHADF 1.54 481

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401 Figure 4 1 Monoenergetic photon SAFs for a uniform blood source in the UFH00M phantom. Figure 4 2 Monoenergetic electron SAFs for a uniform blood source in the UFH00M phantom.

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402 Figure 4 3 Monoenergetic photon SAFs for a uniformly distrib uted blood source in all pediatric and adolescent phantoms in the UF hybrid phantom family as calculated with the newly developed age dependent regional blood distributions. The SAFs were also calculated using the gender dependent adult regional blood dis tributions to

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403 Figure 4 4 Absorbed dose to the blood vessel wall of interest averaged over adjacent vessels located at distances defined by the vessel separation axis and over the number o f directions the additional blood vessels are added For example, the third data point of e to the blood vessel wall at zero separation averaged over the self dose to the blood vessel wall at zero separation, the cross dose from two vessels on either side of the blood vessel wall at zero separation to the blood vessel wall at separation, and the cross dose from two vessels on either side of the blood vessel wall at zero separation to the blood vessel wall at separation. This data is valid for a uniform photon source for blood vessels with a lumen diameter, wall thickness, and vessel length.

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404 Figure 4 5 Top and perspective views of the final irradiation geometry designed to provide estimates of radiation absorbed dose to the walls of blood vessels in the human body (not to scale) Figure 4 6 Monoenergetic photon SAFs to the blood vessel walls for a uniformly distributed blood source

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405 Figure 4 7 Monoenergetic electron SAFs to the blood vessel walls for a uniformly distributed blood source. Figure 4 8 UF newborn hybrid phantom and OR NL adult male stylized phantom fluence to dose response functions for the cervical vertebra for the AM target (Cristy et al. 1987)

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406 Figure 4 9 Comparison of specific absorbed fractions for photons sources in the (A) liver and (B) thyroid as given by the current hybrid phantom study (UF), those from the ORNL stylized newborn (Cristy et al. 1987) and those f rom the GSF 2 month BABY phantom (Petoussi Henss et al. 2002)

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407 Figure 4 10 Validation study comparing electron SAFs for a uniform electron sou rce in the liver of the UFH00M phantom generated using the full transport method (FTM) and the two simulation method (TSM)

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408 Figure 4 11. Internal anatomy comparison between the (A) ORNL stylized 10 year old and (B) UFH10F phantom (Cristy et al. 1987)

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409 CHAPTER 5 CONCLUSION S Organ level dosimetry in nuclear medicine is important for the assessment of stochastic risks associated with nuclear medicine imaging as well as deterministic risks associated with nuclear medicine therapy. Values of administer ed activity (AA) for imaging procedures may be adjusted according to dose estimates for a particular exam type. For instance, if a dose estimate for a patient was generated using older dosimetric models, and an up to date estimate predicted a lower dose p er unit AA than the older estimate, the standard AA for that patient could potentially be increased to provide better diagnostic quality. Alternatively, if the up to date estimate predicted a higher dose per unit AA, the standard AA for that patient might have to be lowered to balance risk versus diagnostic quality. With the current limitations of on the fly whole body patient specific dosimetry, pre computed estimates to reference individuals may be used to compare different imaging procedures for a part icular patient, and this was the main focus of the present study. Blood Vessel Model In consideration of possible future adoption by the scientific community, a blood vessel system was crafted using 3 D surfaces to complete the final updates to the UF hybr i d phantom family, updates that included the addition of a separable adipose tissue layer, muscle, and lymphatic nodes. The blood vessels were designed to reflect major blood vessels in the head and neck, thoracic and abdominal region, arms, and legs. To tal reference vessel volumes were not closely matched due to lack of space in the phantoms, but mathematical apportionment techniques were developed to effectively model a distributed blood source. Relating to the blood vessel model, approximate energy de pendent blood wall dose models were developed for both photons and electrons. If the blood vessel radiopharmaceutical number of nuclear

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410 transformations is known, overall average blood vessel wall dose can be calculated. However, these dose estimates negl ect any localized effects. The addition of the physical blood vessel model and blood vessel wall dose model adds another dimension to the detail that can be obtained by using the internal dosimetry given in the current study. Specific Absorbed Fractions a nd Skeletal Dosimetry The bulk of the final product from this work is the monoenergetic photon and electron SAFs. SAFs were calculated because these values are the quantities that contain the dosimetric information that cannot be obtained through any mean s other than full radiation transport simulations. SAFs contain information regarding the geometry of the phantom organ and body anatomy, and the energy of the radiation of interest W hen they are combined with radionuclide decay and biokinetic informati on, absorbed doses to radiosensitive tissues in the human body may be estimated. Consequently SAFs are the cornerstone of nuclear medicine dosimetry. Several major factors went in to producing these values (1) new blood inclusive tissue elemental comp ositions, (2) skeletal photon fluence to dose response functions, and (3) MCNPX v2.6 radiation transport simulations. The original tissue elemental compositions of the UF phantom series were exclusive of their blood content; resultantly these elemental co mpositions had to be recalculated to include the blood component of all blood bearing organs. Photon and electron interactions with tissue depend on the elemental composition of the tissue through which they pass so the original elemental compositions co uld not be used with confidence. Since the mass of blood in each blood bearing organ was required to adjust the elemental composition, age dependent regional blood distributions were needed. However, current literature only recognizes regional blood dist ributions for the adult male and female Consequently age dependent regional blood distributions were calculated based on age relative organ sizes and the general assumption that

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411 blood volume per unit organ volume was constant for all ages ( a fact assume d for all tissues with the exception of the brain, kidneys, and mineral bone). The results showed that blood distribution does vary with age, as would be expected. Variations in the fraction of blood located in each blood bearing organ influence the rela tive dose contribution of that organ when a radionuclide is uniformly distributed throughout the blood in the human body. Correspondingly both the elemental compositions and regional blood distributions were important advancement s in dose modeling capabi lities of this study Estimating absorbed dose to radios ensitive tissues in the skeleton (AM and TM 50 ) has proven to be a daunting task for dosimetry researchers across the years Complicated skeletal microstructure and age dependent skeletal tissue distr ibutions make it difficult to develop empirical solutions to estimating absorbed dose to these tissues. In addition, the dimensions of the microstructure are such that traditional radiation transport techniques cannot handle the large file sizes needed to faithfully represent the true geometry of the skeletal microstructure at the level of a whole body anatomic model This study introduced a method by which absorbed dose to the radiosensitive skeletal tissues could be estimated per unit photon fluence inc ident upon the spongiosa of the skeleton. Detailed electron transport was performed at the microscopic level of the skeletal tissues the results of which were combined with information regarding the expected secondary electron spectra, photon mass intera ction coefficients, and relative tissue masses to yield a comprehensive set of bone and age dependent skeletal fluence to dose response functions. These response functions were used in conjunction with volume average photon fluence tracking capabilities w ithin MCNPX v2.6 to obtain final estimates of and where is the SAF, is any arbitrary source tissue, and is any arbitrary initial radiation energy. The level of detail inherent to the assembly of the skeletal

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412 photon fluence to dos e response functions, both in physical modeling and age specificity, suggest that the advancements made in the field of skeletal dosimetry through these methods are state of the art. Currently, OLINDA/EXM 1.0 is one of the most widely used internal dosimet ry software programs in the world. At present, t his program uses stylized/mathematical representations of humans and radiation transport that was performed over 20 years ago. Not only are the hybrid phantoms used in the current study far superior in term s of anatomic realism, but computing power has progressed to a point that allows high volume simulations not available to those who developed the monoenergetic photon SAFs used in OLINDA/EXM. Simulations in the past required very careful in code variance reduction techniques to maximize utility of particle histories necessary for the Monte Carlo transport method that were on the order of tens of thousands. Particle histories ranging from ten million to one hundred million were used in the current study, a nd thus statistical reliability of the results in this study is unmatched in that regard. Monoenergetic photon and electron SAFs were calculated in this study for a total of 12 phantoms including male and female phantoms of the newborn, 1 year old, 5 year old, 10 year old, 15 year old, and adult. SAFs were calculated at 21 radiation energies ranging from to for between 92 and 95 source tissues per phantom and between 78 and 80 target tissues per phantom. In contrast, OLINDA/EXM provides only photon SAFs for 21 radiation energies ranging from to for 26 source tissues p er phantom and 27 target tissues per phantom. In the current study, electron SAFs were calculated using a two simulation method wherein collisional and radiative energy loss contributions to absorbed dose are separately

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413 modeled to improve poor statistica l uncertainties associated with the radiative energy loss contributions to tissue dose. Photon energy spectra were generated during the radiative energy loss simulations and were subsequently weighted by the previously calculated monoenergetic photon SAFs The separate collisional and radiative SAFs were then combined to yield final monoenergetic electron SAFs. Electron SAFs were not generated by radiation transport for OLINDA/EXM. In fact, the assumption that electron self dose AFs were unity and cross dose AFs were zero was used in the code, and these assumptions were proven to be poor under certain conditions, specifically for higher energy radionuclide Clearly, the simulation techniques and physical models utilized in the current study are a vast i mprovement over the current standard that is OLINDA/EXM 1.0. These comparisons are not meant to slight the hard work that was put in to developing OLINDA/EXM 1.0. At the time of its inception, both the photon SAFs from the work of Cristy and Ec kerma n in t he mid 1980s and the development of MIRDOSE, the precursor to OLINDA/EXM 1.0, in the early 1990s were state of the art in their own right. In this field, innovation and advancement force updates of models and simulation techniques at a quickening pace. I n fact, with the current research in quantum computing, full patient specific dose estimates using radiation transport codes will probably become everyday practice in the future. The work of Cristy and Ec kerma n was outstanding at the time, and this work i s simply trying to carry forward their efforts. Results from most aims in the current study were used to perform dosimetry for two common nuclear medicine imaging procedures and the resulting dose estimates compared fairly well to current estimates based on stylized phantoms but were a little higher due to decreased inter organ spacing in the UF hybrid phantom family. Individual organ dose estimates differed

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414 from current estimates fairly significantly. As a result the dosimetry models developed in this study could potentially lead to advances in nuclear medicine imaging (as well as therapy) protocols. The two clinical case studies demonstrated that the SAFs computed in the current study are easily applicable to real life situations and provide reasonabl e dose estimates that compare well to current estimates but provide greater detail at the organ level. Internal Dose Scaling Another key contribution from this work was the development of updated photon and electron self and cross dose scaling factors. T he updated self dose scaling factors were of greater consequence than the cross dose scaling factors because cross dose is not as sensitive to changes in source and target size as self dose. These scaling factors allow a user of the internal dosimetry sof tware currently in development to enter the size of any organ in the body and the center to center separation of any organ pair in the body, and the reference self and cross doses will be changed according to these inputs. Validation studies were perfo rmed and showed that in certain applications, the scaling factors greatly improve the dose estimates. At the very worst, no appreciable increase in dose estimate accuracy was observed. OLINDA/EXM 1.0 assumes a self dose mass ratio scaling power of 0.667 for photons and 1.000 for electrons when in reality, self dose scaling powers were found to vary between 0.357 and 0.996 for photons and between 0.600 and 1.000 for electrons over the energy range considered in this study Applications where the UF scaling powers give much better non reference dose estimates were demonstrated and showed that personalized dosimetry could be improved by using the UF scaling factors. OLINDA/EXM 1.0 does not scale cross dose, and thus most non reference irradiation cond itions are better predicted using the UF cross dose scaling factors. When patient specific information on organ volumes is not available, reference SAF (and subsequently, S value) scaling may still be applied given anthropometric measurements of the

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415 patien t To this end dosimetric sensitivity for internal emitters was investigated for dependence on in clinic measurable morphometric characteristics such as sitting height and waist circumference. The idea was that if a patient came in for a nuclear medicin e procedure, a hospital professional could measure the sitting height and waist circumference of the patient and enter this information into the software program. Reference dose estimates are intended for the average person, but dosimetry for a non averag e person can be quite different, and this study attempted to predict this difference so that the sitting height and waist circumference that was entered into the software would adjust the reference dose estimates to attempt to better predict the actual abs orbed doses of the patient of interest. It was shown that patient specific photon absorbed doses could be better estimated by up to using morphometric dose scaling techniques. However, electron dose could not be reliably scaled from patient specific measurements due to the differences in physical interactions in tissue. Nevertheless final absorbed dose estimates for patients will be more accurately calculated using the scaling techniques developed in this study, and this is one step in the direction of more patient specific dose estimat es in nuclear medicine Deliverables All together, the deliverables of the seven specific aims in this study (1) blood vessel model, (2) skeletal photon fluence to dose response functions, (3) monoenergetic photon S AFs, (4) monoenergetic electron SAFs, (5) radionuclide S values for commonly used radionuclides, (6) internal dosimetry scaling factors for photon and electron self and cross dose and scaling factors based on anthropometric characteristics, and (7) implem entation techniques for a future internal dosimetry software code create the core of the nuclear medicine component of a future software package being developed at UF and NCI that will feature combined CT and nuclear medicine dosimetry. Through extensiv e beta testing and peer review, the results of this work are

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416 intended for eventual worldwide use in the nuclear medicine community. It is the hope of this investigator that the information given in this work will be used to optimize the way nuclear medici ne procedures are performed and possibly reduce the risk of secondary cancers for diagnostic studies or the occurrence of normal organ toxicities for therapeutic procedures. Future Work Various checks and validation studies have been performed in this stud y to show the efficacy of the methods developed, and all recommendations made were based on positive outcomes of these checks and validation studies. However, due to the vast quantity of data, even though no bugs or inconsistencies were observed in the cu rrent research, it is possible that small errors may be present. Therefore, before distribution to the scientific community, alpha testing must be performed. Specifically, for a determined period of time, any internal dosimetry studies within the ALRADS research could be performed both with MCNPX v2.6 and with the photon and electron SAFs generated in the current study and the results compared. Care must be taken to ensure that only low uncertainty direct simulation results should be compared to the curr ent SAF results. It was shown through one of the current validation studies that differences up to a factor of 40 could be observed between direct spectrum sampled simulations and assembly of pre computed monoenergetic SAFs. In fact, multiple orders of m agnitude difference could be seen if the statistical uncertainty of the direct simulation is large. That said, once extensive in house testing has been performed, migration to the NCI CT dose software could be achieved and beta testing could begin. Any b ugs or inconsistent data would then be reported back to the ALRADS research group, and troubleshooting would commence. Most of the aims in the current study were completed in their entirety, so no completion by subsequent researchers will be necessary. On e possible area for improvement would be age specific skeletal models for the UFH01MF, UFH05MF, and UFH10MF phantoms, but this

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417 would be an extremely time consuming process that would probably not yield results all too different from the SIRT CBIST model. It is the opinion of this investigator that the limit of computationally based patient specific internal dose scaling is being approached as advances in patient specific modeling may begin to take over. One of the most predictable dose scaling scenarios i s self dose, and mass and energy dependent dose scaling factors were introduced in this study that account for high and low energy situations much better than current approaches. At this point, individual variability in internal anatomy precludes further significant gains in this area, short of patient specific phantom modeling. Patient based modeling of obese patients was treated in the current study by adding layers of subcutaneous fat, but other internal fat deposits such as visceral fat deposits and p ara and perirenal fat are usually found in obese patients. This possibility was not addressed in the current study but is an issue that can be separately investigated in the future. Fat in between the folds of the intestines could decrease absorbed dose to those structures for sources external to the intestines and could decrease absorbed dose to other structures when the intestines are the source. In addition, fat deposits behind the kidneys could push them further into the body cavity, leading to incr eases in absorbed dose to the kidneys and other structures. Further investigation is needed into these issues. Another extension of the work in this study is the evaluation of the benefit of phantom specificity in predicting actual patient doses. An anal ysis would attempt to answer the question, how much more accurately can absorbed doses be predicted for an actual patient by using either patient dependent phantoms or scaled reference doses than by using the reference phantom itself. If significant accur acy could be gained by using either of these methods, then generation of more sets of phantoms or scaling methodologies would be warranted. However, if no further

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418 significant gains in accuracy were observed, then reference phantoms could potentially be us ed to great effect, and the extra effort required to perform dosimetry on patient dependent phantoms could be bypassed. Finally, the deliverable s of this work will be incorporated into a tumor dose algorithm currently in development by Laura Padilla. This algorithm allows for user placement of ellipsoidal tumors and the calculation of tumor self and cross dose based on the integration of point source kern e ls. By adding this module to the internal dosimetry code, a number of dose estimates may be obtained for radiosensitive organs in the human body as well as for stylistically modeled tumors, a truly significant advancement in the study of internal dosimetry.

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419 APPENDIX A LARGE TABLES Some tables spanned several pages each, so instead of placing them between chapters within the main text, they were grouped in Appendix A for easy lookup and to assist the flow of the main text. The contents of Appendix A are as follows: Tissue density information for the UF phantom family Tissue mass information for the UF pha ntom family Blood inclusive tissue elemental compositions for the UF phantom family Non uniform sampling probabilities for the UF phantom family

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420 Table A 1. All tissue names, tag identification numbers, and densities in for all phantoms in the UF hybrid phantom family. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Female Male Female Male Female Male Female Adipose Tissue 1 0.99 0.99 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 Left adrenal 2 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right adrenal 3 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Brain 4 1.03 1.03 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 Le ft breast 5 0.99 0.99 0.96 0.96 0.96 0.96 0.96 0.96 0.94 0.94 0.94 0.94 Bronchi 6 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 Right colon wall 7 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Right col on contents 8 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Ears 9 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Esophagus 10 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.0 3 1.03 External nose 11 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 Eye balls 12 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Gall bladder wall 13 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1. 03 1.03 1.02 1.03 1.02 Gall bladder contents 14 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Heart wall 15 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Heart contents 16 1.07 1.07 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.0 6 1.06 Kidneys Left cortex 17 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Right cortex 18 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Left medulla 19 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Right medulla 20 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Left pelvis 21 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Right pelvis 22 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 Larynx 23 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 Lens 24 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 Liver 25 1.04 1.04 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.06 1.06 Left lung 26 0.61 0.61 0.40 0.40 0.39 0.39 0.33 0.33 0.32 0.31 0.36 0.34 Right lung 27 0.61 0.61 0.40 0.40 0.39 0.39 0.33 0.33 0.32 0.31 0.36 0.34 Anterior nasal layer 28 1.03 1.03 1.03 1.03 1.03 1.03 1. 03 1.03 1.03 1.02 1.03 1.02 Posterior nasal layer 29 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Oral cavity layer 30 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left ovary 31 1.05 1.05 1.05 1.05 1.05 1.05 1. 05 1.05 1.05 1.05 1.05 1.05

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421 Table A 1. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Female Male Female Male Female Male Female Pancreas 32 1.03 1.03 1.03 1.03 1.03 1 .03 1.03 1.03 1.03 1.02 1.03 1.02 Penis 33 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 Pharynx 34 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.03 Pituitary gland 35 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1. 03 1.03 1.02 1.03 1.02 Prostate 36 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Rectosigmoid wall 37 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Rectosigmoid contents 38 1.03 1.03 1.03 1.03 0.86 0.86 1.03 1.03 0.49 1 .02 0.97 1.02 Parotid salivary glands 39 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Scrotum 40 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Small intestine wall 41 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1. 03 Small intestine contents 42 1.03 1.03 1.03 1.03 1.03 1.03 0.54 0.54 0.41 0.45 0.44 0.52 Skin 43 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Spinal cord 44 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.0 4 1.04 Spleen 45 1.04 1.04 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Stomach wall 46 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Stomach contents 47 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1 .02 Testes 48 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 Thymus 49 1.07 1.07 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Thyroid 50 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1 .05 1.05 Tongue 51 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 Tonsil 52 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Trachea 53 1.07 1.07 1.07 1.07 1. 07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 Urinary bladder wall 54 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04 Urinary bladder contents 55 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 Uterus 56 1.05 1.05 1.05 1.05 1.05 1.05 1 .05 1.05 1.05 1.05 1.05 1.05 Air (in body) 57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Left colon wall 58 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 Left colon contents 59 0.65 0.65 0. 95 0.95 0.76 0.76 0.49 0.49 0.34 0.98 0.66 1.02 Submaxillary salivary glands 60 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Sublingual salivary glands 61 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right breast 62 0.99 0. 99 0.96 0.96 0.96 0.96 0.96 0.96 0.94 0.94 0.94 0.94 Right ovary 63 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05

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422 Table A 1. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Fem ale Male Female Male Female Male Female Muscle 64 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 Blood Vessels Head 65 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Thoracic 66 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Arms 67 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Legs 68 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Lymphatic Nodes Extrathoracic 71 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Cervical 72 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Upper thoracic 73 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Lower thoracic 74 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right breast 75 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left breast 76 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right m esentary 77 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left mesentary 78 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right axillary 79 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left axill ary 80 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right cubital 81 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left cubital 82 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right inguinal 83 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left inguinal 84 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Right popliteal 85 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Left popliteal 86 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.03 1.02 Bone associated Cartilage Cranium 101 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Mandible 102 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Scapulae 103 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Clavicles 104 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Sternum 105 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Ribs 106 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Cervical vertebrae 107 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Thoracic vertebrae 108 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10

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423 Table A 1 Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Female Male Female Male Female Male Female Lumbar vertebrae 109 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Sacrum 110 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Os coxae 111 1.10 1.10 1.1 0 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Proximal femora 112 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Distal femora 113 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Proximal tibiae 114 1.10 1.10 1.1 0 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Distal tibiae 115 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Proximal fibulae 116 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Distal fibulae 117 1.10 1.10 1.1 0 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Patellae 118 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Ankles and feet 119 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 P roximal humera 120 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Distal humera 121 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Proximal radii 122 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Di stal radii 123 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Proximal ulnae 124 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Distal ulnae 125 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Wrists and hands 126 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Other Cartilage Cranial cap 127 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Costal cartilage of the ribs 128 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Cervical discs 129 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Thoracic discs 130 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Lumbar discs 131 1.10 1. 10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 Cortical Bone Cranium 151 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Mandible 152 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Scapulae 153 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Clavicles 154 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Sternum 155 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Ribs 156 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Cervical vertebrae 157 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90

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424 Ta ble A 1. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Female Male Female Male Female Male Female Thoracic vertebrae 158 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Lumbar vertebrae 159 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Sacrum 160 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Os coxae 161 1.65 1.65 1.66 1.66 1.70 1.7 0 1.75 1.75 1.80 1.80 1.90 1.90 Proximal femora 162 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Upper shaft of the femora 163 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Lower shaft of the femora 164 1.65 1 .65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal femora 165 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Proximal tibiae 166 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Shaft of the tibiae 167 1. 65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal tibiae 168 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Proximal fibulae 169 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Shaft of the fibulae 170 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal fibulae 171 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Patellae 172 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Ankles and feet 173 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Proximal humera 174 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Upper shaft of the humera 175 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Lower shaft of the humera 176 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal humera 177 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Proximal radii 178 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Shaft of the radii 179 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal radii 180 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Proximal ulnae 181 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Shaft of the ulnae 182 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Distal ulnae 183 1.65 1.65 1.66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Wrists and hands 184 1.65 1.65 1. 66 1.66 1.70 1.70 1.75 1.75 1.80 1.80 1.90 1.90 Teeth 185 1.65 1.65 1.65 1.65 1.65 1.65 2.33 2.33 3.00 3.00 3.00 3.00

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425 Table A 1. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Mal e Female Male Female Male Female Male Female Male Female Spongiosa and Medullary Cavities Cranium 201 1.433 1.433 1.435 1.435 1.374 1.374 1.294 1.294 1.250 1.253 1.491 1.600 Mandible 202 1.244 1.244 1.415 1.415 1.338 1.338 1.258 1.258 1.225 1.225 1.077 1.131 Scapulae 203 1.257 1.257 1.287 1.287 1.258 1.258 1.177 1.177 1.244 1.243 1.134 1.047 Clavicles 204 1.257 1.257 1.295 1.295 1.233 1.233 1.135 1.135 1.142 1.142 1.099 1.067 Sternum 205 1.245 1.245 1.249 1.249 1.163 1.163 1.085 1.085 1.089 1.088 1.086 1.086 Ribs 206 1.244 1.244 1.251 1.251 1.236 1.236 1.135 1.135 1.110 1.109 1.114 1.093 Cervical vertebrae 207 1.338 1.338 1.210 1.210 1.234 1.234 1.150 1.150 1.139 1.139 1.169 1.170 Thoracic vertebrae 208 1.351 1.351 1.169 1.169 1.175 1.175 1.114 1.114 1.115 1.115 1.096 1.114 Lumbar vertebrae 209 1. 307 1.307 1.274 1.274 1.233 1.233 1.160 1.160 1.098 1.098 1.105 1.126 Sacrum 210 1.307 1.307 1.276 1.276 1.160 1.160 1.075 1.075 1.056 1.055 1.117 1.138 Os coxae 211 1.257 1.257 1.214 1.214 1.190 1.190 1.124 1.124 1.093 1.092 1.091 1.046 Proximal femora 212 1.307 1.307 1.344 1.344 1.294 1.294 1.236 1.236 1.167 1.166 1.125 1.199 Upper shaft of the femora 213 1.030 1.030 1.026 1.026 1.018 1.018 1.005 1.005 0.998 0.997 0.994 0.989 Lower shaft of the femora 214 1.030 1.030 1.025 1.025 1.016 1.016 1.004 1.004 0.990 0.990 0.981 0.981 Distal femora 215 1.307 1.307 1.306 1.306 1.256 1.256 1.210 1.210 1.202 1.202 1.112 1.164 Proximal tibiae 216 1.307 1.307 1.354 1.354 1.270 1.270 1.187 1.187 1.057 1.05 7 1.084 1.123 Shaft of the tibiae 217 1.030 1.030 1.025 1.025 1.009 1.009 0.991 0.991 0.980 0.980 0.981 0.981 Distal tibiae 218 1.307 1.307 1.324 1.324 1.161 1.161 1.127 1.127 1.129 1.129 1.093 1.135 Proximal fibulae 219 1.307 1.307 1.369 1.369 1.185 1.185 1.141 1.141 1.102 1.102 1.051 1.091 Shaft of the fibulae 220 1.030 1.030 1.024 1.024 1.009 1.009 0.991 0.991 0.980 0.980 0.981 0.981 Distal fibulae 221 1.307 1.307 1.364 1.364 1.182 1.182 1.140 1.140 1.192 1.192 1.113 1.144 Patellae 222 1.244 1.244 1.215 1.215 1.099 1.099 1.034 1.034 1.078 1.077 1.112 1.149 Ankles and feet 223 1.244 1.244 1.273 1.273 1.243 1.243 1.153 1.153 1.078 1.077 1.112 1.063 Proximal humera 224 1.307 1.307 1.364 1.364 1.295 1.295 1.226 1.226 1.127 1.127 1.078 1.080 Upper shaft of the humera 225 1.030 1.030 1.027 1.027 1.018 1.018 1.005 1.005 0.997 0.997 0.994 0.989 Lower shaft of the humera 226 1.030 1.030 1.026 1.026 1.017 1.017 1.004 1.0 04 0.990 0.990 0.981 0.981 Distal humera 227 1.307 1.307 1.364 1.364 1.281 1.281 1.196 1.196 1.153 1.152 1.117 1.135

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426 Table A 1. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue ID Number Male Female Male Female Male Female Male Female Male Female Male Female Proximal radii 228 1.307 1.307 1.374 1.374 1.186 1.186 1.151 1.151 1.145 1.145 1.061 1.089 Shaft of the radii 229 1.030 1.030 1.025 1.025 1.008 1.008 0.992 0.992 0.980 0.980 0.981 0.981 Distal radii 230 1.307 1.307 1.391 1.391 1.255 1.255 1.199 1.199 1.138 1.137 1.085 1.101 Proximal ulnae 231 1.307 1.307 1.437 1.437 1.296 1.296 1.239 1.239 1.183 1.183 1.125 1.223 Shaft of the ulnae 232 1.030 1.030 1.025 1.025 1.008 1.008 0.992 0.992 0.980 0.9 80 0.981 0.981 Distal ulnae 233 1.307 1.307 1.297 1.297 1.112 1.112 1.095 1.095 1.129 1.129 1.106 1.016 Wrists and hands 234 1.244 1.244 1.281 1.281 1.229 1.229 1.135 1.135 1.078 1.077 1.117 1.062

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427 Table A 2. Tissue masses in grams for all phantoms in the UF hybrid phantom family after voxelization. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Adipose Tissue 661.81 661.12 3486. 82 3488.16 4577.66 4574.50 6733.25 6730.27 7322.78 12237.12 11642.88 13723.20 Left adrenal 2.98 2.98 1.98 1.98 2.48 2.48 3.41 3.41 5.04 4.58 6.96 6.46 Right adrenal 2.95 2.95 1.97 1.97 2.51 2.51 3.44 3.44 4.67 4.55 6.82 6.47 Brain 315.34 315.34 946.10 946.10 1241.14 1241.14 1306.24 1306.24 1416.58 1293.14 1441.65 1298.96 Left breast 0.04 0.04 0.22 0.22 0.47 0.47 3.59 3.77 7.40 149.21 11.04 239.92 Bronchi 0.38 0.38 2.00 2.00 3.02 3.02 3.50 3.50 7.96 7.47 1 6.06 8.98 Right colon wall 6.89 6.89 19.95 19.95 48.78 48.78 84.11 84.11 121.80 121.60 150.28 144.46 Right colon contents 15.51 15.51 15.06 15.06 26.48 26.48 27.52 27.52 70.92 42.85 98.35 50.45 Ears 1.19 1.19 3.22 3.22 5.36 5.3 6 4.04 4.04 6.76 7.11 11.08 6.70 Esophagus 1.93 1.93 4.84 4.84 9.72 9.72 17.58 17.58 28.90 29.29 38.96 34.38 External nose 0.32 0.32 2.17 2.17 3.95 3.95 6.72 6.72 4.27 3.75 7.64 14.90 Eye balls 5.89 5.89 6.93 6.93 10.95 10.95 11.96 11.96 12.99 12.79 15.01 14.86 Gall bladder wall 0.49 0.49 1.38 1.38 2.61 2.61 4.32 4.32 7.73 7.10 10.31 7.94 Gall bladder contents 2.79 2.79 7.95 7.95 14.90 14.90 25.91 25.91 44.86 41.83 57.51 47.81 Heart wall 19.82 19.82 49.83 49.83 84.51 84.51 139.11 139.11 229.60 220.00 328.45 249.38 Heart contents 6.00 6.00 47.70 47.70 134.28 134.28 229.09 229.09 426.77 317.66 507.36 367.05 Kidneys Left cortex 9.13 9.13 25.61 25.61 40.18 40.18 65.8 0 65.80 91.53 87.72 113.56 100.41 Right cortex 9.14 9.14 25.56 25.56 40.22 40.22 65.88 65.88 91.40 87.76 113.14 100.73 Left medulla 3.26 3.26 9.11 9.11 14.38 14.38 23.56 23.56 32.74 31.40 40.62 36.04 Right medulla 3.26 3.26 9.11 9.11 14.4 0 14.40 23.52 23.52 32.77 31.49 40.64 35.93 Left pelvis 0.65 0.65 1.82 1.82 2.86 2.86 4.70 4.70 6.54 6.30 8.04 7.21 Right pelvis 0.65 0.65 1.82 1.82 2.85 2.85 4.71 4.71 6.55 6.19 8.06 7.23 Larynx 1.30 1.30 4.00 4.00 7.0 5 7.05 12.01 12.01 21.99 14.74 27.70 19.09 Lens 0.13 0.13 0.22 0.22 0.33 0.33 0.35 0.35 0.49 0.40 0.41 0.46 Liver 128.94 128.94 327.96 327.96 566.94 566.94 826.13 826.13 1294.23 1295.91 1791.61 1392.31 Left lung 28.19 28.19 68.55 68.55 146.29 146.29 232.41 232.41 392.06 378.11 522.11 415.31 Right lung 30.77 30.77 80.84 80.84 151.12 151.12 257.50 257.50 498.05 379.32 675.32 511.46 Anterior nasal layer 0.09 0.09 0.14 0.14 0.41 0.41 0.46 0.46 2.03 0.44 1. 81 0.49 Posterior nasal layer 0.72 0.72 1.99 1.99 8.22 8.22 9.96 9.96 9.55 8.56 5.43 8.81 Oral cavity layer 0.73 0.73 0.53 0.53 1.29 1.29 1.00 1.00 5.02 7.68 2.24 1.81 Left ovary 0.00 0.15 0.00 0.39 0.00 0.99 0.00 1.74 0.00 3.02 0.00 5.50

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428 Table A 2. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Pancreas 5.94 5.94 19.78 19.78 34.73 34.73 59.40 59.40 109.26 99.44 138.82 119. 45 Penis 0.58 0.00 3.53 0.00 6.74 0.00 6.62 0.00 30.67 0.00 22.50 0.00 Pharynx 0.29 0.29 0.83 0.83 1.88 1.88 2.01 2.01 2.58 2.82 2.25 1.47 Pituitary gland 0.10 0.10 0.15 0.15 0.25 0.25 0.35 0.35 0.49 0.47 0.60 0.58 Prostate 0.79 0.00 1.00 0.00 1.04 0.00 1.64 0.00 4.27 0.00 16.90 0.00 Rectosigmoid wall 2.98 2.98 9.85 9.85 21.75 21.75 39.82 39.82 55.03 56.04 70.25 70.34 Rectosigmoid contents 9.45 9.45 14.37 14.37 24.48 24.48 31.21 31.21 38.66 50.66 73.06 54.93 Parotid saliv ary glands 3.47 3.47 13.86 13.86 19.93 19.93 25.78 25.78 39.07 35.98 49.82 40.71 Scrotum 1.17 0.00 2.17 0.00 2.30 0.00 2.19 0.00 20.13 0.00 39.29 0.00 Small intestine wall 28.89 28.99 81.54 81.52 210.50 210.55 355.50 355.50 499.85 494.61 627.58 578.13 S mall intestine contents 31.09 31.09 48.02 48.02 37.95 37.95 160.04 160.04 264.72 274.45 344.03 273.46 Skin 116.15 115.43 250.75 249.71 535.33 533.26 988.45 986.71 1855.59 1680.36 2664.64 1849.43 Spinal cord 6.27 6.27 22.53 22.53 29.83 29.83 49.08 49.08 46.30 56.74 71.44 45.82 Spleen 9.43 9.43 28.86 28.86 49.67 49.67 79.51 79.51 128.61 128.80 149.20 129.25 Stomach wall 6.93 6.93 19.75 19.75 49.56 49.56 84.21 84.21 118.98 119.16 149.27 139.34 Stomach cont ents 25.18 25.18 66.85 66.85 82.49 82.49 116.83 116.83 197.76 199.76 252.31 230.53 Testes 0.84 0.00 1.50 0.00 1.68 0.00 1.99 0.00 15.80 0.00 34.79 0.00 Thymus 12.91 12.91 15.99 15.99 29.92 29.92 37.41 37.41 35.07 29.78 24.90 20.07 Thyroid 1.29 1.29 1.78 1.78 3.38 3.38 7.81 7.81 11.94 11.94 19.93 16.92 Tongue 3.50 3.50 9.96 9.96 18.81 18.81 31.93 31.93 55.43 52.83 72.40 59.68 Tonsil 0.10 0.10 0.51 0.51 1.96 1. 96 2.96 2.96 3.04 2.95 2.98 2.98 Trachea 0.51 0.51 1.49 1.49 2.51 2.51 4.52 4.52 7.45 5.97 10.02 8.06 Urinary bladder wall 3.96 3.97 8.96 8.94 15.90 15.93 24.97 24.84 39.87 34.78 49.55 39.78 Urinary bladder contents 9.99 9.99 10 .97 10.05 61.58 61.52 98.36 98.38 152.84 133.88 201.58 161.57 Uterus 0.00 3.95 0.00 1.48 0.00 2.99 0.00 3.98 0.00 29.86 0.00 79.67 Air (in body) 0.00 0.00 0.01 0.01 0.03 0.03 0.07 0.07 0.46 0.15 0.10 0.06 Left colon wall 6.96 6.96 19.7 9 19.79 48.64 48.64 84.78 84.78 121.66 122.03 149.56 144.99 Left colon contents 11.91 11.91 19.68 19.68 24.65 24.65 16.24 16.24 30.10 58.30 34.44 73.81 Submaxillary salivary glands 1.79 1.79 6.96 6.96 9.97 9.97 12.95 12.95 19.89 18.94 24.9 4 20.36 Sublingual salivary glands 0.69 0.69 3.01 3.01 3.98 3.98 4.98 4.98 7.88 7.89 10.03 7.95 Right breast 0.04 0.04 0.21 0.21 0.47 0.47 3.53 3.76 7.40 149.63 10.81 239.60 Right ovary 0.00 0.15 0.00 0.40 0.00 0.99 0.00 1.74 0.00 3.02 0.00 5.50

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429 Table A 2. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Muscle 1500.77 1497.83 3189.06 3190.53 7173.08 7173.71 15951.60 15951.60 33800.55 2 5579.05 40062.75 29303.40 Blood Vessels Head 1.31 1.31 2.43 2.43 5.24 5.24 9.69 9.69 19.63 18.51 22.51 19.69 Thoracic 0.49 0.49 0.78 0.78 2.09 2.09 4.68 4.68 8.53 5.43 11.89 5.68 Arms 4.38 4.38 8.67 8.67 22.15 22. 15 47.99 47.99 88.76 79.15 119.14 103.99 Legs 5.18 5.18 11.58 11.58 32.61 32.61 69.33 69.33 128.59 120.91 175.63 145.02 Lymphatic Nodes Extrathoracic 0.45 0.60 2.75 3.30 2.16 4.21 1.23 2.46 4.48 3.50 2.85 2.19 Cer vical 1.36 0.90 6.03 6.48 5.04 4.32 6.14 6.14 13.73 2.09 27.54 14.66 Upper thoracic 0.04 0.02 0.23 0.03 0.74 1.07 0.00 0.00 4.64 3.25 3.77 5.86 Lower thoracic 0.09 0.03 0.08 0.12 1.85 1.28 0.46 0.46 6.97 6.13 5.46 7.28 Right breast 0.60 0 .60 0.16 0.16 2.52 3.24 3.69 4.92 2.29 9.38 7.11 14.27 Left breast 0.60 0.60 0.16 0.16 2.52 3.24 3.69 4.92 2.29 9.38 7.11 14.27 Right mesentary 0.26 0.23 0.92 0.67 1.70 1.82 9.79 9.56 7.88 4.60 12.70 14.17 Left mesentary 0.26 0.23 0.92 0. 67 1.70 1.78 9.79 9.56 7.88 4.60 12.70 14.05 Right axillary 0.75 0.98 2.70 2.55 6.12 6.12 7.37 5.53 19.45 17.72 18.49 2.19 Left axillary 0.75 0.98 2.70 2.55 6.12 6.12 7.37 5.53 19.45 17.72 18.49 2.19 Right cubital 0.45 0.38 1.27 1.43 1.08 1.08 2.46 2.46 11.44 14.60 9.96 21.95 Left cubital 0.45 0.38 1.27 1.43 1.08 1.08 2.46 2.46 11.44 14.60 9.96 21.95 Right inguinal 0.90 1.21 4.61 3.98 6.48 6.48 8.60 8.60 19.45 18.77 27.03 3.29 Left inguinal 0.90 1.21 4.61 3.98 6.48 6.48 8 .60 8.60 19.45 18.77 27.03 3.29 Right popliteal 1.05 0.90 0.32 0.48 4.68 3.24 10.45 10.45 4.58 2.09 9.96 14.27 Left popliteal 1.05 0.90 0.32 0.48 4.68 3.24 10.45 10.45 4.58 2.09 9.96 14.27 Bone associated Cartilage Cranium 38.52 38.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Mandible 2.67 2.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Scapulae 2.75 2.75 0.00 0.00 0.00 0. 00 0.00 0.00 0.00 0.00 0.00 0.00 Clavicles 1.34 1.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Sternum 1.57 1.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Ribs 4.34 4.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Cervical vertebrae 4.15 4.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Thoracic vertebrae 7.92 7.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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430 Table A 2. Cont inued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Lumbar vertebrae 4.19 4.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Sacrum 1.94 1.94 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Os coxae 5.85 5.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal femora 2.67 2.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal femora 2.36 2.36 0.00 0.0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal tibiae 1.77 1.77 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal tibiae 1.66 1.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal fibulae 0.70 0.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal fibulae 0.92 0.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Patellae 0.14 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Ankles and feet 4.14 4.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal humera 1.66 1.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal humera 1.96 1.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal radii 0.65 0.65 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal radii 0.93 0.93 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Proximal ulnae 0.96 0.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Distal ulnae 0.99 0.99 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Wrists and hands 4.27 4.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Other Cartilage Cranial cap 11.14 11.14 4.55 4.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Costal carti lage of the ribs 11.54 11.54 23.07 23.07 22.81 22.81 42.33 42.33 72.87 86.40 52.53 38.01 Cervical discs 0.23 0.23 1.49 1.49 1.03 1.03 2.67 2.67 2.39 2.70 1.93 2.73 Thoracic discs 0.77 0.77 5.57 5.57 16.88 16.88 36.14 36.14 36.66 34.86 33.92 34. 70 Lumbar discs 0.53 0.53 3.57 3.57 14.04 14.04 34.60 34.60 23.53 22.34 31.56 15.30 Cortical Bone Cranium 21.24 21.24 91.06 91.06 214.85 214.85 308.12 308.12 528.48 409.73 1222.18 582.35 Man dible 1.72 1.72 7.05 7.05 17.30 17.30 21.38 21.38 51.70 42.08 32.22 39.12 Scapulae 2.39 2.39 9.67 9.67 28.54 28.54 57.90 57.90 116.10 170.63 318.93 221.27 Clavicles 0.93 0.93 1.44 1.44 6.01 6.01 14.22 14.22 41.23 54.51 50.77 42.20 Sternum 0.18 0.18 0.62 0.62 2.39 2.39 5.32 5.32 22.53 16.04 37.25 18.47 Ribs 6.22 6.22 18.77 18.77 39.31 39.31 61.73 61.73 165.31 171.02 235.45 248.67 Cervical vertebrae 3.68 3.68 3.11 3.11 6.67 6.67 13.73 13.73 32.65 41.74 61.75 43.17

PAGE 431

431 Table A 2. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Thoracic vertebrae 8.32 8.32 11.55 11.55 31.54 31.54 69.43 69.43 87.36 72.53 143.72 84.55 Lumbar vertebrae 2.72 2.72 6.98 6.98 15.30 15.30 37.60 37.60 35.95 46.74 119.08 79.02 Sacrum 1.11 1.11 6.57 6.57 11.16 11.16 1 5.69 15.69 68.97 86.31 90.95 96.06 Os coxae 6.11 6.11 21.14 21.14 55.05 55.05 125.56 125.56 194.00 213.44 418.25 278.12 Proximal femora 0.66 0.66 6.93 6.93 21.71 21.71 77.71 77.71 82.76 66.53 39.65 33.97 Upper shaft of the femora 3.14 3.1 4 7.21 7.21 26.65 26.65 83.88 83.88 226.85 166.63 126.09 112.91 Lower shaft of the femora 4.94 4.94 10.28 10.28 20.49 20.49 70.13 70.13 175.28 189.61 98.19 130.31 Distal femora 0.53 0.53 10.22 10.22 26.38 26.38 81.06 81.06 67.15 62.67 57.50 61. 93 Proximal tibiae 0.53 0.53 8.69 8.69 26.24 26.24 90.80 90.80 100.63 89.27 45.31 41.57 Shaft of the tibiae 3.64 3.64 12.69 12.69 32.43 32.43 102.39 102.39 253.91 211.61 150.63 168.05 Distal tibiae 0.28 0.28 4.83 4.83 12.47 12.47 44.03 44 .03 22.84 20.67 24.05 18.89 Proximal fibulae 0.05 0.05 0.81 0.81 2.59 2.59 8.88 8.88 12.97 9.95 8.61 5.13 Shaft of the fibulae 1.03 1.03 1.50 1.50 4.85 4.85 14.64 14.64 46.22 33.71 52.86 33.26 Distal fibulae 0.10 0.10 0.73 0.73 2.64 2.64 8.90 8.90 12.25 9.94 12.04 7.59 Patellae 0.05 0.05 0.16 0.16 1.24 1.24 2.86 2.86 20.77 17.37 6.48 6.99 Ankles and feet 1.19 1.19 7.17 7.17 32.34 32.34 89.81 89.81 213.07 171.85 286.01 218.29 Proximal h umera 0.44 0.44 6.04 6.04 14.83 14.83 46.62 46.62 45.91 34.17 49.66 27.58 Upper shaft of the humera 1.58 1.58 6.60 6.60 13.53 13.53 40.06 40.06 108.16 88.64 109.50 83.40 Lower shaft of the humera 1.50 1.50 5.13 5.13 11.78 11.78 33.51 33.51 96.2 8 76.94 97.88 72.55 Distal humera 0.24 0.24 4.21 4.21 10.09 10.09 33.33 33.33 73.99 56.27 61.91 35.13 Proximal radii 0.07 0.07 1.27 1.27 2.46 2.46 7.99 7.99 10.16 7.24 9.51 5.77 Shaft of the radii 1.01 1.01 2.78 2.78 8.08 8.08 22.34 22.34 72.59 65.85 78.03 58.90 Distal radii 0.08 0.08 1.58 1.58 4.03 4.03 12.69 12.69 13.06 9.98 17.92 7.77 Proximal ulnae 0.20 0.20 2.38 2.38 6.49 6.49 21.27 21.27 26.63 21.76 33.56 14.46 Shaft of the ulnae 1.27 1.27 4.49 4.49 10.39 10.39 28.9 9 28.99 88.95 77.16 93.80 69.49 Distal ulnae 0.09 0.09 0.57 0.57 1.74 1.74 5.22 5.22 5.69 4.12 4.85 2.59 Wrists and hands 0.79 0.79 9.87 9.87 9.16 9.16 31.55 31.55 126.64 105.72 170.56 141.61 Teeth 0.00 0 .00 0.00 0.00 5.91 5.91 12.32 12.32 29.44 14.14 32.70 16.81

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432 Table A 2. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Male Female Spongiosa and Medullary Cavities Cranium 69.28 69.28 265.98 265.98 464.79 464.79 448.50 448.50 422.09 367.99 502.90 444.06 Mandible 4.77 4.77 12.02 12.02 25.76 25.76 24.29 24.29 32.40 25.67 31.12 28.14 Scapulae 3.75 3.75 13.35 13.35 37.19 37.19 80.01 80.01 99.91 128.73 359.98 194.10 Clavicles 1.40 1.40 1.72 1.72 6.91 6.91 14.95 14.95 18.73 23.28 45.21 30.84 Sternum 0.56 0.56 1.88 1.88 7.27 7.27 18.24 18.24 35.66 24.51 49.48 31.49 Ribs 17.87 17.87 51.87 51.87 71.84 71.84 121.60 121.60 167.79 180.20 207.64 191.79 Cervical vertebrae 6.14 6.14 8.15 8.15 11.92 11.92 26.76 26.76 47.91 59.12 73.11 48.09 Thoracic vertebrae 9.14 9.14 24.93 24.93 64.24 64.24 184.46 184.46 221.66 202.41 255.75 205.79 Lumbar vertebrae 6.71 6.71 19.68 19.68 51.13 51.13 140.90 140.90 215.72 233.61 256.31 258.79 Sacrum 2.67 2.67 13.52 13.52 29.86 29.86 49.28 49.28 102.07 123.94 164.37 162.78 Os coxae 7.27 7.27 30.56 30.56 87.64 87.64 251.60 251.60 438.05 486.57 754.09 510.00 Proximal femora 4.92 4.92 7.96 7.96 22.70 22.70 66.11 66.11 215.29 163.80 268.11 195.86 Upper shaft of the femora 0.57 0.57 0.84 0.84 6.91 6.91 22.78 22.78 44.96 32.25 126.05 64.14 Lower shaft of the femora 0.92 0.92 1.38 1.38 4.83 4.83 15.51 15.51 34.04 36.18 94.70 72.95 Distal femora 4.09 4.09 7.93 7.93 25.36 25.36 81.16 81.16 277.93 246.77 302.43 236.83 Proximal tibiae 3.49 3.49 5.57 5.57 16.48 16.48 46.71 46.71 172.91 149.32 238.57 186.69 Shaft of the tibiae 0.52 0.52 1.93 1.93 7.15 7.15 24.82 24.82 57.73 47.38 145.30 76.69 Distal tibiae 2.15 2.15 1.01 1.01 3.75 3.75 9.92 9.92 75.72 65.74 84.11 67.96 Proximal fibulae 0.47 0.47 0.28 0.28 1.25 1.25 3.48 3.48 14.28 11.22 19.02 14.31 Shaft of the fibulae 0.09 0.09 0.19 0.19 1.66 1.66 5.21 5.21 7.97 5.68 11.91 7.80 Distal fibulae 0.72 0.72 0.22 0.22 1.18 1.18 3.28 3.28 14.79 11.44 17.19 13.13 Patellae 0.14 0.14 0.51 0.51 4.83 4.83 11.77 11.77 21.15 16.72 35.48 25.13 Ankles and feet 3.98 3.98 18.78 18.78 64.65 64.65 150.51 150.51 364.99 291.54 396.24 269.87 Proximal humera 3.00 3.00 7.90 7.90 17.43 17.43 46.31 46.31 147.15 117.83 165.03 120.52 Upper shaft of the humera 0.25 0.25 0.74 0.74 3.16 3.16 8.80 8.80 17.67 13.99 32.82 23.34 Lower shaft of the humera 0.26 0.26 0.70 0.70 3.03 3.03 8.91 8.91 15.39 11.76 28.83 20.53 Distal humera 2.37 2.37 4.11 4.11 9.66 9.66 23.69 23.69 64.05 50.84 86.54 70.25

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433 Table A 2. Continued. UFH00MF UFH01MF UFH05MF UFH10MF UFH15MF UFHADMF Tissue Male Female Male Female Male Female Male Female Male Female Ma le Female Proximal radii 0.51 0.51 0.34 0.34 0.81 0.81 1.85 1.85 11.25 8.56 13.41 10.01 Shaft of the radii 0.10 0.10 0.32 0.32 1.98 1.98 5.93 5.93 6.41 5.52 14.54 15.77 Distal radii 0.92 0.92 0.67 0.67 2.07 2.07 4.67 4.67 23.68 17.61 24.9 2 20.34 Proximal ulnae 1.23 1.23 1.60 1.60 4.49 4.49 10.67 10.67 42.04 32.85 46.81 42.54 Shaft of the ulnae 0.11 0.11 0.51 0.51 2.21 2.21 6.55 6.55 8.17 6.78 18.50 18.58 Distal ulnae 0.63 0.63 0.05 0.05 0.38 0.38 0.86 0.86 7.44 5.38 9.50 6.86 Wrists and hands 2.70 2.70 2.18 2.18 15.11 15.11 35.33 35.33 57.97 46.93 57.44 43.17

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434 Table A 3. Blood inclusive elemental compositions in mass percent for all tissues in the UFH00MF phantoms (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 10.47 15.59 2.44 71.22 0.02 0.00 0.02 0.12 0.04 0.00 0.04 0.00 0.02 0.00 Tongue 10.36 10.60 2.57 75.75 0.10 0.00 0.10 0.11 0.20 0.00 0.20 0.00 0.01 0.00 Esophagus 10.44 15.42 2.55 71.27 0.03 0.00 0.03 0.13 0.05 0.0 0 0.05 0.00 0.03 0.00 Stomach 10.44 11.94 2.69 74.25 0.10 0.00 0.10 0.13 0.20 0.00 0.13 0.00 0.03 0.00 Small intestine 10.42 11.99 2.75 74.16 0.10 0.00 0.10 0.13 0.20 0.00 0.13 0.00 0.03 0.00 Large intestine 10.42 11.98 2.74 74.16 0.10 0.00 0.10 0.13 0. 20 0.00 0.13 0.00 0.03 0.00 Liver 10.20 12.76 3.12 72.88 0.10 0.00 0.24 0.20 0.20 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Pancreas 10.46 16.03 2.61 70.00 0.18 0.00 0.18 0.12 0.2 0 0.00 0.20 0.00 0.02 0.00 Blood 10.00 13.10 4.00 72.00 0.10 0.00 0.10 0.20 0.20 0.00 0.20 0.00 0.10 0.00 Brain 10.76 5.91 1.26 81.08 0.19 0.00 0.29 0.11 0.20 0.00 0.20 0.00 0.01 0.00 Heart 10.50 8.48 2.18 78.02 0.18 0.00 0.10 0.12 0.20 0.00 0.20 0.00 0 .02 0.00 Eye 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.08 29.39 0.96 58.26 0.10 0.00 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Skin 10.38 10.56 2.87 75.29 0.19 0.00 0.10 0.20 0.29 0.00 0.11 0.00 0.01 0.00 Muscle 10.39 10.35 2.43 76.13 0.10 0.00 0.10 0.10 0.20 0.00 0.20 0.00 0.00 0.00 Pituitary gland 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Trachea 10.59 16.23 2.04 71.02 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Larynx 9.64 10. 24 2.39 74.15 0.46 0.00 1.98 0.83 0.29 0.00 0.02 0.00 0.01 0.00 Lung 10.41 9.35 2.50 76.90 0.17 0.00 0.17 0.13 0.20 0.00 0.13 0.00 0.03 0.00 Spleen 10.25 10.89 3.21 74.75 0.15 0.00 0.15 0.15 0.20 0.00 0.20 0.00 0.05 0.00 Thymus 10.54 15.96 2.21 71.11 0. 01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Thyroid 10.34 12.09 2.66 74.09 0.18 0.00 0.10 0.12 0.20 0.00 0.12 0.00 0.02 0.08 Tonsils 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Kidney 10.54 7.96 2.16 78.45 0.18 0.00 0.18 0.12 0.20 0.00 0.20 0.08 0.02 0.00 Ureters 10.60 16.30 2.00 71.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Urinary 10.49 9.68 2.63 76.01 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.60 16.30 2.00 71.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Epididymes 10.60 16.30 2.00 71.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Breast Male 10.97 27.77 1.26 59.62 0.10 0.00 0.10 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Testes 10.56 16.09 2.13 71.06 0.01 0.00 0.01 0.11 0.01 0. 00 0.01 0.00 0.01 0.00

PAGE 435

435 Table A 3. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.53 15.93 2.23 71.12 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Breast Female 10.99 28.10 1.20 59.35 0.10 0.00 0.10 0.11 0.02 0.00 0 .02 0.00 0.01 0.00 Ovaries 10.55 16.04 2.16 71.08 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Fallopian tubes 10.60 16.30 2.00 71.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Uterus 10.54 15.99 2.19 71.10 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Cartilage 9.61 9.94 2.22 74.37 0.49 0.00 2.17 0.89 0.30 0.00 0.00 0.00 0.00 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.60 16.30 2.00 71.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0. 00 0.00 0.00 Soft tissue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0. 00 0.00 Lens 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 4.53 15.83 4.47 51.44 0.01 0.28 7.55 0.29 0.01 0.00 0.01 15.56 0.01 0.00 Spongiosa/MC Cranium 6.29 19.39 4.19 53.36 0.04 0.23 5.31 0.27 0.04 0.00 0.04 10.82 0.03 0.00 Mandible 7.93 25.30 3.91 52.47 0.07 0.20 3.25 0.24 0.05 0.00 0.05 6.47 0.06 0.00 Vertebrae C 7.06 22.16 4.06 52.94 0.06 0.21 4.34 0.26 0.04 0.00 0.05 8.77 0.04 0.00 Vertebrae T 6.95 21.76 4.09 53.00 0.06 0.22 4.48 0.26 0.04 0.00 0.05 9.07 0.04 0.00 Vertebrae L 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Sternum 7.92 25.24 3.92 52.48 0.07 0.20 3.2 7 0.25 0.05 0.00 0.05 6.51 0.05 0.00 Ribs 7.93 25.30 3.91 52.47 0.07 0.20 3.25 0.24 0.05 0.00 0.05 6.47 0.06 0.00 Scapulae 7.81 24.84 3.94 52.54 0.07 0.20 3.42 0.25 0.05 0.00 0.05 6.81 0.05 0.00 Clavicles 7.81 24.84 3.94 52.54 0.07 0.20 3.42 0.25 0.05 0.00 0.05 6.81 0.05 0.00 Os Coxae 7.81 24.84 3.94 52.54 0.07 0.20 3.42 0.25 0.05 0.00 0.05 6.81 0.05 0.00 Sacrum 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Humera proximal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Humera distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Radii proximal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Radii distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Ulnae proximal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00

PAGE 436

436 Table A 3. C ontinued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Ulnae distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Wrists and hands 7.93 25.30 3.91 52.47 0.07 0.20 3.25 0.24 0.05 0.00 0.05 6.47 0.06 0.00 Femora proximal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Femora distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Patellae 7.93 25.30 3.91 52.47 0.07 0.20 3.25 0.24 0.05 0.00 0.05 6.47 0.06 0.00 Tibiae proximal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Tibiae distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Fibulae proximal 7. 34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Fibulae distal 7.34 23.15 4.02 52.79 0.06 0.21 4.00 0.26 0.04 0.00 0.05 8.05 0.04 0.00 Ankles and feet 7.93 25.30 3.91 52.47 0.07 0.20 3.25 0.24 0.05 0.00 0.05 6.47 0. 06 0.00 Humera upper shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Humera lower shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Radii shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Ulnae shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Femora upper shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Femora l ower shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Tibiae shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0.00 0.06 0.00 0.09 0.00 Fibulae shaft 10.39 34.05 3.50 51.19 0.11 0.15 0.19 0.21 0.05 0 .00 0.06 0.00 0.09 0.00 Lymph nodes 10.57 16.13 2.10 71.05 0.01 0.00 0.01 0.11 0.01 0.00 0.01 0.00 0.01 0.00 Ears 9.64 10.24 2.39 74.15 0.46 0.00 1.98 0.83 0.29 0.00 0.02 0.00 0.01 0.00 External nose 9.64 10.24 2.39 74.15 0.46 0.00 1.98 0.83 0.29 0.00 0 .02 0.00 0.01 0.00 Nasal layers 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Oral cavity layer 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Pharynx 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0 .00 0.02 0.00 0.01 0.00 Sal glands 10.54 15.96 2.21 71.11 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00 Spinal cord 10.72 6.31 1.41 80.58 0.19 0.00 0.28 0.11 0.20 0.00 0.20 0.00 0.01 0.00 Penis 10.35 10.62 2.59 75.71 0.10 0.00 0.10 0.11 0.20 0.00 0. 20 0.00 0.01 0.00 Scrotum 10.53 15.93 2.23 71.12 0.01 0.00 0.01 0.11 0.02 0.00 0.02 0.00 0.01 0.00

PAGE 437

437 Table A 4. Blood inclusive elemental compositions in mass percent for all tissues in the UFH01MF phantoms (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 10.45 23.30 2.79 62.45 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 14.07 3.39 71.25 0.10 0.00 0.19 0.29 0.11 0.00 0.39 0.00 0.01 0.00 Esophagus 10.44 22.74 2.82 63.00 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.0 0 0.02 0.00 Stomach 10.52 11.40 2.42 74.98 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Small intestine 10.52 11.39 2.43 74.97 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Large intestine 10.51 11.39 2.44 74.97 0.10 0.00 0.10 0.12 0.22 0.00 0. 12 0.00 0.02 0.00 Liver 10.28 16.88 2.91 68.77 0.18 0.00 0.18 0.28 0.22 0.00 0.28 0.00 0.02 0.00 Gall bladder wall 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pancreas 10.53 15.93 2.38 70.24 0.18 0.00 0.18 0.12 0.22 0.00 0.2 0 0.00 0.02 0.00 Blood 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.68 14.37 2.24 71.32 0.20 0.00 0.39 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Heart 10.38 13.54 2.95 72.14 0.10 0.00 0.19 0.20 0.21 0.00 0.29 0.00 0.01 0.00 Eye 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 59.13 0.74 28.45 0.10 0.00 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 Skin 10.01 20.03 4.16 64.90 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.26 3 .40 71.04 0.10 0.00 0.20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Trachea 10.50 25.42 2.71 60.38 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.64 9.98 2.28 7 4.41 0.47 0.00 2.05 0.85 0.30 0.00 0.01 0.00 0.01 0.00 Lung 10.27 10.67 3.17 74.76 0.17 0.00 0.17 0.27 0.30 0.00 0.20 0.00 0.03 0.00 Spleen 10.26 11.19 3.24 74.24 0.10 0.00 0.23 0.20 0.24 0.00 0.26 0.00 0.04 0.00 Thymus 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Thyroid 10.38 11.80 2.50 74.50 0.19 0.00 0.10 0.11 0.21 0.00 0.11 0.00 0.01 0.09 Tonsils 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Kidney 10.28 12.84 3.05 72.75 0.18 0.00 0.18 0.20 0 .22 0.00 0.20 0.08 0.02 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.50 9.62 2.61 76.07 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0. 20 0.00 0.00 0.00 Epididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.31 56.19 0.89 31.25 0.10 0.00 0.01 0.11 0.11 0.00 0.01 0.00 0.01 0.00 Testes 10.58 9.95 2.06 76.50 0.20 0.00 0.10 0.20 0.20 0.00 0.20 0.00 0.00 0.00

PAGE 438

438 Table A 4. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.48 24.52 2.74 61.26 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Breast Female 11.51 49.16 0.22 39.05 0.01 0.00 0.01 0.01 0.02 0.00 0.01 0.00 0.01 0.00 Ovaries 10.48 24.76 2.73 61.02 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.57 30.13 2.46 56.03 0.10 0.00 0.19 0.20 0.11 0.00 0.20 0.00 0. 01 0.00 Cartilage 9.64 9.98 2.28 74.41 0.47 0.00 2.05 0.85 0.30 0.00 0.01 0.00 0.01 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Soft tissue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 4.33 15.81 4.45 50.25 0.00 0.29 8.18 0.30 0.01 0.00 0.01 16.36 0.00 0.00 Spongiosa/MC Cranium 6.14 20.22 4.11 51.61 0 .04 0.24 5.80 0.27 0.04 0.00 0.04 11.47 0.03 0.00 Mandible 6.31 20.84 4.08 51.50 0.04 0.24 5.59 0.27 0.04 0.00 0.04 11.04 0.03 0.00 Vertebrae C 8.22 28.12 3.71 50.19 0.07 0.20 3.12 0.24 0.04 0.00 0.04 5.99 0.06 0.00 Ver tebrae T 8.67 29.83 3.63 49.89 0.08 0.19 2.54 0.24 0.04 0.00 0.04 4.80 0.06 0.00 Vertebrae L 7.56 25.61 3.84 50.65 0.06 0.21 3.97 0.24 0.04 0.00 0.04 7.73 0.05 0.00 Sternum 7.80 26.53 3.79 50.48 0.06 0.21 3.65 0.24 0.04 0.00 0.04 7.09 0.05 0.00 Ribs 7.79 26.48 3.79 50.49 0.06 0.21 3.67 0.24 0.04 0.00 0.04 7.13 0.05 0.00 Scapulae 7.44 25.14 3.87 50.73 0.06 0.22 4.13 0.25 0.04 0.00 0.04 8.06 0.05 0.00 Clavicles 7.36 24 .85 3.87 50.78 0.06 0.22 4.23 0.25 0.04 0.00 0.04 8.26 0.05 0.00 Os Coxae 8.17 27.95 3.72 50.23 0.07 0.20 3.17 0.24 0.04 0.00 0.04 6.11 0.06 0.00 Sacrum 7.54 25.53 3.85 50.66 0.06 0.21 3.99 0.25 0.04 0.00 0.04 7.79 0.05 0. 00 Humera proximal 6.73 22.35 4.01 51.32 0.05 0.23 5.03 0.26 0.04 0.00 0.04 9.91 0.04 0.00 Humera distal 6.73 22.86 3.95 50.77 0.05 0.23 5.07 0.26 0.04 0.00 0.04 9.99 0.04 0.00 Radii proximal 6.64 22.41 3.98 50.95 0.05 0.23 5. 17 0.26 0.04 0.00 0.04 10.20 0.03 0.00 Radii distal 6.50 21.85 4.01 51.08 0.05 0.23 5.35 0.26 0.04 0.00 0.04 10.56 0.03 0.00 Ulnae proximal 6.13 20.38 4.09 51.40 0.04 0.24 5.83 0.27 0.04 0.00 0.04 11.54 0.03 0.00 Ulnae distal 7.34 25.18 3.83 50.35 0.06 0.21 4.28 0.25 0.04 0.00 0.04 8.38 0.04 0.00

PAGE 439

439 Table A 4. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Wrists and hands 7.47 28.53 3.46 47.28 0.05 0.18 4.29 0.24 0.04 0.00 0.04 8.40 0.03 0.00 Femora proximal 6.90 23.00 3.98 51.21 0.05 0.23 4.81 0.26 0.04 0.00 0.04 9.45 0.04 0.00 Femora distal 7.25 24.96 3.83 50.29 0.05 0.21 4.40 0.25 0.04 0.00 0.04 8.63 0.04 0.00 Patellae 8.15 28.43 3.66 49.65 0.07 0.20 3.23 0.24 0.04 0.00 0.04 6.24 0.06 0.00 Tibiae proximal 6.82 23.11 3.94 50.80 0.05 0.23 4.95 0.26 0.04 0.00 0.04 9.74 0.04 0.00 Tibiae distal 7.08 24.16 3.89 50.58 0.05 0.22 4.61 0.25 0.04 0.00 0.04 9.05 0.04 0.00 Fibulae proximal 6.69 2 2.58 3.97 50.92 0.05 0.23 5.11 0.26 0.04 0.00 0.04 10.09 0.04 0.00 Fibulae distal 6.73 22.77 3.96 50.88 0.05 0.23 5.06 0.26 0.04 0.00 0.04 9.96 0.04 0.00 Ankles and feet 7.55 28.95 3.44 47.11 0.05 0.18 4.19 0.24 0.04 0.00 0.04 8.20 0.03 0.00 Humera upper shaft 10.50 37.12 3.24 48.31 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.09 0.00 Humera lower shaft 10.52 37.50 3.20 47.96 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Radii shaft 10.53 37.89 3.16 47.61 0.11 0. 15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Ulnae shaft 10.53 37.89 3.16 47.61 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Femora upper shaft 10.50 37.12 3.24 48.31 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.09 0.00 Femora lowe r shaft 10.52 37.50 3.20 47.96 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Tibiae shaft 10.53 37.89 3.16 47.61 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Fibulae shaft 10.53 37.89 3.16 47.61 0.11 0.15 0.19 0.20 0.05 0.00 0.04 0.00 0.08 0.00 Lymph nodes 10.49 25.06 2.72 60.73 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Ears 9.64 9.98 2.28 74.41 0.47 0.00 2.05 0.85 0.30 0.00 0.01 0.00 0.01 0.00 External nose 9.64 9.98 2.28 74.41 0.47 0.00 2.05 0.85 0.30 0.00 0.01 0 .00 0.01 0.00 Nasal layers 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Oral cavity layer 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pharynx 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0 .20 0.00 0.01 0.00 Sal glands 10.48 24.57 2.74 61.21 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Spinal cord 10.66 14.25 2.28 71.43 0.19 0.00 0.38 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Penis 10.20 14.06 3.39 71.26 0.10 0.00 0.19 0.29 0.11 0.00 0.39 0 .00 0.01 0.00 Scrotum 10.48 24.52 2.74 61.26 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00

PAGE 440

440 Table A 5. Blood inclusive elemental compositions in mass percent for all tissues in the UFH05MF phantoms (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 10.44 22.63 2.82 63.11 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 13.85 3.39 71.48 0.10 0.00 0.19 0.29 0.13 0.00 0.37 0.00 0.01 0.00 Esophagus 10.42 21.89 2.85 63.84 0.10 0.00 0.17 0.27 0.23 0.00 0.20 0.00 0. 03 0.00 Stomach 10.50 11.37 2.48 74.95 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Small intestine 10.49 11.36 2.51 74.93 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Large intestine 10.49 11.36 2.51 74.93 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0 .00 0.03 0.00 Liver 10.27 16.37 2.95 69.28 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pancreas 10.51 15.64 2.43 70.49 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0. 00 0.02 0.00 Blood 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.67 14.30 2.26 71.39 0.19 0.00 0.38 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Heart 10.37 13.43 2.97 72.24 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Ey e 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.92 0.75 28.64 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 19.96 4.16 64.97 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.24 3.40 71.07 0.10 0.00 0.20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Trachea 10.50 25.37 2.71 60.43 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.68 10.05 2.35 74.4 1 0.45 0.00 1.91 0.80 0.30 0.00 0.03 0.00 0.01 0.00 Lung 10.25 10.73 3.19 74.71 0.15 0.00 0.15 0.25 0.30 0.00 0.20 0.00 0.05 0.00 Spleen 10.25 11.16 3.25 74.29 0.10 0.00 0.21 0.20 0.25 0.00 0.25 0.00 0.05 0.00 Thymus 10.46 23.61 2.78 62.15 0.10 0.00 0.1 9 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Thyroid 10.37 11.76 2.54 74.50 0.18 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.08 Tonsils 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Kidney 10.27 12.50 3.10 73.07 0.17 0.00 0.17 0.20 0.23 0.00 0.20 0.07 0.03 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.61 76.07 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Epididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.24 53.18 1.05 34.14 0.10 0.00 0.01 0.11 0.13 0.00 0.03 0.00 0.01 0.00 Testes 10.58 9.97 2.08 76.47 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.0 0 0.01 0.00

PAGE 441

441 Table A 5. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.46 23.62 2.78 62.14 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Breast Female 11.41 46.28 0.45 41.72 0.01 0.00 0.01 0.03 0.04 0.00 0.03 0.00 0. 01 0.00 Ovaries 10.48 24.51 2.74 61.26 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.55 28.68 2.52 57.42 0.10 0.00 0.19 0.20 0.13 0.00 0.20 0.00 0.01 0.00 Cartilage 9.63 9.96 2.26 74.41 0.48 0.00 2.09 0.86 0.30 0.00 0.01 0.00 0.01 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.0 0 Soft tissue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Le ns 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 4.22 15.82 4.46 47.90 0.10 0.19 8.68 0.30 0.01 0.00 0.01 18.31 0.00 0.00 Spongiosa/MC Cranium 6.88 23.67 3.85 49.26 0.10 0.16 5.10 0.25 0.05 0.00 0.04 10.60 0.04 0.00 Mandible 7.18 24.97 3.78 48.98 0.10 0.16 4.71 0.25 0.05 0.00 0.04 9.76 0.04 0.00 Vertebrae C 8.11 28.46 3.62 48.70 0.10 0.16 3.44 0.23 0.05 0.00 0.04 7.04 0.06 0.00 Vertebr ae T 8.70 30.93 3.48 48.28 0.10 0.15 2.65 0.23 0.05 0.00 0.04 5.33 0.06 0.00 Vertebrae L 8.12 28.50 3.61 48.70 0.10 0.16 3.43 0.23 0.05 0.00 0.04 7.02 0.06 0.00 Sternum 8.84 31.52 3.45 48.17 0.10 0.15 2.46 0.22 0.05 0.00 0.04 4.94 0.07 0.00 Ribs 8.09 28.37 3.62 48.72 0.10 0.16 3.47 0.23 0.05 0.00 0.04 7.10 0.06 0.00 Scapulae 7.87 27.99 3.61 48.36 0.10 0.15 3.78 0.23 0.05 0.00 0.04 7.76 0.05 0.00 Clavicles 8.11 29.09 3.55 48.05 0.10 0.15 3.47 0.23 0.05 0.00 0.04 7.11 0.05 0.00 Os Coxae 8.55 30.99 3.44 47.66 0.10 0.15 2.89 0.23 0.05 0.00 0.04 5.86 0.06 0.00 Sacrum 8.87 32.38 3.36 47.35 0.10 0.15 2.48 0.22 0.05 0.00 0.04 4.96 0.06 0.00 Humera proximal 7.53 26.62 3.69 48.56 0.10 0.16 4.23 0.24 0.05 0.00 0.04 8.74 0.04 0.00 Humera distal 7.66 28.02 3.56 47.51 0.10 0.15 4.12 0.23 0.05 0.00 0.03 8.52 0.04 0.00 Radii proximal 8.57 33.94 3.14 44.62 0.10 0.12 3.02 0 .21 0.05 0.00 0.03 6.14 0.05 0.00 Radii distal 7.88 30.31 3.37 45.92 0.10 0.13 3.90 0.23 0.05 0.00 0.03 8.04 0.04 0.00 Ulnae proximal 7.51 28.37 3.49 46.60 0.10 0.14 4.38 0.24 0.05 0.00 0.03 9.07 0.03 0.00

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442 Table A 5. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Ulnae distal 9.42 38.41 2.87 43.01 0.10 0.11 1.93 0.19 0.04 0.00 0.03 3.82 0.05 0.00 Wrists and hands 8.11 35.02 2.89 41.74 0.10 0.10 3.83 0.21 0.04 0.00 0.03 7.92 0.02 0.00 Femor a proximal 7.55 26.70 3.68 48.53 0.10 0.16 4.21 0.24 0.05 0.00 0.04 8.70 0.05 0.00 Femora distal 7.88 29.07 3.50 47.24 0.10 0.14 3.84 0.23 0.05 0.00 0.03 7.89 0.04 0.00 Patellae 9.57 38.74 2.83 43.21 0.10 0.11 1.73 0.19 0.04 0 .00 0.03 3.38 0.05 0.00 Tibiae proximal 7.75 29.60 3.41 46.18 0.10 0.14 4.07 0.23 0.05 0.00 0.03 8.41 0.04 0.00 Tibiae distal 8.85 35.41 3.05 44.10 0.10 0.12 2.65 0.21 0.04 0.00 0.03 5.37 0.05 0.00 Fibulae proximal 8.59 33.92 3. 14 44.71 0.10 0.12 2.99 0.21 0.05 0.00 0.03 6.09 0.05 0.00 Fibulae distal 8.62 34.07 3.13 44.66 0.10 0.12 2.96 0.21 0.05 0.00 0.03 6.01 0.05 0.00 Ankles and feet 7.97 34.15 2.95 42.15 0.10 0.11 4.00 0.21 0.04 0.00 0.03 8.29 0.02 0.00 Humera upper shaft 10.65 41.18 2.84 44.58 0.10 0.13 0.17 0.18 0.05 0.00 0.04 0.00 0.07 0.00 Humera lower shaft 10.67 41.57 2.80 44.23 0.10 0.12 0.17 0.18 0.05 0.00 0.04 0.00 0.07 0.00 Radii shaft 10.81 45.24 2.42 40.86 0.10 0.10 0.15 0.16 0.04 0.00 0.03 0.00 0.06 0.00 Ulnae shaft 10.81 45.32 2.42 40.80 0.10 0.10 0.15 0.16 0.04 0.00 0.03 0.00 0.06 0.00 Femora upper shaft 10.65 41.12 2.84 44.65 0.10 0.13 0.17 0.18 0.05 0.00 0.04 0.00 0.07 0.00 Femora lower shaft 10.67 41.63 2.80 44.17 0.10 0.12 0.17 0.18 0.05 0.00 0.04 0.00 0.07 0.00 Tibiae shaft 10.81 45.34 2.42 40.77 0.10 0.10 0.15 0.16 0.04 0.00 0.03 0.00 0.06 0.00 Fibulae shaft 10.81 45.14 2.43 40.96 0.10 0.10 0.15 0.16 0.04 0.00 0.03 0. 00 0.06 0.00 Lymph nodes 10.49 24.89 2.73 60.89 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Ears 9.68 10.05 2.35 74.41 0.45 0.00 1.91 0.80 0.30 0.00 0.03 0.00 0.01 0.00 External nose 9.68 10.05 2.35 74.41 0.45 0.00 1.91 0.80 0.30 0.00 0.03 0.00 0. 01 0.00 Nasal layers 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Oral cavity layer 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pharynx 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0. 00 0.01 0.00 Sal glands 10.46 23.61 2.78 62.15 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Spinal cord 10.63 14.02 2.35 71.65 0.19 0.00 0.36 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Penis 10.20 13.85 3.39 71.48 0.10 0.00 0.19 0.29 0.13 0.00 0.37 0.00 0. 01 0.00 Scrotum 10.46 23.62 2.78 62.14 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00

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443 Table A 6. Blood inclusive elemental compositions in mass percent for all tissues in the UFH10MF phantoms (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 10.44 22.63 2.82 63.11 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 13.78 3.38 71.55 0.10 0.00 0.18 0.28 0.13 0.00 0.37 0.00 0.02 0.00 Esophagus 10.42 21.89 2.85 63.84 0.10 0.00 0.17 0.27 0.23 0.00 0.20 0.00 0.03 0. 00 Stomach 10.50 11.37 2.48 74.95 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Small intestine 10.49 11.36 2.51 74.93 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Large intestine 10.49 11.36 2.51 74.93 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0 .03 0.00 Liver 10.27 16.37 2.95 69.28 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pancreas 10.51 15.64 2.43 70.49 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0.00 0. 02 0.00 Blood 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.67 14.31 2.26 71.38 0.19 0.00 0.38 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Heart 10.37 13.43 2.97 72.24 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Eye 9.6 0 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.92 0.75 28.64 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 20.06 4.17 64.86 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.24 3.40 71.06 0.10 0.00 0.20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Trachea 10.49 25.30 2.71 60.49 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.70 10.07 2.37 74.42 0.4 4 0.00 1.87 0.79 0.30 0.00 0.03 0.00 0.02 0.00 Lung 10.25 10.77 3.21 74.68 0.15 0.00 0.15 0.25 0.30 0.00 0.20 0.00 0.05 0.00 Spleen 10.25 11.16 3.25 74.29 0.10 0.00 0.21 0.20 0.25 0.00 0.25 0.00 0.05 0.00 Thymus 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.2 8 0.22 0.00 0.20 0.00 0.02 0.00 Thyroid 10.37 11.76 2.54 74.50 0.18 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.08 Tonsils 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Kidney 10.27 12.50 3.10 73.07 0.17 0.00 0.17 0.20 0.23 0.00 0.20 0.07 0.03 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.61 76.07 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Epididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.21 51.89 1.12 35.37 0.10 0.00 0.02 0.12 0.13 0.00 0.03 0.00 0.02 0.00 Testes 10.58 9.97 2.08 76.47 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.00 0.0 1 0.00

PAGE 444

444 Table A 6. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.45 23.23 2.80 62.52 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Breast Female 11.38 45.56 0.51 42.39 0.02 0.00 0.02 0.03 0.05 0.00 0.03 0.00 0.02 0. 00 Ovaries 10.48 24.51 2.74 61.26 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.54 28.32 2.54 57.77 0.10 0.00 0.18 0.20 0.13 0.00 0.20 0.00 0.02 0.00 Cartilage 9.62 9.93 2.23 74.40 0.49 0.00 2.14 0.88 0.30 0.00 0.01 0.00 0.00 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 So ft tissue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9. 60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 4.06 15.87 4.37 46.34 0.10 0.19 9.26 0.30 0.01 0.00 0.01 19.49 0.00 0.00 Spongiosa/MC Cranium 7.68 28.19 3.47 47.01 0.10 0.14 4.26 0.23 0.05 0.00 0.04 8.79 0.04 0.00 Mandible 7.98 29.76 3.39 46.50 0.10 0.14 3.86 0.23 0.05 0.00 0.04 7.93 0.04 0.00 Vertebrae C 9.03 33.18 3.31 46.87 0.10 0.15 2.34 0.22 0.05 0.00 0.04 4.66 0.07 0.00 Vertebrae T 9.42 35.02 3.22 46.43 0.10 0.14 1.81 0.21 0.05 0.00 0.04 3.51 0.07 0.00 Vertebrae L 8.93 32.72 3.33 46.98 0.10 0.15 2.48 0.22 0.05 0.00 0.04 4.95 0.07 0.00 Sternum 9.77 36.65 3.14 46.04 0.10 0.14 1.33 0.20 0.05 0.00 0.04 2.48 0.07 0.00 Ribs 9.19 33.94 3.27 46.69 0.10 0.15 2.12 0.21 0.05 0.00 0.04 4.19 0.07 0.00 Scapulae 8.74 33.69 3.17 45.23 0.10 0.13 2.85 0.21 0.05 0.00 0.04 5.76 0.05 0.00 Clavicles 9.19 36.27 3.01 4 4.19 0.10 0.12 2.27 0.20 0.05 0.00 0.03 4.51 0.06 0.00 Os Coxae 9.30 35.63 3.12 45.34 0.10 0.13 2.03 0.21 0.05 0.00 0.03 4.00 0.06 0.00 Sacrum 9.90 38.55 2.97 44.50 0.10 0.13 1.23 0.19 0.05 0.00 0.03 2.28 0.06 0.00 H umera proximal 8.27 30.71 3.36 46.59 0.10 0.14 3.44 0.23 0.05 0.00 0.04 7.03 0.05 0.00 Humera distal 8.54 36.85 2.76 41.08 0.10 0.10 3.37 0.20 0.04 0.00 0.03 6.91 0.03 0.00 Radii proximal 9.01 40.64 2.47 38.84 0.10 0.08 2.82 0.19 0. 04 0.00 0.03 5.75 0.03 0.00 Radii distal 8.51 37.31 2.69 40.45 0.10 0.10 3.46 0.20 0.04 0.00 0.03 7.10 0.02 0.00 Ulnae proximal 8.12 34.76 2.87 41.67 0.10 0.11 3.94 0.21 0.04 0.00 0.03 8.13 0.02 0.00

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445 Table A 6. Continued. Eleme nt Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Ulnae distal 9.68 44.98 2.18 36.77 0.10 0.07 1.99 0.17 0.03 0.00 0.03 3.98 0.03 0.00 Wrists and hands 9.20 45.01 2.04 34.89 0.10 0.06 2.78 0.17 0.03 0.00 0.03 5.70 0.01 0.00 Femora prox imal 8.18 30.27 3.39 46.72 0.10 0.14 3.56 0.23 0.05 0.00 0.04 7.28 0.05 0.00 Femora distal 8.40 35.95 2.81 41.49 0.10 0.11 3.54 0.20 0.04 0.00 0.03 7.28 0.03 0.00 Patellae 10.52 50.44 1.81 34.16 0.10 0.06 0.95 0.15 0.03 0.00 0 .02 1.74 0.03 0.00 Tibiae proximal 8.64 38.15 2.64 40.05 0.10 0.09 3.30 0.20 0.04 0.00 0.03 6.76 0.02 0.00 Tibiae distal 9.28 42.41 2.35 38.00 0.10 0.08 2.48 0.18 0.04 0.00 0.03 5.03 0.03 0.00 Fibulae proximal 9.12 41.35 2.42 38 .51 0.10 0.08 2.68 0.18 0.04 0.00 0.03 5.46 0.03 0.00 Fibulae distal 9.14 41.47 2.41 38.45 0.10 0.08 2.67 0.18 0.04 0.00 0.03 5.41 0.03 0.00 Ankles and feet 8.99 43.51 2.15 35.70 0.10 0.06 3.03 0.17 0.03 0.00 0.03 6.22 0.01 0.00 Hu mera upper shaft 10.89 47.70 2.24 38.56 0.10 0.09 0.15 0.16 0.04 0.00 0.03 0.00 0.05 0.00 Humera lower shaft 10.90 47.95 2.21 38.33 0.10 0.09 0.15 0.16 0.04 0.00 0.03 0.00 0.05 0.00 Radii shaft 11.16 54.68 1.53 32.15 0.10 0.05 0.13 0.13 0.03 0.00 0.02 0.00 0.02 0.00 Ulnae shaft 11.16 54.68 1.53 32.15 0.10 0.05 0.13 0.13 0.03 0.00 0.02 0.00 0.02 0.00 Femora upper shaft 10.89 47.70 2.24 38.56 0.10 0.09 0.15 0.16 0.04 0.00 0.03 0.00 0.05 0.00 Femora lower shaft 10.90 47.95 2.21 38.33 0.10 0.09 0.15 0.16 0.04 0.00 0.03 0.00 0.05 0.00 Tibiae shaft 11.16 54.68 1.53 32.15 0.10 0.05 0.13 0.13 0.03 0.00 0.02 0.00 0.02 0.00 Fibulae shaft 11.16 54.68 1.53 32.15 0.10 0.05 0.13 0.13 0.03 0.00 0.02 0.00 0. 02 0.00 Lymph nodes 10.49 24.89 2.73 60.89 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Ears 9.70 10.07 2.37 74.42 0.44 0.00 1.87 0.79 0.30 0.00 0.03 0.00 0.02 0.00 External nose 9.70 10.07 2.37 74.42 0.44 0.00 1.87 0.79 0.30 0.00 0.03 0.00 0.02 0. 00 Nasal layers 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Oral cavity layer 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pharynx 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0. 02 0.00 Sal glands 10.45 23.29 2.80 62.47 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Spinal cord 10.62 13.95 2.37 71.72 0.18 0.00 0.35 0.20 0.30 0.00 0.28 0.00 0.02 0.00 Penis 10.20 13.77 3.38 71.57 0.10 0.00 0.18 0.28 0.13 0.00 0.37 0.00 0.02 0. 00 Scrotum 10.45 23.23 2.80 62.52 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00

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446 Table A 7. Blood inclusive elemental compositions in mass percent for all tissues in the UFH15M phantom (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca F e I Adrenals 10.43 21.99 2.85 63.74 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 13.66 3.38 71.67 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 Esophagus 10.41 21.16 2.88 64.55 0.10 0.00 0.17 0.27 0.23 0.00 0.20 0.00 0.03 0.00 Sto mach 10.48 11.35 2.53 74.92 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Small intestine 10.47 11.33 2.57 74.90 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Large intestine 10.46 11.33 2.58 74.89 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.0 0 Liver 10.27 16.14 2.96 69.49 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pancreas 10.50 15.44 2.47 70.66 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0.00 0.02 0.00 Blood 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.67 14.31 2.26 71.38 0.19 0.00 0.38 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Heart 10.36 13.39 2.97 72.28 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Eye 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.84 0.75 28.72 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 19.97 4.16 64.96 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.23 3.40 71.08 0.10 0 .00 0.20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Trachea 10.48 24.76 2.73 61.02 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Larynx 9.72 10.11 2.41 74.42 0.42 0.00 1.80 0.77 0.30 0.00 0.04 0.00 0.02 0.00 Lung 10.24 10.81 3.22 74.65 0.14 0.00 0.14 0.24 0.30 0.00 0.20 0.00 0.06 0.00 Spleen 10.25 11.14 3.25 74.32 0.10 0.00 0.19 0.20 0.25 0.00 0.25 0.00 0.05 0.00 Thymus 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Thyroid 10.37 11.74 2.56 74.50 0.18 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.08 Tonsils 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Kidney 10.26 12.37 3.11 73.19 0.16 0.00 0.16 0.20 0.24 0.00 0.20 0 .06 0.04 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.62 76.06 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0. 00 Epididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.17 50.41 1.20 36.79 0.10 0.00 0.02 0.12 0.14 0.00 0.04 0.00 0.02 0.00 Testes 10.57 9.97 2.09 76.46 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.00 0.01 0.00

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447 Table A 7. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Breast Female 11.49 48.79 0.25 39.39 0.01 0.00 0.01 0.02 0.02 0.00 0.02 0.00 0.01 0.00 Ova ries 10.48 24.59 2.74 61.19 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.57 29.94 2.47 56.20 0.10 0.00 0.19 0.20 0.12 0.00 0.20 0.00 0.01 0.00 Cartil age 9.61 9.93 2.23 74.40 0.49 0.00 2.15 0.88 0.30 0.00 0.00 0.00 0.00 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Soft tiss ue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9.60 19.5 0 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 3.93 15.89 4.28 45.82 0.20 0.20 9.30 0.30 0.01 0.00 0.00 20.07 0.00 0.00 Spongiosa/MC Cranium 8.16 31.01 3.18 45.85 0.14 0.12 3.60 0 .22 0.05 0.00 0.04 7.58 0.04 0.00 Mandible 8.40 32.34 3.11 45.35 0.13 0.12 3.29 0.22 0.05 0.00 0.04 6.90 0.04 0.00 Vertebrae C 9.23 33.97 3.16 46.81 0.12 0.13 2.05 0.21 0.06 0.00 0.04 4.16 0.06 0.00 Vertebrae T 9.49 35.20 3.10 46.48 0.12 0.13 1.71 0.20 0.06 0.00 0.04 3.41 0.07 0.00 Vertebrae L 9.67 36.07 3.06 46.25 0.11 0.13 1.47 0.20 0.06 0.00 0.04 2.88 0.07 0.00 Sternum 9.78 36.59 3.03 46.11 0.11 0.13 1.33 0.20 0.05 0.00 0.04 2. 56 0.07 0.00 Ribs 9.55 35.48 3.09 46.40 0.12 0.13 1.64 0.20 0.06 0.00 0.04 3.24 0.07 0.00 Scapulae 8.25 31.47 3.16 45.68 0.14 0.12 3.50 0.22 0.05 0.00 0.04 7.35 0.04 0.00 Clavicles 9.20 37.24 2.82 43.19 0. 12 0.11 2.29 0.20 0.05 0.00 0.03 4.70 0.05 0.00 Os Coxae 9.74 38.25 2.85 44.19 0.11 0.12 1.49 0.19 0.05 0.00 0.04 2.92 0.06 0.00 Sacrum 10.18 40.58 2.73 43.42 0.11 0.11 0.90 0.18 0.05 0.00 0.03 1.63 0.06 0.00 Humera proximal 9.36 37.65 2.82 43.36 0.12 0.11 2.06 0.20 0.05 0.00 0.03 4.20 0.05 0.00 Humera distal 9.08 44.26 2.05 35.22 0.13 0.06 2.89 0.17 0.03 0.00 0.02 6.08 0.01 0.00 Radii proximal 9.16 44.87 2.01 34.88 0.13 0.06 2.79 0.17 0.03 0.0 0 0.02 5.87 0.01 0.00 Radii distal 9.24 45.51 1.96 34.52 0.13 0.05 2.69 0.17 0.03 0.00 0.02 5.65 0.01 0.00 Ulnae proximal 8.75 41.81 2.22 36.59 0.13 0.07 3.27 0.18 0.03 0.00 0.02 6.90 0.01 0.00

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448 Table A 7. Continued. Element Ti ssue H C N O Na Mg P S Cl Ar K Ca Fe I Ulnae distal 9.34 46.24 1.91 34.12 0.13 0.05 2.58 0.17 0.03 0.00 0.02 5.40 0.01 0.00 Wrists and hands 9.98 51.07 1.58 31.44 0.12 0.04 1.82 0.15 0.02 0.00 0.02 3.75 0.01 0.00 Femora proximal 8.95 35.39 2.94 44.20 0.13 0.12 2.59 0.20 0.05 0.00 0.04 5.35 0.05 0.00 Femora distal 8.56 40.37 2.32 37.40 0.14 0.07 3.49 0.19 0.04 0.00 0.03 7.39 0.01 0.00 Patellae 9.98 51.07 1.58 31.44 0.12 0.04 1.82 0.15 0.02 0.00 0.02 3.7 5 0.01 0.00 Tibiae proximal 10.26 53.16 1.43 30.29 0.12 0.03 1.49 0.14 0.02 0.00 0.02 3.04 0.01 0.00 Tibiae distal 9.34 46.28 1.91 34.10 0.13 0.05 2.57 0.17 0.03 0.00 0.02 5.39 0.01 0.00 Fibulae proximal 9.67 48.72 1.74 32.74 0. 12 0.04 2.19 0.16 0.03 0.00 0.02 4.56 0.01 0.00 Fibulae distal 8.66 41.13 2.27 36.97 0.13 0.07 3.37 0.18 0.04 0.00 0.03 7.13 0.01 0.00 Ankles and feet 9.98 51.07 1.58 31.44 0.12 0.04 1.82 0.15 0.02 0.00 0.02 3.75 0.01 0.00 Humera u pper shaft 11.04 51.31 1.85 35.26 0.10 0.06 0.13 0.15 0.03 0.00 0.02 0.00 0.04 0.00 Humera lower shaft 11.20 55.69 1.43 31.22 0.10 0.04 0.12 0.13 0.02 0.00 0.02 0.00 0.02 0.00 Radii shaft 11.44 61.92 0.82 25.48 0.10 0.00 0.10 0.11 0.01 0 .00 0.01 0.00 0.00 0.00 Ulnae shaft 11.44 61.92 0.82 25.48 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.00 Femora upper shaft 11.04 51.31 1.85 35.26 0.10 0.06 0.13 0.15 0.03 0.00 0.02 0.00 0.04 0.00 Femora lower shaft 11.20 55.69 1.43 31.22 0.10 0.04 0.12 0.13 0.02 0.00 0.02 0.00 0.02 0.00 Tibiae shaft 11.44 61.92 0.82 25.48 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.00 Fibulae shaft 11.44 61.92 0.82 25.48 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.0 0 Lymph nodes 10.48 24.80 2.73 60.99 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Ears 9.72 10.11 2.41 74.42 0.42 0.00 1.80 0.77 0.30 0.00 0.04 0.00 0.02 0.00 External nose 9.72 10.11 2.41 74.42 0.42 0.00 1.80 0.77 0.30 0.00 0.04 0.00 0.02 0.00 Na sal layers 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Oral cavity layer 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pharynx 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.0 0 Sal glands 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Spinal cord 10.60 13.83 2.41 71.84 0.18 0.00 0.34 0.20 0.30 0.00 0.28 0.00 0.02 0.00 Penis 10.20 13.66 3.38 71.67 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 Sc rotum 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00

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449 Table A 8. Blood inclusive elemental compositions in mass percent for all tissues in the UFH15F phantom (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I A drenals 10.45 23.05 2.80 62.70 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 14.05 3.39 71.27 0.10 0.00 0.19 0.29 0.12 0.00 0.38 0.00 0.01 0.00 Esophagus 10.44 22.44 2.83 63.30 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Stomach 1 0.51 11.39 2.44 74.97 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Small intestine 10.50 11.38 2.46 74.96 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Large intestine 10.51 11.38 2.46 74.96 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Liv er 10.27 16.52 2.94 69.12 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pancreas 10.52 15.78 2.41 70.37 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0.00 0.02 0.00 Bloo d 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.68 14.36 2.24 71.33 0.20 0.00 0.39 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Heart 10.37 13.46 2.96 72.21 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Eye 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.98 0.74 28.58 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 19.99 4.16 64.94 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.24 3.40 71.06 0.10 0.00 0. 20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Trachea 10.49 24.88 2.73 60.90 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.65 9.98 2.28 74.41 0.47 0.00 2.04 0. 85 0.30 0.00 0.02 0.00 0.01 0.00 Lung 10.25 10.77 3.21 74.68 0.15 0.00 0.15 0.25 0.30 0.00 0.20 0.00 0.05 0.00 Spleen 10.26 11.18 3.24 74.26 0.10 0.00 0.22 0.20 0.24 0.00 0.26 0.00 0.04 0.00 Thymus 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0. 20 0.00 0.01 0.00 Thyroid 10.37 11.78 2.52 74.50 0.19 0.00 0.10 0.11 0.21 0.00 0.11 0.00 0.01 0.09 Tonsils 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Kidney 10.27 12.59 3.08 72.99 0.17 0.00 0.17 0.20 0.23 0.00 0.20 0.07 0.0 3 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.61 76.07 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Epi didymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.17 50.41 1.20 36.79 0.10 0.00 0.02 0.12 0.14 0.00 0.04 0.00 0.02 0.00 Testes 10.57 9.97 2.09 76.46 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.00 0.01 0.00

PAGE 450

450 Tab le A 8. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Breast Female 11.49 48.79 0.25 39.39 0.01 0.00 0.01 0.02 0.02 0.00 0.02 0.00 0.01 0.00 Ovaries 10 .48 24.59 2.74 61.19 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.57 29.94 2.47 56.20 0.10 0.00 0.19 0.20 0.12 0.00 0.20 0.00 0.01 0.00 Cartilage 9.6 1 9.92 2.22 74.40 0.49 0.00 2.16 0.89 0.30 0.00 0.00 0.00 0.00 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Soft tissue Fe male 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 3.92 15.91 4.28 45.76 0.20 0.20 9.32 0.30 0.01 0.00 0.00 20.11 0.00 0.00 Spongiosa/MC Cranium 8.12 31.65 3.17 45.00 0.14 0.13 3.69 0.22 0.0 5 0.00 0.03 7.77 0.04 0.00 Mandible 8.36 33.02 3.09 44.48 0.13 0.12 3.38 0.21 0.05 0.00 0.03 7.08 0.04 0.00 Vertebrae C 9.20 34.87 3.15 45.76 0.12 0.14 2.12 0.21 0.05 0.00 0.03 4.29 0.06 0.00 Vertebrae T 9.47 3 6.16 3.09 45.40 0.12 0.13 1.77 0.20 0.04 0.00 0.03 3.52 0.06 0.00 Vertebrae L 9.66 37.08 3.04 45.14 0.11 0.13 1.52 0.20 0.04 0.00 0.03 2.97 0.07 0.00 Sternum 9.77 37.62 3.02 44.99 0.11 0.13 1.37 0.20 0.04 0.00 0.03 2.65 0.07 0.00 Ribs 9.53 36.46 3.07 45.31 0.12 0.13 1.69 0.20 0.04 0.00 0.03 3.35 0.06 0.00 Scapulae 8.20 32.12 3.14 44.82 0.14 0.13 3.58 0.22 0.05 0.00 0.03 7.53 0.04 0.00 Clavicles 9.18 38.04 2.80 42.28 0.12 0.11 2.34 0.19 0.04 0.00 0.03 4.82 0.04 0.00 Os Coxae 9.73 39.21 2.83 43.15 0.11 0.12 1.53 0.19 0.04 0.00 0.03 3.00 0.06 0.00 Sacrum 10.19 41.62 2.71 42.34 0.11 0.12 0.92 0.18 0.04 0.00 0.03 1.68 0.06 0.00 Humera proxima l 9.34 38.49 2.79 42.41 0.12 0.11 2.12 0.19 0.04 0.00 0.03 4.31 0.05 0.00 Humera distal 9.07 44.69 2.03 34.74 0.13 0.06 2.91 0.17 0.03 0.00 0.02 6.13 0.01 0.00 Radii proximal 9.15 45.30 1.99 34.41 0.13 0.06 2.82 0.17 0.03 0.00 0.02 5.92 0.01 0.00 Radii distal 9.24 45.95 1.95 34.05 0.13 0.06 2.71 0.17 0.03 0.00 0.02 5.70 0.01 0.00 Ulnae proximal 8.74 42.26 2.20 36.09 0.13 0.07 3.30 0.18 0.03 0.00 0.02 6.97 0.01 0.00

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451 Table A 8. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Ulnae distal 9.33 46.67 1.90 33.66 0.13 0.05 2.60 0.16 0.03 0.00 0.02 5.45 0.01 0.00 Wrists and hands 9.98 51.48 1.56 31.03 0.12 0.04 1.83 0.15 0.02 0.00 0.02 3.78 0.01 0.00 Femora proximal 8.92 36.16 2.92 43.29 0.13 0.12 2.65 0.20 0.04 0.00 0.03 5.49 0.05 0.00 Femora distal 8.55 40.81 2.30 36.89 0.14 0.07 3.52 0.18 0.03 0.00 0.02 7.46 0.01 0.00 Patellae 9.98 51.48 1.56 31.03 0.12 0.04 1.83 0.15 0.02 0.00 0.02 3.78 0.01 0.00 Tibiae proximal 10.26 53.55 1.42 29.90 0.12 0.03 1.50 0.14 0.02 0.00 0.02 3.05 0.01 0.00 Tibiae distal 9.34 46.71 1.89 33.64 0.13 0.05 2.59 0.16 0.03 0.00 0.02 5.43 0.01 0.00 Fibulae proximal 9.66 49.14 1.72 32.31 0.12 0.04 2.21 0.15 0.02 0.00 0.02 4.59 0.01 0.00 Fibulae distal 8.65 41.57 2.25 36.47 0.14 0.07 3.40 0.18 0.03 0.00 0.02 7.20 0.01 0.00 Ankles and feet 9.98 51.48 1.56 31.03 0.12 0.04 1.83 0.15 0.02 0.00 0.02 3.78 0.01 0.00 Humera upper sh aft 11.06 52.18 1.81 34.42 0.10 0.07 0.14 0.14 0.02 0.00 0.02 0.00 0.04 0.00 Humera lower shaft 11.22 56.35 1.40 30.59 0.10 0.04 0.12 0.13 0.02 0.00 0.02 0.00 0.02 0.00 Radii shaft 11.44 62.23 0.81 25.19 0.10 0.00 0.10 0.11 0.01 0.00 0.0 1 0.00 0.00 0.00 Ulnae shaft 11.44 62.23 0.81 25.19 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.00 Femora upper shaft 11.06 52.18 1.81 34.42 0.10 0.07 0.14 0.14 0.02 0.00 0.02 0.00 0.04 0.00 Femora lower shaft 11.22 56.35 1.40 3 0.59 0.10 0.04 0.12 0.13 0.02 0.00 0.02 0.00 0.02 0.00 Tibiae shaft 11.44 62.23 0.81 25.19 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.00 Fibulae shaft 11.44 62.23 0.81 25.19 0.10 0.00 0.10 0.11 0.01 0.00 0.01 0.00 0.00 0.00 Lymp h nodes 10.49 24.97 2.73 60.82 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Ears 9.65 9.98 2.28 74.41 0.47 0.00 2.04 0.85 0.30 0.00 0.02 0.00 0.01 0.00 External nose 9.65 9.98 2.28 74.41 0.47 0.00 2.04 0.85 0.30 0.00 0.02 0.00 0.01 0.00 Nasal layer s 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Oral cavity layer 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pharynx 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Sal gl ands 10.48 24.49 2.75 61.29 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Spinal cord 10.66 14.23 2.28 71.45 0.19 0.00 0.38 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Penis 10.20 13.66 3.38 71.67 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 Scrotum 10. 44 22.79 2.82 62.95 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00

PAGE 452

452 Table A 9. Blood inclusive elemental compositions in mass percent for all tissues in the UFHADM phantom (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 1 0.43 22.09 2.84 63.63 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 13.57 3.38 71.77 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 Esophagus 10.41 21.30 2.88 64.41 0.10 0.00 0.17 0.27 0.23 0.00 0.20 0.00 0.03 0.00 Stomach 10.48 11.3 5 2.52 74.92 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Small intestine 10.47 11.34 2.56 74.90 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Large intestine 10.47 11.33 2.57 74.90 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Liver 10.27 16.24 2.96 69.40 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pancreas 10.50 15.49 2.46 70.62 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0.00 0.02 0.00 Blood 10.20 1 1.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.68 14.34 2.25 71.35 0.20 0.00 0.39 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Heart 10.37 13.41 2.97 72.26 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Eye 9.60 19.50 5.70 64.60 0.1 0 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.86 0.75 28.70 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 19.97 4.16 64.96 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.23 3.40 71.07 0.10 0.00 0.20 0.30 0 .10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Trachea 10.49 24.96 2.73 60.83 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.73 10.14 2.44 74.42 0.41 0.00 1.74 0.75 0.30 0.00 0.04 0.00 0.02 0.00 Lung 10.24 10.79 3.22 74.67 0.14 0.00 0.14 0.24 0.30 0.00 0.20 0.00 0.06 0.00 Spleen 10.25 11.14 3.25 74.31 0.10 0.00 0.20 0.20 0.25 0.00 0.25 0.00 0.05 0.00 Thymus 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Thyroid 10.37 11.75 2.55 74.50 0.18 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.08 Tonsils 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Kidney 10.26 12.40 3.11 73.16 0.16 0.00 0.16 0.20 0.24 0.00 0.20 0.06 0.04 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.62 76.06 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Epididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.13 49.01 1.27 38.13 0.10 0.00 0.02 0.12 0.14 0.00 0.04 0.00 0.02 0.00 Testes 10.57 9.97 2.08 76.47 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.00 0.01 0.00

PAGE 453

453 Table A 9. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Breast Female 11.47 48.05 0.31 40.07 0.01 0.00 0.01 0.02 0.03 0.00 0.02 0.00 0.01 0.00 Ovaries 10.48 24.5 1 2.74 61.27 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.56 29.57 2.48 56.56 0.10 0.00 0.19 0.20 0.12 0.00 0.20 0.00 0.01 0.00 Cartilage 9.61 9.92 2 .22 74.40 0.49 0.00 2.16 0.89 0.30 0.00 0.00 0.00 0.00 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Soft tissue Female 10. 60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9.60 19.50 5.70 64.60 0. 10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 3.57 15.95 4.19 44.81 0.30 0.20 9.40 0.30 0.00 0.00 0.00 21.28 0.00 0.00 Spongiosa/MC Cranium 5.94 26.80 3.47 42.18 0.23 0.16 6.44 0.25 0.01 0.00 0 .01 14.48 0.02 0.00 Mandible 9.96 46.05 2.23 36.81 0.13 0.09 1.46 0.17 0.03 0.00 0.02 3.03 0.04 0.00 Vertebrae C 8.86 35.99 3.09 43.38 0.15 0.14 2.56 0.21 0.03 0.00 0.02 5.52 0.06 0.00 Vertebrae T 9.68 39.13 2. 92 43.14 0.13 0.13 1.49 0.19 0.04 0.00 0.02 3.06 0.06 0.00 Vertebrae L 9.60 38.23 2.95 43.77 0.13 0.13 1.59 0.19 0.04 0.00 0.03 3.29 0.06 0.00 Sternum 9.82 39.40 2.90 43.35 0.12 0.13 1.31 0.19 0.04 0.00 0.03 2.65 0.07 0.00 Ribs 9.48 37.90 2.97 43.69 0.13 0.13 1.74 0.20 0.04 0.00 0.03 3.63 0.06 0.00 Scapulae 9.27 42.53 2.45 37.96 0.15 0.10 2.30 0.18 0.03 0.00 0.02 4.98 0.04 0.00 Clavicles 9.69 46.05 2.21 35.79 0.14 0.09 1.85 0 .17 0.02 0.00 0.01 3.95 0.03 0.00 Os Coxae 9.77 43.29 2.49 39.04 0.13 0.10 1.59 0.18 0.03 0.00 0.02 3.32 0.05 0.00 Sacrum 9.46 37.61 2.98 43.91 0.13 0.13 1.76 0.20 0.04 0.00 0.03 3.68 0.06 0.00 Humera proximal 9.9 7 48.79 1.96 33.91 0.13 0.07 1.59 0.16 0.02 0.00 0.01 3.36 0.03 0.00 Humera distal 9.49 50.82 1.64 29.98 0.15 0.05 2.41 0.15 0.01 0.00 0.01 5.29 0.00 0.00 Radii proximal 10.25 55.57 1.30 27.76 0.13 0.03 1.53 0.13 0.01 0.00 0.01 3.27 0. 00 0.00 Radii distal 9.91 53.44 1.46 28.76 0.14 0.04 1.93 0.14 0.01 0.00 0.01 4.18 0.00 0.00 Ulnae proximal 9.38 50.11 1.69 30.32 0.15 0.05 2.54 0.16 0.01 0.00 0.01 5.58 0.00 0.00 Ulnae distal 9.63 51.73 1.58 29.54 0.15 0. 05 2.25 0.15 0.01 0.00 0.01 4.91 0.00 0.00

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454 Table A 9. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Wrists and hands 9.49 50.86 1.64 29.93 0.15 0.05 2.41 0.15 0.01 0.00 0.01 5.29 0.00 0.00 Femora proximal 9.37 45.52 2.17 35.15 0.15 0.08 2.31 0.17 0.02 0.00 0.01 5.02 0.02 0.00 Femora distal 9.55 51.18 1.62 29.82 0.15 0.05 2.34 0.15 0.01 0.00 0.01 5.13 0.00 0.00 Patellae 9.55 51.18 1.62 29.81 0.15 0.05 2.34 0.15 0.01 0.00 0.01 5. 13 0.00 0.00 Tibiae proximal 9.91 53.46 1.45 28.75 0.14 0.04 1.92 0.14 0.01 0.00 0.01 4.16 0.00 0.00 Tibiae distal 9.80 52.75 1.51 29.08 0.14 0.04 2.05 0.14 0.01 0.00 0.01 4.47 0.00 0.00 Fibulae proximal 10.38 56.41 1.24 27.38 0 .13 0.03 1.37 0.13 0.01 0.00 0.01 2.91 0.00 0.00 Fibulae distal 9.54 51.12 1.62 29.84 0.15 0.05 2.36 0.15 0.01 0.00 0.01 5.16 0.00 0.00 Ankles and feet 9.55 51.18 1.62 29.81 0.15 0.05 2.34 0.15 0.01 0.00 0.01 5.13 0.00 0.00 Humera upper shaft 11.18 55.52 1.52 31.32 0.10 0.05 0.12 0.13 0.02 0.00 0.01 0.00 0.03 0.00 Humera lower shaft 11.47 63.32 0.75 24.14 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Radii shaft 11.47 63.34 0.75 24.12 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Ulnae shaft 11.48 63.38 0.75 24.08 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Femora upper shaft 11.17 55.43 1.52 31.41 0.10 0.05 0.12 0.13 0.02 0.00 0.01 0.00 0.03 0.00 Femora lower shaft 11.47 63.2 8 0.75 24.17 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Tibiae shaft 11.47 63.28 0.75 24.18 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Fibulae shaft 11.47 63.31 0.75 24.15 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0. 00 Lymph nodes 10.48 24.82 2.73 60.96 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Ears 9.73 10.14 2.44 74.42 0.41 0.00 1.74 0.75 0.30 0.00 0.04 0.00 0.02 0.00 External nose 9.73 10.14 2.44 74.42 0.41 0.00 1.74 0.75 0.30 0.00 0.04 0.00 0.02 0.00 N asal layers 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Oral cavity layer 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Pharynx 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0. 00 Sal glands 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Spinal cord 10.59 13.73 2.44 71.93 0.18 0.00 0.33 0.20 0.30 0.00 0.28 0.00 0.02 0.00 Penis 10.20 13.57 3.38 71.77 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 S crotum 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00

PAGE 455

455 Table A 10. Blood inclusive elemental compositions in mass percent for all tissues in the UFHADF phantom (ICRP 2002) Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Adrenals 10.44 22.84 2.81 62.90 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Tongue 10.20 13.99 3.39 71.33 0.10 0.00 0.19 0.29 0.12 0.00 0.38 0.00 0.01 0.00 Esophagus 10.43 22.18 2.84 63.55 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Stomach 10.51 11.38 2.46 74.96 0.10 0.00 0.10 0.12 0.22 0.00 0.12 0.00 0.02 0.00 Small intestine 10.50 11.37 2.49 74.94 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Large intestine 10.50 11.37 2.48 74.95 0.10 0.00 0.10 0.13 0.23 0.00 0.13 0.00 0.03 0.00 Li ver 10.27 16.37 2.95 69.27 0.17 0.00 0.17 0.27 0.23 0.00 0.27 0.00 0.03 0.00 Gall bladder wall 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pancreas 10.52 15.69 2.43 70.45 0.18 0.00 0.18 0.12 0.22 0.00 0.20 0.00 0.02 0.00 Blo od 10.20 11.00 3.30 74.50 0.10 0.00 0.10 0.20 0.30 0.00 0.20 0.00 0.10 0.00 Brain 10.68 14.37 2.24 71.32 0.20 0.00 0.39 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Heart 10.37 13.42 2.97 72.24 0.10 0.00 0.18 0.20 0.22 0.00 0.28 0.00 0.02 0.00 Eye 9.60 19.50 5.70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Fat 11.38 58.90 0.75 28.66 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Skin 10.01 19.95 4.16 64.98 0.20 0.00 0.10 0.20 0.30 0.00 0.10 0.00 0.00 0.00 Muscle 10.20 14.24 3.40 71.06 0.10 0.00 0 .20 0.30 0.10 0.00 0.40 0.00 0.00 0.00 Pituitary gland 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Trachea 10.49 24.93 2.73 60.85 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Larynx 9.66 10.00 2.30 74.41 0.46 0.00 2.00 0.83 0.30 0.00 0.02 0.00 0.01 0.00 Lung 10.25 10.77 3.21 74.68 0.15 0.00 0.15 0.25 0.30 0.00 0.20 0.00 0.05 0.00 Spleen 10.26 11.17 3.24 74.28 0.10 0.00 0.21 0.20 0.24 0.00 0.26 0.00 0.04 0.00 Thymus 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Thyroid 10.37 11.77 2.53 74.50 0.19 0.00 0.10 0.11 0.21 0.00 0.11 0.00 0.01 0.09 Tonsils 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Kidney 10.27 12.54 3.09 73.03 0.17 0.00 0.17 0.20 0.23 0.00 0.20 0.07 0 .03 0.00 Ureters 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Urinary 10.49 9.63 2.61 76.07 0.20 0.00 0.20 0.20 0.30 0.00 0.30 0.00 0.00 0.00 Urethra 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 E pididymes 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Breast Male 11.13 49.01 1.27 38.13 0.10 0.00 0.02 0.12 0.14 0.00 0.04 0.00 0.02 0.00 Testes 10.57 9.97 2.08 76.47 0.19 0.00 0.10 0.20 0.21 0.00 0.20 0.00 0.01 0.00

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456 T able A 10. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Prostate 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00 Breast Female 11.47 48.05 0.31 40.07 0.01 0.00 0.01 0.02 0.03 0.00 0.02 0.00 0.01 0.00 Ovaries 10.48 24.51 2.74 61.27 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Fallopian tubes 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Uterus 10.56 29.57 2.48 56.56 0.10 0.00 0.19 0.20 0.12 0.00 0.20 0.00 0.01 0.00 Cartilage 9.82 10.31 2.61 74.44 0.35 0.00 1.42 0.64 0.30 0.00 0.07 0.00 0.04 0.00 Teeth 2.20 9.50 2.90 42.10 0.00 0.70 13.70 0.00 0.00 0.00 28.90 0.00 0.00 0.00 Bulk soft tissue 10.50 25.60 2.70 60.20 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Soft tissue Female 10.60 31.50 2.40 54.70 0.10 0.00 0.20 0.20 0.10 0.00 0.20 0.00 0.00 0.00 Water 11.20 0.00 0.00 88.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Air 0.00 0.01 75.53 23.18 0.00 0.00 0.00 0.00 0.00 1.28 0.00 0.00 0.00 0.00 Lens 9.60 19.50 5 .70 64.60 0.10 0.00 0.10 0.30 0.10 0.00 0.00 0.00 0.00 0.00 Cortical bone 3.57 15.95 4.19 44.82 0.30 0.20 9.40 0.30 0.00 0.00 0.00 21.27 0.00 0.00 Spongiosa/MC Cranium 5.96 26.73 3.47 42.34 0.23 0.16 6.41 0.25 0.02 0.00 0.01 14.41 0.02 0.00 Mandible 9.96 46.55 2.22 36.27 0.13 0.09 1.47 0.17 0.02 0.00 0.01 3.07 0.04 0.00 Vertebrae C 8.91 35.08 3.10 44.51 0.15 0.14 2.47 0.21 0.04 0.00 0.03 5.32 0.06 0.00 Vertebrae T 9 .68 39.25 2.92 43.00 0.13 0.13 1.50 0.19 0.03 0.00 0.02 3.07 0.06 0.00 Vertebrae L 9.58 38.80 2.94 43.12 0.13 0.13 1.62 0.19 0.03 0.00 0.02 3.35 0.06 0.00 Sternum 9.81 39.66 2.90 43.06 0.12 0.13 1.32 0.19 0.04 0.00 0.02 2.68 0.07 0.00 Ribs 9.48 38.15 2.97 43.40 0.13 0.13 1.75 0.20 0.04 0.00 0.02 3.67 0.06 0.00 Scapulae 9.27 42.70 2.45 37.77 0.15 0.10 2.31 0.18 0.02 0.00 0.02 5.00 0.03 0.00 Clavicles 9.69 45.89 2.21 35.96 0.14 0.09 1.85 0.17 0.02 0.00 0.01 3.94 0.03 0.00 Os Coxae 9.77 43.36 2.48 38.96 0.13 0.10 1.59 0.18 0.03 0.00 0.02 3.33 0.05 0.00 Sacrum 9.42 39.04 2.96 42.26 0.14 0.14 1.85 0.20 0.03 0.00 0.02 3.88 0.06 0.00 Humera pro ximal 9.97 48.39 1.97 34.35 0.13 0.07 1.57 0.16 0.02 0.00 0.01 3.32 0.03 0.00 Humera distal 9.49 50.86 1.64 29.93 0.15 0.05 2.41 0.15 0.01 0.00 0.01 5.29 0.00 0.00 Radii proximal 10.25 55.52 1.31 27.81 0.13 0.03 1.53 0.13 0.01 0.00 0.01 3.27 0.00 0.00 Radii distal 9.91 53.44 1.46 28.75 0.14 0.04 1.93 0.14 0.01 0.00 0.01 4.18 0.00 0.00 Ulnae proximal 9.38 50.02 1.70 30.42 0.15 0.05 2.53 0.16 0.01 0.00 0.01 5.57 0.00 0.00 Ulnae distal 9.63 52.05 1.56 2 9.19 0.15 0.05 2.26 0.15 0.01 0.00 0.00 4.95 0.00 0.00

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457 Table A 10. Continued. Element Tissue H C N O Na Mg P S Cl Ar K Ca Fe I Wrists and hands 9.49 51.04 1.63 29.73 0.15 0.05 2.43 0.15 0.01 0.00 0.01 5.32 0.00 0.00 Femora proximal 9.37 45.31 2.18 35.38 0.15 0.08 2.30 0.17 0.02 0.00 0.01 4.99 0.03 0.00 Femora distal 9.55 51.16 1.62 29.84 0.15 0.05 2.34 0.15 0.01 0.00 0.01 5.13 0.00 0.00 Patellae 9.55 51.18 1.62 29.81 0.15 0.05 2.34 0.15 0.01 0.00 0.01 5.13 0.00 0.00 Tibiae proximal 9.91 53.45 1.45 28.77 0.14 0.04 1.92 0.14 0.01 0.00 0.01 4.16 0.00 0.00 Tibiae distal 9.80 52.74 1.51 29.08 0.14 0.04 2.05 0.14 0.01 0.00 0.01 4.47 0.00 0.00 Fibulae proximal 10.38 56.36 1.25 27.44 0.1 3 0.03 1.37 0.13 0.01 0.00 0.01 2.91 0.00 0.00 Fibulae distal 9.54 51.13 1.62 29.83 0.15 0.05 2.36 0.15 0.01 0.00 0.01 5.16 0.00 0.00 Ankles and feet 9.55 51.39 1.61 29.57 0.15 0.05 2.36 0.15 0.01 0.00 0.01 5.16 0.00 0.00 Humera up per shaft 11.19 56.31 1.48 30.55 0.10 0.05 0.12 0.13 0.01 0.00 0.01 0.00 0.03 0.00 Humera lower shaft 11.47 63.29 0.75 24.16 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Radii shaft 11.47 63.30 0.75 24.16 0.10 0.00 0.10 0.10 0.01 0. 00 0.00 0.00 0.00 0.00 Ulnae shaft 11.47 63.30 0.75 24.16 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Femora upper shaft 11.19 56.27 1.49 30.59 0.10 0.05 0.12 0.13 0.01 0.00 0.01 0.00 0.03 0.00 Femora lower shaft 11.47 63.27 0.76 24.19 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Tibiae shaft 11.47 63.27 0.76 24.19 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Fibulae shaft 11.47 63.30 0.75 24.16 0.10 0.00 0.10 0.10 0.01 0.00 0.00 0.00 0.00 0.00 Lymph nodes 10.49 24.91 2.73 60.88 0.10 0.00 0.20 0.30 0.20 0.00 0.20 0.00 0.00 0.00 Ears 9.66 10.00 2.30 74.41 0.46 0.00 2.00 0.83 0.30 0.00 0.02 0.00 0.01 0.00 External nose 9.66 10.00 2.30 74.41 0.46 0.00 2.00 0.83 0.30 0.00 0.02 0.00 0.01 0.00 Nas al layers 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Oral cavity layer 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Pharynx 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Sal glands 10.47 24.23 2.76 61.55 0.10 0.00 0.19 0.29 0.21 0.00 0.20 0.00 0.01 0.00 Spinal cord 10.65 14.17 2.30 71.51 0.19 0.00 0.37 0.20 0.30 0.00 0.29 0.00 0.01 0.00 Penis 10.20 13.57 3.38 71.77 0.10 0.00 0.18 0.28 0.14 0.00 0.36 0.00 0.02 0.00 Scr otum 10.43 22.37 2.83 63.36 0.10 0.00 0.18 0.28 0.22 0.00 0.20 0.00 0.02 0.00

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458 Table A 11. Non uniform source sampling probabilities for the UFH00MF phantoms (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.2412 -0.2540 0.1648 0.5170 0.2716 Mandible 0.0433 -0.0456 0.0541 0.0217 0.0215 Scapulae 0.0373 -0.0393 0.0450 0.0375 0.0477 Clavicles 0.0516 -0.05 43 0.0661 0.0572 0.1082 Sternum 0.0470 -0.0495 0.0565 0.0377 0.0345 Ribs 0.0051 -0.0053 0.0067 0.0026 0.0022 Cervical vertebrae 0.1628 -0.1714 0.2031 0.0817 0.0809 Thoracic vertebrae 0.0323 -0.03 41 0.0382 0.0180 0.0309 Lumbar vertebrae 0.0122 -0.0128 0.0144 0.0068 0.0116 Sacrum 0.0631 -0.0664 0.0745 0.0351 0.0778 Os coxae 0.0188 -0.0198 0.0226 0.0151 0.0138 Proximal femora 0.0212 -0.0223 0.0254 0.0170 0.0048 Up per shaft of the femora 0.0045 0.0898 ---0.0197 Lower shaft of the femora 0.0045 0.0893 ---0.0196 Distal femora 0.0166 -0.0175 0.0200 0.0133 0.0038 Proximal tibiae 0.0036 -0.0038 0.0043 0.0029 0.0008 Shaft of the tibiae 0.0017 0.0344 ---0.0132 Distal tibiae 0.0065 -0.0068 0.0078 0.0052 0.0015 Proximal fibulae 0.0086 -0.0091 0.0104 0.0069 0.0020 Shaft of the fibulae 0.0020 0.0393 ---0.0169 Distal fibulae 0.0044 -0.0046 0.0053 0.0035 0.0010 Patellae 0.0242 -0.0255 0.0182 0.0122 0.0106 Ankles and feet 0.0346 -0.0364 0.0416 0.0277 0.0079 Proximal humera 0.0103 0.2049 ---0.0397 Upper shaft of the humera 0.0164 0.3255 ---0.0631 Lower shaft of the humera 0.0286 -0. 0301 0.0344 0.0229 0.0065 Distal humera 0.0013 -0.0014 0.0010 0.0007 0.0006 Proximal radii 0.0246 -0.0259 0.0295 0.0197 0.0056 Shaft of the radii 0.0094 0.1861 ---0.0477 Distal radii 0.0151 -0.0159 0.0181 0.0121 0.0034 Proximal ulnae 0.003 3 -0.0034 0.0039 0.0026 0.0007 Shaft of the ulnae 0.0015 0.0306 ---0.0128 Distal ulnae 0.0050 -0.0053 0.0061 0.0040 0.0011 Wrists and hands 0.0375 -0.0394 0.0282 0.0188 0.0163

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459 Table A 12. Non uniform source sampling probab ilities for the UFH01MF phantoms (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.3274 -0.3257 0.2186 0.6169 0.3146 Mandible 0.0167 -0.0166 0.0095 0.0 268 0.0246 Scapulae 0.0270 -0.0269 0.0218 0.0099 0.0113 Clavicles 0.0944 -0.0940 0.0538 0.0245 0.0396 Sternum 0.0524 -0.0522 0.0682 0.0311 0.0243 Ribs 0.0 055 -0.0054 0.0060 0.0027 0.0022 Cervical vertebrae 0.1506 -0.1498 0.1675 0.0758 0.0702 Thoracic vertebrae 0.0339 -0.0337 0.0544 0.0220 0.0332 Lumbar vertebrae 0.0044 -0.0043 0.0074 0.0030 0.0047 Sacrum 0.1007 -0.1002 0.1059 0.0383 0.0729 Os coxae 0.0359 -0.0357 0.0595 0.0216 0.0188 Proximal femora 0.0148 -0.0144 0.0268 0.0160 0.0208 Upper shaft of the femora 0.0041 0.1122 ---0.0228 Lower shaft of the femora 0.0038 0.1065 ---0.0177 Distal femora 0.0 068 -0.0074 0.0140 0.0084 0.0133 Proximal tibiae 0.0006 -0.0006 0.0012 0.0007 0.0043 Shaft of the tibiae 0.0017 0.0484 ---0.0096 Distal tibiae 0.0010 -0.0011 0.0025 0.0015 0.0055 Proximal fibulae 0.0018 -0.0019 0.0063 0.0037 0.0081 Shaft of the fibulae 0.0027 0.0776 ---0.0155 Distal fibulae 0.0001 -0.0001 0.0002 0.0001 0.0019 Patellae 0.0170 -0.0322 0.0370 0.0220 0.0186 Ankles and feet 0.0164 -0.0160 0.0330 0.0154 0.0237 Proximal humera 0.0048 0.1303 ---0.0249 Upper shaft of the humera 0.0074 0.2069 ---0.0354 Lower shaft of the humera 0.0170 -0.0184 0.0299 0.0140 0.0352 Distal humera 0.0016 -0.0017 0.0011 0.0007 0.0005 Proximal radii 0.0099 -0.0106 0.0185 0.0110 0.0 301 Shaft of the radii 0.0102 0.2905 ---0.0439 Distal radii 0.0021 -0.0022 0.0032 0.0019 0.0166 Proximal ulnae 0.0005 -0.0005 0.0010 0.0006 0.0028 Shaft of the ulnae 0.0010 0.0275 ---0.0051 Distal ulnae 0.0004 -0.0004 0.0008 0.0005 0 .0025 Wrists and hands 0.0254 -0.0480 0.0521 0.0310 0.0249

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460 Table A 13. Non uniform source sampling probabilities for the UFH05MF phantoms (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V C ranium 0.3254 -0.3209 0.2231 0.5437 0.3014 Mandible 0.0212 -0.0209 0.0116 0.0283 0.0254 Scapulae 0.0152 -0.0141 0.0191 0.0096 0.0092 Clavicles 0.0955 -0.0886 0.0763 0.0385 0.0432 Sternum 0.0640 -0.0594 0.0797 0.0402 0.0219 Ribs 0.0113 -0.0105 0.0071 0.0040 0.0032 Cervical vertebrae 0.0850 -0.0789 0.0956 0.0546 0.0504 Thoracic vertebrae 0.0404 -0.0398 0.0662 0.0324 0.0384 Lumbar vertebrae 0.0080 -0.0080 0.0113 0.0055 0.0081 Sacrum 0.1138 -0.1137 0.1193 0.0566 0.0762 Os coxae 0.0429 -0.0429 0.0348 0.0165 0.0153 Proximal femora 0.0166 -0.0166 0.0250 0.0173 0.0197 Uppe r shaft of the femora 0.0063 0.1018 ---0.0183 Lower shaft of the femora 0.0058 0.0966 ---0.0158 Distal femora 0.0083 -0.0095 0.0134 0.0092 0.0135 Proximal tibiae 0.0008 -0.0011 0.0008 0.0006 0.0034 Shaft of the tibiae 0.0030 0.0646 --0.0109 Distal tibiae 0.0016 -0.0022 0.0027 0.0018 0.0053 Proximal fibulae 0.0030 -0.0041 0.0065 0.0045 0.0088 Shaft of the fibulae 0.0035 0.0737 ---0.0137 Distal fibulae 0.0005 -0.0006 0.0002 0.0002 0.0023 Patellae 0.0043 -0.0169 0.0187 0.0129 0.0122 Ankles and feet 0.0216 -0.0216 0.0370 0.0222 0.0292 Proximal humera 0.0138 0.2224 ---0.0359 Upper shaft of the humera 0.0095 0.1571 ---0.0282 Lower shaft of the humera 0.0235 -0.02 68 0.0370 0.0222 0.0351 Distal humera 0.0059 -0.0082 0.0026 0.0018 0.0015 Proximal radii 0.0121 -0.0168 0.0225 0.0155 0.0357 Shaft of the radii 0.0109 0.2310 ---0.0439 Distal radii 0.0038 -0.0052 0.0032 0.0022 0.0167 Proximal ulnae 0.0012 -0.0017 0.0012 0.0009 0.0035 Shaft of the ulnae 0.0025 0.0528 ---0.0065 Distal ulnae 0.0011 -0.0016 0.0012 0.0008 0.0035 Wrists and hands 0.0176 -0.0694 0.0839 0.0579 0.0436

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461 Table A 14. Non uniform source sampling probabil ities for the UFH10MF phantoms (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.1753 -0.1714 0.1455 0.3557 0.1882 Mandible 0.0108 -0.0106 0.0072 0.017 7 0.0143 Scapulae 0.0202 -0.0160 0.0191 0.0116 0.0081 Clavicles 0.1525 -0.1212 0.0983 0.0596 0.0392 Sternum 0.1035 -0.0823 0.1065 0.0646 0.0211 Ribs 0.016 2 -0.0129 0.0052 0.0041 0.0030 Cervical vertebrae 0.0948 -0.0753 0.0592 0.0468 0.0404 Thoracic vertebrae 0.0448 -0.0438 0.0652 0.0420 0.0340 Lumbar vertebrae 0.0092 -0.0093 0.0096 0.0062 0.0083 Sacrum 0.1812 -0.1599 0. 1339 0.0919 0.0740 Os coxae 0.0399 -0.0352 0.0147 0.0101 0.0096 Proximal femora 0.0245 -0.0222 0.0345 0.0300 0.0273 Upper shaft of the femora 0.0059 0.0899 ---0.0234 Lower shaft of the femora 0.0058 0.0897 ---0.0197 Distal femora 0.005 5 -0.0121 0.0169 0.0147 0.0190 Proximal tibiae 0.0004 -0.0011 0.0011 0.0009 0.0046 Shaft of the tibiae 0.0018 0.0606 ---0.0132 Distal tibiae 0.0009 -0.0024 0.0035 0.0030 0.0075 Proximal fibulae 0.0017 -0.0048 0.0089 0.0077 0.0125 Shaft o f the fibulae 0.0020 0.0667 ---0.0169 Distal fibulae 0.0002 -0.0006 0.0003 0.0003 0.0031 Patellae --0.0204 0.0196 0.0171 0.0187 Ankles and feet 0.0342 -0.0310 0.0524 0.0446 0.0447 Proximal humera 0.015 2 0.2310 ---0.0498 Upper shaft of the humera 0.0100 0.1552 ---0.0402 Lower shaft of the humera 0.0183 -0.0401 0.0627 0.0534 0.0471 Distal humera 0.0033 -0.0091 0.0020 0.0018 0.0015 Proximal radii 0.0089 -0.0246 0.0326 0.0284 0.0535 S haft of the radii 0.0077 0.2532 ---0.0595 Distal radii 0.0022 -0.0060 0.0050 0.0043 0.0253 Proximal ulnae 0.0007 -0.0021 0.0019 0.0017 0.0052 Shaft of the ulnae 0.0016 0.0538 ---0.0084 Distal ulnae 0.0007 -0.0019 0.0018 0.0016 0.0051 Wrists and hands --0.0837 0.0925 0.0804 0.0538

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462 Table A 15. Non uniform source sampling probabilities for the UFH15M phantom (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.1198 -0.0941 0.1315 0.2150 0.1646 Mandible 0.0099 -0.0078 0.0102 0.0149 0.0179 Scapulae 0.0252 -0.0145 0.0170 0.0134 0.0102 Clavicles 0.1252 -0.0720 0.0703 0.05 15 0.0275 Sternum 0.1261 -0.0726 0.0638 0.0419 0.0107 Ribs 0.0214 -0.0123 0.0103 0.0062 0.0067 Cervical vertebrae 0.0951 -0.0548 0.0431 0.0366 0.0512 Thoracic vertebrae 0.0277 -0.0217 0.0230 0.04 68 0.0377 Lumbar vertebrae 0.0066 -0.0054 0.0042 0.0056 0.0131 Sacrum 0.2205 -0.1487 0.1291 0.0851 0.0571 Os coxae 0.0559 -0.0377 0.0168 0.0110 0.0211 Proximal femora 0.0589 -0.0462 0.0478 0.0414 0.0129 Upper shaft of t he femora 0.0059 0.0906 ---0.0334 Lower shaft of the femora 0.0030 0.0805 ---0.0297 Distal femora --0.0183 0.0246 0.0244 0.0210 Proximal tibiae --0.0032 0.0038 0.0040 0.0031 Shaft of the tibiae -0.0337 ---0.0226 Distal tibi ae --0.0070 0.0077 0.0083 0.0038 Proximal fibulae --0.0110 0.0149 0.0182 0.0086 Shaft of the fibulae -0.0428 ---0.0274 Distal fibulae --0.0022 0.0026 0.0024 0.0017 Patellae --0.0190 0.0150 0.0127 0.0395 An kles and feet 0.0772 -0.0606 0.0808 0.0768 0.0254 Proximal humera 0.0151 0.2312 ---0.0699 Upper shaft of the humera 0.0066 0.1760 ---0.0532 Lower shaft of the humera --0.0692 0.1002 0.1298 0.0205 Distal humera --0.0 071 0.0056 0.0047 0.0065 Proximal radii --0.0611 0.0450 0.0312 0.0305 Shaft of the radii -0.3034 ---0.0779 Distal radii --0.0227 0.0260 0.0251 0.0070 Proximal ulnae --0.0046 0.0045 0.0040 0.0038 Shaft of the ulnae -0.0418 --0.0143 Distal ulnae --0.0037 0.0053 0.0066 0.0038 Wrists and hands --0.1227 0.0967 0.0821 0.0658

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463 Table A 16. Non uniform source sampling probabilities for the UFH15F phantom (Pafundi 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.0983 -0.0820 0.1169 0.1933 0.1491 Mandible 0.0078 -0.0065 0.0087 0.0129 0.0156 Scapulae 0.0316 -0.0193 0.0231 0.0185 0.0142 Cl avicles 0.1132 -0.0693 0.0690 0.0511 0.0278 Sternum 0.1385 -0.0848 0.0760 0.0505 0.0137 Ribs 0.0149 -0.0091 0.0078 0.0047 0.0052 Cervical vertebrae 0.1036 -0.0634 0.0509 0.043 8 0.0617 Thoracic vertebrae 0.0380 -0.0318 0.0343 0.0705 0.0571 Lumbar vertebrae 0.0085 -0.0075 0.0060 0.0081 0.0188 Sacrum 0.2460 -0.1765 0.1563 0.1041 0.0712 Os coxae 0.0684 -0.0491 0.0223 0.0147 0.0286 Proximal femor a 0.0469 -0.0392 0.0414 0.0362 0.0116 Upper shaft of the femora 0.0047 0.0862 ---0.0297 Lower shaft of the femora 0.0023 0.0752 ---0.0259 Distal femora --0.0154 0.0211 0.0212 0.0184 Proximal tibiae --0.0026 0.0032 0.0033 0.0026 S haft of the tibiae -0.0346 ---0.0220 Distal tibiae --0.0056 0.0063 0.0069 0.0033 Proximal fibulae --0.0091 0.0126 0.0155 0.0074 Shaft of the fibulae -0.0429 ---0.0260 Distal fibulae --0.0018 0.0022 0.0020 0.0014 Patellae --0.0166 0.0133 0.0114 0.0358 Ankles and feet 0.0593 -0.0495 0.0672 0.0647 0.0218 Proximal humera 0.0109 0.2000 ---0.0563 Upper shaft of the humera 0.0071 0.2260 ---0.0637 Lower shaft of the humera -0.0659 0.0973 0.1274 0.0207 Distal humera --0.0061 0.0049 0.0042 0.0058 Proximal radii --0.0565 0.0425 0.0298 0.0295 Shaft of the radii -0.2993 ---0.0714 Distal radii --0.0208 0.0244 0.0238 0.0068 Proximal ulnae --0.0038 0 .0039 0.0034 0.0033 Shaft of the ulnae -0.0357 ---0.0114 Distal ulnae --0.0031 0.0045 0.0057 0.0033 Wrists and hands --0.1045 0.0839 0.0721 0.0586

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464 Table A 17. Non uniform source sampling probabilities for the UFHADM ph antom (Hough et al. 2011) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.0323 -0.0303 0.1160 0.2223 0.2150 Mandible 0.0089 -0.0084 0.0053 0.0047 0.0130 Scapulae 0.0925 -0.0870 0.0817 0.0897 0.0831 Clavicles 0.0093 -0.0100 0.0065 0.0075 0.0114 Sternum 0.0250 -0.0128 0.0094 0.0065 0.0089 Ribs 0.1029 -0.0525 0.0413 0 .0391 0.0594 Cervical vertebrae 0.0274 -0.0140 0.0173 0.0174 0.0138 Thoracic vertebrae 0.1186 -0.0605 0.0432 0.0360 0.0335 Lumbar vertebrae 0.1330 -0.0679 0.0550 0.0450 0.0284 Sacrum 0.0845 -0.0432 0.0362 0.0329 0.0245 Os coxae 0.2589 -0.1928 0.1645 0.1217 0.1071 Proximal femora 0.0433 -0.0619 0.0631 0.0623 0.0098 Upper shaft of the femora 0.0270 0.2670 ---0.0312 Lower shaft of the femora -0.2029 ---0.0237 Distal femora --0.0710 0.0796 0.0694 0. 0139 Proximal tibiae --0.0597 0.0553 0.0445 0.0113 Shaft of the tibiae -0.3118 ---0.0364 Distal tibiae --0.0204 0.0194 0.0167 0.0063 Proximal fibulae --0.0051 0.0033 0.0025 0.0021 Shaft of the fibulae -0.0250 ---0.0127 Dis tal fibulae --0.0040 0.0044 0.0040 0.0030 Patellae --0.0083 0.0093 0.0081 0.0016 Ankles and feet --0.0925 0.1038 0.0905 0.0697 Proximal humera 0.0296 -0.0422 0.0279 0.0256 0.0124 Upper shaft of the hum era 0.0068 0.0675 ---0.0272 Lower shaft of the humera -0.0600 ---0.0242 Distal humera --0.0200 0.0223 0.0203 0.0151 Proximal radii --0.0035 0.0016 0.0019 0.0025 Shaft of the radii -0.0296 ---0.0193 Distal radii --0.00 62 0.0057 0.0046 0.0045 Proximal ulnae --0.0107 0.0110 0.0117 0.0082 Shaft of the ulnae -0.0361 ---0.0235 Distal ulnae --0.0022 0.0026 0.0020 0.0013 Wrists and hands --0.0128 0.0143 0.0130 0.0421

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465 Table A 18. Non u niform source sampling probabilities for the UFHADF phantom (Sinclair et al. 2009) Source Skeletal Site A marrow C marrow T marrow T bone S T bone V C bone V Cranium 0.0318 -0.0305 0.1805 0.3366 0.2014 Mandible 0.0086 -0.0083 0.0040 0.0074 0.0144 Scapulae 0.0742 -0.0713 0.0263 0.0207 0.0710 Clavicles 0.0097 -0.0108 0.0060 0.0047 0.0132 Sternum 0.0204 -0.0107 0.0062 0.0049 0.0060 Ribs 0.1244 -0.0650 0.0418 0.0329 0.0786 Cervical vertebrae 0.0327 -0.0171 0.0235 0.0190 0.0170 Thoracic vertebrae 0.1245 -0.0650 0.0529 0.0428 0.0287 Lumbar vertebrae 0.1559 -0.0814 0.0818 0.0604 0.0243 Sacrum 0.0651 -0.0495 0.0614 0.0453 0.0297 Os coxae 0.2495 -0.1899 0.0565 0.0478 0.0872 Proximal femora 0.0491 -0.0512 0.0912 0.0767 0.0107 Upper shaft of the femora 0.0109 0.2146 ---0.0354 Lower shaft of the femora -0.2450 ---0.0404 Distal femora --0.0654 0.1011 0.0851 0.0203 Proximal tibiae --0.0566 0.0670 0.0542 0.0130 Shaft of the tibiae -0.2585 ---0.0525 Distal tibiae --0.0197 0.0257 0.0208 0.0061 Proximal fibulae --0.0047 0.0041 0.0033 0. 0015 Shaft of the fibulae -0.0255 ---0.0105 Distal fibulae --0.0038 0.0053 0.0043 0.0024 Patellae --0.0072 0.0104 0.0084 0.0021 Ankles and feet --0.0925 0.0579 0.0468 0.0696 Proximal humera 0.03 94 -0.0411 0.0265 0.0214 0.0089 Upper shaft of the humera 0.0039 0.0766 ---0.0261 Lower shaft of the humera -0.0675 ---0.0230 Distal humera --0.0208 0.0270 0.0218 0.0113 Proximal radii --0.0033 0.0029 0.0023 0.0019 Shaft of the radii -0.0515 ---0.0184 Distal radii --0.0066 0.0064 0.0051 0.0024 Proximal ulnae --0.0103 0.0238 0.0193 0.0048 Shaft of the ulnae -0.0608 ---0.0219 Distal ulnae --0.0025 0.0006 0.0005 0.0009 Wrists and hands --0.0148 0.0092 0.0075 0.0445

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466 APPENDIX B SAMPLE FILES To provide a clearer picture of the computational methods used in this work, excerpts from important files along with technical descriptions used during radiation transport are presented. Cont ents of Appendix B are as follows: Lattice file for voxel phantom definition Source file for uniformly distributed radiation sources Source file for non uniformly distributed radiation sources MCNPX v2.6 input file for radiation transport simulations

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467 Lat tice File Filename = ufhadm_pe.lat This is an excerpt of the lattice file generated for the UFHADM phantom for use in the MCNPX input files. indicate the importance of photons and electrons in the problem, and the valu e of unity for these pneumonics indicates that both photons and electrons were being considered in the simulation. y and z directions. For this application, the zeroth voxel index was filled with a voxel tag identification number, so the size of this phantom was 362 voxels in the x direction, 195 voxels in the y direction, and 796 voxels in the z direction. The body of the file lists the tag identification numbers associated with each voxel. identification number 57 applies to voxel number 1 and to the 160839 voxels after voxel number 1. After MCNPX reaches voxel number 362, it begins to fill the next y le vel with tissue tag numbers. In this case, the tissue tag number 57 fills up 2 z levels and 54 y levels and fills 112 x levels before reaching a voxel with the tissue tag number 43. In this fashion, the three dimensional phantom matrix was defined.

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468 ST ART FILE 1000 0 200 lat=1 u=999 imp:p=1 imp:e=1 fill=0:361 0:194 0:795 57 160839r 43 1r 57 134r 43 1r 57 221r 43 2r 57 134r 43 2r 57 65003r 43 2r 57 164r 43 2r 57 188r 43 1r 1 2r 43 57 162r 43 1 2r 43 1r 57 186r 43 1 3r 43 57 162r 43 1 3r 43 57 187r 43 3r 57 164r 43 3r 57 572r 43 3r 57 120r 43 3r 57 230r 43 1r 64 3r 43 1r 57 116r 43 1r 64 3r 43 1r 57 226r 43 1r 64 7r 43 57 114r 43 64 7r 43 1r 57 223r 43 64 9r 43 57 114r 43 64 9r 43 57 221r 43 64 10r 43 57 114r ( ) END FILE

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469 Uniform Source File Filename = liver.src This is an excerpt of a source file generated for the liver of the UFHADM phantom with a uniform source distribution distribution definitions voxel location is a discrete point, and MCNPX should not sample between vo xel locations in the fashion of a bin distribution. The generalized format for each voxel location is represented by Equation X. (X X) where A is the tissue tag identification number of the source tissue, B is the cell numb er of the lattice definition where the tissue tag numbers are assigned to all voxel coordinates in the phantom, C is the location of the voxel in the x direction, D is the location of the voxel in the y direction, E is the location of the voxel in the z di rection, and F is the cell number of the rectangular prism defining the boundaries of the entire voxel phantom. indicates that there is a probability of voxel selection for source sampling of unity assigned to all 307170 voxels in the file. This technique guarantees that the source tissue will be uniformly sampled to the best approximation.

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470 START FILE si5 l (25<1000[113 97 509]<1001) (25<1000[113 98 509]<1001) (25<1000[114 98 509]<1001) (25<1000[113 99 509]<1001) (25<1000[114 99 509]<1001) (25<1000[112 100 509]<1001) (25<1000[113 100 509]<1001) (25<1000[114 100 509]<1001) (25<1000[112 101 509]<1001) (25<1000[113 101 509]<1001) (25<1000[114 101 509]<1001) (25<1000[115 101 509]<1001) (25<1000[ 116 101 509]<1001) (25<1000[112 102 509]<1001) ( ) (25<1000[133 131 579]<1001) (25<1000[134 131 579]<1001) (25<1000[135 131 579]<1001) (25<1000[136 131 579]<1001) sp5 1 307169r END FILE

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471 Non U niform Source File Filename = am.src This is an excerpt of a source file generated for the whole body active bone marrow of the UFHADM phantom with a non uniform source distribution. The voxel location definition format is the same as for a uniform source distribution, but the source sampl ing specification is different to account for non pneumonic indicates that the source distribution consists of a series of sub distributions. The distribution with identification number pneumonic assigns a probability of selection of each sub distribution for source sampling. In this case, sub distribution 201 (spongiosa of the cranium) has a 3.23% chance of being selected for source sampling (with 1,000,000 particle his tories simulated, this is actually a substantial number of particles). Then, for each sub defined in the same way as for the uniform source distribution. Conceptually, MCNPX randomly selects a sub distr ibution to sample based on the assigned probabilities of selection, but once a sub distribution is selected, the source component for which the sub distribution applies is uniformly sampled.

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472 START FILE si5 s d201 d207 d208 d209 d206 d204 d202 d211 d 210 d203 d205 d224 d225 d212 d213 sp5 0.0323 0.0274 0.1186 0.1330 0.1029 0.0093 0.0089 0.2589 0.0845 0.0925 0.0250 0.0296 0.0068 0.0433 0.0270 si201 l (201<1000[182 45 715]<1001) (201<1000[178 46 716]<1001) (201<1 000[179 46 716]<1001) (201<1000[180 46 716]<1001) (201<1000[182 46 716]<1001) (201<1000[183 46 716]<1001) ( ) sp201 1 61291r si207 l (207<1000[176 112 678]<1001) (207<1000[177 112 678]<1001) (207<1000[178 112 67 8]<1001) (207<1000[179 112 678]<1001) (207<1000[180 112 678]<1001) (207<1000[181 112 678]<1001) (207<1000[182 112 678]<1001) (207<1000[183 112 678]<1001) ( ) (207<1000[168 115 720]<1001) (207<1000[16 9 115 720]<1001) (207<1000[167 116 720]<1001) (207<1000[168 116 720]<1001) sp207 1 11367r END FILE

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473 Input File Filename = liv21mp This is an excerpt of an input file generated to model monoenergetic photons of energy 4 MeV for the UFHADM p hantom. of Equation X. (X X) where A is the cell number of tissue H of interest, B is the material number associated with tissue H C is the density associated with tissue H in g/cm 3 D is the surface number within which tissue H is lo cated, E is the tissue tag identification (or universe) number of tissue H F is the importance of photons and electrons in the simulation, G is the volume of tissue H and $ indicates that everything following should be ignored by MCNPX and is used to cla rify information for the user describes the total x y and z boundaries MCNPX that both photons and electrons should be tracked during the simulation. by the material identification number is used. This identification number is used in the definition of the tissues (the variable B in Equation X). Below the material number, a list of element identification numbers (defined in the MCNP manual) is given along with their corresponding mass fractions (or percents). Next, the tallies are listed, and as an example, the pneumonic

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474 electrons in the problem) is being invoked and given an identification number of unity. The numbers that follow this pneumonic tell MCNPX whic h cells (tissues) should be tallied. F4 tallies are used for application of the skeletal photon fluence to dose response functions. These and given an iden tification number of 201 and should be applied to cell 201. The following lines define the energy bins for tallying. indicates that the particle type (par) is photon, the ene rgy (erg) is 4 MeV, the cells (voxels) that should be sampled (cel) is defined in distribution 5, and the x y and z dimensions that should be sampled once a voxel is selected are defined in distributions 1, 2, and 3, respectively. y and z y and z dimensions, respectively. dbcn 17j 1 turns o n the ITS style nearest bin electron energy indexing algorithm.

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475 START FILE c --------------------------------------------------------c --------------------------------------------------------c c Complete Internal Dosimetry Characterization c Mike Wayson c The University of Florida c Department of Biomedical Engineering c ALRADS Research Group c c Phantom = UFHADMF c Gender = Male c Radiation = Photon c c --------------------------------------------------------c --------------------------------------------------------c read file=ufhadm_pe.lat noecho 1001 0 100 fill=999 imp:p,e=1 $ Surrounding Box c c -------------------------------------------------------c --------------------------------------------------------c c Body compositions, densities, and volumes c c --------------------------------------------------------c --------------------------------------------------------c 1 14 0.960 70 u=1 imp:p,e=1 vol=12128.0000 $ Adip ose Tissue 2 1 1.030 70 u=2 imp:p,e=1 vol=6.7572 $ Adrenal (L) 3 1 1.030 70 u=3 imp:p,e=1 vol=6.6196 $ Adrenal (R) 4 11 1.040 70 u=4 imp:p,e=1 vol=1386.2000 $ Brain 5 30 0.940 70 u=5 imp:p,e=1 vol=11.7480 $ Breast (L) 6 18 1.070 70 u=6 imp:p,e=1 vol=15.0060 $ Bronchi ( ) c c --------------------------------------------------------c --------------------------------------------------------c c Surface Card c c --------------------------------------------------------c --------------------------------------------------------c

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476 c -------------------------------------------------------c Phantom/Voxel/Outer Sphere Dimensions c Phantom Array Size = ( 0:361 0:194 0:795 ) c --------------------------------------------------------c 100 rpp 0 57.002 0 30.633 0 175.457 200 rpp 0 0.1579 0 0.1579 0 0.2207 1000 so 500 70 so 500 c c --------------------------------------------------------c MODE Definition c --------------------------------------------------------c mode p e c c --------------------------------------------------------c -------------------------------------------------------c c Material Cards c c --------------------------------------------------------c --------------------------------------------------------c c -Adrenals -c M1 1000 10.428 $ Hydrogen 6000 22.082 $ Carbon 7000 2.845 $ Nitrogen 8000 63.645 $ Oxygen 11000 0.100 $ Sodium 15000 0.176 $ Phosphorus 16000 0.276 $ Sulfur 17000 0.224 $ Chlo rine 19000 0.200 $ Potassium 26000 0.024 $ Iron c c -Tongue -c M2 1000 10.200 $ Hydrogen 6000 14.300 $ Carbon 7000 3.400 $ Nitrogen 8000 71.000 $ Oxygen

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477 11000 0.100 $ Sodium 15000 0.200 $ Phosphorus 16000 0.300 $ Sulfur 17000 0.100 $ Chlorine 19000 0.400 $ Potassium ( ) c c --------------------------------------------------------c -------------------------------------------------------c c Tally Specification c c -------------------------------------------------------c --------------------------------------------------------c c --------------------------------------------------------c General Organ Tally c --------------------------------------------------------c FC18 WBody *f18:p,e (1 2 3 4 5 6 7 9 10 11 12 13 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 39 40 41 43 44 45 46 48 49 50 51 52 53 54 58 60 61 62 64 65 66 67 68 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 128 129 130 131 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 1 67 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234) FC28 Adipose *f28:p,e 1 FC38 LAdrenal *f38:p,e 2 ( ) c c --------------------------------------------------------c Spongiosa Tally c --------------------------------------------------------c f2014:p 201 E2014 0.001 0.003 0.005 0.010 0.015

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478 0.020 0.030 0.040 0.050 0.060 0.080 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.80 1.0 1.5 2.0 3.0 4.0 5.0 6.0 8.0 10.0 f202 4:p 202 E2024 0.001 0.003 0.005 0.010 0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.80 1.0 1.5 2.0

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479 3.0 4.0 5.0 6.0 8.0 10.0 ( ) c c --------------------------------------------------------c -------------------------------------------------------c c Source Definition c c -------------------------------------------------------c --------------------------------------------------------c sdef par=p erg=4.000 cel=d5 x=d1 y=d2 z=d3 read file=liv.src noecho # si1 sp1 si2 sp2 si3 sp3 0 0 0 0 0 0 0.1579 1 0.1579 1 0.2207 1 nps 10000000 dbcn 17j 1 prdmp j 10000 END FILE

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480 LIST OF REFEREN CES The Alliance for Radiation Safety in Pediatric Imaging 2009 Image Gently...Step Lightly Retrieved September 2009 from http://spr.affiniscape.com/associations/5364/ig/index .cfm?page=584 American College of Radiology 2009 Image Gently Campaign Named to Assosications Advance America Honor Roll Retrieved September 2009 from http://www.acr.org/SecondaryMainMenuCategories/NewsPublications/FeaturedCategories/C urrentACRNews/archive/ImageGentlyCampaignHonorRoll.aspx Arnold R, Subramanian G, McAfee J, Blair R and Thomas F 1975 Com parison of tc 99m complexes for renal imaging J. Nucl. Med. 16 357 67 Attix F 2004 Introduction to Radiological Physics and Radiation Dosimetry (KGaA, Weinheim: WILEY VCH Verlag GmbH & Co) Beddoe A H 1976 The microstructure of mammalian bone in relation to the dosimetry of bone seeking radionuclides Bolch W E, Shah A P, Watchman C J, Jokisch D W, Patton P W, Rajon D A, Zankl M, Petoussi Henss N and Ec kerma n K F 2007 Skeletal absorbed fractions for electrons in the adult male: consideratio ns of a revised 50 um definition of the bone endosteum Radiat. Prot. Dosim. 127 169 73 Bolch W E, Ec kerma n K F, Sgouros G and Thomas S R 2009 MIRD Pamphlet No. 21: a generalized schema for radiopharmaceutical dosimetry standardization of nomenclature J. Nucl. Med. 50 477 84 Bouchet L, Bolch W, Howell R and Rao D 2000 S values for radionuclides localized within the skeleton J. Nucl. Med. 41 189 212 Brosius F C, Waller B and Roberts W 1981 Radiation heart disease. Analysis of 16 young (aged 15 to 33 year s) necropsy patients who received over 3,500 rads to the heart Am. J. Med. 70 519 30 Brownell G, Ellett W and Reddy A 1968 MIRD Pamphlet No. 3: absorbed fractions for photon dosimetry 9 27 39 Celsis P, Goldman T, Henriksen L and Lassen N 1981 A method fo r calculating regional cerebral blood flow from emission computed tomography of inert gas concentrations J. Comput. Assist. Tomogr. 5 641 45 Cherry S R, Sorenson J A and Phelps M E 2003 Physics in Nuclear Medicine (Philadelphia, PA: Saunders)

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481 Chiron C, R aynaud C, Maziere B, Zilbovicius M, Laflamme L, Masure M, Dulac O Bourguignon M and Syrota A 1992 Changes in regional cerebral blood flow during brain maturation in children and adolescents J. Nucl. Med. 33 696 703 Christ A, Kainz W, Hahn E G, Honegger K Zefferer M, Neufeld E, Rascher W Janka R Bautz W Chen J Kiefer B Schmitt P Hollenbach H P Shen J Oberle M Szczerba D Kam A Guag J W and Kuster N 2010 The Virtual Family development of surface based anatomical models of two adults and two chi ldren for dosimetric simulations Phys. Med. Biol. 55 N23 N38 Clark L D, Stabin M G, Fernald M J and Brill A B 2010 Changes in radiation dose with variations in human anatomy: moderately and severly obese adults J. Nucl. Med. 51 929 32 Cristy M 1980 Mathe matical phantoms representing children of various ages for use in estimates of internal dose ORNL/NUREG/TM 367 1 110 Cristy M and Ec kerma n K F 1987 Specific absorbed fractions of energy at various ages from internal photon sources. I. Methods ORNL/TM 8381 /V1 1 100 Cristy M and Ec kerma n K F 1987 Specific absorbed fractions of energy at various ages from internal photon sources. VI. Newborn ORNL/TM 8381/V6 1 72 Dekaban A S 1978 Changes in brain weights during the span of human life: relation of brain weigh ts to body weights and body heights Ann. Neurol. 4 345 56 Evans E, Lythgoe M, Anderson P, Smith T and Gordon I 1996 Biokinetic behavior of technetium 99m DMSA in children J. Nucl. Med 37 1331 5 Faw R E and Shultis J K 1999 Radiological Assessment: Sourc es and Doses (La Grange Park, IL: American Nuclear Society, Inc.) Gelfand M, Parisi M and Treves S 2011 Pediatric radiopharmaceutical administered doses: 2010 North American consensus guidelines J. Nucl. Med. 52 318 22 GlaxoSmithKline 2005 October BEXXAR Package Insert Retrieved December 6, 2011 from http://us.gsk.com/products/assets/us_bexxar.pdf Grandmaison G L, Clairand I and Durigon M 2001 Organ weight in 684 adult autopsies: new tables fo r a caucasoid population Forensic Sci. Int. 119 149 54 Hall E J and Giaccia A J 2006 Radiobiology for the Radiologist, 6 th Ed (Philadelphia, PA: Lippincott Williams & Wilkins) Harrison J D and Streffer C 2007 The ICRP protection quantities, equivalent an d effective dose: their basis and application Radiat. Prot. Dosim. 127 12 8

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488 BIOGRAPHICAL SKETCH Mi chael Brice Wayson was born in Orlando, FL. The oldest of three boys to Mark and Niki Wayson, he was raised mostly in Brandon, Florida (a suburb of Tampa), graduating from Bloomingdale Senior High School in 2004. He graduated cum laude with a B.S. in nucle ar engineering in December 2007 and an M.S. in nuclear engineering sciences in December 2009, both degrees earned from the University of Florida. Michael married his best friend and soul mate, Leslie Wayson, in January 2011. Upon completion of his Ph.D. p rogram, Michael will begin a two year residency in diagnostic medical physics at Shands H ospital at the University of Florida in Gainesville FL cancer diagnosis and treatment from his father who works in the oncology division of a pharmaceutical company. His passion for physics ignited while taking advanced placement physics during his senior year of high school. During his undergraduate studies, he discovered the medical physics program which has provided him with a career opportunity combining both term career goal is to become the chief clinical diagnostic medical physicist at a hospital located in the southeast region of the United Sta tes. In his personal time, Michael enjoys traveling with his wife. He has visited 21 of the 50 United States in addition to Jamaica, the Cayman Islands, Canada, Italy, and Austria. He plans on making another trip to Italy in the coming year. He also enjoy s playing competitive sports including basketball, golf, snow skiing and football. Michael has studied classical piano performance since age six and also enjoys composing music in a variety of genres.