A 3D Canine Hybrid Phantom and Software for Radiopharmaceutical Therapy Dosimetry

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Title:
A 3D Canine Hybrid Phantom and Software for Radiopharmaceutical Therapy Dosimetry
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1 online resource (265 p.)
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english
Creator:
Padilla, Laura
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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:
Berry Iii, Clifford Rudd
Gilland, David R
Milner, Rowan J

Subjects

Subjects / Keywords:
buildup -- canine -- dosimetry -- radionuclide -- skeleton -- software -- tumor
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 )
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Abstract:
The full potential of nuclear medicine, especially for therapeutic applications, has not yet been reached.  Accurate dosimetry in patients undergoing radionuclide therapy, or in animal subjects used during pre-clinical trials, is paramount to aid in the progress of the field. Whether dosimetry is used for treatment planning or to establish the dose limits and efficacy of a new drug, its implementation needs to betime-efficient and reliable to ensure success. This work presents two new tools that aim to help mitigate the current issues: a detailed canine skeletal model for skeletal dosimetry in pre-clinical trials, and a dosimetry software for dose calculations in normal and tumor-burdened anatomy. A detailed canine skeletal model was constructed to complement the existing UFDog anatomical phantom.  This skeletal model provides a comprehensive mass table of the different skeletal tissues in each bone site, as well as absorbed and specific absorbed fractions for the active marrow and endosteum targets.  Several different bone and marrow sources are considered.  This model is the first ofits kind and it gives researchers and veterinary doctors the option of using canine-specific values in their calculations instead of having to apply human ones. The dosimetry software constructed during this work performs normal and tumor-burdened anatomy dosimetry in a fast yet reliable manner.  There are several human phantoms, and acanine one embedded in the code.  Normal anatomy calculations are performed following the MIRD schema and using absorbed fractions previously calculated with radiation transport code MCNPX.  Tumor-burdened anatomy calculations require the user to define the center and axis lengths of the ellipsoid that represents the tumor.  Once the information is collected, the code inserts the tumor into the phantom of choice and dosimetry is performed using dose point kernels. This software can handle heterogeneities in the medium and it provides results in just a few minutes with errors well below 10% in most cases, for tumor-burdened dosimetry.
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In the series University of Florida Digital Collections.
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Statement of Responsibility:
by Laura Padilla.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
Local:
Adviser: Bolch, Wesley E.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-08-31

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lcc - LD1780 2012
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UFE0044554:00001


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1 A 3D CANINE HYBRID PHANTOM AND SOFTWARE FOR RADIOPHARMACEUTICAL THERAPY DOSIMETRY By LAURA PADILLA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FO R THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012

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2 2012 Laura Padilla

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3 To my Madrrrre, Pdruskin and Nen

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4 ACKNOWLEDGMENTS First of all, I would like to thank my family for all their support throughout my ten years at the Univer sity of Florida. I could not have gone through a decade of schooling without my parents and my brother! Second, I would like to thank everyone who has been part of my career at UF in one way or another : my advisor, Dr. Bolch, for helping me achieve eve rything that I have, Dr. Milner, for being there for me any time I had questions, the rest of my committee for agreeing to help me construct and finish my doctoral dissertation, my colleagues, especially Michael Wayson, for helping me with my project every time I needed it and all my friends in the department. I also want to mention Edmond Olguin and Timothy Mitchell, who have helped me collect data for the later stages of my work. Lastly, I would like to thank the National Cancer Institute for awarding me the pre doctoral fellowship that has funded my work for the past five years.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ ........ 12 LIST OF ABBREVIATIONS ................................ ................................ ........................... 14 ABSTRACT ................................ ................................ ................................ ................... 17 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 19 2 DETAILED SKELETAL MODEL OF THE UF CANINE PHANTOM ........................ 21 Background ................................ ................................ ................................ ............. 21 Materials and Methods ................................ ................................ ............................ 23 Bone Mass Calculations ................................ ................................ ................... 24 Cortical bone ................................ ................................ .............................. 24 Trabecular bone ................................ ................................ ......................... 27 Teeth ................................ ................................ ................................ .......... 28 Active and inactive marrow ................................ ................................ ........ 29 Endosteum ................................ ................................ ................................ 30 Pre Dos imetry Steps ................................ ................................ ........................ 31 Radiation Transport Simulations: PIRT ................................ ............................ 33 Database of Electron Specific Absorbed Fractions ................................ .......... 35 Resul ts ................................ ................................ ................................ .................... 36 Skeletal Mass Table ................................ ................................ ......................... 36 Specific Absorbed Fractions ................................ ................................ ............. 36 Discussion ................................ ................................ ................................ .............. 38 Skeletal Mass Table ................................ ................................ ......................... 38 Absorbed and Specific Absorbed Fractions ................................ ...................... 39 Comparison to Current Bone Dosimetry Models ................................ .............. 43 Summary ................................ ................................ ................................ ................ 44 3 DOSIMETRY IN NUCLEAR MEDICINE ................................ ................................ 59 Background ................................ ................................ ................................ ............. 59 R oles of Dosimetry in Nuclear Medicine ................................ ................................ 61 Current Dosimetry Tools ................................ ................................ ......................... 62 Calculation Methods ................................ ................................ ......................... 62 Basic absorbed dose equation ................................ ................................ ... 63 Point kernel ................................ ................................ ................................ 64

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6 Monte Carlo codes ................................ ................................ ..................... 65 Patient Data and Modeling ................................ ................................ ............... 66 Current Software Programs ................................ ................................ .............. 69 Summary ................................ ................................ ................................ ................ 71 4 DOSIMETRY SOFTWARE ................................ ................................ ..................... 73 Background ................................ ................................ ................................ ............. 73 Materials and Methods ................................ ................................ ............................ 75 Normal Anatomy Dosimetry ................................ ................................ .............. 76 Tumor Burdened Anatomy Dosimetry ................................ .............................. 77 Tumor insertion algorithm ................................ ................................ .......... 78 Point pair distance distribution ................................ ................................ ... 82 Attenuation coefficie nts ................................ ................................ .............. 85 Dosimetry calculations: homogeneous and heterogeneous cases ........... 85 Results and Discussion ................................ ................................ ........................... 89 Normal Anatomy ................................ ................................ ............................... 89 Tumor Burdened Anatomy ................................ ................................ ............... 89 Tumor insertion algorithm ................................ ................................ .......... 89 Point pair distance distribution ................................ ................................ ... 92 Attenuation coefficients ................................ ................................ .............. 94 Dosimetry calculations: homo geneous and heterogeneous cases ........... 95 Summary ................................ ................................ ................................ ................ 99 5 BUILDUP FACTO RS ................................ ................................ ............................ 127 Background ................................ ................................ ................................ ........... 127 Materials and Methods ................................ ................................ .......................... 130 Basic F actors ................................ ................................ ................................ .. 131 Adjusted Soft Tissue Factors ................................ ................................ .......... 133 Results and Discussion ................................ ................................ ......................... 136 Basic Factors ................................ ................................ ................................ .. 136 Adjusted Soft Tissue Factors ................................ ................................ .......... 137 Summary ................................ ................................ ................................ .............. 138 6 CONCLUSIONS ................................ ................................ ................................ ... 153 APPENDIX A DETAILED SKELETAL DOSIMETRY RESULTS ................................ ................. 158 B MATLAB CODE FOR DOSIMETRY SOFTWARE ................................ ................ 235 C BUILDUP INPUTS ................................ ................................ ................................ 251 LIST OF REFERENCES ................................ ................................ ............................. 257 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 265

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7 LIST OF TABLES Table page 2 1 Volume fractions c alculated in several bone sites in the dog ............................. 46 2 2 Results of the test of different scaling factors for MT ................................ ......... 47 2 3 Marrow and trabe cular bone volume fractions ................................ .................... 47 2 4 Detailed skeletal mass table results for the canine model. ................................ 48 2 5 Fractional masses of the diff erent components of each skeletal site ................. 50 2 6 Condensed version of the skeletal mass table for the UFDog ............................ 51 4 1 Percent differenc es between the F 18 S values ................................ ............... 102 4 2 Percent differences between the I 131 S values ................................ .............. 103 4 3 Percent differences between the Tc 99m S values ................................ .......... 104 4 4 Voxel information for the UF hy brid computational phantoms. ......................... 105 4 5 Tumor insertion algorithm test results ................................ ............................... 106 4 6 Example of the tumor insertion algorithm limitations ................................ ........ 106 4 7 Comparison of the attenuation coefficients ................................ ....................... 107 4 8 Percent differences in S values calculated with point kernel in NBF ................ 108 4 9 Percent differences in S values calculated with poin t kernel in ADM ................ 108 4 10 Calculation time (in seconds) for every organ pair S value in the NBF ............. 109 4 11 Calculation time (in seconds) for every org an pair S value in the ADM. ........... 109 4 12 Dosimetry results for a 0.5cm radius spherical tumor of different compositions inserted in the ADM liver. ................................ ............................ 110 4 13 Dosimetry results for a 3cm radius spherical tumor of different compositions inserted in the ADM liver. ................................ ................................ ................. 111 4 14 Dosimetry results for a 1cm radius spherical tumor of diff erent compositions inserted in the ADM lung. ................................ ................................ ................. 112 4 15 Dosimetry results for a 1cm radius spherical tumor of different compositions inserted in the ADM lumbar vertebra. ................................ ............................... 113

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8 4 16 Dosimetry results for a 1cm radius spherical tumor of soft tissue inserted in the NBF liver. ................................ ................................ ................................ .... 114 4 17 100% Soft tissue coefficients of the regress ion line for electron self AF in spherical tumors ................................ ................................ ............................... 115 4 18 50ST 50B coefficients of the regression line for electron self AF in spherical tumors ................................ ................................ ................................ .............. 115 4 19 100% homogeneous bone coefficients of the regression line for electron self AF in spherical tumors ................................ ................................ ...................... 115 5 1 Summary of the MFP characteristics for 2 photon energies ............................. 140 5 2 Photon energy indices utilized in buildup calculations ................................ ...... 140 5 3 Soft Tissue infinite medium buildup factors for monoenergetic is otropic photon point sources ................................ ................................ ........................ 141 5 4 50ST 50B infinite medium buildup factors for monoenergetic isotropic photon point sources ................................ ................................ ................................ .... 142 5 5 Bone infinite medium buildup factors for monoenergetic isotropic photon point sources ................................ ................................ ................................ .... 143 5 6 Adjustment factors for the NBF PAB factors ................................ ..................... 144 5 7 Adjustment factors for the ADM PAB factors ................................ .................... 145 A 1 Absorbed fractions for the Tibia with active marrow as the target. ................... 159 A 2 Absorbed fractions for the Tibia with endosteum as the target. ........................ 160 A 3 Absorbed fractions for the Radius with active marrow as the target. ................ 161 A 4 Absorbed fractions for the Radius with endosteum as the target. ..................... 162 A 5 Absorbed fractions for the Femur with active marrow as the target. ................. 163 A 6 Absorbed fractions for the Femur with endosteum as the target. ..................... 164 A 7 Absorbed fractions for the Humerus with active marrow as the target. ............. 165 A 8 Absorbed fractions for the Humerus with endosteum as the target. ................. 16 6 A 9 Absorbed fractions for the Fibula with active marro w as the target. ................. 167 A 10 Absorbed fractions for the Fibula with endosteum as the target. ...................... 168

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9 A 11 Absorbed fractions for the Ulna w ith active marrow as the target ..................... 169 A 12 Absorbed fractions for the Ulna with endosteum as the target. ........................ 170 A 13 Absorbed fract ions for the Mandible with active marrow as the target. ............. 171 A 14 Absorbed fractions for the Mandible with endosteum as the target. ................. 172 A 15 Absorbed fractions for the Cranium with active marrow as the target. .............. 173 A 16 Absorbed fractions for the Cranium with endosteum as the target. .................. 174 A 17 Absorbed fractions for the Front Paws with active marrow as the target. ......... 175 A 18 Absorbed fractions for the Front Paws with endosteum as the target. .............. 176 A 19 Absorbed fractions for the L V with active marrow as the target. ....................... 177 A 20 Absorbed fractions for the L V with endosteum as the target. ........................... 178 A 21 Absorbed fractions for the Scapulae with active marrow as the target. ............ 179 A 22 Absorbed fractions for the Scapulae with e ndosteum as the target. ................. 180 A 23 Absorbed fractions for the Sternum with active marrow as the target. .............. 181 A 24 Absorbed fractions for the Sternum with endosteum as the target. .................. 182 A 25 Absorbed fractions for the TV with active marrow as the target. ....................... 183 A 26 Ab sorbed fractions for the TV with endosteum as the target. ........................... 184 A 27 Absorbed fractions for the Ribs with active marrow as the target. .................... 185 A 28 Absorbed fractions for the Ribs with endosteum as the target. ........................ 186 A 29 Absorbed fractions for the Pelvis with active marrow as the target. .................. 187 A 30 Absorbed fractions for the Pelvis with endosteum as the target. ...................... 188 A 31 Absorbed fractions for the CV with active marrow as the target. ...................... 189 A 32 Absorbed fractions for the CV with endosteum as the target. ........................... 190 A 33 Absorbed fractions for the Hind Paws with active marrow as the target. .......... 191 A 34 Absorbed fractions for the Hind Paws with endosteum as the target. ............... 192 A 35 A bsorbed fractions for the CaV with active marrow as the target. .................... 193

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10 A 36 Absorbed fractions for the Ca V with endosteum as the target. ......................... 194 A 37 Absorbed fractions for the Skeletal Av erage with active marrow as the target. 195 A 38 Absorbed fractions for the Skeletal Average with endosteum as the target. ..... 196 A 3 9 Specific absorbed fractions for the Tibia with active marrow as the target. ...... 197 A 40 Specific absorbed fractions for the Tibia with endosteum as the target. ........... 198 A 41 Specific absorbed fractions for the Radius with active marrow as the target. ... 199 A 42 Specific absorbed fractions for the Radius with endosteum as the targ et. ....... 200 A 43 Specific absorbed fractions for the Femur with active marrow as the target. .... 201 A 44 Specific absorbed fractions for the Femur with endosteum as the target. ........ 202 A 45 Specific absorbed fractions for the Humerus with active marrow as the target. 203 A 46 Specific absorbed fractions for the Humerus with endosteum as the target. .... 204 A 47 Specific absorbed fractions for the Fibula with active marrow as the target. .... 205 A 48 Specific absorbed fractions for the Fibula with endosteum as the target. ......... 206 A 49 Specific absorbed fractions for the Ulna with active marrow as the target. ....... 207 A 50 Specific absorbed fractions for the Ulna with endosteum as the target. ........... 208 A 51 Specific absorbed fractions for the Mandible with active marrow as the target. 209 A 52 Specific absorbed fractions for the Mandible with endosteum as the target. .... 210 A 53 Specific absorbed fractions for the Cranium with active marrow as the target. 211 A 54 Specific absorbed fractions for the Cranium with endosteum as the target. ..... 212 A 55 Specific absorbed fractions for the Front Paws with AM as the target. ............. 213 A 56 Specific absorbed fractions for the Front Paws with endosteum as the target. 214 A 57 Specific absorbed fractions for the LV with active marrow as the target. .......... 215 A 58 Specific absorbed fraction s for the L V with endosteum as the target. .............. 216 A 59 Specific absorbed fractions for the Scapulae with AM as the target. ................ 217 A 60 S pecific absorbed fractions for the Scapulae with endosteum as the target. .... 218

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11 A 61 Specific absorbed fractions for the Sternum with active marrow as the target. 219 A 62 Specific absorbed fractions for the Sternum with endosteum as the target. ..... 220 A 63 Specific absorbed fractions for the TV with active marrow as the targe t. ......... 221 A 64 Specific absorbed fractions for the TV with endosteum as the target. .............. 222 A 65 Specific absorbed fractions for the Ribs with active marrow as the target. ....... 223 A 66 Specific absorbed fractions for the Ribs with endosteum as the target. ........... 224 A 67 Specif ic absorbed fractions for the Pelvis with active marrow as the target. .... 225 A 68 Specific absorbed fractions for the Pelvis with endosteum as the target. ......... 226 A 69 Specific absorbed fractions for the C V with active marrow as the target. ......... 227 A 70 Specific absorbed fractions for the C V with endosteum as the target. .............. 228 A 71 Specific absorbed fractions for the Hind Paws with AM as the target. .............. 229 A 72 Specific absorbed fractions for the Hind Paws with en dosteum as the target. 230 A 73 Specific absorbed fractions for the Ca V with active marrow as the target. ....... 231 A 74 Specific absorb ed fractions for the Ca V with endosteum as the target. ............ 232 A 75 Specific absorbed fractions for the Skeletal Average with AM as the target. .... 233 A 76 Specific absorbed fractions for the Skeletal Average with TM 50 as the target. 234

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12 LIST OF FIGURES Figure page 2 1 Long bone subdi visions shown in the femur and tibia. ................................ ....... 52 2 2 Illustration showing the diff erent layers of the bone models ............................... 53 2 3 Summary of the SA F results for the ribs and femora for Active Marrow as both the source and the target for different cellularities ................................ ...... 54 2 4 Summary of the results of different skeletal tissue sources to the activ e marrow for the ribs and femora ................................ ................................ ........... 55 2 5 SAF curves for the ribs with AM source and endosteum target at different cellularities. ................................ ................................ ................................ ......... 56 2 6 SAF values for the ribs with different skeletal tissues as the source and the endosteum as the target. ................................ ................................ .................... 56 2 7 AF curves comparing the values in the literature for Active Marrow target with : A Marrow sources, B Bone sources ................................ ........................... 57 2 8 AF curves comparing the values in the literature for Endosteum target with: A Marrow sources, B Bone sources ................................ ................................ ... 58 4 1 Tri axial ellipse representation of the tumors inserted in the code .................... 116 4 2 Possible phantom slice display for selection of the tumor center in the future GUI for th e dosimetry software. ................................ ................................ ........ 116 4 3 Comparison of the attenuation coefficients for tissues composed of 50%Soft Tissue 50%Cortical Bone versus 50%Soft Tissue 50%Homogeneous Bone. 117 4 4 Example of the rectangular volume formed using the initial and final indices of the voxels forming the longest ray. ................................ ............................... 117 4 5 Three slices throug h the center of a 1 cm radius spherical tumor inserted in the lung of the ADM phantom. ................................ ................................ .......... 118 4 6 Verification of the point pair distance distribution algorithm. ............................. 119 4 7 Change in the shape of the point pair distance distribution for a sphere with increasing number of random rays modeled. ................................ ................... 120 4 8 Graph demonstrating the effe cts of the different smoothing algorithms applied to the point pair distance distribution results. ................................ ....... 121 4 9 Examples of point pair distance distribution results for the NBF ...................... 122

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13 4 10 Examples of point pair distance distribution results for the ADM ...................... 123 4 11 Comparison of the results from the linear attenuation coefficients c alculated with MATLAB TM to the coefficients published by NIST ................................ ...... 124 4 12 Histogram of the distribution of percent errors in all tumor burdened anatomy dosimetry results. ................................ ................................ ............................. 12 5 4 13 Plots of the AF as a function of energy for spherical tumors of different radius and compositions (A Soft Tissue, B 50ST 50B, C Bone). ............................... 126 5 1 Co mparison of the mass attenuation coefficients for Soft Tissue and Lung as obtained in the NIST XCOM database ................................ ............................. 146 5 2 Geometry utilized in the MCNP calculations for buildup ................................ ... 147 5 3 Point pair distance distributions for several organ pairs. The Mean Free Path values corresponding to the 100 150keV bin are shown on the top axis. ......... 148 5 4 Graph of the buildup factors for soft tissue as a function of MFP and photon energy. ................................ ................................ ................................ ............. 149 5 5 Buildup factor curves for Soft Tissue (black), 50ST 50B (red) and bone (blue) for 1,2 and 3MFP. ................................ ................................ ............................. 150 5 6 PAB factors for the NBF ................................ ................................ ................... 151 5 7 PAB factors for the ADM ................................ ................................ .................. 152

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14 LIST OF ABBREVIAT IONS 50ST 50B 50% soft tissue 50% bone Delta value (product of decay yield and energy) Linear attenuation coefficient Mass attenuation coefficient Mass energy absorption coefficient Photon Fluence Cumulated Activity (number of decays in the sour ce) ADM Adult Male phantom AF, Absorbed Fraction AM Active Marrow AM 50 Active Shallow Marrow B Homogeneous bone BU Buildup C Contents C A V Caudal Vertebra CB Cortical Bone CBV Cortical Bone Volume CBVF Cortical Bone Volume Fraction CF Cellularity Factor CV Cervical Vertebra GB Gall Bladder HB Homogeneous Bone H T Heart IM Ina ctive Marrow

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15 IM 50 Inactive Shallow Marrow LV Lumbar Vertebra MB Mineral Bone MCVF Medullary Cavity Volume Fraction MFP Mean Free Path MIRD Medical Internal Radiation Dosimetry M M Me dullary Marrow MST Miscellaneous Tissue NBF Newborn Female phantom PP Point pair distance distribution r S Source region r T Target region RVF Regi on Volume Fraction SAF, Specific Absorbed Fraction S value (absorbed dose in the target per decay in the source) St Stomach ST Soft Tissue S VF Spong iosa Volume Fraction TAM Trabecular Active Marrow TB Trabecular Bone TBS Trabecular Bone Surfaces TBV Trabecular Bone Volume T e VF Teeth Volume Fraction TIM Trabecular Ina ctive Marrow TM 50 Total Shallow Marrow (Endosteum)

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16 TV Thoracic Vertebra UB Urinary Bl adder V SP S pongiosa Volume W Wall

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17 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 A 3D CANINE HYBRID PHANTOM AND SOF TWARE FOR RADIOPHARMACEUTICAL THERAPY DOSIMETRY By Laura Padilla August 2012 Chair: Wesley Bolch Major: Biomedica l Engineering The full potential of nuclear medicine especially for therapeutic applications, has not yet been reached. Accurate dosimetr y in patients undergoing radionuclide therapy, or in animal subjects used during pre clinical trials, is paramount to aid in the progress of the field. Whether dosimetry is used for treatment planning or to establish the dose limits and efficacy of a new drug, its implementation needs to be time efficient and reliable to ensure success. This work presents two new tools that aim to help mitigate the current issues: a detailed canine skeletal model for skeletal dosimetry in pre clinical trials, and a dosime try software for dose calculations in normal and tumor burdened anatomy. A detailed canine skeletal model was constructed to complement the existing UFDog anatomical phantom. This skeletal model provides a comprehensive mass table of the different skeleta l tissues in each bone site, as well as absorbed and specific absorbed fractions for the active marrow and endosteum target s. Several different bone and marrow sources are considered. This model is the first of its kind and it gives

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18 researchers and veter inary doctors the option of using canine specific values in their calculations instead of h aving to apply human ones. The dosimetry software constructed during this work performs normal and tumor burdened anatomy dosimetry in a fast yet reliable manner. T here are several human phantoms, and a canine one embedded in the co de Normal anatomy calculations are performed following the MIRD schema and using absorbed fractions previously calculated with radiation transport code MCNPX. Tumor burdened anatomy cal culations require the user to define the center and axis length s of the ellipsoid that represents the tumor. Once the information is collected the code inserts the tumor into the phantom of choice and dosimetry is performed using dose point kernels. Thi s software can handle heterogeneities in the medium and it provides results in just a few minutes with errors well below 10% in most cases, for tumor burdened dosimetry.

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19 CHAPTER 1 I NTRODUCTION Radiopharmaceutical development depends largely on the resul ts of pre clinical studies with animal subjects. While rodents are oftentimes the laboratory animal of choice due to their cost, wide availability and short lifespan it is difficult to extrapolate the results obtained from mice and rats to humans. The p ossible discrepancy between the rodent and human biological parameters is further aggravated in radiopharmaceutical studies due to the radioactive component. Radiation traverses the same distance in a given tissue, therefore, the large differences in anat omical size between rodents and humans may translate into radically different self and cross organ doses for a given radiopharmaceutical. 1 4 This can prove very challenging when trying to extrapolate the effects o f a radioactive substance from rodents to the human body. Other animals, such as non human primates and can ines have also been used to a lesser extent. The use of non human primates alleviates the anatomical size discrepancy present with rodents, but the se animals are expensive, scarcely available and ethical issues often come into play when using them as part of medical studies. Canines, on the other hand, are sufficiently large to avoid significant size related discrepancies, they are widely available, and they are exposed to the same environment as humans as they are common house pets They are an excellent subject option for pre clinical trials. Additionally there are approximately more than 4 million dogs diagnosed with cancer in the United States every year 5 and the biochemical and genomic similarities between canine and human cancer have been well reported in the literature. 6 8 These traits only further reinforce their role as the ideal representative of humans during early developmental phases of radiopharmaceuticals.

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20 There has been progress made in recent years to construct the dosimetric too ls necessary to establish canines as a viable option for radiopharmaceutical research. An anatomical canine model, the UFDog, was published in 2008 for internal dosimetry purposes. 9 However, the skeleton in this model is composed of homogeneous bone; this does not allow for accurate calculation of doses to the active marrow and endosteum targets to determine dose response curves for possible treatment side effects. Hence, a more detailed skeletal model is needed to complement the exist ing anatomical phantom Furthermore, there are limited options of dosimetric tools available to clinicians and researchers working both on radiopharmaceutical development and standard clinical practice. The software packages for internal dosimetry are either fast but have models that represent the human anatomy very simplistically and are very limited in their tumor dosimetry capabilities, or they are too complex to use in an average clinical setting. None of the current packages allow for canine dosimetry. A new dosimetry software package that allows for reliable dose estimates in anatomically realistic models with normal anatomy and tumor burdened anatomy capabilities would fill the gap tha t is currently in the field.

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21 CHAPTER 2 DETAILED SKELETAL MO DEL OF THE UF CANINE PHANTOM Background Dogs have long been used to study the hematological effects and cancer risks associated with human exposures to radionuclides potentially released to the environment following a nuclear power plant accident. 10 12 The physiological similarities between the canine and human skeleton, as well as the relatively long life span of dogs as compared to that of rodents, ha ve made the adult dog a n optimal candidate for such studies. 13 15 In recent times, the dog h as emerged as one of the most ideal model s for the study of human cancer. 7, 16 Spontaneously occurring tumors in dogs such as osteosarcoma, non Hodgkins lymphoma, leukemia, soft tissue sarcoma, melanoma and mammary tumors, parallel those seen in huma ns in many respects 16, 17 Furthermore, t hese animals are most favorable in the study of new diagnostic and therapeutic tools, not only due to histological and physiological similarities of their diseases, but also because of their very similar exposure to the same environmental factors and condi tions. 7 Resultantly the use of canine subjects in pre clinical trials for new radiopharmaceutical agents is expected to increase in the coming years. Unfor tunately, dosimetric tools for these animals are very limited. While dosimetry software packages have been developed for human anthropomorphic models no such programs exist for canine subjects Starting in the 1940 1950s, several projects utilizing canin e subjects have emerged. Large scale, long term endeavors such as the University of Utah Beagle P roject and the UC Davis Beagle P roject chose the beagle to study the effects of several radionucli d es related to nuclear fallout 10 These and other projects,

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22 encompassing inhalation, intravenous injections and ingestion of several radioactive elements, aime d to shed light on the distribution, retention and bio effects of specific radionuclides as a function of the intake mode and total activity of the exposure Although the distribution of the elements and their retention equations could be derived based on data collected through whole body counting as well as analysis of excreta, the radiation doses imparted to the skeleton could only be roughly estimated. Average skeletal doses for bone seeker radionuclides in subsequent studies were calculated using pre calculated values such as con version factors based on Ra 226 18 and fractions of beta particles absorbed by the skeleton published by Parmley in 1962. 11, 19, 20 While it is obvious that when dealing with bone seeker radionuclides, the prolonged retention of these elements in the skeleton translates to high radiation doses de livered to all skeletal target tissues, the se radiation doses are often crudely estimated due to a lack of anatomic data and dosimetr ic parameters The mass of each of the target skeletal tissues is often not explicitly known, and the microstructure of th e organ is often either homogenized, or is estimated based upon a very limited number of bone samples, which in many cases are of human and not canine origin In several studies, estimates for active marrow and endosteum dose have been obtained based on path length calculations through spongiosa for human adult samples 21 as well as through Monte Carlo calculations 22 This study aims to provide researchers and clinicians with canine specific values for skeletal dosimetry, eliminating the need to run lengthy Monte Carlo simulations to obtain dose estimates.

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23 The University of Florida recently published a canine anat omical phantom for dosimetry studies to start meeting the demand. 9 This phantom modeled the macroscopic anatomy of a 24 kg hound cross female; as a result, the skeleton was modeled as a homogeneous organ. While this suffices when the radiopharmaceutical agent is not a bone seeker, when dealing with radioactive chemicals that will deposit in the skeleton, concern for hematopoietic stem cell dose in the active marrow as well as osteoprogenitor cell dose in the endosteum arise 23, 24 The results from this paper start to fill the void in skeletal dosimetry data for canines. Materials and Methods This study was approved by the University of Florida Institutional Animal Care and Use Committee and was performed in accordance with the Institute for Lab oratory Animal Research Guide for the Care and Use of Laboratory Animals. A wide range of data was necessary to construct the detailed skele tal model for the UFDog phantom. Each individual homogeneous bone model had to be modified to display cortical and spongiosa regions and each spongiosa region had to be assigned a unique and corresponding trabecular microstructure. Furthermore, the masse s of the target tissues of interest in the skeletal model had to be assigned as well The target tissues were defined as the endosteum and active bone marrow. The endosteum is a 50 micron layer of total bone marrow measured from the trabecular bone surfa ce s. This tissue layer serves a s a surrogate for osteoprogenitor cells. 23 The dose to these cells is used to estimate bone cancer risks from skeletal irradiation Active bone marrow is used as a surrogate for the hematopoietic stem cells the cell popu lation defining the target tissue for leukemia risks and hematopoietic complications. 23, 24 Consequently before performing any dosimetry on the skeleton of the UFDog phantom an array of

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24 codes were used to alter its homogenous bone model to reflect both cortical and spongiosa regions, prepare the microstructure images for radiation transport simulation and obtain the necessary data to construct a detailed table of bone specific skeletal tissue mass es To model th e heterogeneous macrostructure of each bone site, the harvested bones from the dog were CT scanned ex vivo. These scans provided clear images of the cortical spongiosa borders. Twelve samples were also cored from the bones and sent to to Scanco Medical A G (Bassersdorf, Switzerland) for microCT imaging. The bone samples were chosen to be representative of the whole skeleton. The microCT scans were performed at a spatial resolution of 30 microns. These images provided a microstructure model for the spon giosa of each bone site. A more detailed explanation on the macrostructure and microstructure construction process is given below. Bone Mass C alculations The mass calculations described below follow the procedure outlined in the paper by Pafundi et al. 2009. 25 Cortical b one The fraction of cortical bone volume to total bone volume in a given bone site is represented by the Cortical Bone Volume Fraction (CBVF). This value was obtained based on ex vivo bone scans. A total of 14 bone sites, listed on Table 2 1, were scanned ex vivo. These sites were chosen to be representative of the whole skeleton. The scans were segmented using the 3D Doctor spongiosa and teeth volumes when appropria te. The ratio of each sub region to the total bone site volume was taken to obtain CBVF, Spongiosa Volume Fraction (SVF) and Teeth Volume Fraction (TeVF). The long bones do not have spongiosa in the shaft but

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25 a medullary cavity instead. Therefore, the M edullary Cavity Volume Fraction (MCVF) is listed in place of the SVF when applicable. The total cortical bone mass inclusive of miscellaneous tissues indicated by *, for every bone site was calculated as follows: (2 1 ) w here is the total cortical bone mass inclusive of miscellaneous tissues for site x is the homogeneous bone volume inclusive of miscellaneou s tissues for site x and MB is the density of mineral bone as given in ICRU46 26 Due to the limited number of samples scanned, some assumptions were made to obtain the cortical bone masses of the remaining sites. In the case of the cervical a nd lumbar vertebrae, the CBVFs obtained from C 3 and L 1 were used for all cervical vertebrae and all lumbar vertebrae respectively. The CBVF of the thoracic vertebrae was assumed to be an average of the C 3 and the L 1 values. To properly account for ce llularity variations along the long bones, these were divided into proximal, shaft and distal regions for dosimetry and bone mass calculations. The CBVF for each one of the 3 regions was acquired using 3D Doctor TM and Rhinoceros TM The region boundaries w ere determined by inspection with the help of Dr. Rowan Milner, a veterinary oncologist at the University of Florida Figure 2 1 shows the subdivisions of the long bones. The bone volume for each region was calculated using the following equation: ( 2 2 ) w here is the bone volume of either the distal, shaft or proximal regions ( R ) of the humerus or femur ( x ), and are the bone volumes of the upper and lower halves respectively, as listed in the homogeneous bone mass table for the anatomical

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26 canine phantom given in Padilla et al 9 Just as previously stat ed, a starred term indicates that it is inclusive of miscellaneous tissues. RVF is the fraction of the region volume to the total bone volume. The RVF values were obtained from 3D Doctor TM and Rhinoceros TM Table 2 1 shows the RVF, CBVF and SVF for the d iffer ent regions of the long bones. The cortical bone masses calculated above include miscellaneous tissues. Miscellaneous tissues are defined as the blood vess els and periosteum in the bone 27 In order to obtain the true cortical bone mass, the miscellaneous tissues were subtracted. The total mass of these tissues in humans is given in ICRP 89. 28 The miscellaneous tissue mass in the dog wa s approximated by scaling the adult male miscellaneous tissue mass by the ratio of the total body weights. This scaling factor proved to be the most accurate when scaling the miscellaneous tissues from adult males to other ages, as seen in Table 2 2 Afte r scaling the adult male miscellaneous tissue mass by body weight, the miscellaneous tissue mass in the dog phantom was determined to be 71g. The miscellaneous tissue mass in each bone site was calculated using the equation below. ( 2 3 ) Where is the miscellaneous bone tissue mass in the cortical bone of site x is the total miscellaneous bone tissue i n the skeleton, is the bone volume of site x is the total skeleton volume, and is the cortical bone volume in site x Finally, the net cortical bone mass in each site ( ) is given by Equation 2 4. ( 2 4 )

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27 Trabecular b one In order to calculate the trabecular bone mass in a given bone site, the SVF and the Trabecular Bone Volume Fraction ( T BVF) are needed. SVF is the fraction of the total homogeneous b one volume that contains spongiosa, while the T BVF is the fraction of the spongiosa volume that is comprised of trabecular bone. The SVF and MCVF values were obtained by segmentation of the ex vivo sca ns using 3D Doctor TM ( Table 2 1 ). All the surrogate s used when assigning CBVF to unsampled bones were also used when assigning SVF. The T BVFs were obtained by an alyzing the microCT images of 12 bone sites using the thresholding method described by Rajon et al 29 This technique requires the user to thr eshold the microCT images to separate trabecular bone from total bone marrow within spongiosa regions Based on this threshold, the images are converted into binary images, 0 for bone and 1 for marrow, and the fraction of the number of voxels that are tag ged as trabecular bone and marrow are tallied Table 2 3 lists the bones sampled, and the resulting TBVFs The T BVF of L 2 was used as a surrogate for the caudal vertebrae and the TBVF of the ribs was used as a surrogate for the scapulae and sternum 30 31 The TBVF of the distal humerus sample was us ed as a surrogate for the radii, ulna e and the front paw bones. The T BVF of the distal fem ora was used as a surrogate for the tibia e, fibulae and the hind paw bones. The T BVF of C 4 was assigned to all the cervical vertebrae and that of L 2 was assigned to all lumbar vertebrae. The average of the T BVF values between T 5 and T 13 was taken and assigned to all thoracic vertebrae. The total trabecular bone ma ss was obtained as follows: ( 2 5 )

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28 w here is the total trabecular bone mass in site x, and ( is the s pongiosa v olume inclusive of miscellaneous ti ssues (later represented by V SP* ) in site x The miscellaneous tissues in trabecular bone also hav e to be subtracted in order to calculate the net trabecular bone mass. The equation below shows how these were achiev ed. ( 2 6 ) Where is the miscellaneous tissues mass in the trabecular bone of site x and is the total trabecular bone volume in site x Therefore, t he net trabecular bone mass ( ) is given by: ( 2 7 ) It should be noted that the shaft of the long bones only contain medullary marrow, therefore no trabecular bone mass can be calculated for them. What would be the V SP for any other bone region can be taken as the volume of medullary marrow in the shaft of the long bones. Teeth The teeth mass ( ) in the mandible and cranium was estimated bas ed on the TeVF shown in Table 2 1. The density of teeth was approximated as the density of dentine = 3 g/cc). 28 The equation below shows the calculation performed to obtain the teeth masses. ( 2 8 )

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29 Active and inactive m arr ow To calculate the mass of active and inactive marrow in a bone site, the Marrow Volume Fraction (MVF), the Cellularity Factor (CF) and the S pongiosa V olume (V SP ) are needed. The V SP wer e calculated as shown in the previous section. The MVF is the fracti on of spongiosa volume that is marrow. This value was obtained using the thresholding method previously described 29 The same approximations that were made when assigning T BVF s apply for the bone sites that do not explicitly have a MVF. There are n o reference cellularity factors for the adult dog, therefore, the CFs for the 40 year old human published in ICRP 70 we re used as a surrogate dataset 27 The total active bone marrow mass ( ) for site x was calculated in the following manner: ( 2 9 ) w here AM is the density of active bone marrow as given in ICRU Report 46 26 The total inactive bone marr ow mass ( ) for site x was calculated using the equation below ( 2 10 ) IM is the density of inactive bo ne marrow as given in ICRU46. 26 The miscellaneous tissues mass for the active and inactive marrow were calculated using: ( 2 11 ) ( 2 12 )

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30 where is the miscellaneous tissues mass in the active marrow of site x is the active marrow volume in site x is the miscellaneous tissues mass in the inactive marrow of site x, is the inactive m arrow volume in site x Finally, the net active and inactive marrow masses ( and respectively) were calculated using the equations below: ( 2 13 ) ( 2 14 ) Endosteum The active and inactive shallow marrow represent the endosteum. In the shaft of long bones, the endosteum is defined as the marrow that is within 50 microns of the cortical bone In all other regions, it is the marrow that is within 50 microns of a trabecular bone surface s In both cases the endosteum mass is denoted by the subscript Total Marrow 50 (TM 50 ). The mass of this tissue is calculated using the Shallow Marrow Volume Fraction (SMVF). The SMVF, except for the shaft of long bones, was obtained using an in house code that analyzes the binary images obtained during the SVF calculations to determine the fraction of spongiosa that is within 50 microns of trabecular bone. The equations below illustrate how this data was u sed in the TM 50 mass ( ) calculations. ( 2 15 ) ( 2 16 ) ( 2 17 ) where is the mass of the trabecular shallow active marrow of bone site x and is the trabecular shallow inactive marrow mass.

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31 The SMVF for the shaft of long bones was calculated by approxi mating the shaft as a cylinder 25 This allows for the calculation of an average shaft radius and using basic geometric concepts, the SMVF. The following equations describe this process. ( 2 18 ) ( 2 19 ) where is the inner radius of the shaft for long bone x in cm, is the volume of the medullary mar row for long bone x h shaft is the length of the shaft. The 0.005 cm that is subtracted from is to account for the 50 microns that encompass the endosteum. Thus the shallow medullary marrow mass ( ) was calculated as follows: ( 2 20 ) ( 2 21 ) ( 2 22 ) w here is the mass of the shallow active medullary marrow of bone site x and is the shallow inactive medullary marrow mass. When calculating the total mass of the endosteum for long bones, the endosteum mass of the proximal and distal en ds is added to the endosteum mass of the shaft. Pre D osimetry Steps The radiation transport software used to perform dosimetry calculations for the skeletal model utilizes both the macrostructure and the microstructure of each bone site. Therefore, the pr eviously homogeneous skeleton model of the dog phantom given in Padilla et al 9 was modified to display cortical and spongiosa regions in each bone. The cortical layer was created using Rhinoceros Each bone was scaled down to match

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32 the volume of spongiosa calculated in the previous section. The layer that remained between the original bone and the newly created spongiosa region became the cortical bone. Figure 2 2 graph ically illustrates this concept. For long bones, this procedure was performed individually for the proximal, shaft and distal regions to accurately model their respective CBVFs and SVFs. The cranium and the mandible were not modified following this proce dure. Due to their complex geometry, and the fact that teeth in the original homogenous skeleton of the canine phantom were included as part of the bone 9 these bones had t o be altered differently. Instead of using the homogeneous bone and manipulating it to display cortical and spongiosa regions, polygon mesh models obtained from the ex vivo segmentation of the cortical and spongiosa regions for each of these two bone site s were exported from 3D Doctor Rhinoceros Rhinoceros Once all heterogeneous bone sites were constructed, they were voxelized to 0.05 x 0.05 x 0.05 cm 3 resolution using an in house MATLAB lized volumes were verified against the previously calculated volumes. The voxelized models were also reviewed using ImageJ properly voxelized and that there were no anomalies in sight. The final pr eparatory step for dosimetry calculations was to obtain a group of spongiosa microstructure models to represent a range of cellularities from 10 100%. The default cellularity for the thresholded microstructure images is 100%. Since dosimetry results are cellularity dependent when active marrow is the source, it was necessary to have a set of microstructures with different cellularities. The microstructure images were modified, using an in house code, to reflect cellularities of

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33 10, 30, 50, 70 and 90%. T he dosimetry values for the intermediate cellularities were calculated by linear interpo lation of the existing results. Radiation Transport Simulations: PIRT All dosimetry calculations for the skeletal model were performed using an EGSnrc based code called Paired Image Radiation Transport (PIRT). This in house software combines the macrostructure and microstructure of each site by modeling radiation transport in the microstructure of the bone, while setting its boundaries based on the This allows the user to model the heterogeneity of the spongiosa accurately, while accounting for electron escape and cortical bone contributions due to the finite geometry of the site. There is a modified version of PIRT for long bones. This software has the same characteristics as the original, but instead of assigning the chosen microstructure to the whole bone, it only assigns it to the proximal and distal ends, while modeling the inner part of the shaft as medullary marrow. The source tissues for these calculations are Trabecular Bone Surface (TBS) and Volume (TBV), Cortical Bone Volume (CBV), Inactive Marrow (IM) and Active Marrow (AM). The target tissues are Active Marrow (AM) and the endosteum (TM 50 ). The energy range used for these calculati ons was from 1 keV to 10 MeV, to cover all possible beta particle energies from internal emitters. The number of particle histories used varied from 10 6 at low energies to 25 000 at high energies. The increased number of particles at low energies compens ates for the worsening statistics with decreasing energy. The elemental compositions for mineral bone and active and inactive marrow used in these calculations were obtained from ICRU Report No. 46 26

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34 The microstructure for both proximal and distal ends of the humeri and femora were available, however, the long bone PIRT software only allows for the insertion of one microstructure per bone site. In order to model these bones as accurately as possible, runs were performed using the proximal mi crostructure in both ends first, and then replacing it with the distal microstructure. The resulting values were averaged to give an estimate of what the dosimetry values would be if the runs could be performed using the two different microstructures in t heir corresponding ends at once. The following equations show how the averaging of j microstructures was performed: 25 ( 2 23 ) ( 2 24 ) ( 2 25 ) ( 2 26 ) where is the surface area of trabecular bone in microstructure j. These e quations were also used to average the dosimetry results from the two microstructure samples (T 5 and T 13) of the thoracic vertebrae. When averaging the results from Cortical Bone Volume sources, a straight average between all the values suffices. In or der to calculate the absorbed fraction for each source to target combination over the whole skeleton, the following equation was used 25 ( 2 27 )

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35 where is the skeletal averaged absorbed fraction, is the mass of the source tissue in bone site x is the mass of the source tissue in the skeleton, and is the absorbed fraction of bone site x Database of Electron Specific Absorbed Fractions The dosimetry calculations performed with PIRT yielded Absorbed Fraction [ AF, ] values for each source (r S ) to target (r T ) combination in every b one. These values were then manipulated to obtain Specific Absorbed Fractions [ SAF, ] The relationship between the two factors is given below: ( 2 28 ) where m T is the mass of the target tissue. In order to calculate the specific absorbed fraction for the endosteum, the dosimetry results from both shallow active marrow ( AM 50 ) and shallow inactive marrow ( IM 50 ) had to be combined. The dosimetry code calculates the fraction of energy that is emitted from the source and deposited in the endosteum, but it displays it for active and inactive marrow separately. Since the osteoprogenitor cells modeled by the endosteum are tied to neither active nor inactive marrow, but are rather believed t o be scattered around the area, the absorbed fraction to both types of marrow ha d to be combined. The equation below shows how this was performed. ( 2 29 ) The skeletal average d SAF, for a given source to target combination, was calcu lated using the equation below : 25 (2 30 )

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36 where is the skeletal averaged specific absorbed fraction, is the mass of the target tissu e in bone site x is the mass of the target tissue in the skeleton, and is the specific absorbed fraction for bone site x R esults Skeletal Mass T able Table 2 4 shows the results from the detailed skeletal mass cal culations. As seen on the table, the mass from the detailed skeleton model differs from that in the homogeneous skeleton given in Padilla et al. 9 by 15.6%. Therefore the equivalent homogeneous skeletal density is 1.6 g/cc, in contrast to the 1.4 g/cc given by Cristy and Eckerman 30 Table 2 5 shows the fractional masses of the different tissues in each bone site with respect to the total mass of the bone site, as well as the overall skeletal mass. For example, the percentage of the total skeletal weight represented by act ive marrow in the UFDog, as shown in Table 2 5, is 6% and the perc entage for inactive marrow is 1 3%. Cortical bone represents 83% of the total mineral bone weight, while trabecular bone comprises 17% of that value Table 2 6 shows a condensed version of the mass table, showing the total masses of the long bones without a break out of the bone subregions The difference in the values between T able 2 4 and 2 6 is due to the fact that T able 2 6 includes the miscellaneous tissues, while T able 2 4 does not. S pecific A bsorbed Fractions The complete set of absorbed and specific absorbed fractions for every bone site can be found in Appendix A of this dissertation Figure 2 3 shows a selection of the SAF results for active marrow as both the source and target. The plots in F igure 2 3 illustrate the general trend in all the results for this source target combination. SAF values for this source target are very cellularity dependent at low energies. On the

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37 other hand, the results all converge to the same value a t high energies. The value of this convergence point is bone site dependent but it occurs at energies of approximately 1 MeV in every case. When analyzing the results with active marrow as the target tissue, and TBS, TBV, TIM and CBV as the sources, dif ferent trends can be observed. Although all the curves converge at high energies, the behavior in the lower to middle energy range differs for each source. When looking at TBS sources, the values of specific absorbed fractions are pretty consistent throu ghout the entire energy range, with a slight increase around a few hundred keV and a further decrease at higher energies. However, for the other sources, the specific absorbed values start at zero for very low energies, and then rise s with increasing ene rgy and finally peak s before decreasing again. The SAFs for inactive marrow sources increase rapidly past 10 keV and display a sharper peak than the other sources. The value of the peak is bone site dependent. The specific absorbed fraction values for b oth TBV and CBV sources display similar trends. TBV values increase and peak at lower energies than the values for CBV sources. The specific absorbed fraction values for TBV also reach higher values than those for CBV sources. Figure 2 4 shows the plots for various TIM, TBS, TBV and CBV sources with active marrow as the target for various bone sites. Although all the source / AM target combinations follow the trends previously described, the specific shape of each curve is bone site dependent. The spe cific absorbed values for endosteum targets follow different trends than those described above. With active marrow as the source, the SAF values are fairly consistent throughout all cellularities, only portraying small changes between them. The curves dec rease with increasing energy, and display two plateaus : one at energies

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38 between 1 and 10 s of keV and another one from approximately 100keV to 1MeV. Figure 2 5 shows a sample of the SAF values for AM as the source and endosteum as the target for different cellularities in the ribs For inactive marrow sources, the specific absorbed fractions follow the same trend as the curves for active marrow sources. The SAFs are almost identical between IM and AM for 70% cellularity sources. When taking TBS as the s ource, the specific absorbed fractions follow a trend very similar to that seen with active marrow targets. However, with endosteum targets the values start to rapidly decreas e at lower energies than those for active marrow targets. The drop starts at ap proximately 100 keV, instead of at 1 MeV. The shape of the SAF curves for both volume sources are the same as those described above. Figure 2 6 displays a sample of the results for IM, TBS, TBV and CBV sources. No matter the source, all the specific abs orbed fractions for endosteum targets are lower than their active marrow counterparts. Discussion Skeletal Mass Table The canine skeletal masses obtained in this study resulted in an equivalent skeletal density 15% higher than that given by the homogeneous bone density of Cristy and Eckerman 30 The homogeneous bone density given by Cristy and Eckerman i s a generic value for an average human skeleton. The density calculated in this study not only uses canine specific values for volume fractions, but it accounts for the specific volume fraction and cellularity variations between different bone sites in th e canine skeleton. Hence, a divergence from the homogenous bone density given by Cristy and Eckerman is to be expected. Equivalent density calculations and masses on the skeletal mass table could be further refined by acquiring more microstructure sample s

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39 to avoid the use of surrogate values, as well as to better account for the local structural variations of cancellous bone in a given bone site. The use of human values could also be entirely eliminated to obtain more accurate canine values. Dog specifi c cellularity factors are very limited in the literature. Pichardo et al measured the cellularity factors in the humerus, femur and upper and lower spine of two dogs. 32 While these values are canine specific, they we re not used in this study. The reference cellularity values for the ad ult human male given in ICRP 70 were used instead. 27 Since the number of canine cellularity values available is limited, the more comprehensive set of human cellularities was used instead This was done to avoid having to mix canine and human cellularity factors or having to take the available canine factors and overly apply them as surrogate values to the rest of the bone sites Using canine specific cellularities across all bone sites would increase the accuracy of the canine specific active and inactive bone marrow mass es in the future The overal l percentage of cortical bone, trabecular bone and total bone marrow versus the total skeletal mass is shown in Table 2 5. The results from this study are in good agreement with previously published values in Parks et al (1986) for beagles 11, 33 The percentage of cortical bone, trabecular bone and total marrow in this study are 63%, 13% and 18%, respectively. Those presented in Parks et al are 58%, 15% and 20%, respectively. Absorbed and Specific A bsorbed F ra ctions The dosimetry values obtained with PIRT display common trends in all bone sites. When active marrow was both the source and target the specific absorbed fraction curves displayed cellularity dependence at low energies that later converge d at highe r energies. This can be explained by the fact that low energy electrons are going to

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40 deposit all their energy locally, yielding the same absorbed fraction values for all cellularity values However, since specific absorbed fraction calculations require d ividing the absorbed fraction by the mass of the target, differences arise due to the decrease of active marrow mass with decreasing cellularity. The lower the cellularity, the smaller the mass, and hence, the higher the specific absorbed fraction. This difference is not observed at higher energies because the electron has enough energy to go through enough marrow cavities to average its energy deposition throughout the active marrow across the entire spongiosa region. When the source tissue is any of the other skeletal tissue aside from the active marrow different trends arise. In contrast to the other sources, trabecular bone surface sources result in non zero specific absorbed fractions at low energies. This is a direct consequence from electrons bei ng emitted isotropically on the bone surface. About half of all the electrons emitted will reach the marrow cavities and deposit their energy there, while the other half will be emitted towards the bone. Therefore, even at really low energies, since the electrons are emitted directly towards the marrow, and they have no bone to traverse, they will deposit energy there. At higher energies, the SAFs display a slight increase. This is due to the fact that the electrons that were emitted inward from the sur face of the bone trabecula will now have sufficient energy to undergo a backscatter event emerge into the adjacent marrow cavity and deposit its residual kinetic energy Conversely, this increase is not permanent because the electrons reach a point wher e their energy is high enough to not only backscatter towards the adjacent marrow cavity, but they can completely traverse the bone trabecula and possibly escape the spongiosa region altogether.

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41 The other sources (TIM, TBV and CBV) result in SAFs of zero at low energies because the electrons are not energetic enough to escape their source tissue to reach the AM or endosteum target s It is therefore expected that electrons emitted in thicker sources, such as CBV, will require higher energies to reach the target tissues The lower SAF values seen in thicker sources are also a result of this same effect. Since an electron will spend more energy trying to leave a thicker source, it will have less residual kinetic energy to deposit in the target tissue Thi s is reflected in the smaller SAF values at a given energy for CBV sources versus TBV sources. The SAFs for inactive marrow sources are higher than for either one of the bone volume sources. The stopping power of bone is much higher than that of inactive marrow. Therefore, the energy deposited by the electrons in bone volume sources, before they escape them, is much higher than that for inactive marrow sources. Since electrons escape the inactive marrow more readily they have more energy to deposit in the active marrow target which results in higher SAF values for any given electron energy. As the electron energy increases, the particle goes through sufficient marrow cavities to average out its energy deposition in the target regardless of the source t issue This results in the convergence of all SAF values at high energies in every bone site, independent of the source tissue ( F igure 2 4). When analyzing the results for endosteum targets, different trends arise. For active marrow sources, the curves a re much more cellularity independent that before. This is due to the fact that now the target includes both inactive and active marrow within 50 micrometers of the bone trabecuale ; therefore the target volume no longer decreases along with cellularity The fraction of energy that is emitted by the source

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42 and deposited in the target does not change with cellularity because the volume of the target does not change with cellularity anymore either. Hence, the absorbed fraction for this source to target comb ination is completely cellularity independent. The slight change in SAF values with cellularity, as seen in F igure 2 5, is simply due to the fact that the mass of the target changes slightly with changing cellularity as a result of the different densities f or active and inactive marrow. When inactive marrow is the source irradiating the endosteum, the SAF values are no longer 0 at low energies, as formerly seen for active marrow targets. Since the endosteum includes both active and inactive marrow, even t he particles that are not energetic enough to escape the inactive marrow and dep osit all of their energy there now contribute to target dose. Since this scenario is parallel to the case where AM is the source, the values in the two instances are very clos e. An inactive marrow source at 70% cellularity is equivalent to an active marrow source at 30%. As previously mentioned, absorbed fractions for active marrow sources to endosteum targets are cellularity independent. Consequently, this should also hold for inactive marrow sources. Therefore, the values for this curve are, as expected, very close to those for the 70% cellularity active marrow source. The curves for the TBS source do not change dramatically for endosteum targets. The main difference is t hat the SAF values start decreasing at lower energies than those for active marrow targets. This stems from the fact that since the target is now smaller, the particles do not need to be as energetic to cross it before depositing the bulk of their energy elsewhere. Therefore, the drop occurs in the range of 100 keV as opposed to 1 MeV. The shape of the SAF curves for both volume sources remains

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43 consistent with that seen for active marrow targets. However, the SAF values are almost an order of magnitude smaller at any give n energy. Again, this is a consequence of the size of the target. Since now there is only a thin portion of the marrow that is of interest, the particles have a much smaller volume to deposit their energy in. Therefore, often times th ey will cross the endosteu m with few interactions, and lo se their energy beyond it. Comparison to C urrent B one D osimetry M odels Although there are currently no detailed skeletal dosimetry models for canine subjects this section aims to compare human valu es previously published by Stabin and Siegel 34 to the ones presented in the current study. Figure 2 7 and 2 8 show the skeletal averaged absorbed fractions for the UF canine skeletal phantom and the 5 and 10 year old stylized human phantoms presented by Stabin and Siegel. 34 These two phantoms were selected based on body weight proximity to the canine phantom Fig ure 2 7 compares the values for the different phantoms with active marrow as the target, while F igure 2 8 shows their endosteum target counterparts. For active marrow source and target, the human models underestimate the absorbed fractions for energies be tween 10 50 keV for the 5 year old and 10 80 keV for the 10 year old The valu es, however, are very close at energies below these values At higher energies, on the other hand, the human results level off, while the canine curve keeps decreasing. This d ifference is due to the fact that the dosimetry calculations performed in this study account for electron escape, while those previously published for the human take spongiosa to be an infinite medium. Therefore, this behavior at high energies is observed in all human source target combinations When looking at the graph for TBS source to AM target, the human values are lower than those for the canine up until the

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44 infinite spongiosa modeling consequences start to dominate. At that point, the canine value s start decreasing while the human values do not The curve of TBV source and AM target shows good agreement for all three models until the electron energy reaches 100 keV. The curves begin to diverg e at higher energies and again, the electron escape ca uses the canine curve to decrease at high energies while the human ones simply level off. Overall, for that source target combination, the 10 year old model offers a much closer estimate than the 5 year old. Nevertheless, the differences in the finite v ersus infinite spongiosa models yield overestimates at high energies. The absorbed fractions for the endosteum as the target and the active marrow as the source are much higher in the canine phantom than in the human. They differ by a factor of 5. This i s a direct consequence of the revised endosteum definition. In this study, the endosteum was defined as the layer of marrow that is within 50 microns from any bone surface which is in concordance with current recommendations from ICRP Publication 110 35 In the Stabin and Siegel work, the endosteum was defined as a 10 micron layer instead as defined in the earlier in ICRP Publication 26 and 30 36, 37 Therefore the volume of the endosteal target in the canine dosimetry calculations is about 5 times larger. This same effect is observed in all the bone sources and endosteum target combinations. The curves for the human models and the canine model all have similar shapes, and they all seem to converge at higher energies. The energy level at which they converge is higher for the canine phantom than for the human phantoms. Summary Dogs are the optimal subject choice in pre clinical studies of radiopharmaceuticals due to the various similarities of certain cancers as a disease between canines and

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45 humans. The advantages are not only due to histological and biochem ical parallels, but are also a result of the exposure to similar environmental factors. The lack of canine specific phantoms for skeletal dosimetry hinders their use in preclinical trials. Although human phantoms can be used to perform dosimetry studies in the dog, using canine specific models improves the reliability of the results. Increasing the accuracy of the information collected during the early stages of clinical trials provides researchers with a sturdier basis for assessing the efficacy of the compound and determining other important parameters such as dose limiting organ for the treatment. Accurate skeletal dosimetry is paramount for such calculations since active marrow is often the dose limiting organ in nuclear medicine treatments. The res ults presented in this paper aim to improve the tools for skeletal canine dosimetry, so that the use of these animals becomes more widespread in radiopharmaceutical development. Acknowledgements This study was supported in part by NCI Grant F31 CA130165, by the Shands He althcare Endowment for Oncology, and the Razors for Raul Foundation for Research Towards C ure of Osteogenic Sarcoma.

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46 Table 2 1. Volume fractions calculated in several bone sites in the dog Volume Fractions Bone Site RVF Co rtical Spongiosa Medullary Cavity Teeth C 3 ---0.7424 0.2576 ------Cranium ---0.7694 0.1306 ---0.1000 Femur Proximal 0.2607 0.3269 0.6731 ------Shaft 0.3419 0.4684 ---0.5316 ---Distal 0.3975 0.2161 0.7839 ------Humerus Proximal 0.3981 0.1873 0.8127 ------Shaft 0.3799 0.4788 ---0.5212 ---Distal 0.2220 0.3732 0.6268 ------L 1 ---0.4070 0.5930 ------Mandible ---0.5657 0.2723 ---0.1621 Pawbone ---0.6413 0.3587 ------Pelvis ---0.4776 0. 5224 ------Radius Proximal 0.1808 0.5844 0.4156 ------Shaft 0.4494 0.5605 ---0.4395 ---Distal 0.3698 0.5134 0.4866 ------Ulna Proximal 0.4690 0.5134 0.4866 ---Shaft 0.4401 0.5629 ---0.4371 Distal 0.0909 0.6472 0.3528 ---Rib ---0.7232 0.2768 ------Sternum ---0.6988 0.3012 ------Scapula ---0.6331 0.3669 ------Tailbone ---0.7479 0.2521 ------Tibia Proximal 0.3643 0.49076 0.5092 ------Shaft 0.4495 0.52395 ---0.4761 ---Dista l 0.1862 0.52997 0.4700 ------Fibula Proximal 0.3781 0.27624 0.7238 ------Shaft 0.368 0 0.41278 ---0.5872 ---Distal 0.2539 0.30154 0.6985 ------

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47 Table 2 2. Results of the test of different scaling factors used to obtain the mis cellaneous mass of other human models based on the male miscellaneous reference mass of 200g. Miscellaneous (ICRP 89) (g) Scaled Miscellaneous (g) % Differences Age Bone Total Skeleton Body Mass Bone Total Skeleton Body Mass 5 years 5 5 45.8 46 52 17% 16% 5% 10 years 90 83.6 86 88 7% 5% 3% 15 years Male 155 147 151 153 5% 2% 1% Female 145 135 137 145 7% 6% 0% Adult Female 160 145 149 164 9% 7% 3% Table 2 3. Marrow and trabecular bone volume fr actions in the 12 canine bone samples analyzed. Volume Fraction Sample Marrow Trabecular Bone 1 Proximal Femur 0.601 0.399 2 Distal Femur 0.696 0.304 3 Proximal Humerus 0.749 0.251 4 Distal Humerus 0.516 0.484 5 Cranium (Parietal) 0.3 48 0.652 6 Pelvis 0.736 0.264 7 C 4 0.609 0.391 8 T 5 0.758 0.242 9 T 13 0.734 0.266 10 L 2 0.740 0.260 11 Mandible 0.810 0.190 12 Rib 0.695 0.305

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48 Table 2 4. Detailed skeletal mass table results for the canine mode l. Skeletal Sites V sp (cc) TBVF TB mass (g) CBV (cc) Cortical Bone Mass (g) Total Mineral Mass (g) TeV (cc) Teeth Mass (g) MVF Total Marrow Volume (cc) CF IM Mass (g) AM Mass (g) Total Bone Mass (g) Cranium 22.8 65.2 27.9 134.0 251.7 279. 5 17.4 52.3 34.8 7.9 0.4 4.6 3.0 339.4 Mandible 22.4 19.0 8.0 46.4 87.2 95.2 13.3 39.9 81.0 18.1 0.4 10.5 6.8 152.4 Scapulae 36.5 30.5 20.9 63.0 118.3 139.2 --------69.5 25.4 0.4 14.7 9.5 163.5 Sternum 3.9 30.5 2.2 9.0 16.9 19.2 --------69.5 2.7 0.7 0.8 1.9 21.8 Ribs 31.5 30.5 18.0 82.3 154.5 172.5 --------69.5 21.9 0.7 6.2 15.1 193.8 CV 30.6 39.1 22.5 88.2 165.6 188.1 --------60.9 18.6 0.7 5.2 12.9 206.2 TV 55.2 25.4 26.3 74.6 140.1 166.4 --------74.6 41.2 0.7 11.6 28.5 206.5 LV 76.6 26.0 37.3 52.6 98.7 136.0 --------74.0 56.7 0.7 16.0 39.2 191.2 Pelvis 67.8 26.4 33.6 62.0 116.5 150.1 --------73.6 49.9 0.5 24.4 23.7 198.1 CaV 6.8 26.0 3.3 20.1 37.7 41.0 --------74.0 5.0 0.7 1.4 3.5 45.8 Femur 28.5 39.9 21.4 13.9 26.0 47.4 --------60.1 17.1 0.3 12.1 4.2 63.7 Proximal Shaft 29.5 0.0 0.0 26.0 48.7 48.7 --------100.0 29.5 0.0 27.6 0.0 76.4 Distal 51.1 30.4 29.2 14.1 26.4 55.6 --------69.6 35.6 0.0 33.3 0.0 89.0 Tibia 21.0 30.4 12. 0 20.3 38.0 50.1 --------69.6 14.6 0.0 13.7 0.0 63.8 Proximal Shaft 24.2 0.0 0.0 26.7 50.1 50.1 --------100.0 24.2 0.0 22.7 0.0 72.8 Distal 9.9 30.4 5.7 11.2 21.0 26.7 --------69.6 6.9 0.0 6.5 0.0 33.1 Fibula 2.3 30.4 1.3 0.9 1.7 3.0 --------69.6 1.6 0.0 1.5 0.0 4.5 Proximal Shaft 1.8 0.0 0.0 1.3 2.4 2.4 --------100.0 1.8 0.0 1.7 0.0 4.1 Distal 1.5 30.4 0.9 0.6 1.2 2.1 --------69.6 1.0 0.0 1.0 0.0 3.1 Hind paw bones 31.2 30.4 17.8 55.8 104.8 1 22.6 --------69.6 21.7 0.0 20.4 0.0 143.0 Front paw bones 24.0 48.4 21.8 43.0 80.7 102.5 --------51.6 12.4 0.0 11.6 0.0 114.2

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49 Table 2 4. Continued Skeletal Sites V sp (cc) TBVF TB mass (g) CBV (cc) Cortical Bone Mass (g) Total Min eral Mass (g) TeV (cc) Teeth Mass (g) MVF Total Marrow Volume (cc) CF IM Mass (g) AM Mass (g) Total Bone Mass (g) Humerus 47.0 25.1 22.2 10.8 20.3 42.5 --------74.9 35.2 0.3 24.8 8.7 75.9 Proximal Shaft 28.8 0.0 0.0 26.4 49.6 49.6 -------100.0 28.8 0.0 27.0 0.0 76.6 Distal 20.2 48.4 18.4 12.0 22.6 41.0 --------51.6 10.4 0.0 9.8 0.0 50.7 Radius 4.7 48.4 4.3 6.7 12.5 16.8 --------51.6 2.4 0.0 2.3 0.0 19.1 Proximal Shaft 12.5 0.0 0.0 15.9 29.8 29.8 -------100.0 12.5 0.0 11.7 0.0 41.5 Distal 11.4 48.4 10.3 12.0 22.5 32.8 --------51.6 5.9 0.0 5.5 0.0 38.3 Ulna 12.3 48.4 11.2 13.0 24.4 35.5 --------51.6 6.3 0.0 6.0 0.0 41.5 Proximal Shaft 10.4 0.0 0.0 13.4 25.1 25.1 --------100.0 10.4 0.0 9.7 0.0 34.8 Distal 1.7 48.4 1.6 3.2 6.0 7.5 --------51.6 0.9 0.0 0.8 0.0 8.4 Total 728.1 378.1 959.1 1801.0 2179.1 30.7 92.2 526.7 345.0 156.9 2773.2

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50 Table 2 5 Fractional masses of the different c omponents of each skeletal site with respect to the total mass of the bone site and the total mass of the skeleton. Sk means skeleton. Cortical Bone Trabecular Bone Active Marrow Inactive Marrow Mineral B All tissues Mineral B All tissues Marrow All tissues Marrow All tissues Site/Sk Skeletal Sites Site Sk Site Sk Site Sk Site Sk Site Sk Site Sk Site Sk Site Sk Total Cranium 0.90 0.13 0.73 0.09 0.10 0.01 0.08 0.01 0.39 0.01 0.01 0.00 0.61 0.01 0.01 0.00 0. 12 Mandible 0.92 0.04 0.56 0.03 0.08 0.00 0.05 0.00 0.39 0.01 0.04 0.00 0.61 0.02 0.07 0.00 0.05 Scapulae 0.85 0.06 0.71 0.04 0.15 0.01 0.12 0.01 0.39 0.02 0.06 0.00 0.61 0.03 0.09 0.01 0.06 Sternum 0.88 0.01 0.76 0.01 0.12 0.00 0.10 0.00 0.71 0.00 0.08 0.00 0.29 0.00 0.03 0.00 0.01 Ribs 0.90 0.08 0.78 0.05 0.10 0.01 0.09 0.01 0.71 0.03 0.08 0.01 0.29 0.01 0.03 0.00 0.07 Vertebrae (Cervical) 0.88 0.09 0.78 0.06 0.12 0.01 0.11 0.01 0.71 0.03 0.06 0.00 0.29 0.01 0.02 0.00 0.07 Vertebrae (Thoracic) 0.84 0.08 0.66 0.05 0.16 0.01 0.12 0.01 0.71 0.06 0.13 0.01 0.29 0.02 0.05 0.00 0.07 Vertebrae (Lumbar) 0.73 0.06 0.50 0.03 0.27 0.02 0.19 0.01 0.71 0.08 0.20 0.01 0.29 0.03 0.08 0.01 0.07 Pelvis 0.78 0.07 0.57 0.04 0.22 0.02 0.17 0.01 0.49 0.05 0.12 0.01 0 .51 0.05 0.12 0.01 0.07 Vertebrae (Caudal) 0.92 0.02 0.80 0.01 0.08 0.00 0.07 0.00 0.71 0.01 0.07 0.00 0.29 0.00 0.03 0.00 0.02 Femur 0.67 0.07 0.43 0.04 0.33 0.02 0.21 0.02 0.05 0.01 0.02 0.00 0.95 0.15 0.31 0.03 0.08 Tibia 0.86 0.06 0.63 0.04 0.14 0 .01 0.10 0.01 0.00 0.00 0.00 0.00 1.00 0.09 0.25 0.02 0.06 Fibula 0.71 0.00 0.44 0.00 0.29 0.00 0.18 0.00 0.00 0.00 0.00 0.00 1.00 0.01 0.35 0.00 0.00 Hind paw bones 0.85 0.06 0.71 0.04 0.15 0.01 0.12 0.01 0.00 0.00 0.00 0.00 1.00 0.04 0.14 0.01 0.05 F ront paw bones 0.79 0.05 0.69 0.03 0.21 0.01 0.19 0.01 0.00 0.00 0.00 0.00 1.00 0.02 0.10 0.00 0.04 Humerus 0.70 0.06 0.44 0.03 0.30 0.02 0.19 0.01 0.12 0.02 0.04 0.00 0.88 0.12 0.29 0.02 0.07 Radius 0.82 0.04 0.64 0.02 0.18 0.01 0.14 0.01 0.00 0.00 0.0 0 0.00 1.00 0.04 0.19 0.01 0.04 Ulna 0.81 0.03 0.64 0.02 0.19 0.01 0.15 0.00 0.00 0.00 0.00 0.00 1.00 0.03 0.19 0.01 0.03 Total 0.83 0.63 0.17 0.13 0.31 0.06 0.69 0.12

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51 Table 2 6 Condensed version of the skeletal mass table for t he UFDog phantom including miscellaneous tissues. Mass (g) Mineral Bone Marrow Teeth Miscellaneous Tissues Skeletal Sites CB TB Total AM IM Total CB TB AM IM Total Total Cranium 251.68 27.87 279.55 2.97 4.60 7.57 52.26 5.66 0.63 0.13 0.21 6.62 345.99 Mandible 87.22 7.97 95.19 6.80 10.53 17.33 39.91 1.96 0.18 0.29 0.47 2.91 155.33 Scapulae 118.29 20.92 139.21 9.52 14.75 24.27 0.00 2.66 0.47 0.41 0.66 4.20 167.68 Sternum 16.93 2.23 19.15 1.87 0.76 2.63 0.00 0.38 0.05 0.08 0.03 0.54 22.32 Ribs 154.50 18.05 172.55 15.13 6.16 21.28 0.00 3.47 0.41 0.65 0.28 4.80 198.64 Vertebrae (Cervical) 165.61 22.46 188.08 12.89 5.24 18.13 0.00 3.72 0.51 0.55 0.24 5.02 211.23 Vertebrae (Thoracic) 140.12 26.33 166.45 28.49 11.59 40.08 0.00 3.15 0.59 1.22 0.52 5.48 212.01 Vertebrae (Lumbar) 98.70 37.33 136.04 39.21 15.95 55.16 0.00 2.22 0.84 1.68 0.72 5.45 196.65 Pelvis 116.48 33.64 150.12 23.68 24.35 48.03 0.00 2.62 0.76 1.01 1.10 5.48 203.63 Vertebrae ( Caudal) 37.67 3.30 40.96 3.46 1.41 4.87 0.00 0.85 0.07 0.15 0.06 1.13 46.96 Femur 101.18 50.55 151.73 4.23 73.02 77.26 0.00 2.28 1.14 0.18 3.29 6.88 235.87 Tibia 109.13 17.68 126.81 0.00 42.92 42.92 0.00 2.45 0.39 0.00 1.93 4.78 174.50 Fibula 5.30 2.18 7.48 0.00 4.21 4.21 0.00 0.12 0.05 0.00 0.19 0.36 12.05 Hind paw bones 104.77 17.83 122.60 0.00 20.36 20.36 0.00 2.36 0.40 0.00 0.92 3.67 146.63 Front paw bones 80.68 21.84 102.52 0.00 11.63 11.63 0.00 1.81 0.49 0.00 0.5 2 2.83 116.98 Humerus 92.54 40.52 133.06 8.69 61.50 70.19 0.00 2.08 0.91 0.37 2.77 6.13 209.38 Radius 64.83 14.63 79.46 0.00 19.47 19.47 0.00 1.46 0.32 0.00 0.88 2.66 101.59 Ulna 55.39 12.75 68.14 0.00 16.51 16.51 0.00 1.25 0.28 0.00 0 .74 2.27 86.92 Total 1801.02 378.08 2179.10 156.93 345.0 501.90 92.17 40.49 8.48 6.71 15.53 71.21 2,844.38

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52 Figure 2 1. Long bone subdivisions (proximal, shaft and distal) shown in A) the femur and B) the tibia

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53 Figure 2 2. Illustration showing the different layers of the bone models. The outer cortical bone, inner spongiosa region, and the two regions together with the cortical bone as a semi transparent layer.

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54 Figure 2 3. Summary of the SAF results for the ribs (A) and femora (B) for Active Marrow as both the source and the target for different cellularities

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55 Figure 2 4. Summary of the results of different skeletal tissue sources to the active marrow for A) the ribs and B) the femora

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56 Figure 2 5. SAF curves for the ribs with A M source and endosteum target at different cellularities. Figure 2 6. SAF values for the ribs with different skeletal tissues as the source and the endosteum as the target.

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57 Figure 2 7. AF curves comparing the values in the literature for Active Mar row target with A ) Marrow sources and B) Bone sources

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58 Figure 2 8. AF curves comparing the values in the literature for Endosteum target with A) Marrow sources and B ) Bone sources. The CBS and CBV source for the UFDog are the same, and all the values for the 10YO and 5YO are the same for all bone sources.

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59 CHAPTER 3 DOSIMETRY IN NUCLEAR MEDICINE Background The use of radiation in medicine has dramatically become more widespread in the past few decades. Several publications have highlighted the steep increase in the contribution of medical procedures to the overall radiation dose to individuals in the United States. 39, 40 The findings of studies conducted by the National Council on Radiation Protection and Me asurements (NCRP), published in its R eport No. 160, show that doses from nuclear medicine procedures contribute to 26% of the medical exposure and to 12% to the total annual collective effective dose per individual. 39 With the growing prevalence of radiation in medicine, dose assessments for both diagnostic and therapy procedures are crucial to care. There has been an increased interest in the inclusion of comprehensive patient 40, 41 Concern from t he public and medical institutions regarding the effects of untracked radiation exposures has stimulated research towards the systematic implementati on of dosimetry calculations in clinical settings 41, 42 Althoug h this movement is mainly towards diagnostic procedures, the same enthusiasm is slowly being applied to therapeutic techniques as well. Patients can greatly benefit from reliable dose estimates during treatment planning across all modalities. Dosimetry in external beam procedures has long been established. Dose calculations are routinely used as part of treatment planning for external beam therapy and their accuracy and reliability are widely accepted in the medical community. 43 Thi s is not the case for internal dosimetry. While e xternal beam doses are required to have

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60 an error of less than 5% during treatment planning 44 nuclear medicine doses can only hope to reach 20% error at best with the existing technology. 45 Factors such as the limited spatial resolution of nuclear medicine images, as well as the unce rtainties in the patient specific uptake and clearance rates, 46 48 limit the overall accuracy of the results. Since the resolution of current nuclear medicine scans is not as high as in other modalities, the infor mation obtained from them may be misleading; radiopharmaceutical uptake may be assigned to neighboring tissues that do not actually have any activity themselves. 49, 50 Furthermore, if the radionuclide is attached to a carrier molecule, uncertainties in the fraction of breaks between the two after administration and before clearance may exacerbate the problem. These issues cannot easily be improved with the current tools. Nevertheless, technological improvements a re resolving these problems, and the dosimetry techniques in nuclear medicine need to develop as well to guarantee advancement in the field. It is also important to note that the basic quantity in dosimetry calculations is absorbed dose. While this value gives information regarding how much energy is absorbed per unit mass of the tissue, it does not account for the type of radiation being used, the rate at which it is being delivered and the radiosensitivity of the tissue of interest, among other factors These simplifications can hinder the dose effect prediction for a given therapy. 51 53 However, having accurate absorbed dose information may lead to better dose effect correlations and mastering the calculation o f this value, albeit using more simplistic techniques could serve as a n important stepping stone towards the development of techniques for determination of more complex quantities such as the biologically effective dose (BED).

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61 There are elements that can presently be controlled to optimize the quality of the absorbed dose estimates. Some examples are: the level of realism in the patient model, how detailed the radionuclide decay scheme information is, and what methodology is used for dose calculations. These can all be selected to enhance the accuracy of the results. Roles of Dosimetry in Nuclear Medicine Dosimetry in nuclear medicine serves different functions depending on whether the procedure is of diagnostic or therapeutic nature In diagnostic pr ocedures, the radiopharmaceutical activity administered to the patient is low enough that health benefits from it clearly outweigh the risks. Therefore, prospective dosimetry is discretionary. However, retrospective dosimetry for diagnostic procedures ca n be used as part of a co mprehensive patient dose tracking report and should be performed. 40 Dosimetry in radionuclide therapy has a different role; it can be used as a treatment planning tool. This step has long been implemented in external beam treatment planning, but it is yet to become prevalent in radionuclide therapy. 54, 55 Dose calculations as part of treatment planning can help the medical team optimize the amount of activity to be administered to the patient. 54, 56 59 Adding this step as part of routine radionuclide therapy planning has benefits that are two fold: it ensures the success and safety of the treatment, and it helps reduce costs to the institution. Dosimetry calculations ca n confirm that the dose imparted to the tumor meets the necessary levels to achieve the expected response. They can also ensure that the doses to normal organs are below the appropriate toxicity limits. By doing so, the amount of activity administered to the patient can be optimized before treatment and costs from over dosage (administration of more activity that necessary) or from repeat

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62 procedures due to unsatisfactory tumor control can be minimized. Unfortunately dosimetry is not commonly performed a s part of treatment planning in radionuclide therapy but rather the patient is given a pre set amount of activity based on general parameters such as body weight. 54, 56 These activity levels are usually establish ed during clinical trials. The lack of effective dose calculation tools that are both fast and medical settings. Current Dosimetry Tools There are a few dosimetry sof tware packages available for dose calculations in nuclear medicine. Their complexity and accuracy span a wide range due to the differences in their approach in patient modeling, tumor modeling and dose computation. Clinicians and researchers also have th e option of utilizing general particle transport Monte Carlo packages to pe rform dosimetry calculations. Particle transport code s are powerful tools, but the level of expertise necessary for use and the length of the calculation time can become prohibitiv e in standard clinical practice. This section presents the different methods, data and programs available in the field. Calculation Methods There are several calculation methods available for dosimetry in nuclear medicine. Each method has its advantage s and disadvantages. Some have calculation times that are highly attractive in a clinical setting where patient turnover is really important, and some provide dosimetry results that are really accurate. This section reviews several of the methods current ly available for dosimetry calculations.

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63 Basic absorbed dose equation The schema published by the Medical Internal Radiation Dose (MIRD) Committee of t he Society of Nuclear Medicine 60, 61 is very commonly used when performing internal dosimetry calculations 59, 62, 63 This method provides absorbed dose estimates and it is based on the number of decays that occur in the source (cumulated activity or residence time, ), the energy emitted per disintegration (delta, ), the fraction of the energy emitted by the source that is absorbed in the target (absorbed fraction, ) and the mass of the target ( ). The cumulated activity stands a lone as the other S are shown below. ( 3 1 ) ( 3 2 ) ( 3 3 ) w here is the absorbed dose from source region to target region the subscript refers to the type of decay particle (electron, photon, etc.), the subscript denotes the different particles of the same type in the decay scheme, is the energy of the decay particle in MeV, is the yield of the decay in particles per decay, and is the specific absorbed fraction (absorbe d fraction divided by mass of the target) for source region to target region for particle of radiation type R. The constant is simply a conversion factor fr om MeV/(g*Bq s) to mGy/(MBq s). This formalism is very convenient as it groups a ll factors that are dependent on the radionuclide physical characteristics (decay particle type, energy, etc.) and separates them from factors that depend on the biological traits of the radiopharmaceutical in the

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64 patient (such as uptake and clearance rate s). For a given radiopharmaceutical, the S value remains unchanged for a patient provided that the target masses and tissue compositions remain constant These may change throughout the progression of the treatment due to factors such as tumor shrinkage. The most commonly used formulation of the schema is the time independent one shown in equations 3 1 through 3 3, but a time dependent version accounting for changes in target masses and absorbed fraction may also be implemented These equations are sho wn below. ( 3 4 ) ( 3 5 ) where the terms are as defined previously, only with the time dependence no ted by the t variable in the parenthesis. is the dose integration period. Occasionally the S value may be referred to as Dose Factor (DF). The two names mean absorbed dose rate per unit activity and they should be taken to be equivalent. In ord er to get the total absorbed dose to a target, the dose contributions from all the different source organs have to be calculated and added. Point kernel The point kernel dose approximation is a useful tool that allows for the calculation of acceptable dos e estimates with very short computational times However, this approximation is only valid for homogeneous infinite media with isotropic sources. Th is presents a challenge when used for human internal dosimetry because of the heterogeneous nature of the human body. Doses are calculated as follows using the point kernel algorithm : ( 3 6 )

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65 w here is the volumetric source strength (1/cm 3 ), is the volume of the target, is the point kernel, is the point pair distance distribution and is the ray length between a point in the source and a point in the target. The poin t kernel is defined as : ( 3 7 ) w here is the energy of the particle in MeV, is the mass energy absorption coefficient for the medium in cm 2 /g, is the build up factor, and is the linear attenuation coefficient of the tissue (1/cm). The linear attenuation coefficient can be The point pair distance distribution is defined as follows: ( 3 8 ) w here is the volume of the source and is the solid angle subtended by all points in the target volume that are a distance r from Point kernels can be viewed as the absorbed dose pe r decay at a distance from the source. 63 They are often calculated using Monte Carlo techniques that model a point source in a homogeneous media. Monte Carlo codes Monte Carlo techniques, generally speak ing, follow the life of a single radiation particle or photon from its creation to its absorption, based on the different probabilities of interaction it has in the medium it traverses. They can be used to calculate several different quantities such as pa rticle fluence and energy deposition. These stochastic particle transport codes are very flexible in their modeling capabilities. The user can

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66 create any geometry and define any source for dosimetry calculations. The results one obtains are as accurate as the exactitude of the model created for the calculation. However, the computation times are lengthy and learning to use these codes properly can be challenging, especially if complicated geometries and source terms are involved. Furthermore, several a rticles have shown discrepancies in the results from different Monte Carlo packages. 57, 64, 65 These differences may exceed 10% depending on the complexity of the geometry, how many different tissue interfaces the re are, the energy and type of particles being modeled, the size of the volume being considered, the cross section libraries embedded in the code and the physics models used. 57, 65 There are several articles in t he literature that present voxel S values that were derived with Monte Carlo codes. 66 69 These voxel values maintain the accuracy of the Monte Carlo techniques while providing faster computation times, but are onl y applicable for tissues of homogeneous density. Furthermore, the published values apply to only certain radionuclides. They would have to be recalculated if the values for the radionuclide of interest are not amongst the published ones. Monte Carlo tech niques have also been used to calculate dose point kernels for several radionuclides. 70, 71 Furhang et al. constructed photon point dose kernels in water for 14 commonly used radionuclides in nuclear medicine. 70 Botta et al. calculated electr on dose point kernels in water and compact bone for monoenergetic electrons and 7 beta emitting radioisotopes used in therapy. 71 Patient Data and Modeling The patient data and modeling used in dosimetry calculations can greatly affect the accuracy of the results. The way the patient anatomy and physiology is defined dic tates features as important as the separation distance between the source and target

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67 regions and their relative position to one another, the composition of the medium through which the radiation emitted in the decay travels, the mass of the target tissue, how quickly the radiopharmaceutical is taken up and cleared from the system, etc. The more patient specific these factors are, the more reliable the dose estimates become. Even if highly sophisticated calculation methods are used to obtain the absorbed f ractions for a given anatomy with really small uncertainties, substantial dose errors may arise in the application of the anatomy to a patient to which it is poorly match ed Hence, how accurately the model represents the patient can be one of the main sou rces of error in dosimetry calculations. Biokinetic data such as uptake and clearance rates can have great effects on dose. If the values used for the calculation differ from those in the real patient, the number of decays in the source will not be corr ect and the dose estimates will suffer. Whether these rates are calculated based on image data from nuclear medicine scans or from values published in the literature, the user should be aware of the assumptions and limitations that are implicit with every option. If standard published data is used for patient dosimetry, it is important to be aware that these values are averages and that they may not necessarily match the actual patient values Organ function and uptake and retention of radiopharmaceutica ls can have large variations amongst individuals, especially when dealing with patients with different disease types and treatment history. Their specific traits can greatly differ from the published values. When data is collected from nuclear medicine scans, issues may arise from the spatial and energy resolution characteristics of the equipment. The data collection process is crucial in the accuracy of the dose estimates. MIRD Pamphlet No. 16

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68 describes in detail how data acquisition should be perform ed to determine the radiopharmaceutical biodistribution for dosimetry. 73 This document is the standard for such procedures and it outlines the techniques that should be utilized to obtain the information as well a s the effects that the limitations of the cameras may have on the quality of the data. Internal dosimetry calculations are performed using computerized models of the patient. Oftentimes, these models are representative of a median individual as described by reports such as ICRP Publication 89. 28 There are three types of models available: mathematical, voxel and hybrid phantoms. Mathematical models represent equations. These phantoms are very flexible, as their surfaces can be altered relatively easily. However, they are stylized models of the human anatomy and they do not realistically represent it. Voxel phantoms are created based on human imaging data such as CT scans. Hence, these models are more anatomically accurate, but they are extremely difficult to alter. Modifications to bring the model closer to patient specific characteristics are very time consuming and complex as the models have to be changed one voxel at a time. Lastly, hybrid phantoms are a mixture of mathematical and voxel models. They are constructed based on patient imaging, but the surfaces are created using the Non Uniform Rational B Spline (NURBS) technology. These surfaces have control points that allow for relatively simple manipulation of the phantom organs. Patient specific modifications are a feasible option when using NURBS phantoms. There are articles in the literature that give a review of the phantom evolution throughout the years. 42, 74 The reader is referred to these for more information.

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69 Current Software Programs Internal dosimetry software packages have evolved from utilizing mathematical stylized phantoms to allowing the user to import imagin g data to construct patient specific models for calculations. At the moment, one of the most commonly used internal dosimetry packages is OLINDA/EXM (Organ Level Internal Dose Assessment/Exponential Modeling). 62 This FDA approved software developed by Stabin et al is a rewrite of the previ ous code termed MIRDOSE. 75 It estimates the S values ( or Dose Facto rs ) for any of the 800 radionuclides embedded in the code in any of 10 stylized human phantoms (6 representing adults and children and 4 representing the adult female nonpregnant and at different stages of gestation). OLINDA/EXM allows the user to input r adiation weighting factors for effective dose calculations as well as patient organ masses for patient specific SAF mass scaling of organ self doses. It also allows for a very simplified version of tumor dosimetry. A sphere model is used to calculate sel f dose to tumors ; no allowance is made for cross organ dose estimates in tumor burdened anatomy. The values of the self absorbed fractions the code uses for these calculations were obtained with MCNP4B AND EGS4 in an infinite unit density medium. OLINDA/ EXM has a main improvement from its predecessor; the user does not have to calculate the number of decays in the source. Up to 10 time points for the time activity curve estimation can be input into the code and a 1, 2 or 3 exponential function fit of the measured kinetic data and an estimate of the number of decays in the source will automatically be conducted. This provides the user with really fast dose estimates, but the tumor dosimetry capabilities are limited and it uses stylized models to represent the human anatomy.

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70 Another software that uses stylized phantoms for dosimetry is MABDOSE (Monoclonal AntiBody DOSimetry). 76, 77 This package allows for placement of arbitrary tumors in the patient geometry repres ented by the ORNL phantoms using the available graphical interface. When a tumor is inserted into the anatomy, the tumor is assumed to replace the organ tissue instead of displacing it. It performs dosimetry calculations using on the fly Monte Carlo for penetrating radiation and it assumes local deposition for non penetrating radiation, except for in walled organs, where it takes the absorbed fraction for particulate radiation to be 0.5. The software also offers mathematical modeling and curve fitting to ols to calculate the cumulated activity in the source. Most of the data used in this software package is based on ORNL reports and databases. This software package offers the advantage of tumor insertion in the phantom for dosimetry calculations, but the anatomy used is still overly simplified and it does not realistically represent the human body. Furthermore, its availability for use by researchers and clinicians seems to be limited as very few publications utilize it for dosimetry studies. There are o ther software packages with variations in their capabilities that allow for dosimetry in stylized anatomy 78 but the number of dosimetry codes that allow for calculations in more advanced phantoms such as the University of Florida family of comput ational hybrid phantoms is nonexistent. There is a gap in sophistication from the type of dosimetry codes described above to the alternative 3 dimensional patient specific anatomy programs also available for internal dosimetry. An example of this type of software packages is the 3 Dimensional Internal Dosimetry (3D ID) software system. 79 This software requires CT/MRI and SPECT/PET images to obtain the density

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71 and composition of the anatomy and the number of disintegrations, respectively. The code estimates doses by convolving dose point kerne ls with the activity or cumulated activity in the source volume. The point kernels used in this code were calculated by performing a Monte Carlo simulation of absorbed dose versus distance for a photon point source in water. This software not only calcul ates absorbed doses but it also provides the user with dose volume histograms. The calculation times for these calculations vary depending on the characteristics of the computer being used, and the number of organs involved in the calculation, the number of voxels in the model, etc. The dosimetry of the two patients presented in the article took in the order of hours to complete. The 3D ID software has been updated, and its new version is called 3 Dimensional Radiobiologic Dosimetry (3DRD). 80 This package is similar to its predecessor, but it better incorporates Monte Carlo calculations to deal with tissue inhomogeneities more accurately. It also includes Equivalent Uniform Dose (EUD) and Biologically Effective Dose (BED) calculations to account for heterogeneous dose distributions in organs and variations in the dose rates during radionuclide therapy, respectively. Summary Internal dosimetry for diagnostic nuclear medicine and radionuclide therapy procedures i s currently an under utilized tool. Although it may offer the advantage of allowing for thorough patient dose tracking records or of providing crucial information for appropriate pre therapy treatment planning, the available tools are not quite optimized for wide clinical use yet. The existing dose packages are either too simplified to be used as part of treatment planning, or too complex to be embedded into the average

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72 clinical setting. The use of stylized phantoms for diagnostic dosimetry is acceptable as the radiopharmaceutical doses administered to the patients are not very high. However, the use of these models in radionuclide therapy dosimetry could yield to misleading results. Furthermore, uncertainties in the biokinetic data necessary for dosim etry calculations present an added obstacle in the establishment of internal dosimetry as a standard procedure. More advances are necessary to use dosimetry to its full potential when dealing with radiopharmaceuticals in medicine. The establishment of a clear dose effect relationship between either absorbed dose or equivalent dose are also needed in order to further refine the direction of current research efforts. New technologies and techniques arise regularly to maximize the reliability of the data c ollected through nuclear medicine images and therefore, new software packages should also be developed to meet both the accuracy and time demands of current standard clinical settings and foment the advancement of the field.

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73 CHAPTER 4 DOSIMETRY SOFTWARE Background Dosimetry calculations can be performed through stochastic and deterministic methods. Although Monte Carlo calculations deliver accurate and reliable results, provided that the scenario is modeled correctly, they are lengthy and may even be ti me prohibitive for standard clinical use. Deterministic methods such as dose point kernels, allow users to obtain dosimetry estimates that are computationally faster and sufficiently accurate The goal of the dosimetry software presented here is to allo w users to perform dosimetry calculations in a time efficient matter while minimally sacrificing the quality of the results. Current software packages for internal dosimetry are either too simplistic to provide reliable results upon which to base medical decisions or too complex to be useful in standard clinical practice. One of the most commonly used codes, OLINDA/EXM 62 performs S value calculations based on normal anatomy in stylized phantoms and it handles tumor dosimetry by only providing the user with self dose to spheres as an estima te for tumor dose. Therefore, this software provides results very quickly, but they are based on unrealistic anatomy and overly simplified assumptions for tumor dosimetry. Another internal dosimetry tool available is MABDOSE. 76, 77 This code also uses stylized phantoms for normal anatomy dosimetry but it handles tumor dosimetry by allowing the user to insert masses into the stylized phantom and performing on the fly Monte Carlo calculations. Although the tumor d osimetry calculations are more advanced in this package, the results can still be improved since they are based on the stylized phantom anatomy. Beyond these packages, the

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74 sophistication and complexity level of the codes and input data necessary to run th em become very advanced. 3D RD is an innovative tool that requires a set of SPECT or PET and CT or MRI patient imaging data to obtain the anatomical information and utilizing it to perform dose calculations with Monte Carlo methods. 80 Although this software provides very patient specific results and it employs the latest techniques to obtain really reliable doses, it is time intensive and it demands input data that not every average center would have available. There is no doubt that the most accurate results are obtained by creating a patient specific model for every dosimetry calculation and running particle transport However, the software developed in this study UFDose, provide s users with a computationally fast and reliable alternative that allows for both normal and tumor burdened anatomy dosimetry calculations in anatomically realistic phantoms UFDose adopts two different calculation procedures for dosimetry: the classical MIRD schema, for normal anatomy calculations, and point kernel for tumor burdened anatomy The code focuses on the calculation of the radionuclide S value Automated c umulated activity calculations based on time activity data are not currently embedded in this package ; the user is req uired to manually pre calculate and input the cumulated activity values into the code to obtain dosimetry results The internal dosimetry package here presented does not have a Graphical User Interface (GUI) at the moment. The GUI is under development b y the Advanced Laboratory for RAdiation Dosimetry Studies (ALRADS) research group at the University of Florida.

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75 Materials and Methods UFDose adopts two different calculation procedures for dosimetry: the MIRD schema, for normal anatomy calculations, and p oint kernel for tumor burdened anatomy The code focuses on calculating the S value s for different scenarios, but it does not currently have the tools to calculate cumulated activity. The user is responsible for obtaining and inputting the cumulated acti vity into the code for absorbed dose calculations. Another limitation of the software is that it only performs photon and electron dosimetry at the moment. Alpha particle dosimetry is not currently part of UFDose. UFDose uses the family of hybrid computa tional human phantoms developed at the University of Florida as the human models for dosimetry. 81 83 These phantoms represent 50 th percentile patients at different ages. Although they are not patient specific, th ey are extremely anatomically realistic. Doses calculated with these phantoms are a lot more reliable than those calculated with stylized phantoms. The location of the organs with respect to one another, their shape and separation are anatomically accura te for a 50 th percentile individual All these characteristics are very important in internal dosimetry calculations as they can greatly affect where the energy deposition of the particles is recorded in dose calculations. Both the absorbed fraction valu es and anatomical data are obtained from that set of phantoms. The radionuclide decay scheme information used in this software follows ICRP Publication 107. 84 The activity in the source tissue is assumed to be homogeneously distributed throughout the source Appendix B compiles the different algorithms written in MATLAB TM used in UFDose

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76 Normal Anatomy Dosimetry The dose values for normal anatomy are calculated using the MIRD schema described i n Chapter 3 (equations 3 1 through 3 3 ). This methodology requir es the values of Specific Absorbed Fractions (SAF) for every decay energy in a given radionuclide decay scheme The SAF values embedded in the code are not for any particular radionuclide, but rather for a set of standard energy indices for photons and ele ctrons Linear interpolation is performed to obtain SAFs for the energies in a given decay scheme. The energy range of the standard SAF values expands from 10 keV to 4 MeV. Complete local deposition is assumed at really low energies. Therefore, an SAF of: ( 4 1 ) is assigned to 0 keV to allow for proper interpolation at energies below 10 keV Particles of energies above 4 MeV are not commonly encountered in nuclear medicine; therefore the upper energy bound is suff icient for the purposes of this software. Once the SAF values for every energy in the decay scheme are calculated, they are multiplied by the corresponding delta value and summed (equation 3 2 ). This results in the radionuclide S value the absorbed dos e to the target tissue per unit decay in the source tissue The S value s for all 333 radionuclides included in the code are pre calculated for normal anatomy. This speeds up the calculation enormously since the S value does not have to be calculated ever y time the user wants to obtain the doses to normal organs. Once the S value is multiplied by the cumulated activity input by the user, the absorbed dose is obtained. The total dose to an organ is the addition of

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77 the absorbed doses to the organ of intere st received from radiation emissions originating in all source organs of the simulated patient Tumor Burdened Anatomy Dosimetry The methodology utilized for tumor burdened anatomy dosimetry is more complex than that for normal anatomy. Dose point kerne ls are used to calculate the photon contribution to both self and cross organ doses in the patient. The dose contributions from electrons are assumed to only be relevant in the source region. Electron contribution to the tumor dose is estimated by appro ximating the escape fraction of the electrons in spherical tumors of different sizes in MCNPX. This is similar to the technique used in OLINDA to estimate tumor self dose. 62, 64 The electron contribution to the n ormal anatomy organs is calculated based on the electron absorbed fractions from the University of Florida family of hybrid computational phantoms. The equations presented i n Chapter 3 to describe the point kernel methodology are the basis for the dose alg orithm implemented in MATLAB TM The point kernel equation was reformulated to match the MIRD schema parameters more closely. The equations below show the equivalent expressions to the SAF and S values: ( 4 2 ) ( 4 3 ) where is the volume of the target region, is the point pair distance distribution value for ray length, The rest of the parameters are as defined in Chapter 3. As seen above, the point kernel requires several factors for dose calculations. Buildup factor s, the point pair distance distribution for the source target organ pair and attenuation coefficients are all needed for the calculation. It is important to note that this

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78 equation will be slightly modified to accommodate heterogeneous cases. This is dis cussed in a subsequent section. Tumor insertion algorithm This algorithm was written in MATLAB TM Tumors are modeled in this software as triaxial ellipsoids as this is a simple yet flexible geometric shape capable of represent ing a wide range of tumor mas ses and shapes ( F igure 4 1 ) This algorithm gives the user complete control of both the location of the tumor and its size/shape Additionally, the code does ensure that the tumor is not inserted outside of the phantom ; if this occurs, an error message i s displayed. Since there is currently no GUI for the software, the user defines the location of the tumor center by typing in the voxel index location. Once the GUI is constructed, a visualization of the phantom slice by slice along the coronal, axial or sagittal plane will be displayed on the screen, and the user will be able to either click on the picture to select the location of the center, or the voxel indices will be clearly displayed along the axes of the figure so that the location can be effortles sly determined. Figure 4 2 illustrates an example of how this can be achieved Once the information has been input, the algorithm reads in the user specified ellipsoid center and the length of the semi axes. With this data, and along with the mathemati cal equation of th e surface of an ellipsoid (E quation 4 4), the code determines the voxels that fall within the theoretical tumor volume, and it retags them with the tumor tag and material. ( 4 4 ) where a b and c are the radius of the ellipsoid semi ax e s along x, y and z respectively.

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79 The determination of what voxels need to be retagged is not trivial. From the surface equation of an ellipsoid, two equations relating the length of the axes and the voxel resolution were derived. The third one shows the values along the x axis that are considered for retagging based on the information obtained from the two preceding equations. These equations dictate what voxels need to be retagged as tumor as the algorit hm steps through the ax e s of the ellipse. for ( 4 5 ) for ( 4 6 ) ( 4 7 ) where the first part of t he top two equations uses the parameters of the basic triaxial ellipsoid equation, while the second part uses the voxelized parameters. The value of increases in increments of the voxel resolution along the z ax i s from 0 to c. The upper bound of is dictated by the value of y in the previous equation and it increases from 0 to y in increments of the voxel resolution along the y ax i s. The value of increases from 0 to x in increments of the voxel resolution along the x ax i s. The or der of these equations illustrates that the z values are dictated by the outer loop of the algorithm and they are set independently of the other equations. They are the basis of the rest of the calculation. The code transforms the information given by th ese equations into voxel indices using the following conversion: ( 4 8 ) ( 4 9 )

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80 ( 4 10 ) where is the voxel index in the x direction, is the x value of the center of the tumor as defined by the user and is the voxel resolution along the x axi s. The other terms are similarly defined for y and z. In order to match the voxelized tumor volume to the theoretical tumor volume, the code keeps track of the voxels retagged and it stops once the voxelized tumor volume matches the theoretical one to within four voxel volumes. The more volume checks the code performs, the longer the time it takes to retag. Therefore, checking it every four voxels is a good com promise between maintaining good volume accuracy and optimizing computation time. Accuracy in volume is prioritized over accuracy in axis lengths. Hence, the inserted shapes may not exactly match the ellipsoid described by the axis input measurements. Ho wever, accuracy in the volume inserted is more important than the exact shape of the tumor for dosimetry purposes. It is important to keep in mind that tumors are not perfect ellipsoids ; that is simply the shape selected for tumor representation in the so ftware. Hence, achieving a perfect voxelized ellipsoid at the expense of the accuracy of the volume would diminish the reliability of the results. Nevertheless, this algorithm can be improved in consequent versions of the software. A couple of issues ari se when using the voxel retagging scheme. First, the voxel indices that now belong to the tumor need to be removed from those of the original host organ index list. Second, the mass of the host organ needs to be recalculated as part of that organ now bel ongs to the tumor. Once the algorithm has inserted the tumor, it re identifies the voxel indices of the host organ and recalculates the masses by tallying the

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81 new number of voxels for that organ and multiplying this value by the density of the tissue. The user has the option of making the tumor 100% soft tissue (ST), 50% soft tissue 50% bone (50ST 50B), or 100% bone (B) Although this does not present every possible tumor composition one may encounter in a patient, it does cover the range of possible tiss ue compositions for tumors. As for the rest of the tissues in the phantoms, the weight percent elemental compositions for soft tissue and homogeneous bone in the tumor insertion code were obtained from the ORNL report TM 8381 V1 30 The composition for the mixed 50ST 50B was determined by multiplying the soft tissue weight percent values by 0.5, multipl ying the homogeneous bone weight percent values by 0.5 and adding the two together. Therefore the 50ST 50B should be taken to be 50% ST and 50% homogeneous bone by weight. The homogeneous bone tissue represents the average composition of all the differen t materials of the skeleton, including both mineral bone and marrow. Marrow is not present in bony tumors, but it Therefore, the elemental composition for homogeneous bone instead of mineral bone, w as used to calculate tumor compositions across the board. UF veterinary oncologist Dr. Rowan Milner supported this conclusion. However, just to ensure that choosing one type of bone over the other would not cause a significant change, the mass attenuatio n coefficients of a tissue with a composition of 50ST 50B using homogeneous bone and one of 50ST 50B using cortical bone (as defined in ICRU44) 85 were compared. The data for the comparison was obtained from the XCOM database. 86 Figure 4 3 shows the two graphs. The total attenuation coefficients for the two tissue compositions are very

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82 similar above 60keV. However, there are discrepancies at low energies; the coefficients for the 50ST 50 Cortical Bone are higher than that for the 50ST 50B with the ORNL homogeneous bone composition due to the dominance of the much higher photoelectric absorption cross section in that energy range. At higher energies, the photoelectric effect becomes less prominent and the similarities in the Compton scatter cross sections between the two materials govern the overall total attenuation coefficients. Point pair distance distribution Radionucli des emit radiation isotropically within the source tissue. Therefore, for a given source target organ pair, not all the radiation that is emitted from the source reaches the target. The probability that the distance between a point randomly selected in t he source organ and a point randomly selected target organ has a certain length is given by the point pair distance distribution. This distribution is defined by equation 3 8 given in Chapter 3. Since the point pair distance distribution does not account for the interaction coefficient of the photon as it travels through the medium, it should not be directly interpreted as the probability that a photon emitted in the source traveling a certain distance will reach the target. A MATLAB TM algorithm was writt en to calculate the point pair distance distribution for a gi ven organ pair. The algorithm recognizes the source and target organs based on the organ specific tag numbers of each voxel. Once the voxels that belong to each of the organs of interest are id entified, the algorithm methodically calculates the ray length between a random sample of voxels in the source and target This is shown in the equation below. ( 4 11 )

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83 where is the ray length between an initial voxel in the source with indices ( ) and a fina l one in the target with indices ( ). These lengths are arranged in ascending order, binned and the probability that a ray will have the length represented by each bin is calculated. The bin size of the distribution is determined based on the voxel resolution of the phantom and the size of the organ The length the set of bins expands is determined based on the shortest and longest ray lengths calculated for the organ pair of interest. The length that each bin represents is calcu lated by taking the average length of all the rays in the bin. The probability that a ray of the average length from each bin from the source will terminate in the target is then calculated by adding all the rays in each individual bin and dividing that r esult by the total number o f rays modeled The equation s below show how these parameters are calculated: ( 4 12 ) ( 4 13 ) ( 4 14 ) where is the shortest voxel resolution for an anisotropic voxel, is the point pair distance distribution probability that a ray will hav e a length of is the number of rays in bin is the number of random voxels selected in the source and target organs for ray length calculations and and correspond to the lower an d upper bounds of the ray lengths for bin respectively. The smoothness of the point pair distance distribution curve is governed by the size of the bins and the total number of rays used in the calculation. The algorithm uses

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84 two different bin widths depending on the size of the organs being considered. Equation 4 12 shows the bin size calculation for organs of less than 25000 voxels and for organs greater than 25000. This voxel cut off was determined by inspecting the results of the point pair dista nce distributions for different organ sizes. The range of ray lengths for smaller organ pairs is much more limited than that of larger organs. Therefore, smaller bin sizes are necessary to properly capture the length distribution of the rays. On the oth er hand, the smaller the bin size, the larger the number of rays modeled needs to be in order to preserve good statistics. The length of the calculation time is directly proportional to the number of rays modeled; hence, it was important to find a number of rays that would preserve the quality of the results without considerably elongating the calculation time. A total of 5,000,000 random numbers were used to organs and 1,000,000 for larger organs. Although these numbers were proven to be sufficiently large to yield reliable distributions, some artifacts were observed in some of MATLAB TM to the probability data calculated. This approach fixed the artifacts without altering the information of the distribution or increasing the calculation time. There are several filter options in the smooth function. The filter option used on the data was the Savitzky Golay filter. This was the option that best smoothed the data while leaving the overall shape and height of the distribution unaffected. This conclusion was reached by using several filter options and observing their effect on the result s. Examples of this study can be found in the R esults section of this chapter.

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85 Attenuation coefficients As evident by the equation of the dose point kernel, the mass energy absorption coefficients for the tissues in the phantom at the energies of the rad ionuclide decay spectrum of interest are required. Since the mass energy absorption coefficient for the tissues used in these phantoms are not readily available in the literature, they had to be computed. Mass attenuation coefficients for a tissue can be calculated by taking the mass atte nuation coefficients of each elemental component and combining them using the following equation: 87 ( 4 15 ) where is the weight fraction of the elemental component of the tissue and is its mass attenuation coefficient. The coefficients for each element were obtained from the XCOM databas e 86 and a M ATLAB TM algorithm was written to perform the calculation. This equation was used for both the calculation of mass energy absorption coefficients as well as total mass attenuation coefficients. Mass attenuation coeffic ient values are used in the calculation of the optical thickness necessary to determine the buildup factors. It is important to note that this mixture rule does not account for any possible changes in the molecular, chemical or crystalline environment of the atom. 85 This may cause significant errors in the attenuation coefficients at low energies. Dosimetry calculations: homogeneous and heteroge neous cases Tumors do not always have the same composition as the medium that surrounds them. The location and composition of tumor metastasis as they spread through the body depend on the primary disease. However, the top three locations for metastasis

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86 for many cancers are the liver, lungs and bone. 88 90 Those three locations have different tissue compositions, so whether the tumor is 100% bone, partly bony or completely soft tissue, it is clear that heterogenei ty issues will arise. The dose point kernel equation is designed for situations that can be approximated as infinitely homogeneous. Therefore, this equation had to be modified to provide acceptable results in scenarios that do not meet that requirement. In order to do so, two changes were made: Adjusted buildup factors were used to account for finite human anatomy Optical thicknesses were calculated accounting for tissue heterogeneities These alterations were used in every tumor burdened anatomy dosime try calculation regardless of whether there were heterogeneities in the volume of interest or not. The use of adjusted buildup factors improves the quality of the dosimetry results independently of the tissue types in the volume. This is due to the fact that utilizing infinite medium build up factors does not account for the finite size of the human anatomy. The construction of the adjusted build up factors is discussed in Chapter 5. The optical thickness correction only changes the equation if there ar e heterogeneities in the medium. The following equation shows how the optical thickness calculation is modified to account for tissue inhomogeneity ( 4 16 ) where is the linear attenuation coefficient for each material found in the volume of interest at energy and is the volumetric fraction of that material. This is how all the in equation 4 2 are calculated. Furthermore, the and shown in

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87 equation 4 2 are for the material of the target region, and the buildup factors used are always for soft tissue. There have been other te chniques published where the optical thickness or mass thickness calculations have been modified to account for heterogeneities in the medium. 87 These methods apply the same concepts as the one presented here, but they do it slightly differently. While the methodology described above adjusts the linear attenuation coefficient based on material volumetric fractions in the medium, the other tec hniques base it on the lengths the ray traverses through each material it encounters as it travels from the source to the target. The system used here, although more simple, it is also much more time efficient while producing reliable results The calculat ion of the volumetric fraction of each material in the volume is performed simultaneously with the point pair distance distribution. While that algorithm is running, the longest ray is recorded. The voxel indices for the initial and final voxels of that ray are stored, and used to create a rectang ular volum e as shown in F igure 4 4. Once the volume has been created, a histogram that bins the voxels in the volume by material type is created, the number of voxels in each column is recorded and divided by th e total number of voxels in the volume. This is how the fractional volume of each material is obtained. Mean free paths greater than 6 are not taken into account in the dosimetry calculations because the probability that a photon will travel that far is 0 .24%. Therefore, their contribution to the final dose values is negligible. If a given organ pair has the peak of the point pair distance distribution at distances beyond 5 MFP, this code will not give accurate dose results due to the limitation in MFPs. However, doses

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88 from source regions that are that far from the target are really small and can be considered negligible when compared to the doses from source regions that are closer. For calculations where the source and target regions are equal, dosimet ry is calculated exactly as outlined above with one exception: photons with energies below 15 keV are assumed to be locally deposited in the region. The electron contribution to the tumor is estimated using self dose to spheres of different radii, as previ ously stated. Spheres of radii between 0.5 cm and 2.5 cm, in increments of 0.5 cm, were modeled in MCNPX in a soft tissue medium with monoenergetic electron volumetric sources between 10 keV 4 MeV. The energy indices were selected to match the SAF table s in the family of computational hybrid phantoms used in the code. A total of 10 7 particles were modeled. Three sets of runs were performed to calculate the electron AF to a tumor of 100% soft tissue, 50ST 50B and 100% homogeneous bone composition. Line ar regressions were performed with these results in order to obtain an equation that could be used in the software to approximate the electron AF for a specific situation without the need of interpolation. This was performed in two steps First, an equat ion as a function of sphere radius was obtained for every energy Second, the coefficients of the linear regression equations for every energy were fit to their own function to obtain an equation that is both a function of tumor sphere radius and electron energy. Although this yields a very complex expression, it is more computationally efficient than interpolating between values every time.

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89 Results and Discussion Normal Anatomy The S value calculator algorithm was tested by calculating the S value s for the NBF for several radionuclides and comparing them to the published results by Wayson et al. 83 Tables 4 1 to 4 3 show the per cent differences between the two sets of values for selected radionuclides; the agreement is excellent. Most of the discrepancies are within 2% of the published results. The differences between the published values and the ones presented here are due to different interpolation techniques between energies. Tumor Burdened Anatomy The following sections present the results of the different algorithms that compose the tumor burdened anatomy dosimetry section of the software. Tumor i nsertion a lgorithm The goal of the tumor insertion algorithm is to allow the user to choose the size and location of the tumor and successfully insert it into the phantom with a voxelized volume that matches the theoretical tumor volume as closely as possible. The code was written so that the tumor insertion would terminate as soon as the volume of the voxelized tumor was within 4 voxel volumes of the theoretical volume. Hence, the accuracy of the results depends on the voxel size of the phantom. However, voxel volumes are really small in all the phantoms available in this software (T able 4 4 ) consequently this does not present a significant issue. Another difference between the phantoms that affects the tumor insertion results is the voxel resolution. The voxel size not only v aries depending on the phantom, but it also varies depending on the direction in some of the phantoms. The NBF and canine phantoms have cubed voxels, but the

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90 rest of the phantoms have one length along x and y and a different one along z. The reader is re ferred to T able 4 4 for more information. Table 4 4 shows that the UF newborn ( NBF ) phantom has the smallest voxel volume and the UF adult male ( ADM ) has the largest. In order to test the capabilities of the tumor insertion algorithm, several tumors wer e inserted into these two phantoms. Table 4 5 summarizes the results. The same size spherical and ellipsoidal tumors were inserted into the two phantoms to study the effects of the different voxel sizes on the code results. Inspection of the results pr esented in the table show that the algorithm has a tendency to underestimate the length along the z axis by up to 34%. This is due to the order of the loops in the code as the voxels are being retagged. It is important to note, however, that although the shape of the tumor is changed the volumes are matched successfully. Volume accuracy is much more important for cross organ dose calculations than the shape. The largest error is 0.89% for a spherical tumor of radius 0.5 cm in the ADM. This is not surp rising, as it is expected that the largest error would occur in the smallest tumor inserted in the phantom with the largest voxels. The limitations of the size of the tumors that can be inserted vary with the phantom and depend on voxel size and phantom si ze. The upper bound in tumor size is dictated by how big the tumor can get before it is outside of the body. The lower bound is dictated by the voxel resolution. Tumors that have axis close to the voxel resolution, or volumes that are smaller than 8 vox els cannot successfully be inserted into the voxel phantom. This is due to the tumor volume check utilized to stop the retagging process. This limitation is clearly illustrated i n T able 4 6 for the spherical tumor of 0.15 cm radius.

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91 This small tumor is successfully inserted in the NBF, but its insertion results in large errors in the ADM. This is because the volume of the tumor is the equivalent to approximately 2 voxels in the ADM and its radius is very close to the x y voxel resolution. This tumor is too small to be accurately inserted. On the other hand, the same tumor is the equivalent to 48 voxels in the NBF, which puts it in the reliable range for the algorithm. The time of insertion is proportional to the number of voxels that need to be reta gged. Therefore, it is greatly affected by the size of the tumor being inserted and the size of the voxels in the phantom. Larger tumors take a lot longer than smaller tumors. Similarly, for a given tumor size, it takes longer to insert it in a phantom with smaller voxels than a phantom with larger ones. The longest insertion time is 52 min for a spherical tumor of 2 cm radius, in the NBF. The time of insertion for a tumor of the same size in the ADM is 3.2 min. The voxel volume for the NBF is approxi mately an order of magnitude smaller than that of the ADM. This is a clear example of how voxel size affects insertion time. An example of a tumor insertion in the ADM phantom is shown in F igure 4 5. The figure displays the phantom along the axial, sagit tal and coronal planes through the center of the tumor. This is a 1cm radius spherical tumor in the lung of the ADM. The shape challenges along the z direction of the tumor insertion are evident in the figure. The axis lengths of the voxelized tumor are 0.9474 cm along the x and y directions and 0.6671 cm along the z direction. The volume discrepancy between the theoretical volume and the inserted volume is 0.03%, and the time of insertion is 2.26 minutes.

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92 Therefore, even though the tumor is slightly flattened along the z direction, the location and volume match the selected specifications adequately. Point p air d istance d istribution The point pair distance distribution algorithm is one of the pillars of the dose point kernel method used here. Theref ore, it was essential to test it before using it for dosimetry. The point pair distance distribution has simple known solutions for spherical geometries. The solution of a distribution for a sphere as the source and target was used for verification. A m odel of a voxelized sphere of 20 cm radius and isotropic voxel resolution of 0.6 cm was imported into MATLAB TM to test the algorithm. Equation 4 17 describes the expected result for this geometry. ( 4 17 ) where is the radius of the sphere. The rest of the variables are as previously defined. Figure 4 6 shows a graph of the analytical results (solid line) versus the MATLAB TM results (dashed line). It can be seen that there is r eally good agreement between the two, proving that the algorithm works as expected. Once the proper function of the algorithm was confirmed, it was necessary to determine the number of randoms needed to obtain reliable results. Figure 4 7 shows the result s from this study. The results start converging when at least 1,000,000 randoms are used. Since increasing the number of randoms elongates the computation time, 1,000,000 5,000,000 randoms was deemed sufficient to obtain reliable results without compromi sing the speed of the code. The smoothing filter was selected based on the results shown in Figure 4 8. This graph shows that the only filter that successfully smooths the distribution while keeping

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93 moving average and the lowess options lower the values of the distribution as they smooth the function. The Loess filter, on the other hand, does not successfully smooth the function ; it simply outputs results that follow the unfiltered values. This indi cated that sgolay is the appropriate smoothing function. Once the optimal characteristics for the algorithm were determined, the point pair distance distribution for several organ pairs was calculated. Figure 4 9 shows the results for the NBF and F igure 4 10 shows the results for the ADM. The organ pairs chosen as examples are the left and right kidney cortex to liver, left and right kidney cortex to spleen, pancreas to stomach wall and urinary bladder contents to urinary bladder wall. These organ pairs aim to illustrate the different distribution shapes one can encounter depending on the size, shape and separation of the organs of interest. These distributions present the traits one would expect from the selected organ pairs. The ray length probability distribution for the right kidney cortex to the liver is centered about a shorter ray length than the left kidney cortex to the liver. Since the liver is located on the right side, the distribution reflects the closer proximity to the right kidney. In a similar manner, the left and right kidney to liver distributions are much closer together than those for the spleen. This arises from the fact that the liver is a much larger organ. Therefore, the separation distances between the left kidney cortex and t he liver are much shorter than those between the spleen and the right kidney. Another expected characteristic of the presented results is the larger height of the peak for the urinary bladder contents to wall distribution versus the pancreas to stomach wa ll, for example. The range of ray lengths in the UBC to UBW is much more limited than

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94 that of the pancreas to stomach wall. Therefore, the probability for any of the given ray lengths in the former distribution is higher than that for the latter. There are simply less and NBF results. The main difference between the two sets is that the NBF distributions have much shorter ray lengths due to the smaller size of phantom. Attenuation c oefficients The accuracy of the calculation of the mass attenuation coefficients for the different tissues used in the phantoms was verified by comparing the attenuation coefficients calculated for the ORNL soft tissue and lung to th e attenuation coefficients published on NIST 86 for those same tissues following the ICRU 44 compositions. 85 Although the compositions of the two are slightly different, it gives a sense of how well the algorithm is working and how much of a discrepancy there is between the two sets. Figure 4 11 and T able 4 7 show the results. Both the values of the total linear attenuatio n coefficients and the mass energy absorption coefficients are shown. These two coefficients were selected because they are the ones used in dose point kernel formula. The results show that there is good agreement between the two sets. The higher percen t differences at lower energies are due to the difference in compositions between the ICRU 44 and ORNL tissues. The photoelectric effect is dominant at low energies and it is highly dependent on the atomic number of the tissue. Therefore, even small diff erences in the effective atomic number of the two compositions will result in noticeable differences in the attenuation coefficients at low energies. The effective atomic number for the ICRU44 soft tissue is 7.71, while that of the ORNL soft tissue is 7.5 0. Since a large part of the lung tissue composition is air, the effective atomic

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95 number of the two lung tissues is very similar. The effective atomic number for the ICRU44 lung tissue is 7.74 while that of the ORNL lung tissue is 7.75. Dosimetry calcula tions: homogeneous and heterogeneous cases Two sets of dosimetry calculations using the dose point kernel formulation were performed. The first set was to verify the reliability of the algorithm by calculating the S values to normal organs with both the point kernel algorithm and the MIRD schema and comparing the results of the two. The second set was to explicitly verify the tumor burdened dosimetry capabilities of the software by inserting several tumors into the phantoms, performing dosimetry with the dose point kernel algorithm and comparing the results to MCNPX values for the same scenario. The results of the normal anatomy dosimetry for commonly used radionuclides in nuclear medicine are shown in T able 4 8 for the NBF and in T able 4 9 for the ADM. It can be seen that most of the errors are well below 10%, with the absolute value of the largest error being 8%. The errors in the doses calculated by the point kernel algorithm versus the MCNPX values arise from the simplicity of the deterministic met hod when compared to the thorough particle transport technique of MCNPX. Differences in tissue compositions between the average soft tissue used in this software versus the more complex organ specific tissues utilized in the MCNPX calculations, may also c ontribute to the discrepancies. Nevertheless, even with the simplifications made by this code versus the complete Monte Carlo calculation, the results for most organ pairs are within nte Carlo particle transport compensates the slight increase in uncertainty. Table 4 10 and 4 11 show the average time it took to calculate each S value These times depend on how many bins the point pair distance distribution has for the organ pair of i nterest, as well as how

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96 many photons there are in the radionuclide decay scheme. The more bins and photons there are, the longer the calculation takes. Once the code has calculated the point pair distance distribution for an organ pair, it gets stored an d it does not need to be calculated again. The code is written so that it checks if the distribution already exists in the pertinent folder before it calculates it. Therefore, if several calculations are being performed with different radionuclides but s ame organ pairs, the time of computation diminishes after the first set. This is reflected in T ables 4 10 and 4 11. The total calculation times for all the radionuclides and organ pairs used in the verification process were 5.25 min and 4.07 min for the NBF and ADM phantoms, respectively. The code provides reliable results as long as the organ pair being considered for a given radionuclide has the peak of the point pair distance distribution between 0.15 4.5 MFPs. Organ pairs whose ray lengths fall mos tly below or above that range cannot be properly estimated by this code. This is because the percentage of photons that interact at lengths shorter than 0.15 MFP or that reach lengths above 4.5 MFP is too small to yield reliable dose estimates with the me thodology used here. As seen on the table of results for normal anatomy organs, this does not represent a very large impediment in the range of uses of this code. It mostly becomes an issue when the radionuclide of interest has most of its photon decay e nergies either below 50 keV or above 1.5 MeV. These are extreme cases that are outside the scope of most radionuclides used in nuclear medicine procedures. The next step for verification was to insert tumors in the phantoms and compare the point kernel do simetry results with the results obtained using MCNPX. The majority of these tests were conducted in the ADM phantom. Four different spherical tumors

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97 were modeled separately: a 0.5 cm radius mass in the liver, a 3 cm radius mass in the liver, a 1 cm radi us mass in the lung and a 1 cm radius mass in one of the lumbar vertebra. Each one of these tumors was modeled three different times with different compositions: 100% soft tissue, 50ST 50B and 100% bone. These three locations were chosen because that is where metastatic lesions are most often found. 88 90 Dosimetry was performed with three different radionuclides: F 18, I 131 and Tc 99m. These were selected because they are three of the most commonly used radion uclides in medicine and they expand a wide range of energies (140 keV 511 keV). Tables 4 12 through 4 15 summarize the results. One tumor insertion example was conducted in the NBF phantom to ensure that phantom voxel resolution did not have a detrimen tal effect on the calculation accuracy. A 1 cm radius spherical tumor of soft tissue composition was inserted into the NBF liver. The results are shown in Table 4 16. The errors calculated based on the differences between the MCNPX S values and the S val ues obtained from the point kernel algorithm are shown in Table s 4 12 through 4 16. In order to give a better sense of the quality of the tumor burdened dosimetry results, the percent errors of all the tumor dosimetry examples were binned in intervals of 2% from 10% to +10%. Figure 4 12 shows a histogram plot of this data. This figure shows that most of the results calculated have discrepancies with MCNPX that are within 5%. The largest error encountered in any of the S value s calculated with the do se point kernel algorithm is 10.5 % for all the examples conducted in the ADM phantom and 2.9% for the soft tissue liver tumor in the NBF phantom. The largest error occurs in the results for the tumor in serted in the lumbar vertebra. This is to be

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98 expected as this case displays the highest level of heterogeneity out of all the scenarios modeled. Despite the larger error in the lumbar mass, the results achieved in this code still show really good agreement with MCNP X especially since the total computation time for dosimetry for the longest calculation, from tumor insertion to final results for all three radionuclides, was 10.6 min. These results meet the expectations set for this code; the discrepancies with the MCNPX results are acceptable yet there is a great gain in calculation speed This make s this software a valuable alternative to current dosimetry software packages. Although UFDose only presents three different options for tumor compositions at the moment, implementing more choices would be a simpl e task. Heterogeneity corrections are performed by altering the optical thickness to account for the different materials, but only soft tissue adjusted buildup factors are used in the calculations. Therefore, if the attenuation coefficients are recalcula ted to reflect other tumor compositions, the code will easily be able to handle alternative tissues without any changes to the point kernel algorithm. The electron absorbed fractions for self dose calculations to the tumor were obtained for spheres of 5 di fferent sizes, electron energies between 10 keV and 4 MeV and for the 3 different tumor compositions. The graphs of the results are shown in F igure 4 13 In order to utilize the data obtained through these calculations as efficiently as possible in the s oftware, linear regressions were performed for all the curves. First, the lines of AF as a function of sphere radius for every energy were fit to a cubic polynomial using SigmaPlot. Equation 4 18 shows the general form of this polynomial.

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99 ( 4 18 ) In this case, x is the radius of the sphere in cm, and f(x) is the AF. An equation like this was created for each energy. These fits were highly successful as the r 2 values for all the equations wer e greater than 0.995. Since having separate equations for each energy would still require interpolation to obtain values at intermediate energies, dependent; therefore a polynomial equation as a function of energy for each one of the coefficients was constructed. The coefficients for soft tissue required a 5 order polynomial. The coefficients for the other two tissues were successfully fit using a 4 order polynomial. The general equation for this fit is shown below: ( 4 19 ) where is the n th coefficient in equation 4 18 and E is the electron energy in MeV. This equation is valid for 50ST 50B and 1 00% homogeneous bone, but an extra term with needs to be added when the tumor composition of interest is 100% soft tissue. The values of the c coefficients for these equations are shown in T ables 4 17 through 4 19. These equations can be used to e stimate the electron self AF for a spherical tumor of radius between 0 and 3 cm and for radionuclides with electron decay energies up to 4 MeV. Summary Current dosimetry software packages in nuclear medicine are either too sophisticated for clinical use, d ue to their high demands in computer power and input data, or too simplistic to properly model the patient anatomy and provide reliable results on which to base medical decisions. This code provides a good alternative to the

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100 existing options. It allows t he user to insert tumors of different compositions and sizes in any location of the body, and to perform dosimetry for a wide range of radionuclides and clinical situations. Although the tumor insertion algorithm has the downfall of underestimating the z axis length of the inserted tumor, the volume and location of the lesion are accurately portrayed. Further benchmarking is necessary in phantoms of other sizes, but the good agreement with MCNPX results in the largest (ADM) and smallest (NBF) phantoms av ailable in the software indicate that accuracy should not be an issue in the intermediate phantom sizes. The phantoms available in this software represent ms, the anatomical representation is very realistic. This signifies an enormous improvement from the stylized phantoms used for dosimetry in codes such as OLINDA and MABDOSE. The addition of a cumulated activity algorithm, similar to that available in O LINDA, where the user can input the time activity points obtained from scans, and the code automatically calculates the value, would be a great addition to the software. Furthermore, more organ specific tissue compositions can be added to the software to substitute the current 3 tissue model. This would unlikely yield noticeable changes to the results in soft tissue organ dosimetry, as the benchmarking process was performed against the results of phantoms with organ specific tissue compositions. However, it would still make the model more sophisticated The allowance of heterogeneous activity uptake in the source tissue, as opposed to current assumption of homogeneous distribution in the source, is also a feature that should be added to future versions o f the

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101 code. The addition of a more thorough technique to handle electron dosimetry and the inclusion of alpha particle dosimetry would also enrich the applicability of UFDose. Although there are many improvements left to be made to this software for compl ete versatility for medical use, it is a great development towards providing a more clinic friendly dosimetry software package. The time efficiency of this software and the accuracy of the results demonstrated in this article, make UFDose a good alternati ve tool for dosimetry calculations in standard clinical situations where both time and resources are limited.

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102 Table 4 1. Percent differences between the F 18 S values calculated with the code and those published in the literature for the NBF. TO \ SO Adren als GB cont Ht cont Kidneys Liver Lungs Marrow Pancreas SI cont Spleen St cont Thyroid UB cont Adrenals 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Brain 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Kidneys 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Liver 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Lungs 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Pancreas 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Spleen 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% St wall 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Thyroid 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% UB wall 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Uterus 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Wbody 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

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103 Table 4 2. Percent differences between the I 131 S values calculated with the code and those publi shed in the literature for the NBF. TO \ SO Adrenals GB cont Ht cont Kidneys Liver Lungs Marrow Pancreas SI cont Spleen St cont Thyroid UB cont Adrenals 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Brain 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Kidneys 0% 0% 0% 0 % 0% 0% 0% 0% 0% 0% 0% 0% 0% Liver 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Lungs 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Pancreas 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Spleen 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% St wall 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Thyroid 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% UB wall 0% 0% 1% 0% 0% 1% 0% 0% 0% 0% 0% 1% 0% Uterus 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 1% 0% Wbody 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

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104 Table 4 3. Percent differences between the Tc 99m S values calculated with the code and those published in the literature for the NBF. TO \ SO Adrenals GB cont Ht cont Kidneys Liver Lungs Marrow Pancreas SI cont Spleen St cont Thyroid UB cont Adrenals 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 0% 1% Bra in 0% 0% 1% 0% 0% 1% 1% 0% 0% 0% 0% 1% 0% Kidneys 1% 1% 1% 2% 1% 1% 1% 1% 1% 1% 1% 1% 1% Liver 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% Lungs 1% 1% 1% 1% 1% 2% 1% 1% 1% 1% 1% 1% 1% Pancreas 1% 1% 1% 1% 1% 1% 1% 3% 1% 1% 1% 1% 1% Spleen 1% 1% 1% 1% 1% 1% 1% 1% 1% 2% 1% 1% 1% St wall 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% Thyroid 0% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 5% 0% UB wall 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 2% 1% Uterus 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 1% 0% 0% Wbody 1% 1% 1% 1% 1% 1% 2% 1% 1% 1% 1% 1% 1%

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105 Table 4 4. Voxel information for the University of Florida family of hybrid computational phantoms. Voxel Resolutio n (cm) Number of Voxels Total Matrix Voxel Volume (cc) Phantom X Y Z X Y Z Size ( x 10 6 ) Canine 0.2000 0.2000 0.2000 196 127 550 13.69 8.0E 03 UFH00MF 0.0663 0.0663 0.0663 350 215 720 54.18 2.9E 04 UFH01MF 0.0663 0.0663 0.1400 396 253 550 55.10 6.2E 04 UFH05MF 0.0850 0.0850 0.1928 416 235 576 56.31 1.4E 03 UFH10MF 0.0990 0.0990 0.2425 428 226 580 56.10 2.4E 03 UFH15M 0.1250 0.1250 0.2832 414 226 590 55.20 4.4E 03 UFH15F 0.1200 0.1200 0.2828 410 238 574 56.01 4.1E 03 UFHADM 0.1579 0.1579 0.2207 36 2 195 796 56.19 5.5E 03 UFHADF 0.1260 0.1260 0.2700 390 241 610 57.33 4.3E 03

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106 Table 4 5. Tumor insertion algorithm test results for several tumors inserted in the NBF and ADM phantoms. True Measurements Voxelized Measurements % Difference lengths (cm) Volume (cc) lengths (cm) Volume (cc) Time (min) # of Voxels lengths (cm) Volume (cc) a b c a b c a b c NBF 1 1 1 0.52 0.50 0.50 0.36 0.52 2.4 1796 1% 1% 27% 0.03% 1.0 1.0 1.0 4.19 1.03 1.03 0.70 4.19 8.0 14373 3% 3% 3 0% 0.00% 2.0 2.0 2.0 33.51 2.02 2.02 1.43 33.51 52.0 114984 1% 1% 29% 0.00% 0.5 1.5 1.0 3.14 0.50 1.49 0.70 3.14 5.4 10779 1% 1% 30% 0.01% 1.0 0.5 1.5 3.14 1.03 0.50 1.09 3.14 5.4 10782 3% 1% 27% 0.02% 1.5 1.0 0.5 3.14 1.49 1.03 0.36 3.14 5. 3 10782 1% 3% 27% 0.02% ADM 0.5 0.5 0.5 0.52 0.55 0.55 0.33 0.53 0.1 96 11% 11% 34% 0.89% 1.0 1.0 1.0 4.19 1.03 1.03 0.77 4.19 0.5 761 3% 3% 23% 0.03% 2.0 2.0 2.0 33.51 1.97 1.97 1.43 33.51 3.2 6089 1% 1% 28% 0.02% 3.0 3.0 3 .0 ##### 2.92 2.92 2.10 113.10 10.4 20554 3% 3% 30% 0.00% 0.5 1.5 1.0 3.14 0.55 1.50 0.77 3.15 0.4 570 11% 0% 23% 0.00% 1.0 0.5 1.5 3.14 1.03 0.55 1.21 3.14 0.4 570 3% 11% 19% 0.01% 1.5 1.0 0.5 3.14 1.50 1.03 0.55 3.14 0.4 570 0% 3% 10% 0.16% Table 4 6. Example of the tumor insertion algorithm limitations for tumors that are too small for the voxel resolution of the phantom. True Measurements Voxelized Measurements % Difference lengths (cm) Volume (cc) lengths (cm) Volume (cc) Time (min) # of Voxels lengths (cm) Volume (cc) a b c a b c a b c NBF 0 0 0 0.01 0.17 0.17 0.10 0.01 0.1 48 11% 11% 34% 1.05% ADM 0 0 0 0.01 0.08 0.08 0.11 0.01 0.0 1 47% 47% 26% 61.08%

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107 Table 4 7. Comparison of the attenuation coefficie nts published in NIST and the ones calculated with the dosimetry software package NIST (ICRU 44) Code (ORNL) % Difference Soft tissue Lung Soft tissue Lung Soft tissue Lung Energy (MeV) (1/cm) en (cm 2 /g) (1/cm) en (cm 2 /g) (1/cm) en (cm 2 /g) (1/cm) en (cm 2 /g) (1/cm) en (cm 2 /g) (1/cm) en (cm 2 /g) 0.010 5.59 4.99 1.62 5.07 5.12 4.54 1.62 5.05 8.5% 9.0% 0.0% 0.2% 0.015 1.77 1.40 0.51 1.42 1.63 1.27 0.51 1 .42 7.9% 9.3% 0.1% 0.1% 0.020 0.86 0.57 0.25 0.57 0.80 0.51 0.25 0.57 6.6% 9.3% 0.1% 0.0% 0.030 0.39 0.16 0.11 0.16 0.38 0.15 0.11 0.16 4.1% 9.0% 0.1% 0.2% 0.040 0.28 0.07 0.08 0.07 0.27 0.07 0.08 0.07 2.3% 7.9% 0.0% 0.3% 0.05 0 0.24 0.04 0.07 0.04 0.23 0.04 0.07 0.04 1.3% 6.3% 0.0% 0.2% 0.060 0.21 0.03 0.06 0.03 0.21 0.03 0.06 0.03 0.8% 4.6% 0.1% 0.2% 0.080 0.19 0.03 0.05 0.03 0.19 0.03 0.05 0.03 0.3% 2.1% 0.1% 0.0% 0.100 0.18 0.03 0.05 0.03 0.18 0.0 3 0.05 0.03 0.1% 0.9% 0.1% 0.1% 0.150 0.16 0.03 0.04 0.03 0.16 0.03 0.04 0.03 0.1% 0.1% 0.1% 0.1% 0.200 0.14 0.03 0.04 0.03 0.14 0.03 0.04 0.03 0.2% 0.1% 0.1% 0.1% 0.300 0.12 0.03 0.03 0.03 0.12 0.03 0.03 0.03 0.3% 0.2% 0.2% 0.1% 0.400 0.11 0.03 0.03 0.03 0.11 0.03 0.03 0.03 0.2% 0.2% 0.2% 0.2% 0.500 0.10 0.03 0.03 0.03 0.10 0.03 0.03 0.03 0.2% 0.2% 0.1% 0.2% 0.600 0.09 0.03 0.03 0.03 0.09 0.03 0.03 0.03 0.2% 0.2% 0.1% 0.2% 0.800 0.08 0.03 0.02 0.03 0.08 0.03 0.02 0.03 0.2% 0.3% 0.1% 0.1% 1.000 0.07 0.03 0.02 0.03 0.07 0.03 0.02 0.03 0.2% 0.2% 0.1% 0.1% 1.500 0.06 0.03 0.02 0.03 0.06 0.03 0.02 0.03 0.2% 0.3% 0.1% 0.1% 2.000 0.05 0.03 0.01 0.03 0.05 0.03 0.01 0.03 0.2% 0.2% 0.1% 0.2% 3.000 0.04 0.02 0.01 0.02 0.04 0.02 0.01 0.02 0.1% 0.2% 0.1% 0.1% 4.000 0.04 0.02 0.01 0.02 0.04 0.02 0.01 0.02 0.1% 0.1% 0.1% 0.1%

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108 Table 4 8. Percent differences in S values calculated with the point kernel algorithm a nd MCNPX in the NBF. Source Target Au 195m C 11 F 18 Ga 67 I 123 I 131 In 111 Ir 191m Kr 81m N 13 O 15 Rb 82 Ta 178 Tc 99m Tl 201 Xe 133 Liver Spleen 1% 0% 0% 1% 3% 1% 0% 1% 3% 0% 0% 0% 5% 0% 2% 3% Pancreas St W 1% 2% 2% 3% 2% 0% 0% 0% 0% 2% 2% 2 % 5% 1% 1% 0% St W Liver 1% 1% 1% 0% 2% 1% 2% 5% 0% 1% 1% 2% 8% 1% 3% 6% St W Spleen 1% 2% 2% 3% 3% 0% 0% 1% 0% 2% 2% 2% 4% 1% 2% 1% H t C H t W 5% 3% 3% 8% 5% 2% 3% 8% 3% 3% 3% 2% 0% 2% 9% 2% GBW St W 0% 2% 2% 1% 2% 0% 0% 1% 0% 2% 2% 2% 5% 1% 0% 2% St C St W 2% 2% 2% 1% 6% 1% 3% 2% 1% 2% 2% 1% 2% 1% 4% 4% GBC GBW 2% 0% 0% 8% 6% 1% 3% 4% 1% 0% 0% 1% 4% 0% 1% 1% UBC UBW 2% 1% 1% 2% 2% 1% 0% 1% 1% 1% 1% 1% 2% 0% 4% 3% Table 4 9. Percent differences in S v alues calculated with the point kernel algorithm and MCNPX in the ADM Source Target Au 195m C 11 F 18 Ga 67 I 123 I 131 In 111 Ir 191m Kr 81m N 13 O 15 Rb 82 Ta 178 Tc 99m Tl 201 Xe 133 Liver Spleen 6% 6% 6% 4% 5% 4% 6% 3% 7% 6% 6% 5% 5% 5% 6% 5% Pancreas St W 2% 1% 1% 1% 1 % 0% 1% 2% 1% 1% 1% 1% 1% 0% 4% 0% St W Liver 3% 2% 2% 1% 1% 1% 2% 0% 3% 2% 2% 2% 0% 2% 3% 3% St W Spleen 1% 1% 1% 1% 3% 1% 0% 1% 1% 1% 1% 0% 2% 1% 4% 5% Ht C Ht W 3% 3% 3% 4% 4% 3% 5% 2% 2% 3% 3% 3% 2% 3% 3% 1% GBW St W 1% 0% 0% 1% 2% 2% 0% 1% 0% 0% 0% 0% 2% 1% 1% 3% St C St W 0% 0% 0% 1% 1% 0% 1% 0% 1% 0% 0% 0% 0% 0% 2% 0% GBC GBW 1% 1% 1% 8% 4% 2% 3% 6% 1% 1% 1% 0% 2% 3% 4% 0% UBC UBW 2% 1% 1% 1% 3% 1% 2% 3% 1% 1% 1% 1% 2% 2% 4% 2%

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109 Table 4 10. Calculation time (in seconds) for every organ pair S value in the NBF Source Target Au 195m C 11 F 18 Ga 67 I 123 I 131 In 111 Ir 191m Kr 81m N 13 O 15 Rb 82 Ta 178 Tc 99m Tl 201 Xe 133 Liver Spleen 2.24 0.10 0.10 1.05 5.92 3.23 1.22 1.98 0.30 0.10 0.10 4.98 4.48 1.91 2.44 1.83 Panc reas St W 3.25 0.10 0.10 1.14 5.92 3.24 1.26 2.84 0.76 0.10 0.10 5.22 5.09 2.62 3.48 1.85 St W Liver 4.65 0.18 0.18 1.88 10.13 5.53 2.12 4.18 0.85 0.18 0.18 8.72 8.25 3.62 5.00 3.16 St W Spleen 3.52 0.12 0.12 1.29 6.83 3.73 1.46 3.12 0.77 0.12 0.12 5.96 5.81 2.97 3.80 2.13 Ht C Ht W 2.63 0.07 0.07 0.80 4.02 2.21 0.86 2.27 0.72 0.07 0.07 3.65 3.68 1.79 2.83 1.28 GBW St W 3.56 0.12 0.12 1.30 6.83 3.74 1.46 3.15 0.78 0.12 0.12 5.98 5.79 2.94 3.83 2.14 St C St W 3.06 0.09 0.09 1.03 5.32 2.92 1.13 2.68 0.75 0.09 0.09 4.73 4.66 2.29 3.28 1.68 GBC GBW 2.20 0.05 0.05 0.59 2.81 1.55 0.60 1.87 0.69 0.05 0.05 2.67 2.75 1.21 2.33 0.91 UBC UBW 2.34 0.06 0.06 0.65 3.20 1.77 0.69 2.00 0.70 0.06 0.06 3.01 3.06 1.39 2.52 1.02 Table 4 11. Calculation time (in second s) for every organ pair S value in the ADM. Source Target Au 195m C 11 F 18 Ga 67 I 123 I 131 In 111 Ir 191m Kr 81m N 13 O 15 Rb 82 Ta 178 Tc 99m Tl 201 Xe 133 Liver Spleen 1.81 0.09 0.09 0.95 4.76 2.44 0.45 1.68 0.14 0.09 0.09 4.38 4.02 0.71 1.83 1.28 Pancreas St W 2.71 0.12 0.12 1.25 6.94 3.81 1.07 2.46 0.36 0.12 0.12 5.90 5.38 1.76 2.97 2.23 St W Liver 2.44 0.11 0.11 1.17 6.00 3.15 0.74 2.23 0.29 0.11 0.11 5.45 5.01 1.30 2.56 1.72 St W Spleen 1.63 0.07 0.07 0.73 3.98 2.18 0.62 1.48 0.24 0.07 0.07 3. 38 3.13 1.03 1.77 1.28 Ht C Ht W 1.74 0.07 0.07 0.77 4.17 2.29 0.66 1.58 0.26 0.07 0.07 3.55 3.33 1.09 1.90 1.34 GBW St W 3.15 0.15 0.15 1.53 8.11 4.35 1.06 2.89 0.36 0.15 0.15 7.19 6.54 1.81 3.36 2.47 St C St W 1.39 0.05 0.06 0.57 3.11 1.71 0.64 1.24 0 .24 0.05 0.05 2.66 2.50 1.03 1.53 0.99 GBC GBW 1.72 0.06 0.06 0.67 3.60 1.97 0.77 1.53 0.34 0.06 0.06 3.11 2.96 1.45 1.90 1.15 UBC UBW 1.75 0.06 0.07 0.69 3.71 2.02 0.79 1.57 0.34 0.07 0.06 3.19 3.04 1.46 1.94 1.18

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110 Table 4 12. Dosimetry results for a 0.5cm radius spherical tumor of different compositions inserted in the ADM liver. S Value (mGy/MBq s) Source: Tumor MCNP Matlab % Difference Target I 131 F 18 Tc 99m I 131 F 18 Tc 99m I 131 F 18 Tc 99m 100% Bone GBW 7.66E 06 1.92E 05 2.65E 06 7.64E 06 1.93E 05 2.68E 06 0.2% 0.6% 1.4% Liver 7.37E 06 1.86E 05 2.56E 06 7.66E 06 1.94E 05 2.69E 06 3.9% 4.2% 5.2% Spleen 4.89E 07 1.23E 06 1.85E 07 4.86E 07 1.25E 06 1.77E 07 0.7% 1.5% 4.3% St W 1.03E 06 2.56E 06 3.93E 07 1. 05E 06 2.70E 06 4.14E 07 2.9% 5.5% 5.5% 50ST 50B GBW 7.66E 06 1.92E 05 2.65E 06 7.64E 06 1.93E 05 2.68E 06 0.3% 0.5% 1.2% Liver 7.38E 06 1.86E 05 2.57E 06 7.66E 06 1.94E 05 2.69E 06 3.9% 4.2% 4.6% Spleen 4.89E 07 1.23E 06 1.85E 07 4.86E 07 1.25E 06 1.77E 07 0.7% 1.6% 4.3% St W 1.03E 06 2.56E 06 3.93E 07 1.00E 06 2.57E 06 3.93E 07 2.3% 0.2% 0.2% 100% Soft Tissue GBW 7.67E 06 1.92E 05 2.66E 06 7.67E 06 1.94E 05 2.69E 06 0.1% 1.0% 1.2% Liver 7.38E 06 1.86E 0 5 2.60E 06 7.63E 06 1.93E 05 2.68E 06 3.4% 3.8% 3.2% Spleen 4.89E 07 1.23E 06 1.85E 07 4.86E 07 1.25E 06 1.77E 07 0.7% 1.5% 4.4% St W 1.03E 06 2.56E 06 3.93E 07 1.06E 06 2.71E 06 4.16E 07 3.2% 5.8% 5.8%

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111 Table 4 13. Dosimetry results for a 3cm radius spherical tumor of different compositions inserted in the ADM liver. S Value (mGy/MBq s) Source: Tumor MCNP Matlab % Difference Target I 131 F 18 Tc 99m I 131 F 18 Tc 99m I 131 F 18 Tc 99m 100% Bone GBW 7.06E 06 1.79E 05 2.39E 06 7.08E 06 1.80E 05 2.52E 06 0.3% 0.7% 5.4% Liver 5.16E 06 1.30E 05 1.80E 06 5.33E 06 1.35E 05 1.91E 06 3.4% 3.9% 6.0% Spleen 4.95E 07 1.25E 06 1.85E 07 4.83E 07 1.25E 06 1.74E 07 2.5% 0.2% 6.0% St W 1.05E 06 2.65E 06 3.95E 07 1.00 E 06 2.57E 06 3.85E 07 4.9% 2.9% 2.6% 50ST 50B GBW 7.07E 06 1.78E 05 2.41E 06 7.14E 06 1.81E 05 2.52E 06 1.0% 1.5% 4.3% Liver 5.17E 06 1.30E 05 1.82E 06 5.33E 06 1.35E 05 1.91E 06 3.2% 3.9% 4.8% Spleen 4.95E 07 1.25E 06 1.86E 07 4.90E 07 1.26E 06 1.78E 07 1.1% 1.4% 4.3% St W 1.05E 06 2.65E 06 3.99E 07 1.02E 06 2.61E 06 3.95E 07 3.2% 1.3% 1.0% 100% Soft Tissue GBW 7.11E 06 1.79E 05 2.47E 06 7.55E 06 1.91E 05 2.65E 06 6.2% 6.9% 7.3% Liver 5.19E 06 1.30E 05 1.86E 06 5.33E 06 1.35E 05 1.91E 06 2.6% 3.7% 2.6% Spleen 4.96E 07 1.25E 06 1.88E 07 4.90E 07 1.26E 06 1.79E 07 1.1% 1.5% 4.6% St W 1.05E 06 2.64E 06 4.03E 07 1.03E 06 2.64E 06 4.02E 07 2.3% 0.3% 0.4%

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112 Table 4 14. Dosimetry results for a 1cm radius spherical tumor of different compositions inserted in the ADM lung. S Value (mGy/MBq s) Source: Tumor MCNP Matlab % Difference Target I 131 F 18 Tc 99m I 131 F 18 Tc 99m I 131 F 18 Tc 99m 100% Bone GBW 3.83E 07 9.2 5E 07 1.29E 07 3.62E 07 9.29E 07 1.37E 07 5.3% 0.5% 6.2% Liver 9.26E 07 2.31E 06 3.46E 07 8.84E 07 2.26E 06 3.47E 07 4.5% 2.3% 0.3% Spleen 2.31E 07 5.90E 07 8.02E 08 2.34E 07 6.09E 07 7.93E 08 1.0% 3.2% 1.1% St W 2.64E 07 6.76E 07 9.24E 08 2.58E 07 6.70E 07 8.93E 08 2.5% 0.8% 3.4% 50ST 50B GBW 3.82E 07 9.25E 07 1.29E 07 3.63E 07 9.30E 07 1.37E 07 5.0% 0.6% 6.2% Liver 9.26E 07 2.31E 06 3.46E 07 8.79E 07 2.25E 06 3.45E 07 5.1% 2.8% 0.4% Spleen 2.31E 07 5.90E 07 8.03E 08 2.33E 07 6.09E 07 7.92E 08 0.9% 3.1% 1.3% St W 2.64E 07 6.75E 07 9.25E 08 2.58E 07 6.70E 07 8.93E 08 2.4% 0.7% 3.5% 100% Soft Tissue GBW 3.82E 07 9.25E 07 1.29E 07 3.63E 07 9.31E 07 1.38E 07 4.9% 0.7% 6.3% Liver 9.27E 07 2.31E 06 3.47E 07 8.84E 07 2.26E 06 3.47E 07 4.6% 2.3% 0.1% Spleen 2.31E 07 5.89E 07 8.04E 08 2.33E 07 6.09E 07 7.92E 08 1.0% 3.3% 1.5% St W 2.64E 07 6.75E 07 9.26E 08 2.58E 07 6.70E 07 8.93E 08 2.4% 0.8% 3.6%

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113 Table 4 15. Dosim etry results for a 1cm radius spherical tumor of different compositions inserted in the ADM lumbar vertebra. S Value (mGy/MBq s) Source: Tumor MCNP Matlab % Difference Target I 131 F 18 Tc 99m I 131 F 18 Tc 99m I 131 F 18 Tc 99m 100 % Bone GBW 3.25E 06 8.09E 06 1.22E 06 2.91E 06 7.37E 06 1.10E 06 10.5% 8.9% 9.1% Liver 1.16E 06 2.91E 06 4.43E 07 1.21E 06 3.09E 06 4.76E 07 3.8% 6.4% 7.6% Spleen 1.22E 06 3.10E 06 4.60E 07 1.22E 06 3.14E 06 4.87E 07 0.6% 1.3% 6.0% St W 1.3 0E 06 3.27E 06 4.92E 07 1.27E 06 3.25E 06 5.00E 07 2.3% 0.4% 1.5% 50ST 50B GBW 3.25E 06 8.10E 06 1.22E 06 2.91E 06 7.37E 06 1.10E 06 10.5% 8.9% 9.3% Liver 1.16E 06 2.90E 06 4.43E 07 1.14E 06 2.93E 06 4.51E 07 1.8% 0.7% 1.7% S pleen 1.22E 06 3.09E 06 4.61E 07 1.22E 06 3.14E 06 4.89E 07 0.4% 1.5% 6.1% St W 1.30E 06 3.27E 06 4.93E 07 1.28E 06 3.27E 06 5.02E 07 1.8% 0.1% 1.9% 100% Soft Tissue GBW 3.25E 06 8.09E 06 1.22E 06 2.91E 06 7.38E 06 1.10E 06 10.5% 8.8% 9.6% Liver 1.16E 06 2.90E 06 4.44E 07 1.14E 06 2.93E 06 4.51E 07 1.7% 0.9% 1.6% Spleen 1.22E 06 3.09E 06 4.61E 07 1.22E 06 3.15E 06 4.90E 07 0.2% 1.7% 6.2% St W 1.30E 06 3.26E 06 4.94E 07 1.27E 06 3.25E 06 4.99E 07 2.6% 0.5% 1.0%

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114 Table 4 16. Dosimetry results for a 1cm radius spherical tumor of soft tissue inserted in the NBF liver. S Value (mGy/MBq s) Source: Tumor MCNP Matlab % Difference Target I 131 F 18 Tc 99m I 131 F 18 Tc 99m I 131 F 18 Tc 99m 10 0% Soft Tissue GBW 2.57E 05 6.59E 05 8.36E 06 2.61E 05 6.78E 05 8.34E 06 1.4% 2.9% 0.3% Liver 3.11E 05 7.94E 05 1.03E 05 3.15E 05 8.14E 05 1.04E 05 1.1% 2.5% 0.9% Spleen 2.14E 06 5.50E 06 7.07E 07 2.18E 06 5.39E 06 7.02E 07 1.9% 1.9% 0.6% St W 4.91E 06 1.26E 05 1.62E 06 4.84E 06 1.24E 05 1.61E 06 1.2% 1.1% 0.6%

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115 Table 4 17. 100% Soft tissue coefficients of the regression line for electron self AF in spherical tumors b 0 b 1 b 2 b 3 c 0 0.98224 0.02199 0.01079 0.00182 c 1 0.41263 0 .50733 0.24946 0.04216 c 2 1.87756 2.31582 1.14032 0.19289 c 3 1.21992 1.50451 0.74045 0.12519 c 4 0.31556 0.37727 0.18252 0.03054 c 5 0.02933 0.03393 0.01609 0.00266 r 0.99752 0.99596 0.99516 0.99484 Table 4 18. 50ST 50B coefficients of the regression line for electron self AF in spherical tumors b 0 b 1 b 2 b 3 c 0 1.01098 0.01253 0.00598 0.00099 c 1 0.31771 0.37724 0.18165 0.03032 c 2 0.30772 0.42069 0.21858 0.03813 c 3 0.14036 0.20831 0.11204 0.01991 c 4 0.01538 0.02314 0.01 257 0.00225 r 0.99982 0.99977 0.99975 0.99974 Table 4 19. 100% homogeneous bone coefficients of the regression line for electron self AF in spherical tumors b 0 b 1 b 2 b 3 c 0 1.01038 0.01218 0.00594 0.00100 c 1 0.29342 0.35588 0.17330 0.029 12 c 2 0.24740 0.32426 0.16537 0.02857 c 3 0.10515 0.14836 0.07812 0.01373 c 4 0.01083 0.01516 0.00798 0.00141 r 0.99981 0.99975 0.99971 0.99969

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116 Figure 4 1. Tri axial ellipse: geometric representation of the tumors inserted in the cod e. Coronal, sagittal and axial slices of the ellipse are shown. Figure 4 2. Possible phantom slice display for selection of the tumor center in the future GUI for the dosimetry software.

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117 Figure 4 3. Comparison of the attenuation coefficients for t issues composed of A) 50%Soft Tissue 50%Cortical Bone and B) 50%Soft Tissue 50%Homogeneous Bone. Figure 4 4. Example of the rectangular volume formed using the initial and final indices of the voxels forming the longest ray.

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118 Figure 4 5. Three slices through the center of a 1 cm radius spherical tumor inserted in the lung of the ADM phantom.

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119 Figure 4 6. Verification of the point pair distance distribution algorithm with the analytical solution for a spherical regi on acting both as the source and target regions.

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120 Figure 4 7. Change in the shape of the point pair distance distribution for a sphere with increasing number of random rays modeled.

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121 Figure 4 8. Graph demonstrating the effects of the different smoothing algorithms applied to the point pair distance distribution results.

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122 Figure 4 9. Examples of point pair distance distribution results for the NBF: A distribution for the left and r ight kidney cortex to Liver, B distribution of the pancreas to stomach wall, C distribution of the left and right kidney cortex to Spleen, D Urinary bladder contents to urinary bladder wall.

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123 Figure 4 10. Examples of point pair distance distribution r esults for the ADM: A distribution for the left and right kidney cortex to Liver, B distribution of the pancreas to stomach wall, C distribution of the left and right kidney cortex to Spleen, D Urinary bladder contents to urinary bladder wall.

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124 Figure 4 11. Comparison of the results from the linear attenuation coefficients calculated with MATLAB TM to the coefficients published by NIST for the same tissues with the ICRU44 compositions.

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125 Figure 4 12 Histogram of t he distribution of percent errors in all tumor burdened anatomy dosimetry results.

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126 Figure 4 1 3 Plots of the AF as a function of energy for spherical tumors of different radius and compositions : A) Soft Tissue, B ) 50ST 50B and C) Bone

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127 CHAPTER 5 BUIL DUP FACTORS Background As radiation travels through a medium and it interacts with it, the fluence in that medium can be viewed as having a scattered and an unscattered radiation component. Buildup factors are defined as the ratio of the total dose versus the unscattered radiation dose. This quantity is most commonly used in shielding applications. 87 Therefore the available build up factor d ata is often geared towards engineering materials rather than biological tissues. 91 Equation 5 1 shows how buildup factors are calculated for monoenergetic photon sources. As seen in the equation, buildup factors are not only dependent on the energy of the photons and the medium being considered, but also the response of interest. The response function relates the response of interest, absorbed dose, exposure, etc. to the fluence in the field. ( 5 1 ) where is the buildup factor as a function of distance, r unscattered fluence component at r, is the scattered fluence at r for energy E, and is the response function. is the energy of the monoenergetic photon source. Buildup factors for isotropic point sources of monoenergetic photons are commonly listed as a function of optical thickness. The optical thickness is the number of Mean Free Paths (MFP) a photon travels between the source and target points. A MFP represents the distance that a photon will travel before it interacts in the medium and it is calculated by taking the reciprocal of the total linear attenuation coefficient of the photon for a given energy in a given medium. The more MFPs there are between

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128 the source point and the target, the less likely it is that a photon will reach it. Build up tables for a given response, in a specific medium, are presented as a function of en ergy and mean free paths. Through the years, the calculation of buildup factors has evolved from its beginnings, when only buildup from Compton scattered photons was taken into account and the calculations were performed based on the moments method, to the current calculations, which include not only Compton scattered photons, but annihilation, fluorescence and bremsstrahlung photons as well. 87, 91 To this date, the most popular buildup data is found in the ANSI/ANS 6.4.3 report. 9 1 This document compiles exposure and energy absorption buildup factor tables for several elements, as well as concrete, water and air. The buildup factors for concrete, iron, water, air and Be, B, C, N, O, Na, Mg, Al, Si, P, S, Ar, K, Ca and Cu in this document were cal culated based on moments method calculations. They do not include coherent scattering or bremsstrahlung, and they assume free electron Compton scattering. The buildup factors for Mo, Sn, La, Gd, W, Pb and U were calculated using the PALLAS code. This co de correctly models the Klein Nishina equation and it accounts for all secondary radiations, including bremsstrahlung. The report also provides the fitting parameters for two empirical approximations for buildup factors: the Taylor approximation and the Geometric Progression approximation. There are other parameterizations available for buildup data 9 2 but they are not presented i n this report.. They are simpler than the Geometric Progression approximation, but less accurate. 87

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129 The use of parameterized formulas for buildup calculations can lead to more time efficient computation. Interpolation algorithms can slow down calculation times. When buildup factors are determined using look up tables, oftentimes both energy and optical thickness interpolation is needed to obtain the factor for the characteristics at hand. When using parameterized formulas, on the other hand, the only interpolation needed for the calculations is the energy interpolation to obtain the fitting parameters of interest. These parameters are tab ulated at standard energy indices. Therefore, if the energy being considered does not match the listed values, interpolation needs to be performed. However, no length interpolation is ever necessary as the empirical fits are functions of optical thicknes s Hence the d ecreased number of interpolations can lead to shorter computing times. Unfortunately, the use of parameterized equations is not always an option due to the limited amount materials for which these values are available. There are articles i n the literature that provide interpolation methods to estimate these fitting parameters for other tissues based on the ir equivalent atomic numbers 9 2 9 3 but this extra interpolation only introduces further uncert ainty into the calculations. The component of energy deposited in a tissue by scattered radiation can be very significant depending on both the photon energy and the medium. Buildup factors account for this phenomenon in point kernel calculations and the ir accuracy is very important if the dosimetry results are to be reliable. For these reasons, a new set of buildup factors for the body tissues was created. This chapter describes how the infinite medium, isotropic point source values for monoenergetic ph otons were generated, as well as the adjusted soft tissue build up factors used for dosimetry calculations.

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130 Materials and Methods The goal of this work was to generate energy absorption build up factor tables for soft tissue, homogeneous bone and a 50% so ft tissue 50% homogeneous bone (50ST 50B) mixture. These three materials were selected because they are useful in internal dosimetry calculations for both normal and tumor burdened anatomy. The soft tissue and homogeneous bone compositions were obtained from the TM 8381 v1 ORNL report. 30 These values represent the average compositions for adult humans The 50ST 50B was chosen to have a more complete representation of the possible tumor compositions encountered in cancer patients. Tumor compositions vary depending on disease type. They can range between 100% soft tissue masses to 100% bone. In order to cover the composition range appropriately, the 50ST 50B tissue was selected as a middle point in the range. Buildup factors for all three tissues were calculated in order to study the differences between them. Lung tissue buildup factors were not cal culated because their mass attenuation coefficient values are very close as shown in F igure 5 1. 86 Therefore, the soft tissue values can be applied to lung by just performing a density correction. 87 factors, is composed of values calculated for an infinite medium composition of each of the three tissue types presented above. The second set, Phantom Adjusted Buildup (PAB) factors, is composed of the buildup factors necessary to accurately calculate doses using the dose point kernel te chnique presented in Chapter 4 These buildup fact ors were empirically adjusted to take into account the finite nature of the human anatomy. PAB factors for soft tissue in the NBF and ADM phantoms were constructed to account for the variation in anatomical size with age. Adjusted build up factors for

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131 ho mogeneous bone and 50ST 50B were not developed because dose calculations in heterogeneous medium are all performed using solely the soft tissue values, as detailed in C hapter 4. Appendix C shows the MCNP and M ATLAB TM inputs used in these calculations. Bas ic Factors homogeneous medium geometry in MCNPX and using the results of these runs to estimate the integral shown in equation 5 1. The response function used for these calc ulations is the absorbed dose response function shown below: ( 5 2 ) where is a constant to convert the units to Gy cm 2 is photon energy in MeV, and is the mass energy absorption coefficient for the medium at energy E. The continuous integral in equation 5 1 was converted to a discrete sum to allow for the use of the MCNP results. This equation, as displayed below, gives the buildup factor for a given energy at a given distance and it requires fluence values as a function of energy fo r every distance. ( 5 3 ) where n denotes the number of energy bins in the discretized form from 0 to The rest of the terms are as defined above.

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132 Energy dependent fluence values w ere obtained by modeling a large sphere of the tissue of interest, with a set of thin concentric shells centered at the origin around an chosen to be sufficiently lar ge that a photon of the energy being modeled would see it as infinite. This was determined based on the mean free path for a photon of that energy in that medium. The radii of the concentric shells were also determined based on the MFP. The values of MF Ps used in these calculations were selected based on the fraction of photons reaching each distance and the physical distance each mean free path represents. The percentage of photons that reach distances longer than 6 MFP is negligible, and the data calc ulated above that range is unreliable as it is difficult to obtain good statistics for the results in this geometry. Table 5 1 shows the 14 MFP values selected, the percent of photons that reach each length and the equivalent distances in centimeters in e ach one of the three tissues for a 15 keV and a 4 MeV photon. Spherical shells of 0.001 cm thickness were modeled at each MFP. Figure 5 2 illustrates the geometry used for buildup calculations. An MCNPX input was created for every photon energy and tis sue type. A total of 20 energies were modeled between 15 keV and 4 MeV. Table 5 2 shows these energy indices. This energy range was chosen because buildup below 15 keV is negligible, and photon energies above 4 MeV are infrequently seen in nuclear medic ine and radionuclide therapy The energy values to be modeled within that range were chosen based on the standard energy indices utilized in the ANSI/ANS 6.4.3 document. 92 The MFP values and energy range used in the buildup runs are not the standard values u sually seen in buildup calculations. Buildup calculations are often performed for

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133 shielding purposes; thus, the mean free path values and photon energies of interest for those applications can be much larger and are outside of the useful range for interna l dosimetry calculations in human phantoms. A fluence tally, represented by f4 in MCNP, was set at each spherical shell and binned by energy. Binning the results of the fluence tallies by energy allowed for the approximation of the integral shown in equat ion 5 1 as a sum of discrete elements (equation 5 3). The thicknesses of the energy bins were selected to be thin enough to accurately approximate the integral yet thick enough to obtain good statistics on the Monte Carlo runs without having to model an u nreasonable amount of particles. The number of energy bins and their thickness was determined based on the energy of the source. The amount of particles modeled depended on the photon energy and it varied between 10 7 10 9 particles. The secondary electro n energy indexing algorithm used was the Integrated TIGER Series (ITS). The physics mode selected was the default physics photon and electron mode. This mode models coherent scattering, therefore, the values of the buildup factors obtained in this study include coherent scattering, as opposed to the values previously published in the literature. 92 Once the fluence values for every energy bin at each MFP were obtained, they had to be multiplied by the corresponding response function. The dose response functio ns for each bin were calculated as shown in equation 5 2 and using the lower bound of each energy bin to represent the overall bin energy. Adjusted Soft Tissue Factors The dominating medium in the human body is soft tissue. Since human anatomy is finite i n dimension the basic buildup factors calculated in an infinite soft tissue medium cannot be directly applied to human phantoms without making size dependent

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134 corrections Therefore, correction factors to account for the limited size of human anatomy had to be developed and applied to the infinite medium build up factors. Since buildup for a given medium has a strong dependence on photon energy and optical thickness it stands to reason that the correction factors would display those same traits. The meth odology for their construction was developed based on this assumption. The delta values for the decay spectrum of all the radionuclides in the software were calculated and binned by energy following the 20 energy in dices utilized for buildup ( T able 5 2 ). Delta is calculated as the product of the photon decay energy times its yield (the probability of emission during decay). This value gives a sense of how much influence a given photon emission has in the overall dose imparted by the radionuclide. The ca lculation and binning of all the delta values in the decay spectrum allow for the determination of what the deltas from each energy bin contributed to the overall percentage of the decay. This data was used to decide what radionuclides should be used to r epresent each bin when creating the correction factors. Radionuclides with energy bins containing 90% or more of the total delta in a single bin were selected when available. For example, Tc 99m was one of the radionuclides selected to represent the 100 150 keV bin. Its main emission is a 140 keV photon, therefore, 98.8% of the total overall delta for this radionuclide was found in that bin. If none of the radionuclides included in the software displayed at least 90% of the delta values in the bin of i nterest, the radionuclides with the highest delta percentage in that bin were used instead. Once the radionuclides of interest for each energy bin were identified, dosimetry calculations for normal anatomy organ pairs were performed using both the point kernel

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135 and MIRD methods. The Newborn Female Phantom (NBF) and Adult Male phantom (ADM) were chosen for this calculation because they represent the end points of the phantom size spectrum available in the software; any phantom size dependence will be made evident by studying these two models. The organ pairs chosen for the calculation were all located in the abdomen to avoid heterogeneity issues in the medium. Large differences in the tissue compositions in the volume of interest could have produced artif acts in the values chosen as correction factors due to differences in interaction coefficients. Therefore, this issue was avoided as much as possible. Each organ pair was selected to cover a wide range of organ separations to allow the MFP dependence to s how in the results. The point pair distance distribution was used to determine which organ pair to use to represent a specific MFP. Figure 5 3 shows the point pair distance distributions of some of the organ pairs and the equivalent MFP value they repres ent for Tc 99m. The peak of the distribution was used to determine what MFP influenced the dosimetry for each organ pair the most. The correction factors were empirically determined by comparing the MIRD and point kernel results. The correction factors were adjusted until the discrepancies in the results were minimized. Acceptable errors were below 10%. Since the correction factors were constructed comparing the doses of organs in the abdomen, tissue composition diffe rences should not be prominent. H owever, these might still have a slight effect on the results. The SAF tables used in the MIRD dosimetry to calculate absorbed doses were obtained from the MCNP calculations performed by Michael Wayson The phantoms used in these runs have organ specific tissue compositions instead of the generic soft tissue composition utilized in the point kernel calculations.

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136 Therefore, the small differences in the compositions of soft tissue organs in the abdomen explicitly modeled for the MIRD results may have affect ed the correction values slightly. As a result the correction factors are mostly to adjust for the difference between infinite medium and finite size phantoms, but they may also account for minor elemental composition differences in the soft tissue organ s of the abdomen. Results and Discussion Basic Factors Tables 5 3 through 5 5 show the buildup factors for the three tissues calculated in this study The trends are as expected. The longer the MFP value, the higher the secondary photon buildup. At lo nger distances, there are less unscattered photons present, as most of them have already had at least one interaction along the way. Therefore, the scattered component is much larger than that of the unscattered photons and the buildup factor increases. For a fixed MFP value, the buildup values increase with energy, reach a peak, and then decrease as energy continues to increase. This is due to the dominance of different interactions along the energy range. At low energies, the photoelectric effect is most prominent and the number of scattered photons in the field is not as large. In the middle of the energy range, Compton scatter is the dominant effect, therefore the scattered component is much larger and the buildup factors increase. At high energie s, the pair production cross section starts to increase, which results in a decrease in the buildup factor values. Figure 5 4 shows a 3D rendition of the buildup factors in soft tissue as a function of MFP and photon energy. The buildup factor trends, whe n looking at the different tissues, also behave as expected. Tissues with higher effective atomic number have lower buildup values at

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137 lower energies. The photoelectric effect is dominant at low energies and it rapidly increases with Z. Hence, the number of scattered photons present at low energies decreases with increasing effective atomic number, which makes the buildup smaller. As the energy increases, the effect of the effective atomic number on the interaction cross section for each tissue becomes l ess noticeable and the buildup factors converge. Figure 5 5 compares the buildup factor curves for the three different tissues at 1, 2 and 3MFP. Bone (blue lines) is the tissue with the highest effective atomic number and soft tissue (black lines) has th e lowest. As seen in the figure, the curves display the expected characteristics. Adjusted Soft Tissue Factors The correction factors for the NBF and ADM are shown in T ables 5 6 and 5 7, respectively. The adjustment factors for the NBF phantom are smal ler than that of the ADM. This is to be expected since the NBF phantom is much smaller than the ADM. The infinite medium buildup factors are a better approximation, and therefore need fewer adjustments, for the ADM than for the smaller NBF. Not all the values shown on the two tables were explicitly derived as explained in the methods section. Certain ray lengths are rarely encountered in the human phantoms. The factors for lengths that are either too short or too long were inferred from the calculated values. The point pair distributions for the organs found in the human phantoms only cover a limited range of distances. Therefore, the adjustment factors for the really short distances encountered at short MFP values for low energies, and the long dist ances for long MFP at higher energies, could not be determined using the established methodology. They were inferred from the available data. Similarly, the factors for energies below 40 keV and above 1.5 MeV are also determined based on the

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138 trends of th e existing data. The dose point kernel technique has limited accuracy at those energy ranges. Since the adjustment factors are determined by comparing the normal anatomy doses obtained with MIRD to the doses obtained with the point kernel, the limited re liability of the values at those energy ranges energies did not allow the proper determination of the adjustment factors. Although it would be ideal to have exact factors throughout the complete energy and MFP range, the current factors cover the necessar y values for standard human internal dosimetry calculations and yield accurate results using the dose point kernel technique, as shown in C hapter 4. The adjustment factors at short MFP for most of the energies studied have values above 1. This was unfore seen at the beginning of this work, but it may be due to the slight differences in the elemental composition of soft tissue organs embedded in data used in the MIRD dose calculations versus the standard soft tissue material assumed for all soft tissue orga ns in the point kernel method. Figures 5 6 and 5 7 show the PAB factors for different MFP for the NBF and ADM, respectively. It is evident that the shapes for the PAB factors are different for the two phantoms. This may present a problem when trying t o interpolate between the two to obtain the factors for phantoms sizes in between. However, this has not yet been verified so no assumptions should be made until further testing. Summary Buildup factors provide very important information regarding dosime try calculations. Three new sets of buildup factors for infinite media of soft tissue, homogeneous bone and 50ST 50B were presented. The M C N P studies provided results that follow the trends previously observed in published values for engineering material s. Furthermore, this article introduced the concept of Phantom Adjusted

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139 Buildup factors. These factors produce accurate dosimetry estimates when utilize d as part of the point kernel method. They are tailored to the finite sizes of the human phantoms uti lized in internal dosimetry. These factors are not constructed to be phantom specific, but rather phantom size specific. This means that if a phantom for an animal used in pre clinical studies is constructed, these factors should apply to it as long as i t is of similar size. This should be tested in the future to ensure that this is the case. The PAB factors for the two extremes in phantom size, the NBF and ADM, should cover the full range of possible values and are meant to be the endpoints to be used in interpolation for middle sized phantoms. However, this also has not been tested yet. Further studies should be performed to ensure that simple interpolation between the factors based characteristics such as total phantom volume and phantom surface are a produce acceptable results. Aside from the work necessary to ensure wide applicability of these factors, the sets of data presented in this article give way to really exciting possibilities for fast and reliable internal dosimetry calculation tools for standard clinical use.

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140 Table 5 1. Summary of the MFP characteristics for 2 photon energies Distance (cm) ST HB 50ST 50B MFP % fluence 15 keV 4 MeV 15 keV 4 MeV 15 keV 4 MeV 0.01 99.0% 0.0061 0.2852 0.0014 0.2152 0.0025 0.2451 0. 02 98.0% 0.0123 0.5704 0.0029 0.4305 0.0050 0.4901 0.03 97.0% 0.0184 0.8556 0.0043 0.6457 0.0076 0.7352 0.05 95.1% 0.0307 1.4261 0.0072 1.0762 0.0126 1.2253 0.08 92.3% 0.0491 2.2817 0.0116 1.7219 0.0202 1.9604 0.15 86.1% 0.0921 4.2782 0.0 217 3.2286 0.0378 3.6758 0.30 74.1% 0.1843 8.5565 0.0434 6.4572 0.0756 7.3515 0.50 60.7% 0.3071 14.2608 0.0723 10.7620 0.1260 12.2525 1.00 36.8% 0.6142 28.5216 0.1445 21.5240 0.2519 24.5050 1.50 22.3% 0.9213 42.7824 0.2168 32.2859 0.3779 3 6.7576 2.00 13.5% 1.2285 57.0432 0.2891 43.0479 0.5039 49.0101 2.50 8.2% 1.5356 71.3041 0.3613 53.8099 0.6298 61.2626 3.00 5.0% 1.8427 85.5649 0.4336 64.5719 0.7558 73.5151 3.50 3.0% 2.1498 99.8257 0.5059 75.3339 0.8817 85.7677 4.00 1.8% 2.4569 114.0865 0.5782 86.0958 1.0077 98.0202 4.50 1.1% 2.7640 128.3473 0.6504 96.8578 1.1337 110.2727 5.00 0.7% 3.0712 142.6081 0.7227 107.6198 1.2596 122.5252 5.50 0.4% 3.3783 156.8689 0.7950 118.3818 1.3856 134.7778 6.00 0.2% 3.6854 171 .1297 0.8672 129.1438 1.5116 147.0303 Table 5 2. Photon energy indices utilized in buildup calculations Energy (MeV) 0.015 0.300 0.020 0.400 0.030 0.500 0.040 0.600 0.050 0.800 0.060 1.000 0.080 1.500 0.100 2.000 0.150 3.000 0.200 4.000

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141 Table 5 3. Soft Tissue infinite medium buildup factors for monoenergetic isotropic photon point sources E (MeV) MFP 0.02 0.03 0.05 0.08 0.15 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.015 1.01 1.01 1.01 1.02 1.04 1.06 1.09 1.14 1.17 1.20 1.22 1.24 1.26 1.27 1.28 1.29 1.31 1.31 0.020 1.01 1.02 1.03 1.05 1.08 1.14 1 .20 1.33 1.42 1.50 1.56 1.62 1.67 1.72 1.76 1.80 1.83 1.87 0.030 1.03 1.04 1.07 1.10 1.19 1.36 1.56 2.03 2.45 2.83 3.19 3.53 3.85 4.15 4.45 4.73 5.01 5.27 0.040 1.04 1.06 1.11 1.17 1.31 1.62 2.03 3.08 4.18 5.31 6.47 7.65 8.84 10.07 11.31 12.56 13.84 15.09 0.050 1.05 1.07 1.12 1.19 1.37 1.77 2.34 3.98 5.87 8.01 10.34 12.95 15.70 18.64 21.74 25.08 28.54 32.14 0.060 1.05 1.07 1.12 1.20 1.38 1.82 2.47 4.47 6.97 9.99 13.46 17.44 21.86 26.88 32.16 37.70 43.99 50.92 0.080 1.05 1.07 1. 11 1.19 1.37 1.79 2.46 4.64 7.59 11.36 15.95 21.59 28.12 35.69 44.21 53.61 64.79 76.78 0.100 1.04 1.06 1.10 1.17 1.33 1.71 2.31 4.29 7.02 10.59 15.06 20.52 27.05 34.73 43.60 53.81 65.34 78.40 0.150 1.03 1.05 1.08 1.14 1.27 1.58 2.07 3.68 5.94 8 .94 12.76 17.53 23.33 30.14 38.19 47.36 58.33 70.27 0.200 1.03 1.04 1.07 1.12 1.24 1.51 1.92 3.29 5.17 7.65 10.76 14.66 19.31 24.81 31.21 38.49 47.14 56.59 0.300 1.03 1.04 1.06 1.10 1.20 1.43 1.78 2.89 4.38 6.29 8.63 11.47 14.82 18.70 23.13 27. 98 33.64 39.83 0.400 1.02 1.03 1.05 1.09 1.17 1.37 1.67 2.63 3.94 5.62 7.67 10.13 13.02 16.34 20.05 24.08 28.81 33.72 0.500 1.02 1.03 1.06 1.09 1.18 1.37 1.67 2.60 3.80 5.26 6.97 8.97 11.23 13.75 16.53 19.47 22.92 26.39 0.600 1.02 1.03 1. 05 1.08 1.16 1.34 1.62 2.45 3.51 4.77 6.23 7.91 9.79 11.85 14.07 16.43 19.17 21.82 0.800 1.02 1.03 1.05 1.08 1.15 1.31 1.55 2.28 3.17 4.21 5.36 6.65 8.08 9.60 11.19 12.88 14.82 16.69 1.000 1.02 1.03 1.04 1.07 1.14 1.29 1.51 2.16 2.94 3.81 4.77 5.82 6.95 8.15 9.40 10.69 12.13 13.55 1.500 1.02 1.02 1.04 1.06 1.12 1.25 1.44 1.99 2.60 3.25 3.93 4.66 5.43 6.21 7.02 7.84 8.74 9.58 2.000 1.01 1.02 1.04 1.06 1.11 1.23 1.41 1.89 2.40 2.93 2.93 4.04 4.62 5.22 5.83 6.44 7.10 7.74 3.000 1. 01 1.02 1.03 1.05 1.10 1.21 1.37 1.77 2.17 2.57 2.96 3.37 3.78 4.19 4.61 5.02 5.46 5.87 4.000 1.01 1.02 1.03 1.05 1.10 1.20 1.34 1.69 2.02 2.35 2.66 2.99 3.31 3.64 3.96 4.27 4.62 4.93

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142 Table 5 4. 50ST 50B infinite medium buildup factors for mon oenergetic isotropic photon point sources E (MeV) MFP 0.02 0.03 0.05 0.08 0.15 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.015 1.02 1.02 1.02 1.03 1.03 1.04 1.06 1.08 1.09 1.10 1.11 1.12 1.12 1.13 1.13 1.14 1.14 1.14 0.020 1.02 1.02 1.03 1.03 1.05 1.08 1.10 1.15 1.19 1.22 1.24 1.26 1.28 1.29 1.30 1.32 1.33 1.34 0.030 1.02 1.03 1.05 1.07 1.11 1.19 1.29 1.46 1.60 1.72 1.81 1.90 1.98 2.05 2.11 2.17 2.23 2.28 0.040 1.04 1.05 1.08 1.12 1.21 1.38 1.59 2.03 2.41 2.75 3.06 3.35 3.62 3.87 4.11 4.34 4.57 4.78 0.050 1.04 1.07 1.10 1.16 1.29 1.56 1.91 2.73 3.51 4.25 4.98 5.69 6.38 7.05 7.75 8.37 8.99 9.61 0.060 1.05 1.07 1.12 1.19 1.34 1.69 2.16 3.37 4.63 5.92 7.24 8.60 9.99 11.37 12.83 14.06 15.65 17.13 0.080 1.05 1.08 1.13 1.20 1.39 1.81 2.44 4.23 6.32 8.67 11.25 14.06 17.11 20.31 23.77 27.27 31.21 35.37 0.100 1.04 1.07 1.11 1.18 1.36 1.76 2.38 4.24 6.54 9.25 12.37 15.87 19.78 24.06 28.73 33.82 39.32 45.23 0.150 1.04 1.05 1.09 1.15 1.29 1.63 2.16 3.86 6.09 8.86 12.15 16.08 20.55 25.65 31.28 37.58 44.83 52.35 0.200 1.03 1.05 1.08 1.13 1.25 1.54 1.99 3.43 5.34 7.72 10.59 14.00 17.98 22.45 27.48 33.04 39.69 46.41 0.300 1.03 1.04 1.07 1.11 1.21 1.45 1.81 2.97 4.48 6.35 8.58 11.20 14.22 17.61 21.46 25.56 30.34 35.33 0.400 1.02 1.04 1.06 1.10 1.19 1.40 1.71 2.70 3.97 5.49 7.29 9.37 11.72 14.32 17.20 20.31 23.90 27.62 0.500 1.02 1.03 1.06 1.09 1.18 1.38 1.68 2.60 3.74 5.11 6.70 8.49 10.49 12.71 15.13 17.78 20.65 23.73 0.600 1.02 1.03 1.05 1.08 1.16 1.35 1.62 2.45 3.46 4.66 6.01 7.56 9.25 11.10 13.09 15.19 17.61 20.05 0.800 1.02 1.03 1.05 1.08 1.15 1.31 1.55 2.27 3.13 4.12 5.20 6.41 7.72 9.13 10.62 12.18 13.92 15.68 1.000 1.02 1.03 1.04 1.07 1.14 1.29 1.51 2.15 2.90 3.74 4.64 5.65 6.71 7.83 9.02 10.22 11.60 12.94 1.500 1.02 1.02 1.04 1.06 1.12 1.25 1.44 1.98 2.57 3.20 3.86 4.57 5.30 6.06 6.84 7.64 8.52 9.35 2.000 1.01 1.02 1.04 1.06 1.11 1.24 1.41 1.88 2.38 2.90 3.43 3.98 4.55 5.13 5.72 6.33 6.95 7.59 3.000 1.01 1.02 1.03 1.05 1.10 1.21 1.37 1.76 2.15 2.54 2.93 3.34 3.74 4.15 4.56 4.97 5.40 5.80 4.000 1.01 1.02 1.03 1.05 1.10 1.20 1.34 1.68 2.01 2.33 2.64 2.97 3.28 3.61 3.93 4.24 4.58 4.90

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143 Table 5 5. Bone infinite medium buildup factors for monoenergetic isotropic photon point sources E (MeV) MFP 0.02 0.03 0.05 0.08 0.15 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.015 1.02 1.02 1.03 1.03 1.04 1.04 1.05 1.06 1.07 1.08 1.08 1.09 1.09 1.09 1.10 1.10 1.10 1.10 0.020 1.02 1.03 1.03 1.03 1.04 1.06 1.08 1.11 1.13 1.15 1.16 1.17 1.18 1.19 1.20 1.20 1.21 1.21 0.030 1.03 1.03 1.04 1.05 1.08 1.14 1.20 1.30 1.38 1.44 1.50 1.54 1.58 1.62 1.65 1.68 1.71 1.73 0.040 1.03 1.04 1.07 1.10 1.16 1.28 1.41 1.68 1.89 2.07 2.22 2.36 2.49 2.60 2.71 2.81 2.91 3.00 0.050 1.04 1.06 1.09 1.14 1.24 1.44 1.68 2.20 2.65 3.05 3.41 3.76 4.09 4.40 4.68 5.00 5.28 5.48 0.060 1.05 1.07 1.11 1.17 1.30 1.58 1.93 2.75 3.53 4.27 4.96 5.66 6.33 7.03 7.64 8.23 8.88 9.47 0.080 1.05 1.08 1.13 1.20 1.38 1.77 2.32 3.75 5.29 6.87 8.52 10.22 11.99 13.76 15.70 17.60 19.62 21.64 0.100 1.05 1.07 1.12 1.19 1.36 1.77 2.35 4.01 5.92 8.02 10.31 12.78 15.42 18.23 21.20 24.36 27.70 31.20 0.150 1.04 1.06 1.10 1.16 1.31 1.67 2.22 3.92 6.04 8.54 11.43 14.75 18.40 22.42 26.91 31.77 37.19 42.96 0.200 1.03 1.05 1.08 1.14 1.27 1.57 2.04 3.52 5.40 7.68 10.33 13.42 16.92 20.79 25.13 29.81 35.40 40.75 0.300 1.03 1.04 1.07 1.11 1.22 1.46 1.84 3.02 4.54 6.36 8.49 10.97 13.78 16.89 20.39 24.18 28.42 32.94 0.400 1.02 1.04 1.06 1.10 1.19 1.40 1.72 2.71 3.94 5.40 7.08 9.03 11.20 13.59 16.22 19.01 22.28 25.59 0.500 1.02 1.03 1.06 1.09 1.18 1.38 1.68 2.59 3.71 5.02 6.51 8.20 10.07 12.12 14.37 16.81 19.45 22.28 0.600 1.02 1.03 1.05 1.08 1.16 1.35 1.62 2.44 3.43 4.58 5.87 7.34 8.94 10.68 12.54 14.53 16.80 19.04 0.800 1.02 1.03 1.05 1.08 1.15 1.31 1.56 2.27 3.11 4.06 5.10 6.26 7.52 8.86 10.29 11.79 13.45 15.14 1.000 1.02 1.03 1.04 1.07 1.14 1.29 1.51 2.15 2.88 3.70 4.57 5.54 6.57 7.65 8.80 9.97 11.30 12.58 1.500 1.02 1.02 1.04 1.06 1.12 1.25 1.45 1.97 2.56 3.17 3.82 4.51 5.23 5.97 6.74 7.52 8.39 9.22 2.000 1.01 1.02 1.04 1.06 1.11 1.24 1.41 1.87 2.37 2.88 3.40 3.95 4.50 5.08 5.67 6.27 6.89 7.51 3.000 1.01 1.02 1.03 1.05 1.10 1.21 1.37 1.75 2.14 2.53 2.92 3.32 3.72 4.13 4.54 4.94 5.37 5.77 4.000 1.01 1.02 1.03 1.05 1.10 1.20 1.34 1.68 2.00 2.32 2.63 2.95 3.27 3.59 3.91 4.22 4.56 4.86

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144 Table 5 6. A djustment factors for the NBF P AB factors E (MeV) MFP 0.01 0.02 0.03 0.05 0.08 0.15 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.015 1.00 1.00 1.00 1.00 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 0.020 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.030 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.00 1.00 0.040 1.10 1.10 1.10 1.10 1.10 1.10 1.10 0.95 0.95 1.00 1.00 0.95 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.050 1.15 1.15 1.15 1.15 1.15 1.15 1.10 0.95 0.90 0.90 0.90 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.060 1.20 1.20 1.20 1.20 1.20 1.20 0.80 0.80 0.80 0.90 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.080 1.20 1.20 1.20 1.20 1.20 1.20 1.00 0.90 0.90 0.90 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.100 1.20 1.20 1.20 1.20 1.20 1.20 1.00 0.90 0.80 0.75 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.150 1.00 1.00 1.00 1.00 1.00 1.00 0.95 0.90 0.78 0.63 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.200 1.05 1.05 1.05 1.05 1.05 1.05 0.95 0.90 0.85 0.74 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.300 1.05 1.05 1.05 1.05 1.05 1.05 0.95 0.90 0.82 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.400 1.05 1.05 1.05 1.05 1.05 1.00 1.00 0.90 0.82 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.500 1.05 1.05 1.05 1.05 1.05 1.00 1.00 0.90 0.75 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.600 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.90 0.80 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.800 0.99 0.98 0.97 0.96 0.93 1.00 1.00 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.000 0.99 0.98 0.98 0.96 0.94 0.89 1.00 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.500 0.99 0.99 0.98 0.96 0.94 0.90 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 2.000 0.99 0.99 0.98 0.97 0.95 1.00 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 3.000 0.99 0.99 0.98 0.97 0.95 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 4.000 0.99 0.99 0.98 0.97 0.95 1.00 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90

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145 Table 5 7. A djustment factors for the ADM P AB fa ctors E (MeV) MFP 0.01 0.02 0.03 0.05 0.08 0.15 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.015 1.00 1.00 1.00 1.00 1.00 1.25 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.15 1.10 1.05 1.00 1.00 0.020 1.00 1.00 1.00 1.00 1.20 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.05 1.05 1.05 1.05 0.030 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.05 1.05 1.00 1.00 0.040 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.15 1.15 1.12 1.12 1.12 1.12 1.05 1.05 1.00 1.00 0.050 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.10 1.07 1.07 1.07 1.00 1.00 1.00 1.00 1.00 1.00 0.060 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.07 1.07 1.07 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.080 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.10 1.10 1.07 1.07 1.07 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.100 1.20 1.20 1.20 1.15 1.15 1.15 1.10 1.05 0.92 1.00 0.95 0.85 0.85 0.85 0.90 0.90 0.90 0.90 0.90 0.150 1.15 1.15 1.15 1.15 1.15 1.10 1.05 0.95 0.92 0.97 0.95 0.85 0.85 0.85 0.90 0.90 0.90 0.90 0.90 0.200 1.15 1.15 1.15 1.15 1.15 1.10 1.05 0.95 0.95 0.95 0.88 0.87 0.85 0.95 0.95 0.95 0.95 0.95 0.95 0.300 1.15 1.15 1.15 1.15 1.15 1.10 1.05 0.97 0.93 0.90 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.400 1.10 1.10 1.10 1.10 1.10 1.10 1.00 0.95 0.93 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.500 1.07 1.07 1.07 1.07 1.07 1.07 1.00 0.93 0.92 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.600 1.05 1.05 1.05 1.05 1.05 1.05 1.00 0.93 0.92 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.800 1.05 1.05 1.05 1.05 1.05 1.05 1.00 0.93 0.92 0.80 0.80 0.80 0.80 0.80 0.80 0.80 1.00 1.00 1.00 1.000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.500 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 3.000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 4.000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

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146 Figure 5 1. Comparison of the mass attenuation coefficients for Soft Tissue and Lung as obtained in the NIST XCOM database

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147 Figure 5 2. Geometry utilized in the MCNP calculations for buildup

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148 Figure 5 3 Point pair distance distributions for several organ pairs. The Mean Free Path values corresponding to the 100 150 keV bin are shown on the top axi s.

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149 Figure 5 4. Graph of the buildup factors for soft tissue as a fun ction of MFP and photon energy.

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150 Figure 5 5. Buildup factor curves for Soft Tissue (black), 50ST 50B (red) and bone (blue) for 1,2 and 3MFP.

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151 Figure 5 6. P AB factors for the NBF

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152 Figure 5 7. P AB factors for the ADM

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153 CHAPTER 6 CONCLUSIONS The detailed canine skeletal model presented early in this dissertation constitutes one of the first of its kind. It provides useful information that may all ow researchers to more accurately determine the doses and effects of new radiopharmaceuticals during pre clinical trials using canine subjects. The correctness of the information collected during that phase not only benefits the animals that are being use d for the study by developing effective products that can be used for their treatment, but it is also crucial for the proper extrapolation to humans. If the information collected during pre clinical stages is more accurate, the data upon which the human trials are developed becomes reliable. Therefore, the development of animal models such as the detailed skeletal canine model here presented is beneficial for veterinary medicine as well as research for human treatments. Since such a comprehensive model had not been constructed before for the canine, some of the data utilized for the calculations was not available for the dog. This issue was overcome by utilizing human data instead. As more thorough data specific to the canine gets published, such as ce llularity factors, the model should be updated to truly reflect the cani ne skeletal anatomy purely using dog data. Furthermore, surrogates had to be used for mass calculations of certain bone sites. For example, the volume fractions from the ribs were us ed in the calculations of the scapulae. In the future, expanding the number of bone samples to include the sites that were not explicitly analyzed would increase the exactitude of the values used for mass calculations, and hence, the values used in canine skeletal dosimetry. The accuracy of these values should be optimized as much as possible since in the future, they will also be incorporated as part of the dosimetry software package described in this dissertation.

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154 The nuclear medicine internal dosimetry code UFDose, presented in this study fills in the current gap in the dosimetry software available in the field. Through its fast yet reliable dose calculations, both in normal anatomy and tumor burdened anatomy, UFDose allows users to perform the dosime try they may need for either patient dose tracking for diagnostic procedures or treatment planning. T he anatomically realistic phantoms embedded in the code put this software a step ahead of other packages that utilize stylized anatomical phantoms to repr esent patients. Furthermore, the capability of performing heterogeneous medium dosimetry opens the possibility of more However there are several aspects that can be improv ed in this software. The following paragraphs detail the work that can still be done to maximize the applicability of UFDose T he t umor insertion algorithm in UFDose currently matches the theoretical volume of the ellipsoid described by the user to the v oxelized volume very successfully. Unfortunately, the length of the axes along the z direction is often underestimated in the voxelized tumor. This does not present a big issue for dose calculations, as the ellipsoid representation of the tumor is an ide alized geometry that does not necessarily accurately represent the mass, but it is still a problem that should be addressed. Although there is always going to exist a discrepancy between the idealized ellipsoid geometry and the voxelized one, simply becau se of the voxel resolution limitation s of the phantoms, it should be possible to rewrite the algorithm to minimize the axis length discrepancies in any one direction while preserving the volume accuracy. The tumor insertion algorithm is also the limiting factor that dictates the speed of the dosimetry

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155 calculations for tumor burdened anatomy. If this script is rewritten to minimize the amount of for loops in it, the time it takes to insert tumors in the phantoms will be greatly reduced. This code perfo rms dosimetry using hybrid phantoms that represent the 50 th percentile of the population. While these phantoms are much more anatomically realistic than the older standard stylized phantoms, they still can only be comfortably applied to patients who have characteristics that are well matched by the 50 th percentile values. Deviations from those anatomical traits between the model and the actual patient can lead to errors in the dose estimates. Therefore, the addition of mass scaling n masses o r the expansion of the phantom library available in the code would signify a great improvement in the dosimetry calculations. Corrections towards increased patient specificity of the dosimetry results are being developed by Michael Wayson for hi s doctoral work and they will be added to the capabilities of this code in the future. The inclusion of organ specific tissue compositions could also be a good improvement for the code. Although this would have a minimal effect on the dose results, it wo uld still eliminate another variable that may contribute, regardless of how slightly, to the overall error in the dosimetry. The adjusted buildup factors constructed in this dissertation work allow for fast yet reliable dose calculations. They have only b een constructed for the Newborn Female phantom and the Adult Male phantom thus far. Calculations using the phantom sizes in between these two extremes have not been performed. The construction of adjusted factors for every phantom in the family, or the c reation of an interpolation mechanism for

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156 the phantom sizes in between the two extremes should be developed to further guarantee the accuracy of the dosimetry for the in between phantom sizes. The current version of the software requires the user to insert the number of decays in the source tissue. This calculation can be cumbersome and it would be a great advancement for UFDose to have an algorithm for cumulated activity calculations. Providing the user the option of inserting time activity measurements into the code and having the software automatically determine the number of decays in the source would increase the usefulness of the package and decrease the time investment of the user to obtain dose estimates with this code. Currently, the software cal culates absorbed dose to the target tissues. While this value can be useful in determining the treatment course for a patient, other quantities such as Equivalent Uniform Dose (EUD) or Biologically Effective Dose (BED) may be just as valuable if not more when making treatment related decisions. At the moment, all the doses calculated by the code are based on the assumption that the source activity is uniformly distributed and that the target tissue receives a uniform dose. These assumptions may not be va lid due to factors such as the often heterogeneous uptake by source tissues. If these heterogeneities are accurately modeled in later versions of this code, the addition of EUD may prove of great use. Furthermore, BED accounts for the rate at which the d ose is being delivered. The effects of a dose delivered in a very short period of time may highly differ from those of the same dose delivered over an extended period. Taking this into account can lead to a more accurate prediction of the dose effects on a given tissue. The addition of the calculation of these two quantities in the code could be of great use for clinicians are researchers.

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157 Despite the improvements that can still be made, the work presented in this dissertation brings internal dosimetry c alculations a step closer towards becoming part of the standard clinical procedure in nuclear medi cine. Both the work performed to aid in the accuracy of pre clinical trial calculations by constructing a detailed skeletal model of the canine and the dos imetry software developed for normal and tumor burdened anatomy dosimetry are important to the nuclear medicine community. It bring s new tools into the nuclear medicine field that can be of great use in the development of new radiopharmaceuticals and the creation of a dosimetry package optimized for general clinical use.

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158 APPENDIX A DETAILED SKELETAL DO SIMETRY RESULTS This appendix is a collection of all the absorbed fraction and specific absorbed fraction tables for the different bone sites in the canin e phantom Note that all TIM sources are run at 70% cellularity

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159 Table A 1. Absorbed fractions for the Tibia with active marrow as the target.

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160 Table A 2 Absorbed fractions for the Tibia with endosteum as the target.

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161 Table A 3 Absorbed fractions for the Radius with active marrow as the target.

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162 Table A 4 Absorbed fractions for the Radius with endosteum as the target

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163 Table A 5 Absorbed fractions for the Femur with active marrow as the target.

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164 Table A 6 Absorbed fractions for the Femur with endosteum as the target

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165 Table A 7 Absorbed fractions for the Humerus with active marrow as the target.

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166 Table A 8 Absorbed fractions for the Humerus with endosteum as the target

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167 Table A 9 Absorbed fractions for the Fibula with active mar row as the target.

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168 Table A 1 0. Absorbed fractions for the Fibula with endosteum as the target

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169 Table A 1 1 Absorbed fractions for the Ulna with active marrow as the target.

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170 Table A 12 Absorbed fractions for the Ulna with endosteum as the target

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171 Table A 13 Absorbed fractions for the Mandible with active marrow as the target.

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172 Table A 14 Absorbed fractions for the Mandible with endosteum as the target

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173 Table A 15 Absorbed fractions for the Cranium with active marrow as the target.

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174 Table A 16 Absorbed fractions for the Cranium with endosteum as the target

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175 Table A 17 Absorbed fractions for the Front Paws with active marrow as the target.

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176 Table A 18 Absorbed fractions for the Front Paws with endosteum as the target

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177 Tabl e A 1 9. Absorbed fractions for the Lumbar Vertebrae with active marrow as the target.

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178 Table A 2 0 Absorbed fractions for the Lumbar Vertebrae with endosteum as the target

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179 Table A 21 Absorbed fractions for the Scapulae with active marrow as the tar get.

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180 Table A 22 Absorbed fractions for the Scapulae with endosteum as the target

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181 Table A 23 Absorbed fractions for the Sternum with active marrow as the target.

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182 Table A 24 Absorbed fractions for the Sternum with endosteum as the target

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183 Ta ble A 25 Absorbed fractions for the Thoracic Vertebrae with active marrow as the target.

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184 Table A 2 6. Absorbed fractions for the Thoracic Vertebrae with endosteum as the target

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185 Table A 27 Absorbed fractions for the Ribs with active marrow as the t arget.

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186 Table A 2 8 Absorbed fractions for the Ribs with endosteum as the target

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187 Table A 2 9. Absorbed fractions for the Pelvis with active marrow as the target.

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188 Table A 30 Absorbed fractions for the Pelvis with endosteum as the target

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189 Table A 31 Absorbed fractions for the Cervical Vertebrae with active marrow as the target.

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190 Table A 32 Absorbed fractions for the Cervical Vertebrae with endosteum as the target

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191 Table A 33 Absorbed fractions for the Hind Paws with active marrow as the target.

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192 Table A 34 Absorbed fractions for the Hind Paws with endosteum as the target

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193 Table A 35 Absorbed fractions for the Caudal Vertebrae with active marrow as the target.

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194 Table A 36 Absorbed fractions for the Caudal Vertebrae with endoste um as the target

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195 Table A 37 Absorbed fractions for the Skeletal Average with active marrow as the target.

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196 Table A 38 Absorbed fractions for the Skeletal Average with endosteum as the target

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197 Table A 39 Specific absorbed fractions for the Tibi a with active marrow as the target.

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198 Table A 40 Specific absorbed fractions for the Tibia with endosteum as the target.

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199 Table A 41 Specific absorbed fractions for the Radius with active marrow as the target.

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200 Table A 42 Specific absorbed fraction s for the Radius with endosteum as the target

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201 Table A 43 Specific absorbed fractions for the Femur with active marrow as the target.

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202 Table A 44 Specific absorbed fractions for the Femur with endosteum as the target

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203 Table A 45 Specific absorbe d fractions for the Humerus with active marrow as the target.

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204 Table A 4 6 Specific absorbed fractions for the Humerus with endosteum as the target

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205 Table A 47 Specific absorbed fractions for the Fibula with active marrow as the target.

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206 Table A 48 Specific absorbed fractions for the Fibula with endosteum as the target

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207 Table A 49 Specific absorbed fractions for the Ulna with active marrow as the target.

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208 Table A 50 Specific absorbed fractions for the Ulna with endosteum as the target

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209 Ta ble A 51 Specific absorbed fractions for the Mandible with active marrow as the target.

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210 Table A 52 Specific absorbed fractions for the Mandible with endosteum as the target

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211 Table A 53 Specific absorbed fractions for the Cranium with active marr ow as the target.

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212 Table A 54 Specific absorbed fractions for the Cranium with endosteum as the target

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213 Table A 55 Specific absorbed fractions for the Front Paws with active marrow as the target.

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214 Table A 56 Specific absorbed fractions for the F ront Paws with endosteum as the target

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215 Table A 57 Specific absorbed fractions for the Lumbar Vertebrae with active marrow as the target.

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216 Table A 58 Specific absorbed fractions for the Lumbar Vertebrae with endosteum as the target

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217 Table A 59 Specific absorbed fractions for the Scapulae with active marrow as the target.

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218 Table A 60 Specific absorbed fractions for the Scapulae with endosteum as the target

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219 Table A 61 Specific absorbed fractions for the Sternum with active marrow as the target.

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220 Table A 62 Specific absorbed fractions for the Sternum with endosteum as the target

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221 Table A 63 Specific absorbed fractions for the Thoracic Vertebrae with active marrow as the target.

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222 Table A 64 Specific absorbed fractions for the Tho racic Vertebrae with endosteum as the target

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223 Table A 65 Specific absorbed fractions for the Ribs with active marrow as the target.

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224 Table A 66 Specific absorbed fractions for the Ribs with endosteum as the target

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2 25 Table A 67 Specific absorbed fractions for the Pelvis with active marrow as the target.

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226 Table A 6 8 Specific absorbed fractions for the Pelvis with endosteum as the target

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227 Table A 69 Specific absorbed fractions for the Cervical Vertebrae with active marrow as the target.

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228 Ta ble A 70 Specific absorbed fractions for the Cervical Vertebrae with endosteum as the target

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229 Table A 71 Specific absorbed fractions for the Hind Paws with active marrow as the target.

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230 Table A 72 Specific absorbed fractions for the Hind Paws wit h endosteum as the target

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231 Table A 73 Specific absorbed fractions for the Caudal Vertebrae with active marrow as the target.

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232 Table A 74 Specific absorbed fractions for the Caudal Vertebrae with endosteum as the target

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233 Table A 75 Specific absor bed fractions for the Skeletal Average with active marrow as the target.

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234 Table A 76 Specific absorbed fractions for the Skeletal Average with endosteum as the target

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235 APPENDIX B MATLAB CODE FOR DOSIMETRY S OFTWARE %~~~~~~~~~~~~~~~~~~ Point kernel A lgorithm ~~~~~~~~~~~~~~~~~~~~~~~ warning( 'off' ) tic %if file is not 0 load tumor burdened anatomy, otherwise, load normal %anatomy model= 'ADM' ; % file=0; file= 'LungSphereHB' ; if file load (strcat( 'Models/' ,model, '/Tumor/' ,file, '.mat' )) list=[13 1 85;25 185;45 185;46 185;]; %Human organ pairs else load (strcat( 'Models/' ,model, '/' ,model, 'VM.mat' )) load (strcat( 'Models/' ,model, '/OrganInfo.mat' )) list=[45 25; 46 32;25 46; 45 46; 15 16; 46 13; ... 46 47; 13 14; ]; %Human organ pairs end format short e delV=(voxrsl_xy)^2*voxrsl_z; % Load nuclide info nuclides={ 'I 131' 'F 18' 'Tc 99m' }; numOfNuclides=size(nuclides,2) S=zeros(size(list,1),size(numOfNuclides)); time_PPdist=zeros(size(list,1)); time_Scalc=zeros(size(list,1)); for x=1:(numOfNuclides) load (strcat( 'DK Schemes/' ,nuclides{1,x}, '_p.mat' )) load (strcat( 'Tissue info/AttnCoeff_' ,nuclides{1,x}, '_ORNL.mat' )) nuclides{1,x} for o=1:size(list,1); %loop through the organ list TO=list(o,1); SO=list(o,2 ); NumVoxTO=size(OVoxIndx{TO,1},1); NumVoxSO=size(OVoxIndx{SO,1},1); tic % ------------------PPdist Calc ----------------------------if file if x==1 chck=exist(strcat( 'Tumor Dosimetry Tests/' ,model, '/' ,file, '/P Pdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' ), 'file' );

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236 if chck load (strcat( 'Tumor Dosimetry Tests/' ,model, '/' ,file, '/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' )); else PPdistHetero(TO,SO,model,fi le); load (strcat( 'Tumor Dosimetry Tests/' ,model, '/' ,file, '/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' )); end else load (strcat( 'Tumor Dosimetry Tests/' ,model, '/' ,file, '/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' )); end else chck=exist(strcat( 'Models/' ,model, '/PPdist/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' ), 'file' ); if chck load (strcat( 'Models/' ,model, '/PPdist/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' ) ); else PPdistHetero(TO,SO,model,file); load (strcat( 'Models/' ,model, '/PPdist/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' )); end clear chck end time_PPdist(o)=toc; % ------------------S Valu e calc ----------------------------%The svalue is calculated in units of mGy/MBq s (this is achieved through %the 0.1602 conversion factor). In order for the conversion factor to be %correct, the input units for all the values have to be MeV cm and grams. tic AFt=zeros(size(PP,1),1); SAF=zeros(size(p_dk,1),1); G=zeros(size(p_dk,1),1); if (sum(p_dk(:,1))==0) S(o,x)=0; else if TO==SO for e=1:size(p_dk,1); if p_dk(e,1)>0.015 for i=1:size(PP,1); mr=r(1,i)*sum((mu(e,Materials(:,1))).*Materials(:,3)'); if mr<=6 AFt(i)=(PP(i,1)/(r(1,i)^2))*BUinterp( mr,p_dk(e,1),1,model)*exp( 1*mr); else AFt(i)=0; end clear mr

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237 end SAF(e)=(delV*NumVoxTO)*(mu_en Rho(e,OMaterial(TO))*ODensity(TO,1))/(4*pi()*OMa ss(TO))*sum(AFt); %units of g 1 clear AFt G(e)=delta_p(e)*SAF(e)*0.1602; clear SAF else G(e)=delta_p(e)*0.1602/O Mass(TO); end end else for e=1:size(p_dk,1); for i=1:size(PP,1); mr=r(1,i)*sum((mu(e,Materials(:,1))).*Materials(:,3)'); if mr<=6 AFt(i)=(PP(i,1)/(r(1,i)^2))*BUinterp(mr,p_dk(e,1),1,model)*exp( 1*mr); else AFt(i)=0; end clear mr end SAF (e)=(delV*NumVoxTO)*(mu_enRho(e,OMaterial(TO))*ODensity(TO,1))/(4*pi()*OMa ss(TO))*sum(AFt); %units of g 1 clear AFt G(e)=delta_p(e)*SAF(e)*0.1602; clear SAF end end S(o,x)=sum(G); %equivalent to S value in units of mGy/MBq s end clear PPdist TO SO G clear r_std time_Scalc(o)=toc; end clear p_dk end time_total=toc; load (strcat( 'Tissue info/BUtables_' ,model, '.mat' )) %

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238 if file mkd ir(strcat( 'MagicFactor Studies \ ,model, \ ,file)); save (strcat( 'Tumor Dosimetry Tests/' ,model, '/' ,file, '_nuclides_I131F18Tc99mlowE Hetero' ), 'S' 'MagicFactor' 'E_BU' 'MFP_BU' ); else save (strcat( 'MagicFactor Studies/' ,model, '/' ,model, common test_tumorPr oof3' ), 'S' 'MagicFactor' 'E_BU' 'MFP_BU' 'time_PPdist' 'time_Scalc' ); end %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~~~~ Point Pair Distance Distribution ~~~~~~~~~~~~~~~ function PPdistCalc(TO,SO,model,f ile) %% Model load tic if file load (strcat( 'Models/' ,model, '/Tumor/' ,file, '.mat' )) else load (strcat( 'Models/' ,model, '/' ,model, 'VM.mat' )) load (strcat( 'Models/' ,model, '/OrganInfo.mat' )) end %% Initial data NumVoxTO=size(OVoxIndx{ TO,1},1); NumVoxSO=size(OVoxIndx{SO,1},1); if (NumVoxTO<25000||NumVoxSO<25000) binSize=voxrsl_xy*1.5; numOfRandoms=5000000; else binSize=voxrsl_xy*2.5; numOfRandoms=1000000; end t_rand=randi(Num VoxTO,numOfRandoms,1); s_rand=randi(NumVoxSO,numOfRandoms,1); %% ray length calculation initial=horzcat(OVoxIndx{SO,1}(s_rand,1)*voxrsl_xy,OVoxIndx{SO,1}(s_rand,2)*v oxrsl_xy,OVoxIndx{SO,1}(s_rand,3)*voxrsl_z); final=horzcat(OVoxIndx{TO ,1}(t_rand,1)*voxrsl_xy,OVoxIndx{TO,1}(t_rand,2)*vox rsl_xy,OVoxIndx{TO,1}(t_rand,3)*voxrsl_z); r_orig=sqrt((initial(:,1) final(:,1)).^2+(initial(:,2) final(:,2)).^2+(initial(:,3) final(:,3)).^2); % voxind_in=OVoxIndx{SO,1}(s_rand,:);

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239 % voxind_fin=OVoxIndx {TO,1}(t_rand,:); %Take the longest ray for corrections maxi=max(r_orig); voxind_in=OVoxIndx{SO,1}(s_rand(find(r_orig==maxi)),:); voxind_fin=OVoxIndx{TO,1}(t_rand(find(r_orig==maxi)),:); clear s_rand t_rand initial final %% Pair Point Dist CALC [r_sort ed ix]=sort(r_orig); %sort the values of r in ascending order. Create a matrix that also keeps the corresponding original indeces bin=min(r_sorted):binSize:max(r_sorted); [n,~]=histc(r_sorted,bin); PP=n./numOfRandoms; PP(PP==0)=[]; bot=1; fo r i=1:(size(n) 1); top=bot+(n(i) 1); r(i)=mean(r_sorted(bot:top)); r_std(i)=std(r_sorted(bot:top)); bot=top; PP(PP==0)=[]; end PP=smooth(PP, 'sgolay' ); PP(PP<0)=[]; PPdist. PP=PP; PPdist.r=r; PPdist.r_std=r_std; %% Fraction of different materials xin=sort(vertcat(voxind_in(1,1),voxind_fin(1,1))); yin=sort(vertcat(voxind_in(1,2),voxind_fin(1,2))); zin=sort(vertcat(voxind_in(1,3),voxind_fin(1,3))); MatDist=sum (hist(VMmat(xin(1,1):xin(2,1),yin(1,1):yin(2,1),zin(1,1):zin(2,1)) ,1:8),2); NumVoxBox=sum(MatDist); percents=MatDist./NumVoxBox; PPdist.Materials=horzcat(find(MatDist),MatDist(find(MatDist)),percents(find(M atDist))); PPdist.MatAdj=sum(density(PPdist.Materi als(:,1),1).*PPdist.Materials(:,2)/Num VoxBox); % Organ specific densities OMatDist=sum(hist(VM(xin(1,1):xin(2,1),yin(1,1):yin(2,1),zin(1,1):zin(2,1)),1 :185),2); Opercents=OMatDist./NumVoxBox; PPdist.OMaterials=horzcat(find(OMatDist),OMatDist(find(OMatDist) ),Opercents(f ind(OMatDist))); PPdist.OMatAdj=sum(ODensity(PPdist.OMaterials(:,1),1).*PPdist.OMaterials(:,2) /NumVoxBox); %% Plot PP vs r

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240 if file mkdir(strcat( 'Models/' ,model, '/PPdist/PPdist Test/' ,file)); save (strcat( 'Models/' ,model, '/PPdist/PPdi st Test/' ,file, '/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' ), struct' 'PPdist' ); else save (strcat( 'Models/' ,model, '/PPdist/PPdist Test/PPdist_' ,OName{SO,1}, 'to' OName{TO,1}, '.mat' ), struct' 'PPdist' ); end timePP=toc; PPdist.time=timePP; clear PP r r_std r_sorted r_orig TO SO NumVoxTO NumVoxSO n top bot MatDist xin yin zin NumVoxBox percents Materials MatAdj voxind_in voxind_fin %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~~~~~~~~ Tumor Insert ion function ~~~~~~~~~~~~~~~~~~~~~~~ %%% Tumor insertion algorithm % The geometry chosen to represent user defined tumors is the tri axial % ellipsoid. The user will declare the center and the length of the 3 % axis. function Tumor=TumorInsertion(x0,y0,z0 ,a,b,c,tmat,model) %(x0,y0,z0) is the center of the tumor, while a, b, and c are the lengths %of the tumor along the x, y and z axis(from center to edge ef ellipsoid) % respectively,in centimeters. % tmat is the material of the tumor (1=ST, 2=L,3=HB,4=25ST 75B,5=50ST50B,6=75ST25B) % NOTE -----------------tumor tag determined by ttag value! % tic load (strcat( 'Models/' ,model, '/' ,model, 'VM.mat' )) load (strcat( 'Models/' ,model, '/OrganInfo.mat' )) ttag=100; OMaterial(end,1)=tmat; OTag(end,1)=ttag; Tumor.VM=VM; Tumor.VMmat=VMmat; Tumor.OTag=OTag; Tumor.OName=OName; Tumor.OMaterial=OMaterial; Tumor.voxrsl_xy=voxrsl_xy; Tumor.voxrsl_z=voxrsl_z; Tumor.center(1,1)=x0; Tumor.center(1,2)=y0; Tumor.center(1,3)=z0; Tumor.trueVol=(4/3)*pi*a*b*c; %% Voxel retagging for tumor insertion voxvol=(voxrsl_xy)^2*voxrsl_z;

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241 tic for nz=0:voxrsl_z:(c) y=b*sqrt(1 (nz/c)^2); for ny=0:voxrsl_xy:y x=a*sqrt(1 (ny/b)^2); for nx=0:voxrsl_xy:x xd=round(nx/voxrsl_xy); yd=round(ny/voxrsl_xy); zd=round(nz/voxrsl_z); if ((Tumor.trueVol size(find(Tumor.VM==ttag),1)*voxvol)
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242 VM(x0 xd,y0 yd,z0 zd)==0) %a voxel tag of 1 indicates air outside of the phantom error( 'Check tumor si ze and location, the tumor appears to lay outside the phantom' ) elseif ( (x0 nx)<0 ||(y0+ny)<0 ||(z0 nz)<0 || ... VM(x0 xd,y0+yd,z0 zd)==0) %a voxel tag of 1 indicates air outside of the phantom e rror( 'Check tumor size and location, the tumor appears to lay outside the phantom' ) %If the tumor is within the phantom, retag voxels else Tumor.VM(x0+xd,y0+yd,z0+zd)=ttag; Tumor.VMmat(x0+xd,y0+yd,z0+zd )=tmat; Tumor.VM(x0+xd,y0 yd,z0+zd)=ttag; Tumor.VMmat(x0+xd,y0 yd,z0+zd )=tmat; Tumor.VM(x0 xd,y0 yd,z0+zd)=ttag; Tumor.VMmat(x0 xd,y0 yd,z0+zd )=tmat ; Tumor.VM(x0 xd,y0+yd,z0+zd)=ttag; Tumor.VMmat(x0 xd,y0+yd,z0+zd )=tmat; Tumor.VM(x0+xd,y0+yd,z0 zd)=ttag; Tumor.VMmat(x0+xd,y0+yd,z0 zd )=tmat; if ((Tumo r.trueVol size(find(Tumor.VM==ttag),1)*voxvol)<(4*voxvol)) break end Tumor.VM(x0+xd,y0 yd,z0 zd)=ttag; Tumor.VMmat(x0+xd,y0 yd,z0 zd )=tmat; Tumor.VM(x0 xd,y0+yd, z0 zd)=ttag; Tumor.VMmat(x0 xd,y0+yd,z0 zd )=tmat; Tumor.VM(x0 xd,y0 yd,z0 zd)=ttag; Tumor.VMmat(x0 xd,y0 yd,z0 zd )=tmat; end end clear xd yd zd nx x end clear ny y

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243 end time_retagging=toc; %% data storage on tumor geometrical characteristics and mass Tumor.vxlVol=size(find(Tumor.VM==ttag),1)*voxvol; Tumor.discrep=(Tumor.vxlVol Tumor.trueVol)/Tumor.trueVol*100; Tumor.voxAx is(1,1)=size(find(Tumor.VM(:,y0,z0)==100),1)*voxrsl_xy/2; Tumor.voxAxis(1,2)=size(find(Tumor.VM(x0,:,z0)==100),2)*voxrsl_xy/2; Tumor.voxAxis(1,3)=size(find(Tumor.VM(x0,y0,:)==100),1)*voxrsl_z/2; Tumor.trueAxis(1,1)=a; Tumor.trueAxis(1,2)=b; Tumor.trueAxis( 1,3)=c; OMass(end,1)=Tumor.vxlVol*density(tmat,1); OVolume(end,1)=Tumor.vxlVol; Tumor.OVolume=OVolume; %% read in tumor voxel indeces OVoxIndx{end,1}=ExtractVI(Tumor.VM,ttag); %% redo organ voxel indeces to adjust for tumor insertion and adjust host or gan masses xmin=min(OVoxIndx{end,1}(:,1)); xmax=max(OVoxIndx{end,1}(:,1)); ymin=min(OVoxIndx{end,1}(:,2)); ymax=max(OVoxIndx{end,1}(:,2)); zmin=min(OVoxIndx{end,1}(:,3)); zmax=max(OVoxIndx{end,1}(:,3)); HostOrgans=find(sum(hist(VM(xmin:xmax,ymin:ymax,zmin: zmax),1:185),2)); for ho=1:size(HostOrgans,1); OVoxIndx{HostOrgans(ho),1}=[]; OVoxIndx{HostOrgans(ho),1}=ExtractVI(Tumor.VM,OTag(HostOrgans(ho))); OMass(HostOrgans(ho),1)=size(OVoxIndx{HostOrgans(ho),1},1)*voxvol*density(OMa terial(HostOrgans( ho),1),1); end %% Save new voxel indeces and masses Tumor.OVoxIndx=OVoxIndx; Tumor.OMass=OMass; time_total=toc; Tumor.time=time_total; %clear tv %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~ Extract Voxel Indices Function ~~~~~~~~~~~~~~~~~~~~~~~~ function Ind=ExtractVI(ModelMatrix,tag) VMsize=[size(ModelMatrix,1),size(ModelMatrix,2),size(ModelMatrix,3)]; Indl=find(ModelMatrix==tag); rem=Indl/(VMsize(1)*VMsize(2)) floor(Indl/(VMsize(1)*VMsize(2))); %remainder (total/(SxSy)) for

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244 %index conversion %take indeces from linear to matrix Ind(:,3)=ceil(Indl/(VMsize(1)*VMsize(2))); Ind(:,2)=ceil(rem*VMsize(2)); size((Ind(:,2) 1)*VMsize(1)) if (size(Indl,2)==1) Ind(:,1)=Indl floor(Indl/(VMsize(1)*VMsize(2)))*(VMsize(1)*VMsize(2)) (Ind(:,2) 1)*VMsize(1); else Ind(:,1)=Indl' floor(Indl/(VMsize(1)*VMsize(2)))'*(VMsize(1)*VMsize(2))' (Ind(:,2) 1)*VMsize(1); end %~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~ BU interpolation function ~~~~~~~~~~~~~~~~~~~~~~~~~~~ function BUfactor=BU(d,E,mat,model) %This function uses the tables of BU factors to approximate the factor for %a given distance an d energy. %................. d=mu*r number of MFPs for that photon at that energy and distance ............... %~~~~~~~~~~~~~~ E is the photon energy ~~~~~~~~~~~~~~ tissue= 'air' ; end if E>4 E=4; end load (strcat( 'Tissue info/BUtables_' ,model, '.mat' )) BUfactor=interp2(MFP_BU,E_BU,BU_STcombolowE,d,E, 'linear' ); %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~ Cumulated Activity and Dose Calc ~~~~~~~~~~~~~~~~~~~~~ Ao=InjAct; CumA(:,2)=SO; switch ActType case 1 CumA(:,1)=totNumDk; case 2 Teff=Tb(:,1).*Tp/(Tb(:,1)+Tp); CumA(:,1)=Ao*f(:,1).*Teff(:,1)./ln(2); end Dose=S(:,x)*CumA(:,1); %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~ Import attenuation coefficients ~~~~~~~~~~~~~~~~~~~~~~ % -----------------------Air and Water attn coefficients ------------------% Load mass and mass energy absorption coefficients for water and air AttnCoef_Air=xlsread( 'Tissue info \ Attenuation Coeff \ AirDry' ); AttnCoef_H2O=xlsread( 'Tissue info \ Attenuation Coeff \ Water' ); % Since mu/rho is never used for anything, but mu is, the mu/rho column

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245 % will be multiplied by the tissue density and replace the mu/rho values % previously stored in column 2. Not necessary for water since rho=1g/cc rho_air= 1.205e 3; % attix, p531. Density @ 20C, 1 atm % Calculate the mass and mass energy absorption coefficients for soft % tissue, homogeneous bone and lung according to ORNL report 8381 % mu/rho=sum[ (weight fraction_i)*(mu/rho_i) ] % Same formula applies for mu_en/rho % ----------------------Body tissues Composition(ST,Lung,Bone) -----------%%%%%%%%%%%%% Load weight fraction elemental compositions of tissues [value symbol]=xlsread( 'Tissue info \ Ti ssue composition_Adult_ORNL' ); symbol(1,:)=[]; % delete first row. It only says "elements" symbol(:,2:(end 1))=[]; % store all the other rows except for the last one which says density %store the density (g/cc) of each tissue (1 ST, 2 Lu ng, 3 Homogeneous Bone) density=zeros(8); density(1:6)=value(end,:); density(7)=rho_air; density(8)=1; value(end,:)=[]; %once stored, delete density values from the file % store the elemental weight fraction for each tissue value(:,1)=value( :,1)/100; %ST value(:,2)=value(:,2)/100; %Lung value(:,3)=value(:,3)/100; %Bone value(:,4)=value(:,4)/100; %ST25% B75% value(:,5)=value(:,5)/100; %ST50% B50% value(:,6)=value(:,6)/100; %ST75 % B25% % Load info about the elemental attenuation coefficients (how many % elements numElements and their names sheets) [type, nameElements]=xlsfinfo( 'Tissue info \ Attenuation Coeff \ AttenCoeff Elements' ); numElements=size(nameElements,2); % ------------------Attn coefficient as a fxn of -----------------------% ------------------decay energy for each radionuclide --------------------%%%%%%%%%%%%% Load decay scheme info % since the elemental attenuation coefficients are given at different % ene rgies for each element, instead of loading them with the given energy, % they will be loaded at the specific radionuclide energy selected by the % user load 'DK Schemes \ RadionuclideList.mat' for r=1:numOfFiles; %loop through all radionuclides load (strcat( 'DK Schemes \ ,Isotopes{r,1}, '_p.mat' ))

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246 % ---------------Calculate the attn coefficients for each body tissue %%%%%%%%%%%%% Load mu/rho and mu_en/rho for each element (n) @ Ei of decay %%% units of attn coefficients in cm2/g nump=size(p_d k,1); mu=zeros(nump,8); mu_Rho=zeros(nump,8); mu_enRho=zeros(nump,8); for t=1:6; %loop through the different body tissues for n=1:numElements; %loop through the elemental composition %load attenu ation coefficient values for elements from xls file elemVal(:,:)=xlsread( 'Tissue info \ Attenuation Coeff \ AttenCoeff Elements' ,n); for i=1:nump; %loop through the E of decay photons mu(i,t)= mu(i,t)+ ... interp1(elemVal(:,1),elemVal(:,2),p_dk(i,1))*value(n,t)*density(t); mu_enRho(i,t)=mu_enRho(i,t)+ ... interp1(elemVal(:,1),elemVal(:,3),p_dk(i,1))*value(n,t); end clear ele mVal end end clear t clear n clear i % ---------------Calculate the attn coefficients for air and water for i=1:nump; %tissue 7 is air mu_Rho(i,7)=interp1(AttnCoef_Air(:,1),AttnC oef_Air(:,2),p_dk(i,1)); mu_enRho(i,7)=interp1(AttnCoef_Air(:,1),AttnCoef_Air(:,3),p_dk(i,1)); %tissue 8 is water mu_Rho(i,8)=interp1(AttnCoef_H2O(:,1),AttnCoef_H2O(:,2),p_dk(i,1)); mu _enRho(i,8)=interp1(AttnCoef_H2O(:,1),AttnCoef_H2O(:,3),p_dk(i,1)); end mu(:,7)=mu_Rho(:,7)*density(7); mu(:,8)=mu_Rho(:,8)*density(8); save (strcat( 'Tissue info \ AttnCoeff_' ,Isotopes{r,1}, '_ORNL.mat' ), ... 'mu' 'mu_enRh o' ); clear mu mu_enRho nump end %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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247 %~~~~~~~~~~~~~~~~~~ Import Voxel Phantom ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %% Import voxelized phantom as 3d matrix %%%%%%%%%%%%Open the voxel ized model save it in matrix model= 'ADM' ; fid=fopen(strcat( 'Models/' ,model, '/Original_Data/ufhadm_362x195x796_lymph.bin )); x=362; y=195; z=796; for n=1:z; VM(:,:,n)=fread(fid,[x,y]); end fclose(fid); % ------CAUTION -------!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!! % Remember to go into the OTagtoMat.m and change the tag numbers that % represent soft tissue organs, the ones that represent the lungs and bones % in order to properly conver t the voxel values from organ tag values to % material number % Save voxelized model as tissue type instead of organ tags VMmat=OTagtoMatHuman(VM,z); %Indicate the voxel resolution for the model in cm %BECAREFUL!! These need to be input by hand!! voxrsl_xy=0.1579; voxrsl_z=0.2207; save (strcat( 'Mode ls/' ,model, '/' ,model, 'VM' ), 'VM' 'VMmat' 'voxrsl_xy' 'voxrsl_z' ); %% Save organ info (name, tag, material, mass, voxel indeces) %%%%%%%%%%%Load Organ info (name, tag, material, voxel indeces) model= 'ADM' ; load (strcat( 'Models \ ,model, \ ,model, 'VM.mat )) [OTag, OName]=xlsread( 'Models/Phantom Info' 'Tag Numbers' 'a2:b185' ); OTag(end+1,1)=0; OName{end+1,1}= 'Tumor' ; %Tag to material conversion OMaterial(1:25,1)=1; %soft tissue OMaterial(26:27,1)=2; %lungs OMaterial(28:56,1)=1; %Soft Tissue OMaterial(57, 1)=7; %Air OMaterial(58:84,1)=1; % ST OMaterial(85:184,1)=3; %homogenous bone OMaterial(185,1)=0; %tumor OVoxIndx=cell(size(OName,1),1); density=[1.04;0.296;1.4;1.31;1.22;1.13;1.205e 3]; [OVolume]=xlsread( 'Models/Phantom Info' 'Volumes' 'l2:l185' ); OVo lume(end+1,1)=0; %tumor [OMass]=xlsread( 'Models/Phantom Info' 'Masses' 'l2:l185' ); OMass(end+1,1)=0; %tumor

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248 % Store voxel indeces for each organ for o=1:(size(OName,1) 1); OVoxIndx{o,1}=ExtractVI(VM,OTag(o,1)); end save (strcat( 'Models \ ,model, \ Orga nInfo' ), 'OName' 'OTag' 'OMaterial' 'OVolume' 'OMass' 'OVoxIndx' 'density' ); %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~~~~~ SAF import ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %********Read in SAF val ues %%%Number of sheets in the file, and their name (1 sheet per organ) modele= '00F' ; model= 'NBF' ; [~, sheets] = xlsfinfo( ... strcat( 'Models/' ,model, '/Original_Data/UFH' ,modele, SAF (FINAL) Electron.xls' )); % OrgN=numel(sheets) 6; % sheets(1:6)=[] ; SourceOrg=sheets'; [Ee] = xlsread( ... strcat( 'Models/' ,model, '/Original_Data/UFH' ,modele, SAF (FINAL) Electron.xls' ), ... 7, 'b2:v2' ); Ee=horzcat(0,Ee); [massTO] = xlsread( 'Models/Phantom Info.xls' 'Targets in order' 'v2:v66' ); [~,TO]= xlsread( ... strcat( 'Models/' ,model, '/Original_Data/UFH' ,modele, SAF (FINAL) Electron.xls' ), ... 7, 'a3:a70' ); SAFe=zeros(size(TO,1), size(Ee,2), size(SourceOrg,1)); for f=1:size(SourceOrg,1); [num] = xlsread( ... strcat( 'Models/' ,model, '/O riginal_Data/UFH' ,modele, SAF (FINAL) Electron.xls' ), ... SourceOrg{f,1}, 'b3:v70' ); SAFe(:,2:end,f)=num; clear num end %Calculate the SAF values for S=T. Mass needs to be changed to kg, that's %why it's divided by 1000. %SAFe(TO,Ee,SO) fo r s=1:size(SourceOrg,1) for t=1:size(TO,1)

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249 if (strmatch(SourceOrg{s,1},TO{t,1}, 'exact' )) SAFe(t,1,s)=1/(massTO(t)/1000); end end end save (strcat( 'Models/' ,model, '/SAFe.mat' ), 'SAFe' 'SourceOrg' 'TO' 'Ee' ) %~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~~~~~~~ MIRD S value Calculator ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ warning off all %Load SAF for model model= 'ADM' ; % load (strcat('Models \ ',model,' \ SAFp.mat')) load (strcat( 'M odels \ ,model, \ SAFe.mat' )) inde=find(isnan(SAFe)); SAFe(inde)=0; indp=find(isnan(SAFp)); SAFp(indp)=0; % Load all radionuclides fid = fopen( 'DK Schemes \ Original Data \ RadListNucmed.txt' ); radionuclides=textscan(fid, '%s' ); nuclides=radionuclides{1,1}'; % Load radionuclide decay scheme information for r=1:size(nuclides,2) %loop through all radionuclides % load (strcat('DK Schemes/',nuclides{1,r},'_p.mat')) load (strcat( 'DK Schemes/' ,nuclides{1,r}, '_e.mat' )) load (strcat( 'DK Schemes/' ,nuclid es{1,r}, '_b.mat' )) r % nump=size(p_dk,1); nume=size(e_dk,1); numb=size(b_dk,1); delta_e=e_dk(:,1).*e_dk(:,2); delta_b=b_dk(:,1).*b_dk(:,2); % Delta is imported from the decay scheme file. % Remember that with the dk arrays, the column1=energy (MeV), column2=yield %%%%%%%%%%%%%%%%%%%%%%%%% Calculate S values % Sval_p=zeros(size(TO,1),size(SourceOrg,1)); Sval_e=zeros(size(TO,1),size(SourceOrg,1)); Sval_b=zeros(size(TO,1),size(SourceOrg,1)); Sval=zeros(size(TO,1),size(SourceOrg,1)); %constant to conv ert from MeV/(kg*Bq s) to mGy/(MBq s) for s=1:size(SourceOrg,1) for t=1:size(TO,1)

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250 % ------------------------------Photons ------------------------for p=1:nump; Sval_p(t,s)=Sval_p(t,s)+ ... 1.602e 4*delta_p (p)*interp1(Ep(:),SAFp(t,:,s),p_dk(p,1), 'spline' ); end % ------------------------------Electrons ------------------------for e=1:nume; Sval_e(t,s)=Sval_e(t,s)+ ... 1.602e 4*delta_e(e)*interp1(Ee(:),SAFe(t ,:,s),e_dk(e,1), 'spline' ); end % ------------------------------Betas ------------------------for b=1:numb; Sval_b(t,s)=Sval_b(t,s)+ ... 1.602e 4*delta_b(b)*interp1(Ee(:),SAFe(t,:,s),b_dk(b,1), 'spl ine' ); end % -----------------------------Together ------------------------Sval(t,s)=Sval_p(t,s)+Sval_e(t,s)+Sval_b(t,s); end end save (strcat( 'Models \ ,model, \ Svalues \ Sval_' ,nuclides{1,r}, '.mat' ), ... 'Sval' ) c lear Sval_p delta_p nump p_dk Sval_eb Sval_e Sval_b delta_e delta_b nume numb e_dk b_dk end %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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251 APPENDIX C BUILDUP INPUTS The following is an example of the MCNP input used for buildup calculations. The inputs are similar for all energies. The only differences from energy to energy are: the source definition, the radii of the spheres, and the energy bins. This appendix also shows the MATLAB TM m files used during the input cons truction. Buildup Factor calculation 15 keV C 1 1 1.040 1 2 $MFP cells 2 1 1.040 3 4 $MFP cells 3 1 1.040 5 6 $MFP cells 4 1 1.040 7 8 $MFP cells 5 1 1.040 9 10 $MFP cells 6 1 1.040 1 1 12 $MFP cells 7 1 1.040 13 14 $MFP cells 8 1 1.040 15 16 $MFP cells 9 1 1.040 17 18 $MFP cells 10 1 1.040 19 20 $MFP cells 11 1 1.040 21 22 $MFP cells 12 1 1.040 23 24 $MFP cells 13 1 1.040 25 26 $MFP cells 14 1 1.040 27 28 $MFP cells 15 1 1.040 29 30 $MFP cells 16 1 1.040 31 32 $MFP cells 17 1 1.040 33 34 $MFP cells 18 1 1.040 35 36 $MFP cells 19 1 1.040 37 38 $MFP cells C 101 1 1.040 1 $in between shells 102 1 1.040 2 3 $in between shells 103 1 1.040 4 5 $in between shells 104 1 1.040 6 7 $in between shells 105 1 1.040 8 9 $in between shells 106 1 1.040 10 11 $in between shells 107 1 1.040 12 13 $in between shells 108 1 1.040 14 15 $in between shells 109 1 1.040 16 17 $in between shells 110 1 1.040 18 19 $in between shells 111 1 1.040 20 21 $in between shells 112 1 1.040 22 23 $in between shells 113 1 1.040 24 25 $in between shells 114 1 1.040 26 27 $in between shells

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252 115 1 1.040 28 29 $in between shells 116 1 1.040 30 31 $in between shells 117 1 1.040 32 33 $in b etween shells 118 1 1.040 34 35 $in between shells 119 1 1.040 36 37 $in between shells 500 1 1.040 100 38 $outside the shells 1000 0 100 $void 1 SO 0.0056 2 SO 0.0066 3 SO 0.0118 4 SO 0.0 128 5 SO 0.0179 6 SO 0.0189 7 SO 0.0302 8 SO 0.0312 9 SO 0.0486 10 SO 0.0496 11 SO 0.0916 12 SO 0.0926 13 SO 0.1838 14 SO 0.1848 15 SO 0.3066 16 SO 0.3076 17 SO 0.6137 18 SO 0.6147 19 SO 0.9208 20 SO 0.9218 21 SO 1.2280 22 SO 1.2290 23 SO 1.5351 24 SO 1.5361 25 SO 1.8422 26 SO 1.8432 27 SO 2.1493 28 SO 2.1503 29 SO 2.4564 30 SO 2.4574 31 SO 2. 7635 32 SO 2.7645 33 SO 3.0707 34 SO 3.0717 35 SO 3.3778 36 SO 3.3788 37 SO 3.6849 38 SO 3.6859

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253 100 SO 300 $Universe mode p e imp:p,e 1 38r 0 C sdef e rg=0.015 pos=0 0 0 $isotropic monoenergetic point source C soft tissue adult ORNL/TM 8381 (density = 1.04 g/cc) m1 1000 0.10454 6000 0.22663 7000 0.0249 8000 0.63525 & 11000 0.00112 12000 0.00013 14000 0.0003 15000 0.00134 & 16000 0.00204 17000 0.00133 19000 0.00208 20000 0.00024 & 26000 0.00005 30000 0.00003 37000 0.00001 40000 0.00001 C skeleton adult ORNL/TM 8381 (density = 1.4 g/cc) C m2 1000 0.07337 6000 0.25475 7000 0.03057 8000 0.47893 & C 9000 0.00025 11000 0.00326 12000 0.00112 14000 0.00002 & C 15000 0.05095 16000 0.00173 17000 0.00143 19000 0.00153 & C 20000 0.1019 26000 0.00008 30000 0.00005 37000 0.00002 & C 38000 0.00003 82000 0.00001 C lung tissue adult ORNL/TM 8381 (density = 0.296 g/cc) C m3 1000 0.10134 6000 0.10238 7000 0.02866 8000 0.75752 & C 11000 0.00184 12000 0.00007 14000 0.00006 15000 0.0008 & C 16000 0.00225 17000 0.00266 19000 0.00194 20000 0.00009 & C 26000 0.00037 30000 0.00001 37000 0.00001 C f14:p 1 $fluence tally f24:p 2 f34:p 3 f44:p 4 f54:p 5 f64:p 6 f74:p 7 f84:p 8 f94:p 9 f104:p 10 f114:p 11 f124:p 12 f134:p 13 f144:p 14 f154:p 15 f164:p 16 f174:p 17 f184:p 18 f194:p 19 E0 0.001 0.005 0.01 0.014985 0.015 C nps 100000000 dbcn 17j 1

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254 %~~~~~~~~~~~~~~ BU input construction Spherical shell radi i ~~~~~~~~~~~~~ %figure out the thickness of the concentric shells in order to calculate %the BU at different MFP for the different energies % [~,sheets]=xlsfinfo('MFP for BU calc.xlsx'); % [MFP_STtemp,txt,raw] = xlsread('MFP for BU calc.xlsx',2); [~,shee ts]=xlsfinfo( 'Build up MCNP/BU factor checks/water BU/MFP water.xlsx' ); [MFP_STtemp,txt,raw] = xlsread( 'Build up MCNP/BU factor checks/water BU/MFP water.xlsx' ,2); MFP=MFP_STtemp(1,2:end); Energy=MFP_STtemp(2:end,1); MFP_STtemp(1,:)=[]; MFP_STtemp(:,1)=[] ; cells(1,:)=[1:1:size(MFP_STtemp,2)]; cells(2,:)=[1:1:size(MFP_STtemp,2)]; MFP_ST=zeros(size(MFP_STtemp,1),size(MFP_STtemp,2)*2); middle=size(MFP_STtemp,2); MFP_ST(:,1:middle)=MFP_STtemp 0.0005; MFP_ST(:,(middle+1):end)=MFP_STtemp+0.0005; MFP_ST=sort( MFP_ST,2); %all the values in the odd positions of the matrix represent the inner boundary of the shell %and all the values in the even spots represent the outer boundaries of the %shells shells(1,:)=[1:1:size(MFP_ST,2)]; for E=1:size(Energy,1) she lls(2,:)=MFP_ST(E,:); fileID=fopen(strcat( 'Build up MCNP/BU factor checks/water BU/BU_E' ,num2str(Energy(E)*1000, '%u' ), 'try.txt' ), 'a+' ); %note that the first number is going to come from the first row,first column and the %second number will come from the second row, first column, then it goes %back to the first row but it starts on the second column. %~~~~~~~~~~~~~Geometry card definitions fprintf(fileID, '% 2u SO %6.4f \ r \ n' ,shells); fclose(fileID); clear n %EnergyBin end %~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~ Response Function Calculation for BU ~~~~~~~~~~~~~~~~~~~~~~~ % ----------------------Body tissues Composition(ST,Lung,Bone) -----------%%%%%%%%%%%%% Load weight fraction elemental compositi ons of tissues [value symbol]=xlsread( 'Tissue info \ Tissue composition_Adult_ORNL' ); symbol(1,:)=[]; % delete first row. It only says "elements" symbol(:,2:(end 1))=[]; % store all the other rows except for the last one which says density

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255 %store the density (g/cc) of each tissue (1 ST, 2 Lung, 3 Homogeneous Bone) density=value(end,:); value(end,:)=[]; %once stored, delete density values from the file % store the elemental weight fraction for each tissue value(:,1)=value( :,1)/100; %ST value(:,2)=value(:,2)/100; %Lung value(:,3)=value(:,3)/100; %Bone value(:,4)=value(:,4)/100; %ST25 HB75 value(:,5)=value(:,5)/100; %ST50 HB50 value(:,6)=value(:,6)/100; %ST75 H B25 % Load info about the elemental attenuation coefficients (how many % elements numElements and their names sheets) [type, nameElements]=xlsfinfo( 'Tissue info \ Attenuation Coeff \ AttenCoeff Elements' ); numElements=size(nameElements,2); %edges of the energy bins used in the MCNP input p_dk(:,1)=[0.010 0.050 0.1 0.125 0.150 0.175 0.200 0.225 0.250 ... 0.275 0.300 0.325 0.350 0.375 0.399600 0.400]; nump=size(p_dk,1); % -----do it if you want the response function based on the low bound %energ y of the bin p_dk(1,2)=0; p_dk(end,2)=p_dk(end,1); for i=2:(nump 1); p_dk(i,2)=p_dk(i 1,1); end % ---------------Calculate the attn coefficients for each body tissue %%%%%%%%%%%%% Load mu/rho and mu_en/rho for each element (n) @ Ei of decay %%% uni ts of attn coefficients in cm2/g mu_enRho=zeros(nump,6); for t=1:6; %loop through the different body tissues for n=1:numElements; %loop through the elemental composition elemVal(:,:)=xlsread( 'T issue info \ Attenuation Coeff \ AttenCoeff Elements' ,n); for i=1:nump; %loop through the E of decay photons mu_enRho(i,t)=mu_enRho(i,t)+ ... interp1(elemVal(:,1),elemVal(:,3),p_dk(i,2))*value (n,t); end clear elemVal

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256 end end clear t clear n clear i ResponseFxn(:,1)=p_dk(:,2); ResponseFxn(:,2)=mu_enRho(:,1); %change the second number to match the tissue of interest Response Fxn(:,3)=1.602e 10*p_dk(:,2).*mu_enRho(:,1); %change the second number to match the tissue of interest %only in mu_enRho, %not p_dk %write t he response functions to a text file. Change the name to indicate %tissue type! fileID=fopen(strcat( 'Build up MCNP/MuEnOverRhoforBUcalcs_ST_lowE ,num2str(p_dk(end,2)*1000), '.txt' ), 'w' ); fprintf(fileID, '%5.3f %5.3e %5.3e \ r \ n' ,ResponseFxn'); fclose(fileID ); %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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265 BIOGRAPHICAL SKETCH L aura Padilla was born in Spain and i n the year 2000, she moved to Florida with her parents and her brother. She started at the University of Florida in August of 2002 and she graduated Summa cum Laude with ngineering in Dec ember of 2006. She studied abroad in Grenoble, France during the f all of 2007 and she gradu hysics in May of 2008. After graduation from the University of Florida with a Ph.D. in medical physics in August of 2012 s he started her three year physics residency at the University of Chicago in the fall of 2012