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1 COMPUTER SIMULATIONS TO ESTIMATE ORGAN DOSES FROM CLINICALLY VALIDATED CARDIAC, NEURO, AND PEDIATRIC PROTOCOLS FOR M ULTI PLE D ETECTOR C OMPUTED T OMOGRAPHY SCANNERS By MONICA GHITA A DISSERTATION PRESENTED TO THE GRADUATE SC HOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009
2 2009 Monica G hita
3 To my family as a tiny thank s for the i nvaluable they do to me
4 ACKNOWLEDGMENTS First I would like to express my gratitude to my advisor s Dr. Glenn Sjoden and Dr. Manuel Arreola for affording me the opportunity to study and work under their direction though always giving me the freedom a nd support to pursue my dreams I am indebted to them for their guidance, patience, and endless encouragement. Their advice regarding my dissertation, my career plans, or any other matters, were consistently insightful m grateful to the m for believing in me and making all this happen I would like to express my sincere thanks to. Dr Wesley Bolch, Dr. Benjamin Frigley, and Dr. Lynn Rill for serving in my PhD committee and to assure them that their suggestions, guidance, and patience wer e and will remain greatly valued and appreciated. I need to extend m y gratitude to Dr s Arreola Sjoden, and Bolch, for all the knowledge they offered me with generosity; having them as p rofessor s was a great fortune and plea sure which decisively shape d my formation as a scientist. This list cannot be complete without paying my tribute to a great professor, Dr. Alireza Haghighat; his eloquence, his daring spirit, and his high expectations inspired me and made me always try to be better But how complete can be a medical physicist without a solid clinical formation? Dr. Rill made the switch from Because of her and of the wonderful people in the QC/GAs office I gained the practical knowledge I needed to really look a s one of them. Bo Hartman especially was always there with her comforting smile when I (sometimes too often) needed. My special thanks go to my colleague, Lindsey Lavoie for her c ontagious optimism, relentless effort and altruism. This work would not be as complete as it is without her help and
5 her contribution. It was a very valuable, enriching, and joyful experience the research collaboration with her. There are several others t hat I would like to acknowledge for their help during these five years. To t he staff at NRE and Radiology that kindly got me through the maze of paperwork truly thankful Diana Dampier especially had always an answer to my questions and requests. On t h e personal side, I know that all the people close to me are smart and sensitive enough to realize how invaluable they are to me. I simply thank them for that. However, I need to speak it out but t he words are not rich enough to express my deepest feeling s to my precious daughter and my dear husband for their patience, continuous support and understanding all along this challenging endeavor They and their sharp spirit and positive attitude gave me the ultimate strength and motivation to fulfill my goals. No study of this nature and complexity can be accomplished without the help, support, and cooperation of many others. I am grateful to all of them.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 9 LIST OF FIGURES ................................ ................................ ................................ ....................... 11 ABSTRACT ................................ ................................ ................................ ................................ ... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 16 1.1 General Considerations ................................ ................................ ................................ 16 1.2 Radiation Dose Issues in C omputed T omography ................................ ........................ 17 1.2.1 C omputed T omography An Increasing Source of Radiation Exposure ......... 17 1.2.2 C omputed T omography Health Risks Concerns ................................ ............ 18 1.2.3 C omputed T omography Special Considerations in Children ......................... 20 1.2.4 C omputed T omography Risk Estimates Discussion ................................ ...... 21 1.2.5 C omputed T omography Dose Assessment Methods ................................ ..... 22 1.3 Objectives of This Research Work ................................ ................................ ............... 25 2 MAT ERIALS AND METHODS ................................ ................................ ........................... 30 2.1 Three Dimensional Radiation Transport Methods ................................ ........................ 30 2.1.1 MCNP5 An Open Source General Purpose Monte Carlo Code .................... 31 2.1.2 PENTRAN a Deterministic Discrete Ordinates (S N ) Code ............................... 34 2.1.3 PENTRAN MCNP5 Hybrid Technique CADIS Methodology ..................... 35 2.2 The UF Series B Voxel Phantoms ................................ ................................ ................ 38 3 A DIAGNOSTIC X RAY SPECTRA GENERATOR CODE DXS ................................ ... 42 3.1 Introduction ................................ ................................ ................................ ................... 42 3.2 Theoretical Formulation ................................ ................................ ................................ 44 3.3 Code Implementation ................................ ................................ ................................ .... 46 3.4 Validation of DXS ................................ ................................ ................................ ........ 49 3.4.1 Comparison with MCNP5 Generated Spectra ................................ .................. 49 3.4.2 Comparison with Published Measured Spectra ................................ ................ 50 3.4.3 MCNP5 Simulations of Clinical Spectral Measurements ................................ 50 3.5 Conclusions ................................ ................................ ................................ ................... 55 4 PENTRAN MP CODE SYSTEM ................................ ................................ .......................... 69 4.1 Pre Processing Codes ................................ ................................ ................................ .... 69 4.1.1 PENMSHXP or ................................ .......... 69
7 4.1.2 DXS The Pilot Code of the PENTRAN MP System ................................ ..... 70 4.1.3 GREPXS The Cross Sections Extractor and Writer ................................ ...... 71 4.1.4 GHOST 3D Computational Human Phantoms Builder ................................ 71 4.2 Post Processing Codes ................................ ................................ ................................ .. 72 5 BENCHMARKS AND VALIDATION TESTS DETERMINISTIC APPROACH ........... 76 5.1 State Transport Benchmark Problems .... 76 5.1.1 Benchmark Problem 1 Plane Source ................................ .............................. 76 5.1.2 Benchmark Problem 2 Solid Spherical Source ................................ .............. 79 5.1.3 Benchmark Prob lem 3 Spherical Shell Source ................................ .............. 80 5.1.4 Benchmark Problem 4 Point Source ................................ .............................. 80 5.2 PENTRAN MP Dose Computations in Voxelized Phantoms ................................ ...... 82 5.2.1 Case Study 1 Flux and Dose Distribution; Volumetric Isotropic Source ...... 82 5.2.2 Case Study 2 Organ Dose Calculations; Is otropic Source ............................. 83 5.2.3 Case Study 3 Dose Calculations; Monodirectional Source ............................ 87 5.2.4 Case Study 4 Optimization Studies ................................ ................................ 88 5.3 Conclusions about the deterministic approach ................................ .............................. 89 6 M ONTE CARLO MODEL FOR MDCT DOSIMETRY SIMULATIONS ......................... 101 6.1 Introduction ................................ ................................ ................................ ................. 101 6.2 Overview of M D CT Technology ................................ ................................ ................ 103 6.3 Broad Beam MDCT Scanners ................................ ................................ ..................... 105 6.4 Development of the Monte Carlo Model for MDCT ................................ .................. 10 6 6.4.1 Monte Carlo Formulation for a Source in Axial and Helical Motion ............. 106 6.4.2 Preliminary Tests to Validate the Source Subroutine ................................ ..... 108 6.4.3 Equivalent Energy Spectra and Filtration Models Based on Measurements .. 109 126.96.36.199 Half value layer ................................ ................................ ......... 110 188.8.131.52 Bowtie filter attenuation profile ................................ ................ 111 6.4.4 Validation of the Monte Carlo Model for MDCT Dosimetry Simulations ..... 112 184.108.40.206 Air kerma measurements in CTDI phantom ............................. 113 220.127.116.11 Simulations for air kerma measurements in CTDI phantoms ... 114 18.104.22.168 Comparison between measurements and simulations in CTDI phantoms ................................ ................................ ......... 118 7 ORGAN DOSE SIMULATIONS FOR THE 320 SLICE MDCT SCANNER ................... 129 7.1 Pediatric Study ................................ ................................ ................................ ............ 131 7.1.2 Organ Dose Compari son with Pr ovided OSL Dosimeter Measurements ....... 132 7.1.1 Organ Dose Comparison from 320 Slice and 64 Slice Studies ...................... 132 7.2 Adult Brain Perfusion ................................ ................................ ................................ 134 7.2.1 Organ Dose Comparison with Provided OSL Dosimeter Measurements ....... 136 7.1.1 Organ Dose Comparison for the 320 Slice and 64 Sl ice Studies ................... 136 7.3 Adult Cardiac CT Angiography ................................ ................................ .................. 137 7.3.1 Organ Dose Compari son with Provided OSL Dosimeter Measurements ....... 139 7.3.2 Organ Dose Comparison for the 320 Slice and 64 Slice Studies ................... 140
8 7.4 General Comment ................................ ................................ ................................ ....... 141 8 CONCLUSIONS ................................ ................................ ................................ .................. 148 8.1 Analysis of the Results ................................ ................................ ................................ 148 8.2 Future Work ................................ ................................ ................................ ................ 151 APPENDIX A CODE DESCRIPTION AND SAMPLES OF OUTPUT FILES PENIMP ....................... 153 B SUBROUTINE AND SAMPLES OF INPUT FILES MCNP5 ................................ ......... 157 Source.F90 Subroutine File ................................ ................................ ................................ .. 157 Input File for the Simulations of Air Kerma Measurements in Head CTDI Phantom ......... 162 Input Fi le for Simulations of the Free in Air Air Kerma Measurements .............................. 163 Input File for the Pediatric Protocol Simulations ................................ ................................ 164 Input File fo r the Cardiac/Brain Perfusion Protocol Simulations ................................ ......... 167 LIST OF REFERENCES ................................ ................................ ................................ ............. 170 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 176
9 LIST OF TABLES Table page 2 1 Comparison of the S N and Monte Carlo (MC) methods ................................ .................... 41 3 1 Percent difference between the original Tucker et al. model (TBC) and measured spectra ................................ .......... 57 3 2 Characteristic x rays for tungsten and their relative intensities ................................ ......... 57 3 3 Parametrization of mass attenuation coefficients ................................ .............................. 57 3 4 Mass stopping power parameters for tungsten ................................ ................................ ... 57 3 5 Parametrization of the Thomson Whiddington constant ................................ ................... 57 3 6 Root mean square deviation of the spectra generated with DXS ................................ ....... 58 3 7 Root mean square ( rms ) deviation from the reference of the DXS generated spectra ...... 58 5 1 Scalar flux solution for the plane source c =0.9, g =0.9, L =12, =10 3 ................................ 91 5 2 Scalar flux solution at x=0.01 mfp for the plane source: effect of the S N order ................ 91 5 3 Scalar flux solution for the plane source: effect of the slab width ................................ ..... 91 5 4 Scalar flux solution for the spherical source: c =0.99, g =0.95, L =20, =10 3 ..................... 91 5 5 Scalar flux solution for the shell source: c =0.9, g =0.9, L =12, =10 3 ................................ 92 5 6 Scalar flux solution for point source: c =0.9, g =0.9, L =12, =10 3 ................................ ..... 92 6 1 Measured HVLs for different tube voltage filter combinations for the 320 slice scanner; Monte Carlo calculated equivalent Al filtration ................................ ................ 120 6 2 Air kerma (mGy) m easured in CTDI head phantom ................................ ....................... 120 6 3 Reproducibility of an axial scan. ................................ ................................ ..................... 120 6 4 Reproducibility of a helical scan. ................................ ................................ ..................... 120 6 5 Scanner settings for the air kerma measurements in CTDI phantoms ............................. 121 6 6 Comparison between air kerma measurements and simulations in CTDI phantoms ...... 121 7 1 Tissue weighting factors. ................................ ................................ ................................ 143
10 7 3 Average organ dose (mGy) comparison for the 320 slice CT pediatric studi es investigated; Monte Carlo simulations (MC) vs. measurements (OSL) ........................ 143 7 4 Average organ dose (mGy) comparison for the pediatric head CT simulations; ............ 144 7 5 Details of 320 slice brain perfusion protocols. ................................ ................................ 144 7 6 Scan parameters for helical adult brain perfusion protocol. ................................ ............ 145 7 7 Average organ dose (mGy) comparison for the 320 slice CT brain perfusion studies investigated; Monte Carlo simulations (MC) vs. measurements (OSL) ........................ 145 7 8 Average organ dose (mGy) comparison for each protocol in the brain perfusion studies investigated; Monte Carlo simulations (MC) vs. measurements (OSL) ............ 146 7 9 Average organ dose (mGy) comparison for the brain perfusion CT simulations; ........... 146 7 10 Scan parameters for adult cardiac CTA protocol. ................................ ............................ 147 7 11 Average organ dose (mGy) comparison for the 320 slice cardiac CTA studies investigated; Monte Carlo simulations (MC) vs. measurements (OSL) ........................ 147 7 12 Average organ dose (mGy) comparison for the cardiac CTA studies sim ulations; ........ 147
11 LIST OF FIGURES Figure page 2 1 Stylized anatomic models of human anatomy developed at the Oak Ridge National Laboratory in the early 1980s. ................................ ................................ ........................... 41 2 2 UF Series B pediatric phantoms ................................ ................................ ........................ 41 3 1 E lectron fractional residual energy ................................ ................................ .................... 59 3 2 Simplified MCNP5 model for the tungsten target ................................ ............................. 59 3 3 DXS generated spectra using the updated formulation for the electron pen etration in the target ................................ ................................ ................................ ............................. 60 3 4 Comparison between DXS (black line) and MCNP5 (red points with error bars) spectra for 50, 65, and 70 kVp tube potentials, 12 target angle, 1.2 mm Al filtration ..... 61 3 5 Comparison between DXS (black line) and MCNP5 (red points with error bars) spectra for 80, 90, 130, and 140 kVp tube potentials, 12 target angle, 1.2 mm Al filtration ................................ ................................ ................................ .............................. 62 3 6 DXS spectra (black lines) compared to MCNP5 results (red points with error bars) for 100 kVp, 10 target angle, and different thicknesses of aluminum filter ..................... 63 3 8 Comparison between the DXS generated spectra and the measured spectra .................... 64 3 9 Ge detector characterization ................................ ................................ ............................. 65 3 10 Simplified MCNP5 model to simulate experimental measurements ................................ 65 3 11 Photon current spectral distribution for 6 direction intervals ................................ ............ 66 3 12 MCNP5 model of the HPGe detector ................................ ................................ ................ 66 3 13 Comparison of the measured and simulated detector response ................................ ......... 67 3 14 Comparison of the measured and MCNP5 simulated detector response usi ng DXS generated source spectra ................................ ................................ ................................ ... 68 4 1 Simulation methodology for dose distribution and organ dose calcul ations using the PENTRAN MP code system ................................ ................................ ............................. 74 4 2 GHOST 3 D down sampled models of the 11 year old male phantom of UF Series B .... 74 4 3 Corresponding axial slices in different voxel phantoms ................................ .................... 75 5 1 Plane source: effect of the source width and fine mesh size ................................ .............. 93
12 5 2 Plane source: effect of the scattering order L ................................ ................................ ..... 93 5 3 Solid spherical source: PENTRAN model (left) and full scalar flux solution (right) ....... 94 5 4 Spherical shell source: PENTRAN model (left) and full scalar flux solution (right) ........ 94 5 5 Point source: PENTRAN model (left) and full scalar flux solution (right) ....................... 95 5 6 Scalar flux solution for the 1 D sources: c =0.9, g =0.9, L =12 ................................ ............ 95 5 7 Computational models for case study 1 ................................ ................................ ............. 96 5 8 D ose distribution ................................ ................................ ................................ ................ 96 5 9 Energy bin probabilities (color lines) for the 8 group S 48 calculation generated by DXS; black line the quasi continuous corresponding DXS generated spectrum used in the state of the art MCNP5 simulation ................................ ................................ .......... 97 5 10 Percent difference from state of the art MCNP5 results of the average organ doses calculated with PENTRAN MP methodology using different energy group struc tures in the case of isotropic x ray source ................................ ................................ .................. 97 5 11 Comparison between average organ doses due to the same x ray radiation exposure ...... 98 5 12 Average organ flux comparison between PENTRAN MP and state of the art MCNP5 results ................................ ................................ ................................ ................... 98 5 13 Mass attenuation and mass energy attenuation coefficients for soft tissue ....................... 99 5 14 Percent difference from state of the art MCNP5 results of the average organ doses calculated with PENTRAN MP methodology using different energy group structures in the case of monodirectional x ray source ................................ ................................ ...... 99 5 15 Effect of the down sampling order of the computational phantom on the accuracy of the calculated organ doses ................................ ................................ ............................... 100 6 1 Schematic representation of th e geometry of the 320 slice scanner ................................ 122 6 2 Flux variation along z axis in a helical scan (flat filter) simulation ................................ 123 6 3 Experimental setup to measure beam intensity profile across the fan beam ................... 124 6 4 Attenuation profile for the small S bowtie filter of the 320 slice scanner ...................... 124 6 5 Attenuation profile for the me dium M bowtie filter of the 320 slice scanner ................. 1 25 6 7 Attenuation profiles at 80 kVp nominal tube voltage for the three bowtie filters of the 320 slice scanner ................................ ................................ ................................ .............. 126
13 6 8 Conventional head and body CTDI phantoms ................................ ................................ 126 6 9 Model for the MCNP5 simulations of the air kerma measurements in the CTDI head pha ntom ................................ ................................ ................................ ............................ 127 6 10 Radiographic image of the 160 mm nominal CT x ray beam ................................ ......... 127 6 11 Beam profile of the 160 mm nominal C T x ray beam. ................................ .................... 128
14 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 COMPUTER SIMULAT IONS TO ESTIMATE ORGAN DOSES FROM CLINICALLY VALIDATED CARDIAC, NEURO, AND PEDIATRIC PROTOCOLS FOR M ULTIPLE D ETECTOR C OMPUTED T OMOGRAPHY SCANNERS By Monica Ghita August 2009 Chair: Glenn E. Sjoden Cochair: Manuel M. Arreola Major: Nuclear Engineering Sciences Recent advances in Compu ted Tomography (CT) technology, particularly that of multiple detector CT (MDCT) scanning, have provided increased utilization and more diverse clinical applications including more advanced vascular and cardiac exams, perfusion imaging, and screening exams Notwithstanding the benefits to the patient undergoing a CT study, the fundamental concern in radiation protection is the minimization of the radiation exposure delivered as well as the implementation of structures to prevent inappropriate ordering and c linical use of these advanced studies. This research work developed a computational methodology for routine clinical use to assess patient organ doses from MDCT scanners. To support the methodology, a computer code (DXS Diagnostic X ray Spectra) was develo ped to accurately and conveniently generate x ray spectra in the diagnostic energy range (45 140 keV). The two accepted standard radiation transport ca lculation methods namely deterministic and Monte Carlo, have been preliminarily investigated for their c apability and readiness to support the proposed goal of the work. Thorough tests demonstrated that the lack of appropriate discrete photon interaction coefficients in the aforementioned diagnostic energy range impedes the applicability of the deterministic a pproach to routine clinical use; improvements in the
15 multigroup treatment may make it more viable. Thus, the open source Monte Carlo code, MCNP5, was adapted to appropriately model an MDCT scan. For this, a new method, entirely based on routine clinical CT measurements, was developed and validated to generate an tomographic h uman phantoms were performed to assess, compare, and optimize pediatric, cardiac and neuro imaging protocols for the new 320 slice scanner at Shands/UF based on dose considerations. Results were compared against organ dose measurements previously obtained at Sha n ds UF. Important dose reductions were assessed for the broad beam volumetric acquisition of this new scanner when compared to the standard 64 slice helical protocols.
16 CHAPTER 1 INTRODUCTION 1.1 General C onsiderations Soon after their discovery in 1895, x rays defined and propelled radiographic imaging into an essential component of medical care, being the first investigative tool for non invasive medicine ever used Since then, different imaging modalities, using ionizing or non ionizing radiation have developed and expanded the field of radiology. Their impressive development over the past quarter century has revolutionized the practice of medicine, but has also significantly increased the cumulative exposure to ionizing radiation of all populatio n s 1 X rays used in medical diagnostic procedures represent the greatest "man made" source of radiation exposure to the population, accounting, in 1987, for about 1 5 % of the total annual exposure of the population of the United States from al l sources 2 and around 50% in 2006, according t o the Program Area Committee 6 (Radiation Measurements and Dosimetry) 3 This dramatic escalation has generated a s erious interest and a scrutiny of radiation dose s resulting from imaging procedures si mply because ionizing radiation is known to increase the risk for cancer induction, and has even recently be en 1 The risk estimates are mostly derived from studies of the Japanese citizens who were exposed to large amounts of radiation during the A bomb attacks of Hiro shima and Nagasaki 62 years ago; BEIR VII the most recent update on this topic indicates that in the United States, a single dose of 10 mSv to the population is associated with a lifetime attributable risk of 1 in 1000 for developing a solid cancer or leukemia. 4 The overall risk of developing a solid cancer or l eukemia from all causes is 42 in 100. Although it is a challenge to define precise risk estimates associ ated to low doses of radiation exposure by extrapolating from data at high doses th e ionizing r adiation exposure from
17 certain medical imaging studies, like abdominal or chest CT, nuclear medicine or interventional fluoroscopic procedures, may be associated with elevated risk s for DNA damage and cancer formation 5,6 1.2 Radiation Dose Issues in C omputed T omogra phy 1.2.1 C omputed T omography An Increasing Source of Radiation E xposure It has been more than three decades since computed tomography (CT) first became available for diagnostic imaging. Technical developments have resulted in a number of distinct gener ations of scanners, including helical CT in the early 1990s and most recently multiple detector computed tomography (MDCT) scanners. Because of these tremendous technical advancements, CT has become an increasingly used tool in a wide variety of clinical studies, including vascular and cardiac exams, perfusion imaging, and screening exams. I t was estimated that there was a 600% increase in all CT examinations in the decade spanning the mid 1980s to the mid 1990s, with an increase in CTs for the pediatric population from about 4% to over 11% of all CT examinations 7 Estimates reveal that more than 60 million CT examinations were performed in 2002 in the United S tates, 8 representing around 70% of the cumulative medical x ray exposure with 6% to 11% of the se exams being performed in children. 7,9 Approximately 33% of all pediatric CT examinations are performed in children in the first decade of life, with 17% of them in children at or under the age of 5. The Hippocratic medicine, which means that the benefit of any procedure should outweigh the risk associated with it. However, in 2001, a series of articles 5, 10 12 published in the American Journal of Roentgenology on the matter of increased risks to pediatric patients from CT generated concerns of the general public regarding the medical appropriateness of CT examinations and people have begun to scruti nize radiation dose levels from all CT scans.
18 1.2.2 C omputed T omography Health Risks Concerns The potential biological influence of ionizing radiation can be expressed with a formally defined quantity called the equivalent dose. This quantity, in turn, depends on the energy absorbed from the radiation beam per unit mass in a given tissue or organ a quantity termed absorbed dose The product between the absorbed dose and a radiation weighting factor yields the equivalent dose. In the case of photon rad iation, the weighting factor is 1. When evaluating the radiation risk resulting from exposures to certain regions and organs of the body, the relative radiosensitivity of the various organs and tissues mus t be taken into consideration. To globally express the risk to an individual exposed to a uniform whole body irradiation equivalent to that of a partial body or organ exposure another formal quantity has been defined, the effective dose, which numerically, is the sum of the products of the equivalent dose and the individual tiss ue weighting factors. The NCRP (1993) defines the tissue weighting factor as expressing the relative biological detriment to a tissue, and accounts for the risk of cancer related death, severe hereditary effects seen in future gener ations, and the length of life lost due to these effects. The debate about the safety of CT has intensified recently, after the 2007 article by Drs. David Brenner and Eric Hall in the New England Journal of Medicine 6 which suggest s that the radiation dose from CT scans is a cause for concern, and may be responsible for a small yet relevant percentage of cancer deaths in the United States. This current review by Brenne r and Hall highlights the need to re evaluate and re understand the radiation exposure risks associated with x ray imaging. R adiosen sitive tissues are frequently within the field of view for routine chest, abdominal, and pelvic CT scans and unfortun ately m any patients undergo multiple radiological examinations which increase their cumulative dose. The authors reported on increased risks associated with even low doses of radiation.
19 Most of the quantitative information on radiation risks and radiation indu ced cancers comes from studies of survivors of the atomic bombing s in Japan in 1945. This cohort of patients has been studied over time. Such studies report a n increase in the overall risk for cancer in these p atients/survivors who received low doses of ra diation, with effective doses ranging f rom 5 to 150 mSv The mean effective dose for this group was approximately 40 mSv, which approximates relevant organ dose levels from a typical CT study in which 2 3 s eries are done according to the estimates reporte d in the above mentioned article. 6 The concerns are further corroborated by a recent study involving over 400,000 radiation workers in the nuclear industry which also reported a significant association between radiation dose and mortality from cancer for a dose range between 5 and 150 mSv 13 The risks were quantitatively consistent with those of the atomic bomb survivors. Since results of prospective dosimetric studies for patients who undergo CT studies will not be available for a long time, the author s stated that it is possible to evaluate the risks of exposure by estimating the radiation dose to individual organs 5 and applying the organ specific cancer incidence or mortality data derived from the studies of the atomic bomb survivors. Brenner and Hall estimated the lifetime risk for death from cancer that was attributabl e to a single "generic" CT scan of the hea d or abdomen. The risks vary depending on the age of the patient at the time of exposure and the organ specific dose. Even tho ugh the doses are higher for a head CT scan, the risks are higher for abdominal sc ans because the digestive tract tissues are more sensiti ve than the brain to develop radiation induced cancer. Extrapolating from the data provided, the risk for cancer related death associated with 1 abdominal CT scan is 0.06% for a patient exposed at 25 ye ars of age and 0.02% for a patient exposed at age 50. Adjusting for the current use of CT scans in the United States, it was estimated that 1.5% to 2.0% of all cancers at present time are attributable to radiation exposure from CT scanning.
20 1.2.3 C ompute d T omography Special Considerations in Children CT is the modality of choice in assessing a variety of disorders in children, including detection and surveillance of cancer trauma, and evaluation for infl ammation. The use of CT scans in pediatric patie nts has mushroomed since 1990, when t he new generation of devices decreased scanning time s from minute s to second s The shorter scans have been a boon to c linicians, who use them to diagnose or rule out dangerous conditions such as appendicitis in younger and less cooperative children. 5 The increasing use of CT in the pediat ric population is notable for several reasons. First, CT is a relatively large r source of radiation exposure as compared to other modalities For example, in a review of CT use and radiation dose, the effective dose of a chest CT was reported to be 54 ti mes that of a mammogram, and nearly 68 times the dose of a chest radiograph 7 Second, there are considerations unique to the pediatric population including increased radiosensitivity of certain tissues, particularly in infancy 4 a longer lifetime for radiation related cancer to occur, and often a lack of size based adjustments in radiological technique. 14 Moreover, the cancer risk i s cumulative over a lifetime. Each CT examination (including multiple series per examination) contributes to the lifetime exposure. In contrast, r adiation exposure for older adults and the elderly does not carry the same cancer risk because many radiation induced cancers, particularly solid malignancies, present long latent periods and do not become evident for decades. 6 In the article by Brenner et al ., 5 in which data were based on certain estimations including the total number of CT examin ations performed during one year in infants and children and a relatively high ra diation dose technique, there i s the potential for inducing an increase in the number of cancer fatalities from a single CT. Brenner and Hall e stimates have put this risk at 1 fatal cancer per 1000 pediatric CT examinations, which results in an estimated increase of less than 0.5% over the baseline for lifetime cancer mortality.
21 1.2.4 C omputed T omography Risk Estimates Discussion The assumptions used in this series of Dr. B d upon a number of debatable assumptions for example, the risk coefficients used by Brenner are derived from studies of the Japanese citizens who were exposed to large amounts of radiation during the A bomb attacks of Hiroshima and Nagasaki 62 years ago. These individuals received whole body doses from a mixture of x ray and particulate radiations, whereas CT examinations involve only x rays over a small region of the head or the torso In addition, the majority of the A bomb survivors experi enced radiation doses many fold those of modern computed tomography, and the extrapolation used in scaling the very high radiation exposures levels d own to the much lower exposure levels typical of partial body CT examinations is considered very controversial by many Another debatable issue is that of the radiation risks derived from the Japanese studies being applicable to patients undergoing CT sca ns in the US in 2007. Patients who require me dically indicated CT scans present a health risk and are far likelier to benefit from the diagnostic information that the CT examination provides to doctors involved in their patient care. The population of pa tients undergoing CT tends to be older than the average population, and although the authors of the articles corrected for age using data derived from the 1945 Japanese population, they did not correct for the many underlying co mp ounding age dependent vari ables that differ between this population and older Americans. These considerations are in addition to the inherent large uncertainties due to the lack of enough statistical data in the risk estimate models. There are, however, important positive recomme ndations from the articles including awareness about the long term collective public health risk (not the individual risk which is very small and, a priori, far offset by the benefit), the need for a better understanding of radiation induced cancer incid ence and mortality, better surveys that may bring realistic confidence limits
22 on the estimated risk, and better dose estimates. As an immediate result, despite all the controversial issues, the importance of reducing CT exposure is now understood in gene ral, and with high priority when used in pediatric exams. Health care providers and manufacturers have made significant efforts, since the publication of the first article in 2001, to reduce the radiation exposure from CT scans while scientists have work ed to provide better and more appropriate methods for dose evaluations. 1.2.5 C omputed T omography Dose Assessment Methods Part of the problem with radiation dose estimates (and assignment of risk) is the lack of consensus fo r the measurement (or estimat es ) of dose. 15,1 6 Basically, risk is determined using either direct measures of dose, such as organ dose, or a weighted measure of radiation dose taking into account various organ doses and sensitivities (effective dose). Measures that are increasingly familiar to radiologists and technologists are the CT do se indices (CTDI, CTDI CTDI 100 CTDI w CTDI vol ) and the dose length product (DLP). The CTDI was defined to characterize the radiation dose properties of a specific scanner, 1 7 representing the average absorbed dose, along the z axis, from a series of contiguous irradiations. To estimate dose values for head examinations, the measurements have to be taken with a 100 mm pencil ion chamber, in a 16 cm diameter polymethylmetha cylate ( PMMA ) Food and Drug Administration ( FDA ) standardized phantom, while for the body examinations a separate phantom with a diameter of 32 cm has to be used. As CT technology evolved, a number of CTDI related modified indices have been defined to pro vide a more appropriate index for the newer scanners. To account for the variation of the CTDI index across the scanned field of view ( FOV ) a weighted index, CTDI w has been defined as the sum of one third of the value taken at the center of the phantom a nd two thirds of the average value measured at the periphery of the phantom. With the adve nt of helical CT, to represent the dose for a specific scan protocol, a new dose
23 descriptor was introduced, CTDI vol in terms of the scan pitch. While CTDI vol estim ates the average radiation dose within the irradiated volume for an object of similar attenuation as the CTDI phantom, it does not represent the average dose for objects of substantially different size, shape, or attenuation. Moreover, it does not indicat e the total energy deposited into the scan ned volume. To better represent the overall energy delivered by a given scan protocol, the absorbed dose can be integrated along the scan ned length to compute the Dose Length Product (DLP). These measurements are not applicable, however, for risk assessments. The usefulness of these measures is that modifications of scan parameters are easily reflected in the CTDI vol or DLP disp layed on the scan monitor. They must only serve as an aid in designing scan protocols or in real time modification s of the examination. For example, doubling one CT scan parameter, the tube current, will double the CTDI vol displayed on the monitor. Without knowing the actual dose to any organ (and therefore risk), this measure tells the r adiologist or technol ogist only that the dose to the patient will also be d oubled. Currently, the need for doc umentation of some measure of radiation dose for CT has been expressed by various medical and regulatory groups and because CTDI vol and DLP are relatively easy measures of radiation that are increasingly availab le on scanners, these have become familiar terms in the everyday practice of radiology. A better way of estimating doses to patients undergoing CT examinations is to directly measure orga n doses 15 or to perform computer simulations 16 in patient like phantoms (anthropomorphic phantoms). Commercial s oftware packages have been developed (CTDOSE, WinDose, ImPACT) based on the simulation data to calculate organ and effective doses. The effecti ve dose values calculated with th e s e type of software packages have been compared to DLP values for corresponding clinical exams and a set of coeffici ents depending only on the region of the body being scanned, have been determined to provide a practical methodology for effective dose
24 estimation. 1 8 Using this methodology, effective dose is calculated multiplying the DLP reported on the scanner by the appropriate conversion factor. These methods assume that the patient resembles the phantom used. When patients differ in size and composition, appropriate corrections need to be made In the computer simulations, the styli zed (based on mathematical surface equations) phantoms can be very easily scaled to represent different type of patients. However, the anatomical representation in these models is not realistic or accurate. 1 9 A better representation of the human anatomy is provided b y voxelized phantoms 20 21 which have been constructed from tomographic images of actual patients. Their major disadvantage is that they are suitable only for uniform scaling. To merge the realistic anatomy afforded to voxel phantoms with the flexibility of stylized phantoms, hybrid computational phantoms are being developed 1 8 22 23 promoting them as important tools for a patient specific dose assessment methodology. Considering the present tr ends in medical imaging, with a tremendous increase in the number of examinations performed a nnually, the development of a national database for radiation dose indices has beco me of real importance. Moreover, concluding their analysis on the radiation exposure issues in medicine, the ACR (American College of Radiology) blue ribbon panel 1 supports a standardized method for archiving individual patient radiation data documenting exposure during medical imaging that it is believed, will highly benefit from a well established patient specific dose evaluation methodology. The information would be used to benchmark good medical practices and to identify patients whose cumulative lifetime dose has reached higher levels from frequent imaging studies involving exposure to ionizing radiation. The information may be used to determine when alte rnative imaging c ould be co nsidered.
25 1.3 Objectives of This Research Work In the past few years, the Radiology Practice Committee formed at Shands Hospital at the University of Florida with a membership of radiologists, technologists, and medical physicis ts has developed a database of standard protocols for CT and MRI to be used for all radiology operations. 24 The committee has also developed a web based tool to allow clinicians to search the database based on a known clinical indication. Just recently, a new broad beam Toshiba 320 slice CT scanner has been installed in the department and specific protocols for cardiac, neuro, and trauma exams are being established and included in the database after thorough clinical validation. Appropriateness criteria, as recommended by ACR, are intended to be added to this protocol database that will ultimately optimize the practice of radiology at Shands UF. As the latest discussions in the diagnostic imaging community show, the patient doses associated with CT exams sho uld become one of these criteria. Therefore, this research work addresses three major goals: to develop a computational methodology to assess specific organ doses resulting from relevant imaging protocols of verified clinical value and image quality on a b road beam 320 slice scanner to compare the radiation doses from the current standard 64 slice scanner with those from the new broad beam 320 slice MDCT scanner to recommend approaches to optimize clinical protocols utilizing dose criteria The overall purpo se of the project was not to generate a library of organ dose values, but to develop a computational methodology that can be clinically used as a tool in the determination of appropriateness of the CT exams. Successfully validated, the methodology may be f urther medical history.
26 Chapter 2 of this proposal briefly describes the computational methods and the associated software tools under consideration for accom plishing the main goals of the project. While the Monte Carlo radiation transport methods are well known and have been validated in medical physics research, little is known and yet to be validated about the usefulness of deterministic methods. There have been some attempts to establish deterministic transport calculations as a viable tool in radiation therapy dosimetry, 25,26 but only very few in diagnostic imaging. Hence, intermediate goals are to investigate the accuracy, computational efficiency, and the readiness of PENTRAN, the deterministic S N radiation transport solver developed by Sjoden and Haghighat 27 to be implemented clinically in the dose evaluation methodologies. The general purpose, open source MCNP5 Monte Carlo code developed at Los Alamos N ational Lab 28 has been chosen as the reference, since it is used worldwide, well validated and benchmarked, with a strong up to date physics package. The hybrid method, CADIS (Consistent Adjoint Driven Importance Sampling) methodology 29 is also introduced to be implemented as a mesh based weight window variance reduction technique in MCNP5 using source biasing and importance functions calculated using PENTRAN adjoint transport simulation. The code developed to facilitate the implementation of the CADIS meth odology, PENIMP, is described in Appendix A, where parts of samples of the output files are also exemplified. Central to this work is the application and use of highly detailed anatomical models (now in place at UF ) to conduct accurate dose attribution Th e UF series of voxelized phantoms, developed by the ALRADS group at UF, 20 is briefly described, highlighting their level of anatomical detail which can significantly impact the accuracy of organ dose evaluation methodologies. Moreover, this series of voxe lized tomographic phantoms is being further developed by the same group, into versatile hybrid phantoms, 22,23 a guarantee for successful patient specific dose assessments.
27 Any computational methodology for dose evaluation based on radiation transport cri tically depends on the availability of reliable x ray spectra for the diverse settings of the clinical CT protocols utilized. Chapter 3 describes DXS (Diagnostic X ray Spectra), the code developed by the author based on the original semi empirical model (T BC) proposed by Tucker et al. in 1991 31 to generate tungsten target x ray spectra in the radiological range. DXS differs from the TBC model because the theoretical formulations have been modified according to recent Monte Carlo meters have been adjusted and validated using MCNP5 simulations. Comparisons with some published measured spectra are also included, as well as the clinical spectral measurements obtained at Shands UF with an HPGe spectrometric system. These measurements, in addition to their scholastic value, demonstrate the value of the DXS code in obtaining reliable and relevant primary x ray source spectra in clinical environments which is practically impossible. The proposed methodology for dose distribution and organ dose calculations is presented in Chapter 4 with the main focus on the development of the PENTRAN MP code system (accomplished in collaboration with Ahmad Al Basheer, a recent NRE UF PhD graduate who conducted research studies for application of this meth odology in radiation therapy), 54 a collection of existing codes (PENTRAN with PENMSHXP and PENDATA code system 32 MCNP5, CEPXS the cross section generator code, product of the Sandia National Lab 33 ) and specially developed codes (GHOST 3D, DXS, GREPXS, 3D DOSE) to streamline the simulation procedure. To determine the methodology (either deterministic, Monte Carlo, or combinations of both) to be used for the evaluation of organ doses from MDCT imaging protocols, several tests have been conducted to further v alidate the accuracy of numerical solutions and soundness of
28 method for diagnostic medical physics applications investigated here. The description of such test s with results, discussions and conclusions about the deterministic method are included in Chapter 5. The introduction of multiple detector computed tomography (MDCT) scanner s in 1998 not only accelerated the implementation of new clinical applications, but also generated an intensified effort to evaluate the radiation doses associated with it. Monte Carlo radiation transport simulations in voxelized human phantoms have established themselves as one of the most accurate and versatile methods for radiation transport based dose computations. Chapter 6 contains a brief description of the MDCT scanners, with emphasis on the special issues encountered by the introduction in to clinical practice of the broad beam 320 slice scanner. It also includes the formulatio n implemented in the new MCNP5 source definition subroutine to probabilistically sample the photon fan beam of an x ray source in axial and helical acquisition mode and the new method developed to obtain an equivalent source spectrum and filtration entirel y based on clinical measurements. The comprehensive tests performed to validate the new method implemented in the MCNP5 code are also presented and discussed in this chapter. To accomplish the main goals of the present research work, Monte Carlo simulation s using the new ly developed source model for MDCT dosimetry and UF Series B tomographic phantoms (9 months and adult male) were performed for clinical pediatric, cardiac, and neuro 320 slice CT studies. The detailed description of these simulations is pres ented in Chapter 7, which also includes the comparisons between calculated organ doses and some available experimentally measured doses using optically stimulated luminescence (OSL) dosimeters. The clinical protocol
29 optimization for the 320 slice scanner a nd the comparison with simulated organ doses resulted from the standard 64 slice protocols is presented in this chapter as well. Finally, Chapter 8 is an overview of the goals and motivations of the research, highlighting the accomplishments and the origi nal contributions of the dissertation.
30 CHAPTER 2 MATERIALS AND METHOD S 2.1 Three D imensional Radiation Transport M ethods Modern radiation dosimetry methods depend increasingly on human anatomical modeling and radiation transport simulation. Regardless of the means by which an ionizing radiation dose is delivered, neutral particle transport and interactions of the radiation can be precisely (Equation 2 1) which describes the behavio r of neutral particles as a function of the spatia l, angular, and energy domains. (2 1) The left side of Equation 2.1 represents streaming and collision terms (loss), and the right side represents scattering and other sources (gain), being the angular flux of particles in the phase space as a function of position, energy, and direction, and Q the density of source particles emitted in the same phase space The Boltzmann equation can be precisely solved by following two main approache s, both based on first principles: statistical Monte Carlo and deterministic solution methods. 29 In the statistical Monte Carlo approach, one solves for the expected value of particle density in the phase space by averaging over a large number of particle histories or events. An alternative to Monte Carlo based radiation dose calculation s can be achieved by a deterministic solution of the Boltzmann equation that models radiation transport through materials. A common approach for calculating radiation doses using the Boltzmann equation is known as the "discrete ordinates" method. This approach discretizes the radiation transport equation in space (finite
31 difference or finite element), angle (discrete ordinates), and energy (multi group cross sections), and then iteratively solves the integro differential form of the transport equation over a discrete, multi dimensional space. Both approaches are very powerful, and can lead to accurate solutions; however, depending on the problem type and overall objective, o ne approach can be more effective than the other. Moreover, often when dealing with large and complex problems, hybrid combinations of the two methods can be most effective. Over time, significant efforts have been dedicated to improving both techniques, resulting in novel clever algorithms, efficient algorithms for parallel processing, variance reduction techniques, and hybrid methodologies implemented in various codes or code systems. With the increasing importance of numerical modeling and simulation to predict radiation transport effects, it is essential to verify that the radiation transport codes used to perform these simulations are accurate. 2.1.1 MCNP5 An Open Source General Purpose Monte Carlo C ode The Monte Carlo method is one of the most often used, accurate techniques for particle transport simulation, and is generally thought to provide the only practical way of performing dose calculations from particle interactions in a complex target such as the human body. The development and application of the technique stemmed from work on the atomic bomb during roulette wheel could be employed to select the random nuclear processes. Today, a computer generated rand om number ( via the use of pseudo random number generators) between 0.0 and 1.0 is used for this purpose. The random number determines which interaction will occur by comparing probabilities ( i.e., cross sections) of each interaction to statistically sample probability tracked in the target geometry until it deposits all its energy or escapes. When a large number of particles histories are tracked, the results of int eractions are tallied and can accurately predict the
32 outcomes of the various interactions and physical processes (depending, of course, on the accuracy of the available cross section data). The widespread acceptance of computational models in radiation dos imetry was made possible by the availability of well validated and maintained Monte Carlo codes. Among them, MCNP5 developed by the Los Alamos National Laboratory, is a M onte C arlo N P article code that can be used for neutron, photon, electron, or coupled neutron/photon/electron transport. 28 The code treats an arbitrary three dimensional configuration of materials in geometric cells, having a generalized input capability that allows a user to model a variety of source and detector Point wise cross section data are typically used, although group wise data are also available. For photons, the code accounts for incoherent and coherent scattering, the possibility of fluo rescent emission after photoelectric absorption, absorption in pair production with local emission of annihilation radiation, and bremsstrahlung. The generation of electrons from photons is handled three ways. If electron transport is explicitly tracked ( i n MCNP5 Mode P E ), then all photon collisions except coherent scatter can create electrons that are banked for later charged particle transport which can be quite computationally demanding If electron transport is turned off (no E on the M CNP5 Mode card), then a thick target bremsstrahlung model (TTB) is used. This model generates electrons, but assumes that they are locally slowed to rest. Any bremsstrahlung photons produced by non transported electrons are then banked for later transpor t. Thus electron induced photons are not neglected, but the computationally expensive electron transport step is omitted. (The TTB production model contains many approximations compared to models used in actual electron transport. In particular, the bremss trahlung photons inherit the direction of the parent electron). If IDES = 1 on the PHYS:P card in MCNP5 then all electron production is
33 turned off, no electron induced photons are created and all electron energy is assumed to be locally deposited. The TTB approximation is the default for MODE P problems. In MODE P E problems, it plays a role when the energy cutoff for electrons is greater than that for photons. In this case, the TTB model is used in the terminal processing of the electrons to account for t he few low range. The default cutoff energy for both electrons and photons is 0.001 MeV. A continuous slowing down model is used for electron transport that includes positron s, K x rays, and bremsstrahlung but does not include external or self induced fields. In the initiation phase of a transport calculation involving electrons, all relevant data are either pre calculated or read from the electron data file and processed. Th ese data include the electron energy grid, stopping powers, electron ranges, energy step ranges, sub step lengths, and probability distributions for angular deflections and the production of secondary particles. For sampling fluctuations in electron collis ional energy loss, MCNP relies on a Class I condensed history algorithm in which parameters of the Landau straggling theory are pre computed for a standard set of energies and step sizes. In order to follow an electron through a significant energy loss, it is necessary to break the electron's path into many steps. These steps are chosen to be long enough to encompass many collisions (so that multiple scattering theories are valid) but short enough that the mean energy loss in any one step is small (so that the approximations necessary for the multiple scattering theories are satisfied). The energy loss and angular deflection of the electron during each of the steps can then be sampled from probability distributions based on the appropriate multiple scatteri ng theories. This accumulation of the effects of many individual collisions into single Finally, appropriate probability distributions are sampled for the prod uction of secondary
34 particles. These include electron induced fluorescent x bremsstrahlung photons. The results of the MCNP5 simulations are reported according to the specified input tally cards. The user can instruct MCNP to make various tallies related to particle current, particle flux, and energy deposition. MCNP tallies are normalized to the number of source particles. Currents can be tallied as a function of direction across any set of surfaces, surface segments, or su m of surfaces in the problem (F1 tally card). Fluxes across any set of surfaces, surface segments, sum of surfaces, and volumetrically in cells, cell segments, or sum of cells are also available (MCNP5 F2 and F4 tally cards). Similarly, the fluxes at desig nated detectors (points or rings) are standard tallies, as well as radiography detector tallies (MCNP5 F5 tally card). Fluxes can also be tallied on a mesh superimposed on the problem geometry (MCNP5 FMESH tally card). Heating tallies give the energy depos ition in specified cells (MCNP5 F6 tally card). A pulse height tally provides the energy distribution of pulses created in a detector by radiation (MCNP5 F8 tally card). 2.1.2 PENTRAN a Deterministic Discrete O rdinates (S N ) C ode A widely used determinist ic method to solve Equation 2.1 is the discrete ordinates S N method. In the S N method, all independent variables (space, energy, and direction) are discretized. For the angular variable, a discrete set of directions are selected (usually symmetric about th e unit sphere), and the Boltzmann equation is solved along these directions only. The selected directions (ordinates) are mathematically weighted to ensure that physical symmetries and particles are conserved. For the energy variable, the energy domain is divided into a number of sub intervals (groups) where the Boltzmann equation is integrated over these intervals to obtain a set of coupled equations (multigroup equations). 29 Since it directly describes the flow of radiation in a 3 D geometry with angular and energy dependence, this is one of the most challenging equations to solve in terms of complexity and phase space, and rendering a
35 deterministic computational solution for a large 3 D problem requires a robust parallel transport algorithm and a high per formance computing system. PENTRAN ( P arallel E nvironment N eutral particle TRAN sport) is a multi group, anisotropic S N code that solves the time independent linear Boltzmann equation using finite volume differencing in 3 D Cartesian geometries; it has been specifically designed for distributed memory, scalable parallel computer architectures using the MPI (Message Passing Interface) library. Automatic domain decomposition among the angular, energy, and spatial variables with an adaptive differencing algorit hm and other numerical enhancements make PENTRAN an extremely robust so lver Numerous simulations have been performed using the PENTRAN code system, including many international benchmark computations. To further validate and augment the confidence in PENT accurate numerical solutions to radiation transport simulations for different type of sources emitting in media with anisotropic scattering properties of various degrees, a recently proposed series of quasi ana lytical benchmark problems 34 has been solved using this code and the results are presented in Chapter 5. In Chapter 4 includes a brief description of the PENTRAN code system (the 3 D parallel S N code with the pre and post processing codes) and the suite o f codes (PENTRAN MP code package) specially developed with contributions from this work to enable deterministic PENTRAN simulations to be used for medical physics applications. 2.1.3 PENTRAN MCNP5 Hybrid T echnique CADIS M ethodology Both the S N and Monte Carlo methods are very powerful for solving particle transport problems; however, depending on the application and/or user needs, one method may be preferable over the other. The inherent and generally considered advantages/disadvantages of the two methods are listed in Table 2 1.
36 A large number of techniques have been developed to reduce the variance of the Monte Carlo calculations. These techniques commonly modify the natural (analog) sampling procedure (related to physical laws of particle transport) to focus computational efforts on the simulation of the determination of the problem dependent variance reduction parameters. A sound way to accomplish this task is to use the S N method to determine the adjoint (importance) function distribution for the given problem, and implement it within the weight window variance reduction technique, following the formulations for the source and transport biasing of the CADIS (Consistent Adjoint Driven Importance Sampling) methodology. 30 Source biasing allows for the simulation of a larger number of source particles, with appropriately reduced weights, in the more important regions of each variable. This technique consists of sampling the source from a biased (non analog) probability distribution rather than from the true (analog) probability distribution, and then correcting the weight of the source particles by the ratio of the actual probability divided by the biased probabi lity. Thus, the total weight of particles started in any given interval is conserved, and an unbiased estimate is preserved objective function (or detector response). For sourc e biasing, it utilizes the following formulation = + ( ) (2 2) where + is the importance function, q(P) is the unbi ased source in phase space (angle, space, energy) P and R is the response for the reaction of interest. To conserve the total number of particles, the weights of source particles are adjusted by = + (2 3)
37 For transport biasing, CADIS alters the number of particles that are transferred from one phase space location to another. This means that if the phase space P has a highe r importance than the phase space particles are split by weight during the course of the simulation according to the ratio of the importance functions, given by + ( ) / + ( ) while if the opposite incorporate particle weight conservation. Therefore, following these splitting/roulette processes, to preserve the exp ected number of particles, the particle statistical weight is modified according to Equation 2 4: = ( ) + ( ) + ( ) (2 4) To adm inister the splitting and rouletting of particles, the weight window facilities that are available within MCNP5, which deal with particle weights, are used. Due to computation efficiency considerations (memory requirements and running times), the space and energy dependent (scalar) adjoint function that can be obtained from a PENTRAN adjoint calculation (Equation 2 5) is used in the above formulation (Equations 2 2 to 2 4) for calculating space and energy dependent source biasing and weight window parameter s. + = + 4 (2 5) To use the weight window facility within the MCNP5 code, one must calculate weight window lower bounds w l suc h that the statistical weights defined in Equation 2 3 are at the center of the weight windows (intervals). The width of the interval is controlled by the parameter C u which is the ratio of upper and lower weight window values ( C u = w u /w l ). Therefore, the space and energy dependent weight window lower bounds w l are given by Equation 2 6. = + 1 2 = + 1 + 1 2 (2 6)
38 In MCNP5 there are several options implemented to utilize the weight window variance red uction technique. One of them, quite suitable to be linked to deterministic adjoint calculations, utilizes a mesh with space and energy dependent importances superimposed on the problem geometry. To facilitate proper use of this variance reduction techniq ue with MCNP5, we developed a code, PENIMP (Appendix A), that reads the adjoint function from the PENTRAN output, and prepares the source biasing parameters and weight window lower bounds in the format required for the MCNP5 Monte Carlo run. 2.2 The UF S er ies B Voxel P hantoms Assuming one could achieve a detailed knowledge of the 3 D radiation fields a nywhere in the human body pre supposes that the human body can be properly represented to precise detail in order to enable proper dose registration and attr ibution. Traditionally, the human body has been modeled with st raight forward stylized (Figure 2 1 phantoms of bone, soft tissue, and lung tissue (ICRP 48 (1992), ICRP Pub 74, (1996)). Recently, image based, voxelized compu ted tomography (CT) and MRI image models have been developed 20,21,35 37 The computational anatomical model KTMAN 2 was initially built from the whole body CT images of a 35 year old Korean male whose height and weight closely matched those of the average Korean man and further transformed into a corresponding American counterpart (organ masses were scaled to those of the American reference male, approximately 176 cm tall and a weight of 72.9 kg). The result of this successive development is a computational phantom with a matrix of 300 x 150 x 344 voxels of 2 mm x 2 mm x 5 mm resolution containing a total of 58 defined organs. Contours segmentation software, and the construction of the first tomographic dosimetry model ( UF Newborn) 21 a series of ped iatric tomographic phantoms have been constructed using actual patient CT images from Shands
39 hospital image archives (Figure 2 2) The set of whole body voxel phantoms of pe diatric patients (9 month male, 4 year female, 8 yea r female, 11 year male and 14 year male) has been developed through the attachment of arms and legs from segmented CT images of a healthy Korean adult (UF Series B) 20 Even though partial body phantoms (head torso) may be used in a variety of medical dose reconstruction studies where the extremities are out of field or receive only very low levels of scatter ed radiation, whole body phantoms play important roles in general radiation protection and in nuclear medicine dosimetry. Inclusion of the arms and leg s is critic al for dosimetry studies of pe diatric patients due to the presence of active bone marrow within the extremit ies of children. While previous phantoms preserved the body dimensions and organ masses as seen in the original patients who were scanned comprehensive adjustments were made for the Series B phantoms to better match International Commission on Radiological Protection (ICRP) age interpolated reference body masses, body heights, sitting heights and internal organ masses. The CT images of arm s and legs of a Korean adult were digitally rescaled and attached to each phantom of the UF series. After completion, 73 distinct organs were defined with a resolution of 0.86 mm0.86 mm 3.0 mm, 0.90 mm 0.90 mm 5.0 mm, 1.16 mm 1.16 mm 6.0 mm, 0.94 mm 0.94 mm 6.00 mm and 1.18 mm 1.18 mm 6.72 mm for the 9 month, 4 year, 8 year, 11 year and 14 year r espectively. Accurate calculations of the patient dose from diagnostic imaging exposures need to rely on sound computational algorithms and faith ful representations of the human body. The two radiation transport methods, Monte Carlo and deterministic, implemented in the computer codes presented above, MCNP5 and PENTRAN, respectively, along with the state of the art UF Series B voxelized phantoms ce rtainly meet these pre requisites.
40 A third essential ingredient for a successful dose assessment endeavor is the knowledge of reliable radiation source energy spectra. This source spectral distribution is particularly important since the radiation interact ions in the human body (inherently low Z ( atomic number ) material) are highly energy dependent in the diagnostic energy range. In the following chapter, the computer code DXS, specially developed to provide reliable tungsten target radiographic x ray spect ra, is presented.
41 Table 2 1. Comparison of the S N and Monte Carlo (MC) methods Method Advantages Disadvantages S N Detailed solutions Short execution time Discretized geometry representation Large computer memory Difficulties in preparation of mesh, quad rature ordinates (directions) and multigroup cross sections MC Accurate geometry Accurate energy treatment (continuous energy dependent cross sections) Small computer memory Long execution time Limited solution detail Difficulty in using variance reductio n techniques Figure 2 1 Stylized anatomic models of human anatomy developed at the Oak Ridge National Laboratory in the early 1980s. Figure 2 2 UF Series B pediatric phantoms courtesy C. Lee
42 CHAPTER 3 A DIAGNOSTIC X RAY SPECTRA GENERATO R CODE DXS 3.1 Introduction Radiation transport simulations using sophisticated Monte Carlo and deterministic algorithms, as presented in the previous chapter, can be employed with detailed human phantoms models to provide important tools for patient dosimetry. To be successful, these methods must rely on precise knowledge of the x ray energy spectrum governing the delivery of the radiation. Unfortunately, routine measurements of diagnostic spectra are not common due to the practical complexities in the performa nce of such measurements in a clinical setting. Saturation of the spectrometric system, spurious signals due to Compton interactions, and x ray production in the detector itself are examples of these difficulties 38 Two useful theoretical models published for computer generation of tungsten target x ray spectra have been proposed: one by Birch and Marshall 39 (BM) in 1978, and a second by Tucker, Barnes, and Chakraborty 31 (TBC) in 1991. However, these models are not fully based on first principles, and requ ire fitting to measurements using a parametric differential energy spectrum (distribution of the bremsstrahlung photons per incident electron of a given kinetic energy). Subsequent studies 40,41 have analyzed the spectra generated using these two models thr ough comparisons to experimentally recorded spectral data. It has been shown that the TBC model, which rectifies an error in the relativistic correction factor originally found in the BM model, and accounts for the variation of the efficiency of characteri stic photon production with depth in the target, generates softer spectra that provide better agreement with measured spectra. 42 Several computer codes have been developed based on these models: IPEM 43 (BM model), X rayb&m (BM model), and X raytbc (TBC mo del) are widely used in the diagnostic imaging community.
43 Powerful and sound alternatives to the semi empirical methods, though much more time consuming, are the methods employing Monte Carlo simulations 44 46 which use full electron and generated photons transport through targets and filters to calculate x ray spectra, providing at the same time an insight into the underlying physics. The accuracy of the spectra generated with these methods has been extensively evaluated by comparisons amongst each other and against experimental data 47 and it has been shown that there is no statistically significant difference between the measured and predicted spectra. The main discrepancy noted was found to be related to the proper representation of the characteristic l ines. DXS ( D iagnostic X r ay S pectra) is a Fortran 90 computer code developed for this research that implements the original semi empirical mo del proposed by Tucker et al in 1991 31 using updated interaction data and analytical formulations 48 The model p arameters in the DXS code were adjusted by comparison with corresponding MCNP5 simulated spectra. Though developed to serve the Monte Carlo and deterministic radiation transport simulations for patient dose assessment s in different ionizing radiation imagi ng modalities (for which it has several features particularly dedicated to this purpose, which will be described in the next chapter), DXS may also be successfully used to generate spectra needed for radiation protection calculations or characterization an d comparison s of imaging systems O btaining DQE (detective quantum efficiency) values, for example, requires knowledge of the x ray sp ectrum incident on the detector The accuracy of these calculations critically depends on the availability of reliable x ray spectra for operational settings. The DXS code generates these spectra, according to user specified input parameters (tube potential, anode angle, type and amount of filtration), and accommodates them to any discretized energy group structure.
44 To fu rther validate DXS, experimental HPGe spectral measurements performed in a Toshiba Infinix VC I (Toshiba America Medical Systems, Long Beach, CA) single plane interventional angiography system at Shands Hospital at the University of Florida were compared w ith corresponding MCNP5 simulations. To minimize the inherently large stochastic errors when modeling the complex measurement setup, a methodology that provides an equivalent source projected on a plane close to the region of interest (i.e., detector site in this study case) used in subsequent simulations for the desired evaluations (such as the detector beneficially assist future transport simulations for dose asse ssments by reducing the computational time, minimizing the Monte Carlo stochastic error or the numerical difficulties (e.g. ray effects, etc) in the deterministic transport approach. 3.2 Theoretical F ormulation In the DXS code, the number N ( E ) of bremsstra hlung photons with energy between E and E+dE from a target with atomic mass A atomic number Z and density is generated according to: ( 3 1) where T 0 the kinetic energy of the incident electron, and T the electron kinetic energy at a distance x with in the target of angle are related by the Thomson Whidding ton constant 31,39 C which we redefined and recalculated based on a recent Monte Carlo study, 47 as will be shown in the following sub sections : ( 3 2)
45 where is the fine structure constant, r e is the classical electron radius, is the target mass stopping power and is the linear attenuation coefficient of the photon with energy E in the target. Finally, B is the polynomial functio n, ( 3 3) whose parameters were determined by fitting to measured bremsstrahlung spectra 4 The formulation for the number N(E i ) of E i characteristic x rays per incident electron with fractional emission f(E i T 0 ) is modeled through parameters A k and n k by: ( 3 4) where R is the distance as given by E quation ( 3 2) with in the target where the average electron kinetic energy is equal to the K she ll binding energy, and ( 3 5) is the related depth dependent probability distribution function. In preliminary versions of DXS, the brems strahlung and characteristic model parameters were those obtained from the TBC model. However, there is a caveat in the TBC model, already mentioned in a previous study 40 that became evident when c omparing DXS generated spectra with experimental ones from the published literature 40,41 (see Table 3 1) : the K peaks require adjustment for various tube potentials. Hence, the fractional emission f(E i ,T 0 ) has been separated into two factors, ( 3 6)
46 the first one, y(E i ), being the published relative intensities of the characteristic K lines of tungsten (Table 3 2 ) while the second term, f ( T o ), is the analytical fitting function (given in Equatio n (3 7) in the next section) of the MCNP5 Monte Carlo simulation results. 3.3 Code I mplementation In DXS, the target generated spectra may be further theoretically attenuated (in a narrow filtration (aluminum, beryllium, copper and tantalum are current options in DXS) and possible air path. The self attenuation in the target and any other attenuation due to inherent and added filtration or air path are expressed through parametric fitting f unctions of the mass attenuation coefficients generated with XCOM 49 for the materials and energy range s of interest. The general form of the fitting function is that proposed by Tucker et al. 31 namely, (3 8) w here u=E (keV)/100 and the resulting coefficients are entered in Table 3 3 For tungsten and tantalum ( used as one of the standard filter materials by Toshiba in all their fluoroscopic and angiographic systems), two different sets of parameters are used, depending on whether the photon energy is below or above their K absorption edge, respectively. In the case of the mass attenuation coefficient of copper, a different analytical function, (3 9) w h ere u=E (keV)/100 resulted in a best fit ( R 2 =0.9999) in the considered energy range. For programming convenience, the mass stopping power in tungsten is also represented by the analytical function in Equation 3 10 1 = + (3 10)
47 whose coeffic ients were determined by iteratively fitting the interaction data from ESTAR dat abase at NIST and entered in Table 3 4. The original TBC model, as well as all the other semi empirical models, is based on a (Equation 3 2). However, a recent s tudy of Poludniowski and Evans 45 shows that the linear dependence breaks down as the electrons slow down in the target (Figure 3 1, based on results of the mentioned study). The departure from linear behavior is more evident at higher incident electron ene rgies. Consequently, in DXS, we elected to model the electron penetration and target self attenuation considering the dependence on electron incident energy (T 0 ) of the parameter C in the Thomson Whiddington relation (Equation 3 2) defined as follows: ( 0 ) = 1 + 2 0 + 3 0 2 + 4 0 3 0 70 1 + 2 0 + 3 0 2 + 4 0 3 0 > 70 ( 0 ) 2 0 45 73200 2 0 > 70 ( 0 ) 2 < 0 45 (3 11) where the coefficients c 1 4 (entered in Table 3 5) were calculated based on the results of the study mentioned before. The new formulation for the electron penetration in the target presented in the same study 45 is used in the updated version of DXS to calculate the distance parameter R in Equations 3 4 and 3 5. To validate the modified formulation and to obtain a better representation of the characteristic x ray production that correctly accounts for dep endence on the tube potential, full photon and electron physics Monte Carlo simulations have been performed for several tube potentials. In the MCNP5 model, depicted in Figure 3 2, the x ray tube consists only of a tungsten target as a 12 wedge in a vac uum held in an aluminum case, 1.2 mm width, which determined by the
48 x ray tube voltage ) electron surface source, 1 mm diameter, mimics the electron beam impinging upon the target (indicated at the bottom in Fig 3 2) on the central axis employing 0. 5 keV energy bins, subsequently normalized to unit area and compared with the corresponding DXS code genera ted spectrum. The improvement provided by the updated description of the electron penetration in the target can be observed in Figure 3 3 which displays spectra for two selected tube potentials, 140 and 90 kVp, generated with the DXS code having implemente d the old formulation (blue triangles) and the improved one (black line) compared to the reference MCNP5 calculated spectra (red points with error bars). For a more quantitative assessment, Table 3 6 contains the rms deviation of the results (in the two im plementations) from the reference Monte Carlo. As expected, the more pronounced improvement is noted at higher tube potentials where the old description was less accurate. Based on the MCNP5 simulations we adjusted the f ( T 0 ) factor in Equation 3 6 for 80, 90, 100, 120, 130, and 140 kVp tube potentials, and then determined the analytical formulation by fitting using least squares techniques: f(T 0 ) =89.972 3.789 T 0 + 0.0642 x 10 2 T 0 2 5.44925 x 10 4 T 0 3 + 2.3117 x 10 6 T 0 4 3.917 x 10 9 T 0 5 (3 12) Using the above discussed formulations for the bremmstralung and characteristic radiation, the DXS code quite accurately calculates central axis spectra in the radiographic range, 45 140 k Vp, with a minimum value of 10 keV (assuming that the amount of inherent filtration of the x ray tube is enough to totally attenuate these low energy photons), in 0.1 keV energy bins according to the user defined input parameters (kVp, target angle, amount of total i.e., inherent plus additional aluminum filtration, type and amount of other filtration, air path). The DXS
49 code outputs the spectra (normalized to unit area) in 0.5 keV intervals, but also allows for accommodating the generated spectrum to a lternate user defined energy group structure s 3.4 Validation of DXS 3.4.1 Comparison with MCNP5 Generated S pectra To assess the quality of the DXS generated spectra for different combinations of tube potential, filtration, target angle, we performed corr esponding MCNP5 simulations (considered as the reference s for this exercise), and then we calculated the rms deviation of the DXS generated spectra (black line in all the following figures) from the reference ones (red points with error bars in all the fol lowing figures). Figure 3 4 displays normalized spectra for three x ray tube potentials at which the characteristic production is not activated in the case of a 12 tungsten anode and 1.2 mm Al inherent filtration. The excellent agreement between the DXS and MCNP5 generated spectra is demonstrated by the rms deviation shown in Table 3 7 T he relative differences in all the energy bins were generally less than 2% wi th few exceptions at the low and high energy tails of the spectra. It should be noted that Table 3 7 contains also the rms of the spectra for six other higher tube potentials, four of which are shown in Figure 3 5 These data demonstrate the same excellent agreement, inclusive of the characteristic K peaks. The effect of the type and amount of filtration on the spectral distribution was studied for a 10 target angle at 100 kVp tube potential by varying the thickness and the material of the filter in the MCNP5 simulations. Figures 3 6 and 3 7 show the fidelity of the DXS code to describe beam hardening effects due to increased aluminum and copper filtrat ion respectively. There is, however, a slight decrease in agreement as the thickness of the copper filter is increased, which may be due to the scattering in the filter, not accounted for in the DXS code.
50 3.4.2 Comparison with Published Measured S pectra Figure 3 8 displays for comparison DXS generated spectra along with measured spectra published by Bhat et al. in 1998. 41, While the DXS spectra still agree relatively well with the measured spectra, there are factors influencing the measured spectra, such as target composition, collimation, voltage ripple, etc, that are not accounted for in the DXS code. Bhat et al. 41 reported the three sets of data for a 12 tungsten target, 1.2 mm inherent Al filtration, recorded on axis at 3.5 m away from the target usin g intense collimation at the detector site to prevent the saturation of the detector and noted the presence of molybdenum K x rays. Other authors 39,42 also observed traces of rhenium in their measured spectra. While these variants may be always present in clinical x ray units, for the sake of generalization, DXS generates spectra for pure tungsten anodes, but may be adjusted if exact composition of the target is available. 3.4.3 MCNP5 Simulations of Clinical Spectral M easurements An HPGe detector (Princeton Gamma Tech NTGC 3020) and Ortec MAESTRO radiation spectroscopy system w ere employed to record on site spectral data for the Toshiba Infinix VC I interventional angiography system which possesses a tu ngsten target x ray tube 11 anode angle, 1.1 mm Al in herent filtration for the x ray tube and 1.5 mm Al for the x ray beam limiting device. 241 Am (E =60 keV), 109 Cd (E =88 keV), 57 Co (E =122 keV, E =136 keV) and 137 C s (E to perform energy and efficiency calibration s o f the detection system. The planar Ge detector, of 2.72 cm radius and 5.7 cm in height, was energy calibrated to record pulses in 1 keV energy bins. The measured full energy peak efficiency of the detector was subsequently validated via MCNP5 simulations ( Figure 3 9 a ). A r adiograph o f the Ge detector (Figure 3 9 b ) used in the clinical validation experiment provided necessary information for an appropr iate geometrical description.
51 Because clinical fluoroscopy systems must comply with 21 CFR 102.32 (a), wh ich establishes that the x ray beam cannot be activated unless the image receptor is fully intercepting the beam, it is impossible to position the Ge detector adequately for meaningful on axis measurements of the primary beam f or the purposes of experiment al validation of the DXS generated spectra In addition to the geometrical limitations, saturation of the HPGe spectrome tric system due to the high fluence of the incident photon beam could not be prevent ed by utilizing the smallest x ray field (tightest c ollimation) and minimum beam current Hence, to prevent saturation, the data had to be collected off axis (~ 6 0) at ~4 00 c m radial distance from the source head. In this configuration, s pectra were recorded f or a highly collimated beam using 1.5 mm Al add ed filtration at 70, 88, 100, and 120 kVp acceleration potential s The special circumstances in which the experimental measurements were performed posed real challenges in the computational effort to validate DXS generated spectra. The MCNP5 pulse height t ally F8 provides the ability to appropriately simulate a detector spectral response. However, a detailed and faithful representation of the complex experimental setup is a real obstacle in the attempt to transport the photons from the source to the detecto r computationally Consequently, significant but reasonable mod ifications had to be made to obtain an efficient and reliable Monte Carlo model to represent the clinically derived results. To accomplish this, it was necessary to place the source housing an d the detector inside a long cylinder of air (Figure 3 10 ). The assumption was made that scattered radiation throughout the room ha d negligible contribution s to the detector response as compar ed to the radiation coming directly from the source. Such an as sumption is supported by the fact that for the materials present in a typical x ray room, in the fluoroscopic range, the photoelectric effect is both significant and inherently dominant Besides, multiple scatterings have a large probability to reduce the energy of the
52 photons under the detector lower level discriminator ( LLD ), set to 25 keV in these measurements and the scattered radiation inside the source housing was also account ed for in availabl e from Toshiba the source was model ed as a small (collimator opening size) surface source with a forward cosine weighted angular distribution placed in a lead housing. The exit window was model ed as an aluminum slab of thickness equal to the specified inh erent filtration thickness of the collimator Methodology in minimizing stochastic errors : D espite the simplifications necessary to facilitate the Monte Carlo model, special techniques still had to be employed to reduce the computation time while achievin g acceptable statistical errors. Hence, we divided our simulation in two separate modeling steps: (i) generation of an equivalent source plane close to the detector region of interest (ii) transport of radiation from the equivale nt surface source (ESS) to the detector Step (i) transport to source plane : A preliminary simulation, in which the large air path between the source head and detector was modeled using cell importance variance reduction and implemented as several regio ns of increasing importance, was meant to provide an equivalent surface source, 1 cm away from the detector. An MCNP5 F1 tally was used to obtain the number of photons in 1 keV energy intervals passing the unit cross sectional area of the cylinder in sever al angular bins defined with a local reference to the long cylinder axis. The relative error is generally less than 10%, increasing for the first and the last energy bins and mostly for higher angle intervals directed away from the cylinder axis Figure 3 11 shows that the photon current is oriented pr imarily tangent to the axis, since the values for the 0 15 bin are notably 2 to 5 orders of magnitude larger than for all the other intervals.
53 Consequently, the ESS is determined as the normalized photon d istribution of the outward current passing the cylinder base along a surface normal vector pointed toward the detector. A l arge number of histories (on the order of 10 9 ) must be executed to achieve an acceptable (<10%) relativ e error in most energy bins. E ven in these conditions, the low and high energy tails of the spectrum are affected by large errors (>20% in certain cases) an inevitable fact due to the inherent poorer sampling induced by the source distribution. To alleviate this effect, the two ends o f the spectrum were tallied in larger energy intervals, typically 25 keV widths vs. 1 keV widths in the mid spectrum. The resulting ESS from this first step was used in subsequent simulations (step ii) of the detector response. Step( ii) transport from source plane to detector : T he model of this second step consists of a detailed MCNP5 geometrical description of the HPGe detector (Figure 3 12 ) and the previously determined ESS located 1 cm away from the detector. Much shorter computer time was required for this simulation to achieve less than 2% relative error in all energy bins. To enable a direct comparison, the results and the measured data are both normalized to unit area under the spectrum. Figures 3 13 and 3 14 show comparisons of the spectra yield ed by MCNP5 simulations with those recorded by the HPGe spectrometric system for potentials of 70, 88, 100, and 120 kVp, respectively. Overall, good agreement was obtained in comparing computational and clinically measured responses the relative differen ce being on average smaller than 10%, with a few exceptions that will be further discussed even though the system was placed at a large off axis distance in the clinic, which presented clear challenges in the computations. In addition, Figure 3 13 contai ns a DXS generated source spectrum that illustrates beam hardening due to the transport of the radiation through the system. This emphasizes why knowledge about the system,
54 including the source, detector design, and structural materials are crucial to obta in accurate results throughout the simulation. Because certain specific details were not available from the manufacturer, we used an intuitive representation of the x ray unit in our models. We believe that the lack of fine details and related information is the primary reason for the disagreement in the spectra corresponding to higher kVps (>90 kVp). Analysis of the results allows for some general remarks regarding the reliability of the computational model to be made : the main features (shape, positio n of the bremsstrahlung peak, presence of tungsten and lead characteristic lines, when theoretically possible) of the measured spectra are also rendered by the simulations; the larg est disagreement is shown for the spectra where the lead characteristic l ines are present (i.e., 100 and 120 kVp) However, their height in the measured spectra is much lower than that resulting from simulations, which suggests the presence in the beam limiting device of components made of a material or compound that has a hig h probability for photoelectric absorption in that energy range This is also corroborated by the shape of the spectrum beyond the tungsten absorption edge Because experience shows that real life medical physics problems usually involve large and compl ex computational models that require either impractically long running times (in the case of Monte Carlo methods) or intractable computer memory demands (for deterministic methods), we consider that the methodology presented here to obtain an equivalent so urce close to the region of interest is indeed a very useful tool that can beneficially support computational investigations in the field.
55 3.5 Conclusions Based on the model proposed by Tucker et al. in 1991 31 (herein referred as TBC model), a new code, DX S, has been developed and evaluated to numerically generate central axis spectra for tungsten target x ray tubes spanning the diagnostic radiographic energy range (50 140 kVp) according to user defined input parameters (target angle, type and amount of fi ltration, air distance, kVp) The code reports the spectra in 0. 5 keV bin probabilities and optional in any user defined energy group structure. It also generates input files for other codes, if opted for, as it will be described in the next chapter. Based on a recent Monte Carlo study of Poludniowski and Evans 45 we implemented in the DXS code a modified description of the electron penetration and self attenuation in the target, which improved the accuracy of the generated spectra. Using MCNP5 Monte Carlo simulations, we were able to improve the description of the characteristic x ray production of the TBC model, adjusting the fractional emission to account for the dependence on the tube potential. The spectra calculated with the DXS code are, however, limi ted to central axis, small target angles (less than 15), and constant tube potentials. Future studies are intended to investigate off axis spectra and the possibility to incorporate the off axis effect in the DXS code, which can be extremely useful for mo deling filtered spectra with bowtie filters in CT scanners. Reasonabl y good agreement was obtained between spectra recorded in a clinical laboratory environment with an HPGe spectrometric system and those results rendered from 3 D Monte Carlo simulations u sing the DXS generated source. We noted i nherent difficulties that arose in our attempt to computationally transport radiation from source to an off axis detector a considerable distance away to model what was performed in the clinic to prevent detector sa turation. The difficulties were overcome by appropriately generating an equivalent plane
56 sour ce (ESS) close to the detector and the n simulating the detector response denoted as a Overall, th e DXS code should be of great benefi t to the medical physics community in providing standard source terms for general Monte Carlo or deterministic transport simulations for diagnostic radiology since attention was paid to necessary clinical and computational parameters in a practical approach. Thi s is particularly important given the growing importance associated with evaluating radiological doses resulting from medical procedures, especially in potentially high dose modalities such as CT and angiography. Particularly for the present work, DXS cod e has been designed to conveniently support and streamline the proposed computational methodology, presented in the next chapter, for patient dosimetry.
57 Table 3 1 the o riginal Tucker et al. model (TBC) and measured spectra reported by Fewell 41 ; rms deviation for the entire spectrum is also included; similar for DXS results Voltage (kV) r ms x 10 3 K Diff (%) K Diff (%) K Diff (%) K Diff (%) DXS TBC DXS TBC DX S TBC DXS TBC DXS TBC 80 0.1 9 0.2 2 0.06 4.54 1. 34 0.64 1.38 8.46 4.56 2.4 100 0.20 1.8 2.35 110.6 2.9 79.6 1.86 65.9 4.4 43.6 Table 3 2 Characteristic x rays for tungsten and their relative intensities E i (keV) y K K K K 59.32 5 8 00 6 7.15 69.13 1.000 0.576 0.321 0.084 normalized relative to K Table 3 3 Parametrization of mass attenuation coefficients (in m 2 /kg) in the 10 to 200 keV energy range; the K edges E k of tungsten and tantalum are 69.5 keV and 67.42 ke V Material a 1 a 2 a 3 a 4 a 5 Al 1.212 x10 2 2.074 x10 3 1.550 x10 3 7.717 x10 4 2.192 x10 5 Be 1.065 x10 2 3.034 x10 3 9.973 x10 4 2.117 x10 4 7.496 x10 6 W, E
58 Table 3 6 Root mean square deviation of the spectra generated with DXS using the classical Thomson Whiddington (rms_oldTW) and updated (rms_DXS) formulation for the electron penetration and self attenuation in the target; compared with the reference MCNP5 calculated spectra kVp 140 130 120 100 90 80 70 rms_oldTW rms_DXS 0.0011 0.0004 0.0009 0.0003 0.0008 0.0003 0.0005 0.0001 0.0004 0.0002 0.0004 0.0002 0.0003 0.0003 Table 3 7 Root mean square ( rms ) deviation from the reference of the DXS generated spectra for several tube potentials; 12 target angle, 1.2 mm Al filtration kVp 50 65 70 80 90 100 120 130 140 rms 0.0004 0.0003 0.0004 0.0003 0.0002 0.0001 0.0002 0.0003 0.0004
59 Figure 3 1 E lect ron fractional residual energy; dependence of the (T/T 0 ) 2 on the mass penetration, x, in the tungsten target, based on the results of Poludniowski and Evans 45 Figure 3 2 Simplified MCNP5 model for the tungsten target
60 A B Figure 3 3 DXS generated spectra using the updated formulation for the electron penetration in the target (black line) are more accurate when compared to the reference MCNP5 spectra (red points with error bars) than the spectra generated using the classical Thomson Whiddington formulation (blue triangles); A) 140 kVp, B ) 90 kVp
61 Figure 3 4 Comparison between DXS (b lack line) and MCNP5 (red points with error bars) spectra for 50, 65, and 70 kVp tube potentials, 12 target angle, 1.2 mm Al filtration
62 Figure 3 5 Comparison between DXS (black line) and MCNP5 (red points with error bars) spectra for 80, 90, 130, a nd 140 kVp tube potentials, 12 target angle, 1.2 mm Al filtration
63 Figure 3 6 DXS spectra (black lines) compared to MCNP5 results (red points with error bars) for 100 kVp, 10 target angle, and different thicknesses of aluminum filter Figure 3 7 DXS spectra (black lines) compared to MCNP5 results (red points with error bars) for 100 kVp, 10 target angle, and different thicknesses of copper filter
64 Figure 3 8 Comparison between the DXS generated spectra and the measured spectra by Bhat et al (left column) and Fewell (right column) for 80 kVp (top raw) and 100 kVp (bottom raw) tube potentials
65 A B Figure 3 9 Ge detector characterization A ) Full peak efficiency of the Ge detector used in the clin ical measurements B ) R adiograph of the G e crystal and Al case (acquired using an SAIC RTR 4 portable x ray imaging system). Figure 3 10 Simplified MCNP5 model to simulate experimental measurements
66 Figure 3 11 Photon current spectral distribution for 6 direction intervals Figure 3 12 MCNP5 model of the HPGe detector
67 Figure 3 13 Comparison of the measured and simulated detector response for the Toshiba Infinix VC I system at 70 kVp; for reference, the DXS generated source spectrum is also included.
68 A B C Figure 3 14 Comparison of the measured and MCNP5 simulated detector response using DXS generated source spectra for the Toshiba Infinix VC I system at : A ) 88 kVp, B ) 100 kVp and C ) 120 kVp
69 CHAPTER 4 PENTRAN MP CODE SYSTEM Monte Carlo methods have been long established as the gold standard for computer simulations in the medical physics community. Chapter 2 discussed that, depending on the simulations may provide a more detailed and faster solution. The accuracy and efficiency of the deterministic methods have been well demonstrated for nuclear reactor and detection problems, but have yet to be proven for wide use in medical physics applicat ions. To investigate the possibility of using deterministic radiation transport simulations as a viable and more convenient tool in real clinical applications, a code system, PENTRAN MP, and a methodology (Figure 4 1) for patient radiation dose calculation s using voxelized human phantoms was developed with contributions from this research work PENTRAN MP is a package of existing (PENTRAN 32 PENMSH 32 PENDATA 32 CEPXS 33 ) or specially developed (DXS GREPXS, GHOST 3D, 3D DOSE) codes to facilitate the simula tion methodology, which is organized in three stages of calculations: pre processing (GHOST 3D, DXS, PENMSHXP and CEPXS), radiation transport calculation (PENTRAN), and post processing (PENDATA and 3D DOSE). 4.1 Pre Processing C odes 4.1.1 PENMSHXP PENTRA enerator PENMSHXP, the code developed by Haghighat and Yi, is a 3 D Cartesian based mesh generator that prepares material and source distribution s for PENTRAN particle transport code. As part of the PENTRAN MP package, PENMSH XP has been ada pted to read two binary input files one for the phantom geometry containing the material distribution ( which can be established from real CT data ) and an other one with the radiation activity value for each voxel/fine mesh ( which can be used to specify the fixed source distribution in the model ) and to
70 combine them to generate the input deck for the PENTRAN transport calculations. More details 4.1.2 DXS The Pilot Code of the PENTRAN MP S ystem Usuall y, a deterministic transport simulation may require a considerable amount of time and effort to prepare all the needed ingredients for the actual execution. Also, there may be considerable effort involved in the post processing of the large amount of data generated. To ease and streamline this effort, which is of great importance in a commonly busy clinical environment, the DXS code, previously described (see Chapter 3 of this work) as a standalone code that generates x ray spectra in the diagnostic radiogr aphic range, has been designated as the pilot code in the PENTRAN MP system and dose computation methodology. Several options have been impleme nted in the code that make DXS an important tool to conveniently and consistently prepare input or part of the in put files, as well as intermediate files needed for the proper execution of other codes in all the stages of a simulation. Namely, it generates the lower energy ) and format to be used by PENMSHXP to write the source definition section of the multigroup macroscopic cross sections mixer, a product of Sandia National Laboratories 33 This capability is extremely convenient, considering the large number of materials (each with several components of different content) that make up the voxelized phantoms, as well as the non standard way in which the parameters required for cross section calculations are defined in CEPXS. It must be mentioned that the CEPXS original code had to be debugged and modified to accommodate the large number of materials, elemental components per material, and energy groups involved in the specific simulat ions ne eded for this work. DXS source
71 probability) for a corresponding MCNP5 simulation. In support of the post processing stage, DXS provides the mid ene rgies of the energy groups employed in the radiation transport simulation needed by 3D DOSE to convert the calculated flux into dose. 4.1.3 GREPXS The Cross Sections Extractor and W riter GREPXS is a small but very handy code designed to strip out from the CEPXS output file see the PENTRAN code manual for details) that can be automatically read by PENTRAN during the execution of the transport simulation. 4.1.4 GHOST 3D Computational Human Phantoms B uilder A key factor to guarantee accurate results with our dose computation methodology is the availability of exact anatomical models for the human body. We showed in Chapter 2 that the ALRADS group at UF has built a stat e of the art series of high resolution voxelized human phantoms using CT images of live patients. These phantoms consist of very large arrays of numbers assigned to the different anatomical tissues and organs; for example, the matrix size for the 11 year o ld male phantom that was used in our evaluation tests presented in Chapter 5 is 398 x 242 x 252, which translates to more than 24 million meshes in the computational model. Due to several constraints in simulating such large models, like limited computer m emory, long running time, slow convergence or unphysical oscillations in the solution, GHOST 3D code has been developed (Ghita & Al Basheer), to provide an equivalent model with a down sampled number of total meshes (adjustable, depending on the user re quirements), overcoming the mentioned difficulties. GHOST 3D transforms the high resolution phantom into a coarser one by direction) and assigning to the equivalent voxe l the dominant and closest approaching material tag number with an averaged density. As a result of this transformation, the geometric volume
72 and the mass of the phantom are conserved, but the size and shape of internal organs are shifted by varying degree (Figure 4 2). Inevitably, a significant price may be paid in certain situations for this computational gain: Discussion about the impact of this down sampling procedure on the efficiency of the simulations, but also on the accuracy of the dose computation results is included in the second sub section of the next chapter. The GHOST 3D generated material distribution is written in a binary file, which is processed by PENMSHXP to generate a PENTRAN computational model and also in a text file, with the correct format to be directly included in the MCNP5 input deck. GHOST 3D also writes the file with all the information needed by PENMSHXP to provid e the complete input deck for the PENTRAN radiation transport simulation. An auxiliary file, containing the tag number for each fine mesh of the deterministic model in the indexing order defined in PENTRAN, is also produced to be used in the post processin g stage for converting the scalar flux into dose. 4.2 Post Processing C odes Post processing in the PENTRAN MP code system includes seamless parallel data extraction using the PENDATA code developed by Sjoden and Haghighat to generate the scalar flux distri bution in the phantom which is converted into dose distribution by 3D DOSE (Al Basheer and Ghita) which applies Eq uation 4 1 to compute the dose in each voxel, D i using fitting functions for the mass energy absorption coefficients, en of four mater ials (dry air, ICRU 44 lung tissue, ICRU 44 soft tis sue and ICRU 44 cortical bone). = (4 1) In Equation 4 1, G is th e number of energy groups used and E g the group midpoint energy. The initial version of the code was used to calculate the dose in each voxel using fitting functions for the mass energy absorption coefficients of the four materials (dry air, ICRU 44
73 lung tissue, ICRU 44 soft tissue and ICRU 44 cortical bone) also employed in the early PENTRAN MP transport calculations The values of the mass energy absorption coefficient, as a function of photon energy, for these compounds were obtained from NIST dat abase However, as the entire code system evolved, 3D DOSE was also modifi ed further for this work to accommodate dose distribution and organ dose calculation based on all materials that define the computational model Hence, the code reports spatial dose distribution for each energy group, total dose distribution, doses for user selected organs, and, optionally, dose volume histograms. Several tests have been performed, using the above described PENTRAN MP code system, to investigate the readiness of the deterministic methodology to be employed for calculations of patient organ doses from MDCT protocols. The n ext chapter includes the results of these tests and the derived conclusions.
74 Figure 4 1 Simulation methodology for dose distribution and organ dose calculations using the PENTRAN MP code system A B Figure 4 2 GHOST 3 D d own sampled models of the 11 year old male phantom of UF Series B (398 x 24 2 x 252 voxels, 73 materials); A ). 3 x 3 x 3 collapsing steps, resulting in a 132 x 80 x 8 4 voxels model (72 materials), B ). 5 x 5 x 5 collapsing steps, resulting in a 79 x 50 x 48 voxels model (66 materials)
75 A B C Figure 4 3 Corresponding axial slices in different voxel phantoms: A ) the original, high resolution phantom B ) the 900k voxels computation al model with 72 materials and C ) the 900k voxels computational model with four equivalent materials
76 CHAPTER 5 BENCHMARKS AND VALID ATION TESTS DETERMINISTIC APPROA CH 5.1 State Transport B ench mark P roblems Recently, a benchmark suite has been developed to provide a set of analytical benchmark problems and solutions to the transport equation in infinite media for a variety of source configurations. 34 The TIEL benchmarks are unique, in that th ey offer a set of problems that are well documented and solved using quasi analytic methods and can be unequivocally used as standards of comparison. Therefore, these benchmarks enable one to directly assess the quality of solutions generated from a varie ty of numerical transport codes and methodologies. The Analytical Benchmark Source Series 1 proposed by Ganapol provides four simple 1 D and two 2 D semi analytical solutions to the one group transport equation in infinite media for a variety of source co nfigurations, including a plane, point, spherical shell, solid sphere, ring, and finite line sources. The benchmark problem solutions are obtained via Fourier Transform inversions performed numerically, along with other involved integrations, depending on the specific case considered. While demonstrating the quality of the benchmark results, several other characteristics of the particle transport in media with different scattering properties are analyzed. 50 To simulate the requisite 1 D and 2 D geometries u sing PENTRAN, full 3 D Cartesian computations are necessary with appropriate boundaries set to be reflected when required to represent the prescribed geometry. 5.1.1 Benchmark Problem 1 Plane S ource The first proposed case is a planar isotropic source p laced at x=0 in an infinite medium. The medium scatters anisotropically, and the benchmark calls for varying the orders of truncation for the Legendre expansion of the scattering kernel. The geometry of the problem was modeled as a rectangular box of dime nsions 30 x 1 x 1 cm, spatially discretized among 7 x 1 x 1
77 coarse meshes, each coarse mesh containing a number of fine spatial meshes. The mid problem coarse mesh (numbered four out of seven), contained only one fine mesh (0.001 cm width), and was used to represent the planar source that was normalized to 1 n/sec. Reflective boundary conditions for the faces perpendicular to the y and z axis secured the infiniteness of the source and medium in these directions, while vacuum boundary conditions were used f or the remaining boundaries perpendicular to the x axis. Several tests were performed to assess the effect of the source width and of the fine mesh size related to solution accuracy (see Figure 5 1). While the width of the source region significantly affec ts the solution in close proximity to the source (within ~1 mfp ), a very fine spatial mesh has little to no effect on it. Consequently, the width of the volumetric source was kept as small as possible to permit resolution by the code; the entire medium out side the source was discretized with 1 mm width fine meshes along the x axis. All planar cases were performed using S 34 angular quadrature (1224 total directions for the angular discretization) and one energy group. Due to the high orders required for the Legendre scattering order prescribed for the benchmark problems, built in Legendre Chebychev quadratures were selected for all PENTRAN computations 51 The cross sections were generated using the prescribed Henyey Greenstein scattering kernel, l =cg l wher e c is the scattering ratio g scattering bias, g=0 corresponding to isotropic scattering. Note that the (2l+1) multiplier of the Legendre expansion of the scatterin g kernel is implemented as an option inside the PENTRAN code. The first test was performed for g =0.9, c =0.9, and L =12, the order of Legendre expansion of the scattering kernel. In PENTRAN, the DTW differencing scheme was used in the source region, while ou tside this region, the new EDI scheme 52 was used. The criterion for the
78 convergence of the flux was set to a 10 3 relative error. Table 5 1 contains the scalar flux yielded by the PENTRAN code compared to the reference (the numerical evaluation of the ana lytical solution provided by Ganapol) at several points along x Excellent agreement between the two solutions is demonstrated by the relative differences provided in Table 5 1, all of which are less than 0.7%, with the exception of the selected point clo se to the source (0.01 mfp ). Again, this is a notable result given that PENTRAN computations are carried out in a full 3 D Cartesian mode. It is also worth noting that in the benchmark reference, Ganapol advises that a user should be cautious at distance s directly adjacent to the sources due to numerical difficulties in the solution. In any case, the accuracy of PENTRAN calculations for the points in the proximity of the source significantly improved with an increasing number of angular quadrature (Legend re Chebychev) directions on the unit sphere, spanning (in each mesh) from 1224 total directions for S 34 up to 4224 total directions for the case of S 64 Results at 0.01 mfp from the source (a distance where again Ganapol notes as numerically difficult) f or various quad ratures are provided in Table 5 2 This larger difference between the PENTRAN and reference solutions adjacent to the planar source can be explained by the inherent limitation of both methods to accurately describe the behavior of the flux (which is infinite on the source plane) in the proximity of the source analytical solution). Again, Ganapol recommends for best results, edit points should be at least 0.05 mfp away from any source considered in th e proposed series of benc hmarks 34 Another remark may be made about the solution far away from the source. Since the PENTRAN model is actually finite in the x direction with vacuum boundary conditions at each end (with a zero reentrant flux), there is a finite leakage from the sy stem, which can be
79 decreased as the width of the slab is increased (see Table 5 3 ). This leakage leads to a very small underestimation of the scalar flux far from the source. The second test was meant to describe the convergence of the scattering kernel wi th respect to the scattering order L An extremely forward peaked scattering kernel with g= 0.99 and c= 0.9 was considered. Figure 5 2 illustrates the behavior of the flux that is quite consistent with that noted by Ganapol, 34 with a reduction of neutrons cl ose to the source as the degree of anisotropic scattering increases. 5.1.2 Benchmark Problem 2 Solid Spherical S ource This case refers to the neutron flux generated by a solid spherical source of radius 1 that isotropically emits in an infinite medium. T he initial PENTRAN model for the problem consisted of a 3 D network of uniform 1 mm size cells having at its central region the source spatial distribution. The volume effect due to the Cartesian discretization of the spatial variables (~0.8% relative volu me difference) was eliminated by normalizing the source to 1 n/sec. To mimic an infinite medium, the system was extended to 8 mfp which posed, when corroborated with the requirements for the angular variable representation, significant parallel computer me mory demands. Therefore, we took advantage of the inherent symmetry of the problem, and the system was mode led only in one octant (Figure 5 3 left) employing reflective boundary conditions at origin and vacuum on the other side on each axis. The model was divided in regions (coarse meshes) with larger fine meshes staged further away from the source, namely, 2 mfp of 1 mm fine mesh size, then 2 mfp of 2 mm fine mesh size, and, finally, 4 mfp of 4 mm fine mesh size. For an accurate solution, based on the st udies already performed for the planar source, the calculations were accomplished using 3024 angular directions/mesh on the unit sphere (S 54 ). Due to memory constraints and to speed up the calculations, the problem was run on 16 processors in parallel (2 a ngular x 8 spatial). The full 3 D distribution of the scalar flux rendered by
80 PENTRAN is displayed in the right side of Figure 5 3. As the results entered in Table 5 4 show, a very good agreement (less than 0.7% relative difference) with the semi analytica l solution was achieved. A higher S N order seems to have little to no effect on the accuracy of the calculations, so the difference between the results for the point just on the surface of the source has to be attributed to the already mentioned numerical difficulties in the proximity of the sources. Note that Table 5 4 contains also the radial positions determined from the Cartesian coordinates of the meshes where the PENTRAN results were computed and reported and these positions are slightly different fr om the reference ones. 5.1.3 Benchmark Problem 3 Spherical Shell S ource This case refers to the neutron flux generated by an infinitesimally thin shell source of radius 1 that isotropically emits in an infinite medium. The geometry of the problem (Figure 5 4 left) was modeled in a similar way as that for the solid spherical source. However, to adequately simulate a spherical shell, a hyper fine mesh of very tiny cells (0.5 mm x 0.5 mm x 0.5 mm) had to be used in the coarse mesh, 10 mm x 10 mm x 10 mm, whe re the shell was d efined The source was uniformly distributed in the space between the two spheres used to define the shell and normalized to 1 n/sec. The results reported in Table 5 5 illustrate again the very good agreement (less than 0.4% relative diff erence) between the numerical PENTRAN and semi analytical reference solutions with again the exception of the first two points, one inside the shell and the other in the very proximity of the source. For completeness, the 3 D spatial distribution of the sc alar flux is illustrated in Figure 5 4, the right side. 5.1.4 Benchmark Problem 4 Point S ource In this problem, a point source emits isotropically in an anisotropically scattering infinite medium. Though the semi analytical solution is relatively simple to obtain when having the explicit representation of the scalar flux in a planar infinite medium known, the numerical
81 solution with a 3 D Cartesian coordinates solver is really quite challenging. There were several issues regarding both geometry represent ation and appropriate radiation transport for this extremely localized source in a large anisotropically scattering medium. The 3 D model of this problem (Figure 5 5, left) consists in a 12 x 12 x 12 mfp box divided in 86,000 fine cells of 5 mm size, excep t in the first coarse mesh where the source was defined at origin as one single fine mesh cell of 0.5 mm size. The results in Table 5 6 suggest that a higher S N order and appropriate spatial discretization are required to resolve the solution in this case. To be effective in resolving these issues and differences, more computer resources must be allocated. The comparison between the scalar fluxes generated by all 1 D sources in media with similar scattering properties (Henyey Greenstein scattering kernel wi th c =0.9 and g =0.9) and computed for the same scattering order L =12 is displayed in Figure 5 6, which clearly illustrates the convergence of the solutions at large distances from the sources with spherical symmetry. The PENTRAN 3 D parallel S N code was use d to sol ve the TIEL benchmark problems. All the problems refer to isotropic sources emitting in infinite media with different scattering properties PENTRAN computations were in excellent agreement with the published semi analytic solutions, with less than 0.7% overall relative difference (excepting the points in the close proximity of the sources where the reference solution is affected by inherent numerical difficulties) in the scalar fluxes for the planar, spherical shell, and solid sphere sources. These results prove that PENTRAN, albeit a general 3 D Cartesian coordinates S N solver, has great flexibility in accurately performing particle transport for both simple and very complex problem geometries The results also demonstrate the soundness of the algo rithms and the high accuracy of the numerical results rendered by PENTRAN computations when exact cross sections are provided.
82 5.2 PENTRAN MP Dose Computations in Voxelized P hantoms The previous set of tests reinforced the confidence in the numerical solut ion rendered by PENTRAN for simple or more complex geometries, extended or localized sources with Cartesian or spherical symmetry, but in a rather highly idealized scenario: monoenergetic source, one energy group, theoretical (exact) cross sections. Unfort unately, this is far from what real life applications suppose. It is therefore essential to assess the accuracy of the results and the computational efficiency, in terms of computer memory demands and running times before considering employing the determin istic PENTRAN MP methodology for dose calculation in clinical imaging applications with real patients. Hence, several tests have been done using the 11 year old male voxelized phantom of the UF Series B pediatric phantoms (see Chapter 2), having as referen ce corresponding MCNP5 simulations. 5.2.1 Case Study 1 Flux and Dose Distribution; Volumetric Isotropic S ource The initial test was performed 53 to compare the individual voxel flux values. For this work, the high resolution phantom was down sampled into a 4.7 mm 4.7 mm 30.0 mm voxel size (79 48 50 matrix size) model using the four equivalent materials method implemented in GHOST 3D (see Chapter 4). Subsequently, using PENMESH XP, the collapsed model was cast into a 3 D spatial distribution and sub divided into six coarse mesh z levels, with five coarse meshes in x y domain containing a corresponding number of fine mesh cells (Figure 5 7). An isotropic volumetric (17.8 cm x 3.65 cm x 30 cm) x ray source was overlaid above the upper left side of the phantom. The source spectrum was generated and linearly binned in 8 energy groups by DXS for an arbitrarily chosen 90 kVp tube potential. The GHOST 3D ASCII formatted matrix file containing the material spatial distribution in the down sampled phantom was incorporated into a lattice defined input, with same multi group source definition, for equivalent MCNP5 simulations. The fluxes were scored in the MC run
83 using the MCNP5 FMESH tally, where the spatial and energy meshes were defined to match the S N fine m eshes and energy bins. Overall, this study showed that deterministic techniques are capable of producing accurate results within the statistical er ror of MC methods with the proviso that the MC method produce s a solution with an acceptable stochastic error The S N calculation was executed on 16 Opteron processors and was completed in 3.8 hours rendering a converged solution over all the system. To achieve an equivalent accuracy Monte Carlo simulation with converged mesh tally information 70 cm away from th e source in energy group 1, the estimate d MCNP5 execution time on 16 processors would be over 2000 hours Using 3D DOSE, spatial dose distribution was calculated in the whole 11 year old male phantom model for broad beam ext ernal photon field Figure 5 8 s hows a selected slice from the high resolution phantom (a), the corresponding slice in the computational 189 k voxels model (b), and the corresponding dose distribution (c). Figure 5 8 (d) displays as well the 3D Dose distribution for the enti re phantom. 5 .2.2 Case Study 2 Organ Dose Calculations; Isotropic S ource The previous test proved that with an adequate quadrature, mesh size, and cross section library, it is possible to produce results with the PENTRAN discrete ordinates code that agree within the proposed model. Parallel deterministic PENTRAN results were obtained within comparable running times to parallel MCNP5 Monte Carlo calculations for tally sites adjacent to the source. A major advantage of the S N method is that it provides a detailed, accurate flux distribution at thousands of cells throughout the system while the Monte Carlo method only provides highly accurate values for selected points near the source. Howeve r, in diagnostic imaging, of main interest are average organ doses rather than dose distributions. Hence, another set of calculations, using same UF Series B phantom, were performed to evaluate the solution accuracy and
84 computational efficiency (computer m emory requirements, execution times) of the deterministic method when compared to state of the art Monte Carlo simulations. For clarity, several things related to this set of calculations have to be mentioned: d eterministic radiation transport in the high resolution phantom cannot be performed on commodity parallel clusters ( e.g. memory (in spite of scalable memory options); however, even simulations using a partial model (for example, just torso of the phan tom) may be challenging due to the difficulty in converging the solution, especial ly for the low energy groups (t his behavior is to a degree problem dependent, and is also subject to the energy structure and available capacity of the parallel machine archi tecture; with thousands of processors available, it is conceivable that little t o no down sampling may be needed) very long execution times are needed for Monte Carlo simulations in the full high resolution phantom ; this is because poor statistics will res ult as one attempts to tally histories far away from the radiation field but also due to the long time required for the geometry to be represented in the computer memory of the ation means radiation transport using the same down sampled voxelized model as in the deterministic calculations, but using quasi continuous (0.5 keV energy bins) source energy spectrum as opposed to the multi group spectrum to preserve a reasonable degre e of detail in the computational phantom, the high resolution phantom was down sampled based on the dominant material method of GHOST 3D code to (79 x 48 x 125) matrix size with 4.7 mm x 4.7 mm x 12 mm voxel size (all the organs/tissues were preserved exce pt for the lens of the eye ) the x ray radiation field was model ed as a thin parallelepiped 21 x 0.5 x 30 cm 3 in close proximity to There are several ways to compute dose using MCNP5 tallies. One ca n use F4 tally to compute the photon flux and then convert it to dose by multiplying with appropriate mass energy absorption coefficients using an FM card. A more convenient and direct way is to obtain the energy deposited by the photon beam in the selecte d region (cell) using F6 tally card with the proviso that charge particle equilibrium (CPE) is valid in the tallied region. This is justified since, for the x ray radiographic energy range, the range of secondary electrons produced is smaller than the voxe l dimensions used in the model. Moreover, the atomic number of the
85 materials present in the model is relatively low, excluding major production of bremsstrahlung radiation. So, practically all of the energy is deposited locally, and consequently kerma is e qual to dose. This fact was confirmed by obtaining the same results with MCNP5 F6 and *F8 (the latter of which scores all the photons and secondary electrons to obtain the energy deposited) tallies for even the smallest organs. Hence, all the doses in the MCNP5 simulations were the execution time because the electrons, though accounted for, are not explicitly transported throughout the model). To ensure that any unphysical oscillations that may result in deterministic solution are eliminated, after several tests, S 48 Legendre Chebychev quadrature order 51 was chosen for the deterministic calculations Several energy group structures for the source spectrum and for the multi group cross sections were tested in the attempt to optimize the deterministic transport calculations. The same 80 kVp energy spectrum (2 mm Al, 140 cm air) produced by DXS was rebinned in 8, 16, 24, and 32 energy groups, as shown in Figure 5 9 Fig ure 5 10 displays the percent difference between the average organ doses calculated with PENTRAN of the MCNP5 simulation. Overall, the best results were obtained using 8 energy groups. In the attempt to understand th is counterintuitive result, the effect of the energy group structure on the energy dependent computational components (source spectrum, cross sections, and mass energy absorption coefficients) has been studied. To estimate the effect of the bin structure o f the source energy spectrum on the computed organ doses, MCNP5 calculations were performed using the same 8 group energy spectrum, and the results were compared with an S 48 discrete ordinates
86 computation and state of the art MCNP5 ones. The percent differ ence for the afore mentio ned comparison is shown in Figure 5 11 Analyzing the graph, one may be tempted, generally, to correlate the differences in the calculated doses with the differences due to the source energy bin probabilities. However, as the compar ison between same multi group calculations (MCNP5 and PENTRAN) reveal, the macroscopic cross sections (flat averaged over the energy bin) and the mass absorption coefficients play an important role. This statement is supported also by the fact that MCNP5 s imulations for another energy spectrum (80 kVp, 10 target angle, 1.2 mm Al) using the same phantom yielded very similar values for all the organ doses independent of the number of energy bins, which were linearly spaced (the spectrum was partitioned in 8, 14, and 35 energy bins and compared to the quasi continuous spectrum). However, when a varying energy bin interval was considered for the 8 group simulation, 2 to 9% differences from the reference case were obtained for the calculated doses. In the case o f the previously discussed spectrum (80 kVp, 12 target angle, 2 mm Al), linearly spacing the energy range in 8 groups affected less than 1% the values of the MCNP5 calculated organ doses compared to the corresponding state of the art MC simulations, while the S 48 yiel ded results were 1 to 12 % different, depending on the organ, and overall worse than the variable energy bin structure 8 group calculation. The comparison between the average organ fluxes obtained with the different deterministic calculations of the 12 ) shows a better and less energy group structure dependent agreement than the doses, but still s o me organ specific behavior. This difficulty in predicting the simulation behavior is expected, consider ing the huge variation of the interaction and mass absorption coefficients of low Z (atomic number) materials involved in these simulations for the radiog raphic x ray energy range (Figure 5 13 ). In 3D
87 DOSE, the scalar fluxes are converted into absorbed dos es based on analytical fitting functions considering the median energy of each energy group. While the mass energy absorption coefficient is highly energy dependent over almost all the diagnostic range, the attenuation coefficient shows this dependence onl y for the low energy x rays. This explains why the deterministic fluxes agree much better with the corresponding MC reference ones than the respective doses. Moreover, the photon (primary and scatter) spectrum is different for each individual organ and hen ce, this leads to the erratic effect of the energy group structure on the associated doses. We can speculate that the 8 group (variable energy bin) calculation seems to provide the best overall solution due to the broad low energy bin, where the most sever e approximations for the source, cross section and absorption coefficients combined may average out better than for thinner energy bins. It can be concluded that the energy group structure considerably impacts the accuracy of the deterministic solution for the radiographic x ray radiation transport through human phantoms. Though an optimization (depending on the level of accuracy needed) for the energy group structure is possible, it is not the only problem The accuracy is also individual organ dependent, which imposes substantial limitations of the deterministic method for practical diagnostic applications. Other work has shown that it is indeed quite viable for therapy photon energies (facilitated by the fact that the photon interaction coefficients for t he materials of interest in these applications vary significantly more slowly in the therapy energy range), using electron dose kernels 5.2.3 Case Study 3 Dose Calculations; Monodirectional S ource The above case studies involved isotropic sources. Howev er, this is far from an appropriate representation of the x ray sources used in diagnostic imaging modalities, whether radiography, fluoroscopy, or computed tomography.
88 Monte Carlo codes in general, and MCNP5 in particular, have a great flexibility in repr esenting the spatial, angular, and energy distribution of the radiation sources. To investigate the performance of the PENTRAN MP code system in rendering an accurate solution for radiation transport problems involving directional sources, the simulations of the previous study case have been repeated, this time for the source emitting the radiation normally toward the phantom. In PENTRAN, this type of source can be modeled by enabling (setting probability 1) only one (appropriate) ordinate (direction) and a ssigning 0 probabilities for all the other ordinates in t he quadrature level. Figure 5 14 illustrates again that the energy group structure is essential (and unfortunately hard to optimize due to strong organ dependence) for the accuracy of the determinist ic solution. 5.2.4 Case Study 4 Optimization S tudies The tests previously presented were intended to assess the performance of the deterministic method and, for that purpose, a coarser voxelized phantom (which reduces considerably the execution time fo r both S N and MC codes) was considered appropriate enough. However, when it comes to accurate dose calculations, it is essential to evaluate the impact of the degree of detail/fidelity in the anatomical description of the phantom. On the other hand, from t he perspective of a methodology that might be routinely employed in the clinical dose assessments (which is not necessary the primary goal of this research work, but evidently taken into consideration) the execution time is an important parameter. Some com putational optimization studies in terms of the joint expected accuracy of the results and execution times have been performed. For the first set of investigations, from practical execution time considerations, the matrix size of the high resolution comput ational phantom has been reduced to (252 x 204 x 33) by eliminating the arms and selecting only the chest region (covered by the radiation field). Using GHOST 3D, two other coarser phantoms have been prepared: one down sampled by (5 x
89 5 x 2) resulting in a matrix size of (51 x 42 x 16) and the other one down sampled by (3 x 3 x 1) with matrix size (84 x 68 x 33). Similar parallel MCNP5 simulations were performed on 24 CPUs with all these three voxelized models until the statistical error was less than 0.1% in all tallies. The execution times (though not dedicated runs) were ~50 min, 5 min, and 4 min for the full resolution, the (5 x 5 x 2), and the (3 x 3 x 1) m odels, respectively. Figure 5 15 displays the percent difference relative to the full resolution c ase of selected organ doses. 5.3 Conclusions about the deterministic approach PENTRAN MP code system has been developed to support the deterministic radiation transport methodology proposed for accurate and rapid dose assessments in medical physics applica tions. The tests presented in this chapter proved the soundness of the algorithms and the high accuracy of the numerical results rendered by PENTRAN computations when exact cross t for similar multi group calculations PENTRAN and MCNP5 results agree very well in the radiation field. If the global dose distribution in a complete voxelized human phantom is the objective of a calculation, then the deterministic method is preferable, s ince it yields a converged solution over the entire system, solution whose accuracy cannot be easily established with Monte Carlo, since stochastic simulations cannot provide whole body results (in a reasonable time) with enough precision for reliable comp arison. For patient dosimetry in diagnostic imaging modalities, of major importance are organ doses. If evaluation of organ doses using the deterministic approach assumes the same execution time as that for an entire system dose distribution calculation, in the Monte Carlo simulation there is a significant reduction in the computational time (tallies are scored in bigger volumes, with better statistics in less time). Moreover, the tests demonstrated that the accuracy of the deterministic solution criticall y depends on the energy group structure. Due to the steep variation
90 with energy of the interaction coefficients for the organ s and tissues in the human body in the radiographic energy range (50 150 keV), it is a real challenge to optimize an energy group s tructure for deterministic simulations. This optimization is problem/objective dependent and needs to be performed for every source energy spectrum and almost for every organ in part. Generation of special weighted cross sections and mass energy absorption coefficients in the radiographic energy range may overcome the present difficulties. Hence, it can be concluded that, at this stage, the PENTRAN MP methodology is a potential solution due to its numerical accuracy and sound algorithms for applications spe cifically calling for whole body dosimetry, but is not ready yet to be generally employed for challenging organ specific diagnostic dose calculations; other work has shown that it is quite viable for therapy photon energies when coupled to electron dose ke rnels (EDK) under the recently developed EDK S N procedure. 54 Theref ore, while continuing to investigate and improve the deter ministic methodology, the focus was in this work, directed toward optimizing the Monte Carlo MCNP5 simulations for dose evaluation using voxelized human phantoms. One of t he challenges in this endeavor wa s to appropriately describe the delivery of radiation from the x ray tube in axial or helical motion to the scanned region after passing through the shaping (bowtie) filter. In the n ext chapter the development and implementation of the sourc e subroutine (option provided in the MCNP5 code) that enable d the planned Monte Carlo simulations is presented
91 Table 5 1 Scalar flux solution for the plane source c =0.9, g =0.9, L =12, =10 3 x ( mfp ) PENTRAN S 34 Ref Rel_diff (%) 0.01 1.12 2.23 3.34 4.45 5.56 6.67 7.78 8.89 10 .00 3.05371 0.9458 0.62624 0.45239 0.33914 0.25937 0.20073 0.15651 0.12256 0.09618 3.29089 0.94499 0.62603 0.45228 0.33908 0.25937 0.20081 0.15671 0.12295 0.096 81 7.20 0.08 0.03 0.02 0.02 0.00 0.04 0.13 0.31 0.65 Table 5 2 Scalar flux s olution at x=0.01 mfp for the plane source: effect of the S N order S 34 S 44 S 54 S 64 Ref Scalar flux Rel_diff (%) 3.05371 7.2 0 3.17748 3.44 3.2678 0.70 3.33902 1.46 3.29089 Table 5 3 Scalar flux solution for the plane source: effect of the slab width x ( mfp ) 15 mfp slab 20 mfp slab Ref 7.78 8.89 10 0.15651 0.12256 0.09618 0.1565 0.12265 0.09644 0.15671 0.12295 0.09681 Table 5 4 Scalar flux solution for the spherical source: c =0.99, g =0.95, L =20, =10 3 r_ref ( mfp ) r ( mfp ) Ref PENTRAN S 54 Rel_diff (%) PENTRAN S 64 Rel_diff (%) 1 .0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0.99373 1.09886 1.20312 1.29928 1.40268 1.49917 1.59609 1.69926 1.79652 1.89934 1 .99687 0.12159 0.08639 0.06865 0.05623 0.04735 0.0408 0 0.03547 0.03113 0.02758 0.02463 0.02216 0.125 0 0.0859 0.069 0 0.0557 0.0474 0.0409 0.0356 0.0311 0.0277 0.0247 0.0221 2.80451 0.5672 0.50251 0.93727 0.11194 0.2451 0 0.36934 0.08353 0.42053 0.2842 1 0.26176 0.125 0 0.0858 0.0689 0.0566 0.0473 0.0408 0.0354 0.031 0 0.0276 0.0245 0.0222 2.80 0.68 0.35 0.66 0.10 0 .00 0.19 0.40 0.06 0.53 0.1 9
92 Table 5 5 Scalar flux solution for the shell source: c =0.9, g =0.9, L =12, =10 3 r_ref ( mfp ) r ( mfp ) PENTRAN S 54 Ref Rel_diff (%) 0.56 444 1.1188 9 1.673 33 2.227 78 2.782 22 3.3366 7 3.891 11 4.445 56 5.0000 0 0.56292 1.11887 1.67351 2.22725 2.78265 3.33663 3.89134 4.44578 5.00006 0.0924 0 0.097 00 0.0306 0 0.0155 0 0.00931 0.00614 0.0 0427 0.00309 0.00233 0.08669 0.09936 0.0306 0 0.01554 0.00931 0.00612 0.00426 0.0031 0 0.00232 6.59 2.37 0.00 0.24 0 .00 0.38 0.15 0.26 0.38 Table 5 6 Scalar flux solution for point source: c =0.9, g =0.9, L =12, =10 3 r_ref ( mfp ) r ( mfp ) Ref PENTRAN S 60 Rel_diff (%) 1.12 2.23 3.34 4.45 5.56 6.67 7.78 8.89 10 .00 1.1211 2.23383 3.33916 4.4486 0 5.56018 6.66938 7.78079 8.89048 10.0015 0.06037 0 0.01427 0 0.00587 0 0.00302 0 0.00175 0 0.00109 0 0.000707 0.000477 0.000329 0.0653 0 0.01435 0.00588 0.00304 0.0018 0 0.0011 0 0.0007 17 0.0004 9 1 0.0003 4 0 8.15 0.59 0.14 0.8 6 3.10 1.35 1.41 2.97 1.30
93 Figure 5 1 Plane source: effect of the source width and fine mesh size Figure 5 2 Plane source: effect of the scattering order L
94 Figure 5 3 Solid spheri cal source: PENTRAN model (left) and full scalar flux solution (right) Figure 5 4 Spherical shell source: PENTRAN model (left) and full scalar flux solution (right)
95 Figure 5 5 Point source: PENTRAN model (left) a nd full scalar flux solution (right ) Figure 5 6 Scalar flux solution for the 1 D sources: c =0.9, g =0.9, L =12
96 A B Figure 5 7 Computational models for case study 1: A) PENTRAN, B ) MCNP5 A B C D Figure 5 8 Dose distri bution: A) S elected slice from the high resolution UF Series B phantom B) the corresponding slice in the comp utational 189 k voxels model, C) the cor responding dose distribution; D ) whole body dose distribution
97 Figure 5 9 Energy bin probabilities (color line s ) for the 8 group S 48 calculation generated by DXS ; black line the quasi continuous corresponding DXS generated spectrum used in the state of the art MCNP5 simulation Figure 5 10 Percent difference from state of the art MCNP5 results of the average organ doses calculated with PENTRAN MP methodology using different energy group structures in the case of isotropic x ray source S48_P3_G8 S48_P3_G24 0.00% 10.00% 20.00% 30.00% S48_P3_G8 S48_P3_G16 S48_P3_G24 S48_P3_G32
98 Figure 5 11 Comparison between average organ doses due to the same x ray radiation exposure but calculated using d ifferent simulations: deterministic 8 group (S48_P3_G3), MCNP5 8 group energy spectrum with continuous cross sections (MCNP5_G8), of the Figure 5 12 Average organ flux comparison between PENTRAN MP and state of the art MCNP5 results 0.00% 5.00% 10.00% 15.00% MCNP5_G8 vs. "state of the art" S48_P3_G8 vs "state of the art" S48 vs. MCNP5_G8 S48_P3_G8 S48_P3_G24 0.00% 5.00% 10.00% 15.00% 20.00% S48_P3_G8 S48_P3_G16 S48_P3_G24 S48_P3_G32
99 Figure 5 13 Mass attenuation and mass energy attenuation coefficients for soft tissue Figure 5 14 Percent difference from state of the art MCNP5 results of the average organ doses calculated with PENTRAN MP methodology using different energy group structures in the case of monodirectional x ray source 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% liver gonads thyroid R lung L lung S48_P3_G8 S48_P3_G16 S48_P3_G32
100 Figure 5 15 Effect of the down sampling order of the computational phantom on the accuracy of the calculated organ doses 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% (5x5x2) down sampling (3x3x1) down sampling
101 CHAPTER 6 MONTE CARLO MODEL FOR MDCT DOSIM ETRY SIMULATIONS 6.1 Introduct ion Computer tomography (CT) is an extremely valuable diagnostic tool. The lif e saving and health benefits of this modality are widely known and accepted Recent advances, particularly multi ple detector CT technology (MDCT) have provided increased and more diverse applications including, but not limited to, multiphase exams, vascular and cardiac exams, perfusion imaging, and screening exams. Notwithstanding the benefits to the patient undergoing a CT study, the fundamental concern in radiation protection is the optimization of the radiation exposure used in order to minimize the potential ly increased risk resulting from inappropriate use of the modality and the corresponding unnecessary radiation dose. Because some data indicate that low dose radiation (such as that in CT) may have a non negligible increase in risk of cancer, especially in young children, 5,6 it is important to limit CT doses by following the ALARA (as low as reasonably achievable) principle. Equally important is to develop a standardized met hodology to evaluate and archive patient radiation dose data, which can be useful in minimizing potential risks from cumulative medical exposures. 1 In the last decade, the work to establish reliable patient radiation dose assessment methods that account fo r the impressive technological advances has significantly intensified. 14 17,55 59 Owing to their known flexibility and accuracy, Monte Carlo simulations using voxelized phantoms in which the helical motion of the source/table combination in modern CT scann ers h as been explicitly modeled seem to be the most successful. 19,60 Comprehensive studies have been conducted to compare Monte Carlo simulation results with experimental dose measurements in physical anthropomorphic phantoms or software generated values f or typical imaging protocols. 19,60 62 While greatly valuing the pioneering work of such efforts, the goal of the present study is to
102 move a step forward and apply this methodology for dose calculation to actual clinical exams as they are conducted for real patients. The focus of this project is to perform such study using the new broad beam Aquilion ONE 320 slice scanner (Toshiba Americ a Medical Systems, Newport B each, CA), since the new geometry of the detector (a larger detector array made of small indivi dual elements) raises important questions about radiation efficiency especially with regard to new applications (the scanner has its most significant advantages in performing perfusion studies, cardiac electrocardiogram (ECG) gated and dynamic 3D imaging, among others). The scanner possesses a larger detector array (16 cm wide) with the same detection quantum efficiency (DQE) per individual element. A justified assumption on the use of the scanner and the radiation dose consequences would be the need for i ncreased tube current values and hence increased radiation dose in order to attain consistent detected signal to noise ratios and therefore same image quality. The manufacturer, however makes the claim that, depending on the clinical application, the scann er allows for significant dose reduction. 63,64 For example, in the case of computed tomography angiography (CTA) studies, the dose reduction in the ECG (electrocardiogram) gated cardiac exams, assumed to require fewer acquisitions, is claimed to be around 50% compared to current CTA protocols. Regarding neuro logical CT exams, the because the entire brain can be scanned in a single tube rotation (shorter exam time), this can lead to a reduction in the amount of contrast needed t o perform the study and hence lower beam techniques and lower dose. For trauma and pediatric applications, the possibility of shorter scan times (the entire pediatric chest abdomen pelvis region is covered in 2 or 3 rotations) is an added bonus for the ped iatricians; however, thorough dose optimization studies need to be done to guarantee the proper use and application of the protocols. Another very attractive possibility in the clinical use of the 320 slice scanners is true dynamic 3 D
103 imaging (volumetric cine imaging) of moving organs such as the heart or lungs. However, these may results in considerable dose increases for larger patients due to the total scan time and wider coverage. Conclusively, each of these applications prompts the need for accurate d ose assessment and optimization studies. 6.2 Overview of MDCT T echnology In a transmission imaging computed tomography system, an x ray source is collimated to form a fan beam with a defined fan beam angle. The fan beam is orientated to lie within the x y plane of a Cartesian coordinate system, termed the "imaging plane" (usually, the axial or axial oblique anatomic plane). Th e x ray beam is transmitted through the imaged anatomy to an x ray detector array orientated within the imaging plane. The detector a rray is comprised of individual detector elements each measuring the intensity of the transmitted beam along a ray projected from the x ray source to that particular detector element. The detector elements are arranged along an arc each to capture phot o ns from the x ray source along a different ray of the fan beam. The intensity of the transmitted radiation is solely dependent on the attenuation of the x ray beam by the scanned anatomy The source and the detector array in a CT system are rotated inside the gantry within the imaging plane and around the patient so that the angle at which the x ray beam intersects the scanned anatomy constantly changes. A group of x ray attenuation measurements from the detector array at a given angle is referred to as a "vie w" while a "scan" of the object refers to the set of views made at different angular orientations during one revolution of the x ray source and detector around the patient. In a 2 D scan, data is processed to reconstruct an image that corresponds to a two dimensional cross section taken through the anatomy of interest. Earlier x ray CT scanners, called single detector CT (SDCT), imaged one slice at a time by rotating the x ray tube, i.e., the source and a single array of detectors while the patient remained Newer multiple
104 detector (MDCT) scanners make use of multiple detector rows along the z direction (perpendicular to the axial CT plane) which give the scanner the ability to acquire several slices sim ultaneously. In addition, the acquisition of projection data can be made considerably faster by continuously translating the patient table along the z direction during the x ray tube detector primarily determined by the pre patient x ray beam collimation, while in MDCT, the z extent of the data acquisition is determined by the pre patient x ray beam collimation, but the slice width of the image is primarily de fined by the de tector configuration, that is, the way in which detector elements are combined into data channels the smallest units in the z direction from which data can be independently collected along the z direction. From a radiation dose perspective, when specifying an imaging protocol, it is very important to note the detector configuration used to acquire the desired slice thickness because slices of the same thickness may be acquired with different beam collimations. Another important imaging param table travel per x ray tube rotation and the total beam collimation. The pitch describes the amount of overlap of the radiation beam over the scanned anatomy; a pitch of one indicate s contiguous radiation beams, while a pitch value less than one indicates overlap of the radiation beams and a pitch greater than one indicates gaps between the radiation beams. The tube voltage filtration, mAs (tube current times exposure time per rotat ion) and the effective mAs (mAs/pitch), are other decisive parameters which impact the radiation dose from a given imaging protocol. Due to the circular geometry of a CT scanner, the amount of beam attenuation is non uniform as the x ray beam rotates aroun d and passes through the object scanned, which results in non uniform harden ing of the x ray beam having a negative effect on
105 image quality. In order to obtain uniform noise levels in a given CT image, a shaping filter, called a bowtie filter because of it s particular profile, is placed close to the x ray tube within the gantry. The goal of a bowtie filter is the attenuation of the x ray beam to a greater degree at the edges of the beam, as compared to the minimum amount of attenuation at the center of the beam, where the distance between the x ray source and the subject is the shortest and amount of attenuating material is the largest. Clinically, the selection of the bowtie filter is dependent on the beam energy and on the field of view (FOV) required by t he specific study and anatomical region of interest (for example, a head scan requires a small filter while a larger filter is needed in a chest or abdominal study due to the larger area to be imaged). 6.3 Broad Beam MDCT S canners Since the introduction of MDCT scanners, there has been a trend to expand the coverage in the z axis by increasing the width of the detector array. The first wide area detector CT system, manufactured by Toshiba became commercially available in late 2007. The Aquilion ONE scanner (Toshiba America Medical Systems, Newport Beach, CA) has a 320 x 0.5 mm detector array that provides 16 cm coverage in the z axis in one gantry rotation (see Figure 6 1 for a enabling the imaging of ent ire organs (like brain or heart) without table movemen t. The gantry rotation time of 350 ms assures a temporal resolution of 175 ms with half reconstruction. In addition to the broad beam acquisition full coverage, the scanner also offers conventional mult islice modes such as axial or helical with varying beam collimation from 1 to 32 mm and five different choices for beam shaping filtration (Small SS, Small S, Medium M, Large L, and Large LL).
106 6.4 Development of the Monte Carlo Model for MDCT 6.4 .1 Monte C arlo F ormulation for a S our ce in Axial and Helical M otion One of the challenges faced when using a Monte Carlo approach for dose calculations in MDCT is the faithful modeling of the source which can produce a collimated photon beam in axial and helical mot ion. MCNP5 provides the user with great flexibility for source definition by using standard sources implemented in the code or by editing the available source subroutine. When choosing the source subroutine option, the user needs to specify the spatial coo rdinates, the direction vector and the energy and weight of the emitted particle. The Monte Carlo formulation implemented in the source subroutine to sample the required parameters from appropriate probability distribution functions that was derived for th is work is describe d below. The starting position of the source particles is randomly sampled on a helix defined by the parametric functions, = + 0 = + = 0 (6 1 ) with the position of the imaging plane = 1 uniformly sampled along the scan length, L, 1 being a random number between 0 and 1. The helix parameter b is related to the scan pitch (ratio of the table displacement per rotation and the beam width) through: = 2 (6 2) Hence, = 2 1 (6 3) where r, the helix radius, corres ponds to the source (focal spot) to isocenter (defined by x 0 and y 0 in the axial imaging plane) distance ( sid )
107 The direction of the particle is uniformly sampled in the fan beam defined by the fan beam angle ( ) and the beam width at isocenter. The funda mental formulation of Monte Carlo (Equation 6 4) = 2 0 1 = 3 (6 4) enables the derivation for the random sampling of t he polar angle cos = within the fan beam. Giving the isotropic distribution of the azimuthal angle =2 2 and the extent of the polar angle ( m ) limited to half the fan beam angle, the maximum solid angle within the direction can be sam pled is: = 2 0 0 = 2 1 (6 5) Substituting Equation 6 5 in Equation 6 4, the formulation for the polar angle becomes: = 3 1 1 = 2 ( 180 ) (6 6) Based on the formulations for and the direction of the source particle, consistent with the notation used in the MCNP5 code, is given by: = = = (6 7) with the constraint that the direction of the particle is within the z collimation of the fan beam: / 2 = = / 2 (6 8) T o provide the direction cosines as required by a proper MCNP5 run, a rotation transforma tion (due to the rotation of angle of the reference frame Equation 6 9) need ed to be applied to the direction vector defined by Equation 6 7: = 0 0 0 0 1 (6 9)
108 yielding, = + = + = (6 10 ) For validation, the above derived formalism has been implemented in the subroutine sample provided by the MCNP5 code, with the energy of the source particle randomly sampled from the discrete probability function (the energy spectrum provided in an external file by the DXS code ) us ing the fundamental formulation of Monte Carlo for discrete variables and the weight of the source particle arbitrarily set to one, meaning that all source particles have equal weight. The code has been recompiled (in the Unix cluster) using the instructio ns from the MCNP5 manual and a series of simple preliminary tests have been done to verify the subroutine. 6.4 .2 Preliminary T ests to Validate the Source Subroutine In the test, a box 40 x 20 x 40 cc was centered at isocenter ( x 0 = 20 cm, y 0 = 10 cm) and a helical scanning was modeled with the following parameters: 10 cm z start position, 20 cm scan length, 0.5 cm beam width, pitch=1, 26 fan beam angle. The energy spectrum was generated in 1 keV bins using DXS code for 100 kV, 11 target angle, 1.2 mm Al filtration. The flux was tallied using a 1 x 1 x 1 cc cell mesh over the entire box. Figure 6 2 (a) displays the flux per source particle along the z axis at different y positions in the central sagi t tal plane (x=20 cm) for the box filled with water For c omparison, Figure 6 2 (b) displays the variation of the flux in the midscan plane for water (red dots) and air (black squares). As expected, the flux is uniform for the air case due to the symmetry of the problem and the absence of attenuation and scatteri ng effects. The smaller values of the flux for the first 2 cells and the last two are explained by the underexposure of these cells since the beam width was 0.5 cm, half the size of the cells. The effect of attenuation is evident in the water case, the flu x being lower at the center y position (y=10 cm) (more attenuation) and increasing towards the periphery. Scatter effects in water are
109 also reflected in the graphs by the decreasing of the flux along z axis from center toward the end points of the scan len gth, with non zero values outside the area exposed by the primary beam The se preliminary qualitative tests prove the fidelity of the source subroutine to emulate the radiation exposure due to the helical motion of the x ray tube However, to completely va lidate the source representation for a confident use in the intended MDCT dose assessments the crucial effect of the bowtie filter needs to be incorporated and validated as well 6.4.3 Equivalent Energy Spectra and Filtration Models Based on Measurements An accurate MC simulation for MDCT typically requires a detailed description of the scanner under investigation, including photon energy spectra, total (inherent and bowtie) filtration design, and scan geometry (focal spot to isocenter distance, fan beam a ngle, beam collimation, etc). Some of this information may be available from the scanner documentation but the scanner specific source spectra and filtration are proprietary and to obtain them special disclosure agreements with the manufacturer are needed. To overcome these restrictions, a method to generate an equivalent scanner specific source model for MC simulations based entirely on physical measurements with standard clinical CT equipment has been developed. y an equivalent energy spectrum and an analytical function to generate the weight of the source particles in the MC simulation that emulates the variable attenuation of the actual photon beam across the fan angle by the actual total filtration (including t model, two type of air kerma measurements were performed using a traditional 6 cc ionization chamber and corresponding monitor unit (10X6 6 and 9095, Radcal, Monrovia, CA) with a non rotating gantry (a feature accessible through the service mode of the scanner): (a) half value layer (HVL) and (b) bowtie filter attenuation profile across the fan beam. DXS (see Chapter 3) generated spectra for a 7 tungsten target anode an gle (as specified for the x ray tube in the
110 documentation of the 320 slice scanner) with varying amount of Al filtration were used in Monte Carlo simulations to determine the equivalent Al filtration that provides an x ray beam of similar quality (same HVL ) as the actua l beam. The attenuation profile across the fan beam was subsequently fitted using the OriginPro 8 Student Version software package and the analytical function was implemented in the Monte Carlo formulation to generate directional dependent we ights for the source particles. Once generated, the equivalent source model was incorporated in the source subroutine described in Section 6.4.1 (see Appendix B for the complete version of the subroutine used in the MC simulations for the 320 slice scanner ) the MCNP5 code was recompiled, and comprehensive tests were performed to validate the method by comparing physical air kerma measurements in a CTDI phantom with results from corresponding simulations. It is important to note that even though the method has been developed and validated for the 320 slice scanner ( the object of investigation in this work) it can be applied to characterize any given scanner, eliminating the need to obtain proprietary information. 22.214.171.124 Half value layer Standard HVL measu rements were performed for the nominal beam energies and the three filters (Small S, M edium M, and Large L) used in the clinical protocols investigated in the present work. The gantry was set so the x ray tube remained stationary during each exposure while the ion chamber was fixed at the A lead shield with a small aperture was placed in the CT gantry (between the x ray tube and the ionization chamber) to collimate the beam to approximately the size of the cham ber to attain good geometry conditions T he initial measurement was made without filtration in the beam using a particular kVp, mAs and beam collimation followed by exposures made for the same settings but with increasing amounts of 1100 aluminum alloy fi lters of known thickness placed on top of the lead collimating device until the resulting exposure was less than half of the initial value
111 Table 6 1 displays the measured HVL for the nominal beam energies and filter combinations along with the Monte Carlo calculated equivalent Al filtration that generates beams of similar quality It is worth noting that the medium and the large filter s provide same attenuation along the central ray (meaning they have same central thickness) however, as may be seen in the next section, their attenuating properties are different across the fan beam span 126.96.36.199 Bowtie filter attenuation profile These exposure measurements were performed to characterize the attenuation across the and inherent filtration. Again with the gantry parked, the x free in air exposure measurements as much as possible, the ion chamber was fixed at the end of a wooden stick 3 ). The table height was adjusted so that the ion chamber was initially positioned at isocenter and then incrementally decreased to obtain the beam profile across the entire lower half of the fan beam. The experimental setup enabled measurements for the entire vertical opening of the gantry; thus, one full set of measurements was done to verify the assumed symmetry of the scanner design and then the measurements for all the other tu be voltage filter combinations were done for just one half of the gantry opening. The measured values as a function of distance were normalized to the central value and then best fitted with a Boltzmann function (Equation 6 11) using an iterative algor ithm provided by the software package. = 1 + ( 2 1 ) / ( 1 + 0 ) (6 11) Figure s 6 4 to 6 6 illustrate the beam profiles for the tube voltage filter combinations presented in the previou s section using both the normalized raw data and the fitting functions Though not very prominent, the differences in the beam profiles at different nominal tube
112 voltages provide the way to characterize the expected energy dependence of the attenuation pro perties of a given filter i n the developed Monte Carlo source model. The parametric functions are implemented in the source subroutine (see Appendix B) to generate directional dependent source particle weights. This aim was achieved using the relationship (Equation 6 12) among the irectional cosines u and v from Equation 6 7, the fo cal spot to isocenter distance, sid and the distance x across the fan beam. = (6 12) It is important to note that in the current source formulation the directional dependence of the source particles is limited to the x axis (across the fan angle direction); no y axis (across the beam w idth) variation is assumed. Of course, this assumption is reasonable for narrow beams (usually used in helical CT acquisitions) the broad beam used in the volumetric acquisitions ; this issue is addressed and discussed later in thi s chapter Although the HVL measurements made along the central ray of the fan beam yielded same results for the medium M and large L filters at a given nominal tube voltage (Table 6 1) in Figure 6 7 it can be seen that the att enuating properties of thes e filters differ across the beam, which proves that their design (size, thickness) is different. 6.4.4 Validation of the Monte Carlo Model for MDCT Dosimetry Simulations To validate the MCNP5 model for MDCT dosimetry simulations, comprehensive tests consis ting in comparisons between air kerma measurements in CTDI phantoms for various scanning scenarios and corresponding simulation results were done. The scanning scenarios for these validation tests were mostly chosen based on the scanner settings of the cli nical protocols investigated for patient organ dose assessments including axial narrow beam acquisitions, axial
113 broad beam acquisitio ns (named axial scans volume scans for the rest of this dissertation) and helical acquisitions. 6.4.4. 1 Air kerma measurements in CTDI phantom Conventional CTDI 100 type experiments using the standard head (16 cm in diameter, 15.4 cm in length) and body (32 cm in diameter, 15.6 cm in length) polymethylmethacylate (PMMA) phantoms (Figure 6 8 ) and the standar d 100 mm 3 cc pencil ionization chamber (10X6 3 CT Radcal Corporation, Monrovia, CA) were used for validation and comparison purposes. The tests involving one single tube rotation (i.e. the axial and volume scans) were performed in the de, which provides the user greater flexibility in selecting the scan settings. kerma positions in the phantom). Before the actual experiments for validation purposes, preliminary were performed. It was found t hat for the single axial acquisitions the smallest CV (coefficient of variation) was 1.2% at the center position, and the provided in Table 6 2. Explanation for these findings could be accounted for operation: w hen the is reached, the x ray exposure is initiated. It is likely that the manufacturer set a margin in the rotation time so that to avoid signal loss at the end of on e tube rotation. The difference among these measurements is most likely due to the variation in the starting position of the x ray tube for each acquisition corroborated with the overexposure at the end position It follows that t he center position experie nces the least amount of variation in the dose measurements as this location is independent of x ray tube starting position; the
114 measurement is made at isocenter and the material surrounding the center position is uniform in the radial direction. This can service mode again. This mode provides a second option monitor) to perform the axial scans in a reproducible manner T he measurement s performed using several different scan settings, but all yielded air kerma values at the 3 6% higher than those at the 9 position as can be seen in Table 6 3 Though not desire d, these findings additionally support the which, from the clinical use perspective, does slightly affect patient dose Regarding the validation tests, this mode of acquisition has been selected for the axial and volume scans since it provided a more predictable systematical error. For the helical protocol, the measured doses were reproducible at all phantom positions, as shown in Table 6 4 The coefficients of va riation were 0.1% or less. This high degree of reproducibility shows that the helical mode is not affected by the starting position of the x ray tube during acquisition While the starting position of the x ray may be just as variable as seen in the axial s can the x ray tube rotates around the phantom so many times during the full scan that any variability in tube starting position is negated. The actual settings for the entire set of experiments performed for validation and comparison purposes are entered in Table 6 5 188.8.131.52 Simulations for air kerma measurements in CTDI phantoms Analogous Monte Carlo simulations using the model developed and implemented in the MCNP5 code (as described in Section 6.4.1 6.4.3) have been performed for the CTDI experiments summarized in Table 6 5.
115 simulated using standard MCNP5 geometry and material description (Figure 6 9 ). The ion chamber was explicitly model ed as three concentric cylinders of 0.07, 0.32, and 0.5 radii filled with air. The table was modeled as two 5 mm thick shells of carbon separated by air based on measurements performed on CT images. l spot to isocenter distance and fan beam angle) and the particular scan settings ( scan start position, scan length, beam width, pitch, isocenter position in the MCNP5 simulation reference frame, filter type) were entered in the RDUM card of the input file as the developed method requires for a proper simulation (see Appendix B for explanation and illustration of the RDUM card). While the scan settings are distan ce were made available by the manufacturer (as a note, the focal spot to isocenter distance was initially estimated through magnification measurements using a computed radiography CR imaging detector and then confirmed by the manufacturer). In order t o satisfy signal to noise ratio requirements across the entire MDCT detector array, the actual beam width in the z direction is larger than the nominal beam collimation Because this parameter defines the actual radiation field used, it directly impacts th e dose so it is essential to be measured. There are several ways in which this task can be accomplished, such as using a small volume ion chamber and displace it across the beam width, or using optically stimulated luminescence (OSL) dosimeters. For this w ork, actual beam width measurements were conducted using a CR imaging detector (AGFA CR MD4.0) 35 cm x 43 cm in size. A 1 mm copper filter was placed between the x ray tube and imaging plate to attenuate the x ray beam and better match the exposure expecte d by the CR imaging plate. The images were processed by a CR digitizer (CR85 X, AGFA) using a flat field algorithm (Figure 6 10 ) and
116 analyzed using Image J (National Institutes of Health, Bethesda, MD) software analysis program. The beam profiles were gene rated across the mid line of the CT x ray beams (Figure 6 1 1 ) and the beam widths were calculated using the full width at half maximum (FWHM) of the profiles. These values are entered in Table 6 5 as well. Clearly, be ca use the actual beam width is 10 mm wi der than the nominal width, this result in exposure of regions for which images are not reconstructed, but this is a margin set by the manufacturer for image quality purposes, to prevent any detector element from entering the penumbra and hence losing sign als. 68 This overbeaming is not covered by the FDA in its manufacturing regulations for CT scanners (21CFR1020.33), and thus it is not add ressed from that perspective. To obtain air kerma in the simulations, energy deposition F6 tally (as described in Sect ion 5.2.2) was used in the cell defining the active volume of the ion chamber. A large number of photon histories were generated in each performed simulation so that the statistical relative error associated to every tallied quantity was less than 0.1% (at one standard deviation). In MCNP5 the tally results are reported per source particle. Therefore, to obtain the simulated air kerma values D scan normalization factors as described by Jarry et al 60 had to be applied to the reported results ( Dsim ) scan as shown in Equation 6 13 = / # / = / ( ) (6 13) The normalization factors were calculated from air kerma measured with the 100 mm pencil chamber free in air at the s isocenter ( Dmeas ) axial,air in one axial scan with id entical settings (kVp rotation time, mA, nominal beam collimation, filter, focal spot) as the investigated scan and the analogous simulation for the single axial scan in air measurements ( Dsim ) axial,air If preliminary exposure linearity measurements for the same scan settings (kVp,
117 collimation, filtration, focal spot) have been performed then those can be used to obtain the normalization factor per mAs/rot and multiply it by the total mAs in the investigated scan. While the free in air measurements are t rivial when using narrow beams, especially in the broad beam acquisitions that exceed the active length of the standard 100 mm ion chamber. Since a longer ion chamber is not commercially available (t hough the use of a 300 mm penci l ion chamber has been reported 6 3,65 66 ) the air kerma for the broad beams was to be obtained by performing two successive measurements: a first measurement obtained during the volume scan of interest performed with the ion c hamber aligned with the z axis using a wood bar tightly fixed at the edge of the scanner table and positioned with the end of the active volume at isocenter a second measurement for the same volume scan but obtained after stepping up the table 10 cm horizo ntally until the other end of the chamber was at isocenter For the needed normalization factors, two axially contiguous ion chambers have been simulated and the F6 tally results in their active lengths were summed. Taking into account the non standard way in which they needed to be performed, the 12% difference between the values obtained in these two successive measurements corresponding to the two transversal halves of the beam provided an additional insight about the particularities of the new broad bea m scanner, namely, a noticeable heel effect across the anode cathode direction of the beam, i.e. across the width profile. Indeed, a detailed investigation of the intensity distribution across the width of the 160 mm nominal beam of this scanner 67 showed a gradual decrease in the intensity to about 20% on one half of the beam. This effect seems to decrease at positions further away from the center of the fan angle. Moreover, similar beam profile investigations on the Toshiba 256 slice scanner prototype 68 sho wed that the scatter radiation averages out the heel effect present in the primary beam from measurements done inside a CTDI
118 phantom. From a patient dose perspective, these findings indicate that the average dose for the deep organs is insignificantly affe cted by the heel effect, which may not be the case for surface organs as the lens of the eye or the skin. 184.108.40.206 Comparison between measurements and simulations in CTDI phantoms The percent difference between the air kerma values measured and simulated i n the five available positions of the CTDI phantoms are shown in Table 6 6 for all of the performed test scans described in Table 6 5. All the relative differences are less than 9%. The root mean square (RMS) of the percent error s reported for every valida tion test is between 1.32 % fo r one of the helical scans and 5.33 % for one of the broad beam (volume) scans ; the overall RM S of the reported percent differences is 3.35% Excellent agreement is seen in the results for the axial and volume scans at the cente volume scans, respectively, were expected since the simulation model is mirror symmetric relative t o the sagittal plane, but the actual measurement conditions were not. The exposure position for the volume scan case due to the larger overlap area of the bro ad beam. This effect was not experimentally seen in the helical acquisitions, which is a fact reflected by the simulation results also. An Successful (however not thorough due to obvious unpractical usefulness) attempt has been made in the source model to account for this scan overlap by sampling the source particles more than one full rotation, by an arbitrary small degree at the overlap position. Since this inherent variability in the starting and the end position of the x ray tube that correlates observ ed increased doses in completing the scan can be neither controlled clinically
119 nor such accounted for in the simulations, it remains a systematic, though not significant, source of errors in the developed computational methodology. The validity of the simu lations relies on the accuracy with which the x ray spectra, the filtration and the geometry are modeled. While their exact knowledge and representation would certainly guarantee high accuracy for the results, it is unlikely their availability for any scan settings of the actual clinical exams. Moreover, the information that a manufacturer would eventually provide may not exactly characterize the actual scanner being evaluated. Therefore, the x ray tube bowtie filter combinat ion used in the CT exam investigated may be not only a convenient solution, but also a n even more accurate one in some situations. The approximations in representing the source along with the uncertainties in the exact co error of the simulation results in addition to the st atistical error inherent to any Monte Carlo approach and uncertainties in the experimental ion chamber measurements (4%) Despite the discusse d limitations of the model developed, the very good agreement with the various experimental measurements in diverse scanning scenarios proves its robustness and provides the necessary confidence in its use for assessments of patient organ doses from clinic al CT studies performed on the 320 slice scanner.
120 Table 6 1 Measured HVLs for different tube voltage filter combinations for the 320 slice scanner; Monte Carlo calculated equivalent Al filtration Nominal tube voltage (kV p ) Filter HVL (mm Al) Equivalent Al filtration (mm Al) 80 S 3.87 2.0 80 M/L 4.65 3.3 100 S 4.88 2.1 100 M/L 5.80 3.8 120 S 5.91 2.3 120 M/L 6.85 4.2 Table 6 2 Air kerma (mGy) measured in CTDI head phantom (axial scan in service mode of the 320 enabled) Air Kerma (mGy) 80 kVp 100 kVp 120 kVp 135 kVp Center 22.46 45.52 71.91 95.31 3 o'clock 26.99 52.28 80.63 105.91 6 o'clock 25.49 49.82 77.43 102.05 9 o'clock 25.41 49.30 76.05 99.78 12 o'clock 27.13 52.20 80.13 104.77 Rel diff (%) 6.20 6. 04 6.02 6.15 Table 6 3 Reproducibility of an axial scan Position within phantom Center Measured air kerma (mGy) 20.10 22.12 24.65 22.74 18.96 20.15 21.33 22.98 22.13 20.03 20.64 22.00 2 5.32 21.88 21.12 20.35 21.72 24.52 24.08 19.31 20.68 21.80 23.00 23.58 19.47 20.17 22.60 26.18 24.74 19.62 20.65 23.30 23.07 26.29 20.67 20.13 21.74 24.10 23.82 19.61 20.59 21.63 23.93 24.99 19.54 20.59 21.31 26.40 21.88 20.95 Coefficient of variation 1.2% 2.8% 5.1% 6.2% 3.7% Table 6 4 Reproducibility of a helical scan Position within phantom Center Measured air kerma (mGy) 76.49 78.78 77.08 81.65 80.13 76.59 78.83 77.20 81.76 80.23 76.60 78.83 77.11 81.80 80.21 Coefficient of variation 0.1% 0.0% 0.1% 0.1% 0.1%
121 Tab le 6 5 Scanner settings for the air kerma measurements in CTDI phantoms Scan name kVp Filter mAs Nominal beam collimation B eam width FWHM (mm) S can length (mm) P itch axial scan1 80 S 200 0.5 x 32 mm 26 axial scan2 100 S 200 0.5 x 32 mm 26 axial scan3 120 S 200 0.5 x 32 mm 26 axial scan4 135 S 200 0.5 x 32 mm 26 axial scan5 80 M 200 0.5 x 32 mm 26 axial scan6 100 M 200 0.5 x 32 mm 26 axial scan7 120 M 200 0.5 x 32 mm 26 helical scan1 100 S 225 0.5 x 32 mm 26 160 0.656 helical scan2 120 S 225 0.5 x 32 mm 26 160 0.656 helical scan3 120 M 225 0.5 x 32 mm 26 160 0.656 volume s can1 100 S 120 0.5 x 24 0 mm 13 0 volume scan2 120 S 120 0.5 x 24 0 mm 13 0 volume scan3 80 M 300 0.5 x 32 0 mm 17 0 volume scan4 120 M 300 0.5 x 32 0 mm 17 0 Table 6 6 Comparison between air kerma measurements and simulations in CTDI phantom s Scan name Relative difference (MC CTDI)/CTDI (%) RMS Center 3 o'clock 6 o'clock 9 o'clock 12 o'clock (%) axial scan1 0.02 1.44 1.45 4.19 1.67 2.22 axial scan2 0.13 0.08 0.35 5.51 3.94 3.0 3 axial scan3 0.18 0.91 0.22 5.09 3.34 2.75 axial scan4 0.43 1.78 0.85 4.91 3.24 2.78 axial scan5 0.08 1.82 0.98 6.88 4.25 3.73 axial scan6 0.23 1.58 0.48 5.75 3.66 3.14 axial scan7 0.15 1.84 1.35 5.22 3.46 2.98 helical scan1 0.15 3.65 5.61 1.65 0.24 3.08 helical scan2 2.31 4.6 7 6.10 3.18 1.11 3.89 helical scan3 2.21 0.30 1.09 1.60 0.14 1.32 volume scan1 0.96 1.89 3.02 8.38 6.77 5.09 volume scan2 2.51 1.91 1.79 8.79 7.18 5.33 volume scan3 0.06 1.57 0.12 6.02 4.20 3.36 volume scan4 0.01 0.99 0.00 5.01 3.23 2.70
122 Figure 6 1 Schematic representation of the geometry of the 320 slice scanner
123 A B Figure 6 2 Flux variation along z axis in a helical scan (flat filter) simulation: A) at different y positions in the central sa g gital plane of th e box fil led with water; B ) comparison of the central flux in air (black squares) and water (red dots)
124 Figure 6 3 Experimental setup to measure beam intensity profile across the fan beam Figure 6 4 Attenuation profile for the small S bowtie filter of the 320 slice scanner
125 Figure 6 5 Attenuation profile for the medium M bowtie filter of the 320 slice scanner Figure 6 6 Attenuation profile for the large L bowtie filter of the 320 slice scanner
126 Figure 6 7 Attenuation profiles at 80 kVp nominal tube v oltage for the three bowtie filters of the 320 slice scanner Figure 6 8 Conventional head and body CTDI phantoms
127 Figure 6 9 Model for the MCNP5 simulations of the air kerma measurements in the CTDI head phantom Figure 6 10 Radiograph ic image of the 160 mm nominal CT x ray beam
128 Figure 6 1 1 Beam profile of the 160 mm nominal CT x ray beam.
129 CHAPTER 7 ORGAN DOSE SIMULATIO NS FOR THE 320 SLICE MDCT SCANNER The value and applicability of Monte Carlo dosimetry simulations using tomographic phan toms have been proven and have become quite popular due to their versatility and accuracy. For dose assessment in CT, the lack of availability of proprietary information about various critical components of the scanner has prevented a more widespread use o f these simulations. Therefore, the approach presented here, which is based on measurements performed in the clinical setting, can be easily implemented in an open source code like MCNP. This easier approach may awaken the interest in computer simulations in response to the increased demand for patient dose assessments in CT. Besides the novel method presented to model the scanner specific source, the present work also includes an original approach to the way in which the patient dosimetry in CT is perform ed. The dose assessment by Monte Carlo simulations introduced here was performed for real, complete clinical CT studies using corresponding computational tomographic phantoms and not just for a few typical scans. In addition, the results from these simulat ions were compared with organ doses measured with optically stimulated luminescence (OSL) dosimeters previously obtained by Lavoie. 67 To investigate potential dose reductions resulting from the novel broad beam acquisition mode in the 320 slice scanner, co mparisons with simulated organ doses from corresponding CT studies using clinical protocols from a standard 64 slice scann er were performed. The imperative need for access to certain ce, table design and material, which are essential in conventional MC approaches, is eliminated using this approach, so the contribution of the intrinsic acquisition mode alone can be such investigated. Moreover, variability in patient positioning is also obviated.
130 of the art hybrid tomographic phantoms, the choice of the computational anatomical models utilized in this project was determined by the physical tomographic phantoms used by Lavoie in th e experimental measurement of CT doses. Namely, the UF Series B nine month voxel phantom for the pediatric studies and the adult male KTMAN 2 phantom for the neuro and cardiac studies, respectively, as described in Section 2.2. All the simulations were per formed on a fast parallel cluster of 24 CPUs. However, the geometrical representation in MCNP5 of these high resolution voxelized phantoms requires a large amount of computer time ( typically more than 12 hours prior to proceeding with any radiation transpo rt calculations). Using GHOST_3D, the code described in Section 4.1.4, the matrix of the original phantoms was reduced while preserving the voxel resolution, by cropping out the arms and the legs (same as in the physical phantoms used for measurements). Si nce the were substituted in the MCNP5 model by a box with water on each side to mimic the attenuation and scatter from the missing part of the anatomy. The scan ner table was represented as described in Chapter 6, Section 220.127.116.11. Special attention was given to best simulate the scanning conditions regarding the positioning of the phantom (scan start position, x and y relative positions of the gantry isocenter an of the MCNP5 Monte Carlo simulations are included in Appendix B, showing the geometrical representation of the model, the RDUM cards for the scan settings, and the F6 tally sites. The average organ doses were calculated by multiplying the tally results per source photon with the normalization factor (Equation 6 13) determined as described in the previous chapter, Section 18.104.22.168. The statistical error for all the reported values was less than 1% (on averages 0.5%) at
131 one standard deviation. However, due to the normalization factor, all the organ doses are affected by the 4% uncertainties in the ionization chamber air kerma measurements. The doses reported are for organs of prioritized interest as determined both by their proximity to the primary CT x ray beam and by their radiosensitivity as indicated in Table 7 1, which contains the corresponding tissue weighting factors according to the ICRP 2007. 4 In order to address deterministic effects, the dose to the lens of eye and skin dose were also estimated. Lens of the eye doses were estimated for the head protocols (pediatric and neuro studies) to compare against threshold doses for radiation induced cataracts (i.e., from an acute dose of 2 3 Gy) In terms of average skin dose, two approaches were used: for comparison with corresponding 64 slice protocols, the average skin dose for the entire phantom used was calculated and reported for comparison with experimental OSL dosimeter skin dose measurem ents (for which the dosimeters are placed on the phantom along an axial slice) to compare against threshold doses for erythema, a separate simulation using only the part of the phantom delineated by the scan range was performed and the average skin dose (i n these simulations, the missing part of the phantom was substituted with boxes with water to approximate the scattering conditions). 7.1 Ped iatric Study The increased coverage combined with the 0.35 ms rotation time make the 320 slice scanner conducive to pediatric studies, where patient motion during the acquisition is frequently a problem. A common CT study for pediatric patients is a non contrast head scan to evaluate for craniosynostosis, a deformity of the skull caused by irregular fusing of cranial s utures. While this study has traditionally been performed on a 64 slice scanner, the ability to scan the entire head in a single rotation with the 320 slice scanner made this study a good candidate for organ dose evaluation and comparison. The scan paramet ers for the 320 slice pediatric head CT study are listed in Table 7 2.
132 7.1.2 Organ Dose Comparison with Provided OSL Dosimeter M easurements The craniosynostosis study has traditionally been performed using a 120 kVp beam To evaluate the potential ability to perform the study at a reduced dose, a second series of simulations was performed using the same phantom in the 320 slice protocol but decreasing the tube voltage from 120 kVp to 100 kVp. As expected, all organ doses are higher for the studies using a t ube voltage of 120 kV p as compared to 100 kV p The results of all the simulations for the organs that were accessible to the OSL dosimeter measurements 67 are summarized in Table 7 3 and show good agreement with the measured doses. As discussed in Section 6 .4.4.2, the 160 mm radiation field of this 320 slice scanner presents an evident heel effect. The small difference in radiation output from one end of the beam profile to the other may affect the measured absorbed doses of superficial organs such as skin a nd lens of the eye. Since the heel effect was not accounted for in the simulations, this may explain the slightly larger difference in the measured and simulated skin dose for both nominal tube voltages investigated, while the very good agreement for the l ens of the eye dose is likely due to the axial position (anode cathode direction) of the eyes in the radiation field corresponding to the average exposure. In the comparative measured results, the fact that the OSL dosimetry is based on point measurements could explain the comparison results for the average thyroid dose which was estimated experimentally through just one point measurement. 7.1.1 Organ Dose Comparison from 320 S lice and 64 S lice S tudies For organ dose comparison purposes, the corresponding traditional 64 slice head protocol was also simulated. The scan parameters for this protocol are also included in Table 7 2, while the results of these simulations and comparisons are summarized in Table 7 4. Again, only the doses to the most radiosensitiv e organs inside or proximal to the scanned region were reported. The rest of the tally results, though available, were intentionally omitted because of being either
133 negligibly small or unreliable due to insufficient statistical sampling. Even though red bo ne marrow and breast are more highly radiosensitive tissues and thus of special dosimetric interest in pediatric studies, their corresponding doses could not be evaluated since these organs are not defined in the UF Series B nine month pediatric phantom. A t the same tube voltage (120 kV p ), the organ doses that resulted from the 64 slice helical scanning are roughly 50 % higher than the doses from the 320 slice broad beam acquisition. Since the scan range was the same for both acquisitions, the difference in organ doses is most likely due to the difference between the volumetric axial and helical acquisitions, which require higher total mAs due to the numerous rotations of the x ray tube during the helical scan. This total mAs is calculated by multiplying the tube current, rotation time and the number of tube rotations. The fact that the scan pitch was less than 1 resulted in significant beam overlapping which is augmented by the fact that the actual beam width is larger than the nominal beam collimation. Ther efore, the organs inside the primary x ray field experience higher exposure to the beam and hence higher doses while the organs outside the scan range experience higher scatter radiation and the effect of the intrinsic extra half rotation at the beginning and end of the helical scan, also known as helical overscan. One parameter that impacts the measured organ doses and which is patient dependent is the total scan length. For a volumetric acquisition, the scan range is selectable from 100 mm to 160 mm in 2 0 mm increments. The scan length needed to cover the entire brain is determined clinically from the localizing tomogram. For this project, a range of 120 mm was selected to adequately cover the phantom. Clearly, an increase in scan range will increase some organ doses, especially that of the thyroid as the scan length extends down towards the neck bringing the primary radiation field closer to the organ. It is therefore essential from the dose reduction perspective to keep the FOV and range of the scan as s mall as is needed for a proper diagnosis
134 One limitation of the simulations, in general, is the inability to assess patient motion. A single volumetric acquisition acquired in 0.6 seconds will most likely result in significantly less patient motion than th e helical comparison. While the actual x ray tube rotation time is less (0.5 second), the smaller beam width of the 64 slice scanner requires several rotations of the x ray tube about the patient to adequately cover the entire scan range. This longer total scan time may prove too long to prevent the patient from moving during the scan. This phantom study did not allow for investigation into this issue however one can conclude that the lower dose and decreased total scan time make this protocol a more viabl e option on the 320 slice scanner than on a 64 slice scanner. 7.2 Adult Brain Perfusion One of the most powerful tools of a 320 slice volumetric CT scanner is its ability to image an entire organ in a single rotation of the x ray tube. O ne clinical applica tion for this type of acquisition is the evaluation of suspected stroke patients using brain perfusion data. The Radiology Practice Committee ( RPC ) took on the task of optimizing this protocol in the clinical setting to maximize image quality and reduce do se. Organ dose assessments were made for each of the required iterations and then compared to the previous standard of perfusion imaging as preformed on a 64 slice scanner The volumetric adult brain perfusion protocol used for the evaluation of stroke con sists of four general acquisitions. First among these is a non contrast scan of the head to evaluate for potential bleeding. At Shands at UF, this is performed as a helical acquisition. This non contrast scan is immediately followed by several dynamic volu me scans to acquire perfusion data. Depending on th e particular study protocol, a helical CT angiogram (CTA) of the head followed by a helical head scan with contrast may complete the study These acquisitions are further detailed in Table 7 5
135 While the s canning parameters used in the non contrast head, head with contrast and CTA of the head remained the same for all iterations of the protocol optimization parameters for the dynamic volumes were varied to reflect the clinical changes the protocol underwen t during development. The first p erfusion study assessed was the one originally suggested by the manufacturer la p optimization process, volumetric acquisitions were done with the tu be voltage increased from 80 kV p to 100 kV p and 120 kV p p cturer at 120 kV p with all other scanning and acquisition parameters remaining the same The fourth iteration (the perfusion study labeled involved changing the timing of the arterial phase acquisitions from intermittent to continuous and adding the helical acquisitions (CTA and head with contrast) at the end of the study. Finally, an altogether different acquisition protocol (l was evaluated. In this protocol, the initial helical head CT without contrast was followed by twenty intermittent volume scans with th e tube current increased during certain portion s of the arterial phase. For c omparison, the protocol used for evaluation of stroke utilized in the 64 slice scanner was also evaluated. Because of the smaller beam width (32 mm) compared to the volumetric scanner (160 mm), the entire brain is not covered during a single acquisition of the perfusion data. Therefore, using the full width of the beam the perfusion images are acquired during 1 minute of continuous axial acquisitions (a total of sixty tube rotations) As was the case with the 320 slice scanner, a helical scan of the head w ithout contrast is acquired before the perfusion acquisition. Helical CTA of the head and a second helical of the head with contrast are also acquired following the perfusion scan. The parameters for each of these acqu isitions are detailed in Table 7 6.
136 7. 2.1 Organ Dose Comparison with Provided OSL Dosimeter M easurements Table 7 7 lists the average organ doses resulting from the brain perfusion protocols investigated by Monte Carlo (MC) simulations and the available OSL dosimeter measurements performed by L avoie 67 for comparison purposes. A more thorough comparison analysis is provided in Table 7 8 where the resulting organ doses are detailed per individual acquisition type. Some general observations can be made regarding the comparison results: Good agreeme nt, especially in the case of the volume scans, is obtained for small (i.e. eye) or well sampled (i.e. skin) organs which are inside the radiation field, proving the soundness of both methods For larger organs, which lie partially inside and partially outs ide the radiation field, it is clear that a certain number and spatial distribution of OSL dosimeter within such organs is required to guarantee a proper average organ dose T he previous statement is crucial in the case of large organs which extend in the craniocaudal direction outside the edges of the radiation field (as is the case of esophagus in this study) since there is a large variation of the dose with distance from the isocenter. Because in a helical scan the dose distribution from the primary be am in the phantom varies significantly, obtaining an accurate average organ dose from point dose measurements is likely to be more challenging; meanwhile the simulations also may not accurately model all the aspects of the actual helical scan (amount of th e helical overscan for example) ) 7.1.1 Organ Dose Comparison for the 320 Slice and 64 Slice Studies Of the three original manufacturer protocols, the simulations for the acquisitions performed at 120 kV p (which provided images of adequate diagnostic quali ty) resulted in the highest mean organ doses, as expected. While initially the 100 kV p volume acquisitions seemed n doses for all organs, roughly p radiologists, the patient dose consideration was the deciding factor in the selection of the tandard 320 slice brain perfusion protocols.
137 When compared to the doses resulting from the simulation of the standard 64 slice brain perfusion protocol (Table 7 9), the current ly implemented (after the iteration process just described) 320 slice protocols show considerable dose savings for the most radiosensitive organs. Since the three helical acquisitions (head without contrast, head CTA, and head without contrast) are included (with the same scan settings) in all these compared protocols from both scann ers it is the dynamic volume acquisition of the perfusion data that determines these differences in absorbed doses. Despite the total scan volume being much smaller (32 mm compared to 160 mm nominal beam collimation), the long acquisition time in the 64 s lice study (one minute of continuous axial acquisitions, while the patient table remains stationary) generates a much higher total mAs (9000 compared to 3180 or 3157.5) which clearly results in higher organ doses especially for those organs exposed by the primary beam, such as the brain. The smaller volume does slightly spare some of the dose to the eyes, but this benefit is far outweighed by all the other dose considerations since the risk of deterministic effects (such as cataract formation, which is the main concern regarding the eyes from a radiation dose perspective) is practically null in these compared perfusion studies. Therefore, it is reasonable to slice protocols are recommended for the brain perfu sion studies in place of the 64 slice protocol whenever possible. 7.3 Adult Cardiac CT Angiography Cardiac imaging is another area that greatly benefits from the expanded craniocaudal coverage provided by the 160 mm wide CT x ray beam. Like the brain, the entire heart can be imaged with a single gantry rotation and, as in the case of brain perfusion studies, the short rotation time allows the contrast bolus to be imaged at a single moment in time producing temporally uniform images 70 with a temporal resolut ion of 175 ms using half rotation reconstruction.
138 Cardiac CTA offers an advantageous alternative to invasive coronary angiography catheterization for adequate detection of coronary artery disease (CAD). While the American College of Cardiology (ACC) consi ders the 64 slice system as the current standard for cardiac CT studies, high doses have been seen as a limitation of its more widespread applicability. However, the particularities of the new broad beam volumetric acquisition allow for important dose savi ngs as reported in several cardiac CTA studies, 70 72 even though these results are based on effective doses measured with pencil chambers and CTDI phantoms. Three cardiac CTA protocols were investigated to assess organ doses for the 320 slice volumetric sc anner (Aquilion ONE, Toshiba America Medical Systems, Tustin, CA): 1. Cardiac functional analysis (CFA) : If cardiac function needs to be assessed, the CT exposure begins with a half rotation acquisition just before the R R interval in the cardiac cycle, a s represented by an electrocardiogram (ECG), continuing through the full R R interval and ending with another half rotation acquisition just after the R R interval. Image acquisition during the entire heartbeat allows reconstruction images at any point dur ing the cardiac cycle. 2. CFA with dose modulation (CFA/Mod) : In an effort to reduce dose to the patient, the CFA protocol may be modified by using dose modulation. While the image acquisition process is the same, the tube current (mA) can be decreased dur ing the systole and in creased during the diastole portion of the heartbeat cycle by selecting a corresponding phase window (the portion of the R R interval) for the scan 3. Propective electrocardiogram (ECG) gating (ProspECG) : When functional information heart rate is below 65 beats per minute (bpm), images can be acquired during one heart beat limiting the x ray exposure to just a portion of the diastole (phase window).Th e minimum
139 exposure time needed is 350 ms (one rotation) but can be lengthened (selecting the phase acquisitions occur during different heartbeats. In the case of pr ospective ECG gating, less contrast is administered to the patient because of the decreased time needed for the entire study. 71 For comparison, the most commonly performed 64 slice cardiac CTA protocol at Shands was investigated. The protocol consists of a single helical scan that covers the entire heart. The details of all these cardiac CTA protocols investigated for organ dose assessment are listed in Table 7 10. 7.3.1 Organ Dose Comparison with P rovided OSL Dosimeter M easurements The average organ doses resulting from the simulations of the 320 slice cardiac CTA studies investigated are listed in Table 7 11. The estimated doses based on OSL dosimeter measurements provided by Lavoie 67 are entered in the same table for comparison. The relative differences (considering the simulation results as reference) between the doses evaluated with these two methods validate their soundness, but also indicate their limitations. The excellent agreement (for CFA and CFA/Mod studies) in the case of the thyroid and lungs p roves the fidelity of the computational approach in modeling the actual scanning conditions. This statement is ensured by the fact that the average dose to the lungs, even though they are large organs, was evaluated based on a very well sampled set of poin t measurements (see Lavoie 67 ). The slightly larger disagreement in values simulated for the case of the Prospective ECG gated study is very likely to be due to the already discussed (Section 22.214.171.124) limitation of the simulations to account for exposures f rom partial rotations. For this particular cardiac study, a minimum of one rotation of the tube is required. However, depending on the selected phase window (60% 100% for the investigated protocol), more than one rotation is necessary to complete the scan. Despite the fact that the total primary beam exposure was correctly
140 represented by the normalization factor (determined as described in Section 126.96.36.199) non symmetric irradiation of the phantom introduces additional errors in the simulation results. In th e case of the stomach dose, the choice of the number and spatial distribution of the point measurements to estimate average organ dose is extremely important since this is a relatively large organ which happened to be just at the edge of the primary x ray beam, so it experienced a larger non uniform irradiation. 7.3.2 Organ Dose Comparison for the 320 Slice and 64 Slice Studies Significant dose reductions are provided by the broad beam volumetric acquisition of the 320 slice CT scanner for the cardiac CTA s tudies when compared to standard 64 slice protocol, as can be seen from the results of the simulations listed in Table 7 12. As expected due to the short exposure time, the largest patient dose savings resulted from the prospectively gated protocol (ProspE CG). Whenever possible, and clinically indicated, this is the protocol that should be used. The clinical limitation of this protocol is the requirement of a low heart rate. The manufacturer specifies a maximum heart rate of 60 bpm; if the heart rate is too high, one heart beat is not long enough to acquire the necessary data in one diastole. Therefore, patients with heart rates higher than 60 bpm need to be given medication to slow the heart during the scan or receive higher doses because more than one hear t beat and hence more exposures are needed for acquisition of data for proper diagnosis This may not be clinically possible all times. In addition to this fact, arrhythmias and others indications of CAD or a myocardial episode are to be detected an d infer red from evaluating the heart at the altered rate, thus defeating the actual purpose of the study. When complete functional analysis of the heart is clinically necessary, the prospectively gated protocol is not an option. Of the two functional analysis pro tocols, the protocol that includes dose modulation resulted in lower organ doses, as expected. On average, there was a
141 55% dose reduction in all mean organ doses (and even more significant ( as high as 72% ) for organs in the primary beam such as skin and lu ng) using the dose modulation feature for the functional analysis protocol and should be the preferred protocol for functional analysis. 7.4 General Comment Some considerations about the practicality of these MCNP5 Monte Carlo simulations using voxelized t omographic phantoms of huge matrices need to be addressed from a clinical patient dosimetry perspective. The computer time required by a simulation using the full phantom (more than 12 hours, depending on the size and resolution of the phantom, just for re presenting the model, followed by adequate running time to achieve reliable precision in the simulated results) is unpractical. However, the results of the simulations in this research work show that the doses to the organs outside of the primary x ray bea m are reasonably small as compared with those from organs in the beam and therefore can be neglected. Consequently, in order to estimate the average doses for the organs of interest (depending on the CT study) the full phantom can be adjusted using a code like GHOST_3D (described in Chapter 2) so that only the relevant part of it (according to the user needs) can be used in the simulations. The attenuation and scatter from the missing part of the anatomy can be reasonably modeled by cylinders or boxes fille d with water or soft tissue. Huge savings in the simulation time can be such achieved with very small compromise in the accuracy of the results. For example, for simulations of the perfusion studies performed with a reduced model, only the head and part of the torso (just below the end of the esophagus) rendered in one hour of simulation time average doses for eyes, brain, esophagus, overestimated, as this is one example of a large organ for which an extremely non uniform radiation dose distribution occurs, indicating that the average organ dose may not be the most adequate dosimetric quantity. It appears then that an evaluation of the average dose which
142 includes only the part of the skin irradiated by the primary beam may be more useful, at least for assessing risk for deterministic effects until more realistic and reliable risk estimate models for stochastic effects are developed. Since the main goal of this research work wa s to develop a computational methodology that can be clinically used for MDCT patient dosimetry purposes, the computational approach using partial tomographic phantoms is the choice for routine use.
143 Table 7 1 Tissue weighting factors. Tissue w T w T Bon e marrow (red), colon, lung, stomach, breast, remainder tissue* 0.12 0.72 Gonads 0.08 0.08 Bladder, esophagus, liver, thyroid 0.04 0.16 Bone surface, brain, salivary glands, skin 0.01 0.04 Total 1.00 Remainder tissues: adrenals, extrathoracic (E T) region, gall bladder, heart, kidneys, lymphatic nodes, muscle, oral mucosa, pancreas, prostate, small intestine, spleen, thymus, uterus/cervix. Table 7 2 Scan parameters for the protocols of the pediatric head studies investigated Scan Parameter Heli cal Volume Nominal Tube Voltage 120 kV p 120 kV p Tube Current 200 mA 200 mA Tube Rotation Time 0.5 sec 0.6 sec Effective mAs 157 121 Helical Pitch 0.641 Scan Range 120 mm 120 mm Nominal Beam Collimation 0.5 mm x 64 0.5 mm x 24 0 Focal Spot Small Small Filter Small S Small S Table 7 3 Average o rgan dose (mGy) comparison for the 320 slice CT pediatric studies investigated ; Monte Carlo simulations (MC) vs. measurements (OSL) 120 kV p 100 kV p OSL MC Rel. Diff. (%) OSL MC Rel. Diff. (%) max mean max mean Skin 22.57 18.98 19.96 4.93 14.21 12.02 13.11 8. 32 Lenses 24.08 22.14 21.36 3. 52 15.33 13.85 13.62 1. 72 Thyroid 2.13 1.95 2.20 11.38 1.22 1.15 1.28 9.83 The statistical relative error for all reported dos es is less than 1% (at one standard deviation)
144 Table 7 4 Average organ dose (mGy) comparison for the ped iatric head CT simulations; 320 slice vs. 64 slice corresponding studies 64 slice 320 slice Rel. Diff.(%) Salivary glands 18.37 8.06 56.11 S tomach 0.34 0.18 47.17 B rain 34.03 21.32 37.34 L ung 2.32 1.20 48.27 S kin 8.86 5.27 40.54 T hyroid 5.42 2. 20 59 44 L iver 0.35 0.19 45.68 E sophagus 1.64 0.76 54.03 E ye 36.98 21.36 42.25 The statistical relative error for all reporte d doses is less than 1% (at one standard deviation) Table 7 5 Details of 320 slice brain perfusion protocols. Scan name Scan type kV p Tube current (mA) Rotation Time (s) Number of volumes Head without Helical 120 300 0.5 CTA head Helical 120 40 0 0.5 Head with Helical 120 300 0.5 Manufacturer at 80 kV p Dynamic volume 1 80 310 0.75 5 Dynamic volume 2 80 150 0.75 1 Dynamic volume 3 80 150 0.75 13 Manufacturer at 100 kV p Dynamic volume 1 100 310 0.75 5 Dynamic volume 2 100 150 0.75 1 Dynamic volume 3 100 150 0.75 13 Manufacturer at 120 kV p Dynamic volume 1 120 310 0.75 1 Dynamic volume 2 120 150 0.75 13 Dynamic volume 3 120 150 0.75 5 Continuous Dynamic volume 1 80 300 1.0 1 Dynamic volume 2 80 120 1.0 17 Dyna mic volume 3 80 120 1.0 7 mA B oost Dynamic volume 1 80 310 0.75 1 Dynamic volume 2 80 150 0.75 2 Dynamic volume 3 80 300 0.75 7 Dynamic volume 4 80 150 0.75 4 Dynamic volume 5 80 150 0.75 6
145 Table 7 6. Scan parameters for helical adult brain perfusion protocol. Scan name Scan type kV p Tube current (mA) Rotation Time (s) Helical Pitch Nominal collimation Head without Helical 120 300 0. 5 0.641 0.5 x 64 mm Perfusion Dynamic volume 120 150 1.0 -8.0 x 4 mm CTA Head Helical 120 400 0.5 0.641 0.5 x 64 mm Head with delay Helical 120 300 0. 5 0.641 0.5 x 64 mm sixty continuous axial acquisitions with patient table stationary Table 7 7 Average o rgan dose (mGy) comparison for the 320 slice CT brain perfusion studies investigated ; Mo nte Carlo simulations (MC) vs. measurements (OSL) Study Organ Dose (mGy) Esophagus a Thyroid b Brain c Skin d Eye e Manufacturer 80 kVp OSL 3.23 4.99 199.82 258.41 301.58 MC 2.04 5.81 265.24 280.46 285.95 Rel. Diff. (%) 58.07 14.07 24.67 7.86 5.46 Manufacturer 100 kVp OSL 5.98 9.05 356.57 424.97 496.88 MC 4.04 11.03 464.20 444.32 466.92 Rel. Diff. (%) 48.13 17.96 23.19 4.36 6.42 Manufacturer 120 kVp OSL 9.78 14.37 561.66 602.34 735.15 MC 6.87 18.33 722.24 654.04 713.83 Rel. Diff. (%) 42 .33 21.58 22.23 7.90 2.99 Continuous OSL 3.46 5.01 193.56 233.33 269.74 MC 2.29 6.40 260.18 273.12 264.43 Rel. Diff. (%) 51.35 21.70 25.61 14.57 2.01 mA Boost OSL 3.43 5.14 191.76 241.38 273.24 MC 2.29 6.42 261.28 274.42 265.60 Rel. Diff. ( %) 49.59 19.92 26.61 12.04 2.87 a long (axially) organ outside the radiation field; b smaller organ outside the radiation field; c large organ inside the radiation field; d only the area of the skin inside the radiation field included in the simulation; e s mall organ inside the radiation field The statistical relative error for all reported doses is less than 1% (at one standard deviation)
146 Table 7 8 Average organ dose (mGy) comparison for each protocol in the brain perfusion studies investigated; Monte Carlo simulations (MC) vs. measurements (OSL) Protocol kVp Organ Dose (mGy) Esophagus Thyroid Brain Skin Eye Head without 120 OSL 0.76 1.09 30.86 32.57 37.62 MC 0.31 1.27 43.96 44.81 40.86 Rel. Diff. (%) 143.34 14.10 29.80 27.31 7.94 CTA H ead 120 OSL 0.93 1.34 40.59 42.32 48.02 MC 0.40 1.61 55.86 56.94 51.93 Rel. Diff. (%) 134.32 16.90 27.34 25.68 7.53 Head with 80 OSL 0.76 1.09 30.86 32.57 37.62 MC 0.31 1.27 43.96 44.81 40.86 Rel. Diff. (%) 143.34 14.10 29.80 27.31 7.94 Cont inuous 80 OSL 1.01 1.49 91.25 125.87 146.48 MC 0.50 2.06 121.45 126.56 147.92 Rel. Diff. (%) 102.08 27.67 24.87 0.54 0.98 mA B oost 80 OSL 0.98 1.62 89.45 133.92 149.98 MC 0.50 2.08 122.58 127.86 149.17 Rel. Diff. (%) 94.27 22. 09 27.03 4.74 0.54 Manufacturer 80 OSL 1.71 2.81 138.10 193.27 226.34 MC 0.75 3.10 182.93 190.84 222.58 Rel. Diff. (%) 127.15 9.44 24.51 1.27 1.69 Manufacturer 100 OSL 4.46 6.87 294.85 359.83 421.64 MC 2.01 8.09 385.32 354.71 412.10 Rel. Diff. (%) 121.80 15.10 23.48 1.44 2.31 Manufacturer 120 OSL 8.26 12.19 499.94 537.20 659.91 MC 3.89 15.14 647.14 564.42 670.52 Rel. Diff. (%) 112.11 19.50 22.75 4.82 1.58 The statistical relative error for all reported doses is less than 1 % (at one standard deviation) Table 7 9 Average organ dose (mGy) comparison for the brain perfusion CT simulations; 320 slice vs. 64 slice corresponding studies 64 slice C ont Rel. Diff. (%) mABoost Rel. Diff (%) E ye 240.57 273.14 13.5 4 274.44 14.08 S kin 29.58 20.60 30.37 20.69 30.07 B rain 690.58 265.23 61.59 266.36 61.43 T hyroid 7.34 6.21 15.36 6.23 15.10 C olon 0.07 0.04 41.07 0.04 40.90 S tomach 0.27 0.17 35.50 0.17 35.30 L iver 0.39 0.24 38.55 0.24 38.38 E sophagus 2. 01 1.52 24.34 1.53 24.11 L ung 1.62 1.12 30.85 1.12 30.63 The statistical relative error for all reported doses is less than 1% (at one standard deviation)
1 47 Table 7 10 Scan parameters for adult cardiac CTA protocol. Protocol Tube voltage (kV p ) Tube current (mA) Rotation time (s) Nominal collimation (mm) Helical pitch Prosp ECG 120 P400 0.35 0.5 x 320 -CFA/Mod 120 M500 0.35 0.5 x 320 -CFA 120 M500 0.35 0.5 x 320 -64 slice 120 490 0.4 0.5 x 64 0.21 2 Table 7 11 Average organ dose (mGy) comparison for the 320 slice cardiac CTA studies investigated; Monte Carlo simulations (MC) vs. measurements (OSL) Study Organ Dose (mGy) Thyroid a Lung b Stomach c Skin d Prospectively G ated CTA OSL 2.50 13.94 2.08 21.29 MC 2.76 15.21 2.97 17.34 Rel. diff. (%) 9.36 8.35 30.03 22.81 Functional A nalysis (CFA) OSL 7.81 43.77 6.25 67.71 MC 8.12 44.76 8.75 51.02 Rel. diff. (%) 3.78 2.22 28.56 32.72 CFA with Dose M odulation OSL 4.61 26.07 3.73 41.84 MC 4.88 26.90 5.26 30.66 Rel. diff. (%) 5 .48 3.08 29.05 36.47 a small organ outside the radiation field; b large organ all inside the radiation field; c large organ at the edge of the radiation field; d large surface organ The statistical relative error for all reported doses is less than 1% (at one standard deviation) Table 7 12 Average organ dose (mGy) comparison for the cardiac CTA studies simulations; 320 slice vs. 64 slice corresponding studies S kin T hyroid C olon S tomach L iver E sophagus L ung 64 slice 74.30 10.69 1.41 9.73 11.14 61.99 99.25 CFA 33.41 8.12 1.29 8.75 7.30 60.31 44.76 Rel. Diff. (%) 55.04 24.04 8.21 10.10 34.49 2.71 54.90 CFA/Mod 20.08 4.88 0.78 5.26 4.39 36.24 26.90 Rel. Diff. (%) 72.98 54.35 44.84 45.97 60.63 41.53 72.90 ProspECG 11.35 2.76 0.44 2.97 2.48 20.49 15.21 Rel. Diff. (%) 84.72 74.19 68.81 69.45 77.74 66.94 84.67 64 slice considered reference
148 CHAPTER 8 CONCLUSIONS 8.1 Analysis of the Results The overall purpose of this project was to develop an efficient and r eliable computational methodology that can be clinically used for the assessment of average organ doses resulting from MDCT scans in general, and specifically from the new 320 slice MDCT scanner at Shands Hospital at the University of Florida. In order to accomplish this goal, the two available radiation transport methods, Monte Carlo and deterministic, were investigated using two robust and well validated computer codes, MCNP5 and PENTRAN, respectively. While the Monte Carlo method has been already used fo r MDCT dosimetry applications, the deterministic approach is yet to be validated for this particular application. A required step in the successful implementation of either of these methods was the availability of reliable x ray spectra. To fulfill this n eed, a new code, DXS (Diagnostic X ray Spectra), based on the model proposed by Tucker et al. 31 (TBC model), was developed and evaluated to numerically generate central axis spectra for tungsten target x ray tubes spanning the diagnostic ra diology energy r ange (50 140 keV ) according to user defined input parameters such as target angle, type and amount of filtration, air distance and kVp. Using MCNP5 Monte Carlo simulations, the description of the characteristic x ray production of the TBC model was improve d in the DXS code, by adjusting the fractional emission to better account for the dependence on the x ray tube potential. Though developed to serve the Monte Carlo and deterministic radiation transport simulations for patient dose assessments in different ionizing radiation imaging modalities, including computed tomography for this research, DXS may also be successfully used to generate the spectra needed for radiation protection calculations or characterization and comparisons of imaging systems.
149 A code s ystem, PENTRAN MP, was assembled from existing and specially developed (as a result of this work) codes to support the deterministic radiation transport methodology proposed for dose assessments in medical physics applications. The preliminary tests perfor med proved the soundness of the algorithms and the high accuracy of the numerical results rendered by PENTRAN computations when exact or faithful cross sections for the physical particle interactions are provided. However, following tests demonstrated that the accuracy of the deterministic solution for photon radiation transport in the low energy (up to 200 keV) range critically depends on the energy group structure for which the required cross sections are to be provided. Because of the steep variation (1/ E 3 ) with energy of the interaction coefficients for organs and tissues in the human body in the diagnostic energy range (50 150 keV), the optimization of an energy group structure for deterministic simulations appears to be insurmountable with present time cross section and computer resources availability. This optimization is dependent on both the problem and the objective sought and thus needs to be performed for every source energy spectrum and almost for every organ. Hence, at this stage it can be concl uded that due to its numerical accuracy, sound algorithms, and capability of rendering fast and global results, the PENTRAN MP methodology remains a potential solution to radiation transport problems in diagnostic medical physics but without further work o n multigroup approaches is not currently ready to be employed for routine organ dose calculations for diagnostic imaging procedures. Consequently, the Monte Carlo method was the selected approach to accomplish the objectives of the research and for that purpose, the source subroutine of the MCNP5 code was edited to appropriately model the source for the 320 slice MDCT scanner. An accurate MC simulation for MDCT typically requires a detailed description of the scanner under investigation,
150 including photon energy spectra, total inherent and bowtie filtration design, and scan geometry (i.e., focal spot to isocenter distance, fan beam angle, beam collimation, etc). In state of the art systems, most of this information (the scanner specific source spectra and f iltration, for example) is usually proprietary. To overcome these restrictions, a method to generate an equivalent scanner specific source model for MC simulations was developed and thoroughly validated. This method is based entirely on physical measuremen ts performed on standard clinical CT analytical function to generate the weight of the source particles in the MC simulation that emulates the variable attenuation of the actual photon beam across the fan angle by the actual The developed equivalent source and filtration method was used to perform patient organ dose assessments, maki ng use of the valuable UF tomographic phantoms, for the Aquilion ONE 320 slice CT system. Dose measurements from the 320 slice scanner that have been reported to date are in the form of effective doses and CTDI values displayed by the scanner, rather than actual organ doses. Simulations were performed for the complete neuro, cardiac, and pediatric CT studies that were conducted on physical tomographic phantoms in parallel research work dosimeters for organ dose evaluatio ns 67 The expected variation of the organ doses when changing the scan settings ( such as the tube voltage or the mAs) were correctly predicted by the simulations and confirmed by comparison with the available measurements. If these effects, at least qualit atively, could be anticipated without sophisticated simulations, less predictable were organ doses variations from modifications of the scan sequence in the protocol for a complete study (such as introducing or substituting volumetric scan acquisitions wit h helical ones, which was the case with the brain perfusion
151 studies investigated). The power of the computational method stemmed from the fact that a small database with the results from the simulations for the most used type of scans can be relatively eas ily built and in a reasonable amount of time (a good part of it has already been achieved as a result of this research work). Then, using normalization factors based on common air kerma measurements (also archived in the database), the organ doses for any new proposed protocol can be predicted almost immediately The standard 320 slice brain perfusion protocol at Shands at UF was optimized based on this methodology, in overall very good agreement with the results of the corresponding OSL dosimetric measurem ents. Furthermore, comparisons were made between volumetric and standard helical protocols showing a potential reduction in organ doses using the volumetric scanner for the protocols evaluated. The clinical impact of such result s is very significant, espe cially in the case of pediatric patients and of traditionally high dose cardiac CTA studies. For example 50% in average dose reductions were estimated for the 320 slice volumetric pediatric head CT protocol. For the cardiac CTA, the dose reductions estima ted were more significant in the case of the Prospective ECG gated protocol, more than 80% for the dose to lungs and around 65% for other radiosensitive organs inside or proximal to the primary x ray beam (such as thyroid, colon, or liver ) A lso 56% in ave rage dose reduction was estimated in the case of the Cardiac Functional Analysis protocol when tube current modulation is to be used. To conclude, the present research work provides a validated computational tool ready to be implemented clinically in the c protocols database. 8.2 Future Work As normally should occur with radiation transport numerical methodology, this research work is perfectible and open to future work. There are several aspe cts that can be improved or further developed such as the modeling of the heel effect and of the bowtie filtration through a
152 more faithful source particle weighting or by direct modification of the DXS code to provide off axis spectra accounting for the he such as that resulting from the use of a bowtie filter. Of immedi ate practical benefit will be the use of scanners at Shands Hospital for dosimetric assessment by computer simulations. A natural extension of this research should be to further develop and tune the computational methodology for retrospective patient dose estimation that can be archived in the pa Regarding the deterministic method, generation of special weighted cross sections and mass energy absorption coefficients in the radiographic energy range may overcome the present difficulties. If enough computer resources are available (super clusters) a large number of proper ly weighted energy groups may also make viable the determinist ic solution for diagnostic medical physics applications However, studies need to be made regarding the practicality of super computers for routine clinical use.
153 APPENDIX A CODE DESCRIPTION AND SAMPLES OF OUTPUT FI LES PENIMP PENIMP is a Fortran 90 code developed to automatically generate source biasing parameters and space energy dependent weight window lower bounds to be used in conjunction with the mesh based option of the weight window variance reduction technique in MCNP5 (see MCNP5 manual, vol. II, p.3 43 to 3 50). The CADIS methodology (see A 3 MCNP manual) is implemented in the code to provide the parameters needed to increase the efficiency of MCNP5 simulation based on importance function calculated with PENTRAN adjoint transport. The execution of the code requires: the "penmsh.inp" or "phantom.inp" file (the user is prompted to select which one is to be used by PENIMP) used to generate PENTRAN's input deck the "problem_name1.inp" file (the input file of the first z level) if "penmsh.inp" is going to be used the "en_bin.txt" file (a file having on top a comment line, then on the second line the number of energy groups used in the PENTRAN adjoint calculation, and then, in ascending order, upper limits in keV of the energy groups); NOTE: if DXS was us ed to generate the energy spectrum or the input file "cepinp" to calculate the cross sections with CEPXS, then this file is automatically produced by DXS' execution. the "problem_name.flx" files generated with PENDATA having the group scalar adjoint functi on in all the fine meshes (the files needs to have on the first four columns the x,y,z coordinates, and scalar adjoint, respectively) the extent of the source (xmin, xmax, ymin, ymax, zmin, zmax) going to be used in the Monte Carlo run (the current version of the code works only for parallelepiped sources) the user will be prompted to enter it from keyboard the detector response factor (e.g. reaction rate, dose, etc.); if a rough estimation of the response function is available (for example calculated fro m the forward or adjoint transport), it is highly recommended to be used the user is also prompted to enter it from keyboard
154 The code generates two files ready to be used in the MCNP5 run: "wwinp" containing the mesh specification and the space and ene rgy dependent importances in the exact format required by MCNP5 (see Appendix J in the MCNP5 manual, vol. II) "sdef.txt" containing the spatial distribution of the source (only volumetric source defined by points it's presently implemented) "SI" cards, so urce probabilities "SP" cards, and energy dependent source biasing parameters "SB" cards; at its last part the "sdef" card defined as: sdef erg=d1 pos=Ferg=d2 followed by SI 1 and SP1, source spectrum definition. Again, if DXS was used to produce this spectrum, all this part of the source definition is automatically generated in the "mc_spc.txt" file. transport simulation. sdef erg=d1 si1 H 0.01 0.0300 0.0350 0.0400 0.0450 0.0500 0.0550 0.0600 0.0800 sp1 D 0.00 0.2312445E+00 0.1439297E+00 0.138125 0E+00 0.1222826E+00 0.1027741E+00 0.8291232E 01 0.7116665E 01 0.1075652E+00
155 As can be seen, the user needs to edit the first line of the file adding the string To complete the MCNP5 deck the user are shown below: DS2 S 3 4 5 6 7 8 9 10 SI3 L 9.6093 4.4531 90.6000 10.0780 4.4531 90.6000 10.5470 4.4531 90.6000 11.0160 4.4531 90.6000 11.4840 4.4531 90.6000 11.9530 4.4531 90.6000 12.4220 4.4531 90.6000 12.8910 4.4531 90.6000 13.3590 4.4531 90.6000 13.8280 4.4531 90.6000 --------------------------------------------------// -------------------------------SP3 1 999r SB3 6.862E+23 6.339E+23 5.679E+23 5.115E+23 4.654E+23 4.189E+23 3.739E+ 23 3.371E+23 3.061E+23 2.773E+23 2.506E+23 2.271E+23 2.054E+23 1.854E+23 1.690E+23 1.681E+23 1.818E+23 1.819E+23 1.984E+23 2.042E+23 -------------------------------------------------// ---------------------------------4.889E+23 4.948E+23 5.015E+23 5.083E+23 5.150E+23 5.208E+23 5.257E+23 5.300E+23 5.336E+23 5.379E+23 5.509E+23 5.757E+23 5.752E+23 5.612E+23 5.827E+23 wwp:p 4j 1 *f6:p ctme p rint needs/requirements of each simulation in part.
156 1 1 2 10 0 8 79 48 125 0.20000E 01 0.20000E 01 0.20000E 01 1 6 5 1 0.20000E 01 79.000 37.051 1.0000 0.20000E 01 8.0000 3.7500 1.0000 8.0 000 7.5000 1.0000 8.0000 11.250 1.0000 8.0000 15.000 1.0000 8.0000 18.750 1.0000 8.0000 22.520 1.0000 0.20000E 01 25.000 30.000 1.0000 25.000 60.000 1.0000 25.000 90.000 1.0000 25.000 120.00 1.0000 25.000 150.02 1.0000 0.30000E 01 0.35000E 01 0.40000E 01 0.45000E 01 0.50000E 01 0.55000E 01 0.60000E 01 0.80000E 01 0.43871E 23 0.42294E 23 0.39328E 23 0.36163E 23 0.33653E 23 0.32204E 23 0.31969E 23 0.33011E 23 0.35358E 23 0.38908E 23 0.43200E 23 0.47114E 23 0.49025E 23 0.47925E 23 0.44419E 23 0.40140E 23 0.36479E 23 0.34143E 23 0.33418E 23 0.3451 7E 23 0.37820E 23 0.44047E 23 0.54395E 23 0.70309E 23 0.91462E 23 0.10975E 22 0.10888E 22 0.88248E 23 0.65203E 23 0.49000E 23 0.39768E 23 0.35881E 23 0.36585E 23 0.42650E 23 0.57355E 23 0.89288E 23 0.15954E 22 0.31392E 22 0.58201E 22 0.64366E 22 0.36195E 22 0.17744E 22 0.98714E 23 0.64596E 23 0.49170E 23 0.42830E 23 0.42090E 23 0.46071E 23
157 APPENDIX B SUBROUTINE AND SAMPL ES OF INPUT FILES MCNP5 Source.F90 Subroutine F ile subroutine sour ce dummy subroutine. aborts job if source subroutine is missing. if nsr=0, subroutine source must be furnished by the user. at entrance, a random set of uuu, vvv, www has been defined. the following variables must be defined within th e subroutine: xxx, yyy, zzz, icl, jsu, erg, wgt, tme and possibly ipt, uuu, vvv, www. subroutine srcdx may also be needed. use mcnp_global use mcnp_debug use mcnp_random implicit real(dknd) (a h,o z) real, dimension(140 ) :: spec trum scanner specific variables sid=RDUM(1) focal spot to iso center distance fan_angle=RDUM(2) fan beam angle scan specific variables scanstart=RDUM(3) start position of the scan on the z axis scanlenght=R DUM(4 ) scan range (z extent of the scan length) ; 0 if axial acquisition beam width=RDUM(5 ) actual beam width pitch=RDUM(6 ) pitch of the helical acquisition; 0 if axial acquisition ifilter=RDUM(7 ) type of the shaping filter used in the acquisition 1 for small S at 80 kVp 2 for small S at 100 kVp 3 for small S at 120 kVp 4 for small S at 135 kVp 5 for large L at 80 kVp 6 for large L at 100 kVp 7 for large L at 120 kVp 8 for large L at 135 kVp 9 for medium M at 8 0 kVp 10 for medium M at 100 kVp 11 for medium M at 120 kVp 12 for flat filter mod el specific variables xcenter=RDUM(8) ycenter=RDUM(9)
158 n_source_cell=RDUM(10) c -----------------------------------------------------------------------c Over scanning: half rotation before and after the scan range c ----------------------------------------------------------------------scanstart=scanstart 0.5*beam width*pitch scanlenght=scanlenght+beam width*pitch -------------------------------------------------------------------------! Sample starting position (xxx,yyy,zzz) alpha is the helix parameter -------------------------------------------------------------------------zzz=rang()*scanlenght+scanstart if (pitch==0) then alpha=0 alpha=rang()*2*pie zzz=scanstart else alp ha=((zzz scanstart)*2*pie)/(beam wid th*pitch) end if xxx=sid*sin(alpha)+xcenter yyy=sid*cos(alpha)+ycenter ---------------------------! Sample within actual beam width ; particle frame of reference ---------------------------theta_min =(fan_angle*pie/180.)/2. in=0 Do 100 while (in==0) the ta=acos(rang()*( 1 cos ( theta_min ) ) 1) phi=2.*pie*rang() !d irection cosines u=sin(theta)*sin(phi) v=cos(theta) w=sin(theta)*cos(phi) !particle x and z coordinates d=sid/v z=d*w x=abs(d*u) if ((z > ( beamwidt h/2)) .and. (z < beam width/2)) then
159 in=1 end if 10 0 continue Assign direct ional cosines (rotate the spherical coordinate system ) in the code frame of reference uuu=u*cos(alpha)+v*sin(alpha) vvv= u*sin(alpha)+v*cos(alpha) www=w As sign "icl" source cell number, "jsu" =0 if the particle starting point not on any surface, and "tme" icl=namchg(1,n_source_cell) jsu=0 tme=0 ipt=2 !type of the source particle; 2=photon ---------------------! Sample the particle energy according to the input spectrum ----------------------open(1,file='probabil.txt', status='old') spectrum=0 read(1,*)n Do i=1,n read(1,*)spectrum(i) end do close(1) iflag=0 do 20 0 while (iflag==0) erg=rang()*n+3 prob=rang()*0.08 ie n bin= erg 1 ie n bin =iebin 0.5 if (prob < spectrum(ie n bin)) then iflag=1 end if 20 0 continue erg=erg*0.001 !transform energy in MeV
160 ------------------------------------------------------------------------------------! Assign source particle weight based on nominal kVp and shaping filter -------------------------------------------------------------------------------------if (ifilter==1) then wgt=0.008184459183+(1.080446839107 0.008184459183)/ & &(1+exp((x 6.511525165043)/2.410834827386)) end if if (ifilter==2) then wgt=0.011572813393+(1.074326421266 0.011572813393)/ & &(1+exp((x 7.410843351045)/2.594 081798962)) end if if (ifilter==3) then wgt=0.01465711441+(1.071606462458 0.01465711441)/ & &(1+exp((x 7.884709630416)/2.712182381585)) end if if (ifilter==4) then wgt=0.017021271941+(1.069003646586 0.017021 271941)/ & &(1+exp((x 8.179943569255)/2.783519960571)) end if if (ifilter==5) then wgt=0.011901953471+(1.151824934094 0.011901953471)/ & &(1+exp((x 7.186449694024)/3.359213631267)) end if if (ifilter==6) then wgt=0.01248875341+(1.159459753996 0.01248875341)/ & &(1+exp((x 7.83105445929)/3.754683239101)) end if if (ifilter==7) then wgt=0.012854174257+(1.159532943306 0.012854174257)/ & &(1+exp((x 8.384760008667)/4.031701345148)) end if if (ifilter==8) then wgt=0.02836838399+(1.140602851738 0.02836838399)/ & &(1+exp((x 8.76840943394)/3.93379138499)) end if if (ifilter==9) then wgt=0.00537849721+(1.066680802101 0.00537849721)/ &
161 &(1 +exp((x 7.11889431028)/2.382517070947)) end if if (ifilter==10) then wgt=0.008533695997+(1.067184467959 0.008533695997)/ & &(1+exp((x 7.659468200997)/2.549873644541)) end if if (ifilter==11) then wgt=0.01171 1866976+(1.064053422213 0.011711866976)/ & &(1+exp((x 8.077007171583)/2.668894860883)) end if if (ifilter==12 ) then wgt=1 end if return end subroutine source
162 Input File for the Simulations of Air Kerma Measurements in Head CTDI Phantom c cells 1 2 1.19 2 3 4 5 6 7 $ head phantom 12 1 0.00129 33 $ central electrode 22 1 0.00129 33 23 $ ion chamber active volume 2 1 0.00129 23 3 $ ion chamber wall 3 1 0.00129 4 $ 3 o'clock hole 4 1 0.00129 5 $ 12 o'clock 5 1 0.00129 6 $ 9 o'clock 6 1 0.00129 7 $ 6 o'clock 7 3 1.4 8 9 10 11 12 $ inner table shell 10 3 1.4 13 14 10 11 12 $ outer table shell 8 1 0.00129 1 #1 #2 #3 #4 #5 #6 #7 #10 #12 #22 9 0 1 c surfaces 1 rcc 0 0 10 0 0 30 75 2 rcc 0 0 7.7 0 0 15.4 8 3 rcc 0 0 5 0 0 10 0.5 23 rcc 0 0 5 0 0 10 0.32 33 rcc 0 0 5 0 0 10 0.07 4 rcc 7 0 7.7 0 0 15.4 0.65 5 rcc 0 7 7.7 0 0 15.4 0.65 6 rcc 7 0 7.7 0 0 15.4 0.65 7 rcc 0 7 7.7 0 0 15.4 0.65 8 c/z 0 43 51.1 9 c/z 0 43 51.4 10 pz 14 11 pz 14 12 py 3 13 c/z 0 23.3 35 14 c/z 0 23.3 35.3 mode p m1 8000. 0.24 $Air 7000. 0.76 m2 1000. 0.08 $PMMA 600 0. 0.6 8000. 0.32 m3 6000. 1 $Carbon (fiber) imp:p 1 10r 0 *f6:p 22 rdum 60 49.2 8.0 16.0 2.6 0 .656 9 0 0 8 $ helical scan c rdum 60 49.2 0 0 2.6 0 9 0 0 8 $ axial scan nps 1600000 print
163 Input File for Simulations of the Free in Air Air Kerma Measurements c cells 1 1 0.00129 1 $central electrode 2 1 0.00129 1 2 $ion chamber active volume 3 1 0.00129 2 3 $ion chamber wall 4 1 0.00129 3 4 5 0 4 c surfaces 1 rcc 0 0 5 0 0 10 0.07 2 rcc 0 0 5 0 0 10 0.32 3 rcc 0 0 5 0 0 10 0.5 4 rcc 0 0 10 0 0 20 75 mode p m1 8000. 0.24 $ air 7000. 0.76 imp:p 1 3r 0 *f6:p 2 rdum 60 49.2 0 0 2.6 0 9 0 0 4 nps 100 0000 print
164 Input F ile for the Pediatric Protocol S imulations c UF nine month voxel MCNP model c Ma trix size [289,180,155 ] c Voxel resolution=0.0859376*0.0859376*0.3 c -------------------------------------------------------------------------------------c Body composition and density c ---------------------------------------------------------------------------------------1 5 0.00129 70 u=1 imp:p=1 vol=2.600895E+03 $Air 2 9 1.05 70 u=2 imp:p=1 vol=2.002490E+03 $Muscle+connective 3 2 0.97 70 u=3 imp:p=1 vol=2.186976E+02 $Adipose 4 14 1.04 70 u=4 imp:p=1 vol=1.504E+00 $Pelvis Kidney (Left) 5 14 1.04 70 u=5 imp:p=1 vol=1.480E+00 $Pelvis Kidney (Right) 6 14 1.04 70 u=6 imp:p=1 vol=7.123E+00 $Medular (Left) 7 14 1.04 70 u=7 imp:p=1 vol=6.631E+00 $Medular (Right) 8 1 1.03 70 u=8 imp:p=1 vol=9.616E 01 $Prostate 9 20 1.04 70 u=9 imp:p=1 vol=1.287E+00 $Testes 10 1 1.03 70 u=10 imp:p=1 vol=1.899657E+01 $Salivary glands 11 8 1.07 70 u=11 imp:p=1 vol=4.763544E 01 $Lenses 12 1 1.03 70 u=12 imp:p=1 vol=3.177395E+01 $Spinal C ord 13 18 1.03 70 u=13 imp:p=1 vol=1.626E+01 $Stomach(Wall) 14 6 1 70 u=14 imp:p=1 vol=6.968E+00 $ST(Content) 15 1 1.03 70 u=15 imp:p=1 vol=1.329E 01 $Pituitary gland 16 9 1.05 70 u=16 imp:p=1 vol=8.148984E +00 $Tongue 17 1 1.03 70 u=17 imp:p=1 vol=3.744E 01 $Tonsil 18 7 1.03 70 u=18 imp:p=1 vol=8.380E+02 $Brain 19 18 1.03 70 u=19 imp:p=1 vol=1.625E+01 $Right Colon(W) 20 6 1 70 u=20 imp:p=1 vol=6.463E+01 $Righ t Colon (Content) 21 18 1.03 70 u=21 imp:p=1 vol=1.627E+01 $Left Colon (W) 22 6 1 70 u=22 imp:p=1 vol=1.086E+02 $Left Colon (Content) 23 18 1.03 70 u=23 imp:p=1 vol=7.429E+00 $Rectosigmoid (W) 24 6 1 70 u=24 imp:p=1 vol=3.399E+01 $Rectosigmoid (Content) 25 22 1.10 70 u=25 imp:p=1 vol=3.024E+00 $ET2 (larynx) 26 1 1.03 70 u=26 imp:p=1 vol=6.868366E 01 $ET2 (pharynx) 27 1 1.03 70 u=27 imp:p=1 vol=1.241E+00 $Trachea 28 1 1 .03 70 u=28 imp:p=1 vol=1.458E+00 $Bronchi 29 10 1.06 70 u=29 imp:p=1 vol=1.901E+01 $Blood vessel (aorta) 30 3 0.3711 70 u=30 imp:p=1 vol=1.610E+02 $L Lung 31 3 0.3711 70 u=31 imp:p=1 vol=1.826E+02 $R Lung 32 8 1. 07 70 u=32 imp:p=1 vol=5.862E+00 $Eyes 33 6 1 70 u=33 imp:p=1 vol=2.805E+00 $Gall Bladder(content) 34 1 1.03 70 u=34 imp:p=1 vol=1.157E+00 $Gall Bladder (wall) 35 1 1.03 70 u=35 imp:p=1 vol=2.185E+00 $L Adren al 36 1 1.03 70 u=36 imp:p=1 vol=2.054E+00 $R Adrenal 37 12 1.09 70 u=37 imp:p=1 vol=2.876405E+02 $Skin 38 5 0.001205 70 u=38 imp:p=1 vol=1.557E+02 $Gas(LI+SI) 39 5 0.001205 70 u=39 imp:p=1 vol=2.738E+01 $Gas(ST)
165 40 14 1.04 70 u=40 imp:p=1 vol=1.946E+01 $L Kidney (Cortex) 41 14 1.04 70 u=41 imp:p=1 vol=1.975E+01 $R Kidney (Cortex) 42 11 1.05 70 u=42 imp:p=1 vol=1.595E+00 $Thyroid 43 13 1.04 70 u=43 imp:p=1 vol=4.144E+01 $Hear t(wall) 44 10 1.06 70 u=44 imp:p=1 vol=4.627E+01 $Heart(content) 45 15 1.05 70 u=45 imp:p=1 vol=2.937E+02 $Liver 46 17 1.06 70 u=46 imp:p=1 vol=2.374E+01 $Spleen 47 19 1.04 70 u=47 imp:p=1 vol=7.593E+00 $Bladder( Wall) 48 6 1 70 u=48 imp:p=1 vol=3.096E+01 $Bladder(Contents) 49 18 1.03 70 u=49 imp:p=1 vol=6.882E+01 $SI (Wall) 50 6 1 70 u=50 imp:p=1 vol=1.044E+02 $SI (Content) 51 1 1.03 70 u=51 imp:p=1 vol=4.103E+0 0 $Esophagus 52 16 1.04 70 u=52 imp:p=1 vol=1.459E+01 $Pancreas 53 1 1.03 70 u=53 imp:p=1 vol=2.499E+01 $Thymus 54 101 1.490 70 u=54 imp:p=1 vol=2.025E+02 $cranium 55 103 1.366 70 u=55 imp:p=1 vol=2.625E+01 $Femur(u pper) c 56 106 1.324 70 u=56 imp:p=1 vol=3.316E+01 $Tibiae, patellae c 57 105 1.324 70 u=57 imp:p=1 vol=2.300E+01 $ankle and feet c 58 107 1.445 70 u=58 imp:p=1 vol=5.488E+00 $fibula 59 103 1.366 70 u=59 imp:p=1 vol=1.40 9E+01 $Humerus (upper) 60 106 1.324 70 u=60 imp:p=1 vol=2.628E+01 $Radii + Ulnae 61 105 1.324 70 u=61 imp:p=1 vol=1.679E+01 $hand 62 104 1.402 70 u=62 imp:p=1 vol=1.866E+01 $Scapulae 63 103 1.366 70 u=63 imp:p=1 vol=3.80 1E+01 $Os coxae 64 103 1.366 70 u=64 imp:p=1 vol=2.304E+00 $Clavicles c 65 104 1.402 70 u=65 imp:p=1 vol=2.663E+01 $Femur(lower) 66 104 1.402 70 u=66 imp:p=1 vol=1.441E+01 $Humerus (lower) 67 103 1.366 70 u=67 imp:p=1 vo l=6.404E+01 $Ribs 68 101 1.490 70 u=68 imp:p=1 vol=1.510E+01 $Mandible 69 102 1.170 70 u=69 imp:p=1 vol=1.597E+01 $Vertebrae (C ) 70 102 1.170 70 u=70 imp:p=1 vol=4.681E+01 $Vertebrae (T ) 71 102 1.170 70 u=71 imp:p=1 vo l=2.762E+01 $Vertebrae (L ) 72 108 1.374 70 u=72 imp:p=1 vol=2.898E+00 $Sternum 73 108 1.374 70 u=73 imp:p=1 vol=1.737E+01 $Sacrum C ******************* Lattice definition************************************** 1001 0 100 fill=10000 imp:p=1 $ surrounding box 555 0 200 lat=1 u=10000 imp:p=1 fill = 144:144 89:90 0:154 C **************** Image data start from here********************************* 1 1 1 1 1 1 -------------------------------------------------// --------------------------------------------------------1002 200 1.4 8 9 10 11 12 imp:p=1 1003 200 1.4 13 14 10 11 12 imp:p=1 1004 5 0.00129 100 70 #1002 #1003 imp:p=1 1005 0 70 imp:p=0 c ---------------------------
166 c surface card c ---------------------------C Voxel resolution=0.0859376*0.0859376*0.3 100 rpp 12.3750144 12.3750144 7.6484464 7.734384 0 46.5 200 rpp 0 0.08593 76 0 0.0859376 0 0.3 70 rcc 0 0 15 0 0 70 70 8 c/z 0 41.5 51.1 9 c/z 0 41.5 51.4 10 pz 12 11 pz 50 12 py 3 13 c/z 0 21.4 35.5 14 c/z 0 21.4 35.8 mode p C Material Ca rds ------------------------------// ------------------------c -----------------------------------------c Tally c -----------------------------------------*f16:p 10 13 14 18 19 21 23 30 31 37 42 45 47 51 11 *f26:p 2 4 5 9 25 26 27 34 35 36 46 49 50 52 53 rdum 60 49.2 0 12.0 4.2 0.641 3 1 3 1004 c rdum 60 49.2 6.5 0 13 0 3 1 3 1004 ctme 1500 print
167 Input File for the Cardiac/Brain Perfusion Protocol Simulations c UF_KTMAN_CARDIAC c Matrix size [ 171 ,121,285] C Voxel re solution=0.2cm*0.2cm*0.5cm c 2009 c Monica Ghita c c ---------------------------c Body composition and density c ---------------------------1 24 0.00129 70 u=1 imp:p=1 vol=4.059174E+04 $ outside air 2 17 1.09 70 u=2 imp:p=1 vol=2.656880E+03 $ skin 3 2 1.03 70 u=3 imp:p=1 vol=7.796000E+01 $ salivary gland 4 12 1.05 70 u=4 imp:p=1 vol=3.888000E+01 $ tongue 5 12 1.05 70 u=5 imp:p=1 vol=2.960000E+00 $ tonsil 6 2 1.03 70 u=6 imp:p=1 vol=1.028000E+01 $ adrenal 7 20 1.05 70 u=7 imp:p=1 vol=1.252000E+01 $ thyroid 8 22 1.07 70 u=8 imp:p=1 vol=1.538000E+01 $ eye ball 9 1 0.95 70 u=9 imp:p=1 vol=2.589820E+03 $ adipose 10 21 1.04 70 u=10 imp:p=1 vol=32.8 $ bladder 11 22 1.04 70 u=11 imp:p=1 vol=222.7 $ contents 12 2 1.03 70 u=12 imp:p=1 vol=16.4 $ prostate 13 2 1.03 70 u=13 imp:p=1 vol=29.0 $ gall bladder (W+C) 14 19 1.04 70 u=14 imp:p=1 vol=18.8 $ testes 15 4 1.04 70 u=15 imp:p=1 vol=1.350080E+03 $ brain 16 2 1.03 70 u=16 imp:p=1 vol=0.8 $ pituitary gland 17 7 1.03 70 u=17 imp:p=1 vol=666.9 $ small b owel 18 22 1 70 u=18 imp:p=1 vol=368.0 $ contents 19 18 1.06 70 u=19 imp:p=1 vol=157.0 $ spleen 20 7 1.03 70 u=20 imp:p=1 vol=167.5 $ ULI 21 22 1 70 u=21 imp:p=1 vol=65.0 $ contents 22 7 1.03 70 u=22 imp:p=1 vol=122.4 $ LLI 23 22 1 70 u=23 imp:p=1 vol=63.3 $ contents 24 7 1.03 70 u=24 imp:p=1 vol=126.3 $ stomach 25 22 1 70 u=25 imp:p=1 vol=29.5 $ contents 26 10 1.06 70 u=26 imp:p=1 vol=1194.4 $ liver 27 7 1.03 70 u=27 imp:p=1 vol=3.674000E+01 $ esophagus 28 8 1.06 70 u=28 imp:p=1 vol=1.277600E+02 $ heart(with blood) 29 2 1.1 70 u=29 imp:p=1 vol=5.300000E+00 $ ET1(ant nasal passage) 30 11 0.296 70 u =30 imp:p=1 vol=3.660760E+03 $ lung(with blood) 31 2 1.1 70 u=31 imp:p=1 vol=5.618000E+01 $ ET2(post nasal passage) 32 15 1.03 70 u=32 imp:p=1 vol=1.224000E+01 $ trachea 33 12 1.05 70 u=33 imp:p=1 vol=2.638216E+04 $ muscle 34 2 1.03 70 u=34 imp:p=1 vol=2.618000E+01 $ thymus 35 9 1.05 70 u=35 imp:p=1 vol=193.4 $ kidney(cortex) 36 9 1.05 70 u=36 imp:p=1 vol=64.2 $ kidney(medulla)
168 37 9 1.05 70 u=37 imp:p=1 vol=15.2 $ kidney(pe lvis) 38 24 0.00129 70 u=38 imp:p=1 vol=1.578800E+02 $ in body air 39 14 1.04 70 u=39 imp:p=1 vol=66.0 $ pancreas 40 23 1.4 70 u=40 imp:p=1 vol=8.351000E+02 $ cranium 41 23 1.4 70 u=41 imp:p=1 vol=1.330800E+02 $ mandible 42 23 1.4 70 u=42 imp:p=1 vol=2.727000E+02 $ scapulae 43 23 1.4 70 u=43 imp:p=1 vol=1.068000E+02 $ clavicles 44 23 1.4 70 u=44 imp:p=1 vol=3.148000E+01 $ sternum 45 23 1.4 70 u=45 imp:p=1 vol=1.7086 00E+02 $ cervical vertebrae 46 23 1.4 70 u=46 imp:p=1 vol=2.509800E+02 $ thoracic vertebrae 47 23 1.4 70 u=47 imp:p=1 vol=326.3 $ lumbar vertebrae 48 23 1.4 70 u=48 imp:p=1 vol=231.0 $ sacrum 49 23 1.4 70 u=4 9 imp:p=1 vol=836.0 $ os coxae 50 23 1.4 70 u=50 imp:p=1 vol=502.2 $ femora(upper half) 51 23 1.4 70 u=51 imp:p=1 vol=664.9 $ femora(lower half) 52 23 1.4 70 u=52 imp:p=1 vol=1030.7 $ tibiae, fibulae, patellae c 53 2 3 1.4 70 u=53 imp:p=1 vol=569.4 $ ankle and foot bones 54 23 1.4 70 u=54 imp:p=1 vol=2.293400E+02 $ humeri (upper half) c 55 23 1.4 70 u=55 imp:p=1 vol=169.8 $ humeri (lower half) c 56 23 1.4 70 u=56 imp:p=1 vol=1 48.2 $ ulnae and radii 57 23 1.4 70 u=57 imp:p=1 vol=353.1 $ wrist and hand bones 58 23 1.4 70 u=58 imp:p=1 vol=2.570400E+02 $ ribs C ******************* Lattice definition************************************** 1001 0 100 f ill=10000 imp:p=1 $ surrounding box 555 0 200 l at=1 u=10000 imp:p=1 fill = 85:85 60:60 0:284 C **************** Image data start from here********************************** 1 1 1 1 1 1 --------------------------------------------------// --------------------------------------------------------1002 200 1.4 8 9 10 11 12 imp:p=1 1003 200 1.4 13 14 10 11 12 imp:p=1 1004 22 1.0 20 imp:p=1 1005 22 1.0 21 imp:p= 1 1006 22 1.0 22 imp:p=1 1007 24 0.00129 100 70 #1002 #1003 #1004 #1005 #1006 imp:p=1 1008 0 70 imp:p=0 c ---------------------------c surface card c ---------------------------C Voxel size= 0. 2* 0. 2* 0. 5 100 rpp 17.0 17.0 12 12 0 142.5 200 rpp 0 0.2 0 0.2 0 0.5 70 rcc 0 0 5 0 0 170 70 8 c/z 0 31 51.1 9 c/z 0 31 51.4 10 pz 2
169 11 pz 160 12 py 14 13 c/z 0 11.3 35.5 14 c/z 0 11.3 35.8 20 rpp 15 15 10 10 145 160 $box substituting legs 21 rpp 27 17.1 5 5 3 16 $box substituting left arm 22 rpp 17 27 5 5 3 16 $box substituting right arm mode p C Material Cards ------------------------------// ------------------------c -----------------------------------------c Tally c -----------------------------------------*f16:p 2 3 7 10 14 15 17 24 26 27 30 8 *f26:p 6 12 13 19 20 22 2 8 29 31 32 33 34 35 36 37 39 rdum 60 49.2 0 1 6 4.2 0.641 11 0 1.5 1007 c rdum 60 49.2 8.5 0 17 0 11 0 1.5 1007 ctme 1500 print
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176 BIOGRAPHICAL SKETCH M onica Ghita wa s born in 1968 in Pingarati Romania. Sh e attended the Petru Rares High School, Math Physics profile, in Piatra Neamt and then enrolled in the Physics Department at the University of Bucharest in 1987. Upon graduation with an engineering physics d iploma, in 1992, s he enjoyed a nine year experience as a high school teacher in her hometown During 2001 2004, s he completed her m aster hysics at Cen tral Michigan University, developing essential skills in computational materials s cience In August 2004, the Nuclear and Radiological Engineering Department at the University of Florida offered her adm ission to the Ph.D. Program in nuclear e ngineering and appointed h er as a graduate assistant doing research in Computational Medical Physics Since January 2006 Monica has been working as graduate assistant i n the Department of Radiology, Shands Hospital at the University of Florida gaining clinical exper ience as medical physicist. In A ugust of 2007 she passed P Certification E xam in Diagnostic Radiological Physics. In rec ognition of her outstanding scholastic and professional achievements in Medical P hysics the NRE Department presented her in December, 2007. She received her Ph.D. from the University of Florida in August 2009. Sh e is married to Gabriel and has a daughter, Gabriela Livia.