Citation |

- Permanent Link:
- http://ufdc.ufl.edu/UFE0021934/00001
## Material Information- Title:
- An a Priori Dose Uncertainty Model and Its Clinical Applications
- Creator:
- Jin, Hosang
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2008
- Language:
- english
- Physical Description:
- 1 online resource (190 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Nuclear Engineering Sciences
Nuclear and Radiological Engineering - Committee Chair:
- Kim, Siyong
- Committee Members:
- Gilland, David R.
Hintenlang, David E. Mendenhall, William M. - Graduation Date:
- 5/1/2008
## Subjects- Subjects / Keywords:
- Collimators ( jstor )
Coordinate systems ( jstor ) Dosage ( jstor ) Head ( jstor ) Histograms ( jstor ) Matrices ( jstor ) Modeling ( jstor ) Radiotherapy ( jstor ) Subroutines ( jstor ) Systematic errors ( jstor ) Nuclear and Radiological Engineering -- Dissertations, Academic -- UF application, clinical, dose, imrt, model, radiation, radiotherapy, uncertainty - Genre:
- Electronic Thesis or Dissertation
bibliography ( marcgt ) theses ( marcgt ) Nuclear Engineering Sciences thesis, Ph.D.
## Notes- Abstract:
- The overall dose uncertainty in step-and-shoot intensity-modulated radiation therapy (IMRT) arises from a complex interplay of uncertainties associated with each subfield. To provide accurate prediction of uncertainty distribution during IMRT planning, a novel dose uncertainty model was introduced using statistically quantified uncertainty parameters of IMRT planning and delivery. Clinical applications of the model for IMRT were also developed and their efficacy was investigated. An analytic form of overall dose uncertainty in IMRT was given by bar I sub overall + Z dot sigma sub overall with a confidence level (Z). The dose uncertainties in IMRT were categorized into space-oriented dose uncertainty (SOU) and non-space-oriented dose uncertainty (NOU). The model further divided the uncertainty sources into planning and delivery. Both SOU and NOU of planning were defined as inherent dose uncertainty (IU; I sub overall). It was assumed to arise from three distinct sources: discrete calculation grid size (I sub grid), inaccuracy of calculation algorithm (I sub algo), and possible asymmetric beam delivery (m sub oa). Both SOU and NOU associated with radiation delivery were employed to describe a statistical dose uncertainty (sigma sub overall). Various model parameters for the uncertainty sources were quantified through measurements, accumulated routine quality assurance (QA) data, and peer-reviewed publications. To examine the applicability of the model to IMRT dose verification, dose uncertainty maps were compared with dose difference distributions between calculation and measurement for 32 clinical IMRT fields and one composite dose distirubiton. In all QA measurements, most of the dose difference points (more than 96%) were confined within the uncertainty bound of bar I sub overall + 2 dot sigma sub overall as statitiscally predicted. In addition, a conventional gamma dose verification test was done for all QA measurements. The failed regions of the gamma test remarkably overlaid on regions of high dose uncertainty. It shows that the dose uncertainty map plays an important role as a space-dependent acceptance level of dose verification. Uncertainty-based IMRT plan evaluation tools such as confidence-weighted dose volume histograms (CW-DVH), confidence-weighted dose distributions (CWDD), and dose uncertainty volume histograms (DUVH) were developed to assess the potential risks of treatment plans. CW-DVH provided an overall inspection of the potential risk of the plans with quantitative evaluation indices. CWDD was an essential method to assess a local risk of plans through slice-by-slice examination. A plot of a cumulative dose uncertainty-volume frequency distribution (DUVH) visually summarizes the uncertainty distribution within a volume of interest. These evaluation tools differentiated candidate treatment plans in terms of uncertainty, which were clinically comparable by the conventional plan evaluation methods. This study is highly significant in that it provides a framework to minimize the impact of all known uncertainties in the IMRT process and improve the accuracy of dose delivered to patients. The proposed uncertainty model is expected to radically change how dose uncertainty is assessed and controlled. It will significantly contribute to improving the quality and reliability of radiotherapy, resulting in the most accurate dose delivery to patients. ( en )
- General Note:
- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2008.
- Local:
- Adviser: Kim, Siyong.
- Electronic Access:
- RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31
- Statement of Responsibility:
- by Hosang Jin
## Record Information- Source Institution:
- UFRGP
- Rights Management:
- Copyright Hosang Jin. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Embargo Date:
- 5/31/2010
- Classification:
- LD1780 2008 ( lcc )
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PAGE 1 1 AN A PRIORI DOSE UNCERTAINTY MODEL AND ITS CLINICAL APPLICATIONS By HOSANG JIN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 PAGE 2 2 2008 Hosang Jin PAGE 3 3 To my lovely wife, Sunjung. PAGE 4 4 ACKNOWLEDGMENTS Undoubtedly, the perso n to whom I owe the greatest debt of my gratitude is Dr. Siyong Kim for his outstanding mentoring and advice on my work which has led to a number of brilliant, paradigm-shifting ideas and critic al review. My special thanks go to Dr. Jatindar R. Palta for the principle contribution to the groundwork of this study thr ough brainstorming and priceless professional knowledge. I would also like to acknow ledge the contributions of Dr. Tae-Suk Suh for his continous encouragement and support. Th anks are extended to my committee members: Dr. David E. Hintenlang and Dr. David R. Gilland representing the Department of Nuclear and Radiological Engineering; and Dr William M. Mendenhall representing the Department of Radiation Oncology at the Univers ity of Florida. I give sincere thanks to Dr. Chihray Liu, Dr. Jonathan G. Li, Dr. James F. Dempsey, and Mr. Huey Yang who helped me to do the research more effectively and have never wavered in thei r support of me. I need to express my gratitude to my friend and colleague, Mr Heeteak Chung, who provided me with valuable comments, cooperation, and support in many ways. His passi on for medical physics inspired me to devote myself to taking a fundamental step toward b ecoming a qualified medical physicist. I wish to thank the many friends and colleagues from both the Department of Radiation Oncology and the Department of Nuclear and Radiological Engineering, too nume rous to mention by name, who presented me with numerous suggestions, collabor ation, and their affectio n. Finally, I owe a debt of gratitude to my wife Sunjung for all her pa tience, dedication, and continuous encouragement. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 TABLE OF CONTENTS.............................................................................................................. ...5 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES.........................................................................................................................9 LIST OF ABBREVIATIONS........................................................................................................ 12 ABSTRACT...................................................................................................................................14 CHAP TER 1 INTRODUCTION..................................................................................................................16 General Introduction........................................................................................................... ....16 Uncertainties in Radiation Therapy........................................................................................18 Need for Dose Uncertainty Prediction in Intensity-Modulated Radiation Therapy (IMRT) ................................................................................................................................21 Study Aims.............................................................................................................................22 2 DISCRETIZED GRID SIZE EFFECT AND UNCERT AINTIES OF DOSE CALCULATION IN RADIATION TREATMENT PLANNING......................................... 26 Introduction................................................................................................................... ..........26 Materials and Methods...........................................................................................................27 Experimental Treatmen t Setup and T argets.................................................................... 27 Discretization Effect of Calcula tion Grid on Dose Calculation ...................................... 29 Accuracy of Dose Calculation in Surface and Build-Up Regions.................................. 31 Results and Discussion......................................................................................................... ..31 Discretization Effect of Calcula tion Grid on Dose Calculation ...................................... 31 Dose difference between calculation and measurement........................................... 31 Effect of grid origin shift..........................................................................................32 Dose difference in differe nt dose gradient ranges .................................................... 33 Comparison with measurement................................................................................ 34 Clinical cases............................................................................................................35 Accuracy of Dose Calculation in Surface and Build-Up Regions.................................. 37 Conclusions.............................................................................................................................40 PAGE 6 6 3 CONCEPTUAL DOSE UNCERTAINTY MO DEL AND ITS VERIFIC ATION USING ONE-DIMENSIONAL (1-D) SIMULATION.......................................................................58 Introduction................................................................................................................... ..........58 Methods and Materials...........................................................................................................58 Uncertainty in Dose Calculation and Measurement........................................................ 58 Test Dose Distributions...................................................................................................61 Results.....................................................................................................................................63 Discussion...............................................................................................................................65 Conclusions.............................................................................................................................68 4 GENERALIZED A PRI ORI DOSE UNCERTAINTY MODEL OF IMRT DELIVERY..... 75 Introduction................................................................................................................... ..........75 Methods and Materials...........................................................................................................77 Generalized Dose Uncertainty Model............................................................................. 77 Inherent dose uncertainty for planning.....................................................................77 Revision of space-oriented dose uncertainty (SOU) for delivery............................ 79 Revision of non-space-oriented dose uncertainty (NOU) for de livery....................81 Generalized dose uncertainty model........................................................................ 81 Quantification of Model Parameters............................................................................... 83 Model parameters for inhere nt dose uncertainty (IU) .............................................. 83 Model parameters for SOU and NOU...................................................................... 85 Verification of Expected Dose Un certainty Using Test Patterns ....................................86 Results.....................................................................................................................................87 Quantification of Model Parameters............................................................................... 87 Distance offset parameter of Igrid for IU................................................................... 87 Constants of Ialgo and moa for IU............................................................................... 88 Input parameters for SOU........................................................................................ 89 Input parameters for NOU........................................................................................90 Verification of Uncertainty Prediction............................................................................ 90 Discussion...............................................................................................................................91 Conclusions.............................................................................................................................94 5 APPLICATIONS OF THE UNCERTAINTY MODEL FOR IMRT PLAN VERIFICATION ..................................................................................................................102 Introduction................................................................................................................... ........102 Materials and Methods for Dose Verification...................................................................... 104 Single Field-Based Quality Assurance (QA) Measurem ents........................................ 104 Quality Assurance Measurement of a Composite Plan................................................. 105 Results of Dose Verification................................................................................................. 106 Single Field-Based QA Measurements......................................................................... 106 Quality Assurance Measurement of a Composite Plan................................................. 107 Discussion.............................................................................................................................109 Conclusions...........................................................................................................................110 PAGE 7 7 6 CLINICAL EFFICACY OF UNCERTAI NTY-BASED IMRT PLAN EVALUATION .... 118 Introduction................................................................................................................... ........118 Methods and Materials.........................................................................................................119 Confidence-Weighted Plan Evaluation Tools...............................................................119 Confidence-weighted dose volume histogram (CW-DVH)................................... 119 Confidence-weighted dose distribution (CW DD)..................................................119 Dose uncertainty volume histogram (DUVH)....................................................... 120 Confidence-Weighted Plan Evaluation of Clinical IMRT Cases..................................120 Results...................................................................................................................................121 Discussion.............................................................................................................................123 Conclusions...........................................................................................................................125 7 CONCLUSIONS.................................................................................................................. 134 Establishment of the New Uncertainty Prediction Model.................................................... 134 Efficacy of the Model and Its Clinical Applications............................................................ 136 Issues and Future Works....................................................................................................... 138 APPENDIX A DERIVATIONS OF SPACE-ORIEN TED DOS E UNCERTAINTY AND NONSPACE-ORIENTED DOSE UNCERTAINTY....................................................................140 Derivation of Space-Oriented Dose Uncertainty (SOU) ...................................................... 140 Generalized Functional Form of SOU...........................................................................140 Translational Displacement Parameters........................................................................ 141 Rotational Displacement Parameters............................................................................. 144 Derivation of Non-Space-Oreint ed Dose Uncertainty (NOU) ............................................. 145 B FLOWCHART AND SOURCE PROGRAMS OF UNCERTAINTY COMPUTATION.. 148 LIST OF REFERENCES.............................................................................................................176 BIOGRAPHICAL SKETCH.......................................................................................................189 PAGE 8 8 LIST OF TABLES Table page 1-1 Magnitude of patient -induced uncertainties .......................................................................24 2-1 Cumulative dose differences for the 95, 90 a nd 85% regions of interest are shown for the shallow and deep target cases...................................................................................... 43 2-2 Dose differences for the 95, 90, and 85% re gions of interest for origin shift are shown for the shallow and deep target cases..................................................................... 43 2-3 Mean, standard deviation ( ) and full width half maximum (FWHM) are tabulated for the three relative dose gradient ranges fo r the shallow target case and deep target case.....................................................................................................................................43 2-4 Dose differences for the 95, 90 and 85% regions of interest are displayed for the shallow target case when compared with the measurement.............................................. 44 2-5 Dose differences for the 95 and 90% regi on of interest are displayed for all three clinical cases................................................................................................................. .....44 2-6 Dose difference for Pinnacle3 and Corvus for shallow and de ep target cases is listed for the 90 and 95% regions of interest...............................................................................44 5-1 Summary of five selected head and neck cases for IMRT dose verification using the uncertainty model............................................................................................................. 111 6-1 Summary of five IMRT cases studied.............................................................................126 6-2 Confidence-weighted dose and volume indices...............................................................126 A-1 Summary of normal distribu tions, systematic errors, random errors, and transformed coordinate systems for the rotational degrees of freedom (DOFs).................................. 146 PAGE 9 9 LIST OF FIGURES Figure page 1-1 New paradigm in radiotherapy using the dose uncertainty model..................................... 25 2-1 Solid phantom set-up....................................................................................................... ..45 2-2 Shallow and deep target cases with thr ee critical structures (spinal cord and two parotids).............................................................................................................................46 2-3 Sensitometric curve for the radiochromic film.................................................................. 46 2-4 Histograms for the shallow target ca se with varying cal culation grid size........................ 47 2-5 Histograms for the shallow target case with calculation gr id origin shift......................... 48 2-6 Relative dose difference histograms for th ree relative dose gradient ranges for the shallow target case.............................................................................................................49 2-7 Plot of full width half maximum (FWH M) in relative dose difference histogram verses relative dose gradient range.................................................................................... 50 2-8 Dose difference maps fo r the shallow target case.............................................................. 51 2-9 Simple one-dimensional (1-D) dose profile which illustrates that dose difference may not continuously increase with increasing grid size..........................................................51 2-10 Dose difference histograms between the treatment planning system (TPS) and the measurement for the shallow target case........................................................................... 52 2-11 Dose difference distribution for case 1.............................................................................. 53 2-12 Dose histogram for case 1................................................................................................. .54 2-13 Shallow target case dose dist ribution and the dose difference..........................................55 2-14 Dose difference among Corvus, Pinnacle3, and the measurement..................................... 56 2-15 Calculation accuracy of both the treatment planning systems........................................... 57 3-1 Fit of a one-dimensional calculated dose distribution....................................................... 70 3-2 Planned dose distribution consis ts of two small beam segments....................................... 70 3-3 Two test dose distributions have three beam segments to make the same dose profile.... 71 3-4 Dose bounds of one-beam field (Figure 3-1).....................................................................72 PAGE 10 10 3-5 Dose bounds of a two-beam field (Figure 3-2).................................................................. 72 3-6 Dose bounds of two three-beam fields (Figure 3-3).......................................................... 73 3-7 Dose Uncertainty-Length Histograms (with Z =1) of two test dose distributions (Figure 3-3)........................................................................................................................74 4-1 International Electrotechni cal Commission (IEC) coordinate systems with all angular positions set to zero............................................................................................................95 4-2 Calibration jig containing 4 IR (Infrared) markers............................................................95 4-3 Calculated dose distri butions of test patterns..................................................................... 96 4-4 Inherent dose discrepancy in penumbra regions and its approximation using a dose gradient distribution...........................................................................................................96 4-5 Prediction of inherent do se uncertainty for 5 5 cm2 field size at the depth of 10 cm. A profile of a central scan line is shown below in each figure.......................................... 97 4-6 Scatter diagrams between inherent dose uncertainty and dose difference for a sample set of 9 measurements chosen for constant determination of I (3 depths of 4 7 and 10 cm and 3 field sizes of 3 3, 5 5, and 10 10 cm2).................................................98 4-7 Relative standard deviation (SD) of 15 measurements using an ionization chamber normalized to 195 MU....................................................................................................... 99 4-8 Dose difference distributi on between calculation and EDR2 film measurement of the test patterns........................................................................................................................99 4-9 Calculated uncertainty distributions disp layed according to uncertainty type in the rows and test patterns in the columns.............................................................................. 100 4-10 Scatter diagrams of the test patterns................................................................................ 101 4-11 The test using 2% and 2 mm as criteria is performed for the test patterns................... 101 5-1 Sensitometric curve for the EBT radiochromic film........................................................ 112 5-2 Scatter diagrams of all 32 intensity-modulated (IM) fields between uncertainty and dose difference.................................................................................................................113 5-3 Relationship between dose un certainty and failed points using test.............................114 5-4 Dose uncertainty-failure-histogram (DUHF) of all 32 QA measurements...................... 114 5-5 Isodose distributions of calc ulation and two QA measurements.....................................115 PAGE 11 11 5-6 Checkerboard images between dose uncertainty distributions and dose difference distributions......................................................................................................................115 5-7 Scatter diagrams between the dose uncertainty and the dose difference......................... 116 5-8 Failed dose points of test results overlaid on uncertainty distribution of 95.4% confidence level...............................................................................................................117 5-9 Dose uncertainty failure histogram (DUFH) of the film measuremen............................ 117 6-1 Dose volume histograms of th ree comparative treatment plans...................................... 127 6-2 Confidence-weighted dose distributions (CWDDs) for Patie nt 1 overlaid with one of CT slices...........................................................................................................................128 6-3 Confidence-weighted dose distributions for Patient 1 w ith organs at risk (OARs)......... 128 6-4 Confidence-weighted dose volume histogr ams of planning target volume (PTV) for Patient 2 (head and neck).................................................................................................129 6-5 Confidence-weighted dose distributions for Patient 2 w ith PTV (light green) and brainstem (brown)............................................................................................................ 129 6-6 Confidence-weighted dose di stributions for Patient 5 with PTV (light green), bladder (brown), and rectum (blue).............................................................................................. 130 6-7 Confidence-weighted dose volume hist ograms of PTV for Patient 5 (prostate)............. 130 6-8 Confidence-weighted dose di stributions for Patient 3 with PTV (light green), spinal cord (blue), and parotid glands (yellow).......................................................................... 131 6-9 Dose uncertainty volume histogram of PTV for Patient 3............................................... 131 6-10 Confidence-weighted dose di stributions for Patient 4 with PTV (light green), bladder (brown), and rectum (blue).............................................................................................. 132 6-11 Confidence-weighted dose volume histogram s of rectum and bladder for Patient 4...... 133 A-1 Fixed coordinated system (x y z ) is rotated by g and b and converted to a new coordinate ( u, v w )...........................................................................................................147 B-1 Flowchart of dose uncertainty computation..................................................................... 148 PAGE 12 12 LIST OF ABBREVIATIONS 1/2/3/4-D One/two/th ree/four-dimensional AAPM American association of physicists in medicine CRT Conformal radiation therapy CT Computed tomography CTV Clinical target volume CW-DVH Confidence-weighted dose volume histogram CWDD Confidence-weight ed dose distribution DOF Degree of freedom DTA Distance-to-agreement DUFH Dose uncertainty failure histogram DULH Dose uncertainty-length histogram DUVH Dose uncertainty volume histogram DVH Dose volume histogram EPID Electronic portal imaging device FWHM Full width half maximum GTV Gross tumor volume IEC International electrotechnical commission IMRT Intensity-modulat ed radiation therapy IR Infrared IU Inherent dose uncertainty MLC Multileaf collimator MOSFET Metal oxide semiconducto r field-effect transistor MU Monitor unit NAT Normalized agreement test PAGE 13 13 NOU Non-space-oriented dose uncertainty OAR Organ at risk OD Optical density PDF Probability distribution function PRV Planning organs at risk volume PTV Planning target volume QA Quality assurance RCF Radiochromic film SAD Source-to-axis distance SD Standard deviation SOU Space-oriented dose uncertainty SSD Source-to-surface distance TG Task group TLD Thermoluminescence dosimeter TPS Treatment planning system PAGE 14 14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN A PRIORI DOSE UNCERTAINTY MODEL AND ITS CLINICAL APPLICATIONS By Hosang Jin May 2008 Chair: Siyong Kim Major: Nuclear Engineering Sciences The overall dose uncertainty in step-and-s hoot intensity-modulated radiation therapy (IMRT) arises from a complex in terplay of uncertainties associ ated with each subfield. To provide accurate prediction of uncertainty distribution during IMRT planning, a novel dose uncertainty model was introduced using statistically quantified uncertainty parameters of IMRT planning and delivery. Clinical ap plications of the model for IM RT were also developed and their efficacy was investigated. An analytic form of overall dose uncertainty in IMRT was given by overall overallZI with a confidence level ( Z ). The dose uncertainties in IMRT were categorized into space-oriented dose uncertainty (SOU) and non-space-oriented dose un certainty (NOU). The model further divided the uncertainty sources into planning and delivery. Both SOU and NOU of planning were defined as inherent dose uncertainty (IU; Ioverall). It was assumed to arise from three distinct sources: discrete calculation grid size ( Igrid), inaccuracy of calculation algorithm ( Ialgo), and possible asymmetric beam delivery ( moa). Both SOU and NOU associated with radiation delivery were employed to describe a statistical dose uncertainty (overall). Various model parameters for the uncertainty sources were quantified thr ough measurements, accumulated routine quality assurance (QA) data, and peer-reviewed publications. PAGE 15 15 To examine the applicability of the model to IMRT dose ve rification, dose uncertainty maps were compared with dose difference distributions between calculation and measurement for 32 clinical IMRT fields and one composite dose distirubiton. In al l QA measurements, most of the dose difference points (more than 96%) we re confined within th e uncertainty bound of overall overallI 2 as statitiscally predicted. In addition, a conventional dose verification test was done for all QA measurements. The failed regions of the test remarkably overlaid on regions of high dose uncertainty. It shows that the dose uncertainty map plays an important role as a spacedependent acceptance leve l of dose verification. Uncertainty-based IMRT plan evaluation tool s such as confidence-weighted dose volume histograms (CW-DVH), confidence-weighted dose distributions (CWDD), and dose uncertainty volume histograms (DUVH) were developed to assess the potential risks of treatment plans. CWDVH provided an overall inspection of the potential risk of the pl ans with quantitative evaluation indices. CWDD was an essential method to assess a local risk of plan s through slice-by-slice examination. A plot of a cumulative dose uncer tainty-volume frequenc y distribution (DUVH) visually summarizes the uncertain ty distribution within a volume of interest. These evaluation tools differentiated candidate treatment plans in terms of uncertainty, which were clinically comparable by the conventiona l plan evaluation methods. This study is highly significant in that it provides a framewor k to minimize the impact of all known uncertainties in the IMRT process an d improve the accuracy of dose delivered to patients. The proposed uncertainty model is expect ed to radically change how dose uncertainty is assessed and controlled. It will si gnificantly contribute to improving the quality and reliability of radiotherapy, resulting in the most accurate dose delivery to patients. PAGE 16 16 CHAPTER 1 INTRODUCTION General Introduction Along with chem otherapy, surgery, and hormone therapy, radiation therapy is one of the most important treatment methods in the fight ag ainst cancer. According to the National Cancer Institute (NCI), in the United States more than half of a ll cancer patients (about 60%) undergo radiotherapy at some stage duri ng the course of their disease.1 More than half a million cancer patients undergo radiotherapy each year, either al one or with other forms of cancer treatment. Due to an increasingly multidisciplinary oncology e nvironment, radiation therapy is expected to play a more significant role in achieving the hi ghest probability of cancer cure with the least morbidity. The main challenge in radiation therapy is to control the dose to the target while sparing surrounding health tissues. In principle, modern-d ay external beam radiotherapy techniques such as intensity-modulated radiation therapy (IM RT) enable highly conf ormal radiation dose distributions to be delivered to a clinical target volume. IMRT utilizes a number of small subfields aimed at a tumor from many angles to conform a prescribed dose distribution to the tumor. During treatment, the radiation intensity of each subfield is controlled, and the field shape changes hundreds of times during each treatment. As a result, IMRT has the potential to improve tumor control while protecting su rrounding critical organs. In many clinical ca ses, investigators demonstrated that IMRT significantly reduced dose and a degree of complications of normal tissues and improved patients health-related quality of life more than the conventional or threedimensional (3-D) conformal radiation therapy (CRT) did.2-10 In a comparison study of IMRT and CRT, CRT induced a significant and clinical ly relevant deterioration in pain, role functioning, and urinary symptoms, while only a clinically relevant improvement existed in the PAGE 17 17 IMRT group.3 For brain and head and neck cases (o ropharyngeal carcinoma and meningioma of the skull base), overall survival rates of IMRT ranged from 94% to 98%.7, 10, 11 A 2-year diseasefree survival rate of postoperative IMRT was 92% compared to 68% (preoperative), 74% (postoperative), and 58% (def initive) with CRT for or opharyngeal carcinoma cases.9 This improvement does not come without a price and a risk. The price is in the fact that IMRT is very complex and requires significant amounts of time and resources for quality assurance (QA). The risk is in the fact that IMRT can be easily misunderstood and misapplied, resulting in excess tumor recurrences or excess complications that ne gate its potential benefi ts. The complexity of IMRT is attributed to the fact that each intensity-modulated (IM) field consists of hundreds of subfields. Each of these subfie lds has its own uncertainties that arise from different components such as leaf position accuracy a nd reproducibility. The ove rall uncertainty in an IM field arises from a complex interplay of uncertainties associ ated with each subfield. The effect of such uncertainties can vary from one IMRT plan to another. For instance, an in terinstitutional study of IMRT verification supported by 15 radiotherapy institutions from nine European countries showed a maximum local deviation of 3.5% in the mean dose of the planning target volume (PTV) and 5% in the organ at risk (OAR) ev en with the same computed tomography (CT) dataset and dosimetric planning objectives.12 An independent study of patient-specific IMRT QA from a single institution came to a similar conclusion.13 These deviations are larger than the 23% tolerance for dose calculation accuracy of conventional radiation therapy recommended by the American Association of Physicists in Me dicine (AAPM) Task Group (TG) 40 report and other researchers.14-16 Both studies showed that the maximum differences between calculated and measured dose for some data points were over 4 st andard deviations (SDs). Such high deviations can not be logically attributed to statistical uncertainty in measurements because frequency of PAGE 18 18 their occurrence is extremely low. In other clinic al studies, failures of IMRT have been also reported.5, 10, 11, 17-20 In some cases IMRT improved the PTV coverage but delivered greater doses to the OARs than 3-D CRT did.5 Periparotid failure after defini tive parotid-sparing IMRT for head and neck patients and a slightly larger dose inhomogeneity in the PTV were reported.4, 20 A follow-up study (ranging from 4 to 60 months) show ed there were local -regional recurrences after IMRT treatment.18, 20 These studies clearly imply that there are certain IMRT cases for which the overall uncertainty is clinically unacceptable. Uncertainties in Radiation Therapy Uncertainties in radiation treatm ents arise from a variety of sources throughout the whole process of radiation therapy. Image artifacts and distortion du ring image acquisition may cause the errors. A finite size of CT image voxel cons trains the accurate delin eation of tumor volume. The dose calculation grid size and algorithm of a treatment planning system (TPS) are restraining factors, which make the difference between th e prescribed dose dist ribution and actual dose delivery. Slight dosimetric mismatch can sometimes be critical for a lo cal control of tumors. Inaccuracies in the radiation production and delivery system mu st not be discounted when analyzing the uncertainty of radiation therapy. An inaccurate patient setup leads to a failure to irradiate the defined tumor volum e. Proper patient immobilization is of extreme importance for successful treatment. Internal organ motion should be taken into account particularly for organs with significant movement such as the lungs. Imaging errors. During imaging, 3-D patient info rmation is obtained for treatment planning. Any problem in the acquisition, transfer, conversion, registration, or use of imaging data can lead to increased geometrical uncertainties.16, 21, 22 It is important to properly convert CT numbers to relative electron density for dose calc ulation. Artifact and distortion in the images PAGE 19 19 may change the relative electron density information. A mismatch between the physical position of the object and the imaging coordinate system is also possible. Dose calculation discrepancies. Improving the accuracy of trea tment planning is an active topic of research in radiotherapy.15, 23-29 Dose calculation algorithms in radiation TPSs can be broadly categorized into thr ee groups: correction-based (analy tical), model-based, and Monte Carlo (MC)-based approaches. All of these calcul ation algorithms have inherent errors because they are based on approximate solutions to a comple x physical situation. It is difficult to assess the impact of approximations in calculation algo rithms on the overall accuracy of a specific treatment plan. Therefore, it is necessary to perform treatment planning exercises and compare them with measurements for both routine and ex treme conditions. The calculation grid size of a radiation TPS also contributes to the difference between calculated dose distribution and actual dose delivery. Dempsey et al.23 have reported the influence of grid size on the accuracy of dose calculation. It was concluded that the grid size of approximately 2.5 mm was required to prevent dose errors larger than 2% caused by point sampling and discretized volume averaging. A number of studies have also been performed to provide tolerances for the accuracy of photon beam dose calculations in radiation TPSs.15, 30-34 Geometrical errors. Assumptions about a radiation TPS in modeling a treatment machine significantly impact dose calculation accuracy. Such model parameters of the machine include multileaf collimator (MLC) leakage, transmi ssion, tongue and groove effect, sagging of the treatment head and couch, scatte r radiation from the linac hea d, and beam profile and output characteristics.28, 35-44 Xing et al.44 showed that in an extreme case a 3-mm movement of the couch in the anterior-posterior direction can cau se a 38% decrease in the minimum target dose or a 41% increase in the maxi mum critical organ dose. PAGE 20 20 Dosimetric errors. In general, the mechanical integrity of the treatment machine is ensured during the commissioning process and routine QA.14-16, 21, 45 The accuracy of the beam geometry depends on the tolerance of each machine parameter and the magnitude of setup errors. Since the dosimetry is evaluated by dosimeters, which have their own er rors, dosimeter errors need to be included in the evaluation of overa ll dosimetric errors. Conve ntional dosimetric data using the ion chamber, thermoluminescence do simeter (TLD), and metal oxide semiconductor field-effect transistor (MOSFET) are suitabl e for one-dimensional (1-D) measurement. Film, electronic portal imaging device (EPID), diode array, and/or polymerizing gels are twodimensional (2-D) or 3-D dosimeters which are us ed for relative IMRT verifications. However, these dosimeters generally suffer from their in herent dosimetric inaccuracies when the dose verification is performed.28, 30, 33, 46-59 The ion chamber measurements, when volume averaging is not taken into account, lead to up to 8% of local differences between calculation and measurement and 10% of deviations in some hybrid phantom studies.55, 60 Even when volume averaging is taken into account, many of the m easurements still show a few outliers which can not be explained.13 Kapulsky et al.58 reported that the average per centage of pixels with dose differences greater than % wa s 1.7 1.0% when utilizing a phantom-film dosimetry system for 37 prostate carcinoma patients. Higgins et al. found that about 90% of in vivo diode measurements agreed to within % of the planned doses (45/ 51 fields) and 63% (32/51 fields) achieved % agreement using rout ine diode dosimetry for IMRT QA.59 Patient-related uncertainties. Patient-related uncertainties in radiation therapy primarily consist of external patient setup errors and internal organ motions. The most common approach to deal with these uncertainties has been to a dd safety margins to the clinical target volume (CTV) based on geometric uncertain ties and the variations in pos ition and shape of the CTV to PAGE 21 21 define the PTV.16, 26, 61-66 Studies of this nature focused on how to calculate the safety margins using known systematic and random setup errors and internal organ motions. The concepts of gross tumor volume (GTV), CTV, and PTV are well established and widely adopted in radiation therapy, although how to exactly defi ne the safety margin is contr oversial. In recent years, we owe a deepened understanding of patient set up and motion to advanced patient imaging modalities such as cone-beam CT, tomotherapy CT, and four-dimensional (4-D) CT imaging. Using cone-beam CT imaging, Guckenberger et al. 67 reported that, in head and neck regions, overall patient-related errors were 1.4 2.6 mm in translation and 1.1 1.4 (pitch), 0.7 1.5 (roll), and 1.1 1.7 (yaw) in rotation. In thoracic regions, relatively larg er uncertainties ranging from 2.4 7.1 mm to 7.6 7.1 mm were observed.67-69 Table 1-1 summarizes the patient-related uncertainties reported by many research groups in three different regions using various imaging devices. It is abundantly clear from thes e publications that there are a large number of error sources that can contribute to the dose uncertainty in radiation therapy in many different ways. Error sources in the treatment planning and delivery pr ocess must be clearly identified to understand the uncertainty in dose delivered to a patient with IMRT. It is also necessary to properly account for these uncertainties in IMRT to improve th e accuracy of the dose de livered to patients. Need for Dose Uncertainty Prediction in In ten sity-Modulated Radiation Therapy (IMRT) Most research on the uncertainties in radiation therapy stated above has narrowly focused on the management of individual e rror sources. While these studies play an important role in identifying the errors and securing the treatment, they are passive responses to existing errors. These studies were limited to how to detect a nd/or compensate for the local uncertainties by mainly expanding the clinical target with a ma rgin in treatment planning. Furthermore, the PAGE 22 22 tolerance levels for each uncertainty were defined in different units, and thus it is not intuitive to compare the amount of one uncertainty to others. For an IMRT case, various IMRT plans can be made using different beam parameters and optimization methods. Evaluation methods such as dose volume histogram (DVH) and isodose lines have been widely adopted to compare many candidate treatment plans. In these conventional methods spatial information on dose uncertainty and dose accumulation history are not explicitly considered. Hence, although one tr eatment plan seems better than others based on calculated dose distributions, in reality, it may be worse in local control probability due to a potentially high risk originating from a comp licated combination of small IMRT segments. Simply applying a margin to a clinical target in IMRT is not a sufficient condition to ensure that a clinical target gets the prescribed do se and the critical structure is spared. If the point-dependent dose uncertainty is provided, it will effectiv ely assist radiation therapy practitioners to select an optimal plan. Accurate prediction of un certainty during therapy planning provides the radiation oncology community with a tool that can assist in preparing reliable, safe, and pre-evaluated treatment pl ans. This tool identifies areas which have unacceptable dose uncertainty based on predefined clin ical criteria of accept ability. It is possible to track and manage potential risks in the treatment planni ng stage as well as predict a priori dosimetric errors and account for them during pl an evaluation as shown in Figure 1-1. Managing the known errors in the IMRT process does requ ire a paradigm shift. In other words, the a priori uncertainty prediction provides an opportunity for the radiation therapy community to employ alternate strategies to mitigate +dose uncertainties. Study Aims Our aim was to improve the quality of external beam radiotherapy through an a priori prediction of dose uncertainty in treatment planning. Our study focused on (but was not limited PAGE 23 23 to) a currently used MLC-based step-and-shoot IM RT technique in which the dose uncertainty is of more clinical significance than ot her conventional treatment techniques. Specific aim 1 : Explore the uncertainty sources in radiation treatment planning systems (Chapter 2). Specific aim 2 : Introduce a novel dose uncertainty model and its verification through simulations and experi ments (Chapters 3-4). Specific aim 3 : Develop the applications of the uncertainty model for IMRT plan verification (Chapter 5). Specific aim 4 : Establish the clinical efficacy of uncertainty-based IMRT plan evaluation (Chapter 6). PAGE 24 24 Table 1-1. Magnitude of pa tient-induced uncertainties. Setup translation (mm) Setup rotation () Study Number of patients Image registration modality DirectionAverage System aticRandom Pitch Roll Yaw Head and neck region Hunt et al .70 6 (Head and neck) Portal films AP LAT SI 0.3 -2.1 0.6 N/A 1.7 1.8 0.8 -0.15 (1.3) 0.1 (0.9) 0.2 (1.0) Hong et al .71 10 (Head and neck) Optical alignment (Infrared markerbased) AP LAT SI 2.1 0.8 0.4 N/A 5.1 4.4 3.4 0.5 (2.3) 1.4 (3.2) 0.5 (1.6) Guckenberger et al .67 8 (Head and neck) kV Cone Beam-CT AP LAT SI 0.7 0.8 0.9 N/A 1.2 1.4 1.9 1.1 (1.4) 0.7 (1.5) 1.1 (1.7) C2 AP LAT SI -0.5 -0.7 0.9 2.3 2.6 1.6 1.7 1.5 1.8 C6 AP LAT SI -0.3 -1.0 -1.1 2.5 3.2 2.0 2.0 2.3 2.2 Zhang et al .72 14 (Head and neck) CT-LINAC system (Varian EXaCT) PPM AP LAT SI 0.4 -1.2 1.9 2.4 1.5 4.2 1.7 2.9 1.1 0.96 (1.99) -0.62 (1.44) -0.17 (0.97) Thoracic region Borst et al .69 58 (Lung) kV Cone Beam-CT AP LAT SI -0.1 0.7 -2.3 2.0 3.1 4.0 2.0 2.5 3.4 N/A N/A N/A Guckenberger et al .67 6 (Thoracic tumors) kV Cone Beam-CT AP LAT SI 1.7 1.8 2.0 N/A 3.2 2.9 4.3 0.9 (2.1) 1.0 (2.1) 0.9 (2.2) Weiss et al .68 14 (Lung) 4D CT AP LAT SI 3.0 6.6 2.4 N/A 2.6 6.4 1.8 N/A N/A N/A Kim et al .73 Olivier et al .74 9 8 kV Cone Beam-CT Spine AP LAT SI Lung AP LAT SI 0.5 0.7 0.9 0.7 0.5 0.8 N/A 0.4 0.4 0.5 0.7 0.6 0.8 N/A N/A N/A Pelvic region Guckenberger et al 67 10 (Prostate) kV Cone Beam-CT AP LAT SI 1.6 0.7 1.1 N/A 3.3 2.6 2.3 0.6 (1.2) 0.6 (1.0) 0.4 (0.7) Hunt et al .75 9 (prostate; gynecological) EPID images AP LAT SI -0.1 0.0 0.1 N/A 0.5 0.6 0.5 -0.17 (2.03) 0.47 (1.46) -0.30 (1.07) Haslam et al .76 46 (Gynecological) EPID images AP LAT SI 2.6 2.4 1.9 N/A 3.7 2.8 2.6 2.1 (4.4) N/A 1.3 (2.4) Meijer et al .77 10 (Bladder) Portal images AP LAT SI N/A 2.7 3.0 2.5 1.8 2.2 1.5 N/A N/A N/A A systematic error is the SD of the mean setup errors A random error is the SD of the setup error over all treatment fractions. The values in parenthses are SDs of the rotational setup errors. Abbreviations: AP=anterior-posterior, SI=superior-inferior, LAT= medio-lateral, RMS=average root-mean-square, C2=C2 vertebra, C6= C6 vertebra, PPM=the palatin e process of the maxilla, and N/A=Not applicable. PAGE 25 25 Figure 1-1. New paradigm in radiotherapy using the dose uncertainty model. While an error is detected after delivery and feedback is made in the conventional a pproach, an error is a priori predicted and mitigated durin g planning in this new method. P P l l a a n n n n i i n n g g D D e e l l i i v v e e r r y y feedback E E r r r r o o r r p p r r e e d d i i c c t t i i o o n n C auses o f error C auses o f error C onven ti ona l paradigm E E r r r r o o r r d d e e t t e e c c t t i i o o n n U U n n c c e e r r t t a a i i n n t t y y m m o o d d e e l l ( ( R R i i s s k k a a s s s s e e s s s s m m e e n n t t ) ) P ropose d paradigm PAGE 26 26 CHAPTER 2 DISCRETIZED GRID SIZE EFFECT AND UNCE RT AINTIES OF DOSE CALCULATION IN RADIATION TREATMENT PLANNING Introduction It is comm only understood that there are certain uncertainties involved with radiation TPSs. Unlike conventional therapy, IMRT uses many subf ields to modulate the intensity of the field. This difference adds high conformality to the ta rget with high dose gradient to OAR. With the development of IMRT, the consequence of discretized dose calculati on and inaccurate dose calculation is expected to be more severe due to the complexity of the pl an. Prior to establishing an uncertainty predicti on model, uncertainties of TPS in IMRT (discretization effect of calculation grid size and accuracy of dose cal culation) are intensively investigated. Discretization of dose distribu tion introduces an unavoidable error in the planning system due to interpolation between cal culation points. During the early development era of radiation TPS, many investigators studied the dosimetric consequence of the discretization of the computed dose distribution.78-81 These investigators initially looked at how these discrete calculation points affected the beam profiles, especially in the high gradient region ( i.e. penumbra region), using a combination of analyti cal models of the beam profile and measured beam profiles. They experimented with the c oncept of random grid samples and uniform grid distributions. They also looked at methods to compute dose distribution more accurately without compromising calculation time. The general consen sus among investigators at the time was that more calculation points would produce more accurate dose distribution at the cost of calculation time. They concluded that it is important for the users to determine the optimized number of calculation points at a reasonable calculation time without signifi cantly compromising accuracy. Recently, Dempsey et al .23 presented a theoretical and empirical analysis of the e rrors to predict and validate that a calculation grid size of <2.5 mm spacing would prevent a dose distribution PAGE 27 27 error of 1 percent. Bortfeld et al .82 also presented a general Fourier analysis of the discrete MLC size which would be applied to the design of an IMRT MLC system by considering resultant dose distributions. There remains dosimetric uncertainty in IMRT (especially, in the surface and build-up region). The TG-53 report has provided guidelines for accuracy of the 3-D radiotherapy TPSs and these are expected to be achie ved by all IMRT planning systems.21 In dose comparison between calculation and measurem ent, however, IMRT TPSs have difficulty in meeting the 2 to 4% tolerance limit for the percent dose-difference in the high-dose gradient region and 1 to 5 mm distance-to-agreement (DTA) in the low-dos e gradient region suggested by van Dyk et al.15 Many investigators have shown that linear accele rators have significant electron contamination which originates from gantry.83-87 Previously, there have been se veral investigations regarding dosimetric uncertainty in the surface and build-up region.88-93 In this chapter, the error due to grid spaci ng was empirically investigated for a commercial TPS by comparing the dose distri butions obtained with varying cal culation grid sizes. Calculated dose distributions were compared with the measured dose distributions using a radiochromic film (RCF). Several clinical cases were also invest igated with varying calculation grid sizes. In addition, it was determined how accurately two co mmercially available TPSs calculate dose in IMRT by comparing them with RCF measurements. Materials and Methods Experimental Treatment Setup and Targets Two sem i-cylindrical solid water slabs with 7 cm thick back scattering solid water were used to simulate head and neck treatments (Figure 2-1). The slab s had a base length of 20 cm, a height (measured as the distance from the base to the top surface of the slab) of 11.7 cm and a thickness of 6 cm. The film used in this experime nt was a GafChromic film (Nuclear Associates, PAGE 28 28 Division of Victoreen, Inc.) mode l HS (lot no. K0223HS). The film was inserted in the middle of the two slabs and the edge of the film was carefu lly cut with a razor blade to conform to the surface edge of the slabs. The width of the f ilm was 13.2 cm and the height was 11.7 cm. To fill the air gap between the film and the two slabs, two small pieces of used film were cut to fit the surface contour of the slabs and in serted (Figure 2-1(B)). Plastic clamps (Figure 2-1(C)) were used to further reduce this gap. The BrainLab ExacTrac system is routinely used to set up head and neck cancer patients. An infrared (IR) camera system alone has the ab ility to accurately set up a patient on the couch in the order of sub-millimeters.94-96 For this study, eight IR marker s (Figure 2-1(A)) were placed on the solid water slabs and the back scattering solid water at the time of the CT scan and used to position the solid water slabs on the linear acce lerator. Once the solid water phantom was positioned properly on the CT, it was scanned at 3 mm slice thickness. For planning, two target cases were consider ed. The first target was shallowly located about 0.5 cm from the top surface of the phantom (Figure 2-2). The second was located deeply about 6 cm from the top surface of the phantom. Both targets had the same width, length and thickness of about 4, 13 and 6 cm, re spectively. Three critical structur es (the spinal cord and two parotid glands) were included. Fi ve-field step and shoot IMRT head and neck plans (gantry angles of 20 90 165 240 and 310 for the shallow target case and 0 70 145 220 and 290 for the deep target case following the International Electrotechnical Commission (IEC) gantry angle convention) with a prescription of 54 Gy total with 180 cGy per fraction were calculated using both Corvus (North Am erican Scientific, Inc.) and Pinnacle3 (Philips Medical Systems) TPSs. For the shallow target case, the nu mber of segments ranged from 7 to 21 and the PAGE 29 29 collimator size ranged from 6 7 to 14 7 cm2. The number of segments ranged from 10 to 16 and the collimator size ranged from 8 7 to 13 6 cm2 for the deep target case. Discretization Effect of Calculation Grid on Dose Calculation Four different dose calculati on grid sizes of the Pinnacle3 TPS only were considered for this study (1.5, 2, 3, and 4 mm). The Pinnacle3 TPS used a two-step ( i.e. fluence optimization and leaf sequence optimization) inverse planning process and pe ncil beam calculation algorithm during IMRT optimization; however, a super position convolution dose calculation method was used for final dose distribution calculation. To inve stigate the effect of sh ifting the grid origin, three additional cases were calc ulated: (1) 1 mm grid origin sh ift for a 2 mm grid size, (2) 1.5 mm grid origin shift for a 3 mm grid size and (3) 2 mm grid origin shift for a 4 mm grid size in all three coordinates. Then, the dose distributions were computed for varying grid sizes and a planar dose distribution was extracted at a 1 mm pixel size via linear interpolation. A Varian 2100C linear accelerator (6 MV) was used to deliver the planned beams. For dose delivery, the amount of monitor units for fi ve fractions was used to increase the overall dose delivered to the film to a level that would be at the middle of the linear region of the sensitometric curve. For data analysis, however, the measured dose was scaled to 30 fractions ( i.e. 5400 cGy prescribed dose). To rectify the non-uniformity of the RCF, a double exposure technique described by Zhu et al .97 and Dempsey et al .98 was applied. A Molecular Dynamics HeNe scanning-laser (633 nm wavelength) film digitizer was used to digitize the film.99, 100 The measurement film was digitally scanned at a 100 m/pixel and re-binned to a 1 mm/pixel grid spacing to match the same grid spacing as the planar dose distri butions from the TPS. Due to th e inherent noise generated by the light scattering artifacts of the scanning-laser film scanner,97, 99, 100 a low-pass Wiener noise filter algorithm was applied to the raw optical density (OD) file from the scanner. Afterwards, a PAGE 30 30 discrete-fast-Fourier-tra nsform deconvolution of transmitted images (converted from OD) with a measured transmission line-spread function was carried out to remove the light scattering artifacts. A detailed process of noi se filtration can be found elsewhere.99 The calibration films were exposed to radiation at the time of the e xperiment to minimize any variations that could arise due to the difference in room temperature and humidity. They were also digitized at the same time as the films. Subsequent to their digitization, the films were registered to the calculated planar dose distribution manua lly by matching up with known geometry. To investigate the effect of the dose gradie nt, the dose difference was analyzed according to three relative dose gradient ranges. A relative dose gradient range was determined in the 1.5 mm grid size calculation using the following equation: y y D x x D D D D 11 (2-1) where D is the dose and x and y represent the directional vectors. The relative gradient ranges considered for this study were 0 to 5% mm-1, 5 to 10% mm-1 and 10 to 15% mm-1. Three head and neck clinical cases were also considered. In all cases, dose distributi ons were calculated in 1.5 mm, 2 mm, 3 mm and 4 mm grid sizes. Once the dose distributions were computed, a single planar dose distribution at an axia l plane was generated for each grid size at 1 mm pixel size. The origin of the calculation grid wa s kept consistent for all grid sizes so that the planar dose distributions could be placed in the same gr id space. The dose difference histogram and the cumulative dose difference histogram were evaluate d. The dose difference histogram is a plot of the number of dose points according to dose differen ce. If both dose distributions to be compared are exactly the same, a delta function at zero dose is expected. To calculate a cumulative dose difference histogram, the relative number of dose points is accumulated according to the absolute dose difference. For example, if a cumulative dose difference histog ram shows x=100 cGy and PAGE 31 31 y=0.9, it indicates that 90% of dose points are w ithin a cGy dose difference. In this study, dose bin sizes of 15 cGy, 2.5 cGy, and 1% were used for the dose difference histogram, cumulative dose difference histogram and relative dose difference histogram, respectively. Accuracy of Dose Calculation in Surface and Build-Up Regions Once the optim al IMRT beam leaf sequence for the shallow and deep targets was generated by the Corvus TPS, the leaf sequence was transferred to the Pinnacle3 TPS. Thus, dose distributions for both planning sy stems were calculated using the same optimized beam leaf sequences. In Corvus, the dose distribution was ca lculated using 1 mm resolution in the axial plane. For longitudinal directi on, a 3 mm resolution (the same as the CT slice thickness) was used by default. In Pinnacle3, the dose distribu tion was computed using 2 mm resolution in all directions. Once computed, the planar dose distri bution was extracted in 1 mm pixel size via interpolation in Pinnacle3 system. The Varian linear accelerat or was used to deliver the planned beams. The film dosimetry and measurement were performed with the same method as presented in the previous section. The dose calculations from both TPSs were compared with the film measurements to investigate the accuracy of dose calculation in surface and build-up regions. Results and Discussion Discretization Effect of Calculation Grid on Dose Calculation Dose difference between calculation and measurement The sensitom etric curve of the RCF is given in Figure 2-3. A third-order polynomial curve was obtained and used for the OD to the dose conversion. All the films were delivered at around the 1000 cGy region, where the error bars were re latively small. The results of the dose difference between calculation a nd film measurement for the shallow target case are shown in Figure 2-4. To obtain a dose difference between th e TPS and the measurement, each individual pixel value from the dose matrix of the TPS was subtracted from the corresponding individual PAGE 32 32 pixel value from the measurement film. The regi stration of the TPS and measurement was made mechanically using known geometry. Figure 24(A) shows the dose difference histogram for varying calculation grid sizes ( i.e. 1.5, 2, 3 and 4 mm) in detail. A grid size of 1.5 mm was established as the reference and all other grid size s were considered as the grid size of interest. Figure 2-4(B) shows the relative dose difference histogram for varying gr id sizes. The relative dose difference was obtained by taking a ratio between the dose difference and its corresponding reference pixel value. All three dose difference histograms (Figure 2-4(A)) peak at around 0 cGy and fall off at around cGy (3.7% of the 5400 cGy prescription dose) The relative dose difference histogram (Figure 2-4(B )) also shows a similar trend to the dose difference histogram (which peaks at around 0% and falls off at around %). Figure 2-4(C) shows the cumulative dose difference histogram. The values of the cumu lative dose difference hi stogram were read at 95, 90 and 85% of the region of interest and are summarized in Table 2-1. These values span from 66.0 cGy (1.2% of the 5400 cGy prescrib ed dose) to 301.8 cGy (5.6% of the 5400 cGy prescribed dose). Table 2-1 indicates that th e dose difference between 2 mm grid size and 1.5 mm grid size in 95% of the region of interest is equal to or less than 126 cGy (2.3% of prescribed dose of 5400 cGy) for the shallow target case. The results for the deep target case were very similar to those of the shallow target. Effect of grid origin shift A dose variation was investigated for the sam e calculation grid size but with a grid origin shift. The origin was shifted in the x-, y-, and z-co ordinates by half of its grid size for 2, 3, and 4 mm grid cases ( i.e. 1, 1.5 and 2 mm origin shift for 2, 3 a nd 4 mm grid sizes). A dose difference histogram was generated by taking the differen ce between the original calculation and the calculation with the grid origin shifted. The re sults are shown in Figure 2-5 ((A) for the dose difference histogram, (B) for the relative dose difference histogram and (C) for the cumulative PAGE 33 33 dose difference histogram). It is not surprising th at the dose difference histogram for the smaller grid size ( i.e. 2 mm) had a higher frequency of around 0 cGy with narrower distribution. On the other hand, the larger grid sizes ( i.e. 3 and 4 mm) tended to have a lower frequency at around 0 cGy with slightly broader dist ribution. The relative dose diffe rence histogram also shows a similar trend. This tendency is an obvious indica tion that the dose variati on becomes larger as the grid size increases. The cumulative dose differences are summarized in Table 2-2 and span from 50 cGy (0.9% of the 5400 cGy prescribed dose) to 202.9 cGy (3.8% of the 5400 cGy prescribed dose). Similar results were obtai ned for the deep target case. According to Tables 2-1 and 2-2, no significant difference of the overall grid size effect was observed between the shallow target and deep target. Even though th e shallow target is located close to the anterior su rface, the overall dose distribution is a composite result of multiple beams coming from many directions. Th erefore, the effect of the anterior beam is not likely to be dominated, resulting in no significan t difference from the deep target. Dose difference in different dose gradient ranges Figure 2-6 shows dose difference histogram s fo r three relative dose gr adient ranges. For the low relative dose gradient range (0 to 5% mm-1), all three peaks have high frequencies with narrow spread (Figure 2-6(A)). But, with incr easing relative dose grad ient ranges (5%/mm to 10%/mm and 10%/mm to 15%/mm), the frequencies ap pear to be lower and have broader spread (Figures 2-6(B) and (C)). This effect is indicativ e of the fact that the vast majority of relative dose distribution has a relatively low gradient with good dose agre ement. At a higher gradient, however, the dose agreement gets worse. It is al so important to note that even though the dose agreement is worse at a high dose gradient, the smaller grid size still produces a significantly better dose agreement than the larger grid size. Fo r this reason, it is imperative to have a small grid size for a high gradient. To better quant ify, the relative dose difference histogram was PAGE 34 34 assumed to be a Gaussian distribution and th e full width half maximum (FWHM) value was computed. The Gaussian distribut ion was also included in Figure 2-6 and its mean, standard deviation and FWHM values are summarized in Ta ble 2-3 ((A) for the shallow target and (B) for the deep target). FWHM values were plotted acc ording to relative dose gr adient range. Figure 27 shows that with an increase in the relative dose gradient range, the FWHM also increases. Comparison with measurement Dose difference m aps for the shallow target case were obtained and appear in Figure 2-8. Figure 2-8 shows dose difference maps for (A) 1.5 mm, (B) 2 mm, (C) 3 mm and (D) 4 mm grid size calculations while taking the reference as th e measurement. It also shows dose difference maps for (E) 2 mm, (F) 3 mm and (G) 4 mm grid size calculations while taking the reference as the 1.5 mm grid size calculation. The color bar shown on the right side of each dose difference map is the dose difference in cGy from 1000 cGy (blue) to +1000 cGy (red). From Figure 2-8, it is obvious that calculation inaccuracy increases with grid size at su rface where very high dose gradient is expected. At dept h, most of the dose difference streaks can be observed to be increasing in thickness with increasing calculation grid size. However, two blue streaks on the left side of Figures 2-8(A) to (D) appear to ge t thicker until the 3 mm grid size but diminish in the 4 mm grid size. Interestingly, similar effects can be observed in Figures 2-8(E), (F), and (G), where the blue streak on the left side gets darker in the 3 mm gr id size but becomes lighter in the 4 mm grid size. This phenomenon can be illustrate d with a simple 1-D dos e profile, as shown in Figure 2-9. The x-axis is an arbitrary length in mm and the y-axis is an arbitrary dose in cGy. The circular-cross points represent the calculation points. The grid origin is located at x = 0 and the rest of the calculation points are located at their respective grid size ( e.g. 1.5 mm grid size is located at length 1.5 mm). The conne cting lines from the grid origin to various calculation points are the interpolation lines. For il lustration purposes, the dose compar ison point is located at x = 1 PAGE 35 35 mm (indicates as valley). This comparison point is compared with interpol ated dose from four other calculation grid points ( i.e. 1.5, 2, 3 and 4 mm grid size). It is easy to see that the interpolated dose from the 1.5 mm grid size is the closest to th e dose comparison point. With increase in the grid size, the interpolated dose gets worse until a 3 mm grid size. But at the 4 mm grid size, the interpolated dose is be tter than the 2 and 3 mm grid sizes. Dose difference histograms were also generated using the measurement from RCF as the reference to see the overall effect. The results for the shallow target case are shown in Figure 210 ((A) for the dose difference histogram, (B) fo r the relative dose difference histogram and (C) for the cumulative dose difference histogram). When comparing the dose difference histograms, which each represent the effect on the overall area, no significant difference was observed among the varying grid sizes. While the effect of grid size can be observed in the dose difference map ( i.e., locally increasing the size of the dose di fference at the surface and area of dose difference streaks), it is not clea rly seen in the dose difference histogram because of the number of points that the area of high dose difference oc cupy compared to the whole region of interest, which is too small to affect the histogram. Table 2-4 summarizes the cumulative dose difference result for the 95, 90 and 85% regions of interest. From the Table, it can be seen that the biggest difference between all four grid sizes percent region of interest is 1.60%. Clinical cases The results of the first clinical case are s hown in Figure 2-11. The grid size of 1.5 mm was used as the reference. Do se distribution is shown in Figur e 2-11(A) and dose difference distributions between the referen ce and other grid sizes are show n in Figures 2-11(B), (C) and (D) for 2, 3 and 4 mm grid sizes, respectively. It is apparent that as the gr id size increases, the streak in the middle of the plane increases. This streak indicates regi ons of high dose and high PAGE 36 36 dose discrepancy. On closer inspection, the dose difference for all grid sizes are as high as 1000 cGy (14% of the prescribed 7200 cGy dose) near the surface area while the inner-most region shows a dose difference of less than 200 cG y (3%). Figure 2-12 shows a dose difference histogram ((A) is the dose difference histogram and (B) is the cumulative dose difference histogram). The histogram is taken within th e whole area of the slice shown in Figure 2-11 excluding the air. In Figure 212(A), the peak becomes broader and shallower as the grid size increases. For a 4 mm grid size, the peak seems to taper off at around 200 cGy, which is consistent with the streaks in Figure 2-11(D). It can be observed that the histogram seems to be broadening towards the negative dos e difference. Similar results were observed for cases 2 and 3. In an ideal case of an infinite number of calcu lation points, all dose values of peaks and valleys can be obtained. However, dose calculations with a finite number of calculation grid points inevitably lose information about some of the peak points, thus resulting in underestimations of peak doses. The opposite effect can be observed fo r dose valleys, that is, overestimations of valley doses. If the sharpnesses ( i.e. gradient) of both peak and valle y are similar, the degree of overand underestimation would be the same. Howeve r, if they are in different gradients, the overall effect can be dominated by the shar per one. In our clin ical cases, overall underestimations of dose distributions were obser ved. Hence, it is considered that peaks are generally sharper than valleys in a dose gradie nt. The results of all three clinical cases are summarized in Table 2-5. Even though this st udy looks at dose difference due to various calculation grid sizes, there ar e other compounding factors that contribute to absolute dose differences between the calculated and measur ed IMRT dose distributions. One of these contributions can be from the imperfection of RCF dosimetry. Depending on the accuracy of the modeling of TPS, IMRT sequencing can also cause some extent of inaccuracy. There are other PAGE 37 37 factors which add to uncertainty, such as the e ffect of electron contamination on the surface and the build-up area, which is further investigated in the following section. Although it is almost impossible to get rid of the whole uncertainty, it is important to understand the sources of uncertainty and their order of magnitude. Accuracy of Dose Calculation in Surface and Build-Up Regions Figure 2-13 shows the dose distribution for the s hallow target case from (A) Pinnacle3, (B) Corvus, and (C) the measurement. The color bar next to the dose distribution ranges from 0 to 6000 cGy. The dose differences between calculati on and measurement are shown in Figure 213(D) (Pinnacle3) and (E) (Corvus) with th e color bar ranging from 2000 to +2000 cGy. Although the scanned measurement matrix was convert ed to 1 mm grid spacing to match that of the calculation, the origin was not matched. Theref ore, a maximum of 0.5 mm inherent mismatch could be possible in both x a nd y directions. Figure 2-13(F) is the dose difference between Corvus and Pinnacle3 ( i.e. subtraction of Pinnacle3 from Corvus). Dose difference histograms between the TPS and the measurement are shown in Figure 2-14(A). The x axis indicates the dose difference in cGy and the y axis indicates the distribution. The histogram is a representation of the dose difference distribution of the entire fi lm area except air. In an ideal case, the dose difference histogram would show th e form of a delta function at x =0. In Figure 2-14(A), Pinnacle3 appears to have a slightly broader cu rve than Corvus. Figure 2-14(B) shows the cumulative dose difference histogram where the y axis indicates the normalized distribution in the region of interest. The region of interest fo r the dose difference histogram includes the area of the phantom which corresponds with the area of RCF. This includes th e target, spinal cord, and both parotid glands. In Pinnacle3, dose differences are within approximately 420 cGy (7.8% of the total prescribed dose of 5400 cGy) and 300 cGy (5.6% of th e total prescribed dose of 5400 cGy) in 95% and 90% of the region of intere st, respectively. Here, the dose difference was PAGE 38 38 evaluated according to percent area, especially for 95% and 90 % that were arbitrary chosen, instead of having one point value such as the maximum and the mean dose difference. On the other hand, Corvus system shows about 390 cGy ( 7.2% of the total prescr ibed dose of 5400 cGy) and 240 cGy (4.4% of the total prescribed dose of 5400 cGy). This is summarized in Table 2-6. Figure 2-14(C) is the dose difference histogram between the two TPSs ( i.e. Corvus Pinnacle3). As can be seen in Figure 2-14(C), both systems agree within approximately cGy (3.7% of the total prescribed dose of 5400 cG y) in most areas. The results for the deep target case are also very similar to those of the sh allow target case (see Table 2-6). Although the overall dose distri bution is very similar between the measurement and calculation, a significant dose uncertainty can be seen on the surface. One of the biggest uncertainties of the surface and build-up dose is du e to the electron contamination from the linear accelerator head. But on top of this, there are other compounding factors that add more uncertainty to this matter. One of those factor s can be the imperfect im age registration of the dose distribution between the TPS and the measur ement. The second factor is the nonuniformity of the radiochromic film itself. This is even mo re so in the area where the film was cut. When there is a physical insult to the film ( i.e. the film was cut along the su rface edge of the slab), the film automatically starts to de velop and produces additional nonuni formity within the area of the insult. This effect was minimized with careful cu tting within 0.6 mm in this study. Any impacted pixel on the edge showed signi ficantly higher intensity and was eliminated from histogram calculation. The third factor can be attributed to the surface cont ouring. For Corvus, the external contour was made using auto-contour. The contou r was intentionally made slightly larger by appropriately setting the window and level to ma ke certain that all th e surfaces were included. The additional volume can be taken care of by heterogeneity correction because the density of PAGE 39 39 the additional volume is the same as air. For Pinnacle3, automatic surface detection was used with a threshold value of 0.6 g/cm3. It was checked that clear outlines of the surface were produced on the CT image. Therefore, the th reshold value could produc e the proper external contour. Thus, the error associated with cont ouring the external surface can be considered minimal. The fourth factor is the finite grid size for the dose calc ulation. This effect can be more significant for Pinnacle3 system where it computes the dose di stribution using a 2 mm grid size (by default, Corvus system computes the dose di stribution using a 1 mm grid size in the axial plane. Along the longitudinal dire ction, the grid size is the same as the CT slice thickness, 3 mm in this case). Once computed, the dose distributio n is extracted from the TPS in a 1 mm grid size by interpolation. Meanwhile, the measurem ent film is digitally scanned at 100 m/pixel and rebinned to a 1 mm/pixel grid space to match the sa me grid space as the TPS. This effect can be seen on the high dose gradient area (notice the streaks in Figures 2-13(D) and 4(E)). Figures 2-15(A) and (B) illustrate the depth dose profile on the center-line for Corvus and Pinnacle3 compared to measurement for the shallow target case. Figures 2-15(A) and (B) also show the dose difference with the green solid line. The x axis indicates th e depth from the surface of the slab in centimeters and the y axis indicates the dose (left side) and dose difference (right side) in cGy. It is easily seen that all de pth dose profiles are very similar to each other. However, there were some noticeable discrepanc ies for both TPSs at shallow depth, especially from the surface to a few millimeters. This can be easily seen in Figures 2-15(A) and (B) where the dose differences are plotted along with the depth dose profile. The largest dose difference can be seen for the first 1 cm of depth as indicate d by the dose difference curve. These discrepancies were quantified by using the DTA distribution and the dose difference distribution from the surface to a depth of 2.0 cm.16, 32, 101 The DTA and the dose difference are shown in Figure 2- PAGE 40 40 15(C) for Pinnacle3 and Figure 2-15(D) for Corvus. The x axis is the depth in centimeters and the y axis indicates both the dose diffe rence in % (left side) and DTA in mm (right side). The typical tolerance level was drawn at 3 mm and at 3% for the DTA and the dose-difference, respectively.16, 30, 33, 102 From Figure 2-15(C) and (D), it is clearly shown that the DTA and the dose difference are well within the tolerance criteria for the most part. There were, however, severe discrepancies from the surface down to 0.2 cm. From the quantitati ve analysis of the depth dose distribution, the first 0.2 cm depth dose calculation and the measurement for both TPSs are not reliable for surface and superficial dose evaluations. These types of discrepancies were also seen for the deep target case. Conclusions The purpose of this chapter was to evaluate dose distribution variabil ity w ith respect to varying calculation grid size and to determ ine how two most commonly used commercial radiation TPSs (Pinnacle3 and Corvus) handle the surface and build-up dose. In the calculation grid size study, the varyi ng calculation grid size considered for this investigation ranged from 1.5 mm to 4 mm. Taking the 1.5 mm grid size as the re ference, the dose difference for the shallow target ranged from 126.0 cGy (2.3% of the 5400 cGy prescribed dose) to 301.8 cGy (5.6% of the 5400 cGy prescribed dose) in 95% of the region of interest. For the deep target, the dose difference ranged from 110.0 cGy (2.0% of th e 5400 cGy prescribed dose) to 249.0 cGy (4.6% of the 5400 cGy prescribed dose) in 95% of the region of interest. When observing the origin shift, the dose difference for the shallow target ranged from 100 cGy (1.9% of the 5400 cGy prescribed dose) to 202.9 cGy (3.76% of the 5400 cG y prescribed dose) in 95% of the region of interest. For the deep target, th e dose difference for origin sh ift ranged from 128.7 cGy (2.4% of the 5400 cGy prescribed dose) to 202.0 cGy (3.7% of the 5400 cGy prescribed dose). It was found that the FWHM of the Gaussian fit of rela tive dose difference increased as the calculation PAGE 41 41 grid size increased for all of the relative dos e gradient rangeswith the effect being more significant in the higher re lative dose gradients. While the effect of grid size can be observed in the dose difference map, it is unclear in the dose difference histogram because the number of points that the area of high dose difference occupies compared to the whole region of interest is too small to affect the histogram. While 3 mm and 4 mm grid sizes are considered acceptable for most IMRT plans, it is apparent that a 2 mm grid size is require d, at least in the region of the high dose gradient, to accurately predict the dose distribution. In the study of accuracy of dose calculati on in surface and buildup regions, it was determined that the overall dose distributions were very similar to the measurement when comparing both TPSs. The dose difference for th e shallow target case ranged from 240 cGy (4.4% of the 5400 cGy prescribed dose) to 300 cG y (5.6% of the 5400 cGy prescribed dose) in 90% of the region of interest. For the deep target case, th e dose difference ranged from 260 (4.8% of the 5400 cGy prescribed dose) to 350 cG y (6.5% of the 5400 cGy prescribed dose) in 90% of the region of interest. However, it was determined that there were significant discrepancies from the surface to about 0.2 cm in depth for both shallow and deep target cases. This discrepancy was ascertained by the usage of DTA and the dose difference distribution for both TPSs for shallow and deep target cases. For the surface dose, it was concluded that both TPSs overestimated the surface dose for both shal low and deep target cases. The amount of overestimation ranges from 400 to 1000 cGy (~7.4% to 18.5% of the 5400 cG y prescribed dose). In conclusion, this investigation quantitatively showed that both TPSs acceptably predicted the dose except from the surface down to a very shallow depth ( i.e. 0.2 cm). Relatively large amounts of dose differences in a shallow depth may or may not be significant depending on a PAGE 42 42 specific clinical situa tion. It is strongly recommended th at users analyze and understand how their TPS estimate the surface dose. PAGE 43 43 Table 2-1. Cumulative dose differe nces for the 95, 90 and 85% region s of interest are shown for the shallow and deep target cases. 95% region 90% region 85% region Grid size Shallow target Deep target Shallow target Deep target Shallow target Deep target 2 mm 126.0 cGy (2.3%) 110.0 cGy (2.0%) 86.0 cGy (1.6%) 85.2 cGy (1.6%) 66.0 cGy (1.2%) 65.1 cGy (1.2%) 3 mm 248.2 cGy (4.6%) 185.0 cGy (3.4%) 118.0 cGy (2.2%) 147.2 cGy (2.7%) 138.0 cGy (2.6%) 117.0 cGy (2.2%) 4 mm 301.8 cGy (5.6%) 249.0 cGy (4.6%) 181.8 cGy (3.4%) 189.2 cGy (3.5%) 141.8 cGy (2.6%) 165.0 cGy (3.1%) The values in parentheses are the per ce nt of the prescribed 5400 cGy dose. Table 2-2. Dose differences for the 95, 90, and 85% regions of intere st for origin shift are shown for the shallow and deep target cases. 95% region 90% region 85% region Grid size Shallow target Deep target Shallow target Deep target Shallow target Deep target 2 mm 100.0 cGy (1.9%) 128.7 cGy (2.4%) 64.2 cGy (1.2%) 88.7 cGy (1.6%) ~50.0 cGy (0.9%) 68.7 cGy (1.3%) 3 mm 148.9 cGy (2.8%) 182.8 cGy (3.4%) 108.9 cGy (2.0%) 122.8 cGy (2.3%) ~85.0 cGy (1.6%) 92.0 cGy (1.7%) 4 mm 202.9 cGy (3.8%) 202.0 cGy (3.7%) 132.9 cGy (2.5%) 142.0 cGy (2.6%) ~100.0 cGy (1.9%) 122.0 cGy (2.3%) The values in parentheses are the per ce nt of the prescribed 5400 cGy dose. Table 2-3. Mean, standard deviation ( ) and full width half maximum (FWHM) are tabulated for the three relative dose gradient ranges fo r the shallow target case and deep target case. 0%/mm-5%/mm 5%/mm-10%/mm 10%/mm-15%/mm Mean (cGy) (cGy) FWHM (cGy) Mean (cGy) (cGy) FWHM (cGy) Mean (cGy) (cGy) FWHM (cGy) (A) Shallow 2 mm 3 mm 4 mm -0.02 -0.45 -0.16 0.97 1.8 2.42 2.27 4.23 5.69 0.35 -0.75 0.68 2.61 4.40 4.64 6.14 10.35 10.90 -1.91 -3.51 -0.85 2.99 5.34 7.16 7.02 12.55 16.83 (B) Deep 2 mm 3 mm 4 mm -0.33 -0.99 -1.33 0.74 1.10 1.74 1.74 2.60 4.08 0.02 -2.15 -0.71 2.17 2.52 4.56 5.11 5.92 10.72 0.82 -4.24 1.00 3.74 4.02 9.08 8.78 9.44 21.34 PAGE 44 44 Table 2-4. Dose differences for the 95, 90 and 85% regions of interest are displayed for the shallow target case when compared with the measurement. Grid size 95% region 90% region 85% region 1.5 mm 2 mm 3 mm 4 mm 681.2 cGy (12.6%) 706.7 cGy (13.1%) 766.7 cGy (14.2%) 767.7 cGy (14.2%) 381.2 cGy (7.1%) 386.8 cGy (7.2%) 466.8 cGy (8.6%) 426.8 cGy (7.9%) 261.2 cGy (4.8%) 266.8 cGy (4.9%) 286.8 cGy (5.3%) 306.8 cGy (5.7%) The values in parentheses are the per ce nt of the prescribed 5400 cGy dose. Table 2-5. Dose differences fo r the 95 and 90% region of intere st are displayed for all three clinical cases. Case 1 Case 2 Case 3 95% regions (cGy) 90% regions (cGy) 95% regions (cGy) 90% regions (cGy) 95% regions (cGy) 90% regions (cGy) 2 mm 50 (0.7%) 28 (0.4%) 70 (1.0%) 40 (0.6%) 38 (0.9%) 18 (0.3%) 3 mm 236 (3.3%) 62 (0.9%) 222 (3.1%) 66 (0.9%) 78 (1.6%) 44 (0.6%) 4 mm 324 (4.5%) 95 (1.3%) 296 (4.1%) 106 (1.5%) 360 (5.0%) 46 (0.6%) The values in parentheses are the per ce nt of the prescribed 7200 cGy dose. Table 2-6. Dose difference for Pinnacle3 and Corvus for shallow and de ep target cases is listed for the 90 and 95% regions of interest. Shallow target Deep target 95% region 90% region 95% region 90% region Pinnacle3 420 cGy (7.8%) 300 cGy (5.6%) 480 cGy (8.9%) 350cGy (6.5%) Corvus 390 cGy (7.2%) 240 cGy (4.4%) 330 cGy (6.1%) 260 cGy (4.8%) The values in parentheses are the per ce nt of the prescribed 5400 cGy dose. PAGE 45 45 Figure 2-1. Solid phantom set-up. A) Two semicy lindrical solid water slabs and backscattering solid water (7 cm thick). Two semicyli ndrical solid water slabs were secured properly, and it was positioned on top of a 7-cm-thick ba ckscattering material. For accurate positioning, IR fiducial markers were utilized. B) Radiochromic film (model HS) was cut along the surface edge of the phantom and positioned in the middle of the phantom. To reduce the air gap, an expos ed film was positioned on the side. C) Radiochromic film was sandwiched between the two semicylindrical solid water slabs and plastic clamps were placed to further reduce the air gap. PAGE 46 46 Figure 2-2. Shallow and deep target cases with three critical structures (spinal cord and two parotids). Figure 2-3. Sensitometric curve for the radiochr omic film. The dose ranges from 0 cGy to 1700 cGy. A third-ordered polynomial wa s used to best fit the plot. PAGE 47 47 Figure 2-4. Histograms for the sha llow target case with varying calculation grid size. A) Dose difference histogram (grid size of interest reference), B) relative dose difference histogram ((grid size of interest refe rence)/reference), and C) cumulative dose difference histogram. PAGE 48 48 Figure 2-5. Histograms for the sha llow target case with calculati on grid origin shift. A) Dose difference histogram, B) relative dose di fference histogram, and C) cumulative dose difference histogram. In the legend, the 2 mm sh ift refers to the 2 mm calculation grid size with a 1 mm origin shift. The 3 mm shift refers to the 3 mm calculation grid size with a 1.5 mm origin shift. The 4 mm shift refers to the 4 mm calculation grid size with a 2 mm origin shift. PAGE 49 49 Figure 2-6. Relative dose differen ce histograms for three relative dose gradient ranges for the shallow target case. A) Relative dose diffe rence histogram for 0 to 5% mm-1 relative dose gradient range, B) relati ve dose difference histogram for 5 to 10% mm-1 relative dose gradient range, and C) relative dose difference histogram for 10 to 15% mm-1 relative dose gradient range. The dotted lin e is the Gaussian distribution fit for each of the grid sizes. PAGE 50 50 Figure 2-7. Plot of full width half maximum (FWHM) in rela tive dose difference histogram verses relative dose gradient range. A) The shallow target and B) the deep target. PAGE 51 51 Figure 2-8. Dose difference maps for the shallow target case. Dose difference map between the TPS and the measurement: A) 1.5 mm grid size, B) 2 mm grid size, C) 3 mm grid size, and D) 4 mm grid size. Dose differen ce map between two difference grid size calculations: E) 2 mm grid size, F) 3 mm gr id size, and G) 4 mm grid size while taking 1.5 mm grid size as the reference. (The color bar indica tes dose range from 1000 cGy to 1000 cGy). Figure 2-9. Simple one-dimensional (1-D) dose profile which illustrates that dose difference may not continuously increase w ith increasing grid size. Th e x-axis is the length in mm and the y-axis is the dose in cGy. The circular-cross points represent the calculation points. The connect ing lines represent the interpolation lines from grid origin to various calculation points. Note that 4 mm grid si ze has better agreement at the dose comparison point than 2 mm and 3 mm grid sizes. PAGE 52 52 Figure 2-10. Dose difference histograms between the treatment planning system (TPS) and the measurement for the shallow target case. A) Dose difference histogram, B) relative dose difference histogram, and C) cumulativ e dose difference histogram. For this study, the reference was radiochromic film. PAGE 53 53 Figure 2-11. Dose difference distribution for case 1. A) Dose distribution fo r 1.5 mm grid size is shown as a reference (dose range is from 0 cGy to 6000 cGy). B) Dose difference distribution for 2 mm grid size (dose range is from 1000 cGy to 1000 cGy). C) Dose difference distribution for 3 mm grid size. D) Dose difference di stribution for 4 mm grid size. PAGE 54 54 Figure 2-12. Dose histogram for case 1. A) Dose difference histogram. B) Cumulative dose difference histogram. PAGE 55 55 Figure 2-13. Shallow target case dose distribution and the dose difference. A) Philips Pinnacle3 radiation treatment planning dose distribution. B) North American Scientific Corvus radiation treatment planning dose distribution. C) The measurement dose distribution. D) Dose difference distribution for Pinnacle3 and measurement (measurementPinnacle3). E) The dose difference distribution for Corvus and the measurement (measurementCorvus). F) The dose difference distribution for both radiation treatmen t planning systems (CorvusPinnacle3). The color bar on the right side of each figure is in unit of cGy. PAGE 56 56 Figure 2-14. Dose differe nce among Corvus, Pinnacle3, and the measurement. A) The dose difference histogram for the treatment plan ning system and the measurement (entire area of film except air). B) The cumula tive dose difference histogram for the treatment planning system and the measurement. C) The dose difference histogram for Corvus treatment planning system and Pinnacle3 treatment planning system. PAGE 57 57 Figure 2-15. Calculation accuracy of both the trea tment planning systems. A) The shallow target case central axis depth dose profile and the dose difference for Corvus taking the radiochromic film as the reference. Corvus is the solid blue line and radiochromic film is the dotted blue line. The green solid line indicates the dose difference in cGy. B) The shallow target case central axis depth dose profile and the dose difference for Pinnacle3. Pinnacle is the solid blue line. The biggest discrepancy is located in the first 1 cm from the surface. C) The dose difference distribution and DTA (distance-toagreement) for Corvus system. D) The dose distribution and the DTA for Pinnacle3 system. The horizontal line for C) and D) is the dose difference and the DTA tolerance level ( i.e. 3% for the dose difference and 3 mm for DTA). PAGE 58 58 CHAPTER 3 CONCEPTUAL DOSE UNCERTAINTY MODEL AND ITS VERIFIC ATION USING ONEDIMENSIONAL (1-D) SIMULATION Introduction The advent of m ore complex technologies in radiotherapy such as 3-D conformal therapy and IMRT increases demand for a more accurate to ol to evaluate the dose difference between calculation and measurement. In general, IMRT pl ans consist of a number of small fields. Dose calculation is performed for hundreds of small fiel ds in IMRT rather th an a few large fields.33 Uncertainties and inaccuracies arise during the many different pha ses of the entire procedure. They can depend on typical mechanical featur es of the linear acceler ator, MLC, and/or calculation algorithms.48 In this chapter, a novel dose uncertainty mode l is introduced and its application for dose verification is described using 1-D simulation. In the model, the intrinsic dose uncertainty characteristics of the test points are considered. At any given point, the do se uncertainty depends on many dose levels and gradients from multiple sma ll beams rather than that of the overall dose profile. The dose level and gradient information of each small field were utilized in determining dose uncertainty of the overall field. Then, a tolerance level is se t as a function of space based on predicted uncertainty. Methods and Materials Uncertainty in Dose Calculation and Measurement There are discrepancies in dose distributions b etween the calculated and the measured dose because of a variety of uncertain ties involved. The method provided here uses a statistical model to estimate the dose uncertainty with the known calculated dose. The predicted dose distribution of the measured dose, )( rD in space r can be expressed by )( )()()( )( rZrDrDrZrDoverall cal overall cal, (3-1) PAGE 59 59 where ) ( rDcal is the calculated dose distribution, Z is a constant for confidence level (z-score for a normal distribution), ) ( roverall is an overall standard deviation, and is adjustable errors ( e.g., detectable systematic errors and backgr ound noise in film measurement).The error is not taken into account in the study in that it is assumed to be adjusted throughout the study. The predicted dose distributi on is assumed to be a Gaussian dist ribution with the standard deviation of ) ( roverall Supposing ) ( roverall is known and the confidence level constant Z is 1.96, 95% of the measured distributions fall within ) (96.1)( r rDoverall cal The dose uncertainty is divided in two pa rts: space-oriented and non-space-oriented. Space-oriented dose uncertainty (S OU) is the uncertainty caused by all spatial displacements such as a mechanical variation of the treatment machine, spatial variations of measurement, dose calculation grid size, and regi stration misalignment for dose co mparison. On the other hand, nonspace-oriented uncertainty (NOU) is mainly cause d by dosimetric uncertainties such as the dose calculation algorithm and dosimetry techniques. Even if these uncer tainties are correlated as a function of position, it is assumed that these two parts are independent be cause the contribution of space displacement to the non-spatial uncertain ty is significantly small. Therefore, dose difference between measurement and calculation is a linear combination of SOU and NOU. The overall dose standard deviation is a quadratic sum of SOU () ( rSOU ) and NOU () ( rNOU ): 2 2)()()( r r rNOU SOU overall (3-2) Assuming that SOU is proportional to the gradient of dose, )( rSOU is given: i i ical SOUrrGr )()(,, (3-3) PAGE 60 60 where Gcal,i( r ) is the calculation dose gradient ()(,rDical ) for a direction i and ri is the spatial displacement. For the x, y, and z components, the spatial dose deviation becomes: zrGyrGxrGrzcal ycal xcal SOU )( )( )()(, (3-4) where ) (,rGxcal, ) (,rGycal, and ) (,rGzcal are the dose gradients in x, y, and z components, respectively. Spatial displacement ri is a value with which 68.26% of measurements are within the ) ( rDcal)( rSOU bound if there is no nonspatial dose error. If x for a 1-D dose distribution is 1 mm, the confidence level constant Z for the spatial error is 3, and there is no non-spatial error, then 99.74% of dose measurements fall within ) (3)( r rDSOU cal In radiation measurement, an expected standard deviation of the dose level is proportional to D. Hence, the relative standard deviation of doserel (= /D) is inversely proportional to the dose deviation Supposing the known relative deviation is orel at the reference point or with dose level ) (ocalrD the relative dose deviation rel at a dose point r is: )( )( )( )( )(, ,rD rD r r rcal ocal orel cal ocal orel rel (3-5) Providing there is a 1% dose devi ation at the 100% dose level (e.g., 1 cGy if ) (ocalrD =100 cGy), it demonstrates that there is a 10% do se deviation at the 1% dose level (i.e., 0.1 cGy at )( rDcal=1 cGy). For 200% dose level, the relative dos e deviation is 0.71% (equivalent to 1.41 cGy). Thus, the non-spatial dose deviation ) ( rNOU (probable dose error at a point r ) between dose calculation and measurement is defined: )()( )()()(,ocal calorel cal rel NOUrDrD rDrr (3-6) PAGE 61 61 The relative dose deviation rel,o is theoretically a value with which 68.26% of measurements are contained within the ) ( rDcal) ( rNOU bound when there is no spatial uncertainty. In case the reference relative dose deviation rel,o is 1%, the confidence level Z for the non-spatial dose error is 3, and there is no sp atial displacement then 99.74% of measurements fall within ) (3)( r rDNOU cal If the overall dose is a combination of multiple fields, the overall dose standard deviation is a quadratic sum of contributions from each field. 2 ,)( )(N j joverall overallr r (3-7) where )(,rjoverall is the overall dose standard deviation of j-th element field and N is the total number of element fields. Test Dose Distributions A 1-D normalized dose distribut ion as shown in Figure 3-1 is used to examine the capability of prediction of measured dose. The data fit of penumbra regions uses a fitting equation proposed by Low et al.101 employing an error function (the integral of the normalized Gaussian distribution). The )(roverall is calculated using SOU a nd NOU as given in Equation 32, 3-4, and 3-6. For all calculations of dose deviation, rel,o=1% at 100% dose level and x =1 mm are used. A Gaussian random number gene rator in MATLAB, a high-level technical computing language, is used for the determina tion of spatial and non-sp atial variations to simulate possible measurements. The smallest sel ected increments of sp atial displacement and dose change for the simulated measurements are 0.1 mm and 0.1%, respectively. The simulated measurements are compared with the dose bound ) ( )( rZrDoverall cal with two different PAGE 62 62 confidence levels ( Z =2 and 3 for 95.44% and 99.75% confiden ce levels, respectively) to verify robustness of the model. Even in a conventional radiation treatment, multiple beams are combined to make a large field (e.g., a mantle field or a head & neck fiel d including a supra-clav icular field). For simulation of such case, a 1-D dose distribution consisting of two identical beams is made to investigate the dose prediction of the model in the overlapped regi on as shown in Figure 3-2. The total dose standard deviation is computed by dose standard deviations of each beam using Equation 3-7. Each beam is m oved by a randomly selected spatia l displacement and a small dose selected from the Gaussian di stribution is added to or s ubtracted from the moved dose distribution. The simulations are made 20 times and the modified total dose distributions are compared with the dose bound by changing the confidence level Z To investigate the influence of different ra diation treatment plans (or delivery sequences) on dose uncertainty, two different fields that have the same dose distribution but different combination of beam segments are made as show n in Figure 3-3. Beam se t 1 consists of three beam segments that have different field size but same beam fluence (Figure 3-3(A)). On the other hand, beam set 2 is composed of three beam segments that have the same field length but a different beam fluence (Figure 3-3(B)). The dose deviation for each beam segment is calculated to acquire the total dose uncertainty for beam set 1 and 2. The dose measurements are obtained by moving each beam segment by random spatia l displacement and by applying random dose variation, assuming the Gaussian distributions. In the conventional dose comparison methods, the most commonly used dose difference and DTA tolerances for IMRT are 3% and 3 mm, respectively.15, 16, 48, 103, 104 To make the percentage measurement error correspond to these values, th e confidence level for the PAGE 63 63 uncertainty bound can be set to 3 (i.e., Z =3 in Equation (3-1)) with wh ich statistically 99.75% of measurements are contained within the dose bound of the model. In fact, the tolera nce level of a treatment delivery system is dependent on the determination of Z. Since one system has a different tolerance level to ot her systems, based on the clinic al experience and mechanical reliability a proper Z value of a system as the comparison acceptance should be searched. A dose uncertainty-length histogram (DULH) is defined as a plot of the cumulative length of the 1-D field according to the dose uncertainty bound (for Z =1). Similar to a cumulative dosevolume histogram (DVH), from the 1-D dose un certainty distribution all dose points whose uncertainty are above a certain uncertainty leve l are included to calcula te a total length. The levels (x-axis) and the corre sponding lengths (y-axis) are plotted to make the DULH. If there are two different treatment plannings for the same target, a treatment plan ning which has shorter length at the same uncertainty level is prefer able. The DULH of an ideal treatment delivery system is a delta function at the dose uncertainty =0. Similarly, for 2-D and 3-D dose distributions, dose uncertainty -area, and dose unc ertainty-volume histograms (DUAH and DUVH) can be obtained, respectively. By calculating the uncertainty histogram, it is possible to choose a less risky plan among multiple candidate plans during treatment planning. Results Figure 3-4 shows the dose bound of the si ngle test field calculated with Z =2 (thick dotted lines) and Z=3 (thick dashed lines) and 20 simulated m easurements (thin solid lines) achieved by randomly selected dose changes and spatial movements. As expected, all of 20 simulated measurements fall within a 99.75% confidence bound (i.e., Z =3). For 95.44% confidence bound (i.e., Z =2), 1 out of 20 is slightly out of th e bound, which looks reasonable. Note that Z =3 bound PAGE 64 64 in the figure is close to the conventional accep tance level of a 3% dose difference and a 3 mm spatial shift for dose comparison. Figure 3-5 shows the result of the case of two contiguous fields. As can be seen, the uncertainty model predicts significantly high uncertainties (more than 20% in the 99.75% confidence level) around the region where two beams meet. The simulated measurements also show similar trend and most of them are within the 95.44% c onfidence level uncertainty bound. As mentioned earlier, this kind of case is not unusual in most clinics. An example is the typical one point set-up of the head and neck field in which two lateral fields and one anterior field match in one plane. In general, the calculated dose from the treatment planning system for this case is pretty smooth even at the region of fiel d matching because the treatment planning system assumes a perfect matching. In reality, however, measurements hardly show such a perfect dose distribution. Thus, if the conven tional 3% and 3 mm dose variation tolerance is applied to this case, the system fails, which is intuitively not a fa ir conclusion. Contrary to this, the uncertainty model can logically predict such a behavior. Figure 3-6 shows the results of the comparison of two different treatment plans that have the same overall dose distribution. Although both pl ans provide the same dose distribution, there is a significant difference in dose bound between th em. For beam set 1, the highest value of dose uncertainty is in the region 65 mm < x < 80 mm, where three beams are superimposed (Figure 36(A)) to make high dose level. The dose uncertain ty is the highest in the region 10 mm < x < 40 mm in beam set 2, where two combined beam se gments have not only a high dose gradient, but also a high dose level as shown in Figure 3-6(B). In beam set 1, dose uncertainty bound does not vary significantly among three di fferent intensity regions. Howeve r, beam set 2 shows a severe variation of dose uncertainty bound according to space. The dose un certainty is obviously higher PAGE 65 65 where both dose level and dose gradient are higher. However, it is ev ident that the dose gradient is a more dominant factor to the total dose uncer tainty than the dosimetric difference in the high gradient region. Simulated measur ements also show similar trends as prediction in both cases. Figure 3-7 shows the uncertainty length histograms of beam se ts 1 and 2. In addition, the DULH for a plan that can provide the same dos e distribution by a single radiation exposure (e.g., intensity-modulation with compensators) is also computed and plotted. In an ideal case, DULH will show a line at 0% dose level. Obviously, a treatment plan that has smaller area under the curve and smaller maximum dose deviation is bette r in terms of uncertainty. The beam set 1 is superior to the beam set 2 in that the beam set 1 has a smaller dose deviation level at the same length of the field. Interestingl y, the beam set 1 shows less un certainty than even the single exposure plan. It is because the high dose level and high gradient region on the right side that causes high risk in a single beam is divided into three low risk beams in beam set 1. It is controversial to assess the superiority of a tr eatment plan or system by the histogram only because there are many other factors to be consider ed, however it can be used for one of useful tools to evaluate a plan or system. Discussion The study of this chapter serves as a conceptual description of the method of examining the dose uncertainty. The model has a variety of a pplications including a dos e comparison tool and an assessment of the treatment delivery system The existing dose comparison tools based on dose difference and DTA put more focus on finding the similar dose point corresponding to the point of interest. A disadvantage of these tools is the necessity of searching DTA, which makes computation time consuming. The model presente d in this study places more emphasis on dose points themselves in order to convert the information on dosimetric errors and spatial displacements to the possible dose un certainty at the points. Venselaar et al.16 proposes 10 to PAGE 66 66 15% tolerance for relative dose de viation in the build-up or penum bra region of profile and 30 to 50% for low gradient, low dose regions based on geometric complexity. These values mean a shift of approximately 1 mm corresponding to a dose variation of 5%. Instead of using one single value for comparison, a more precise dose devia tion derived from the dos e level of all of dose points using the dose gradient is proposed. The calculated dose uncer tainty is combined with the calculated dose distributions during radiation treatment pla nning as the acceptable dose bound (Figures 3-4~6). Accordingly, it makes possible a much faster and more meaningful comparison between calculation and measurement because the tolerance level is made without measurement if it is integrated in TPSs. The assumption of independence between NOU and SOU was made. In fact, NOU is affected by the spatial displacement because th e uncertainty is a func tion of the position. Therefore, a precise NOU is )(])()([)(, ocal cal calorel NOUrDrrDrD r in the Equation (3-6). However, according to the 1-D simulation the contribution of a tolerable spatial offset 3 mm to the non-spatial uncertainty was less than 0.2% to a maximum dose level. The correlation is postulated to be small enough to be discounted. It is possible to consider three other diffe rent schemes of the dose comparison tolerance T ( r ) which can be derived from the model: Scheme 1: ) )(,)(max()(NOU SOUrZrZrT (3-8a) Scheme 2: 2 2)()()(NOU SOUr rZrT (3-8b) Scheme 3: ) )()(()(NOU SOUrrZrT (3-8c) The first scheme is analogous to the composite distribution analysis in which the point needs to satisfy either one of dose difference or DTA criteria.32 While the composite analysis employs a single value for the dose differen ce in the percent of a reference value (e.g., 3% of the PAGE 67 67 dose at dmax) and DTA (e.g., 3 mm) over the entire distributions, the tolerance of the first scheme varies point by point because ) ( rSOU and ) ( rNOU are point r dependent. The second scheme is similar to the and tests (especially, test).31, 101 The model takes into account the dose uncertainty of each beam segment, whereas the and tests utilize the total cumulated dose distributions. Therefore, both the and tests are not able to take in to account the effect of field misalignment as shown in Figure 3-5 and 3-6. Th e dose difference and DTA criteria for the tests depend on the geometric complexity of the radiation treatment. Thus, it is possible that a system has the different tolerances of the dose difference and DTA for different test configurations. Contrary to the dose difference and DTA criteria, in the dose uncertainty model the spatial displacement (r ) and the relative dose difference (orel ) are solely predetermined for the individual system by the users. As a result, they are independent of the geometric complexity of beam delivery. Instead, the geometric complexity of the field is inherently included in the calculation of uncertainty. Improvement of dos imetric and spatial accuracy of the system minimizes r and orel The third scheme is the least conservative method. The linear combination of the dosimetric and gradient dos e deviations establishes the possible maximum dose difference between the calcul ation and the measured dose. Spatial movement of dose dist ribution used in this study is discrete. To figure out the dependence of the dose gradient ) (rDcal on the size of the discrete element, three types of unit lengths (1 mm, 2 mm, and 3 mm) were used for the calculation of the dose gradient at a point. The dose gradient is also dependent on a direction of derivative. The curve of dose distributions turned out to be smooth enough not to make significant difference in the absolute dose gradient by the changing of spatial increment and the direction of derivative (less than 1%). In addition, the magnitude of dose gradient is dependent on the dose calculation grid resolution of a PAGE 68 68 treatment planning system. It is noted that th e dependence is significan t in the high gradient regions. As demonstrated in the previous chapter, a 2.5 mm dose grid was required for their TPS to approximate IMRT dose di stributions by point sampling a nd discretized volume averaging discretizaitons within 2% error. To minimi ze the uncertainty calculation error, the dose calculation grid size is required to be less than around this level. The spatial displacement r in the proposed uncertainty model can be used as a mathematical reference for the DTA acceptance criteria )( rd proposed by Bakai et al.31 as the subject of future re search provided that orel is known by accurate measurement. With orel known, histogram of the absolute value of D /(3 ) is obtained by changing r .The smallest r that makes almost every point get less than 1 of absolute D /(3 ) value in statistically meaningful number of trials, can be approximated as the spatia l displacement of the system. Hence this chapter provides a mathematical mode l that can determine the uncertainty of dose delivery by spatial displacement generated by the w hole links of a treatment delivery system. Conclusions In this chapter, a dose uncertainty model usi ng the dose level and gradient information of each field was reported and a concept of SOU and NOU was proposed. A dose bound based on the statistical prediction mode l provides a tool for dose comparison between calculation and measurement. The dose limit by a confidence level Z =3 in this comparison method presents a similar tolerance level of the existing dose comparison methods (i.e., 3% for the dose difference and 3 mm for the DTA). However, the comparis on method presented is different from other comparison tools because the tolerance determin ed by the uncertainty model is a function of space, whereas the previous methods apply one single criterion to the entire points for dose comparison. 1-D simulations using different b eam compositions to make a treatment field PAGE 69 69 showed the model could provide an appropriate dose bound for dos e comparison as a statistical prediction. The confidence limit fo r the dose bound depends on an individual therapy system that should be determined by a careful inspection of w hole treatment steps of the system and clinical experience. An uncertainty histog ram obtained with dose uncertainty distribution can be used as a tool to analyze radiotherapy plans and the degree of achieved improvement of a treatment plan or system. PAGE 70 70 Figure 3-1. Fit of a one-dimensiona l calculated dose distribution. Figure 3-2. Planned dose distri bution consists of two small b eam segments. Beam 1 and 2 are identical and a calculated dose distributi on is a summation of the two beams. PAGE 71 71 Figure 3-3. Two test dose distri butions have three beam segments to make the same dose profile. A) Beam set 1 consists of three beams that have the same field size but the different beam fluence. B) Beam set 2 is composed of three beams that have the different field size but the same fluence. PAGE 72 72 ` Figure 3-4. Dose bounds of one-beam fi eld (Figure 3-1). Th e dose bounds with Z =2 (95.44% confidence level) and Z =3 (99.74% confidence level) and 20 simulated measurements made by random spatial movement and dose ch ange based on Gau ssian distributions are shown. Figure 3-5. Dose bounds of a two-beam field (Figure 3-2). The dose bounds with Z=2 (95.44% confidence level) and Z=3 (99.74% confidence level) and 20 simulated measurements are shown. The beams 1 and 2 are m odified and overlapped by random spatial displacement and dose change based on Gaussian distributions. PAGE 73 73 Figure 3-6. Dose bounds of two three-beam fields (Figure 3-3). The dose bounds with Z =2 (95.44% confidence level) and Z =3 (99.74% confidence level) and 20 simulated measurements are shown. A) The bounds of beam set 1 with the 20 simulated measurements, and B) the bounds of beam se t 2 with the 20 simulated measurements are displayed. PAGE 74 74 Figure 3-7. Dose Uncertainty-Length Histograms (with Z=1) of two test dose distributions (Figure 3-3). The uncertainty histogram of a system, which can make the same dose profile by a single exposure, is also plotted for comparison (One Beam in legend). For the same length, beam set 1 is superior to beam set 2 because the former has the smaller dose uncertainty than the latter. The one-beam method (e.g., compensator) has smaller dose uncertainty than beam set 2; however, it is inferior to beam set 1 in terms of dose uncertainty. PAGE 75 75 CHAPTER 4 GENERALIZED A PRIORI DOSE UNCERTAINTY MODEL OF IMRT DELIVERY Introduction The concept of predicting dose uncertainty considering dose accumulation history was introduced in the previous chap ter. The previously developed dose uncertainty model adopted a novel approach to predict the tota l dose uncertainty in IMRT by introducing the concepts of SOU and NOU. While the uncertainty prediction is practic ally acceptable, the previous model is based on two controversial assumptions: proportionality of SOU to dose gradient and negative correlation of NOU to a spatial displacement of a treatment system. In addition, the previous model oversimplifies the realistic situations with two simple i nput parameters. To solve these issues and apply the model for cl inical situations, the uncertainty model was thoroughly modified and improved. In the revised dose uncertainty mode l, it is assumed that the dose uncertainty is associated with error sources from two distinct radiation therapy steps: planning and delivery. A new concept of inherent uncertain ty (IU) is introduced to ac count for both the SOU and NOU of the planning system. Thus, only de livery-related uncertainty sources are explicitly dealt with in names of SOU and NOU. In addition, a convolu tion method is applied to obtain IU, SOU in seven degrees of freedom (DOFs), and NOU. IU is related to the imperfection of the dose calcul ation. It is mainly attributed to inaccurate modeling of scattered radiation, beam asymmetry, a finite si ze of the calculation grid, and penumbra (e.g., due to a volume averaging effect of a detector) in the radiation TPS,105 which was investigated in Chapter 2. SOU is caused by all spatial displacements such as a mechanical variation of the treatment machin e, inaccuracy of patient setup, and external/internal motion of the patient. Although the previous uncertainty model was able to provide good estimations, the gradient-based application was limited to cases within a small range of spatial displacement. PAGE 76 76 Prediction of dose uncertainty was reasonable within typical DTA values for IMRT dose verification (usually, 2 mm105, 3 mm21, 33, 102 or 4 mm15). However, many patient-related motions are reported to be larger than 5 mm.106-110 In order to make a generalized form which elucidates any possible clinical situations including patient-related moti ons, the convolution method was adopted. Since Leong111 first introduced the conv olution method to describe an effect of random positioning error on a calculated dose distribution, the method using the patients spatial displacements has been mainly used to determin e an expected dose distribution after fractionated treatments and a proper margin for PTV.27, 65, 111-119 The convolution-based method was also used to compute the SD of the mean expected dose distribution.113 The convolution method was extended to predict dose uncertainty considering both the translational and angular displacements caused by both patient and machine. In princi ple, NOU is caused by quantum statistics of any irradiator through the beam line such as the mon itor chamber, the detector system used during commissioning, and the patient. Assu ming that the effects of the detector system and the patient are relatively small and implicitly included in the IU, only the effect of the monitor chamber is explicitly considered. Thus, the relative SD of the NOU is assume d to be inversely proportional to the monitor unit (MU). The ability to accurately predict dose uncer tainty at the time of planning will allow clinicians to objectively evaluate each IMRT plan and discard plans that have potentially large uncertainties. The advance minimization of ove rall uncertainty during the treatment planning process will significantly improve the quality of IMRT. In this chapter, the uncertainty model proposed in the previous chapter is generalized for clinical IMRT cases and the robustness of the model is examined using test patterns. PAGE 77 77 Methods and Materials Generalized Dose Uncertainty Model Inherent dose uncertainty for planning The IU (; inherent error of dose calculation) accounts for dose uncertainty inherently existing in the radiation TPS. It originates because of a variety of reasons and can be explained by three distinct observations. First, a significant dose difference exists in high-dose gradient regions. This phenomenon is assumed to be mainly caused by the finite size of the calculation grid, the finite size of the detector system during treatment planning commissioning, and a po ssible mismatch of reference field sizes between actual measuremen ts and mathematical calculations (i.e., a field of 10 10 cm2 during commissioning may not be exactly 10 10 cm2 while it is in a TPS). The IU related to this phenomenon is defined as grid and it is approximated with i i icalrrD)(, where i is a directional component. Although it was not exactly the same, a concept similar to this was adopted in a gradient compen sation method for IMRT QA to compensate for geometrical uncertainties such as the effect of the calculation and measurement grids by multiplying the generalized gradient (Gi) of overall dose distribution with a distance parameter (dgc).120 For 2-D analysis, gridon a point r on a plane p perpendicular to beam axis, grid is expressed as: yrDxrDrIpycal pxcal pgrid )( )()(, ,, (4-1) where x and y are the spatial offset parameters fo r each direction, respectively. In lowgradient regions within a subfield, grid(r) is close to zero, implying insignificant uncertainty in an inner area of the field. However, grid(r) can be significant in high-gr adient regions, representing large uncertainties in penumbra regions. PAGE 78 78 Second, a fair amount of dose discrepancy can be observed near th e field edge and it decreases along with the distance fr om the edge. This may be due mainly to an imperfection of the dose calculation algorithm itself and partly a typical normalization method used in relative dosimetry (i.e., normalization at the center). The IU ba sed on this observation is defined as algo and it is approximated as a linear function that d ecreases according to the distance from the edge. To apply this, the field edges of the 2-D dose dist ribution of any given subfield are detected as a binary image with 1s for edges and 0s elsewhere. The binary image is converted into a distance map in which the pixel value is the distance between that pixel and the nearest nonzero pixel (i.e., the nearest field edge). The linear function algo( rp) of the plane p is given by: algo( rp) =[C1d( rp) + C2] Dmax( rp), (4-2) where C1 and C2 are constants, d( rp) is the distance dist ribution in mm, and Dmax( rp) is the maximum dose level of the field. In the region outside the field, dose un certainty can decrease only to a certain level (i.e., a level of uncertainty caused by ei ther the background or the noise of the detector system during commissioning). Thus, if (C1d( rp) + C2) < C3 (the minimum uncertainty level outside the field), algo( rp) is reset to C3Dmax( rp). A similar situation applies to the region inside the field and when algo( rp) is lower than a certain uncertainty level, algo( rp) of the plane p is expressed as: algo( rp) =C4 Dmax( rp), (4-3) where C4 is the minimum uncertainty level inside the field. Third, a greater dose difference is observed at the off-axis compared to the central axis. This is assumed to be mainly attributed to in accurate modeling of off-axis fluence (or spectrum) and a possible variati on of beam symmetry (i.e., while a field from most radiation TPSs is symmetric, an actual beam is not). The IU asso ciated with this observation is accounted for by PAGE 79 79 multiplying Ialgo with a linear function that increases acco rding to the distance from the central axis. And this linear function, defined as moa, is given by: moa( rp)=C5|rp-rpo| + 1, (4-4) where C5 is a constant and |rp-rpo| is a distance between the point of interest, rp and the point of central beam axis, rpo on the plane p. Now, assuming that Igrid and both Ialgo and moa are uncorrelated, the total IU, ( r), in 3-D space r becomes: ( r)=grid( r ) + algo( r ) moa( r). (4-5) Revision of space-oriented dose uncertainty (SOU) for delivery In the revised model, SOU is limited to the dose uncertainty caused by any spatial displacement during beam delivery such as a mech anical variation of th e treatment machine and patient motion. The error sources from patients are further categorized into two parts: external setup and internal organ motion.61, 66 When the model is applied to IMRT dose verification instead of patient treatment, spatial variations of measurement and registration misalignment for dose comparison should replace patient motion. Seven DOFs (three tran slations and four rotations) in radiation deli very are taken into account to compute the SOU (SOU) using the convolution method. The expected dose of a subfield is obtained by applying convolution (d enoted as *) to the calculated dose distribution and is given by ),(*)(*)()( rNrNrDrDtrans rot cal cal (4-6) where Dcal( r ) is dose calculation, Nrot( r) is a probability distributi on function (PDF; assumed to be Gaussian) of rotational DOFs: pitch (x: a rotation about the x-axis), roll (y: a rotation about the y-axis and a gantry rotation), yaw (z: a rotation about the z-axis and a table rotation), and PAGE 80 80 collimator angle (b), and Ntrans( r) is a PDF of translational DOFs, x y, and z. In this study, linac coordinate systems defined by IEC are adopted to describe the DOFs for SOU as shown in Figure 4-1.121 The vector r is expressed in the orthogonal coordinate system ( x y, z) for translation, but transformed to cylindrical coordinates for rotati onal convolution. The PDF of a DOF, NDOF( r), is given by: 2 )( exp 2 1 )(2 2 DOF DOF DOF DOFr rN (4-7) where DOF and DOF are an SD (i.e., random error) and a mean (i.e., systematic error) of the DOF respectively. The systematic error (denoted by in this study) is assessed by the mean value of all the displacements measured during the whole treatment and the total random error (denoted by ) is the dispersion around the systematic error.26, 122, 123 In reality, discrete convolutions are performed within range on a grid resolution of 1 mm with a bin size of 0.1 for a rotational PDF and a bin size of 1 mm fo r a translational PDF. C ontrary to approaches commonly used in other studies,27, 65, 111-119 it should be noted that the uncertainty model explicitly includes the systematic error of each DOF. Hence, it is not necessary to assume that the center of normal distribution of spatial displacements is located at zero. By definition, the SOU is given: 2 2 2)()(*)(*)()( rDrNrNrDrcal trans rot cal SOU (4-8) The convolution with rotations and translations is implemented consecutively. In case more than one rotational deviation is present, th e output matrix of the pr evious calculation is used as input for the next. The order is arbi trary for mutually uncorrelated distributions. However, in case both rotational a nd translational deviations are considered, the rotations must be performed first.61 Refer to Appendix A for a detailed de rivation and application of the SOU. PAGE 81 81 Revision of non-space-oriented dose uncertainty (NOU) for delivery In theory, NOU is defined as dose uncertain ty produced by quantum characteristics of photon interactions with material s existing along the beam line such as the monitor chamber, the patient (or phantom), and the detector used fo r commissioning. Among these, the effect of the patient and the detector is considered to be re latively small and implicitly included in IU. Thus, in this revised model, explicit consideration of NOU is limited to dose uncertainty related to the monitor chamber and NOU is simply assumed to be inversely proportional to the monitor unit (MU). Using the convolution method considering spatial displacements, NOU is converted to a generalized form (see Appendix A fo r detailed derivation of the NOU): )( )(,rD MU MU rcal cal o orel NOU, (4-9) where MUo is a known MU to obtain rel,o and MUcal is an MU for the calculated dose distribution Dcal(r). Generalized dose uncertainty model Assuming that an actual dose delivered Dactual( r ) is its expectation value SD, it can be expressed as: )()()()()()()( rZrIrDrDrZrIrDtotal cal actual total cal (4-10) where )( rI is the expectation value of ( r ) based on the spatial displacement distribution, Z is the z-score for the particular confidence level in a normal distribution, and total( r ) is the total SD of the calculated dose. Assuming the correlation betw een the SOU and the NOU is insignificant, the total SD is expressed with a general form: 2 2)()()( r r rNOU SOU total (4-11) PAGE 82 82 An output from the linear accelerator shows day-to-d ay variation that may not be negligible. This effect is also considered to be one of the deliver y errors if the dose uncertainty is predicted in the patient, and the total SD is thus given by: 2 2 2)( )()()( rD r r rcal output NOU SOU total (4-12) where output (in unit of %) is an SD for day-to-day out put variation of the treatment machine. In this study, the output variation is not considered because detectors are cali brated to the output of the reference field before measuring. It also mean s the systematic error of relative dose deviation at a known dose level is negligible (rel,o0). If an overall dose is a combination of multiple sub fields, the overall IU is linear summation of contributions from each sub field. Similarly, SD is quadratic summation of contributions from each sub field. Therefore, S s scal overallrIrI )()(, (4-13) and S s stotal overallr r2 ,)( )( (4-14) where s is each subfield, S is the total number of sub fields, and total,s is the total SD of the sub field s. ( r) can also be influenced by the spatial di splacement distribution. Thus, the SOU for ( r) exists as well, and the total SOU ()(,rtotalSOU ) is given by 2 2 ,)()( r rISOU DSOUcal When 2 ,)( rISOU is much smaller than 2 ,)( rcalDSOU as expected in most clinical cases, 2 ,)( rtotalSOU can be easily approximated with2 ,)( rcalDSOU (i.e., 2 2 ,)()( r rcalDSOU totalSOU ). PAGE 83 83 Quantification of Model Parameters Model parameters for inherent dose uncertainty (IU) In order to determine the distance offset parameter for grid, a 10 10 cm2 field of 6 MV photon beam from an Elekta SLi-20 acceler ator was delivered to a 30 30 15 cm3 solid water phantom. An EDR-2 film was placed at a depth of 10 cm with a s ource-to-axis distance (SAD) of 100 cm. The same measurement was repeated twi ce and the films were scanned with a VIDAR Dosimetry PRO x-ray film digitizer with a spatial resolution of 0.18 0.18 mm2/pixel and 16bit depth. Then, the images were resized to a resolution of 1 1 mm2/pixel. Dose distribution for the measurement setup was computed with the Pinnacle3 TPS using a 2 mm calculation grid size in all directions. The calculated dose distribution was interpolated with a pixel size of 1 1 mm2 using a bilinear interpolation method. The dosedifference distribution between the computation and the measurement was evaluated to obtain the distance offset parameter r. A sample set of nine measurements which consis ts of three different fi eld sizes (3 3, 5 5, and 10 10 cm2) and three different buildup depths (4 7, and 10 cm) were performed to determine the constants (C1, C2, C3, and C4 for algo and C5 for moa) assuming negligible spatial displacement in this simple geometry. A water equivalent solid water phantom was employed as buildup material. Because the MU of IMRT subfields generally ranges from 5 to 20, 10 MU was delivered for the measurements although no si gnificant MU dependency of parameters was expected. The dose-difference distribu tion between calculation by the Pinnacle3 TPS and measurements using a 2-D 445 diode array detector, Sun Nuclear MapCHECK, was investigated to determine the constants. A falloff of dose difference from the edges of the fields was observed in all directions to determine C1 and C2. The maximum dose difference in the periphery of the difference distri bution was used to determine C3 and C5. The dose difference PAGE 84 84 inside the field of 10 10 cm2 (a plateau region) was used to determine C4. The comparison was implemented such that at least 95% of dose di fference values for the sample set were bounded by the distribution computed with the previ ously determined distance parameter r. A scatter diagram between the inherent dose uncertainty a nd the dose difference was obtained to visually relate two quantitative variables: having dose uncertainty on a horizontal axis and the corresponding absolute dose diffe rence on a vertical axis. As a quantitative measure of the correlation, a correlation coefficient ( between IUs and absolute dose differences was calculated as n d d n d d n d d dDD II DDII1 2 1 2 1) ()( ) )((, (4-15) where d is each dose point, n is the total number of dose points, <> is the mean value of the overall IU distribution, D is the dose difference between th e calculation and the measurement, and <|D |> is the mean value of the absolute dose difference.124 To verify the applicability of the constant s, a verification set of measurements were performed with six different field sizes (2 2, 3 3, 4 4, 5 5, 10 10, and 15 15 cm2) and 3 different buildup depths (4, 7, and 10 cm). For each case, three measurements were made using 10 and 20 MUs (total of 108 measurements = 6 field sizes 3 depths 2 MUs 3 measurements). The dose difference was compar ed with the inherent dose uncertainty to investigate if the constants were pertinent to th e uncertainty prediction. The scatter diagram and the correlation coefficient were also analyzed. PAGE 85 85 Model parameters for SOU and NOU The model requires 16 input parameters for SOU and NOU: both mean deviation and SD of eight DOFs. The mean deviation and the SD of each DOF are used for the systematic error and the random error in Equation 47, respectively. For SOU, it is necessary to quantify errors of the treatment machine (gantry angle, collimator angle, and positions of both the collimator and the MLC), external patient setups, and internal organ motions. To classify and quantify the known sources of machine-related uncertainties 6-years of annual QA data of the Elekta accelerator since 2001 were examined, specifically looking at field sizes (collimator positions; i.e., x and y) measured using radiographic films and s ource-to-surface distan ces (SSD) of 85 cm, 100 cm, 120 cm, and 140 cm (i.e., z) measured with the mechanical distance indicator. For uncertainty sources of which quantified data wa s not available from the annual QA, the amounts of errors were quantified through repeated m easurements and peer-reviewed publications. The mechanical error of the collimator angle was measured by comparing a Kodak X-Omat V film image of a 100 MU delivery with 4 cm solid wate r build up at an SAD of 100 cm to that of 10 irradiations of 10 MU with repositioning the co llimator for each irradiation. This test was repeated four times to increase the reliability of the experiment. The quantification of MLC position accuracy was evaluated through a survey of peer-reviewed publications. Because measurements were performed at a gantry angle of 0 set with a level, the accuracy of the gantry angle was not considered in this phantom-based study. To measure phantom setup accuracy, the realtime infrared (IR) marker-based tracking system (BrainLAB ExacTrac) was employed with a calibration jig containing four IR markers as shown in Figure 4-2. First, a 7 cm solid wate r phantom was set up using the laser system. The calibration jig was attached to the solid water phantom and the marker positions were registered. Then, the phantom was intentionally displaced and reset. After the reset, IR marker positions PAGE 86 86 were recorded and the setup difference from th e initial setup was calculated. This test was repeated a total of 83 times for a period of two weeks and the data was analyzed to determine systematic and random setup erro rs of three translations along x-, y-, and z-axis and three rotations of pitch, roll, and yaw. Because a phantom study is independent of internal organ motions, they were not considered in this study. However, quantified errors for internal organ motions are available with increased attenti on on image-guided radiati on therapy (IGRT) as performed by many researchers,125-132 which are readily incorporated in the model as shown in Table A-I (see Appendix. A). For verification of the functional form of NOU, a farmer-type ionization chamber (CNMC PTW Type N30001) was used to examine th e proportionality of the relative SD (rel( r)) to a reciprocal of the square root of MU. With 10 cm water equivalent buildup at an SAD of 100 cm and a field size of 10 10 cm2, eight dose levels (5 cGy (7 MU), 10 cGy (13 MU), 20 cGy (26 MU), 50 cGy (65 MU), 100 cGy (130 MU), 150 cGy (195 MU), 200 cGy (260 MU), and 300 cGy (390 MU)) were delivered 15 times using the 6 MV photon beam. The normalized relative SD, rel of each MU level was calculated and compar ed with the normalized theoretical value of MU /1. Verification of Expected Dose Uncertainty Using Test Patterns Validity of the model for dose uncertainty prediction was tested with simple four test patterns as shown in Figure 43: (A) pyramid, (B) valley, (C ) wedge, and (D) checkerboard. These were similar to user-controlled intensity shapes used for IMRT dosimetric-commissioning tests.133 Dose distributions of the test patterns were computed with the Pinnacle3 TPS and delivered to a 15 cm solid water phantom using th e Elekta machine. EDR-2 films were placed at PAGE 87 87 an SAD of 100 cm and a depth of 10 cm for dos imetry. The films were calibrated with a rapid film-calibration method using automated MLC fields proposed by Childress et. al.134 The scatter diagram between the ov erall inherent dose uncertainty ( )( rIoverall) and the dose difference ( )()( rDrDcal t measuremen) of all measurement points was plotted. In addition, the uncertainty prediction was qualitativ ely verified with results of test using 2% and 2 mm as criteria. The failed points were overlapped with the dose uncertainty dist ribution to demonstrate a possible correlation between the uncertainty pred iction and the risk of the treatment plan. In principle, regions of high uncertain ty refer to those of high risk in IMRT delivery in the sense of conventional dose verification. In other words, failed dose points by conventional IMRT QA methods are expected to be found in the re gions of relatively high dose uncertainty. At the present time, none of the commercially available TPSs allows planners to calculate the dose uncertainty. Therefore, the clin ically validated TPS (Philips Pinnacle3) for dose calculations and an in-house developed process for dose uncertainty calculations were employed. The 3-D dose distribution of each subfield was e xported to an independent computing resource. Using this dose distribution, a 3-D dose uncertain ty map of the subfield was constructed in the MATLAB programming environment af ter interpolating the calculation with a spatial resolution of 1 1 1 mm3/voxel. Refer to Appendix B for a workflow and MATLAB source codes of the uncertainty calculation. Results Quantification of Model Parameters Distance offset parameter of Igrid for IU The distance offset parameter r for grid was obtained by comparing the computation with the high-resolution film measurem ent. Figure 4-4(A) shows the disagreement in dose profiles of PAGE 88 88 a calculation and a measurement of a 10 10 cm2 field in the x direction posterior to intentionally minimizing spatial displacement and registration errors. The shapes of the penumbra can be easily differentiated. The dos e difference profile between calculation and measurement was approximated with xxDcal )( as shown in Figure 4-4(B). In Figure 4-4(B), 0.8 mm of spatial offset turned out to be appropriate. However, considering the effect of the origin shift in the calculation grid as demonstrated in Chapter 2,105 the spatial displacements of x and y for the treatment system were determin ed to be 1 mm and 1 mm, respectively. Interestingly, it is the same as the size of the distance parameter (1 mm for all directions) used in the gradient compensation method to remove spatial inaccuracies due to volume-averaging effects in the detector and the discrepancies between finite dose calculation and measurement grids.120 The relatively large dose difference outside the field in the Figure 4-4(B) (0 mm x <~12 mm) was due mainly to overestimating the radiographic EDR2 film in the low-dose regions,51 which was not a concern for determining the distance offset parameter. Constants of Ialgo and moa for IU Using the distance offset parameter obtained in the previous s ection, the inherent uncertainty distribution I of the sample set was estimated and compared to the dose difference distribution to determ ine the constants for Ialgo and moa. The constants determined with the sample measurements were C1 = -0.03%/mm, C2 = 1.9%, C3 = 0.4%, C4 = 0.6%, and C5 = 0.015 /mm. Here, the percent is based on the central ax is dose. Figure 4-5 shows (A) the calculated dose distribution (% of cen tral axis dose), (B) the Igrid distribution (% of central axis dose), (C) the Ialgo distribution (% of central axis dose), (D) the moa distribution (number larger or equal to 1), and (E) total inherent uncertainty distribution I (% of central axis dose) of the field size of 5 5 cm2 at 10 cm depth. A profile following a horizontal central scan line of each distribution is PAGE 89 89 also shown below the correspondi ng distribution. For the sample set of 9 measurements, 97.3 1.9% of the measurement points were confined within the IU bound. The scatter diagram for the sample set visually validated the correlation betw een the IU and the dose difference as shown in Figure 4-6. The dashed line represents the IU bound, on which the dose difference is the same as the dose uncertainty. The average linear correlation coefficient of the sample set was 0.81 0.04, which indicated a strong linear correlation betw een the predicted IU and the dose difference. To verify the constants determined, the dose di fference distributions ca lculated with a total of 108 measurements of the verification set were compared with the IU distributions. The IU prediction well confined the maximum dose diffe rence for the 108 verification measurements. The average percentage that dose difference wa s confined within the IU bound was 98.7 1.7%, and the average correlation coefficient was 0.80 0.04. These were comparable to those of the sample measurements for determination of the IU constants. Input parameters for SOU The errors in field sizes of the treatment mach ine from the 6 years of annual QA data were 0.2 0.9 mm (x x; mean SD) and 0.1.8 mm (y y) for the xand y-axis, respectively. The SSD deviation was 0.3 1.0 mm (z z) for the z-axis. Using the radiographic film measurements for the collimator angle, no signi ficant error was detected. Other investigators reported that the total error of about 0.0 0.5 mm (MLC MLC; x direction) was found in the Elekta MLC position using electronic portal imaging.135, 136 Phantom setup errors of 83 measurements for 2 weeks using the IR markers were 0.0 0.5 mm (x x), -0.2 0.4 mm (y y), 0.3 0.4 mm (z z), 0.0 0.1 (x x ), -0.1 0.2 (y y ), and 0.1 0.2 (z z ). In summary, taking into account that the systematic error of machine was opposed to accounting for the patient setup, the total errors of the machine and setup for SOU inputs were PAGE 90 90 0.2 1.1 mm for x x, 0.3 0.9 mm for y y, 0.0 1.1 mm for z z, 0.0 0.1 for x x 0.1 0.2 for y y -0.1 0.2 for z z and 0.0 0.0 for b b Input parameters for NOU To evaluate the robustness of the functional form of the NOU, it was investigated whether the relative SD was inversely pr oportional to the square root of the MU level by using an ion chamber results shown in Figure 4-7. It shows th at the relative SD of the ionization chamber measurements overall agreed with the theoretical value of 1/ MU normalized to the 195 MU level. The relative SDs for the ionization chamber measurements were 0.32% (7 MU), 0.25% (13 MU), 0.18% (26 MU), 0.11% (65 MU), 0.08% (130 MU), 0.06% (195 MU), 0.05% (260 MU), and 0.05% (390 MU). Verification of Uncertainty Prediction The dose difference distributions ( )()( rDrDcal t measuremen) of the test patterns were obtained as shown in Figure 4-8. Due to overestimation of film measurement in low-dose regions, dose points whose dose was less than 10% of the maximum dose level were excluded from the analysis. Regions of large dose difference we re generally superimposed upon high-gradient areas. Calculated uncertainty distributions are sh own in Figure 4-9 in wh ich the columns indicate test patterns and the rows indicate uncertainty types (i.e., row I: the overall IU distributions ( )( rIoverall); row II: the overall statistical uncertainty distributions (1overall( r)); row III: overall uncertainty distributions of )( rIoverall+2overall( r); column A: pyramid; column B: valley; column C: wedge; and column D: checkerboard). The overal l SD distribution was similar in shape to the IU distribution, but the magnitude of the SD was considerably smaller due to minor spatial PAGE 91 91 displacement in the phantom study. Note that an individual scale has been applied to each uncertainty distribution to enhance visu alization of the uncertainty pattern. The uncertainty prediction model analytical ly highlighted the regions of large dose difference. The scatter diagrams between the ov erall IU and the dose difference as shown in Figure 4-10 ((A) pyramid, (B) valley, (C) wedge, a nd (D) checkerboard) i ndicated that the IU distributions reasonably predicte d the possible bound of dose diffe rence. All dose points above the IU dose bound (dashed line) were confin ed within the sta tistical dose bound of )( rIoverall+2overall( r) (confidence level 95.4%) in all test patterns. The test using 2% and 2 mm as criteria was performed and the pass rate was greater than 95% in all test patterns. Figure 411 shows the failed points of the test overlaid on the overall uncertainty distribution ( )( rIoverall+2overall( r )). The failed regions remarkably correlated to relatively high dose uncertainty. Discussion The feasibility of a generalized dose uncertain ty model for dose uncertainty prediction in radiotherapy was investigated. Accurate pred iction of dose uncertainty strongly relies on the proper quantification of model inputs. To obtain the distance offset parameter (r) of Igrid, the registration error between cal culation and film measurement was minimized by manually matching the centers of the beam profiles. Ialgo and moa were approximated with a linear relation to the distance map. In reality, the relation may obey other mathematical fittings such as an exponential or high-degree polynomia l equation; however, in pract ice, the linear fitting is convenient to apply and the predic tion error caused by using the lin ear fitting instead of a more complicated fitting is insignificant, as shown in Figure 4-6. PAGE 92 92 To accurately determine the constants for I, a dose measurement of high resolution such as film dosimetry is preferred. However, film dosimetry suffers from issues such as a high chance of registration error, ove r-response of low-energy photons (radiographic), non-uniformity (radiochromic), and digitizer-induced problems, which are undesirable for this purpose. The uncertainty sources for total were categorized into eight DOFs. In order to quantify them, extensive studies were performed using the accumulated annual QA data, mechanical measurements, dosimetric measurements (using th ree different detectors: ionization chamber, radiographic film, and diode), a nd a literature survey Although quantification of DOFs can be performed with any existing and newly developed me thods available at an individual institute, it is highly recommended that quantif ied model parameters should be verified using a set of test patterns prior to clini cal implementation. Furthermore, even though the quantified parameters may be adequate for one system, these values sh ould be carefully validated for other systems even in the same institute. The dose uncertainty model relies on severa l approximations of physical conditions in preparing its model parameters. First, the dose discrepancy for IU was approximated in 2-D space. In principle, the dose difference in the z-direction should also be included. However, its magnitude is relatively small and 2-D approxima tion is reasonably appropr iate. Second, relative NOU was assumed to be inversely proportional to MU. However, there was a distinguishable discrepancy between measurements and theoreti cal values in the NOU calculation as shown in Figure 4-7. This is considered due mainly to th e fact that the quantity detected in the monitor chamber system is not exactly proportional to the number of photons in teracted, because of several reasons such as photon beams heterogeneous spectrum and the systems electrical noise. Third, the convolution method pos tulates a normal distribution of PDF for each DOF, for which PAGE 93 93 a true distribution is not known. In other convol ution-based studies, the systematic error (the mean value of the PDF) for each DOF was set to zero assuming an ideal and static treatment condition.27, 65, 111-119 In the uncertainty prediction model, the systematic errors are intrinsically included in the convolution calculation as shown in Equation (4-7). Fourth, in this study all input parameters for IU were obtained based on homogeneous media. The uncertainty model may not accurately predict the dose uncertainty near th e interface between two media of significantly different density and the surface of the patient. The dose in these regions is not accurately calculated by most commonly used dose calculation methods and cu rrently its variation is too significant to be considered a perturbation. Therefore, it is a prerequisite to improve dose calculation accuracy. Another i ssue is that the convolution method underestimates the dose perturbation in these regions.114 The convolution errors can be improved using the separate convolutions for each region of similar density and the Corrected Convolution method proposed by Craig et al.115 The dose uncertainty model accurately predicted the regions of high risk as shown in Figure 4-11. During treatment planning, the dose uncertainty maps provide additional information on the acceptability of a treatment pl an. An ideal treatment plan has little dose uncertainty. When critical organs are adjacent to th e target, a plan with le ss dose uncertainty at the interface of the target and critical organs is preferable. The uncertainty maps place great emphasis on the regions where extra care must be taken, thereby reducing the chance of making risky plans and assisting physicists to determine the more appr opriate points of interest for dose verification measurements. To be fully facilitated for clinical a pplications, the uncertainty model should be integrated into the treatment planni ng system. Clinical appl ications of the dose uncertainty model are investigated in the following chapters. PAGE 94 94 Conclusions The dose uncertainty model theoretically introduced in the previous chapter was revised to better simulate actual delivery situations. In the revised model, the dose uncertainties were categorized into planning uncertainty (inherent dose uncertainty) and delivery uncertainty (space-oriented dose uncertain ty and non-space-oriented dose uncertainty). A convolution method was applied to account fo r spatial displacements during i rradiation. Model parameters were quantified through a variet y of measurements, routine QA data, and peer-reviewed publications. It was demonstrated that dose uncertainty in IMRT could be a priori predicted during radiotherapy treatment planning. Agreement betw een the predicted dose uncertainty distribution and the dose difference distributi on in 108 verification measurements and four test patterns demonstrated the validity of the uncertainty prediction model. The correlation coefficient between the dose uncertainty and the dose difference of the veri fication measurements showed that there was a strong linear correlation. In addition, failed regions using a test in the test patterns correlated to high-dos e uncertainty, which supports a pplicability of the model in a priori predicting regions of high risk in a treatment plan. This advancement of the understanding of uncertainties has the potential to increase the safety and efficacy of IMRT, while at the same time, minimizing the effort expended in timeconsuming and onerous QA processes related to IMRT. PAGE 95 95 Figure 4-1. International Electrotechnical Commission (IEC) coordinate systems with all angular positions set to zero. All detected errors are conve rted into the fixed system. Total of 7 degrees of freedom ( x y, z, pitch, roll, yaw, and b) are quantified as the model input parameters. Note that the collimator angle (b) is an independent variable. Figure 4-2. Calibration jig cont aining 4 IR (Infrared) markers. The jig was placed on top of a phantom and the phantom setup was carried out based on the IR tracking system. A total of 83 measurements for 2 weeks were made to evaluate the setup reproducibility. PAGE 96 96 Figure 4-3. Calculated dose distributions of test patterns. A) Py ramid, B) valley, C) wedge, and D) checkerboard using the Pinnacle3 treatment planning system (dose scale is in cGy and image is in mm). Figure 4-4. Inherent dose disc repancy in penumbra regions and its approximation using a dose gradient distribution. A) In general, the dose difference between calculation and measurement exists in the high-gradient regi ons mainly due to finite size of both the calculation grid and the detector used for commissioning. B) The dose uncertainty is approximated with the value of the dose gradient multiplied by the magnitude of spatial offset. PAGE 97 97 Figure 4-5. Prediction of inhere nt dose uncertainty for 5 5 cm2 field size at the depth of 10 cm. A profile of a central scan line is shown below in each figure. The scale is a percent normalized to dose at the center. A) The cal culated dose distribution. B) The inherent uncertainty distribution mainly due to finite size of both the grid and the detector used for commissioning, grid is presumably related to th e dose gradient and obtained by multiplying the dose gradient with the distance offset parameter. C) Inherent uncertainty distribution related to mainly dose calculation algorithm and normalization, algo is obtained with a distance map. It s magnitude is the largest at the field edge and decreases with the distance fr om the field edge. However, it is always larger than 2 minimum values, one for insi de the field and the other for outside the field. D) The effect at off axis, moa is assumed to be proportional to a distance from the central axis. E) Total inherent uncertainty distribution of the calculation, is computed using the equation: gridalgo moa. (Unit of dose is a percent for A) to C) and E). No unit for D). The unit of the image is mm.) PAGE 98 98 Figure 4-6. Scatter diagrams between inherent dose uncertainty and dose difference for a sample set of 9 measurements chosen for constant determination of (3 depths of 4, 7, and 10 cm and 3 field sizes of 3 3, 5 5, and 10 10 cm2). Dashed lines on the plots show the IU bound where the dose uncertainty is same as the dose difference. The correlation coefficient between the inhere nt dose uncertainty and dose difference demonstrates there is a strong li near correlation between them. PAGE 99 99 Figure 4-7. Relative standard deviation (SD) of 15 measuremen ts using an ionization chamber normalized to 195 MU. Theoretical value of 1/ MU is also normalized and compared to the measurements. The measurements ar e in good agreement w ith the theoretical values, which demonstrates that the relative SD is proportional to a reciprocal of the square root of MU. Figure 4-8. Dose difference di stribution between calculation and EDR2 film meas urement of the test patterns. A) Pyramid, B) valley, C) wedge, and D) checkerboard. (Dose is in % of the maximum calculation dose; image size is in mm.) PAGE 100 100 Figure 4-9. Calculated uncertain ty distributions displayed according to uncertainty type in the rows and test patterns in the columns. Row (I): the overall IU distributions ( )( rIoverall), row (II): the overall statistical uncertainty distributions (1overall( r)), and row (III): overall uncertainty distributions of )( rIoverall+2overall( r ). Column A): pyramid, column B): valley, column C): wedge, a nd column D): checkerboard. Regions of large dose difference in Figure 4-9 corres ponded to those of high-dose uncertainty. An individual scale has been applied to each uncertainty distribution to enhance visualization of the uncertainty pattern. (Dose is in % of the maximum calculation dose; image size is in mm.) PAGE 101 101 Figure 4-10. Scatter diagrams of the test patt erns. A) Pyramid, B) valley, C) wedge, and D) checkerboard between dose difference and overallI. The maximum dose difference is well confined within the IU bound. The dose points above the bound are confined within the uncertainty bound at a 95.4% confidence level ( overall overallI 2). Figure 4-11. The test using 2% and 2 mm as criteria is performed for the test patterns. A) Pyramid, B) valley, C) wedge, and D) checkerboard. The failed points are superimposed on the overall dose uncertainty ( )( rIoverall+2overall( r )) distribution. In general, the failed points fall on the high dose uncertainty regions. This fall indicates that the uncertainty model can predict the regi ons at high risk of fa ilure. (Dose is in % of the maximum calculation dose; image size is in mm.) PAGE 102 102 CHAPTER 5 APPLICATIONS OF THE UNCERTAINTY MODEL FOR IMRT PLAN VERIFICATION Introduction IMRT allows improved dose conformity to the target volume while sparing surrounding normal tissues. Contrary to th is advantageous feature, the enhanced capabilities and functionalities of IMRT systems present a challenge for radiation therapists to maintain the quality, safety, and reliability of radiotherapy without resorting to extensiv e efforts in QA. The increased complexity of advanced technologies is of ten inevitably associated with an increase in possible uncertainties, which can potentially result in unfavorable clinical consequences. Thus, IMRT requires more complex QA and 2-D dose verification.46 The dose verification is performed by comparing dose measurements with e ither other measurements or calculated dose distributions. However, several difficulties exist in carrying out multi-dimensional IMRT verification because of not only st eep dose gradient regions of IMRT dose distributions, but also because of a lack of reliable comparison tools. Superimposing the measured and calculated is odose distributions using software tools are the most commonly used met hods for qualitative evaluation.32, 33, 48, 103 While these methods can be useful for determining whether or not gro ss errors are present, they do not provide a quantitative assessment and are greatly influenc ed by the selection of isodose lines. Most conventional quantitative methods are based on a pe rcent dose difference and DTA. Quantitative verification of the IMRT dose dist ribution will help determine the acceptance levels for the dose difference and DTA. The acceptance criteria are usually 2 to 4% for dose difference and 2 mm to 5 mm for DTA depending on the comp lexity of treatment geometry.15, 16, 21, 105 A composite distribution, which is a binary image of pass-f ail criteria of both the dose difference and DTA, has been introduced.32 It emphasizes the failed regions of the high-dose gradient by displaying PAGE 103 103 the dose difference in the areas. Childress and Rosen33 introduced a 2-D normalized agreement test (NAT) for dose comparison as well as a si ngle parameter which summarized all of the differences of the dose di stribution (NAT index). A distribution, a dose comparison using the combined ellipsoidal dose-difference and DTA test s, has been one of the most commonly used dose verification methods since it was proposed in 1998.30, 31, 35, 46, 48, 101, 102, 104 The function test enables a quick and effici ent evaluation by providing a numerical quality index. In the test, the selected dose difference and DTA have an equivalent significance, so it is critical to determine a proper set of criteria for dose diffe rence and DTA. Standards of 3% and 3 mm are commonly chosen for IMRT QA plans. Although thes e tolerance levels are widely adopted, there are no accepted standards for dose difference a nd DTA values. Based on the gamma index test, an evaluation index has been introduced for faster search of the minimum of a whole set of points.31 The test employed a dose gradient of the ca lculated dose distribution to define an acceptance tube analogous to the acceptance ellipsoid for test. If the ratio of the dose grid spacing and the maximum acceptable DTA ( dmax) is sufficiently small, then both methods correspond. While it is the consensus that patient-specifi c QA is necessary for IMRT fields, no clear standardized action levels and/or recommendations exist for when a test result is not satisfactory, partly because of the lack of information that can be extracted from the QA test. Very often, users encounter varying QA test results. There are well-documented clinical cases in which even a detailed QA procedure was unable to resolv e large discrepancies between measured and calculated dose distributions.12, 137 Current dose verification methods do not provide solid information to guide users to the next step. In other words, these dose verification methods passively evaluate the dose calculation with QA measurements. Furthermore, quantities like dose PAGE 104 104 difference, DTA, and/or -index are evaluated based on overa ll dose distributions. The existing dose comparison methods usually make little account of individual influences of dose uncertainties from the error sources. Thus, the current QA tests do not account for possible complications of dose accumulation history, which can determine whether one plan has inherently higher uncertainties than others. As a result, it may be more desirable to perform the dose comparison with space-dependent and adju stable acceptance levels based on stronger mathematical and physical bases. In this chapter, the applicability of the dose uncertainty model to IMRT dose verification is ex amined with clinical cases. Materials and Methods for Dose Verification Single Field-Based Quality Assurance (QA) Measurements Clinically approved 32 st ep-and-shoot IMRT fields from five head and neck cases were retrospectively investigated to verify the appli cability of the model for IMRT dose verification. The IMRT plans consisted of five to seven fields which had 8 to 16 subfields. Table 5-1 presents details of all the selected cases. Th ese were computed with the Pinnacle3 TPS using a 2 mm calculation grid and delivered with the Elekta Precise linear accelerator. The patient-specific IMRT QA measurements were performed usi ng the 2-D diode array detector. The QA measurement was individually done for each field of a clinical case with a treatment head located at 0 Each diode measurement point of MapCHECK was used to compute the dose deviation between calculation and measurement. The scatter diagram between the overall dose uncertainty ( )(2)( r rIoverall overall) and the dose difference of all measurement points ( )()( rDrDcal t measuremen) was plotted for qualitative comp arison. The uncertainty and dose difference were rescaled to percent of calcula ted maximum dose. As a quantitative measure of PAGE 105 105 the correlation, a correlation coefficient ( ) between overall dose uncerta inty and dose difference was calculated using Equation (4-15). The p-values for the correlation using a Student's t distribution will also be computed. The uncertainty prediction was compar ed with results of a conventional test using 1%-1 mm (dose difference-DTA), 2%-2 mm, and 3%-3 mm criteria. The failed dose points were overlapped with the dose uncerta inty distribution to examine possible correlation between the uncertainty prediction and risk of treatment plan. The correlation coefficient between overall dose uncertainty and the index was also computed. A dose uncertainty failure histogram (DUFH: a ratio of the number of failed points during dose verification to total number of points having the same dose uncertainty) was employed to investigate the correl ation of failed points with the dose uncertainty. The failed dose poi nts by conventional IM RT QA methods were expected to be more likely in the regi ons of relatively high dose uncertainty. Quality Assurance Measurement of a Composite Plan An IMRT head and neck plan consisted of five fields (total 50 s ubfields) with gantry angles of 20, 70, 225, 290 and 340. A prescribed dose was 180 cGy/fraction and total dose to a target was 5400 cGy (30 fractions ). The IMRT plan was delivered to two semicylindrical solid water slabs with 7 cm backscattering solid wate r using the Elekta linac. The phantom setup was the same as shown in Figure 2-1(A) A GAFCHORMIC EBT film (lot no. 36348-011) was vertically sandwiched in the middle of two semicylindrical solid water slabs. In order to conform to the surface edge of the solid water slabs, the edge of the film was cut out with a razor blade. The width and the height of the film were 19. 9 cm and 11.7 cm, respectively. The film was digitized on an Epson Expression 1680 charge-coupled device (CCD )-based flatbed scanner at a resolution of 50 dpi or 0.508 mm per pixel. The images were saved as 48-bit RGB uncompressed PAGE 106 106 tagged image file format (TIFF) image files. The images were imported into MATLAB for analysis. Pixel values of images were converted into OD only with the 16-bit red color channel. A film calibration method presented by Zeiden et al 138 was used for the OD to dose conversion. A sheet of film (20.3 25.4 cm2) was cut into 5 5 cm2 pieces and then the film pieces were placed on central axis at 6 cm depth which was a mean depth of the isocenter from the rounded surface in the phantom. The pieces were irradiated to 12 dose le vels (10, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, and 300 cGy) at the time of the experiment. One nonirradiated film piece was used for background measurement (0 cGy). The film pieces were scanned after 24 hour post exposure and a 3 3 cm2 region in the middle of film pieces was measured for the OD to the dose conversion. Figure 5-1 shows the sensitometric curve of the film measurement using a third-ordered polynomial fit. Similar to the field based IMRT verificat ion, the scatter diagram between the dose uncertainty and the dose differen ce was plotted and the correlat ion coefficient was computed. The uncertainty prediction was verified with results of test using 3% and 3 mm criteria. The failed dose points were overlapped with dos e uncertainty distribu tion and the DUFH was obtained. Results of Dose Verification Single Field-Based QA Measurements The average correlation coefficient be tween the overall dose uncertainty ( )( rIoverall+2 overall( r )) and the dose difference of 32 QA measurements was 0.75 0.07. The pvalues jointly computed with 445 dose points were extremely small (close to 0), which indicated a strong linear correlation between them. The scatter diagram betw een the inherent uncertainty and the dose difference of all 32 IM fields (total 13,184 comparison points) indicated that the IU PAGE 107 107 distributions reasonably predic ted the possible bound of dose di fference as shown in Figure 52(A). In theory, a dose point whose dose difference was greater than the IU ( )( rIoverall) was expected to arise from setup and delivery. Most points (about 99%) were confined within the overall dose uncertainty of )( rIoverall+2 overall( r) (Figure 5-2(B)). In pr inciple, the number of points having dose difference of larger than )( rIoverall+2 overall( r) (95.4% of confidence level) is expected to be equal to or smaller than 4.6%. The average correlation coefficient between the overall dose uncertainty and the index of all comparison points in the 32 IMRT fields was 0.62 0.07, which implied a tendency of more failures in higher dose uncertainty regions. Figure 5-3 shows (A) a computed dose distribution of an IMRT field with diode measurement points and dose uncertainty maps overlaid with failed points of test using the (B) 1%-1 mm (dose differ ence-DTA), (C) 2%-2 mm, and (D) 3%-3 mm criteria. It can be seen that points of high un certainty more likely fail the conventional dose verification. The relationship was further veri fied with DUFH. Figure 5-4(A) and (B) are uncertainty histograms of all dos e points and failed points of test using the 2%-2 mm criterion for the all 32 IM fields, respectively, and Figur e 5-4(C) is the correspond ing DUFH, the ratio of (B) to (A). As shown in Figure 54, as the overall dose uncertainty increased, the ratio of failure also increased. This result was consistent with that of the test patter n study in Chapter 4. Quality Assurance Measurement of a Composite Plan Figure 5-5 shows isodose lines of the calculation and the film measurement. Most of the isodose lines of the calculation were outside the corresponding those of the measurement indicating the calculation over-estimated the meas urement. The deviation was more remarkable in low dose regions. PAGE 108 108 Figure 5-6 shows checkerboard images between the overall dose uncertainty distribution and the dose difference. Streaks of high dose uncerta inty regions were well aligned with those of large dose difference. It also shows that th e predicted dose uncertain ty (bright checkers) overestimates the dose difference (dark checkers) es pecially in low dose gradient regions due to the inherent dose uncertainties. Figure 5-7 shows the scatte r diagrams between the dos e uncertainty and the dose difference. The IU distributions reasonably predicte d the possible bound of dose difference. The scatter diagram between the inhere nce uncertainty and the dose di fference shows that there was a strong correlation between them (Figure 5-7(A)). Most of th e measurement points (96.3%) were confined within the overall dose uncertainty of )( rIoverall+2 overall( r ) (Figure 5-7(B)). Most of the points above the bound resulted from noise of film measurement. Th e correlation coefficient between the overall dose uncertainty and the dos e difference was 0.81, which indicated a strong positive linear correlation between them. The availability of the uncertainty model to predict potential risk of the treatment plan was evaluated with the test. Figure 5-8 shows the failed points of the test overlaid on the uncertainty distribution of 95% confidence level. The failed regions were overlapped with the streaks of relatively high dose uncertainty. The DUFH (Figure 5-9) quantitatively proves that high uncertainty is more likely to correlate to fa ilure of dose verification. Figure 5-9(A) and (B) are uncertainty histograms of a ll dose points and failed points of test using the 3%-3 mm criterion, respectively, and Figure 5-9(C) is the corresponding DUFH. As the overall dose uncertainty increased, the ratio of failure also increased. PAGE 109 109 Discussion The a priori uncertainty map is a useful tool to evaluate potential risk of a treatment plan in dose verification. The uncertainty model could a priori predict probable dose difference between calculation and QA measurements as show n in Figure 5-2 and 5-7. The uncertainty map highlighted regions of failure by the conventional test. It demonstrates that the uncertainty distribution can assist physicists to determine more appropriate points of interest for dose verification measurement. When the dosimetric measurement is spatially limited, intensive measurements may be performed in regions of high uncertainty for more reliable verification. Another example is that, if the QA is performed by film measurement combin ed with an absolute point dose measurement, the measurement point can be chosen based on the uncertainty distribution. For example, a point in low dose uncertainty regions can be utilized for more robust and reproducible measurement. The model can be used as an additional veri fication tool for QA m easurement. Although it was recommended that, if the pass rate of test is between 90% and 95%, the QA measurement must be examined with an additional tool to verify whether or not it is acceptable,102 no clear standardized method for additional examination exis ts. This is partly b ecause of the lack of information that can be extracted from the QA test. In contrast, the dose uncertainty model can provide space-specific dose uncertainty informa tion. Hence, users can investigate whether the failure is related to the plan itself or abnormal operation of the machine. In addition, the confidence level of the overall uncertainty itself is a good verification tool. If the QA measurement is properly done, in the scatter diagram a ratio of dose points within the dose bound is comparable to the corresponding confidence level. PAGE 110 110 Conclusions The uncertainty map of clinical cases reasona bly predicted the dose di fference distribution, although it overestimated the dose difference in lo w dose regions due to inherent uncertainty prediction. In all IMRT QA measurements, most of the dose difference points (more than 96%) were confined within the uncertainty bound of )( rIoverall+2overall( r) (95.4% of confidence level). In principle, the number of points ha ving dose difference of larger than )( rIoverall+2 overall( r ) is expected to be equal to or smaller than 4.6%. The uncertainty map also accentuated regions of failure by the conventional test, which overlaid on high uncer tainty regions. The uncertainty bound plays a role as a space-dependent acceptance le vel of dose verification. Planners, thus, can determine whether the failure is related to the plan itself or abnormal operation of the machine. PAGE 111 111 Table 5-1. Summary of five selected head and neck cases for IMRT dose verification using the uncertainty model. Patient number Number of fields per fraction Total number of subfields per fraction (number of subfields for each field) Total monitor units per fraction Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 7 7 7 5 6 70 (8, 9, 12, 13, 8, 9, 11) 68 (9, 8, 11, 13, 9, 7, 11) 76 (9, 12, 11, 14, 13, 9, 8) 60 (11, 14, 16, 9, 10) 65 (10, 8, 9, 14, 13, 11) 588 668 598 545 533 PAGE 112 112 Figure 5-1. Sensitometric curve for the EBT radiochromic film. The dose ranges from 0 cGy to 300 cGy. Error bars ( SD) and a third-or dered polynomial fit are plotted together with data (errors are very small in all measurements). PAGE 113 113 Figure 5-2. Scatter diagrams of all 32 intensity-modulated (IM) fields between uncertainty and dose difference. A) The IU reasonably pred icts the probable dose difference. B) The dose points whose dose difference is greater th an the predicted IU (a dashed line) are well confined within IU+2 PAGE 114 114 Figure 5-3. Relationship between dose uncertainty and failed points using test. A) A computed dose distribution of an IM field and the co rresponding uncertainty maps overlaid with failed points of test using B) 1%-1 mm, C) 2%-2 mm, and D) 3%-3 mm (dose difference-DTA) criteria. The failed points are correlated with relatively higher uncertainty as the criteria become less stringent. (scalebar unit: % of maximum dose level) Figure 5-4. Dose uncertainty-failure-histogr am (DUHF) of all 32 QA measurements. A) An uncertainty histogram of all dose points, B) an uncertainty histogram of the failed points of test using the 2%-2 mm criterion, and C) the corresponding DUHF (a ratio of B) to A)). As the uncertainty increases, the failed ratio also increases, which indicates that high uncertainty generally correlates to failure of dose verification. PAGE 115 115 Figure 5-5. Isodose distributions of calculati on and two QA measurements. Thick and thin solid lines represent calculation and measurem ent, respectively. Isodose lines of measurement are inside the corresponding thos e of the calculation (i mage scale: mm). Figure 5-6. Checkerboard images between dose uncertainty distributions and dose difference distributions. Streaks of hi gh dose uncertainty well corres pond to those of large dose difference between calculation and measurem ents (scalebar unit: cGy; image scales: mm). The predicted dose uncertainty (bright checkers) overestimates the dose difference (dark checkers) due to pred iction of inherent dose uncertainty. PAGE 116 116 Figure 5-7. Scatter diagrams between the dose uncertainty and the dose difference. A) The scatter diagram between the IU and the dose difference. B) The scatter diagram between the overall dose uncertainty (IU+2 ) and the dose difference. The dose points whose dose difference is greater than the predicted IU are confined within IU+2 Most of outliers originate from the noise of film measurement. PAGE 117 117 Figure 5-8. Failed dose points of test results overlaid on uncertainty distribution of 95.4% confidence level. The failed regions are generally overlapped with regions of relatively high dose uncertainty (scalebar unit: cGy; image scales: mm). Figure 5-9. Dose uncertainty failure histogram (DUFH) of th e film measurement. A) An uncertainty histogram of all dose points, B) an uncertainty histogram of the failed points of test using the 3%-3 mm criterion, and C) the corresponding DUHF (a ratio of B) to A)). PAGE 118 118 CHAPTER 6 CLINICAL EFFICACY OF UNCERTAINT Y-B ASED IMRT PLAN EVALUATION Introduction IMRT plan evaluation methods such as DVH a nd isodose lines have been widely adopted to compare many candidate treatment plans. In the conventional methods of plan evaluation, spatial information on dose uncertainty is not co nsidered; thus, one treatment plan may appear better than another simply on the basis of dose metrics.139 However, as demonstrated in the previous chapters, the dose uncertainty can chan ge from one point to another point within the irradiated volume. It is possible that a plan which appears to be better may have large dose uncertainties due to a complex combination of many small subfields, and thus be less accurate. This implies a necessity of incorporating 3-D in formation of uncertainty into the IMRT planning process to avoid a potential high risk of treatment. The existing paradigm of dealing with uncertainties in radiation therapy is to incorporate these errors by expanding the clinical target wi th a generalized margin in treatment planning.26, 61, 63, 65, 119, 139-142 It does not guarantee that a clinical targ et will get the prescribed dose or the critical structure will be spared. If the point-dependent dose uncerta inty is considered together, it will effectively assist radiotherapy treatment planners to evaluate potential risks of target control and probable complication of critical stru ctures. The uncertainty model predicts a priori dosimetric errors as shown in Chapter 5. Furtherm ore, regions of high uncertainty correlate with those of failure in IMRT QA. If it is taken in to account at the time of treatment planning, potential risks of candidate pl ans can be effectively managed. The prediction of uncertainty during treatment planning can provide tools of plan evaluation prio r to delivery to make reliable and safe treatment plans. In this chap ter, plan evaluation tools based on the a priori uncertainty PAGE 119 119 prediction are proposed and applicab ility of the tools is examined with clinical cases. These tools are expected to be very useful for head-tohead objective comparison of treatment plans. Methods and Materials Confidence-Weighted Pl an Evaluation Tools Confidence-weighted dose volume histogram (CW-DVH) Dose uncertainty distribution is applied to the calculated dose dist ribution to make the upper and lower bounds of a conventional DVH called confidence-weighted dose volume histogram (CW-DVH). The upper and lower bounds of 95.4% confidence level are obtained with )(2)()( r rIrDoverall overall cal and )(2)()( r rIrDoverall overall cal, respectively. A similar concept has been reported by other research groups.112, 143, 144 However, the reported analyses did not account for dose accumulation history and were primarily limited to patient-induced uncertainties. Note that the dose uncertainty model explicitly accounts for dose uncertainty contribution from each subfield and deals with both treatment planning and delivery uncertainties. For quantitative analysis, dose a nd volume indices such as CW-D95 and CW-V20 are also calculated. CW-D95 guarantees that 95% of the target volume receives the prescribed dose within a specified confid ence interval. The upper bound of CW-V20 for OARs indicates the maximum possible volume receiving 20 Gy or higher dose within a specified confidence interval. Confidence-weighted dose distribution (CWDD) The confidence-weighted dose distribution (C WDD) is comprised of isodose contours where the contour line thickness is proportional to the local dose uncertainty map. CWDD on each CT slice reflecting the 95.4% confidence level is used to assess the fidelity of each IMRT plan when targets are closel y bounded on critical organs (e.g., a bladder and a rectum in prostate cases and spinal cords, brainstem, and parotid gl ands in head and neck cases). The uncertainty PAGE 120 120 distribution ( )( rIoverall+2overall( r )) is added to and subtracted from the mean calculated dose distribution to make the confidence-weighted isodose lines. The isodos e lines among plans are compared to choose the optimal plan in terms of local control of PTV and protection of OAR. The CWDD provides clinicians with a quantitative tool that weighs in the potential risk based on planning and delivery uncertainti es during plan evaluation. Dose uncertainty volume histogram (DUVH) The dose uncertainty volume histogram (DUV H) is an accumulated histogram of dose uncertainty as a function of volume. The theore tical applicability of DUVH to IMRT planning evaluation is demonstrated using DULH in Chapter 3. In an ideal case, DUVH is a delta function at zero dose uncertainty for targets and OARs. Ob viously, a treatment plan that has smaller area under the curve and smaller maximum dose uncertainty is preferable in terms of potential risk. In the DUVH plan evaluation tool, a plan which has smaller area under the DUVH curve is preferred for both targets and cri tical organs in deference to th e DVH-based plan evaluation tool, where a larger area under the DVH curve is more desirable for targets, while smaller area is preferred for critical organs. Confidence-Weighted Plan Evalua tion of Clinical IMRT Cases Practical application of our un certainty model for IMRT plan evaluation was investigated with five clinical IMRT cases of three head and neck treatments (denot ed as Patient 1 through Patient 3) and two prostate treatments (denoted as Patient 4 and 5). In the prostate cases, a conventional 4-beam external radiotherapy with a prescription dose of 5,0 40 cGy is implemented. It mainly consists of a single beam of radiati on delivered to the patien t from four directions: often front, back, and both sides. IMRT is additionally utilized with a pr escription dose of 2,520 cGy to boost dose to a target. Three competitive pl ans (denoted as Plan 1, 2, and 3) for each PAGE 121 121 IMRT case were generated by changing beam angles and number of subfields using the Philips Pinnacle3 planning system. Table 6-1 summarizes the clinical cases and corresponding treatment plans used in this study. For all plans, 95% of PTV was covered by the prescribed dose and other plan constraints were met. Figur e 6-1 shows DVHs of three comparative treatment plans (Plan 1: solid line, Plan 2: dotted line, and Plan 3: dot-dashed line) for (A) a head and neck case (Patient 1) and (B) a prostate case (Pat ient 4). Three plans for each case were evaluated with CWDD, CW-DVH, and DUVH. Optimal IMRT plans having the minimum dose uncertainty in clinically important regions (e.g., PTV and/or sensitive OARs) were selected. To calculate the 3-D dose uncertainty, the model parameters quantified in Chapter 4 were utilized. Patient-induced errors detected by Guckenberger et al.67 were applied for the overall uncertainty computation in both the head and neck and prostate treatments (see Table 1-1). Results In all cases, three comparative IMRT plans for each case did not show any significant differences by the conventional pl an evaluation methods as shown in Figure 6-1. However, the uncertainty-based evaluation methods differentia ted the plans in term s of uncertainty for planners to select optimal plans having th e least amount of uncertainty. Table 6-2 shows confidence-weighted dose and volume indices of all PTVs and OARs of five clinical cases. Higher dose is desirable in CW-D95 of PTV meani ng less probability of underdose to the target. For the CW-V index of OARs tolerance dose of normal tissues (TD5/5: 5% risk of complication within 5 years) proposed by Emami et al.145 was used. TD5/5 of spinal cord for the entire volume, for instance, is 47 Gy; thus, CW-V47 is used for the volume index of the spinal cord with the 95.4% confidence interval. In general, lower value of the CW-V index is preferable which indicates a less volume of OAR pot entially receives the tolerance dose. PAGE 122 122 In Patient 1, Plan 3 is the most desirabl e in terms of PTV coverage based on CW-D95 (Table 6-2). The difference, howev er, is not significant enough to tell the superiority. Figure 6-2 shows CWDDs of Patient 1 for (A ) Plan 1, (B) Plan 2, and (C ) Plan 3 overlaid on one of CT image slices. PTV (light green) was well confined within the isodose line of the prescribed dose of 5,040 cGy (a thick red line) w ith the 95.4% confidence level in all plans. When the plans were evaluated by the statistical lowe r bound of the prescribed dose (a n inner thin red line), Plan 1 shows higher risk of underdose to the target than Plan 2 and 3 do, which is conformable with the result of CW-D95 evaluation. Th e potential risk of OARs was evaluated with the CWDDs as shown in Figure 6-3. An optic chiasm (blue) was spared from the prescribed dose by the conventional isodose line (a thick red line) in all plan s, while the upper bound of 95.4% confidence-weighted isodose line shows that Plan 3 is likely to give the prescribed dose to more volume of the optic chiasm than Plan 1 and 2 do. Plan evaluation by the CW-V50 index of the optic chiasm shows the same result (Table 6-2). The CW-V index evaluation did not make any dis tinction of the plans for Patient 2. Plan 3 is, however, the most preferred in terms of PTV coverage as show n in Figure 6-4. It was further verified with CW-D95 in Table 6-2 and the CWDD (Figure 6-5). In CWDD, the lower bound of the prescribed isodose line (4,500 cGy) did not show up in Pl an 1 and 2 indicating high risk of underdose to the PTV. A similar result was observed in Patient 5. It is hard to conclude that one plan is superior to the others when these are evaluated using DVH and the CW-V index for OARs (rectum and bladder). However, in Figur e 6-6 the lower bound of the prescribed isodose line (2,520 cGy) did not show up in Plan 2 and 3, while Plan 1 is relative ly less risky by showing the lower bound. Since the conventional therapy was first implemented for the prostate cases (Patient 4 and 5), the tolerance doses for rectum and bladder were conservatively determined as PAGE 123 123 1,000 cGy and 1,500 cGy, respectively, assuming th ese OARs received the prescription dose of 5,040 cGy. CW-DVH (Figure 6-7) and CW-D95 (Table 6-2) of PTV also show that Plan 1 is more desirable than the others to avoid the poten tial risk of underdos e to the target. In Patient 3, Plan 1 was less preferred due to more dose uncertainty than Plan 2 and 3, when they were evaluated by CW-D95 of PTV (T able 6-2), the CW-V32 index of right parotid gland (Table 6-2), and CWDD as shown in Figure 6-8. The DUVH-based evaluation tool (Figure 6-9) presents the consistent result. A treatmen t plan that has smaller area under the DUVH curve and smaller maximum dose uncertainty is prefer able in terms of potential risk. DUVHs of OARs (brainstem, spinal cord, and paro tid glands) do not show any diffe rences (figures are not shown), while that of PTV clearly shows that the dose uncer tainty is much higher in Plan 1 compared to Plan 2 and 3. CW-D95 of PTV (Table 6-2) and CWDDs for Patie nt 4 (Figure 6-10) sh ow that there is no significant difference among plans. Figure 6-11 show s CW-DVHs of (A) rectum and (B) bladder. Because the rectum was very closely bounded to the PTV, the majority of the rectum can not be saved from the prescribed dose. The CW-V10 index of rectum also represents that all plans can not completely spare the rectum. The CW-DVH of rectum, however, shows that Plan 3 has more dose uncertainty than Plan 1 and 2 (Figure 6-11( A)). When complication risk of bladder is evaluated by the CW-V15 index (Table 6-2) and CW-DVH (Figure 6-11(B)), Plan 1 is most preferred. Discussion The applicability of the confidence-weighed plan evaluation methods such as CW-DVH, CWDD, and DUVH was investigated. These were useful tools to differentiate plans whose potential risk could not be determined by the conventional eval uation tools. If treatment plans are PAGE 124 124 evaluated using these uncer tainty-based tools, planners can di scard plans which have potentially high risk during treatment planning stage. In general, plans should be multilaterally ev aluated when these tools are used. 2-D CWDVH and DUVH evaluations do not consider 3-D spatial distribution of uncertainty. Even though one plan appears better than others using these 2-D tools, slice-by-slice examination of CWDD is necessary to evaluate local risk of the plan. As in case of Patient 4, when the CW-D95 index could not make any distinction, a role of CWDD became of great importance. The uncertainty-based risk assessment occasionally gi ves conflicting results for different organs of interest. In Patient 1, the optimal plan for PT V and right lens was Plan 3, while Plan 1 was optimal for brainstem and optic chiasm and Plan 2 was for right optic nerve. More research, therefore, is required to make a consensus on selection of optimal treatment plan when evaluation results are contradictory. DUVH-based evaluation should be examined with DVH analysis, especially for OARs. Even though the optimization constraints were me t to generate various candidate plans for a clinical case, their DVHs of a crit ical organ varied much in shape (see the left optic nerve in the Figure 6-1(A)). Simply compari ng DUVHs of OARs in the plans leads to a false decision. As shown in Patient 3, usually DUVH was a great tool for PTV comparison because the DVHs of PTV were relatively identical in all example cases. The same TPS (Philips Pinnacle3) using the same optimization of inverse planning and leaf sequencing algorithm was used to generate candidate treatment plans of the clinical cases. Thus, even if the uncertainty-based evaluation tools gi ve distinction among plans, the difference of the dose uncertainty in the compared plans was not significant enough to choose optimal plans in terms of uncertainty especially in the prostate ca ses. As shown in Figure 3-3 and 3-6, if different PAGE 125 125 leaf sequencing algorith ms for the same beam fluence are used, the dose uncertainty may be significantly different. Ultimately, if the uncertainty prediction model is integrated into IMRT plan optimization, an optimal plan which has the least amount of uncertainty can be generated. It is obvious from this chapter that the uncer tainty-based evaluation provides planners with a quantitative tool that weighs in the potential risk based on pl anning and delivery uncertainties during plan evaluation. This type of quantitative information has never been made available to clinicians in the past. Hence, it is believed that the dose uncertainty model will change the conventional paradigm of plan evaluation that is based on the inspecti on of isodose distribution only. Conclusions The confidence-weighted evaluation methods of IMRT plan such as CW-DVH, CWDD, and DUVH were very useful tools to assess the potential risks of treatment plans. These tools successfully differentiated the candidate treatment plans for the same clinical cases which could not be distinguished using th e conventional plan evaluati on methods. CW-DVH provided an overall inspection of the poten tial risks of PTV and OARs. The plans were quantitatively evaluated with the CW-D index for PTV and the CW-V index for OARs. CWDD was suitable for analyzing the local risk of plan s through slice-by-slice examination (i.e., underdose to PTV and overdose to OARs). DUVH was a useful evaluation tool especially for risk of PTV coverage. These confidence-weighed evaluation tools are e xpected to provide an opportunity for the radiation therapy community to employ strategi es for mitigation of dose uncertainties during treatment planning stage. PAGE 126 126 Table 6-1. Summary of five IMRT cases studied. Patient 1 P atient 2 Patient 3 Patient 4 Patient 5 Plan 1 Plan 2Plan 3 Plan 1 Plan 2Plan 3Plan 1Plan 2Plan 3Plan 1Plan 2 Plan 3 Plan 1 Plan 2Plan 3Site Head and neck Head and neck Head and neck Prostate Prostate Prescription 5040 cGy 4500 cGy 4500 cGy 2520 cGy 2520 cGy Number of fraction 28 25 25 14 (boost) 14 (boost) Number of subfields 49 50 50 50 50 48 39 40 40 49 50 50 40 45 45 Total MU per fraction 276 274 261 297 288 269 278 257 264 372 357 347 306 304 298 OARs Brainstem, optic chiasm, optic nerves, retinas, lenses Brainstem, optic chiasm, optic nerves, spinal cord, right parotid Brainstem, spinal cord, right parotid Bladder, rectum Bladder, rectum Table 6-2. Confidence-weight ed dose and volume indices. Patient 1 Patient 2 Patient 3 Index (TD5/5* for CW-V) Plan 1 Plan 2 Plan 3 Plan 1 Plan 2 Plan 3 Plan 1 Plan 2 Plan 3 PTV: CW-D95 (cGy) 4860 4880 4900 4240 4260 4340 4400 4440 4480 Brainstem: CWV50 28.2% 29.3% 29.1% 0.04% 0.03% 0 0 0 0 Spinal cord: CWV47 0 0 0 0 0.03% 0.02% Right parotid: CWV32 0 0 0 80.4% 77.5% 76.5% Right lens: CWV10 8.7% 9.2% 7.0% 0 0 0 Optic chiasm: CWV50 29.0% 29.8% 36.3% 0 0 0 Right optic nerve: CW-V50 12.6% 10.8% 11.0% 0 0 0 Patient 4 Patient 5 Index (TD5/5* for CW-V) Plan 1 Plan 2 Plan 3 Plan 1 Plan 2 Plan 3 PTV: CW-D95 (cGy) 2400 2400 2400 2300 2280 2260 Rectum: CW-V10 100% 100% 100% 53.1% 51.5% 51.8% Bladder: CW-V15 77.2% 81.9% 83.9% 46.6% 44.9% 48.3% *TD5/5: tolerance dose of normal tissues for 5% risk of complication within 5 years PAGE 127 127 Figure 6-1. Dose volume histograms of three co mparative treatment plans. A) A head and neck cases (Patient 1) and B) a prostate case (Patient 4). Solid, dotted, and dot-dashed lines represent Plan 1, Plan 2, and Plan 3 in the Table 6-1, respectively. For all plans, 95% of PTV is covered by the prescribed dose and other plan constraints are met. PAGE 128 128 Figure 6-2. Confidence-weighted dose distributions (CWDDs) for Patient 1 overlaid with one of CT slices. PTV and brainstem are colorwashed with light green and brown, respectively. A thick solid red line sta nds for the prescription of 5,040 cGy isodose line and thin red solid lines are the uppe r and lower bounds of the prescribed dose with 95% confidence level. A) Plan 1 shows higher risk of underdose to the target than B) Plan 2 and C) Plan 3 which is conformable with the result of CW-D95 evaluation. Figure 6-3. Confidence-weighted dose distributions for Patient 1 with organs at risk (OARs). Brainstem, optic chiasm, optic nerves, and retinae are colorwashe d with brown, blue, gray, and yellow, respectively. A thick solid red line stands for an isodose line of the prescribed dose of 5,040 cGy and a thin red solid line is the upper bound of the prescribed dose with 95% confidence level. A) Plan 3 shows higher risk of overdose to the optic chiasm than B) Plan 1 and C) Plan 2 which agrees with the result of CWV50 evaluation. PAGE 129 129 Figure 6-4. Confidence-weighted dose volume histograms of planning target volume (PTV) for Patient 2 (head and neck). The bound co rresponds to 95% confidence level. Figure 6-5. Confidence-weighted dose distributions for Patient 2 with PTV (light green) and brainstem (brown). A solid red line represen ts the prescription of 4,500 cGy. A) Plan 1 and B) Plan 2 show higher probability of underdose to the target than C) Plan 3, because the lower bound of pr escription does not show up. PAGE 130 130 Figure 6-6. Confidence-weighted dose distributions for Patient 5 with PTV (light green), bladder (brown), and rectum (blue). A solid red line represents the prescription of 2,520 cGy. B) Plan 2 and C) Plan 3 show higher proba bility of underdose to the target than A) Plan 1, because the lower bound of prescription does not show up. Figure 6-7. Confidence-weighted dose volume hi stograms of PTV for Patient 5 (prostate). The bound corresponds to 95% confidence level. PAGE 131 131 Figure 6-8. Confidence-weighted dose distributions for Patient 3 with PTV (light green), spinal cord (blue), and parotid gla nds (yellow). A solid red line represents the prescription of 4,500 cGy. A) Plan 1 show higher probability of underdose to the target than B) Plan 2 and C) Plan 3. Figure 6-9. Dose uncertainty volume histogram of PTV for Patient 3. Smaller area under the DUVH curve is preferable. PAGE 132 132 Figure 6-10. Confidence-weighted dose distribu tions for Patient 4 with PTV (light green), bladder (brown), and rectum (blue). A solid red line represents the prescription of 2,520 cGy. There is no significant difference in PTV coverage among plans. PAGE 133 133 Figure 6-11. Confidence-weighted dose volume hi stograms of rectum and bladder for Patient 4. In both A) rectum and B) bladder, Plan 3 (red) has more dose uncertainty than Plan 1 (blue) and 2 (green). PAGE 134 134 CHAPTER 7 CONCLUSIONS Establishment of the New Uncertainty Prediction Model The dose uncertainty in IMRT from planning and delivery was effec tively described with both space-oriented dose uncerta inty (SOU) and non-space-oriented dose uncertainty (NOU). SOU is defined as the uncertainty caused by all sp atial displacements such as finite calculation grid size, origin shift effect in dose calculation, mechanical mismatch of the treatment machine, and spatial variations. NOU is mainly caused by quantum statistics in dosimetric measurements. The combination of SOU and NOU, which inherently exist in radiotherapy treatment planning, is defined as inherent dose uncertainty (IU). The IU sources in dose calculation of two commercially available TPSs (Pinnacle3 and Corvus) were examined in Chapter 2. This study determined the effect of calculation grid si ze on dose calculation and how accurately the two TPSs calculated dose. The dose calc ulation with calculation grid si zes of 1.5, 2, 3, and 4 mm using Pinnacle3 TPS was investigated by taking the 1.5 mm grid size as the reference. The dose difference ranged from 110.0 cGy (2.0% of th e 5400 cGy prescribed dose) to 301.8 cGy (5.6% of the 5400 cGy prescribed dose) in 95% of the region of interest. The dose difference by the origin shift of the calcu lation grid ranged from 100 cGy (1.9 % of the prescribed dose) to 202.9 cGy (3.76% of the prescribed dose) in 95% of the region of interest. The effect of calculation grid size was more significant in regions of re latively higher dose gradient. It was found that while the grid size up to 4 mm was acceptable fo r most IMRT plans, a 2 mm grid size was necessary to accurately predict th e dose distribution at least in the regions of high dose gradient. The study on accuracy of dose calculation in buildup regions of two TPSs (Pinnacle3 and Corvus) showed that the dose difference between the calculation and the film measurement ranged from 240 cGy (4.4% of the prescribed dose) to 350 cGy (6.5% of the prescribed dose) in PAGE 135 135 90% of the region of interest. The dose ve rification using DTA and the dose-difference distribution demonstrated that there were significant discrepanc ies from the surface to about 2 mm in depth and both TPSs overestimated the surface dose ranging from 400 to 1000 cGy (7.4% to 18.5% of the prescribed dos e). Overall, both TPSs predicted the dose relatively well except from the surface down to a very shallow depth. Based on these observations, the IU model wa s proposed in Chapter 4 assuming the IU was attributed to three main sources: the finite grid size, the imperfecti on of the dose calculation algorithm (especially near the field edge), and probable asymmetric beam delivery. The IU model exploited a dose gradient di stribution and a spatial offset parameter for the grid size effect (Equation 4-1) as well as distance maps for th e imperfection of the algorithm and the beam asymmetric effect (Equations 4-2 and 4-4). Th e acceptance study showed that the IU reasonably predicted a possible dose difference between calculation and actua l delivery as shown in Figure 4-6. In radiation delivery, SOU is associated with the dose gradient a nd statistical spatial displacement and NOU originates from quantum statis tics of any irradiator through the beam line. The theoretical and experimental verification for SOU and NOU of delivery was performed in Chapter 3 and 4. In Chapter 3, assuming there was no inherent dose uncertainty, the theoretical dose bound of dose distributions were obtained w ith SOU and NOU. The 1-D simulations using different beam compositions to make treatment fields showed that uncertainty model could provide the appropriate dose bound for dose comparison. The statistical dose limit confined the number of simulated measurements within the corresponding confidence level. The uncertaintybased comparison was different from other conven tional comparison tools in that the tolerance bound by the uncertainty model was a function of space, whereas the previous methods applied PAGE 136 136 one single criterion to the entire points. In Ch apter 4, the conceptual models of SOU and NOU were generalized and empirically proven by introducing convoluti on and a probability distribution function (PDF) of spatial displ acement. SOU was obtained with calculated dose distribution convolved with transl ational and rotational PDFs usi ng Equation 4-8. The robustness of the NOU model was verified using an ioniza tion chamber measurement as shown in Figure 47. The model parameters were quantified through accumulated QA data, experiment, and peerreviewed publications. It was demonstrated that the overall dose uncertainty ( overall overallZI) with a certain confidence level (Z) could a priori predict a possible dose difference between calculation and actual delivery in the test pattern study. Efficacy of the Model and Its Clinical Applications Agreement between the predicted dose uncertainty map and the dose difference distribution in both the te st patterns in Chapter 4 and the clini cal cases in Chapter 5 demonstrated the validity of the dose uncertainty model. In all IMRT QA measurements, most of the dose difference points (more than 96%) were confined with the uncertainty bound of )( rIoverall+2overall( r) (95.4% of confidence level) as statistically predicted. The correlation coefficients between the dos e uncertainty and the dose difference of the verification measurements (0.75 0.07 for 32 single fiel d-based QA measurements and 0.81 for the QA measurement of the composite plan) proved that there was a strong positive linear correlation. The scatter diagrams qualitatively demonstrated the linear relation between them as shown in Figure 5-2 and 5-7. Failed regions of the conventional test correlated to region s of high dose uncertainty as shown in Figure 4-11, 5-3, and 5-8. It was further validated with dose uncertainty failure histograms (DUFH). As the overall dose uncertainty increased, the ratio of failure also increased. PAGE 137 137 These results show that the dose uncertainty map can play an important role as a spacedependent acceptance level of dose verification. Planners can predict the regions where the failure is more likely to exist; thus, more care needs to be taken during treatment planning. The a priori uncertainty prediction enabled the pl anners to perform the confidenceweighted IMRT plan evaluation. The evaluation tools such as confidence-weighted dose volume histogram (CW-DVH), confidenceweighted dose distribution (CWDD), and dose uncertainty volume histogram (DUVH) introduced in Chapter 6 we re very useful to assess the potential risks of the treatment plans. These to ols discerned candidate treatment plans in terms of uncertainty, which were clinically comparab le by the conventional plan evaluation methods. CW-DVH is a DVH with the statistical upper and lower bounds where band widths correspond to the confidence interval. This evaluation tool provide d an overall inspection of the potential risk of the plans with quantitative eval uation indices (the CW-D index for PTV and the CW-V index for OARs). CWDD is a tool for assessing confidence-weighted isodose lin es where the line thickness represents the confidence interval and evaluate the local risk of plans through slice-byslice examination (i.e., underdose to PTV and overdose to OA Rs). A plot of a cumulative dose uncertainty-volume frequency distribution ( DUVH) visually summarizes the uncertainty distribution within a volume of interest. In pa rticular, DUVH presented excellent evaluation for a risk of PTV coverage. Due to the loss of 3-D spatial information in the volume, it is highly recommended that the CW-DVH and DUVH plan evaluation should be compensated for with CWDD. The confidence-weighted evaluation to ols could provide the planners with an opportunity to generate plans which are less risky and more reliable. IMRT represents one of the most significant technical advances in radiation therapy in the recent era. The task of safely and accurately im plementing this technology in the clinics still PAGE 138 138 remains a significant challenge. The goal of this re search was to improve the quality of external beam radiotherapy by the a priori accurate prediction of dose uncertainty in treatment planning and delivery. This research was highly significan t in that it provided a framework to minimize the impact of all known uncertainties in the IMRT process and improved the accuracy of dose delivered to patients. The dose uncertainty map showed the potential to minimize the effort expended in patient specific-QA without compromi sing the quality of radiation treatments. Using the plan evaluation tools, the planners will have an opportunity to select an optimal treatment plan that has the least amount of dose uncertainty The proposed uncertainty model is expected to radically change how dose uncertain ty is assessed and controlled. It will significantly contribute to improving quality, safety, and reliability of ra diotherapy, resulting in the most accurate dose delivery to patients. Issues and Future Works The use of the current uncertainty model is limited to static segmental radiotherapies. However, IMRT delivery is made with dynamic MLC in some institutions. To enhance the generality of the model, it is necessary to e xpand the model for dynamic IMRT delivery. It is believed that, even if the radiation delivery t echniques are different, the concept of SOU and NOU is still valid for uncertainty prediction. Ther efore, if a method of quantification of dynamic MLC movement is presented, the model can be effectively modified for the dynamic IMRT. The model was validated with the relatively small amount of spatial displacement of the static phantom studies assuming the model parameters obeyed the Gaussian distribution. In some clinical cases, patient motions are significantly sizable and do not simply follow the Gaussian distribution. To establish a univers al uncertainty model, it needs to be tested for a moving object with a fair amount of displacement during a simulated treatment. PAGE 139 139 In general, the margin recipe based on the quantified spatial displ acement applies the same safety margin to CTV for all directions to define PTV.16, 26, 61-66 As demonstrated in this study, however, the local uncertainty of dose distribution is not identical as assumed in the margin recipe but space-dependent. A priori knowledge of potential uncertain ties in the form of an uncertainty map in conjunction with conventional dose distributions is likely to change the way we evaluate treatment plans and analyze outcome and toxicity data in the future. The current paradigm of evaluating dose-vol ume relationships for PTV and pl anning organs at risk volume (PRV) will be replaced with dose-volume relationships for CTV and OAR. The uncertainty bound on dose distribution (with a pr e-defined confidence interval ) will, for the first time, provide an accurate estima te of dose delivered to clinical targ ets and critical structures. We can do away with margin recipes and focus on trea tment planning and delivery uncertainties, the knowledge of which is going to come from th e evolution of imaging and image-guidance technologies. The three-beam study shown in Figure 3-6 demonstrated that the amount of dose uncertainty in IMRT delivery strongly correlated to the sequence of subfields. Therefore, the integration of an uncertainty model into a leaf sequencing of IMRT optimization can ultimately minimize uncertainty in IMRT delivery. PAGE 140 140 APPENDIX A DERIVATIONS OF SPACE-ORIENTED DOS E UNCERTAINTY AND NON-SPACEORIENTED DOSE UNCERTAINTY Derivation of Space-Oriented Dose Uncertainty (SOU) Generalized Functional Form of SOU The expected distribution of the calculated dose, ( )( rDcal), by known random spatial displacements can be approximated by a convolution of the static dose distribution with a probability distribution function (PDF). ')'()'()( drrrNrDrDcal cal (A-1) where N is the PDF describing a random spatial distribution ( 2 )'(2 22/)'( r rrre rrN). The convolution-based method is extended to compute the standard deviation of the mean expected dose distribution.113 Hence, the standard deviation in dose D is given: ')'()]()'([)(2drrrNrDrDrcal cal D (A-2) This approach is further extended to consider systematic errors. When there is systematic deviation r, the value r of the PDF is replaced with (r+r). Any spatial displacement of each degree of freedom (DOF) in the ra diation delivery process is take n into account to compute the SOU. The amount of spatial displacement is conve rted to the fixed coordinate system as shown in Figure 4-1 and convolved with the static dos e distribution to obtai n the corresponding dose uncertainty. In detail, considering both translation and rotation PDFs (Ntrans and Nrot) of the treatment machine and the patient, the predicted average dose for a subfield (or segment) is: ),'()]'()'()'()'()',',',','(''''[' )(*)],,,(*),,,,([),,,,( rrNNNNN rDdddddr rN N rD rDbbzzyyxxbzyxcalbzyx trans bzyxrotbzyxcal bzyxcal (A-3) PAGE 141 141 where x is pitch (a rotation about the x-axis), y is roll (a rotation about the y-axis and a gantry rotation), z is yaw (a rotation about the z-axis and a table rotation), b is collimator angle, and the vector r is expressed in the ort hogonal coordinate system (x, y, z) for translation. However, it is transformed to cylindrical coordinates for ro tational convolution. From Equation A-2, the SOU is given: .),,,,( )'()'()'()'()'()',',',','(''''' )'()'()'()'()'( ),,,,()',',',','('''''),,,,(2 2 2 2 bzyxcal bbzzyyxx bzyxcalbzyx bbzzyyxx bzyxcal bzyxcalbzyx bzyx SOUrD rrNNNNN rDdddddr rrNNNNN rD rDdddddr r (A-4) The detailed description of parameters for tran slational and rotational displacement is presented in the following sections. Translational Displacement Parameters If all systematic and random errors of the translation are included for convolution, the normal distribution of independent devi ations in translation is given by: 2 2 2 2 2 22 )(' 2 )(' 2 )(' 38 1 )',','()'(z z y y x xzz yy xx zyxe zzyyxxNrrN (A-5) where x, y, and z are systematic errors along the x-, y-, and z-axes and x, y, and z are the SDs of the distributions in the directions. The systematic errors are linear summation of systematic deviations from all error sources al ong the same direction and the random deviations are the quadratic combination of the SDs. The uncertainty sources during treatment delivery are both the treatment machine and the patient. Th e error sources from patients are further categorized into two parts: external setup and internal organ motion. The systematic and random PAGE 142 142 errors for translation are defined as I i iDOF DOF )( and I i iDOF DOF 2 )( respectively, where the subscription DOF is x, y, or z for error sources i through I, I being the total number of error sources of the DOF. When g=b=0, for instance, the errors in the x direction consist of deviations in field size by the collimators, MLC, external se tup, and internal organ motion (subscribed by x,field, x,MLC, x,ext, and x,int, respectively); theref ore, the systematic and random errors are int, x ext x MLCx fieldxx and 2 int, 2 2 2 x ext x MLCx fieldx x respectively. Note that signs of systematic errors of a patient are opposite to th ose of a machine. The patient moti on counteracts the machine offset, if both movements are in the same di rection. In addition, the error sources are not limited to those stated above. If there are more uncertainty source s, their errors can be combined by linear and quadratic summation in the co rresponding manner. In the z direction, a distance from the source to a plane of interest (SPD; source-to-plane dist ance) is considered. If we take beam divergence into account, (x,field), (y,field), (x,MLC) and (y,MLC) instead of x,field, y,field, x,MLC and y,MLC are used, where is a scaling factor calculated by di viding the SPD by a source-to-axis distance (SAD). The divergence effect similarly applies to random errors x,field, y,field, x,MLC, and y,MLC. If the gantry and the co llimator are rotated by g and b respectively, systematic and random errors associated with the linac should be converted into the fixed coordinate system. When coordinate conversion is needed for translation, the mean gantry angle value g and the mean angle of beam limiting device (principally collimator) b are used for transformation matrices. A new coordinate system (u, v, w) which is the rotated fixe d coordinate system by the angles of g and b is defined as illustrated in Figure A-1. PAGE 143 143 A matrix for rotations about an arbitrary vector (k, m, n) in the fixed coordinate system by the collimator angle b (clockwise) is: 222 222 222 222 222 222 222 222 222 222 222 222 222 222 222 222 222 222cos)( sin )cos1( sin )cos1( sin )cos1( cos)( sin )cos1( sin )cos1(sin )cos1( cos)( nmk mkn nmk nmkk mn nmk nmkm kn nmk nmkk mn nmk nkm nmk nmkn km nvk nmkm kn nmk nmkn km nmk nmk Rb b b b b b b b b b b b b b b b (A-6) And, if the gantry is rotated by g in a clockwise direction when looking towards the isocenter, a rotation matrix is given by: g g g g gR cos0sin 010 sin0cos. (A-7) A direction vector of the z-axis in the fixed system is uz=(0, 0, 1). When the vector uz is rotated by angle g, it makes a new axis w which is given by: zguRw 1 0 0 cos0sin 010 sin0cosg g g g )cos,0,(sing g. (A-8) When w denotes the rotational axis vector of the collimator (k, m, n), then m=0, k2+m2+n2=1, and the matrix Rb can be rewritten as: b b b b b b b b b bknk kn k n kn n nk R cos sin)cos1( sin cos sin )cos1( sin cos22 22. (A-9) Now, translational systematic displacement at the angles of g and b of the treatment machine, ),,(wvu can be converted into the fixed coordinate system as )',','(zyx using the matrices Rg and Rb: PAGE 144 144 w v u bg z y xRR 1 1' w v u b b b b b b b b b g g g gkn k kn k n kn n nk cos sin)cos1( sin cos sin )cos1(sin cos cos0sin 010 sin0cos22 22. (A-10) The random errors are converted in the same manner. The absolute values of )',','(zyx will be used for the SDs. This conversion with angles is only applied to the tran slational errors of the treatment machine and is inde pendent of patient motion. Rotational Displacement Parameters In order to be able to handle rotati onal displacement, the input dose matrix D(x, y, z) is transformed into cylindrical coordinates D(, a), where is the radial coordinate, refers to the azimuthal coordinate, and a is the rotation axis (x, y, or z). The angular convolution is thus given: ')'(),',(),,( dNADAD (A-11) and ')'()],,(),',([),,(2 2 dNADADAD (A-12) where 2 22 )('2 1 )'( e N. and are the systematic error and the random error of the angle, respectively. Table A-1 summarizes the normal distributions, systematic errors, and random errors for the rotational DOFs. The ga ntry angle and the patient couch angle are analogous to roll and yaw, respect ively. The collimator angle is regarded as an independent variable because it is not incorporated with the other angles. PAGE 145 145 Derivation of Non-Space-Oreint ed Dose Uncertainty (NOU) NOU is mainly caused by a monitor chamber, a detector during commissioning, and quantum behavior of radiation in patient. In Chapter 3, it is assumed that an expected SD of calculation dose Dcal (D) is proportional to calD. Dcal is proportional to the monitor unit delivered (MUcal), and thus D is proportional to calMU. A relative SD of dose rel (=D/Dcal) is inversely proportional to D (i.e., calD) Supposing relD (=D 2/ Dcal) is constant and rel,o is a known relative SD with MUo, rel is given by: cal o orel cal o orel D D orel relMU MU D Do, (A-13) Thus, the non-spatial dose deviation )( rN (probable dose error at a point r) between dose calculation and delivery in a st atic condition is assumed: )( )()()(,rD MU MU rDrrcal cal o orel cal rel N (A-14) Providing that the spatial displacem ent is taken into account in an actual delivery situation, NOU is given by: )(*)(*)( )(*)(*)()(,rNrNrD MU MU rNrNrrtrans rot cal cal o orel trans rot N NOU ).(,rD MU MUcal cal o orel (A-15) PAGE 146 146 Table A-1. Summary of normal distributions, systematic errors random errors, and transformed coordinate systems for the rotati onal degrees of freedom (DOFs). DOF Normal distribution for convolution Systematic error Random error Transformed coordinate Pitch x 2 22 )('2 1 )'(x x xx x xe Nxx ,int ,x xext 2 int, 2 ,x xext D (yz x, x ) Roll y 2 222 1y y yy y ye Nyy )(')'( int, ,y y gext 2 ,int 2 2y y gext D (xz, y, y ) Yaw z 2 222 1z z zz ze Nzzz )(')'( int, ,z z cext 2 int, 2 2z z Cext D (xy, z, z ) b 2 222 1b b bb b be Nbb ))('()'( b b D (bbyx, b, zb ) yz stands for the yz plane. It is applied for the other subscriptions for the radial coordinates. It is valid only if the treatment is isocentric, so the couch rotation is about z -axis. PAGE 147 147 Figure A-1. Fixed c oordinated system (x, y, z) is rotated by g and b and converted to a new coordinate (u, v, w). PAGE 148 148 APPENDIX B FLOWCHART AND SOURCE PROGRAMS OF UNCERTAINTY COMPUTATION The commercially available TPS, Pinnacle3, was used for dose calculation using a calculation grid size of 2 2 2 mm3 and it was exported to an independent computing resource as Radiation Therapy Oncology Group (RTOG)-forma tted files. Then, it was interpolated to a 1 1 1 mm3 voxel size using bilinear and spline inte rpolation methods and convolved with rotational and translational PDFs to compute 3-D dose uncertainty maps. The main programs were written in MATLAB. To accelerate the co nvolution computation some subroutine codes were written in C and complied into a shared library called a MEX-file, executable from within MATLAB. The flowchart of the entire process (Figure B-1) and MATLAB source codes are as follows. Figure B-1. Flowchart of dos e uncertainty computation. 3-D dose calculation usin g Pinnacle3 ( 2 2 2 mm3 calculation g rid size ) MATLAB Source Code B1 : Reconstruction of RTOG-formatted dose distribution to 3-D dose distribution MATLAB Source Code B3 : 3-D dose uncertainty computation [Subroutines] Subroutine Code B3-1: Calculation of inherent dose uncertainty (MATLAB function) Subroutine Code B3-2: Convolution for gantry and collimator rotation (C source format; complied into a shared library called a MEX-f ile, executable from within MATLAB) Subroutine Code B3-3: Convolution for pitch (C source format) Subroutine Code B3-4: Convolution for roll (C source format) Subroutine Code B3-5: Convolution for yaw (C source format) Ex p ortin g the calculation to MATLAB com p utin g resources ( RTOG format ) MATLAB Source Code B2 : Interpolation of 3-D dose distribution to the 1 1 1 mm3 voxel size using bilinear and spline interpolation methods PAGE 149 149 [MATLAB Source Code B1] Reconstruction of RTOG-formatted dose dist ribution to 3-D dose distribution % CODE DESCRIPTION % This is a MATLAB Code for reconstruction of 3-D dose matrix from % a RTOG-formatted file of Pi nnacle for a subfield. All specific % numbers in this code are presented as an example. % Reading a RTOG-formatted file of dose distribution %%%%%%%%%%%% [filename filepath]=uige tfile('*.dose', 'Open a dose distribution file') % File extention name for RTOG dose distribution should be '.dose' fid=fopen([filepath filename]); % To open the dose file temp=fread(fid); % To read binary data from the file index=find(temp==10); % To find indices of RETURN key of the binary data group_index=ceil(dx*dz/6); % Size of one axial s lice of dose matrix fclose all; % To close the file % MU delivered for a subfield %%%%%%%%%%%%%%%%%%%%%%%% MU_delivered=5; % 5 is offered as an example % Size of 3-D dose matrix (numbers are presented as an example) %%%%%%% dx=94; % length of x axis in 2 mm grid spacing / Lateral (LAT) dz=120; % length of z axis in 2 mm grid spacing / Anterior-Posterior (AP) dy=63; % length of y axis in 2 mm grid spacing / Superior-Inferior (SI) % Reconstruction of dose matrix from 6-column RTOG formatted dose distribution %%% for i=0:dy-1 % Index of i-th dose map % Conversion from binary data to the i-th dose map dose_char=char(temp(index(3+(group_index+2)*i)+1:in dex(3+group_index+(group_index+2)*i)-1)'); % An index group for the i-th dose map index_temp=find( temp (index(3+(group_index+2)*i)+1:index(3+group_index+(group_index+2)*i)-1)==10); % Conversion from string to number array of the i-th dose map of (group_index-1) dose=str2num(dose_char(1:index_temp(group_index-1)-1)); % Reconstruction from (group_index-1)-by-6 to 1-by-((group_index-1)*6) array dose_temp=reshape(dose', 1, (group_index-1)*6); % From string to number array of remainder (length of dose2: 1~5) dose2=str2num(dose_char(index_temp(group_index-1)+1:end)); % Combining 'dose' with 'dos e2' to make the i-th full dose array dose_temp=[dose_temp dose2]; % Reconstruction from 1-by-(dx*dz) array to dx-by-dz array dose_3D_temp(1:dx, 1:dz, 1, i+1)=reshape(dose_temp*MU_delivered, dx, dz); clear dose_temp dose2 dose % clear variables to save memory end clear dose_char index index_temp temp % clear variables to save memory % Conversion for st anding axial view %%%%%%%%%%%%%%%%%%%%%%%%%%% dose_3D(1:dz,1:dx,:,1:dy)=0; % Matrix creation of 3-D dose distribution for i=1:dy PAGE 150 150 dose_3D(:,:,:,i)=imrotate (flipud(dose_3D_temp(:,:,i)),-90); end % The dose distribution is actually 4-D for 'montage' display. eval([filename(1:end-9) '=dose_3 D;']); % Replacement of 'dose_3D' with the input file name eval(['save filename(1:end-9) filename(1:end-9)]) % To save 3-D dose distribution [MATLAB Source Code B2] Interpolation of 3-D dose distribution to the 1 1 1 mm3 voxel size using bilinear and splin e interpolation methods % CODE DESCRIPTION % This is a MATLAB Code for reconstruction of 3-D dose matrix from % a RTOG-formatted file of Pi nnacle for a subfield. All specific % numbers in this code are presented as an example. % Opening the 3-D dose distribution from the previous step %%%%%%%%%%%% [filename filepath]=uigetfile('*.mat', 'Open a 3-D dose distribution file') eval(['load(''' filename(1:end-4) ''')']) % filename(1:end-4)=3-D dose distribution eval(['dose_3D=squeeze(' file name(1:end-4)) ');']); % Size of 3-D dose matrix (numbers are presented as an example) %%%%%%% dx=94; % length of x axis in 2 mm grid spacing / Lateral dz=120; % length of z axis in 2 mm grid spacing / Anterior-Posterior dy=63; % length of y axis in 2 mm grid spacing / Superior-Inferior % Range of y-axis coordinate (len gth=dy(63); 2 mm grid space) %%%%%%% dose_y_coord=20.9:.2:33.3; % Range of y-axis coordinate for in terpolation (1 mm grid space) %%%%%%% dose_y_coord_1mm=20.9:.1:33.4; temp=zeros(dz*2, dx*2, dy); % Temporary matrix for 2-D interpolation Dose_interp=zeros(dz*2, dx*2, 1, dy*2); % Matrix for 3-D interpolation % Bilinear interpolation of 2-D axial dose map %%%%%%% for i=1:dy temp(:,:,i)=imresize(dos e_3D(:,:,i), 2, 'bilinear'); end % Spline interpolation for axial direction (y) %%%%%%% for j=1:dz*2 for k=1:dx*2 dose_2D_temp=squeeze(temp(j,k,:)); dose_2D=interp1(dose_y_coord, dose_2D_temp, dose_y_coord_1mm, 'spline'); Dose_interp(j,k,:,:)=round(dose_2D*10)/10; end end Dose_interp(Dose_interp<0)=0; % Eliminating negative doses eval([filename(1:end-4) '_1mm=Dose_interp;']); % Repl acement of 'Dose_interp' w ith 'filename(1 :end-4)_1mm' eval(['save filename(1:end-4) '_1mm filename(1:end-4) '_1mm']); % To save the 3-D dose distribution inte rpolated with 1 mm* 1 mm*1 mm voxel size PAGE 151 151 [MATLAB Source Code B3] 3-D dose uncertainty computation % CODE DESCRIPTION % This is a MATLAB Code for un certainty calculation using uncertainty % model. All specific numbers in this code are presented as an example. To run this code, % all dose distributions of the subfields for a gantry angle should be in the % same folder and a sub-folder for saving data (named as Uncertainty) must be made. % % Subroutines % (1) Calculation_of_IU.m / For inherent uncertainty calculation % (2) mex_SOU_gantry_collima tor_rotation_pen.dll / For convolution of collimator rotation % (3) mex_SOU_pitch_conv_pen.dll / For convolution of pitch % (4) mex_SOU_roll_conv_pen.dll / For convolution of roll % (5) mex_SOU_yaw_conv_pen.dll / For convolution of yaw %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Input parameters % Angle bin size for rotation convolution angle_bin=.5; % in degree / 100 mm (distance from CAX) .5 degree = 0.8726 mm spatial_diff=1; % in mm; for Igri d calculation in inherent uncertainty % NOU calculation / Ion chamber measurement see Equation (4-9) MU=257; % cGy s_rel_o=0.0005; % 0.05% s_output=0; % Output consistancy % MU delivered for subfields % In this example gantry angl e, 9 subfields are delivered. MU_delivered=[10.42 6.93 3.40 3.39 10.40 3.39 3.60 4.49 2.98]; % Input parameters for translation and rotation PDFs gantry_angle_sys=0; % de gree / Systematic error of gantry angle gantry_angle_rand=0; % degree / Random error of gantry angle collimator_angle_sys=0; % degree / Systematic error of collimator angle collimator_angle_rand=0; % degree / Random error of collimator angle table_angle_sys=0; % degree / Systematic error of couch angle table_angle_rand=0; % degree / Random error of couch angle MLC_sys=0; % mm / Systematic error of MLC MLC_rand=0.5; % mm / Random error of MLC machine_x_sys=0.5; % mm / Systematic error of x jaw machine_x_rand=0.4; % mm / Random error of x jaw machine_y_sys=0.4; % mm / Systematic error of y jaw machine_y_rand=0.4; % mm / Random error of y jaw machine_z_sys=0.4; % mm / Systematic error of z (SPD) machine_z_rand=1; % mm / Random error of z (SPD) mean_gantry_angle=335; % degree / Mean gantry angle mean_collimator_angle= 0; % degree / Mean collimator angle external_pitch_sys=1.1; % degree / Systematic error of pitch (setup) external_pitch_rand=1.4; % degree / Random error of pitch (setup) external_roll_sys=0.7; % de gree / Systematic error of roll (setup) external_roll_rand=1.5; % degree / Random error of roll (setup) external_yaw_sys=1.1; % degr ee / Systematic error of yaw (setup) external_yaw_rand=1.7; % degr ee / Random error of yaw (setup) external_x_sys=0.8; % mm / Systematic error of x; LAT (setup) external_x_rand=1.4; % mm / Random error of x; LAT (setup) PAGE 152 152 external_y_sys=0.9; % mm / Systematic error of y; SI (setup) external_y_rand=1.9; % mm / Random error of y; SI (setup) external_z_sys=0.7; % mm / Systematic error of z; AP (setup) external_z_rand=1.2; % mm / Random error of z; AP (setup) internal_pitch_sys=0; % degree / Systematic error of pitch (organ motion) internal_pitch_rand=0; % degree / Random error of pitch (organ motion) internal_roll_sys=0; % degree / Systematic error of roll (organ motion) internal_roll_rand=0; % degree / Random error of roll (organ motion) internal_yaw_sys=0; % degree / Systematic error of yaw (organ motion) internal_yaw_rand=0; % degree / Random error of yaw (organ motion) internal_x_sys=0; % mm / Systematic error of x; LAT (organ motion) internal_x_rand=0; % mm / Random error of x; LAT (organ motion) internal_y_sys=0; % mm / Systematic error of y; SI (organ motion) internal_y_rand=0; % mm / Random error of y; SI (organ motion) internal_z_sys=0; % mm / Systematic error of z; AP (organ motion) internal_z_rand=0; % mm / Random error of z; AP (organ motion) % Origin of dose distribuiton from Pinnacle (Dose Grid menu of Beam) in mm Slice_origin_X=-93; Slice_origin_Y=209; Slice_origin_Z=-642; % Location of isocenter fr om Pinnacle (POI) in mm Isocenter_X=-21; Isocenter_Y=245; Isocenter_Z=-524; ISO=[Isocenter_X Isocenter_Z Isocenter_Y]; % Dose matrix size = 240 (z size) x 188 (x size) x 126(y size) % Patient-specific data X_range=[-93, 95]; % slice origin slice end = # of X slices, X1 PAGE 153 153 % inverse matrix for collimator rotation (see Equation (A-9)) machine_re_sys=Rg_inv*Rb_inv*[u_sys; v_sys; w_sys]; % See Equation (A-10) machine_re_rand=Rg_inv*Rb_inv*[u_rand; v_rand; w_rand]; % See Equation (A-10) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Systematic and Random errors for translation x_sys_total=machine_re_sys(1)-external_x_sys-internal_x_sys; y_sys_total=machine_re_sys(2)-external_y_sys-internal_y_sys; z_sys_total=machine_re_sys(3)-external_z_sys-internal_z_sys; x_rand_total=sqrt(machine_re_rand(1)^2 +external_x_rand^2+internal_x_rand^2); y_rand_total=sqrt(machine_re_rand(2)^2 +external_y_rand^2+internal_y_rand^2); z_rand_total=sqrt(machine_re_rand(3)^2+external_z_rand^2+internal_z_rand^2); % Angles for PDFs (see Table A-1) % Total Pitch pitch_sys=-external_pitch_sys-inte rnal_pitch_sys; % Systematic pitch_rand=sqrt(external_pitch_rand.^2+internal_pitch_rand.^2); % Random % Total Roll roll_sys=gantry_angle_sys-external_ro ll_sys-internal_roll_sys; % Systematic roll_rand=sqrt(gantry_angle_rand^2+external_roll_rand^2+internal_roll_rand^2); % Random % Total Yaw yaw_sys=table_angle_sys-external_yaw_sys-internal_yaw_sys; % Systematic yaw_rand=sqrt(table_angle_rand^2+external_yaw_rand^2+internal_yaw_rand^2); % Random % End of input parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Reading a folder containing dose distributions of subfields cd_name=cd; it=dir; it_size=length(it); index_for_save=1; % Index for save / 1 for the first file; 0 for the others for ind=3:it_size % The file name of dose distributions: ?????????_1mm.mat if length(it(ind) .name)>7 & it(ind).n ame(end-2:end)=='mat' & it(ind).name(end-6:end-4)=='1mm' % Loading the dose distributions load(it(ind).name(1:end-4)) eval(['dose_dist_4D=' it(ind).name(1:end-4) ';']) clear(it(ind).name(1:end-4)) % Size of matrix (viewing from inferior) [z_ap x_lat dummy y_si]=size(dose_dist_4D); dose_in=squeeze(dose_dist_4D); % Ca lculated dose for convolution input (Dcal; Equation (4-6)) % Subroutine 1: "Calculation_of_I U.m" for calculation of inherent uncertainty dose_in_IU=Calculation_of_IU(dose_dist_4D, ISO, mean_gantry_angle, X_range, Y_range, Z_range); dose_cal=dose_in; % Dcal in Equation (4-6) dose_out=zeros(z_ap, x_lat, y_si); % Mean Dcal in Equation (4-6) clear dose_dist_4D dose_cal_IU=dose_in_IU; % I; Inherent dose uncertainty in Equation (4-10) PAGE 154 154 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Convolution starts here. % Order: Rotation -> Translation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1st Convoultion for mean calculation (Dcal bar in Equation (4-6)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Rotational convolution % 1. Collim ator angle convolution if collimator_angle_rand~=0 % Angular PDF for collimator convolution sigma=collimator_angle_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(collimator_angle_sys/angle_bin): ... f_size+round(collimator_angle_sys/angle_bin)); % Systemic error shift f=normpdf(s, collimator_angl e_sys/angle_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Rotation of z axis in the fixed coordinate system (see Equation (A-7)) z_axis=[0; 0; 1]; Rg=[cos(mean_gantry_angle*pi/180) 0 sin(mean_gantry_angle*pi/180); 0 1 0; -sin(mean_gantry_angle*pi/180) 0 cos(mean_gantry_angle*pi/180)]; Zc=Rg*z_axis; % Rotation of z_axis about y axis % Convolution for gantry & collimator rotation % Subroutine 2: "mex _SOU_gantry_collimator_ rotation_with_pen.dll" [dose_out, dose_out_IU]=mex_SOU_gantry_ collimator_rotation_with_pen(dos e_in, dose_in_IU, f, Zc, ... Slice_origin_X, Slice_origin_Y, Slice_origin_Z, ... Isocenter_X, Isocenter_Y, Isocenter_Z, ... collimator_angle_sy s, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for collimator angle %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2. Pitch convolution if pitch_rand~=0 % Angular PDF for pitch convolution sigma=pitch_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(pitch_sys/angle_bin): ... f_size+round(pitch_sy s/angle_bin)); % Systemic error shift f=normpdf(s, pitch_sys/ angle_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Convolution for pitch % Subroutine 3: "mex_SOU_pitch_conv_with_pen.dll" PAGE 155 155 [dose_out, dose_out_IU]=mex_SOU_pitch_conv_with_pen(dose_in, dose_in_IU, f, ... Slice_origin_Y, Slice_origin_Z, ... Isocenter_Y, Isocenter_Z, ... pitch_sys, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for pitch %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 3. Roll convolution if roll_rand~=0 % Angular PDF for roll convolution sigma=roll_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(roll_sys/angle_bin): ... f_size+round(roll_sys/a ngle_bin)); % Systemic error shift f=normpdf(s, roll_sys/a ngle_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%% % Convolution for roll % Subroutine 4: "mex_SOU_roll_ conv_with_p en.dll" [dose_out, dose_out_IU]=mex_SOU_roll_conv_with_pen(dose_in, dose_in_IU, f, ... Slice_origin_X, Slice_origin_Z, ... Isocenter_X, Isocenter_Z, ... roll_sys, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for roll %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Yaw convolution if yaw_rand~=0 % Angular PDF for yaw convolution sigma=yaw_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(yaw_sys/angle_bin): ... f_size+round(yaw_sys/angle_bin)); % Systemic error shift f=normpdf(s, yaw_sys/angle_ bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%% % Convolution for yaw % Subroutine 5: "mex_SOU_yaw_conv_with_pen.dll" [dose_out, dose_out_IU]=mex_SOU_yaw_conv_with_pen(dose_in, dose_in_IU, f, ... Slice_origin_X, Slice_origin_Y, ... PAGE 156 156 Isocenter_X, Isocenter_Y, ... yaw_sys, angle_bin); % Substitution of matrices for inputs of the next convolution dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for yaw %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 5. Translation convolution % Range of translation PDFs; plus minus 4 sigmas (99.993%) f_size_x=round(x_rand_total*4)+abs(round(x_sys_total)); f_size_y=round(y_rand_total*4)+abs(round(y_sys_total)); f_size_z=round(z_rand_total*4)+abs(round(z_sys_total)); dist_x=-f_size_x:f_size_x; dist_y=-f_size_y:f_size_y; dist_z=-f_size_z:f_size_z; % PDFs for translation; Gaussian distribution px=normpdf(dist_x, -x_sys_total, x_rand_total); py=normpdf(dist_y, -y_sys_total, y_rand_total); pz=normpdf(dist_ z, z_sys_total, z_rand_total); len_x=length(dist_x); len_y=length(dist_y); len_z=length(dist_z); sum_px=sum(px); sum_py=sum(py); sum_pz=sum(pz); % Normalization of PDFs px=px/sum_px; py=py/sum_py; pz=pz/sum_pz; % Convolution order: Z -> X -> Y if z_rand_total~=0 for j=1:x_lat for k=1:y_si dose_out(: ,j,k)=conv2(squeeze(dose_in(: ,j,k))', pz, 'same')'; dose_out_IU(:,j,k)=conv2(squeeze(dose_in_IU(:,j,k))', pz, 'same')'; end end dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end if x_rand_total~=0 for i=1:z_ap PAGE 157 157 for k=1:y_si dose_out(i ,:,k)=conv2(squeeze(dose_in(i ,:,k)), px, 'same'); dose_out_IU(i,:,k)=conv2(squeeze(dose_in_IU(i,:,k)), px, 'same'); end end dose_in=dose_out; dose_out=zeros(z_ap, x_lat, y_si); dose_in_IU=dose_out_IU; dose_out_IU=zeros(z_ap, x_lat, y_si); end if y_rand_total~=0 for i=1:z_ap for j=1:x_lat dose_out(i,j ,:)=conv2(squeeze(dose_in(i,j,:))', py, 'same')'; dose_out_IU(i,j,:)=conv2(squeeze(dose_in_IU(i,j,:))', py, 'same')'; end end dose_in=dose_out; dose_in_IU=dose_out_IU; clear dose_out dose_out_IU end %End of tran slation convolution %%%%%%%%%%% mean_dose=dose_in; % Mean Dcal mean_dose_IU=dose_in_IU; % Mean I %End of 1st convolution %%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2nd Convoultion for SOU (Dcal bar in Equation (4-8)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dose_in=dose_cal.^2; % input for SOU dose_in_IU=dose_cal_IU.^2; % input for SOU of I clear dose_cal_IU dose_cal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Rotational convolution % 1. Collim ator angle convolution if collimator_angle_rand~=0 % Angular PDF for collimator convolution sigma=collimator_angle_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.99 3%) s=(-f_size+round(collimator_angle_sys/angle_bin): ... f_size+round(collimator_angle_sys/angle_bin)); % Systemic error shift f=normpdf(s, collimator_angle_ sys/angle_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Rotation of z axis in the fixed coordinate system (see Equation (A-7)) z_axis=[0; 0; 1]; Rg=[cos(mean_gantry_angle*pi/180) 0 sin(mean_gantry_angle*pi/180); 0 1 0; -sin(mean_gantry_angle*pi/180) 0 cos(mean_gantry_angle*pi/180)]; Zc=Rg*z_axis; % Rotation of z_axis about y axis % Convolution for gantry & collimator rotation PAGE 158 158 % Subroutine 2: "mex _SOU_gantry_collimator_ rotation_with_pen.dll" [SOU_var, SOU_va r_IU]=mex_SOU_gantry_collimator_rotation_with_pen(dos e_in, dose_in_IU, f, Zc, ... Slice_origin_X, Slice_origin_Y, Slice_origin_Z, ... Isocenter_X, Isocenter_Y, Isocenter_Z, ... collimator_angle_sy s, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for collimator angle %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2. Pitch convolution if pitch_rand~=0 % Angular PDF for pitch convolution sigma=pitch_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(pitch_sys/angle_bin): ... f_size+round(pitch_sys/an gle_bin)); % Systemic error shift f=normpdf(s, pitch_sys/a ngle_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Convolution for pitch % Subroutine 3: "mex_SOU_pitch_conv_with_pen.dll" [SOU_var, SOU_var_IU]=mex_S OU_pitch_conv_with_pen(dose_in, dose_in_IU, f, ... Slice_origin_Y, Slice_origin_Z, ... Isocenter_Y, Isocenter_Z, ... pitch_sys, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for pitch %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 3. Roll convolution if roll_rand~=0 % Angular PDF for roll convolution sigma=roll_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(roll_sys/angle_bin): ... f_size+round(roll_sys/angl e_bin)); % Systemic error shift f=normpdf(s, roll_sys/angl e_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%% % Convolution for roll % Subroutine 4: "mex_SOU_roll_conv_with_pen.dll" [SOU_var, SOU_var_IU]=mex_SOU_roll_conv_with_pen(dose_in, dose_in_IU, f, ... PAGE 159 159 Slice_origin_X, Slice_origin_Z, ... Isocenter_X, Isocenter_Z, ... roll_sys, angle_bin); % Substitution of matrices for in puts of the next convolution dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for roll %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Yaw convolution if yaw_rand~=0 % Angular PDF for yaw convolution sigma=yaw_rand/angle_bin; % degree / SD of PDF f_size=round(sigma*4); % Range of PDF; plus minus 4 sigmas (99.993%) s=(-f_size+round(yaw_sys/angle_bin): ... f_size+round(yaw_sys/angle_bin)); % Systemic error shift f=normpdf(s, yaw_sys/angl e_bin, sigma); % Gaussian distribution %%%%%%%%%%%%%%%%%%%%%% % Convolution for yaw % Subroutine 5: "mex_SOU_yaw_conv_with_pen.dll" [SOU_var, SOU_var_IU]=mex_S OU_yaw_conv_with_pen(dose_in, dose_in_IU, f, ... Slice_origin_X, Slice_origin_Y, ... Isocenter_X, Isocenter_Y, ... yaw_sys, angle_bin); % Substitution of matr ices for inputs of the next convolution dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end % End of convolution for yaw %%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 5. Translation convolution % Range of translation PDFs; plus minus 4 sigmas (99.993%) if z_rand_total~=0 for j=1:x_lat for k=1:y_si SOU_var(:, j,k)=conv2(squeeze(dose_in(: ,j,k))', pz, 'same')'; SOU_var_IU (:,j,k)=conv2(squeeze(dose_in_IU(: ,j,k))', pz, 'same')'; end end dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end PAGE 160 160 if x_rand_total~=0 for i=1:z_ap for k=1:y_si SOU_va r(i,:,k)=conv2(squeeze(dose_in(i,: ,k)), px, 'same'); SOU_var_IU(i ,:,k)=conv2(squeeze(dose_in_ IU(i,:,k)), px, 'same'); end end dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end if y_rand_total~=0 for i=1:z_ap for j=1:x_lat SOU_var(i, j,:)=conv2(squeeze(dose_in (i,j,:))', py, 'same')'; SOU_var_IU(i,j ,:)=conv2(squeeze(dose_in_IU (i,j,:))', py, 'same')'; end end dose_in=SOU_var; SOU_var=zeros(z_ap, x_lat, y_si); dose_in_IU=SOU_var_IU; SOU_var_IU=zeros(z_ap, x_lat, y_si); end %End of tran slation convolution %%%%%%%%%%% %End of 2nd convolution %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculation of SOU and NOU SOU_var=dose_in-mean_dose.^2; NOU=s_rel_o^2*MU/MU_delivered(n_MU)*mean_dose.^2; SOU_var_IU=dose_in_IU-mean_dose_IU.^2; clear dose_in dose_in_IU % Calculation of mean Dcal, mean I, and total sigma if index_for_save==1 % for the first subfield total_mean_dose=mean_dose; total_mean_dose_IU=mean_dose_IU; total_uncertainty=(sqrt(SOU_var+NOU+SOU_var_IU)+s_output*mean_dose).^2; % Equation (4-12) index_for_save=0; f_name=it(ind).name(1:4); else % for the other subfields other than the 1st subfield total_mean_dose=total_mean_dose+mean_dose; total_mean_dose _IU=total_mean_dose_IU+mean_dose_IU; total_uncertainty=total_uncertainty+ ... (sqrt(SOU_var+NOU+SOU_var_IU)+s_output*mean_dose).^2; % Equation (4-12) end clear SOU_var NOU mean_dose mean_dose_IU SOU_var_IU end % Saving mean Dcal, mean I, and total sigma if ind==it_size PAGE 161 161 % Saved in the pre-made sub-folder "Uncertainty" cd([cd_name '\Uncertainty']); eval([f_name '_tota l_UD=sqrt(total_unc ertainty);']); eval(['save f_name '_total_UD f_name '_total_UD']); eval(['clear f_name '_total_UD']) eval([f_name '_mean_IU=total_mean_dose_IU;']); eval(['save f_name '_mean_IU f_name '_mean_IU']); eval(['clear f_name '_mean_IU']) eval([f_name '_ mean_dose=total_mean_dose;']); eval(['save f_name '_mean_dose f_name '_mean_dose']); eval(['clear f_name '_mean_dose']) cd(cd_name); end end [Subroutine Code B3-1] Calculation of inherent dose uncertainty (Calculation_of_IU.m) function IU_3D=Calculation_of_IU(dose_calculation, ISO, Gangle, X_range, Y_range, Z_range) % This subroutine is for calculation of inherent dose uncertainty % % INPUTS % dose_calculaiton: 3-D dose calculation % ISO: isocenter (x, z, y) % Gangle: mean gantry angle (degree) % X_range: range of x coordinate [x start, x end] % Y_range: range of y coordinate [y start, y end] % Z_range: range of z coordinate [z end, z start] % % OUTPUT % IU_3D: 3-D inherent uncertainty distribution I Equation (4-5) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Input constants spatial_diff=1; % the spatial offset para meter in Equation (4-1) (x, y)=(1 mm,1 mm) % Obtaining the pivot coordinate T_matrix=[cos(Gang le*pi/180) -sin(Gangle*pi/180); sin(Gangle*pi/180) cos(Gangle*pi/180)]; % Matrix for gantry rotation X_origin=sum(X_range)/2; Z_origin=sum(Z_range)/2; X_origin_coord=I SO(1)-X_origin; Z_origin_coord=I SO(2)-Z_origin; Rot_origin=T_matrix*[X_origin_coord; Z_origin_coord]; % Matrix for off-axis correction Equation (4-4) [z_size_temp x_size_temp]=size(im rotate(squeeze(dose_calculation(:, :,:,1)), Gangle, 'bilinear')); dist_correction=zeros(x_size_temp, y0_size); dist_correction(round(x_size_temp/2+Rot_origin(1)), round(y0_size/2+Rot_origin(2)))=1; dist_correction=bwdist(dist_corr ection)*3/200+1; % Distance map % Size of dose calculation PAGE 162 162 [z0_size x0_size y0_size] =size(dose_calculation); % End of inputs %%%%%%%%%%%%%%%%%%%%%%%%%%%% % Step 1/3: Rotating images to an upright position %%%%%%%%%%%%%%%% for i=1:y0_size temp_slice=imrotate(squeeze(dose_ calculation(:,:,:,i)), Gangle, 'bilinear'); temp_rot_3D(:,:,i)=temp_slice; end clear temp_slice % Size of dose calculation rotated by gantry angle [z_ap x_lat y_si]=size(temp_rot_3D); % Step 2/3: Constructing IU images %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:z_ap dose_planar_temp=s queeze(temp_rot_3D(i,:,:)); max_dose_planar=max(dose_planar_temp(:)); if max_dose_planar~=0 % Constructing I_grid in Equation (4-1) [gx gy]=gradient(dose_planar_temp); total_grad=(abs(gx)+abs(gy))*spatial_diff; % Constructing I_algo in Equation (4-2) dose_dist=bwdist(edge(dose_planar_temp, 'canny', .5, 1)) ; dose_dist_per(1:x_lat, 1:y_si)=0; dose_dist_per=(1.5-0.03*dose_dist); dose_dist_per(dose_dist_per<0)=0; dose_dist_per=dose_dist_per+0.4; dose_dist_per(dose_dist_per<0.6 & dose_planar_temp>max_dose_planar*0.8)=0.6; % I_algo m_oa in Equation (4-2) and (4-4) dose_dist_per=dose_dist_per.*dist_correction; % I_grid + I_algo m_oa in Equation (4-5) IU_temp(i,:,:)=total_grad+dose_dist_per*max_dose_planar/100; else IU_temp(i,:,:)=dose_planar_temp; end end clear temp_rot_3D dose_dist dose_dist_per total_grad gx gy dose_planar_temp % Cropping ranges of the rotated image to match with original image size_rot=size(imrotate(squeeze(IU_tem p(:,:,1)), -Gangle, 'bilinear')); z_crop=round(size_rot(1)/2-Z_origin_coord)+(ISO(2)-Z_range(1))+1: ... round(size_rot(1)/2-Z_origin_coord)-(Z_range(2)-ISO(2)); x_crop=round(size_rot(2)/2+X_origin_coord)-(ISO(1)-X_range(1))+1: ... round(size_rot(2)/2+X_origin_coord)+(X_range(2)-ISO(1)); % Step 3/3: Rotating images back and Cropping %%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:y0_size temp_slice_IU=imrotate(squeeze(I U_temp(:,:,i)), -Gangle, 'bilinear'); IU_3D(:,:,1,i)=temp_slice_IU(z_crop, x_crop); end PAGE 163 163 % Eliminating negative inhe rent dose uncertainty IU_3D(dose_calculation==0)=0; [Subroutine Code B3-2] Convolu tion for collimator rotation /* ============================================================= Source code name: mex_SOU_gantry_collimator_rotation_with_pen.c This is a subroutine ME X-file for MATLAB Code 3. Convolution for gantry and collimator rotation ============================================================= */ #include "mex.h" #include "math.h" /* The gateway routine ////////////////////////////// */ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { /* Declaration of Variables */ const int *dims; /* Dimension of the input matrix */ double *dose_out, *dose_out_IU /* Dose output and IU output matrices */ double *dose_in_matrix, *dose_in_matrix_IU /* Dose input and IU input matrices */ double *filter, *Zc; /* PDF for collimator convo lution and rotated z-ax is coordinate */ double collimator_ang le_sys, angle_bin; /* Systematic error of colli mator angle and angular convolution bin size */ int filter_size, mrows, nc ols, lslcs, NDIMs=3; /* PDF size, size of matrix (row, column, slice), and dimension of output matrix */ int slice_origin_x, sli ce_origin_y, slice_origin_z; /* Origin of dose distribuiton from Pinnacle (x, y, z) */ int iso_x, iso_y, iso_z; /* Isocenter (x, y, z) */ /* Check for proper number of input and output arguments. */ if (nrhs != 12) mexErrMsgTxt("12 Inputs required."); if (nlhs != 2) mexErrMsgTxt("Two outputs required."); /* Create variables of the input matrices. */ dose_in_matrix = mxGetPr(prhs[0]); dose_in_matrix_IU = mxGetPr(prhs[1]); filter = mxGetPr(prhs[2]); Zc = mxGetPr(prhs[3]); slice_origin_x = mxGetScalar(prhs[4]); slice_origin_y = mxGetScalar(prhs[5]); slice_origin_z = mxGetScalar(prhs[6]); iso_x = mxGetScalar(prhs[7]); iso_y = mxGetScalar(prhs[8]); iso_z = mxGetScalar(prhs[9]); collimator_angle_sys = mxGetScalar(prhs[10]); angle_bin = mxGetScalar(prhs[11]); PAGE 164 164 /* Get the dimensions of the in put dose matrix and PDF. */ dims = mxGetDimensions(prhs[0]); mrows = dims[0]; ncols = dims[1]; lslcs = dims[2]; filter_size = mxGetN(prhs[2]); /* Check if the first input argument is a 3-D matrix. */ if ( mrows == 1 || ncols == 1 || lslcs == 1) { mexErrMsgTxt("Input matrix must be a 3D matrix."); } /* Create the output matrices. */ plhs[0] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); plhs[1] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); /* Create variables of the output matrices. */ dose_out = mxGetPr(plhs[0]); dose_out_IU = mxGetPr(plhs[1]); /* Call the C subroutine. */ mex_SOU_coll_gantry_rot_conv_with_pen (dose_out, dose_out _IU, dose_in_matr ix, dose_in_matrix_IU, filter, Zc, mrows, ncols, lslcs, filter_size, sli ce_origin_x, slice_origin _y, slice_origin_z, iso_x, iso_y, iso_z, collimator_angle_sys, angle_bin); } /************************ The C subroutine ************************/ void mex_SOU_coll_gantry_rot_conv_with_pen(double *dose_out, double *dose_out_IU, double *dose_in_matrix, double *dose_in_matrix_IU, double *filter, double *Zc, int m, int n, int l, int f_size, int slice_origin_x, int slice_ origin_y, int slice_origin_z, int iso_x, int iso_y, in t iso_z, double coll_angle_sys, double a_bin) { int i, j, k, fi, coord_index, point_coord[3], Converted_point[3]; double angle_about_Zc, temp_coord; double sum_temp=0.0, sum_temp_IU=0.0, temp=0.0, temp_IU=0.0; for (i = 0; i < n; i++) /* for x coordinate */ { for (j = 0; j < l; j++) /* for y coordinate */ { for (k = 0; k < m; k++) /* for z coordinate */ { /* Coordinate conversion: isocenter => matrix origin point_coord=(u, v, w) */ point_coord[0] = i+(slice_origin_x-iso_x); point_coord[1] = j+(slice_origin_y-iso_y); point_coord[2] = m-(iso_z-slice_origin_z)-k-1; for (fi = 0; fi PAGE 165 165 a_bin 3.1415/180.0; /* Rotate the 'point_coord by 'angle_about_Zc'; clockwise direction using Equation (A-9) Converted_point=(x, y, z) */ /* For (u, v, w) => x conversion */ temp_coord=(((double)point_coord[0]*(Zc[0]*Zc[0]+Zc[2]*Zc[2]*cos(angle_about_Zc))+ (double)point_coord[1]*Zc[2]*sin(angle_about_Zc)+ (double)point_coord[2]*Zc[0]*Zc[2]*(1.0-cos(angle_about_Zc)))); /* Round-up of x (LAT) for integer index */ if (temp_coord < 0) { Converted_point[0] = -(-temp_coord+0.5); } else { Converted_point[0]=temp_coord+0.5; } /* For (u, v, w) => y conversion */ temp_coord=(((double)point_coord[0]*(-Zc[2]*sin(angle_about_Zc))+ (double)point_coord[1]*(cos(angle_about_Zc))+ (double)point_coord[2]*(Zc[0]*sin(angle_about_Zc)))); /* Round-up of y (SI) for integer index */ if (temp_coord < 0) { Converted_point[1] = -(-temp_coord+0.5); } else { Converted_point[1]=temp_coord+0.5; } /* For (u, v, w) => z conversion */ temp_coord=(((double)point_coord[0]*(Zc[0]*Zc[2]*(1-cos(angle_about_Zc)))+ (double)point_coord[1]*(-Zc[0]*sin(angle_about_Zc))+ (double)point_coord[2]*(Zc[2]*Zc[2]+Zc[0]*Zc[0]*cos(angle_about_Zc)))); /* Round-up of z (AP) for integer index */ if (temp_coord < 0) { Converted_point[2] = -(-temp_coord+0.5); } else { Converted_point[2]=temp_coord+0.5; } /* Conversion of (x, y, z) into the MATLAB index system */ if ( (m-(iso_z-slice_origin_z)-Converted_point[2]-1) >= 0 && (m-(iso_z-slice_origin_z)-Converted_point[2]-1) <= m-1 && (Converted_point[0]-(slice_origin_x-iso_x)) >= 0 && (Converted_point[0]-(slice_origin_x-iso_x)) <= n-1 && (Converted_point[1]-(slice_origin_y-iso_y)) >= 0 && (Converted_point[1]-(slice_origin_y-iso_y)) <= l-1 ) PAGE 166 166 { coord_index=(m-(iso_z-slice_origin_z)-1-Converted_point[2]) + (Converted_point[0]-(slice_origin_x-iso_x))*m + (Converted_point[1]-(slice_origin_y-iso_y))*m*n; /* Convolution for collimator angle; Dcal*PDF */ te mp = *(dose_in_matrix + coord_index) filter[fi]; temp_I U = *(dose_in_matrix_IU + co ord_index) filter[fi]; } else { temp=0.0; temp_IU=0.0; } sum_temp=sum_temp + temp; sum_temp_IU=sum_temp_IU + temp_IU; } /* Substitution of temporary matrices with the output matrices */ *(dose_out+k+i*m+j*m*n)=sum_temp; /* Dcal convolved with collimator angle errors */ sum_temp = 0.0; *(dose_out_IU+k+i*m+j*m*n)=sum_temp_IU; /* I convolved with collimator angle errors */ sum_temp_IU = 0.0; } } } } [Subroutine Code B3-3] Convolution for pitch /* ============================================================= Source code name: mex_SOU_pitch_conv_with_pen.c This is a subroutine ME X-file for MATLAB Code 3. Convolution for pitch ============================================================= */ #include "mex.h" #include "math.h" /* The gateway routine ////////////////////////////// */ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { /* Declaration of Variables */ const int *dims; /* Dimension of the input matrix */ double *dose_out, *dose_out_IU ; /* Dose output and IU output matrices */ double *dose_in_matrix, *dose_in_matrix_IU; /* Dose input and IU input matrices */ double *filter; /* PDF for collimator convolution*/ double pitch_sys, angle_bin; /* Systematic error of pitch and angular convolution bin size */ int filter_size, mrows, nc ols, lslcs, NDIMs=3; PAGE 167 167 /* PDF size, size of matrix (row, column, slice), and dimension of output matrix */ int slice_origin_y, slice_origin_z; /* Origin of dose distribuiton from Pinnacle (y, z) */ int iso_y, iso_z; /* Isocenter (y, z) */ /* Check for proper number of input and output arguments. */ if (nrhs != 9) mexErrMsgTxt("Nine inputs required."); if (nlhs != 2) mexErrMsgTxt("Two outputs required."); /* Create variables of the input matrices. */ dose_in_matrix = mxGetPr(prhs[0]); dose_in_matrix_IU = mxGetPr(prhs[1]); filter = mxGetPr(prhs[2]); slice_origin_y = mxGetScalar(prhs[3]); slice_origin_z = mxGetScalar(prhs[4]); iso_y = mxGetScalar(prhs[5]); iso_z = mxGetScalar(prhs[6]); pitch_sys = mxGetScalar(prhs[7]); angle_bin = mxGetScalar(prhs[8]); /* Get the dimensions of the input dose matrix and PDF. */ dims = mxGetDimensions(prhs[0]); mrows = dims[0]; ncols = dims[1]; lslcs = dims[2]; filter_size = mxGetN(prhs[2]); /* Check if the first input argument is a 3-D matrix. */ if ( mrows == 1 || ncols == 1 || lslcs == 1) { mexErrMsgTxt("Input matrix must be a 3D matrix."); } /* Create the output matrices. */ plhs[0] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); plhs[1] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); /* Create variables of the output matrices. */ dose_out = mxGetPr(plhs[0]); dose_out_IU = mxGetPr(plhs[1]); /* Call the C subroutine. */ mex_SOU_pitch_conv_with_pen(dose_out, dose_out_IU, dose_in_matrix, dose_in_matrix_IU, filter, mrows, ncols, lslcs, filter_size, slice_origin_y, slice_origin_z, iso_y, iso_z, pitch_sys, angle_bin); } /************************ The C subroutine ************************/ void mex_SOU_pitch_conv_with_pen(double *dose_out, double *dose_out_IU, double *dose_in_matrix, double *dose_in_matrix_IU, double *filter, int m, int n, int l, int f_size, PAGE 168 168 int slice_origin_y, int slice_origin_z, int iso_y, int iso_z, double pitch_sys, double a_bin) { int i, j, k, fi, y_index, z_index, temp_tri, coord_index; double y, z, r, angle, angle_fi; double sum_temp=0.0, sum_temp_IU=0.0, temp=0.0, temp_IU=0.0; for (i = 0; i < n; i++) /* for x coordinate */ { for (j = 0; j < l; j++) /* for y coordinate */ { for (k = 0; k < m; k++) /* for z coordinate */ { /* Coordinate conversion: isocenter => matrix origin */ y=(slice_origin_y-iso_y)+j; z=m-(-slice_origin_z+iso_z)-k-1; r=sqrt(y*y+z*z); /* Pitch angle for convolution */ if (y==0.0 && z>0.0) angle=90.0; else if (y==0.0 && z<0.0) angle=270.0; else if (z==0.0 && y>0.0) angle=0.0; else if (z==0.0 && y<0.0) angle=180.0; else if (y!=0.0 && z!=0.0) { angle=acos(y/r)*180.0/3.1415; if (z < 0.0) angle=360.0-angle; } for (fi = 0; fi PAGE 169 169 } else { temp_tri = (r*sin(angle_fi)+0.5); } z_ index=m-(-slice_origin_z +iso_z)-temp_tri-1; if (y_index>=0 && z_index>=0 && y_index PAGE 170 170 /* Dose input and IU input matrices */ double *filter; /* PDF for collimator convolution*/ double roll_sys, angle_bin; /* Systematic error of roll and angular convolution bin size */ int filter_size, mrows, nc ols, lslcs, NDIMs=3; /* PDF size, size of matrix (row, column, slice), and dimension of output matrix */ int slice_origin_x, slice_origin_z; /* Origin of dose distribuiton from Pinnacle (x, z) */ int iso_x, iso_z; /* Isocenter (x, z) */ /* Check for proper number of input and output arguments. */ if (nrhs != 9) mexErrMsgTxt("Nine inputs required."); if (nlhs != 2) mexErrMsgTxt("Two outputs required."); /* Create variables of the input matrices. */ dose_in_matrix = mxGetPr(prhs[0]); dose_in_matrix_IU = mxGetPr(prhs[1]); filter = mxGetPr(prhs[2]); slice_origin_x = mx GetScalar(prhs[3]); slice_origin_z = mxGetScalar(prhs[4]); iso_x = mxGetScalar(prhs[5]); iso_z = mxGetScalar(prhs[6]); roll_sys = mxGetScalar(prhs[7]); angle_bin = mxGetScalar(prhs[8]); /* Get the dimensions of the in put dose matrix and PDF. */ dims = mxGetDimensions(prhs[0]); mrows = dims[0]; ncols = dims[1]; lslcs = dims[2]; filter_size = mxGetN(prhs[2]); /* Check if the first input argument is a 3-D matrix. */ if ( mrows == 1 || ncols == 1 || lslcs == 1) { mexErrMsgTxt("Input matrix must be a 3D matrix."); } /* Create the output matrices. */ plhs[0] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); plhs[1] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); /* Create variables of the output matrices. */ dose_out = mxGetPr(plhs[0]); dose_out_IU = mxGetPr(plhs[1]); /* Call the C subroutine. */ mex_SOU_roll_conv_with_pen(dose_out, dose_out_ IU, dose_in_matrix, dose_in_matrix_IU, filter, mrows, ncols, lslcs, filter_size, slice_origin_x, slice_origin_z, iso_x, iso_z, roll_sys, angle_bin); } PAGE 171 171 /************************ The C subroutine ************************/ void mex_SOU_roll_conv_with_pen(double *dose_out, double *dose_out_IU, double *dose_in_matrix, double *dose_in_matrix_IU, double *filter, int m, int n, int l, int f_size, int slice_origin_x, int slice_origin_z, int iso_x, int iso_z, double roll_sys, double a_bin) { int i, j, k, fi, x_index, z_index, temp_tri, coord_index; double x, z, r, angle, angle_fi; double sum_temp=0.0, sum_temp_IU=0.0, temp=0.0, temp_IU=0.0; for (i = 0; i < n; i++) /* for x coordinate */ { for (j = 0; j < l; j++) /* for y coordinate */ { for (k = 0; k < m; k++) /* for z coordinate */ { /* Coordinate conversion: isocenter => matrix origin */ x=(slice_origin_x-iso_x)+i; z=m-(-slice_origin_z+iso_z)-k-1; r=sqrt(x*x+z*z); /* Roll angle for convolution */ if (z==0.0 && x>0.0) angle=90.0; else if (z==0.0 && x<0.0) angle=270.0; else if (x==0.0 && z>0.0) angle=0.0; else if (x==0.0 && z<0.0) angle=180.0; else if (z!=0.0 && x!=0.0) { angle=acos(z/r)*180.0/3.1415; if (x < 0.0) angle=360.0-angle; } for (fi = 0; fi PAGE 172 172 x_index=-(slice_origin_x-iso_x)+temp_tri; /* Round-up of z (AP) for MATLAB integer index */ if ( r*cos(angle_fi) < 0.0) { temp_tri = (-(-r*cos(angle_fi)+0.5)); } else { temp_tri = (r*cos(angle_fi)+0.5); } z_ index=m-(-slice_origin_z +iso_z)-temp_tri-1; if (x_index>=0 && z_index>=0 && x_index PAGE 173 173 { /* Declaration of Variables */ const int *dims; /* Dime nsion of the input matrix */ double *dose_out, *dose_out_IU ; /* Dose output and IU output matrices */ double *dose_in_matrix, *dose_in_matrix_IU; /* Dose input and IU input matrices */ double *filter; /* PDF for collimator convolution*/ double yaw_sys, angle_bin; /* Systematic error of yaw and angular convolution bin size */ int filter_size, mrows, nc ols, lslcs, NDIMs=3; /* PDF size, size of matrix (row, column, slice), and dimension of output matrix */ int slice_origin_x, slice_origin_y; /* Origin of dose distribuiton from Pinnacle (x, y) */ int iso_x, iso_y; /* Isocenter (x, y) */ /* Check for proper number of input and output arguments. */ if (nrhs != 9) mexErrMsgTxt("Nine inputs required."); if (nlhs != 2) mexErrMsgTxt("Two outputs required."); /* Create variables of the input matrices. */ dose_in_matrix = mxGetPr(prhs[0]); dose_in_matrix_IU = mxGetPr(prhs[1]); filter = mxGetPr(prhs[2]); slice_origin_x = mx GetScalar(prhs[3]); slice_origin_y = mxGetScalar(prhs[4]); iso_x = mxGetScalar(prhs[5]); iso_y = mxGetScalar(prhs[6]); yaw_sys = mxGetScalar(prhs[7]); angle_bin = mxGetScalar(prhs[8]); /* Get the dimensions of the in put dose matrix and PDF. */ dims = mxGetDimensions(prhs[0]); mrows = dims[0]; ncols = dims[1]; lslcs = dims[2]; filter_size = mxGetN(prhs[2]); /* Check if the first input argument is a 3-D matrix. */ if ( mrows == 1 || ncols == 1 || lslcs == 1) { mexErrMsgTxt("Input matrix must be a 3D matrix."); } /* Create the output matrices. */ plhs[0] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); plhs[1] = mxCreateNumericArray(NDIMs, dims, mxDOUBLE_CLASS, mxREAL); /* Create variables of the output matrices. */ dose_out = mxGetPr(plhs[0]); dose_out_IU = mxGetPr(plhs[1]); /* Call the C subroutine. */ PAGE 174 174 mex_SOU_yaw_conv_with_pen(dose_o ut, dose_out_IU, dose_ in_matrix, dose_in_matrix_IU, filter, mrows, ncols, lslcs, filter_size, slice_origin_x, slice_origin_y, iso_x, iso_y, yaw_sys, angle_bin); } /************************ The C subroutine ************************/ void mex_SOU_yaw_conv_with_pen(double *dose_out, double *dose_out_IU, double *dose_in_matrix, double *dose_in_matrix_IU, double *filter, int m, int n, int l, int f_size, int slice_origin_x, int slice_origin_y, int iso_x, int iso_y, double yaw_sys, double a_bin) { int i, j, k, fi, x_index, y_index, temp_tri, coord_index; double x, y, r, angle, angle_fi; double sum_temp=0.0, sum_temp_IU=0.0, temp=0.0, temp_IU=0.0; for (i = 0; i < n; i++) /* for x coordinate */ { for (j = 0; j < l; j++) /* for y coordinate */ { for (k = 0; k < m; k++) /* for z coordinate */ { /* Coordinate conversion: isocenter => matrix origin */ x=(slice_origin_x-iso_x)+i; y=(slice_origin_y-iso_y)+j; r=sqrt(x*x+y*y); /* Yaw angle for convolution */ if (x==0.0 && y>0.0) angle=90.0; else if (x==0.0 && y<0.0) angle=270.0; else if (y==0.0 && x>0.0) angle=0.0; else if (y==0.0 && x<0.0) angle=180.0; else if (x!=0.0 && y!=0.0) { angle=acos(x/r)*180.0/3.1415; if (y < 0.0) angle=360.0-angle; } for (fi = 0; fi PAGE 175 175 temp_tri = (-(-r*cos(angle_fi)+0.5)); } else { temp_tri = (r*cos(angle_fi)+0.5); } x_index=-(slice_origin_x-iso_x)+temp_tri; /* Round-up of y (SI) for MATLAB integer index */ if ( sin(angle_fi) < 0.0) { temp_tri = (-(-r*sin(angle_fi)+0.5)); } else { temp_tri = (r*sin(angle_fi)+0.5); } y_index=-(slice_origin_y-iso_y)+temp_tri; if (x_index>=0 && y_index>=0 && x_index PAGE 176 176 LIST OF REFERENCES 1National Cancer Institute, Radiation Therapy and You: Support for People with Cancer (National Cancer Institute, 2007). 2E. 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Mohan, "Quantifying the effe ct of intrafraction motion during breast IMRT planning and dose delivery," Med. Phys. 30, 552-562 (2003). PAGE 188 188 144P. C. M. Koper, W. D. Heemsbergen, M. S. Hoogeman, P. P. Jansen, G. A. M. Hart, A. J. Wijnmaalen, M. van Os, L. J. Boersma, J. V. Le besque, and P. Levendag, "Impact of volume and location of irradiated rectum wa ll on rectal blood loss after radiothe rapy of prostate cancer," Int. J. of Radiat. Oncol. Biol. Phys. 58, 1072-1082 (2004). 145B. Emami, J. Lyman, A. Brown, L. Coia, M. Goitein, J. E. Munzenrider, B. Shank, L. J. Solin, and M. Wesson, "Tolerance of normal tissue to ther apeutic irradiation," Int. J. Radiat. Oncol. Biol. Phys. 21, 109-122 (1991). PAGE 189 189 BIOGRAPHICAL SKETCH Hosang Jin was born in Na mwon, South Korea, in 1975. He r eceived his B.S. degree in nuclear engineering from Seoul National Univers ity, Seoul, South Korea. He served in the Republic of Korea Army from 1997 through 1999 after his junior year of college. He joined a graduate program in medical physics after grad uating of college in 2001 and received his M.S. 2 years later from the Catholic University of Korea, Seoul, South Korea. While working towards his masters degree years, he conducted research on medical image registration and analysis of digital subtraction angiography (DSA), com puted tomography (CT), magnetic resonance imaging (MRI), single photon emission computed tomography (SPECT), and electric portal imaging (EPI) using Visual C++, MATLAB, and ID L. In 2003, he entered a doctoral program in nuclear and radiological engineeri ng (medical physics) at the Univer sity of Florida, Gainesville, Florida. Hosang will receive a Ph.D. in May of 2008. He married Sunjung Eum in 2004 and currently they are expecting their first child. Mr. Jin is the co-inventor of a patented phantom for accuracy evaluation of image registration. He has developed computer software tools for computing dose uncertainty in intensity-modulated radiation therapy (IMRT) and verifying pa tient setup using MATLAB as part of his doctoral research. He has published and presented dozen s of scientific and technical articles. He received the nationa l nuclear fellowship from the Korean nuclear R&D program in 2003, the outstanding academic accomplishment award from the University of Florida international center in 2004, and the young medical physicist award from the Korean society of medical physicists in 2005. His main research interests are in uncertain ty prediction of IMRT, image-guided radiation therapy (IGRT) and adaptive radiation thera py using kV cone-beam CT, multimodal image PAGE 190 190 registration, and verifica tion of patient setup and immobiliza tion. Currently, he is working on a project with his collegues at the Unversity of Florida to improve the quality of IMRT. |