Citation
Intensity-Modulated Radiosurgery Treatments Derived by Optimizing Delivery of Sphere-Packing Plans

Material Information

Title:
Intensity-Modulated Radiosurgery Treatments Derived by Optimizing Delivery of Sphere-Packing Plans
Creator:
Hermansen, Michael C
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (126 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
BOVA,FRANK J
Committee Co-Chair:
HINTENLANG,DAVID ERIC
Committee Members:
GILLAND,DAVID R
Graduation Date:
12/18/2015

Subjects

Subjects / Keywords:
Algorithms ( jstor )
Collimators ( jstor )
Diameters ( jstor )
Dosage ( jstor )
Fluence ( jstor )
Gantry cranes ( jstor )
Geometric lines ( jstor )
Radiosurgery ( jstor )
Spheres ( jstor )
Term weighting ( jstor )
Biomedical Engineering -- Dissertations, Academic -- UF
dampening -- fluence -- imrt -- radiosurgery -- sphere-packing
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Biomedical Engineering thesis, M.S.

Notes

Abstract:
Radiosurgery involves the precise delivery of a full radiation prescription dose in a single fraction, rather than multiple fractions over a period of time. This ability is due to precise stereotactic imaging of the target, the ability to precisely deliver the prescribed dose, and steep dose gradients to spare healthy tissues. The radiosurgical plan optimization technique known as sphere-packing has been developed into a highly effective automated planning tool. This technique involves filling a tumor volume with spheres of radiation dose of varying diameters and intensities. The goal is to completely cover volume with a very steep dose gradients aligned to the tumor and the normal tissue boundary. While this planning method is effective, each spherical dose distribution is delivered independently. The result is a treatment that increases in time as more sphere are required to pack the target volume. Post-processing optimization of sphere-packing plan to remove unnecessary dose can increase the efficiency of delivery, while maintaining the tumor coverage and steep dose gradient. This is accomplished by transforming a multiple sphere-packing plan into an IMRT plan using multi-leaf collimators to irradiate multiple spheres simultaneously and dampening the dose profile to remove unnecessary intra-target hotspots. ( 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 (M.S.)--University of Florida, 2015.
Local:
Adviser: BOVA,FRANK J.
Local:
Co-adviser: HINTENLANG,DAVID ERIC.
Statement of Responsibility:
by Michael C Hermansen.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Hermansen, Michael C. 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.
Classification:
LD1780 2015 ( lcc )

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INTENSITY MODULATED RADIOSURGERY TREATMENTS DERIVED BY OPTIMIZING DELIVERY OF SPHERE PACKING PLANS By MICHAEL C. HERMANSEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2015

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2 © 2015 Michael C. Hermansen

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3 To my loving family for all the support they have given to me while being so far away

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4 ACKNOWLEDGMENTS I would like to acknowledge first and foremost my advisor and committee chair, Dr. Frank Bova, for taking me on as one of his graduate students. It has been an honor and a privilege to work under his t utelage. He sincerely makes a point to teach me every opportunity that he can. I have learned more from our short meetings than all the time I have spent in lectures combined. He challenges me and tests me in order to expand my understanding and skill sets . I am profoundly grateful to have a chair in his lab. Secondly, I would like to acknowledge the other members of my committee, Dr. David Hintenlang and Dr. David Gilland. I have spent many hours in their lectures trying to answer their most challenging qu estions. I appreciate how both Dr. Hintenlang and Dr. Gilland fostered class environments where I never felt afraid to open my mouth. They have been open to talk cordially, which helped a student far from home and unsure of what he was doing feel immediate ly he was where he was meant to be. Thirdly, I would like to acknowledge the work by previous graduate students, principally Dr. Bonnie Velsco and Dr. Theodore St. John, who set the foundation for my research project. I have not met either of them, but I l ook forward to thanking them personally one day. Fourthly, I would like acknowledge the support of my friends and classmates. I never would have made it through two straight years of arduous classes without your help. I also never would have succeeded in D gave to me. He prepared me for working for Dr. Bova, as well as being a true friend. made my way to the other side of the country. Their prayers have strengthened me in every step of this journey far more than they will ever know.

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TABLE OF CO NTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 8 LIST OF FIGURES ................................ ................................ ................................ ....................... 14 LIST OF OBJECTS ................................ ................................ ................................ ....................... 20 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 21 ABSTRA CT ................................ ................................ ................................ ................................ ... 22 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 23 History of Stereotactic Radiosurgery ................................ ................................ ...................... 23 SRS at the University of Florida ................................ ................................ ............................. 23 2 PREVIOUS WORK ................................ ................................ ................................ ................ 26 Work b y Theodore J. St. John ................................ ................................ ................................ 26 Work by Bonnie Velasco ................................ ................................ ................................ ........ 27 3 METHODS ................................ ................................ ................................ ............................. 30 Motivation ................................ ................................ ................................ ............................... 30 Program ................................ ................................ ................................ ................................ ... 30 Arcs versus Static Beams ................................ ................................ ................................ 30 Dose Algorithm Formulism ................................ ................................ ............................. 31 TPS Dose Form ................................ ................................ ................................ ............... 32 OAR Fits ................................ ................................ ................................ .......................... 32 TPR Tables ................................ ................................ ................................ ...................... 33 Programming Languages ................................ ................................ ................................ . 34 C++ ................................ ................................ ................................ ........................... 34 MATLAB ® ................................ ................................ ................................ ............... 34 Dose Algorithm Validation ................................ ................................ ................................ ..... 34 Plan Configurations ................................ ................................ ................................ ......... 34 Single beam ................................ ................................ ................................ .............. 34 Multi beam ................................ ................................ ................................ ............... 35 Single sphere ................................ ................................ ................................ ............ 35 Multi sphere ................................ ................................ ................................ ............. 36 Validation Param eters ................................ ................................ ................................ ..... 36 Dose at isocenter ................................ ................................ ................................ ...... 37

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6 Maximum dose ................................ ................................ ................................ ......... 37 1 Dimensional line dose profiles ................................ ................................ .............. 3 7 Fluence Dampening ................................ ................................ ................................ ................ 38 Single Sou rce Point SRS Method Corrections ................................ ................................ 39 Geometric and attenuation corrections ................................ ................................ ..... 39 Combined OF correction ................................ ................................ .......................... 40 Fluence Dampening Methodology ................................ ................................ .................. 41 4 RESULTS ................................ ................................ ................................ ............................... 56 Dose Algorithm Validation of Normal Source Point SRS Method ................................ ........ 56 Single Beam ................................ ................................ ................................ .................... 56 10 mm diameter circularly collimated beam ................................ ............................ 56 20 mm diameter circularly collimated beam ................................ ............................ 57 30 mm diameter circularly collimated beam ................................ ............................ 59 Multi Beam ................................ ................................ ................................ ...................... 60 12 mm beam set inside a 40 mm, with unequal weights: 12 mm < 40 mm ............. 60 12 mm beam set inside a 40 mm, with unequal weights: 12 mm > 40 mm ............. 62 Two 16 mm beams set laterally, with equal weights: #1 = #2 ................................ . 64 Two 16 mm beams set laterally, with unequal weights: #1 > #2 ............................. 66 Two 16 mm beams set laterally, with unequal weights: #1 < #2 ............................. 68 14 mm beam set on edge of 40 mm, with unequal weights: 14 mm < 40 mm ........ 70 14 mm beam set on edge of 40 mm, with unequal weights: 14 mm > 40 mm ........ 72 Single sphere ................................ ................................ ................................ ................... 74 10 mm diameter circularly collimated sphere ................................ .......................... 74 20 mm diameter circularly collimated sphere ................................ .......................... 77 30 mm diameter circularly collimated sphere ................................ .......................... 79 Multi sphere ................................ ................................ ................................ .................... 82 Two 16 mm spheres offset laterally, with equal beam weights: #1 = #2 ................. 82 Two 16 mm spheres offset laterally, with equal beam weights: #1 > #2 ................. 84 Two 16 mm spheres offset laterally, with equal beam weights: #1 < #2 ................. 86 Two 16 mm spheres above and below, with equal beam weights: #1 = #2 ............. 88 Two 16 mm spheres above and below, with equal beam weights: #1 > #2 ............. 90 Two 16 mm spheres above and below, with equal beam weights: #1 < #2 ............. 92 Dose Algorithm Validation of Single Source Point SRS Method ................................ .......... 94 Dose at Isocenter ................................ ................................ ................................ ............. 94 Multi beam ................................ ................................ ................................ ............... 94 Multi sphere ................................ ................................ ................................ ............. 95 Maximum Dose ................................ ................................ ................................ ............... 96 Multi beam ................................ ................................ ................................ ............... 96 Multi sphere ................................ ................................ ................................ ............. 97 1 Dimensional Line Dose Profiles ................................ ................................ .................. 97 Multi beam ................................ ................................ ................................ ............... 97 Multi sphere ................................ ................................ ................................ ........... 102 Fluence Dampening ................................ ................................ ................................ .............. 106 Overlap Removal Method ................................ ................................ ............................. 107 1 Di mensional line dose profiles ................................ ................................ ............ 107

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7 1 Dimensional line dose profiles results analysis ................................ .................. 110 Dose intensity maps ................................ ................................ ............................... 111 Dose int ensity map results analysis ................................ ................................ ........ 113 Dose Correction of Overlap Removal Method ................................ .............................. 114 OUT voxel dose correction method ................................ ................................ ....... 115 R x dose voxel comparison analysis ................................ ................................ ........ 116 OUT voxel dose correction results analysis ................................ ........................... 120 5 CONCLUSIONS AND DISCUSSIONS ................................ ................................ .............. 121 Dose Algorithm ................................ ................................ ................................ .................... 121 Conclusion f or Dose Algorithm Validation ................................ ................................ .. 121 Normal source point SRS method conclusion ................................ ........................ 121 Single source point SRS point method conclusion ................................ ................ 121 Discussion of Dose Algorithm Validation ................................ ................................ .... 122 Fluence Dampening ................................ ................................ ................................ .............. 123 Conclusion for Fluence Dampening ................................ ................................ .............. 123 Overlap removal method conclus ion ................................ ................................ ...... 123 OUT voxel correction method conclusion ................................ ............................. 123 Discussion of Fluence Dampening ................................ ................................ ................ 124 LIST OF REFERENCES ................................ ................................ ................................ ............. 125 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 126

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8 LIST OF TABLES Table page 2 1 Different cases and the MUs needed after fluence dampening as a factor the original MUs. ................................ ................................ ................................ ................................ ... 29 4 1 The dose at isocenter for a 10 mm beam. ................................ ................................ .......... 56 4 2 The maximum dose for a 10 mm beam. ................................ ................................ ............ 56 4 3 The spatial difference between isodose contours for a 10 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ .................... 56 4 4 The dose percent difference between spatial diameters for a 10 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ ............... 57 4 5 The dose at isocenter for a 20 mm beam. ................................ ................................ .......... 57 4 6 The maximum dose for a 20 mm beam. ................................ ................................ ............ 57 4 7 The spatial difference between isodose contours for a 20 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ .................... 58 4 8 The dose percent difference between spatial diameters for a 20 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ ............... 58 4 9 The dose at isocenter for a 30 mm beam. ................................ ................................ .......... 59 4 10 The maximum dose for a 30 mm beam. ................................ ................................ ............ 59 4 11 The spatial difference between isodose contours for a 30 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ .................... 59 4 12 The dose percent difference between spatial diameters for a 30 mm beam for the UF in house TPS and the dose algorithm. ................................ ................................ ............... 60 4 13 The dose at isocenter for a setup consisting of a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. ................................ ................................ .... 61 4 14 The maximum dose for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. ................................ ................................ ................................ ........ 61 4 15 The spatial difference between isodose contours for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted. ................................ ................................ ....... 61 4 16 The dose percent difference between spatial diameters for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. ................................ ........................ 61

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9 4 17 The dose at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. ................................ ................................ ................................ ....... 62 4 18 The maximum dose for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. ................................ ................................ ................................ ....... 63 4 19 The spatial difference between isodose contours for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. ................................ ............................ 63 4 20 The dose percent difference between spatial diameters for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. ................................ ....................... 63 4 21 The dose at isocenter for two 16 mm beams offset laterally by 18 mm with equal beam weights. ................................ ................................ ................................ .................... 64 4 22 The maximum dose for two 16 mm beams offset laterally by 18 mm with equal beam weights. ................................ ................................ ................................ .............................. 65 4 23 The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with equal beam weights. ................................ ................................ ... 65 4 24 The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm from each other so as to not overlapping with equal beam weights. ................................ ................................ ................................ .............................. 65 4 25 The dose at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. ................................ ................................ ................................ .... 66 4 26 The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. ................................ ................................ ................................ .... 66 4 27 The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. ................................ ....................... 67 4 28 The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. ................................ ....................... 67 4 29 The dose at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. ................................ ................................ ................................ ..... 68 4 30 The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. ................................ ................................ ................................ ..... 68 4 31 The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. ................................ ........................ 69 4 32 The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. ................................ ........................ 69

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10 4 33 The dose at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ................................ ................................ ............................ 70 4 34 The maximum dose for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ................................ ................................ ................................ . 70 4 35 The spatial difference between isodose contours for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ................................ ..................... 71 4 36 The dose percent difference between spatial diameters for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ................................ ........ 71 4 37 The dose at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. ................................ ................................ ........................... 72 4 38 The maximum dose for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. ................................ ................................ ................................ 72 4 39 The spatial difference between isodose contours for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. ................................ .................... 73 4 40 The dose percent difference between spatial diameters for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. ................................ ....... 73 4 41 The dose at isocenter for a 10 mm sphere. ................................ ................................ ......... 74 4 42 The maximum dose for a 10 mm sphere. ................................ ................................ ........... 74 4 43 The spatial difference between isodose contours for a 10 mm sphere. ............................. 76 4 44 The dose percent difference between spatial diameters for a 10 mm sphere. .................... 76 4 45 The dose at isocenter for a 20 mm sphere. ................................ ................................ ......... 77 4 46 The maximum dose for a 20 mm sphere. ................................ ................................ ........... 77 4 47 The spatial difference between isodose contours for a 20 mm sphere. ............................. 79 4 48 The dose percent difference between spatial diameters for a 20 mm sphere. .................... 79 4 49 The dose at isocenter for a 30 mm sphere. ................................ ................................ ......... 79 4 50 The maximum dose for a 30 mm sphere. ................................ ................................ ........... 80 4 51 The spatial difference between isodose contours for a 30 mm sphere. ............................. 81 4 52 The dose percent difference between spatial diameters for a 30 mm sphere. .................... 8 1

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11 4 53 The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with equal beam weights. ................................ ................................ ................................ .................... 82 4 54 The maximum dose for two 16 mm beams offset laterally by 18 mm with equal beam weights. ................................ ................................ ................................ .............................. 82 4 55 The spatial difference between isodose contours for two 16 mm spheres offset laterally by 17 mm with equal beam weights. ................................ ................................ ... 83 4 56 The dose percent difference between spatial diameters for two 16 offset laterally by 18 mm with equal beam weights. ................................ ................................ ...................... 83 4 57 The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2. ................................ ................................ ................................ .... 84 4 58 The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. ................................ ................................ ................................ .... 84 4 59 The spatial difference between isodose contours for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2. ................................ ....................... 85 4 60 The dose percent difference between spatial diameters for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2. ................................ ....................... 85 4 61 The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. ................................ ................................ ................................ ..... 86 4 62 The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 lower higher than #2. ................................ ................................ ................................ ................... 86 4 63 The spatial difference between isodose contours for two 16 mm spheres offset laterally by17 mm with #1 weighted lower than #2. ................................ ......................... 87 4 64 The dose percent difference between spatial diameters for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. ................................ ........................ 87 4 65 The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with equal weights. ................................ ................................ ........... 88 4 66 The maximum dose for two 16 mm spheres set above and below each other separated by 17 mm with equal weights. ................................ ................................ ........... 88 4 67 The spatial difference between isodose contours for two 16 mm spheres set above and below each other separated by 17 mm with equal weights. ................................ ........ 89 4 68 The dose percent difference between spatial diameters for two 16 mm spheres set above and below each other separated by 17 mm with equa l weights. ............................. 89

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12 4 69 The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted higher than #2. ................................ ..................... 90 4 70 The maximum dose for two 16 mm spheres set above and below each other separated by 17 mm with equal with #1 weighted higher than #2. ................................ .... 90 4 71 The spatial difference between isodose contours for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted high er than #2. .................. 91 4 72 The dose percent difference between spatial diameters for two 16 mm spheres set above and below each other se parated by 17 mm with #1 weighted higher than #2. ........ 91 4 73 The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. ................................ ...................... 92 4 74 The maximum dose for two 16 mm diameter circularly collimated sph eres set above and below each other separated by 17 mm with equal with #1 weighted lower than #2. ................................ ................................ ................................ ................................ ....... 92 4 75 The spatial difference between isodose contours for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. ................... 93 4 76 The dose percent difference between spatial diameters for two 16 mm diameter spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. ................................ ................................ ................................ ............................... 93 4 77 The dose at isocenter for each multi beam setup with each beam weighting combination for the single source point SRS method. ................................ ....................... 94 4 78 The dose at isocenter for each multi sphere setup with sphere beam weighting combination for the single source point SRS method. ................................ ....................... 95 4 79 The maximum dose for each multi beam setup with each beam weighting combination for the single source point SRS method. ................................ ....................... 96 4 80 The maximum dose for each multi sphere setup with each sphere weighting combination for the single source point SRS method. ................................ ....................... 97 4 81 The spatial difference between isodose contours for each multi beam setup with each beam weighting combination for the single source point SRS method. .......................... 101 4 82 The dose percent difference between spatial diameters for each multi beam setup with each beam weighting combinat ion for the single source point SRS method. .......... 102 4 83 The spatial difference between isodose contours for each multi sphere setup with each sphere weighting combination for the single source point SRS method. ................ 105

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13 4 84 The dose percent difference between spati al diameters for each multi beam setup with each beam weighting combination for the single source point SRS method. .......... 106 4 85 The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset lateral ly by 17 mm with equal sphere weighting (#1 = #2). ................................ ................................ .... 117 4 86 The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2). ................................ ................................ 118 4 87 The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 < #2). ................................ ................................ 118 4 88 The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with equal sphere weighting (#1 = #2). ................................ ................................ .... 119 4 89 The percentage of the target volume matched, missed, and added after th e overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 > #2). ................................ ................................ 119 4 90 The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 < #2). ................................ ................................ 120

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14 LIST OF FIGURES Figure page 1 1 Photograph of the first stereotactic instrument use for tumor localization and ................................ ................................ ................................ . 25 1 2 tem based on a stereotactic head ring attached to a floorstand. The linac rotates with a circular collimator mounted to the gantry head. Image taken from ............. 25 2 1 Beam eye view of the fluence map of multiple spheres at a single table and gantry angle combination. The grayscale intensity is proportional t o the fluence in the ............................ 28 2 2 Beam modulated ............................ 28 3 1 This figure shows the beam paths of a five arc set for a single sphere. This figure was radiosurgery ................................ ................. 42 3 2 This figure shows the 15 static beam set to replace a five arc set for a single sphere. Three static beams are used to approximate each arc. This figure was taken from ................................ ................................ . 42 3 3 This is an example of a dose form with a single sphere. ................................ ................... 43 3 4 The geometric penumbra produced by partial obstruction of the source by a collimator. ................................ ................................ ................................ .......................... 44 3 5 The effects of the empirical fit parameters, and on the OARs given by Equations 3 3 and 3 4. ................................ ................................ ................................ ....... 44 3 6 Example of axial, coronal, and sagittal MR images of the single beam plan for the 20 mm diameter circularly collimated beam. ................................ ................................ ......... 45 3 7 Example of axial, coronal, and sagittal MR images of the multi beam plan for the 12 mm diameter circularly collimated beam set inside a 40 mm diameter cir cularly collimated beam at equal depths. ................................ ................................ ....................... 46 3 8 Example of axial, coronal, and sagittal MR images of the multi beam plan for the t wo 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other. ................................ ................................ ....................... 47

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15 3 9 Example of a xial, coronal, and sagittal MR images of the multi beam plan for the 14 mm diameter circularly collimated beam overlapping the edge of a 40 mm diameter circularly collimated beam at equal depths. ................................ ................................ ....... 48 3 10 Example of axial, coronal, and sagittal MR images of the Single sphere plan for the 20 mm diameter circularly collimated sphere. ................................ ................................ ... 49 3 11 Example of axial, coronal, and sagittal MR images of the Multi sphere plan for the two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 18 mm from each other. ................................ ................................ ....................... 50 3 12 Example of axial, coronal, and sagittal MR images of the Multi sphere plan fo r the two 16 mm diameter circularly collimated spheres set 17 mm above and below each other axially. ................................ ................................ ................................ ...................... 51 3 13 Example of a 1 dimens ional line dose profile for comparing the spatial and dosimetric accuracy of the dose algorithm along the steep dose gradient. ........................ 52 3 14 This figure shows how two beams for separate spheres can overlap when considered together. The blue and green lines correspond to the intensities of isocenters #1 and intensi ties, and the purple represents the fluence dampened combined beam profile intensity. ................................ ................................ ................................ ............................. 53 3 15 The process by which an SRS via sph ere packing plan using arcs is transformed to an SRS via IMRT plan using MLCs by the single source point SRS Method. ................. 54 3 16 The g eometric translation from the normal source point SRS method to the single source point SRS method is shown. ................................ ................................ ................... 55 4 1 The 1 dimensio nal line dose profiles along the AP axis at isocenter for a 10 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. .......................... 56 4 2 The 1 dimensional line dose profiles along the AP axis at isocenter for a 20 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. .......................... 58 4 3 The 1 dimensional line dose profiles along the AP axis at isocenter for a 30 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. .......................... 59 4 4 The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. ............................ 61 4 5 The 1 dimensional line dose profiles the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. ................................ .......... 63 4 6 The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset laterally 18 mm with equal beam weights. ................................ .............................. 65

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16 4 7 The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with # 1 weighted higher than #2. ................................ ............. 67 4 8 The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset lateral ly by 18 mm with #1 weighted lower than #2. ................................ .............. 69 4 9 The 1 dimensional line dose profiles the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ............................. 71 4 10 The 1 dimensional line dose profiles the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. ............................ 73 4 11 The 1 dimensional line dose profiles along the AP axis at isocenter for a 10 mm sphere. ................................ ................................ ................................ ................................ 75 4 12 The 1 dimensional line dose profiles along the Lat axis at isocenter for a 10 mm sphere. ................................ ................................ ................................ ................................ 75 4 13 The 1 dimensional line dose profiles along the Ax axis at isocenter for a 10 mm sphere. ................................ ................................ ................................ ................................ 76 4 14 The 1 dimensional line dose profiles along the AP axis at isocenter for a 20 mm sphere. ................................ ................................ ................................ ................................ 77 4 15 The 1 dimensional line dose profiles along the Lat axis at isocenter for a 20 mm sphere. ................................ ................................ ................................ ................................ 78 4 16 The 1 dimensional line dose profiles along the Ax axis at isocenter for a 20 mm sphere. ................................ ................................ ................................ ................................ 78 4 17 The 1 dimensional line dose profiles along the AP axis at isocenter for a 30 mm sphere. ................................ ................................ ................................ ................................ 80 4 18 The 1 dimensional line dose p rofiles along the Lat axis at isocenter for a 30 mm sphere. ................................ ................................ ................................ ................................ 81 4 19 The 1 dimensional line dose profiles along the Ax axis at iso center for a 30 mm sphere. ................................ ................................ ................................ ................................ 81 4 20 The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offs et laterally by 17 mm with equal beam weights. ................................ ............ 83 4 21 The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2. ................................ 85 4 22 The 1 dimensional line dose profiles along th e Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. ................................ . 87

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17 4 23 The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with equal weights. ........... 89 4 24 The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted higher than #2. ................................ ................................ ................................ ............................... 91 4 25 The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weigh ted lower than #2. ................................ ................................ ................................ ............................... 93 4 26 The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. ............................ 98 4 27 The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. .......................... 98 4 28 The 1 dimensional line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with equal beam weights. ................................ .............. 99 4 29 The 1 dimensional line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally 18 mm with #1 weighted higher than #2. ................................ ....... 99 4 30 The 1 dimension al line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. ................................ . 100 4 31 The 1 dimensional line dose profiles along the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted lower. ............ 100 4 32 The 1 dimensional line dose profiles along the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm weighted higher. ..................... 101 4 33 The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with equal beam weights. ................................ .......... 102 4 34 The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weight ed higher than #2. .............................. 103 4 35 The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset lat erally by 17 mm with #1 weighted lower than #2. ............................... 103 4 36 The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with equal weights. .......................... 104 4 37 The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with #1 weighted higher than #2. ..... 104

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18 4 38 T he 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with #1 weighted lower than #2. ...... 105 4 39 The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with equal sphere weighting (#1 = #2). ................................ .. 107 4 40 The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2). .............................. 108 4 41 The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with unequal s phere weighting (#1 < #2). .............................. 108 4 42 The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset axi ally by 17 mm with equal sphere weighting (#1 = #2). ................................ .... 109 4 43 The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset axially 17 mm with unequal sphere weighting (#1 > #2). ................................ ..... 109 4 44 The effect of dampening on a 1 dimensiona l line dose profile for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 < #2). ................................ 110 4 45 Dose intensit y maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with equal weights (#1 = #2). ................................ ........................... 111 4 46 Dose intensity maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 > #2). ................................ ....................... 111 4 47 Dose intensity maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 < #2). ................................ ....................... 112 4 48 Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with equal weights (#1 = #2). ................................ ................. 112 4 49 Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 > #2). ................................ ............. 113 4 50 Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 < #2). ................................ ............. 113 4 51 Analysis of the target volume following dampening using the overlap removal method. The green marks are voxel at the R x dose level, and the red crosses a re voxels below the R x dose level. ................................ ................................ ....................... 114 4 52 The distribution of OUT voxels, in the region highlighted in red, of two adjacent sph eres. ................................ ................................ ................................ ............................. 115 4 53 Effect of the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with equal sphere weighting (#1 = #2). ................................ .. 11 7

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19 4 54 Effect of the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2). .............................. 117 4 55 Effect of the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 < #2). .............................. 118 4 56 Effect of the overlap removal metho d with dose correction for two 16 mm spheres offset axially by 17 mm with equal sphere weighting (#1 = #2). ................................ .... 118 4 57 Effect of the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 > #2). ................................ 119 4 58 Effect of the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 < #2). ................................ 119

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20 LIST OF OBJECTS Object page 3 1 Pdf of the .cpp file containing ................................ ....... 34

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21 LIST OF ABBREVIATIONS AP Anterior posterior Ax Axial BRW Brown Roberts Wells IMRT Intensity modulated radiotherapy Lat Lateral Linac Linear accelerator MLCs Multi leaf collimators MUs Monitor Units OAR Off axis ratio OF Output factor R x Prescription SAD Source to axis distance SRS Stereotactic radiosurgery SSD Source to surface distance STD Source to target distance TPR Tissue phantom ratio TPS Treatment planning system UF University of Florida

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22 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Mas ter of Science INTENSITY MODULATED RADIOSURGERY TREATMENTS DERIVED BY OPTIMIZING DELIVERY OF SPHERE PACKING PLANS By Michael C. Hermansen December 2015 Chair: Frank J. Bova Major: Biomedical Engineering Radiosurgery involves the precise delivery of a full radiation prescription dose in a single fraction, rather than multiple fractions over a period of time. This ability is due to precise stereotactic imaging of the target, the ability to precisely deliver the prescribed dose, and steep dose gradients t o spare healthy tissues. The radiosurgical plan optimization technique known as sphere packing has been developed into a highly effective automated planning tool. This technique involves filling a tumor volume with spheres of radiation dose of varying diam eters and intensities. Th e goal is to completely cover volume with a very steep dose gradients aligned to the tumor and the normal tissue boundary. While this planning method is effective, each spherical dose distribution is delivered independent ly . The re sult is a treatment that increases in time as more sphere are required to pack the target volume. Post processing optimization of sphere packing plan to remove unnecessary dose can increase the efficiency of delivery, while maintaining the tumor coverage a nd steep dose gradient. This is accomplished by transforming a multiple sphere packing plan into an IMRT plan using multi leaf collimators to irradiate multiple spheres simultaneously and dampening the dose profile to remove unnecessary intra target hotspo ts .

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23 CHAPTER 1 INTRODUCTION History of Stereotactic Radiosurgery Stereotactic radiosurgery (SRS) was first proposed in 1951 by neurosurgeon Lars Leksell as a means to precisely deliver an external radiation dose to a precise location by utilizing a stereotactic technique . The stereotactic technique was previously developed for guiding needles and electrodes into the brain. Dr. Leksell adapted the stereotactic instrument to guide a beam of radiation, ra ther than a needle or electrode. The arc center ed apparatus allowed the beam guide to rotate around the head while the beam s converged at the target from each angle 1 ( Figure 1 1) . Early on Dr. Leksell experimented with protons, but the expense and difficulty in obtaining a cyclotron to generate the protons made them impractical . 2 Dr. Leksell then developed the first dedicated SRS treatment system, called t he Gamma Knife, using Cobalt 60 as the gamma ray source. It was first installed at the S ophiahemmet Hospita l in 1968 . 3 The modern Gamma Knife utilizes a large number of individ ual Cobalt 60 sources collimated to converge to form a sphere of concentrated dose . A stereotactic head ring w ring allowing for accurate target and beam planning. The collimator helmet rigidly atta ched to ring aligns the large num ber of Cobalt 60 sources and spreads the radiation radially around the head . SRS a t the University of Florida In the 1980 s, linear accelerators (linac) were implemented for the first time proving their usefulness as a platf orms for SRS 4 . Subsequently here at the University of Florida (UF), Physicist Dr. Frank J. Bova, Ph.D, and neurosurgeon Dr. William Friedman, M.D., set out to deve lop a linac based SRS system . 5 They succeeded in formulating a SRS system involving a Brown Roberts Wells (BRW) head ring, to provide the stereotactic precision, attached to

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24 floorstand connected to gimbal mounted external collimating cone on the treatment head of an isocentric linac for photon irradiation. The floorstand connection to the collimating cone reduces the localization errors due to flexing of the gantry as it rotates (see Figure 1 2). They further developed an in house computer based treatment planning system (TPS) which allows for CT early real 6 The speed and accuracy of the UF SRS system using a linac made radiosurgery a practical therapy in terms of speed, accuracy, and cost. The key to the UF SRS system is the use of non coplanar arcs and circular collimators to generate spheres of dose with very steep dose gradients at the tu mor and normal tissue interface. A dose sphere rotating the gantry around a single point in space , the isocenter, while irradiating. Each dose sphere is defined by the location of it s isocenter and the diameter of its circular collimator. A set of arcs become s non coplanar by rotating the couch to a unique fixed angle for each arc. By geometrically covering the full two pi solid angle of the head with non coplanar arcs having unique e ntry and exit points, the dose becomes highly concentrated resulting in a very steep dose gradient falloff at the edge of the sphere . 7 Treatment planning for the UF SRS system first involves using registered computed tomography and magnetic resonance images to clearly identify the tumor, which is referred to as the target volume. The target volume is subsequently packed with the necessary number of non overlapping spheres of appropriate diameter aligned to th e tumor and normal tissue boundary either manually or by an automated algorithm. The pr ocess of packing a target volume with multiple spheres packing 8 The UF SRS system for treatment planning is referred to as SRS planning via sphere packing.

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25 Figure 1 1. Photograph of the first stereotactic instrument use for tumor localization and targeting developed by Figure 1 2 linac rotates with a circular collimator mounted to the gantry head. Im age taken from Friedman et . Linear accelerator

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26 CHAPTER 2 PREVIOUS WORK Work by Theodore J. St. John Dr. Theodore J. St. John devised a system of conducting SRS plans via intensity modulated radiotherapy (IMRT) using m ulti leaf collimators (MLCs) 9 . IMRT utilizes th thin tungsten leaves that can generate irregular radiation portals and through temporal modulation of irregular dose profiles . For target volumes that require multiple sphere s, an SRS plan via IMRT using MLCs has one major advantage over a correspo nding SRS plan via sphere packing: much shorter treatment times. Currently, to treat a multi sphere target volume via sphere packing each sphere , comprised of a set of non coplanar arcs, is treated independent ly . Therefore, the amount of time needed to tre at a multiple sphere target grows linearly with the number of spheres needed to pack the target volume. Conversely, SRS plans via IMRT using MLCs allow for the grouping of beams with common table and gantry angles to simultaneous treatment of the multiple spheres . This can reduce the treatment time to a little more than the time needed to treat a single sphere . sphere targets at one particular table and gantry angle is analyzed region s of overlapping fluence are produce d within the target volume ( Figure 2 1). These regions of overlapping fluence result in high dose accumulation . However, the extra fluence in the overlapping region may not be necessary. M odified profiles with sphere ove rlaps removed could be re produced. These modified plans could be delivered much quicker, while simultaneously maintaining a relatively steep dose gradient compared to the gradient generated SRS plans via sphere packing 10 .

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27 Work by Bonnie Velasco Bonnie Velasco was subsequently tasked with providing a proof of principle for Dr. St. Johns hypothesis for improved treatment times by modifying the fluence maps of multi sphere SRS plans via sphere packing. The modification of the fluence maps to remove the unnecessary dose was 11 each radiation arc for sphere packing was replaced with three static beams. Bonnie ma nually dampened the combined fluence map of each static beam. Two unique overlap removal method involves the reducing overlapping fluence regions to a level equal to the largest single fluence contribution at that location (see Figure 2 involves reducing the entire fluence map to a single fluence value (e.g., the la rgest fluence contribution) 11 . Bonnie succeeded in proving that fluence dampening does produce new fluence maps that take less time to treat and much less beam on time measured in monitor units (MUs). The time needed to treat a dampened sphere packing can be as little as 12% of the original SRS plan via sphere packing treatment time. She also proved the overlap removal method best produces a fluence map that most closely conforms to the original spher e pack plan (see Table 2 1) 11 . The overlap removal method will form the base strategy for fluence dampening later in this work.

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28 Figure 2 1. Beam eye view of the fluence map of multiple sphere s at a single table and gantry angle c ombination. The grayscale intensity is proportional to the fluence in the Figure 2 2. Beam eye views of the fluence map of a four sphere plan. a) Simplified view of the fluence. b) The original fluence map. c) The fluence map after the overlap removal modula ted

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29 Table 2 1. Different cases and the MUs needed after fluence dampening as a factor the original MUs. Case Number of sphere s Factor of decrease in MUs 1 4 1.5 2.8 2 3 1.7 1.8 3 6 1.6 2.6 4 13 1.9 7.8 modulated radiosurgery treatment planning optimization by

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30 CHAPTER 3 METHODS Motivation The key motivation of this work was to determine whether or not fluence dampening of SRS plans via sphere packing will produce superior plans. A fluence dampened plan is considered superior to its corresponding SRS plan via sphere packing if it delivers the prescribed dose to the target volume, requires fewer MUs, less treatment time, and maintains a steep dose gradient. Bonnie succeeded in proving that fluence dampened SRS plans via IMRT using MLCs require fewer MUs and less treatment time 11 . Therefore, the task of proving if fluence dampened SRS plans via IMRT using MLCs will deliver the prescribed dose to the target volume and maintain the steep dose gradient remain was the subject of this work . A program was needed that can take a SRS plan via sphere packing using static beams house TPS and accurately reproduce its 3 dimensional dose distribution, and then perform fluence dampening on it. the in house TP S, and fluence dampening methodology are detailed in this chapter. Program Arcs v ersus Static Beams In SRS plans via sphere packing , each sphere is generated by a set of non coplanar arcs of radiation with a circular collimator attached to the gantry head (see Figure 3 1) . This technique can only be used to produce spherical and elliptical dose distributions. To provide a conformal distribution to an irregularly shaped target volume , multiple sphere s are used to pack the volume. By approximating each arc with three static beams as proposed by Dr. St. John in his dissertation , a set of fluence maps are defined at the table and gantry angle for each static beam for multi sphere plans (see Figure 3 2) . All the beams present at one table and gantry angle

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31 combi combined . can modulated by IMRT using MLCs , allowing for the creation of SRS plans via IMRT using MLCs . Dose Algorithm Formulism A custom dose algorithm was written in C++ to replicate the UF in house TPS's 3 dimensional dose distributions for SRS plans via sphere packing using static beams on which fluence dampening can subsequently be applied. T he program does not compute fluence, but rather computes dose delivered at depth. S ince fluence and dose are proportional, it is assumed the dose (which is actually computed) will be analogous to the fluence. The term fluence dampening will in actuality refer to the removal of unnecessary dose since that is what is actually computed and dampened, but the effect is equivalent to dampening the fluence map. dose profile because analysis was done that can only be quantified in terms of dose. The dose calculation methodology for circular collimat ors was developed by Suh et al . The dose , , at a single point due to a single circular beam is given by Eq. 3 1 12 below: (3 1) where is the dose for the reference set up (typically equal to 1 MU per cGy at a source to axis distance of 100 cm at a depth of 10 cm for a 10 x10 cm field); is the source to axis distance; is the source to target distance at the point of interest ; is the collimator size at ; is the depth at ; is the field size at ; is the off axis distance;

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32 is the output factor defined by the ratio of dose for to the dose for a field s ize of 10 x 10 cm at ; is the tissue phantom ratio, defined by the ratio of the dose at to the dose at ; is the off axis ration defined by the ratio of the dose at an off axis distance to the dose at For multi sphere plans, the d ose at each point is simply the superposition of dose contributions from each beam present in the plan. TPS Dose Form When the UF in house TPS generates a SRS plan via sphere packing plan, it produces a summary dose form of the completed plan. For static, circular beams particularly, it provides each beam s isocenter coordinates in BRW space, the table and gantry angles, the circular collimator diameter and corresponding OF, the TPR and dose at isocenter, and the MUs. Figure 3 3 shows how the summary dose f orm is formatted. The dose algorithm reads in the information from the summary dose form for each beam and then organizes every beam at identical table and gantry angle combinations into beam sets. isocenter to the source point are defined geometrically. After each beam is defined geometrically within the BRW coordinate space, its contribution at any point can be determined by Eq. 3 each point with the dose d istribution volume recreates the 3 dimensional dose distribution for the SRS plan via sphere packing using static beams. OAR Fits The dose algorithm utilizes analytical fits to empirical data provided by Dr. Harold Johns and Dr. John Cunningham in their by textbook, The Physics of Radiology, to compute the OAR 13 . Before t he OAR can be computed, the geometric penumbra must first be computed. The geometric penumbra is given by Eq. 3 2 below:

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33 (3 2) where is the source size; is the distance from the source to depth along the central axis; is the distance from the source to the end of the collimator along the central axis. A diagram of the geometry of how the geometric penumbra equation related to the dose profile is shown in Figure 3 4. Therefore, the analytical OAR fits are given by Eq. 3 3 and 3 4 below: for (3 3) for (3 4 ) where is the off is the geometric penumbra; is the collimation at depth; and are empirical constants that describe the actual geometric penumbra regions; and is the effective transmission through the collimator. The effects of and on the geometric penumbr a of the dose profile are shown in Figure 3 5. TPR Tables The dose form only gives the TPR at SAD for each beam. The corresponding TPR table was found by matching the dose form TPR at isocenter with the table containing that TPR at SAD, for the correspondi ng collimator field size. Thus, the TPR at any depth could be easily accessed. Subsequently, matching the TPR at SAD gave the depth, and source to surface distances (SSD) to be used in a number of geometric calculations.

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34 Programming Languages C++ C++ was c hosen for writing the dose algorithm. This choice was based on speed and compatibility with commercial TPSs (i.e., Eclipse and Pinnacle), which are typically based on C++. Using C++ will allow for easy future integration into a commercial TPS. There is a l ink to the .cpp file in the object below. Object 3 1. Pdf of the .cpp file containing the C++ program code. MATLAB ® MATLAB ® was used to display and analyze the 3 dimensional dose distributions produced by the C++ dose algorithm. Dose Algorithm Validation The dose algorithm was validated by comparing the 3 dimensional dose distributions it generated against the 3 dimensional dose distributions generated by the in house TPS for identical plans. Basic SRS plans via sphere packing using static beams were generated in both the in ho use TPS and the dose algorithm. Plan Configurations Four general plan co nfigurations were used to compare the 3 dimensional dose distribution outputs of the UF in house TPS with the dose algorithm: single b eam , multi beam , s ingle sphere , and m ulti sphere . Single b eam The single beam cy to reproduce the most basic plan configuration, being a single beam for a single isocenter. The single beam plans included the 10 mm, 20 mm, and 30 mm diameter circularly collimated beams to represent small, medium, and large beams respectively. Figure 3 6 shows the single beam plan of the 20 mm

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35 diameter circularly collimated beam on axial, sagittal and coronal MR images from the UF in house TPS. Multi b eam The multi b eam individually overl apping beams. The plan combinations included two beams in basic arrangements: one beam completely inside another beam, one beam overlapping the edge of another beam, and two beams side by side so as to not overlap. The plan setups included a 12 mm diamete r circularly collimated beam set inside a 40 mm diameter circularly collimated beam at equal depth s , two 16 mm diameter circularly collimated beams set at equal depth s and offset laterally 18 mm from each other so as to not overlapping, and a 14 mm diameter circularly collimated beam overlapping the edge of a 40 mm circularly collimated beam at the equal depth s . For each multi beam plan , the relative beam weights were also varied to include equal and both unequal weighting combinations. Figure 3 7 s hows the multi beam plan of the 1 2 mm diameter circularly collimated beam set inside a 40 mm diameter circularly collimated beam at equal depths on axial, sagittal and coronal MR images from the UF in house TPS. Figure 3 8 shows the multi beam plan of the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally by 18 mm on axial, sagittal and coronal MR images from the UF in house TPS. Figure 3 9 shows the multi beam plan of the 14 mm diameter circularly collimated beam overla pping the edge of a 40 mm diameter circularly collimated beam at equal depths on axial, sagittal and coronal MR images from the UF in house TPS. Single sphere The Single sphere dimensio nal dose distribution for a sphere of dose generated by a complete set of static beams on

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36 a single isocenter. The Single sphere plans included the of 10 mm, 20 mm, and 30 mm diameter circularly collimated sphere s to represent small, medium, and large spher es respectively. Figure 3 10 shows the Single sphere plan of the 20 mm diameter circular collimator isocenter on axial, sagittal and coronal MR images from the UF in house TPS. Multi sphere The Multi sphere reproduce 3 dimensional dose distribution of simple two sphere arrangements. The plan combinations included two spheres in basic arrangements: two spheres side by side laterally, and two spheres side by side axially. For Multi sphere configurations, plans included two 16 mm diameter circularly collimated spheres set at equal depth s and offset 17 mm laterally from each other so as to not overlapping, and two 16 mm diameter circularly collimated sphere s set 17 mm above and below each ot her axially so as to not overlapping. For Multi sphere plans, the relative beam weights were also varied to include equal and both unequal weighting combinations. Figure 3 11 shows the Multi sphere plan of the two 16 mm diameter circular ly collimated sphe re s set at equal depths and offset laterally by 17 mm on axial, sagittal and coronal MR images from the UF in house TPS. Figure 3 12 shows the Multi sphere plan of the two 16 mm diameter circularly collimated sphere s set 17 mm above and below each other ax ially on axial, sagittal and coronal MR images from the UF in house TPS. Validation Parameters For each plan, the 3 dimnesional dose distributions for the UF in house TPS and dose algorithm were compared by evaluating the dose at isocenter, the maximum dos e the prescription (R x ) and half R x isodose contours, and the spatial dose agreement of 1 dimensional line dose profiles. The UF in house TPS served as the expected result for each test.

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37 Dose at isocenter The dose at isocenter quantified the absolute nume rical accuracy of the dose algorithm. weight for the intended isocenter by the of which are found in the summary dose form . A percent error relative to the UF in house TPS dose at isocenter for the dose algorithm was computed. The dose at isocenter was computed from information present in the dose form for each isocenter present. For most quality assurance systems, a dose within 3% of the predicted value is considered passing. Therefore, all dose percent errors less than 3% were considered acceptable. Maximum dose The maximum dose quantified the overall 3 numerical accuracy of the dose algorithm. The maximum dose is computed by multiplying the A percent error relative to the UF in computed. The dose at is ocenter was computed from information present in the dose form for each isocenter present. For most quality assurance systems, a dose within 3% of the predicted value is considered passing. Therefore, all percent errors less than 3% were considered accepta ble. 1 D imensional line dose profiles The 1 dimensional line dose profiles provided both geometric and dosimetric verification of the steep dose gradient regions. Graphs of the prescription line dose through isocenter were generated , as shown in Figure 3 1 3 . Computationally, the spatial distance between corresponding isodose points and dose percent difference for corresponding spatial locations in 1 dimensional line dose profiles of the UF in house TPS and dose algorithm were measured for the dose

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38 percentag e range of 20% to 95% of the maximum dose . The statistical maximum, minimum, and mean of the differences for each line profile comparison were compiled. The spatial difference between isodose contours of the dose algorithm and the UF in house TPS was considered acceptable if the spacing was within 3 mm. The dose percent difference at each spatial location between the dose algorithm and the UF in house TPS was considered acceptable if the difference was within 3%. Fluence Dampening For Multi sphere plan s, fluence dampening involves the identification of and removal of dose profile. Figure 3 14 shows how the beams of separate isocenters can overlap. Fluence dampening identify the region of overlapping dose and dampening those specific regions. After combining ence dampened 3 dimensional dose distribution was created. Three different 3 dimensional dose distributions were generated by the dose algorithm using three different calculation methods: normal source point SRS method, single source point SRS method, and single source point SRS method with fluence dampening. The first method treats each isocenter as independent to each other with its corresponding source point, while the second and third methods treat each isocenter as originating from a single source poin t. The third method applies fluence dampening to the single source point SRS method. Figure 3 15 shows the arcs and static beams are organized for each SRS method. It is important to note that the second and third only exist as an option for Multi sphere p lans. The normal source point SRS method replicates the original SRS plan via sphere packing using static beams. Whereas, the single source point SRS method models a single source point

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39 for each beam set to simulate SRS plans via IMRT using MLCs. Fluence dampening was only applied to 3 dimensional dose distributions generated by the single source point SRS method because only SRS plans via IMRT using MLCs have the capability to dampen the fluence. Single Source Point SRS Method Corrections In order to sim ulate an SRS plan via IMRT using MLCs, the single source point SRS method was used, as opposed to SRS plans via sphere packing using static beams using the normal source point SRS method where each isocenter is at SAD relative to its corresponding source p oint. The source point corresponding to the first isocenter was selected to be the central source point for each beam set because the first sphere typically covers the most tumor volume and is weighted the highest. Each subsequent sphere is added and weigh ted accordingly to fill in the remaining target volume not included in the first sphere source point serves as an adequate central location for irradiating the entire target volume for each beam set as would be the case an SRS plan via IMRT using MLCs. Figure 3 16 shows the geometric difference between the normal source point SRS method and the single source point SRS method. Geometric and attenuation corrections rce point of irradiation for each beam set requires a vector and distance correction for each isocenter except for the first source point. The new vector a point were computed and corrected for geometrically to maintain the planned dose at isocenter for each other isocenter. es a geometric correction, and the new depth requires an attenuation correction. The geometric correction was made by

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40 computing the new inverse square distance factor to the . T he attenuation correction was made by shifting the TPR table to the new depth relative to the first . After the geometric and attenuation corrections were made, the resulting 3 dimensi o nal dose distributions using the single source point SRS method was compared to the original SRS plans via sphere packing plan using static beams generated using the 3 dimensional dose distribution using the normal source point SRS method. The impact on the 3 dimensional dose distribution due to the change in source point for all but the first iso center was examined using the same configurations and parameters as were previously discussed in the Plan Configurations and Validation Parameters section s. Combined OF correction The main objective of delivery of the SRS plans via IMRT using MLCs is to i rradiate the sphere one by as is the case with SRS plans via sphere packing. Tabulated OFs were determined from experimental data based on field size collimation at SAD fo r circular and square fields only. Each combined beam profile will have an irregular shape when the union of the overlapping beam areas is projected at SAD. Therefore the union area carries a unique OF that cannot be modeled easily using circular or square field size OFs. Method of integration . The Clarkson Method, as presented by Dr. Faiz M. Khan in his textbook, The Physics of Radiation therapy, computes the dose due to scatter at point for irregular shaped fields 14 . The Clarkson Method was adapted to determine the unique OFs of irregular combined beam profiles by dividing the profiles radially into sections, then determin ing the average radius

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41 of the section and thus the corresponding circular OF for that section. The average OF of all Fluence Dampening Methodology The motivation to perform fluence dampening is t hat in regions of overlapping fluence the largest beam fluence will deliver the necessary radiation dose to all the tissue along its path. With SRS plans via sphere packing using static beams, the beams in a beam set are treated one by one independent of e ach other. Thus, whether or not their fluencies overlap is never considered. Regions of fluence overlap receive more dose than is necessary. Therefore, the overlapping fluence is not necessary and can be removed. The overlap removal method previously inve stigated by Bonnie Velasco formed the basis for the fluence dampening methodology used in this work. For each beam set, the dose contribution by each beam at each volume element of the in the 3 dimensional dose distribution , called a voxel, was examined to determine which beam contrib uted the largest dose. The largest contribution was preserved and all other contributions were simply removed. The dose algorithm performs fluence dampening automatically on the 3 dimensional dose distribution generated by the single source point SRS method. The fluence dampened 3 dimensional dose distribution can be delivered as a n SRS plan via IMRT using MLCs.

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42 Figure 3 1. This figure shows the beam paths of a five arc set for a single sphere . This figure was taken from B Figure 3 2. This figure shows the 15 static beam set to replace a five arc set for a single sphere . Three static beams are used to approximate each arc. This figure was taken from

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43 Figure 3 3. This is an example of a dose form with a single sphere .

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44 A B Figure 3 4. The geometric penumbra produced by partial obstruction of the source by a collimator. A) S hows the line of sight for the source size , S. B) S hows the relative intensity of dose profile produced by S . Figure 3 5. The effects of the empirical fit parameters, and on the OARs given by Equations 3 3 and 3 4.

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45 Figure 3 6. Example of a xial, coronal, and sagittal MR images of the single beam plan for the 20 mm diameter circular ly collimated beam.

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46 Figure 3 7. Example of a xial, coronal, and sagittal MR images of the multi beam plan for the 12 mm diameter circularly collimated beam set inside a 40 mm diameter circularly collimated beam at equal depths.

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47 Figure 3 8. Example of a xial, coronal, and sagittal MR images of the multi beam plan for the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other.

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48 Figure 3 9. Example of a xial, coronal, and sagittal MR images of the multi beam plan for the 14 mm diameter circular ly collimated beam overlapping the edge of a 40 mm diameter circularly collimated beam at equal depths.

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49 Figure 3 10 . Example of a xial, coronal, and sagittal MR images of the Single sphere plan for the 20 mm diameter circularly collimated sphere .

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50 F igure 3 1 1 . Example of a xial, coronal, and sagittal MR images of the Multi sphere plan for the two 16 mm diameter circularly collimated sphere s set at equal depths and offset laterally 18 mm from each other.

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51 Figure 3 1 2 . Example of a xial, coronal, and sagittal MR images of the Multi sphere plan for the two 16 mm diameter circularly collimated sphere s set 17 mm above and below each other axially.

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52 Figure 3 13 . Example of a 1 dimensional line dose profile for comparing the spatial and dosimetric accuracy of the dose algorithm along the steep dose gradient.

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53 Figure 3 14. This figure shows how two beams for separate spheres can overlap when considered together. The blue and green lines correspo nd to the intensities of isocenters #1 and #2 respectively. The red line represents the superposition of the two profile intensity.

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54 Figure 3 1 5 . The process by which an SRS via sphere packing plan using arcs is transformed to an SRS via IMRT plan using MLCs by the single source point SRS Method.

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55 Figure 3 1 6 . The geometric translation from the normal source point SRS method to the single source point SRS method is shown.

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56 CHAPTER 4 RESULTS Dose Algorithm Validation of Normal Source Point SRS Method Single Beam The plan setups for single beam s cover the relevant range of circular collimator sizes. The collimator sizes selected were 10 mm, 20 mm, and 30 mm, to represent small medium and large diameter circularly collimated beams respectively. 10 mm diameter circularly collimated beam Table 4 1. T he dose at isocenter for a 10 mm beam . Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 1 0 1874.3 1871.6 0.14 % Table 4 2 . The maximum dose for a 10 mm beam . Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 10 1874.3 1893.9 1.05% Figure 4 1. The 1 dimensional line dose prof iles along the AP axis at isocenter for a 10 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. Table 4 3 . The spatial difference between isodose contours for a 10 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum difference (mm) Minimum difference (mm) Average difference (mm) 10 0.5 7 0.0 1 0 .21

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57 Table 4 4 . The dose percent difference between spatial diameters for a 10 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum dose percent difference Minimum dose percent difference Average dose percent difference 10 5.44 % 1.91 % 3.67 % Results analysis . For 10 mm diameter circularly collimated beam plan, t he dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 dimensional dose distribution with percent errors of 0.14% a nd 1.05% respective ly, which are well within the 3% dose tolerance as compared to the UF in house TPS for the 10 mm diameter circularly collimated beam . For the steep dose gradient region of the 10 mm diame ter circularly collimated beam 3 dimensional dose distributio n , t he 1 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.2 1 mm , which is within the 3 mm tolerance, and good dose percent agreement with the UF in house TPS with an average difference of 3.67 % , which is just outside the 3% dose tolerance . At the high low dose region , the dose percent agreement was most po or, contribut ing to a greater than tolerance average, but the maximum dose percent difference of 5.44% corresponds to a maximum spatial difference of only 0.5 7 mm , which is still within a very close proximity. 20 mm diameter circularly collimated beam Table 4 5. The dose at isocenter for a 20 mm beam . Collimator diameter (mm) UF in hou se TPS dose (cGy) Dose algorithm dose (cGy) Percent error 2 0 1702.3 1703.4 0.04% Table 4 6. The maximum dose for a 20 mm beam . Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 2 0 1872.9 1875.8 0.15%

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58 Figure 4 2 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 20 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. Table 4 7. The spatial difference between isodose contours for a 20 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum difference (mm) Minimum difference (mm) Average difference (mm) 2 0 2.54 0.04 0.32 Table 4 8. The dose percent difference between spatial diameters for a 20 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum dose percent difference Minimum dose percent difference Average dose percent difference 2 0 3.76 % 0.12 % 0.80 % Results analysis . For 20 mm diameter circularly collimated beam plan, t he dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 dimensional dose distribution with percent errors of 0.04% and 0.15% respectively, which are well within the 3% dose tolerance as compared to the UF in house TPS for the 2 0 mm diameter circularly collimated beam. For the steep dose gradient region of the 20 mm diame ter circularly collimated beam 3 dimensional dose distribution dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.32

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59 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0.80 cGy, which is wh ich is within the 3% dose tolerance. The maximum dose percent difference is 3.76%, which is just greater than the 3% tolerance, but it corresponds to a spatial distance of 2.54 mm, which is still within the 3 mm tolerance. 30 mm diameter circularly collima ted beam Table 4 9 . The dose at isocenter for a 30 mm beam . Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 30 1713.5 1713.5 0.00% Table 4 10 . The maximum dose for a 30 mm beam . Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 30 1874.5 1875.0 0.03% Figure 4 3 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 30 mm beam. The AP and Lat 1 dimensional line dose profiles are symmetric. Table 4 11 . The spatial difference between isodose contours for a 30 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum difference (mm) Minimum difference (mm) Average difference (mm) 30 0.32 0.02 0.15

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60 Table 4 12 . The dose percent difference between spatial diameters for a 30 mm beam for the UF in house TPS and the dose algorithm. Collimator diameter (mm) Maximum dose percent difference Minimum dose percent difference Average dose percent difference 30 3.75 0.01 0.52 Results analysis . For 30 mm diameter circularly collimated beam plan, t he dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 dimensional dose distribution with percent errors of 0.0% and 0. 03 % respectively, which are well within the 3% dose tolerance as compared to the UF in house TPS for the 3 0 mm diameter circularly collimated beam. For the steep dose gradient region of the 3 0 mm diameter circularly collimated beam 3 dimensional dose distribution dimensional line dose profile showed excellent spatial agreem ent with the UF in house TPS with an average difference of 0. 15 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0. 52% , which is within the 3% dose tolerance. The maximum do se percent difference is 3.7 5 %, which is just greater than the 3% tolerance, but it corresponds to a spatial distance of 0.32 mm, which is still within very close proximity . Multi Beam 12 mm beam set inside a 40 mm , with unequal weights: 12 mm < 40 mm This plan setup consists of a 12 mm diameter circularly collimated beam set inside a 40 mm diameter circularly collimated beam at equal depths. The beam weights were set so that the 12 mm diameter circularly collimated beam was weighted lower than the 40 mm di ameter circularly collimated beam.

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61 Table 4 13 . The dose at isocenter for a setup consisting of a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower . Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 12 mm < 40 mm 12 mm 1974.0 1974.1 0.01% 40 mm 1974.0 1974.1 0.01% Table 4 1 4 . The maximum dose for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 12 mm < 40 mm 2142.9 2143.0 0.01% Figure 4 4 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. Table 4 1 5 . The spatial difference between isodose contours for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) 12 mm < 40 mm 0.36 0.01 0.15 Table 4 1 6 . The dose percent difference between spatial diameters for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower . Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference 12 mm < 40 mm 2.47% 0.14% 0.67%

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62 Results analysis . For the 12 mm diameter circularly collimated beam set inside a 40 mm circularly collimated beam with the 12 mm diameter circularly collimated beam weighted lower than the 40 mm diameter circularly collimated beam plan, t he dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with a percent error of 0.01% for each isocenter and the maximum dose with a percent error of 0.0 1 %, which are well within the 3% dose tolerance as compare d to the UF in house TPS. For the steep dose gradient region of the 12 mm diameter circularly collimated beam set inside a 40 mm circularly collimated beam with the 12 mm diameter circularly collimated beam weighted lower than the 40 mm diameter circularl y collimated beam 3 dimensional dose distribution dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.15 mm, which is within the 3 mm tolerance, and excell ent dose percent agreement with the UF in house TPS with an average difference of 0.67%, which is within the 3% dose tolerance. 12 mm beam set inside a 40 mm, with unequal weights: 12 mm > 40 mm This plan setup consists of a 12 mm diameter circularly coll imated beam set inside a 40 mm diameter circularly collimated beam at equal depths. The beam weights were set so that the 12 mm diameter circularly collimated beam weighted higher than the 40 mm diameter circularly collimated beam . Table 4 1 7 . The dose at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher . Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 12 mm > 40 mm 12 mm 1990.8 1991.0 0.01% 40 mm 1990.8 1991.0 0.01%

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63 Table 4 1 8 . The maximum dose for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 12 mm > 40 mm 2142.8 2143. 2 0.02% Figure 4 5 . The 1 dimensional line dose profiles the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. Table 4 1 9 . The spatial difference between isodose contours for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) 12 mm > 40 mm 0.80 0.01 0.22 Table 4 20 . The dose percent difference between spatial diameters for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher. Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference 12 mm > 40 mm 3.43 % .002 % 0. 83 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with a percent error of 0.01% for each isocenter and the maximum dose with a percent error of 0.02%, which are well within the 3% dose tolerance as compared to

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64 t he UF in house TPS for the 12 mm diameter circularly collimated beam set inside a 40 mm circularly collimated beam with the 12 mm diameter circularly collimated beam weighted higher than the 40 mm diameter circularly collimated beam. For the steep dose gr adient region of the 12 mm diameter circularly collimated beam set inside a 40 mm circularly collimated beam with the 12 mm diameter circularly collimated beam weighted higher than the 40 mm diameter circularly collimated beam 3 dimensional dose dis tribution dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0. 22 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0. 83 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 3.43%, which is just greater than the 3% tolerance, but i t corresponds to a maximum spatial difference of only 0.80 mm, which is still within a very close proximity. Two 16 mm beams set laterally, with equal weights: #1 = #2 This plan setup consists of two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping. The beam weights were set to be equal. The two 16 mm beams were designated #1 and #2. #1 was placed at the c enter of the distribution with #2 Table 4 21 . The dose at isocenter for two 16 mm beams offset laterally by 18 mm with equal beam weights . Weighting Beam UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 = #2 #1 1674.3 1673.1 0.07% #2 1674.3 1673.1 0.07%

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65 Table 4 22 . The maximum dose for two 16 mm beams offset laterally by 18 mm with equal beam weights. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 = #2 1874.9 1885.3 0.55% Figure 4 6 . The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset laterally 18 mm with equal beam weights. Table 4 23 . The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with equal beam weights. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 = #2 0.50 0.01 0.28 Table 4 24 . The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm from each other so as to not overlapping with equal beam weights. Weighting Maximum dose percent difference Minimum dose percent difference Average dos e percent difference #1 = #2 4.05 % 0.02 % 1.03 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with a percent error of 0.0 7 % for each isocenter and the maximum dose with a percent error of 0. 55 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping with equal beam weights .

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66 For the steep dose gradient region of the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping with equal beam weights 3 dimensional dose distribution , the dose algo dimensional line dose profile showed excellent spatial agreement with the UF in house TPS wi th an average difference of 0.28 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average dif ference of 1.03%, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 4.05 %, which is just greater than the 3% tolerance, but it corresponds to a maxim um spatial difference of only 0.50 mm, which is still within a very close proximity. Two 16 mm beams set laterally, with unequal weights: #1 > #2 This plan setup consists of two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping. The beam weights were set to be unequal. The two 16 mm beams were designated #1 and #2. #1 was placed at the weighted higher than #2. Table 4 25 . The dose at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. Weighting Beam U F in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 > #2 #1 1621.7 1620.1 0.01% #2 1459.3 1458.2 0.08% Table 4 26 . The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2 . Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 > #2 1874.8 1884.9 0.54%

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67 Figure 4 7 . The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2 . Table 4 27 . The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2 . Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 > #2 0.37 0 .003 0.19 Table 4 2 8 . The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2 . Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference #1 > #2 4.00 % 0.02% 0.97 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isoc enter with percent error s of 0. 10 % and 0.08% for #1 and #2 respectively, and the maximum dose with a percent error of 0.5 4 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping with #1 weighted higher than #2 . For the steep dose gradient region of the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping with #1 weighted higher th an #2 3 dimesional dose distribution -

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68 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0. 19 mm, which is within the 3 mm tolerance, and excellent dose perc ent agreement with the UF in house TPS with an average difference of 0.97 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 4.0 0 %, which is just gr eater than the 3% tolerance, but it corresponds to a maximum spatial difference of only 0. 37 mm, which is still within a very close proximity. Two 16 mm beams set laterally, with unequal weights: #1 < #2 This plan setup consists of two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping. The beam weights were set to be unequal. The two 16 mm beams were designated #1 and #2. #1 was placed at the weighted lower than #2. Table 4 2 9 . The dose at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Weighting Beam UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 < #2 #1 1412.6 1411.4 0 .08 % #2 1569.8 1568.1 0. 11 % Table 4 30 . The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 < #2 1874.8 188 4.8 0.5 3 %

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69 Figure 4 8 . The 1 dimensional line dose profiles the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Table 4 31 . The spatial difference between isodose contours for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 < #2 0.78 0.004 0.21 Table 4 32 . The dose percent difference between spatial diameters for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent differe nce #1 < #2 3.86 % 0.02% 0.9 3 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0. 08 % and 0. 11 % for #1 and #2 respectively, and the maximum dose with a percent error of 0.5 3 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping with #1 weighted lower t han #2. For the steep dose gradient region of the two 16 mm diameter circularly collimated beams set at equal depths and offset laterally 18 mm from each other so as to not overlapping

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70 with #1 weighted lower than #2 3 dimensional dose distribution , dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0. 21 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0.9 3 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 3.86 %, which is just greater than the 3% tolerance, but it correspo nds to a maximum spatial difference of only 0. 78 mm, which is still within a very close proximity. 14 mm beam set on edge of 40 mm, with unequal weights: 14 mm < 40 mm This plan setup consists of a 14 mm diameter circularly collimated beam set on the edge of a 40 mm diameter circularly collimated beam at equal depths. The beam weights were set so that the 14 mm diameter circularly collimated beam was weighted lower than the 40 mm diameter circularly collimated beam. Table 4 33 . The dose at isocenter for a 1 4 mm beam set on the edge of a 40 mm beam with the 1 4 mm beam weighted lower. Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 1 4 mm < 40 mm 1 4 mm 885.7 776.5 12.33% 40 mm 1460.0 1461.9 0.13% Table 4 34 . The maximum dose for a 1 4 mm beam set on the edge of a 40 mm beam with the 1 4 mm beam weighted lower. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 1 4 mm < 40 mm 2142.6 2094.4 2.25 %

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71 Figure 4 9 . The 1 dimensional line dose profiles the AP axis at isocenter for a 1 4 mm beam set on the edge of a 40 mm beam with the 1 4 mm beam weighted lower. Table 4 35 . The spatial difference between isodose contours for a 1 4 mm beam set on the edge of a 40 mm beam with the 1 4 mm beam weighted lower. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) 1 4 mm < 40 mm 1.47 0.03 0.71 Table 4 36 . The dose percent difference between spatial diameters for a 1 4 mm beam set on the edge of a 40 mm beam with the 1 4 mm beam weighted lower. Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference 1 4 mm < 40 mm 13.75 % 0.04 % 2.34 % Results analysis . For the 14 mm diameter circularly collimated beam weighted lower than the 40 mm diameter circularly collimated beam plan , t he dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent error s of 12.33 % and 0.13% for the 14mm and 40 mm beams respectively , and the maximum dose with a percent error of 2.25 % compared as to the UF in house TPS. All but the dose at isocenter for the 14 mm beam fell with in the 3% dose tolerance . The dose for the 14 mm beam was far outside of the 3% tolerance, which can be attributed to the isocenter for the 14 mm beam being set very close to the dose gradient of the 40 mm beam.

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72 For the steep dose gradient region of the 1 4 mm diameter circularly collimated beam set on the edge of a 40 mm circularly collimated beam with the 1 4 mm diameter circularly collimated beam weighted lower than the 40 mm diameter circularly collimated beam 3 dimensional dose distribution dimensional line dose profile showed good spatial agreement with the UF in house TPS with an average difference of 0.71 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 2.34 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 13.75%, which is much greater than the 3% tolerance, but it corresponds to a maximum spatial difference of only 1.47 mm, which is still within close proximity. 14 mm b eam set on edge of 40 mm, with unequal weights: 14 mm > 40 mm This plan setup consists of a 14 mm diameter circularly collimated beam set on the edge of a 40 mm diameter circularly collimated beam at equal depths. The beam weights were set so that the 14 m m diameter circularly collimated beam was weighted higher than the 40 mm diameter circularly collimated beam. Table 4 37 . The dose at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 14 mm > 40 mm 14 mm 1535.4 1491.8 2.84% 40 mm 591.4 595.8 0.74% Table 4 3 8 . The maximum dose for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 14 mm > 40 mm 2143.3 2084.6 2.74%

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73 Figure 4 1 0 . The 1 dimensional line dose profiles the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher . Table 4 3 9 . The spatial difference between isodose contours for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher . Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) 14 mm > 40 mm 1.11 0. 0 03 0. 33 Table 4 40 . The dose percent difference between spatial diameters for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm beam weighted higher . Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference 14 mm > 40 mm 5.00 % 0.04% 1.31 % Results analysis . For the 14 mm diameter circularly collimated beam weighted higher than the 40 mm diameter circularly collimated beam plan, the dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 2.84 % and 0. 74 % for the 14mm and 40 mm beams respectively, and the maximum dose with a percent error of 2. 74 % compared as to the UF in house TPS. All the dose s predicted fell within the 3% dose tolerance. For the steep dose gradient region of the 14 mm diameter circularly collimated beam set on the edge of a 40 mm circularly collimat ed beam with the 14 mm diameter circularly

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74 collimated beam weighted lower than the 40 mm diameter circularly collimated beam 3 dimensional line dose profile showed good spatial agreement with the UF in house TPS with an average difference of 0. 33 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 1.31 %, which is within the 3% dose tolerance. At the high low dose regio n, the dose percent agreement was most poor, with giving maximum dose percent difference of 5.00 %, which is much greater than the 3% tolerance, but it corresponds to a maximum spatial difference of only 1. 11 mm, which is still within close proximity. Singl e sphere The plan setups for Single sphere s cover the relevant range of circular collimator sizes. The collimator sizes selected were 10 mm, 20 mm, and 30 mm, to represent small medium and large diameter circularly collimated spheres respectively. 10 mm d iameter circularly collimated sphere Table 4 41 . The dose at isocenter for a 10 mm sphere . Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 10 1875.1 1875.0 0.01% Table 4 42 . The maximum dose for a 10 mm sphere . Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 10 1875.1 1881.9 0.36%

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75 Figure 4 1 1 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 10 mm sphere . Figure 4 1 2 . The 1 dimensional line dose profiles along the Lat axis at isocenter for a 10 mm sphere.

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76 Figure 4 1 3 . The 1 dimensional line dose profiles along the Ax axis at isocenter for a 10 mm sphere. Table 4 43 . The spatial difference between isodose contours for a 10 mm sphere . Collimator diameter (mm) Axis Maximum difference (mm) Minimum difference (mm) Average difference (mm) 10 AP 0.55 0.01 0.22 Lat 0.59 0.01 0.21 Ax 0.70 0.02 0.22 Table 4 4 4 . The dose percent difference between spatial diameters for a 10 mm sphere . Collimator diameter (mm) Axis Maximum dose percent difference Minimum dose percent difference Average dose percent difference 10 AP 3.73 % 0.50 % 2.40 % Lat 3.24 % 0.97 % 1.97 % Ax 3.33 % 0.39 % 1.89 % Results analysis . For 10 mm diameter circularly collimated sphere plan, the dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 dimensional dose distribution with percent errors of 0. 01 % and .036 % respectively, which ar e well within the 3% dose tolerance as compared to the UF in house TPS.

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77 For the steep dose gradient region of the 10 mm diameter circularly collimated sphere 3 dimensional line dose profile show ed excellent spatial agreement with the UF in house TPS with an maximum average difference of 0.2 2 mm, which is within the 3 mm tolerance, and good dose percent agreement with the UF in house TPS with a maximum average difference of 2.40 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, contributing to a greater than tolerance average, but the maximum dose percent difference of 3.73 % corresponds to a maximum spatial difference of only 0. 70 mm, wh ich is still within a very close proximity. 20 mm diameter circularly collimated sphere Table 4 45. The dose at isocenter for a 20 mm sphere. Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 20 1852.3 1853.2 0.05% Table 4 46. The maximum dose for a 20 mm sphere. Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 20 1875.3 1882.1 0.37% Figure 4 14 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 20 mm sphere.

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78 Figure 4 15 . The 1 dimensional line dose profiles along the Lat axis at isocenter for a 20 mm sphere. Figure 4 16 . The 1 dimensional line dose profiles along the Ax axis at isocenter for a 20 mm sphere.

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79 T able 4 47. The spatial difference between isodose contours for a 20 mm sphere. Collimator diameter (mm) Axis Maximum difference (mm) Minimum difference (mm) Average difference (mm) 20 AP 0.29 0.01 0.12 Lat 0.27 0.01 0.09 Ax 0.31 0.01 0.10 Table 4 48. The dose percent difference between spatial diameters for a 20 mm sphere. Collimator diameter (mm) Axis Maximum dose percent difference Minimum dose percent difference Average dose percent difference 20 AP 2.58% 0.10% 1.09% Lat 1.99% 0.04% 0.62% Ax 2.68% 0.11% 0.72% Results analysis . For 20 mm diameter circularly collimated sphere plan, the dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 dimensional dose distribution with percent errors of 0.0 5 % and .03 7 % respectively, which are well within the 3% dose tolerance as compared to the UF in house TPS. For the steep dose gradient region of the 20 mm diameter circularly collimated sphere 3 dimensional line dose profile showed excellent spat ial agreement with the UF in house TPS with an maximum average difference of 0. 11 mm, which is within the 3 mm tolerance, and good dose percent agreement with the UF in house TPS with a maximum average difference of 1.09 %, which is within the 3% dose toler ance. 30 mm diameter circularly collimated sphere Table 4 4 9 . The dose at isocenter for a 30 mm sphere. Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 30 1816.2 1816.5 0 .02 %

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80 Table 4 50 . The maximum dose for a 30 mm sphere. Collimator diameter (mm) UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 30 1879.4 1882.1 0.3 8 % Figure 4 17 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 30 mm sphere.

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81 Figure 4 18 . The 1 dimensional line dose profiles along the Lat axis at isocenter for a 30 mm sphere. Figure 4 19 . The 1 dimensional line dose profiles along the Ax axis at isocenter for a 30 mm sphere. Table 4 51 . The spatial difference between isodose contours for a 30 mm sphere. Collimator diameter (mm) Axis Maximum difference (mm) Minimum difference (mm) Average difference (mm) 30 AP 0.29 0.01 0.12 Lat 0.27 0.01 0.09 Ax 0.31 0.01 0.10 Table 4 52 . The dose percent difference between spatial diameters for a 30 mm sphere. Collimator diameter (mm) Axis Maximum dose percent difference Minimum dose percent difference Average dose percent difference 30 AP 2.58% 0.10% 1.09% Lat 1.99% 0.04% 0.62% Ax 2.68% 0.11% 0.72% Results analysis . For 30 mm diameter circularly collimated sphere plan, the dose algorithm accurately reproduced the dose at isocenter and the maximum dose of the 3 -

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82 dimensional dose distribution with percent errors of 0.0 2 % and .03 8 % respectively, which are well within the 3% dose tolerance as compared to the UF in house TPS. For the steep dose gradient region of the 30 mm diameter circularly collimated sphere 3 dimensional dose distribution, the dose algorit dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an maximum average difference of 0.1 9 mm, which is within the 3 mm tolerance, and good dose percent agreement with the UF in house TPS with a maximum aver age difference of 0.91 %, which is within the 3% dose tolerance. Multi sphere Two 16 mm sphere s offset laterally, with equal beam weights: #1 = #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping. The beam weights were set to be equal. The two 16 mm spheres were designated #1 and #2. #1 was placed at the T able 4 53 . The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with equal beam weights. Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 = #2 #1 1771.6 1762.3 0. 52 % #2 1771.2 1763.0 0. 46 % Table 4 54 . The maximum dose for two 16 mm beams offset laterally by 18 mm with equal beam weights. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 = #2 2142.9 2082.5 2.82 %

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83 Figure 4 20 . The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 1 7 mm with equal beam weights. Table 4 55 . The spatial difference between isodose contours for two 16 mm spheres offset laterally by 1 7 mm wi th equal beam weights. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 = #2 0.45 0.01 0.14 Table 4 56 . The dose percent difference between spatial diameters for two 16 offset laterally by 18 mm with equal beam weights. Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference #1 = #2 1.70 % 0.0 1 % 0.45 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distr ibution dose at isocenter with percent error s of 0.0 8 % and 0.15% for sphere #1 and #2 respectively, and the maximum dose with a percent error of 2.82 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly col limated spheres set at equal depths and offset laterally 1 7 mm from each other so as to not overlapping with equal beam weights.

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84 For the steep dose gradient region of the two 16 mm diameter circularly collimated spheres set at equal depths and offset late rally 1 7 mm from each other so as to not overlapping with equal beam weights 3 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0. 14 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0.45 %, which is within the 3% dose tolerance. Two 16 mm spheres offset laterally, with equal beam weights: #1 > #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping. The beam weights were set to be unequal. The two 16 mm spheres were designated #1 and #2, with #1 weighted Table 4 57. The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than # 2. Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 > #2 #1 2059.4 2051.7 0. 37 % #2 1212.1 1203.5 0. 71 % Table 4 58. The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 weighted higher than #2. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 > #2 2143.0 2 133.9 0.42 %

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85 Figure 4 21 . The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2 . Table 4 59. The spatial difference between isodose contours for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2 . Weighting Maximum di fference (mm) Minimum difference (mm) Average difference (mm) #1 > #2 0.62 0.002 0.16 Table 4 60. The dose percent difference between spatial di ameters for two 16 mm spheres offset laterally by 1 7 mm with #1 weighted higher than #2 . Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference #1 > #2 2.56 % 0.01% 0. 59 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0. 37 % and 0. 71 % for sphere #1 and #2 respectively, and the maximum dose with a percent error of 0.42 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping with #1 weighted higher than #2 .

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86 For the steep dose gradient region of the two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping with 3 dimensional dose distribution, dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.1 6 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with a n average difference of 0. 59 %, which is within the 3% dose tolerance. Two 16 mm spheres offset laterally, with equal beam weights: #1 < #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set at equal depths and offset laterall y 17 mm from each other so as to not overlapping. The beam weights were set to be unequal. The two 16 mm spheres were designated #1 and #2, with #1 weighted latera Table 4 61 . The dose at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 < #2 #1 1211.7 1203.0 0. 72 % #2 2059.8 2051.3 0. 4 1% Table 4 62 . The maximum dose for two 16 mm beams offset laterally by 18 mm with #1 lower higher than #2. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 < #2 2143.0 2133.6 0.4 4 %

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87 Figure 4 22 . The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. Table 4 63 . The spatial difference between isodose contours for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 < #2 0.58 0.001 0.14 Table 4 6 4 . The dose percent difference between spatial diameters for two 16 mm spheres offset laterally by 17 mm with #1 weighted lower than #2. Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference #1 < #2 2. 44 % 0.0 04 % 0. 60 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0. 72 % and 0. 41 % for sphere #1 and #2 respectively, and the maximum dose with a percent error of 0.4 4 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping with #1 weighted lower than #2.

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88 For the steep dose gradient region of the two 16 mm diameter circularly collimated spheres set at equal depths and offset laterally 17 mm from each other so as to not overlapping dimensional dose distribution, t dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.1 4 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0. 60 %, which is within the 3% dose tolerance. Two 16 mm spheres above and below, with equal beam weights: #1 = #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm. The beam weights were set to be equal. The two 16 s isocenter set 17 mm axially below Table 4 65 . The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with equal weights . Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 = #2 #1 1688.9 1687.6 0. 08 % #2 1710.1 1712.6 0. 15 % Table 4 66 . The maximum dose for two 16 mm spheres set above and below each other separated by 17 mm with equal weights . Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 = #2 2142.7 2086.7 2.61 %

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89 Figure 4 23 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with equal weights . Table 4 67 . The spatial difference between isodose contours for two 16 mm spheres set above and below each other separated by 17 mm with equal weights . Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 > #2 0.82 0.01 0.19 Table 4 68 . The dose percent difference between spatial diameters for two 16 mm spheres set above and below each other separated by 17 mm with equal weights . Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference #1 > #2 3.23 % 0.01 % 0. 6 5 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0. 08 % and 0. 15 % for sphere #1 and #2 respectively, and the maximum dose with a percent error of 2.61 %, which are within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated spheres set above and below each other separ ated by 17 mm with equal weights . For the steep dose gradient region of the two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm with equal weights -

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90 1 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0. 1 9 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0. 6 5 %, which is within the 3% dose tolerance. At the high low dose region, the dose percent agreement was most poor, with giving maximum dose percent difference of 3.23%, which is just greater than the 3% tolerance, but it corresponds to a maximum spati al difference of only 0.82 mm, which is still within a close proximity. Two 16 mm spheres above and below, with equal beam weights: #1 > #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm. The beam weights were set to be unequal. The two 16 mm spheres were designated #1 and #2 with #1 weighted higher than #2. #1 was placed at the c axially below Table 4 6 9 . The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted higher than #2. Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 > #2 #1 2012.9 2010.9 0.10% #2 1191.8 1197.7 0.50% Table 4 70 . The maximum dose for two 16 mm spheres set above and below each other separated by 17 mm with equal with #1 weighted higher than #2. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 > #2 2142.6 2113.6 1.35%

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91 Figure 4 24 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted higher than #2. Table 4 71 . The spatial difference between isodose contours for two 16 mm spher es set above and below each other separated by 17 mm with #1 weighted higher than #2. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 > #2 0.55 0.02 0.17 Table 4 72 . The dose percent difference between spatial diameters for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted higher than #2. Weighting Maximum dose percent difference Minimum dose percent difference Average dose perce nt difference #1 > #2 2.20% 0.01% 0.66% Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0.10% and 0.50% for sphere #1 and #2 respectively, and the maximum dose with a percent error of 1.35%, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm with #1 weighted higher than #2.

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92 For the steep dose gradient region of the two 16 mm diameter circularl y collimated spheres set above and below each other separated by 17 mm with #1 weighted higher than #2 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.17 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0.66%, which is within the 3% dose tolerance. Two 16 mm spheres above and below, with eq ual beam weights: #1 < #2 This plan setup consists of two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm. The beam weights were set to be unequal. The two 16 mm spheres were designated #1 and #2 with #1 weigh ted lower than #2. #1 was placed at the axially below Table 4 73 . The dose at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. Weighting Sphere UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 < #2 #1 1150.6 1151.6 0. 09 % #2 1970.7 1969.7 0. 05 % Table 4 74 . The maximum dose for two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm with equal with #1 weighted lower than #2. Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error #1 < #2 2142.8 2117.1 1. 20 %

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93 Figure 4 25 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. Table 4 75 . The spatial difference between isodose contours for two 16 mm sphere s set above and below each other separated by 17 mm with #1 weighted lower than #2. Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) #1 < #2 0.59 0.02 0.17 Table 4 76 . The dose percent difference between spatial diameters for two 16 mm diameter spheres set above and below each other separated by 17 mm with #1 weighted lower than #2. Weighting Maximum dose percent difference Minimum dose percent difference Average do se percent difference #1 < #2 2. 38 % 0.01% 0.6 0 % Results analysis . The dose algorithm accurately reproduced the 3 dimensional dose distribution dose at isocenter with percent errors of 0. 09 % and 0. 05 % for sphere #1 and #2 respectively, and the maximum dose with a percent error of 1. 20 %, which are well within the 3% dose tolerance as compared to the UF in house TPS for the two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm with #1 weighted lower than #2.

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94 F or the steep dose gradient region of the two 16 mm diameter circularly collimated spheres set above and below each other separated by 17 mm with #1 weighted lower than #2 dimensional line dose profile showed excellent spatial agreement with the UF in house TPS with an average difference of 0.17 mm, which is within the 3 mm tolerance, and excellent dose percent agreement with the UF in house TPS with an average difference of 0.6 0 %, which is withi n the 3% dose tolerance. Dose Algorithm Validation of Single Source Point SRS Method The single source point SRS method was used to simulate the 3 dimensional dose distributions generated by SRS via IMRT using MLCs. IMRT plans utilize a single source poin t with MLCs to spatially and temporally modulate the fluence. Each multi beam and multi sphere plan was generated using the single source point SRS method. Single beam and single isocenter 3 dimensional dose profiles generated by the single source point SR S method are identical to their normal source point SRS method counterparts because each beam set has a single source point. Dose at Isocenter Multi beam Table 4 77 . The dose at isocenter for each multi beam setup with each beam weighting combination for the single source point SRS method . Beams setup Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error Beam Inside a beam 12 mm = 40 mm 12 mm < 40 mm 12 mm 1974.0 1974.2 0.01% 40 mm 1974.0 1974.2 0.01% 12 mm > 40 mm 12 mm 1990.8 1991.0 0.01% 40 mm 1990.8 1991.0 0.01% Beams side by side

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95 Table 4 77 Continued. Beams setup Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error #1 = #2 16 mm (#1) 1674.3 1673.3 0.06% 16 mm (#2) 1674.3 1677.2 0.17% #1 > #2 16 mm (#1) 1621.7 1620.2 0.09% 16 mm (#2) 1459.3 1461.8 0.17% #1 < #2 16 mm (#1) 1412.6 1411.6 0.07% 16 mm (#2) 1569.8 1572.1 0.15% Beam on 14 mm = 40 mm 14 mm < 40 mm 14 mm 885.7 777.3 12.24% 40 mm 1460.0 1461.9 0.13% 14 mm > 40 mm 14 mm 1535.4 1493.8 2.71% 40 mm 591.4 595.9 0.76% The dose at isocenter for every isocenter in each multi beam , plan except for one , gave a percent error within the acceptable level of 3%. The dose at isocenter for the lower weighted beam for 14 mm diameter circularly collimated beam set inside a 40 mm diameter circularly collima ted beam plan recorded a percent error of 12.24%. This percent error correlates to the same normal source point SRS method percent error of 12.33%. This percent error is attributed to the isocenter of the 14 mm beam falling within the dose gradient of the 40 mm beam. Multi sphere Table 4 78 . The dose at isocenter for each multi sphere setup with sphere beam weighting combination for the single source point SRS method . Spheres setup Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorit hm dose (cGy) Percent error Spheres side by side #1 = #2 16 mm (#1) 1771.6 1763.9 0.43% 16 mm (#2) 1771.2 1766.6 0.26% #1 > #2

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96 Table 4 78 continued. Spheres setup Weighting Collimator diameter (mm) UF in house TPS dose (cGy) Dose algorithm dose (cGy) Percent error 16 mm (#1) 2059.4 2052.7 0.33% 16 mm (#2) 1212.1 1206.1 0.50% #1 < #2 16 mm (#1) 1211.7 1205.2 0.54% 16 mm (#2) 2059.8 2057.4 0.12% Sphere above a sphere #1 = #2 16 mm (#1) 1688.9 1704.1 0.90% 16 mm (#2) 1710.1 1744.1 1.99% #1 > #2 16 mm (#1) 2012.9 2021.6 0.43% 16 mm (#2) 1191.8 1216.4 2.06% #1 < #2 16 mm (#1) 1150.6 1171.9 1.85% 16 mm (#2) 1970.7 2009.6 1.97% The dose at isocenter for every isocenter in each multi beam plan gave a percent error within the acceptable level of 3%. Maximum Dose Multi beam Table 4 79 . The maximum dose for each multi beam setup with each beam weighting combination for the single s ource point SRS method . Beams setup Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error Beam Inside a beam 12 mm = 40 mm 12 mm < 40 mm 2142.9 2143.1 0.01% 12 mm > 40 mm 2142.8 2143.2 0.02% Beams side by side 16 mm (#1) = 16 mm (#2) 1874.9 1885.1 0.54% 16 mm (#1) > 16 mm (#2) 1874.7 1884.8 0.54% 16 mm (#1) < 16 mm (#2) 1874.8 1843.5 1.67% Beam on 14 mm = 40 mm

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97 Table 4 79 continued. Beams setup Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error 14 mm < 40 mm 2142.6 2107.8 1.62% 14 mm > 40 mm 2143.3 2067.1 3.65% The maximum dose for each multi beam plan, except for one, gave a percent error within the acceptable level of 3%. The percent error for the maximum dose for the 14 mm diameter circularly collimate beam set on the edge of a 40 mm diameter circularly collimated beam was 3.65%, which is just greater than 3%. This can be attributed to the maximum dose point falling along the dose gradient of the 40 mm diameter circularly collimated beam. Multi sphere Table 4 80 . The maximum dose for each multi sphere setup with each sphere weighting combination for the single source point SRS method . Spheres setup Weighting UF in house TPS maximum dose (cGy) Dose algorithm maximum dose (cGy) Percent error Spheres side by side 16 mm (#1) = 16 mm (#2) 2142.9 2086.6 2.63% 16 mm (#1) > 16 mm (#2) 2143.0 2137.2 0.27% 16 mm (#1) < 16 mm (#2) 2143.0 2141.8 0.06% Sphere above a sphere 16 mm (#1) = 16 mm (#2) 2142.7 2122.7 0.93% 16 mm (#1) > 16 mm (#2) 2142.6 2134.6 0.37% 16 mm (#1) < 16 mm (#2) 2142.8 2157.1 0.67% The maximum dose for each multi beam plan gave a percent error within the acceptable level of 3%. 1 Dimensional Line Dose Profiles Multi beam 12 mm beam set inside a 40 mm, with unequal weights: 12 mm < 40 mm.

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98 Figure 4 26 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted lower. Figure 4 27 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 12 mm beam set inside a 40 mm beam with the 12 mm beam weighted higher.

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99 Figure 4 28 . The 1 dimensional line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with equal beam weights. Figure 4 29 . The 1 dimensional line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally 18 mm with #1 weighted higher than #2.

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100 Figure 4 30 . The 1 dimensional line dose profiles along the AP axis at isocenter for two 16 mm beams offset laterally by 18 mm with #1 weighted lower than #2. Figure 4 31 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 14 mm beam se t on the edge of a 40 mm beam with the 14 mm beam weighted lower.

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101 Figure 4 32 . The 1 dimensional line dose profiles along the AP axis at isocenter for a 14 mm beam set on the edge of a 40 mm beam with the 14 mm weighted higher. Table 4 81 . The spatial difference between isodose contours for each multi beam setup with each beam weighting combination for the single source point SRS method . Beams setup Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) Beam inside a Beam 12 mm = 40 mm 12 mm < 40 mm 0.36 0.01 0.15 12 mm > 40 mm 0.80 0.01 0.22 Beams side by side 16 mm (#1) = 16 mm (#2) 1.32 0.01 0.53 16 mm (#1) > 16 mm (#2) 0.36 0.003 0.18 16 mm (#1) < 16 mm (#2) 0.79 0.004 0.21 Beam on 14 mm = 40 mm 14 mm < 40 mm 1.81 0.003 0.78 14 mm > 40 mm 1.44 0.01 0.37 The maximum, minimum, and average spatial differences between isodose contours for each multi beam plan were within the acceptable distance of 3 mm.

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102 Table 4 82 . The dose percent difference between spatial diameters for each multi beam setup with each beam weighting combination for the single source point SRS method . Beams setup Weighting Maximum dose percent difference Minimum dose percent difference Average dose percen t difference Beam inside a Beam 12 mm = 40 mm 12 mm < 40 mm 2.47% 0.13% 0.67% 12 mm > 40 mm 3.43% 0.01% 0.83% Beams side by side 16 mm (#1) = 16 mm (#2) 13.75% 0.01% 2.50% 16 mm (#1) > 16 mm (#2) 3.99% 0.04% 0.99% 16 mm (#1) < 16 mm (#2) 3.78% 0.02% 0.95% Beam on 14 mm = 40 mm 14 mm < 40 mm 14.21% 0.02% 2.82% 14 mm > 40 mm 5.91% 0.01% 1.51% The average dose percent difference between spatial diameters for each multi beam plan within the acceptable level of 3%. The maximum dose for each multi beam plan, except for one, was greater than the acceptable level of 3%. The maximum dose level for most was just greater the 3% acceptable level, but Table 4 # shows that these dose percent difference s are within well the spatial difference of 3 mm. Multi sphere Figure 4 33. The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with equal beam weights.

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103 Figure 4 3 4 . The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterally by 17 mm with #1 weighted higher than #2. Figure 4 3 5 . The 1 dimensional line dose profiles along the Lat axis at isocenter for two 16 mm spheres offset laterall y by 17 mm with #1 weighted lower than #2.

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104 Figure 4 3 6 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with equal weights. Figure 4 3 7 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with #1 weighted higher than #2.

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105 Figure 4 3 8 . The 1 dimensional line dose profiles along the Ax axis at isocenter for two 16 mm spheres set above and below separated by 17 mm with #1 weighted lower than #2. Table 4 83 . The spatial difference between isodose contours for each multi sphere setup with each sphere weighting combination for the single source point SRS method . Beams setup Weighting Maximum difference (mm) Minimum difference (mm) Average difference (mm) Spheres side by side 16 mm (#1) = 16 mm (#2) 0.36 0.01 0.14 16 mm (#1) > 16 mm (#2) 0.59 0.01 0.15 16 mm (#1) < 16 mm (#2) 0.49 0.001 0. 12 Sphere above a sphere 16 mm (#1) = 16 mm (#2) 1.27 0.01 0.25 16 mm (#1) > 16 mm (#2) 0.88 0.003 0.18 16 mm (#1) < 16 mm (#2) 1.94 0.004 0.25 The maximum, minimum, and average spatial differences between isodose contours for each multi sphere plan were within the acceptable distance of 3 mm.

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106 Table 4 84 . The dose percent difference between spatial diameters for each multi beam setup with each beam weighting combination for the single source point SRS method . Beams setup Weighting Maximum dose percent difference Minimum dose percent difference Average dose percent difference Spheres side by side 16 mm (#1) = 16 mm (#2) 1.65% 0.02% 0.45% 16 mm (#1) > 16 mm (#2) 2.41% 0.002% 0.55% 16 mm (#1) < 16 mm (#2) 2.29% 0.002% 0.54% Sphere above a sphere 16 mm (#1) = 16 mm (#2) 1.89% 0.24% 1.02% 16 mm (#1) > 16 mm (#2) 1.82% 0.04% 0.76% 16 mm (#1) < 16 mm (#2) 2.18% 0.02% 1.00% The maximum, minimum, and average dose percent differences between spatial diameters were within the acceptable level of 3%. Fluence Dampening The goal of fluence dampening is to create new 3 dimensional dose distributions that maintain the clinical characteristics of their original normal source point SRS plan, while allowing for a faster reproducibility via IMRT using MLCs. To be clinically viable, the new fluence dampened plans must meet the key plan objectives. The key plan objectives, in order of importance, are to principally deliver the R x dose to the entire target volume, then to minimize the dose to surroun ding normal tissue, and lastly, to maintain a steep dose gradient at the target to normal tissue boundary. The target volume was defined to contain every voxel in the original normal source point SRS method generated 3 dimensional dose distribution. The ab ility of fluence dampening to generate 3 dimensional dose distributions that meet the key plan objectives was evaluated.

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107 Overlap Removal Method The overlap removal method was the primar y method investigated in this work. In the overlapping regions, the overlap removal method involves removing the dose delivered by the lower contributing beam(s), only preserving the largest single beam contribution. For the sake of space , the results for the multi sphere plans only will be presented. The multi sphere res ults are also the most relevant because most SRS plans involve spheres with multiple beam s each . 1 D imensional line dose profiles of multi sphere plans generated using the single source SRS method with dampening were compared to the same 1 dimensional line dose profiles generated using the normal source point SRS method as was done in the Dose Algorithm Validation section. Dose intensity maps were gener ated at isocenter to show the dose intensity levels present in the 3 dimensional dose distribution. The normal source point SRS method generated intensity maps were compared to single source point SRS method with dampening by the overlap removal method gen erated intensity maps. 1 Dimensional line dose profiles Figure 4 39 . The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with equal sphere weighting (#1 = #2) .

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108 Figure 4 40 . The effect of dam pening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2) . Figure 4 41 . The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 < #2) .

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109 Figure 4 42 . The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset axially by 17 mm with equal sphere weighting (#1 = #2) . Figure 4 43 . The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset axially 17 mm with unequal sphere weighting (#1 > #2) .

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110 Figure 4 44 . The effect of dampening on a 1 dimensional line dose profile for two 16 mm spheres offset a xially by 17 mm with unequal sphere weighting (#1 < #2) . 1 Dimensional line dose profiles results analysis The overlap removal method successfully removed the hot spots for the combined 3 dimensional dose distribution as shown by the 1 dimensional line dos e profiles for overlap removal method dose distributions . The resulting 3 dimensional dose distribution showed each sphere to be clearly differentiated from each other . The 1 dimensional line dose profiles also demonstrate that the overlap removal method a dequately maintains the steep dose gradient. The 1 dimensional line dose profiles exhibited two main side effects of the overlap removal method: an overall reduction of the dose in the 3 dimensional dose distribution, and significant loss of dose to the ta rget volume between spheres . The 1 dimensional dose profiles demonstrate d an over dampening of the target volume between spheres . Also, s ignificant portions of each profile fall well below the previously defined R x level of 70% on each 1 dimensional line dose profile above , especially for plans involving unequal sphere weights .

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111 Therefore, the overlap removal method generated 3 dim ensional dose distribution failed to deliver the Rx dose to the target volume. The mos t significant dose was lost by portions of the target volume that fall between spheres. Figure 4 39 above showed this effect as the region between the two spheres was a hot spot before the overlap removal method was applied. After the overlap removal metho d was applied the dose dropped to well below the required R x dose level. Dose intensity maps A B Figure 4 45 . Dose intensity maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with equal weights (#1 = #2). A) shows the original dose intensity, B) shows the dampened dose intensity. A B Figure 4 46 . Dose intensity maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal w eights (#1 > #2). A) shows the original dose intensity, B) shows the dampened dose intensity.

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112 A B Figure 4 47 . Dose intensity maps of axial slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 < #2). A) shows the original dose intensity, B) shows the dampened dose intensity. A B Figure 4 48 . Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with equal weights (#1 = #2). A) show s the original dose intensity, B) shows the dampened dose intensity.

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113 A B Figure 4 49 . Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 > #2). A) shows the orig inal dose intensity, B) shows the dampened dose intensity. A B Figure 4 50 . Dose intensity maps of sagittal slices through isocenter for a two 16 mm spheres offset laterally by 17 mm with unequal weights (#1 < #2). A) shows the original dose intensity, B) shows the dampened dose intensity. Dose intensity map results analysis The dose intensity maps above demonstrate clearly the overlap removal method s ability dimensional dos e distribution. The overlap removal method improves on the third key plan objective of minimizing intensity levels

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114 over the corresponding original plan. The overlap removal method generated distribution s clearly had a more uniform dose compared to the origi nal dose distribution. The intensity maps also show ed how the overlap removal method c ompletely removed hot spots that lay between spheres. The overlap removal me thod also clearly differentiated from each other. This result was attributed to the over damp ening of the target volume between spheres as previously observed in the analysis of the 1 dimensional line dose profiles. Dose Correction of Overlap Removal Method The over dampening caused by the overlap removal method necessitated further modification o f the 3 dimensional dose distributions to compensate for the excessive loss of dose. As observed in the analysis of the dampened 1 dimensional line dose profiles, the overlap removal method removed a substantial amount of dose from many regions of the targ et volume which previously at the R x dose level. Primarily, it was identified that the regions between sphere s where hot spots were previously found , suffered the largest dose reduction to below the R x dose level. Figure 4 51 below shows where target volum e voxels were maintained , and where they were lost . Figure 4 51 . Analysis of the target volume following dampening using the overlap removal method. The green mark s are voxel at the R x dose level , and the red crosses are voxels below the R x dose level.

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115 Furthermore, Figure 4 51 shows that target volume voxels between the spheres that are not within a geometrically defined sphere suffered the largest reduction in dose. Target volume voxels that are not within a geometrically defined sphere re ceive their dose by falling along the paths of multiple radiation beams intersecting in the region between spheres. Th erefore , regions of target volume between spheres but not within a geometrically defined sphere will see fewer overlapping beams and lose a more severe amount of dose due to dampening . A method of identifying these voxels in order to correct for the ir over dampening was developed. OUT voxel dose correction method The target volume voxels that are not within a defined sphere in the original p dimensional dose distribution were labeled OUT voxels, for not being located inside any of the spheres. The OUT voxels were identified and examined in each beam set to see which beam(s) they fall or do not fall within. Figure 4 52 shows how OUT vox els are concentrated between two adjacent spheres Figure 4 52 . The distribution of OUT voxels, in the region highlighted in red, o f two adjacent spheres. Since the OUT voxels are concentrated primarily between spheres they are inherently very close to if not within at least one beam in each beam set. By taking advantage of the dose modulation provided by the SRS via IMRT plan using MLCs, the MLCs can be opened along the

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116 edge of a defined beam to add dose coverage to OUT voxels that fall just outside a beam. This technique preserve s the number of dose levels within in the 3 dimensional dose distribution of a beam set , wh ile adding lost dose to the OUT voxels. 3 dimensional dose distribution in a plan was analyzed to identify the location of each OUT voxel relative to each beam in the beam set. If the OUT voxel did not fall within any beam it was assigned the dose intensity of the beam closest to it. This algorithm was applied only to beam sets with at least 25% of all the OUT points lying out of all the beams in the beam set. After the 3 dimensional dose distribution for each beam set was sum, a significant overall loss of dose was still present. Therefore, a new dose percent level was chosen to which the R x dose level would be re prescrib e. This is analogous to renormalizing the R x level to a new dose percent level. The dampened with subsequent dose correction 3 dimensional dose distribution was analyzing to see whether target volume voxels were returned to above the R x dose level or not. If the target volume voxel w as returned to above the R x dose level, then they were considered to be matched volume , meaning the voxel matched the R x dose level . If the target volume voxel did not return to above the R x dose level, then that voxel was consi dered to be missed volume, meaning the dampening with subsequent dose correction plan failed to maintain the R x to that voxel. If a voxel in the dampened with subsequent dose correction plan was above the R x dose level , but was below the R x dose level in t he original plan, then that voxel was considered to be added volume . These added volume voxels represents an increase in dose to the surrounding normal tissue. R x dose voxel comparison analysis The new R x dose levels for the dampened with subsequent dose correction plans used to raise the dose to target volume voxels were 85% and 80% of the previous R x dose level.

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117 A B Figure 4 53 . Effect of the overlap removal method with dose correction for t wo 16 mm spheres offset laterally by 17 mm with equal sphere weighting (#1 = #2) . A) S hows the 85% R x dose level, B) shows the 80% R x dose level. Table 4 85 . The percentage of the target volume matched, missed, and added after the overlap removal method w ith dose correction for two 16 mm spheres offset laterally by 17 mm with equal sphere weighting (#1 = #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 93.8% 6.2% 14.4% 80% 99.2% 0.8% 30.3% A B Figure 4 54 . Effect of the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2) . A) S hows the 85% R x dose level, B) shows the 80% R x dose level.

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118 Table 4 86 . The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 > #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 95.4% 4.6% 13.1% 80% 96.2% 3.8% 21.6% A B Figure 4 55 . Effect of the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weighting (#1 < #2) . A) S hows the 85% R x dose level, B) shows the 80% R x dose level. Table 4 87 . The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset laterally by 17 mm with unequal sphere weight ing (#1 < #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 95.3% 4.7% 13.4% 80% 96.3% 3.7% 22.1% A B Figure 4 56 . Effect of the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with equal sphere weighting (#1 = #2) . A) S hows the 85% R x dose level, B) shows the 80% R x dose level.

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119 Table 4 88 . The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with equal sphere weighting (#1 = #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 91.5% 8.5% 11.8% 80% 99.0% 1.0% 26.7% A B Figure 4 57 . Effect of the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 > #2) . A) S hows the 85% R x dose level, B) shows the 80% R x dose level. Table 4 89 . The percentage of the target volume matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 > #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 93.0% 7.0% 9.4% 80% 94.3% 5.7% 17.7% A B Figure 4 58 . Effect of the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 < #2) . A ) S hows the 85% R x dose level, B ) shows the 80% R x dose level.

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120 Table 4 90 . The percentage of the target volum e matched, missed, and added after the overlap removal method with dose correction for two 16 mm spheres offset axially by 17 mm with unequal sphere weighting (#1 < #2) . R x dose percent level Volume percent matched Volume percent missed Volume percent added 85% 94.6% 5.4% 13.7% 80% 95.7% 4.3% 21.9% OUT voxel dose correction results analysis The OUT voxel dose correction method as shown by the target volume voxel analysis of the previous section was effective in adding dose to the OUT voxels between spheres of equal weighting (see Figure 4 # and 4 #), but was not effective in adding dose to OUT voxels which fall between spheres of unequal weighting. It was observed in analysis of the 1 dimensional li ne dose profiles that the overlap removal method over dampened unequally weighted sphere. The OUT voxel dose correction method is not strong enough to overcome the over dampening of unequally weighted multi sphere plans. The OUT voxel method also qui ckly a dded a significant amount of normal tissue to the R x dose volume as the new R x dose percent level is lowered to include more of the target volume in the dampened with subsequent dose correction 3 dimensional dose distribution . This complicates the re lationship between to the first two key plan objectives. As shown in Table 4 # (for two 16mm equal), the drop from the 85% to 80% Rx dose l evel lower ed the amount of missed volume to below 1.0%, but more than double d the volume added from an already signif icant amount of 14.4% to 30.3%.

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121 CHAPTER 5 CONCLUSION S AND DISCUSSION S Dose Algorithm Conclusion for Dose Algorithm Validation Normal source point SRS method conclusion The demonstrated its ability to accurately reproduce numerically as well as spatially the 3 dimensional dose distribution of the UF in house TPS for SRS via sphere packing plans using static beams . It computed numerical values of dose at isocenter and maximum dose for nearly every plan w ith in the acceptable dose percent tolerance of 3%. It also managed to produce 1 dimensional line dose profiles that on average agreed spatially within the 3 mm tolerance, and on average agreed numerically in terms of dose within the 3% tolerance for each point compared to the UF in house TPS. tolerances mainly for plans involving multi beams with unequal weightings. For example, the 14 mm diameter circularly col limated beam set on the edge of a 40 mm diameter circularly collimated beam with the 12 mm beam weighte d less than the 40 mm beam plan gave a dose at isocenter that exceed the 3% dose tolerance with a percent error of 12.3%. The 1 dimensional line dose pr ofiles also showed that the steep dose gradient was Single source point SRS point method conclusion tain the fidelity of its 3 dimensional dose distribution by applying the appropriate correction factors. Therefore, the dose

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122 proved to accura tely replicate the 3 dimensional dose distribution of the UF in house TPS. dose at isocenter and maximum dose for multi beam and multi sphere plans that were nearly identical to the normal sources point SRS method and in many instances slightly more accurate. Evaluation of the 1 dimensional line dose profiles for the single source point SRS method once again produced results nearly identical and in some instances slightly more accurate than the normal source point SRS method. It also accurately modeled the steep dose gradient. Discussion of Dose Algorithm Validation accurate tools for computing th e 3 dimensional dose distributions of SRS via sphere packing plans using static beams. Furthermore, the single source points SRS method accurately models the 3 dimensional dose distribution of an SRS via IMRT plan using MLCs for the purpose of allowing for experimental modification of the 3 dimensional dose distribution by fluence dampening using the MLCs. constitute the building blocks for more complex SRS plans (i.e., si ngle beam, multi beam, single sphere, and multi sphere). Each plan had at most two beams or two spheres. Further more than two beams or two spheres is needed.

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123 Flue nce Dampening Conclusion for Fluence Dampening O verlap removal m ethod conclusion Fluence dampening by the overlap removal method successfully accomplish ed its goal of removing the radiation hot spots generated by the unnecessary overlapping fluence in each beam set. The new 3 dimensional dose distributions generated at each beam set contained fewer intensity levels . T he dimensional dose distributions contained a more uniform dose than the original dose distribution . Ho wever, the overlap removal method proved to over dampen the target volume betwe en spheres. The dose to target volume voxels that lie between spheres that do not fall geometrically within a sphere lost a significant portion of their dose, such that they typ ically fell far below the R x dose level. For fluence dampening using the overlap removal method to be clinically viable, it must meet the first key plan objective of delivering the R x dose to the entire target volume. The overlap removal method fails to ma intain the dose to each target volume voxel , and therefore required a correction method be applied to augment the dose to target volume voxels . OUT voxel correction method conclusion The OUT voxel correction method was devised to add dose to the target vol ume between spheres that fell below the R x dose level after fluence dampening using the overlap remo val method . The OUT voxel correction method successfully augmented the dose to the OUT voxels, but not before a substantial amount of normal tissue was adde d to the Rx dose level volume. The overall dose lost by in the target volume voxels required a new R x dose percent level. As the new R x dose percent dose was lowered to include more of the target volume, the amount of normal tissue added to the Rx dose level accumulated too quickly. Therefore, the OUT voxel correction

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124 method violated the second key plan objective before adequately correct ing the dose to OUT voxels to meet the demands of the first key plan objective. Discussion of Fluence Dampening Fluence dampening by the overlap removal method was able remove the unnecessary overlapping fluence as it was designed to do, but the resultant 3 dimensional dose distribution proved to not be clinically viable as it removed too much dose from the entire distribution. After subsequent correction using the OUT voxel correction method, the 3 dimensional dose distributions added too much normal tissu e to the R x dose volume . In the process of augmenting the dose to the target volume due to over dampening to satisfy the first key objective, the plans failed to be clinically viable by violating the second key plan objective. The proven ability of fluence dampening by the overlap removal method to reduce MUs and treatment times shows promise if a method can be devised to carefully augment the dose to the over dampened target volume between spheres without adding significant amounts of normal tissue to the R x dose level. An effective method for correcting the over dampening could be found by taking advantage of the ability of the MLCs to modulate the dose to regions between spheres.

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125 LIST OF REFERENCES 1 L. Leksell, "The stereotaxic method and radiosurgery of the brain," Acta Chir Scand 102 , 316 319 (1951). 2 A. Wu, G. Lindner, A.H. Maitz, A.M. Kalend, L.D. Lunsford, J.C. Flickinger, W.D. Bloomer, "Physics of gamma knife approach on convergent beams in stereotactic radiosurgery," Int J Radiat Oncol Biol Phys 18 , 941 949 (1990). 3 L. Leksell, "Stereotactic radio surgery," J Neurol Neurosurg Psychiatry 46 , 797 803 (1983). 4 F. Colombo, A. Benedetti, F. Pozza, R.C. Avanzo, C. Marchetti, G. Chierego, A. Zanardo, "External stereotactic irradiation by linear accelerator," Neurosurgery 16 , 154 160 (1985). 5 W.A. Friedma n, F.J. Bova, "The University of Florida radiosurgery system," Surg Neurol 32 , 334 342 (1989). 6 W.A. Friedman, F.J. Bova, R. Spiegelmann, "Linear accelerator radiosurgery at the University of Florida," Neurosurg Clin N Am 3 , 141 166 (1992). 7 S.L. Meeks, F.J. Bova, W.A. Friedman, J.M. Buatti, W.M. Mendenhall, "Linac scalpel radiosurgery at the University of Florida," Med Dosim 23 , 177 185 (1998). 8 T.H. Wagner, T. Yi, S.L. Meeks, F.J. Bova, B.L. Brechner, Y. Chen, J.M. Buatti, W.A. Friedman, K.D. Foote, L. G. Bouchet, "A geometrically based method for automated radiosurgery planning," Int J Radiat Oncol Biol Phys 48 , 1599 1611 (2000). 9 T.J. St. John, University of Florida, 2002. 10 T.J. St John, T.H. Wagner, F.J. Bova, W.A. Friedman, S.L. Meeks, "A geometrically based method of step and shoot stereotactic radiosurgery with a miniature multileaf collimator," Phys Med Biol 50 , 3263 3276 (2005). 11 B. Velasco, University of Florida. 12 T. s. Suh, University of Florida, 1990. 13 H. Johns, J. Cunningham, The Physics of Radiology, Fourth Edition . (Charles C Thomas, Springfield, Illinois, 1983). 14 J.R. Clarkson, Br. J. Radiol 14 , 265 (1941).

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126 BIOGRAPHICAL SKETCH Michael C. Hermans en was born in Logan, Utah to Chris and Kristine Hermansen in 1986 . He grew up in Moorpark, California where he graduated from Moorpark High School in 2004. After completing his freshman year of college at Brigham Young University (BYU) in Provo, Utah, he left for two years to serve a full time mission for the Church of Jesus Christ of Latter day Saints in Rosario, Argentina in September of 2005. After his return from Argentina, he resumed his studies at BYU. He completed his Bachelor of Science in applied p hysics in April of 2012 . He was accepted by the J. Crayton Pruitt Family Departm ent of Biomedical Engineering at the University of Florida and subsequently began a Master of Science in biomedical engineering with a concertation in medical p hysics in Augu st of 2013 . He currently works for Dr. Frank J. Bova in his Radiosurgery and Biology Lab where he performs radiosurgery research.