Uncertainties in Adaptive Radiation Therapy for Patients with Cancers of the Head and Neck

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Uncertainties in Adaptive Radiation Therapy for Patients with Cancers of the Head and Neck
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1 online resource (2 p.)
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english
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Pukala, Jason A
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University of Florida
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Degree:
Doctorate ( Ph.D.)
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
MILNER,ROWAN J
LANGEN,KATJA MARIA
MEEKS,SANFORD L

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Subjects / Keywords:
adaptive -- deformable -- image -- radiation -- registration -- therapy
Biomedical Engineering -- Dissertations, Academic -- UF
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Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
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Abstract:
Adaptive radiation therapy (ART) is an emerging area of interest within radiation oncology that aims to estimate the doses actually delivered to patients and adapt their treatment plans to mitigate any changes from the planned dose. Recently introduced technologies, including dose recalculation on repeated volumetric patient imaging and deformable image registration (DIR), are required to perform state-of-the-art ART. The inherent uncertainties of these new technologies are not well known, however, undermining the confidence in clinical decisions made using these tools. This work presents a methodology to quantify the uncertainties of ART for the purpose of providing clinicians with a better foundation for making such decisions. To accomplish this goal, this dissertation is divided into four distinct aims: quantify the dosimetric uncertainty of dose recalculations performed on inter-fraction volumetric patient images, determine the uncertainty introduced by using a plan dose overlay instead of performing dose recalculation, quantify the uncertainty of DIR, and translate the quantified uncertainties into clinically useful tools. The first aim was satisfied by developing a methodology to quantify the uncertainties of dose recalculation using megavoltage CT that could be extended to other imaging modalities. For the head-and-neck cancer cases examined, it was found that dose recalculation uncertainties could be maintained within 2.5% with minimal additional quality assurance effort. Comparing the plan dose overlay to dose recalculation showed that dose recalculation would be preferred for the most accurate results, but valuable dosimetric trend data could be still be observed if only the dose overlay were available. A library of ten virtual patient phantoms was developed to quantify the spatial uncertainty of DIR. The phantoms were derived from images of head-and-neck cancer patients and could be used with any DIR algorithm. Finally, a method of translating the spatial uncertainty of DIR into dosimetric uncertainty was developed and validated. Using this method, the dosimetric uncertainties for any head-and-neck patient could be displayed as dose-volume histograms useful for making clinical decisions. In conclusion, we have developed quality assurance methods for ART that are clinically relevant and report standard metrics that are useful for decision making.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Statement of Responsibility:
by Jason A Pukala.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: BOVA,FRANK J.
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Co-adviser: HINTENLANG,DAVID ERIC.

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UNCERTAINTIES IN ADAPTIVE RADIATION THERAPY FOR PATIENTS WITH CANCERS OF THE HEAD AND NECK By JASON PUKALA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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2014 Jason Pukala

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To our patients may I never forget that you are the reason that I do what I do

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4 ACKNOWLEDGMENTS I thank my family, whether by blood or by faith for all of their encouragement and t have done it without them I especially thank my mother who has no idea what I do, my father, who pretends to know what I do, and my brother, who just makes up cool jobs for me to do. You always point me back to love, joy, and peace. I also thank my grandparents who worked tirelessly and sacrificed greatly to give me the opportunities that I have. I thank Dr. Frank Bova for his guidance, patience, and generosit y. He introduced me to medical physics as an und ergraduate student and invested in me both academically and financially, as an inexperienced graduate student. Without Dr. Bova, I can safely say that I would have never pursued or likely even heard of a career in medical physics. I thank Dr. Sanford Meeks for his advice, experience, and leadership. Dr. Meeks encouraged me to pursue a PhD and gave me the opportunity to do it in his clinic. He always had an open door to give me advice, point me in the rig ht direction, and teach me about therapy physi cs and the benefits of drinking coffee. I thank Dr. Katja Langen for her direction, collaboration, and confidence in me. Dr. Langen believed in me enough to provide me with unique opportunities to go places an d meet people that were invaluable to my professional growth. She was always avail able for advice, brainstorming, research guidance, and German chocolate. I also extend a sincere thanks to all of my colleagues at UF Health Cancer Center Orlando Health. They allowed me to take up space in physics, showed me how to care for patients, and let me be a part of the family.

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5 Finally, I thank God for the love of Christ that surpasses all knowledge and the His peace that surpasses all understanding. For his invi sible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 11 LIST OF ABBR EVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 16 The Adaptive Radiotherapy Process ................................ ................................ ...... 16 Adaptive Radiotherapy for Head and Neck Cancers ................................ .............. 17 Adaptive Radiotherapy Tools ................................ ................................ .................. 21 Volumetric Image Guided Radiotherapy ................................ .......................... 21 Deformable Image Registration ................................ ................................ ........ 24 Biological Considerations of Dose Accumulation ................................ ............. 27 Uncertainties in Adaptive Radiotherapy ................................ ................................ .. 28 Volumetric Image Guided Radiotherapy ................................ .......................... 28 Deformable Image Registration ................................ ................................ ........ 33 Novel Methods for the Quantification of Uncertainties in Adaptive Radiotherapy ... 35 Objectives of this Research ................................ ................................ .................... 38 2 THE UNCERTAINTY OF DOSE RECALCULATIONS ................................ ............ 46 Materials and Methods ................................ ................................ ............................ 47 Image Acquisition Parameters ................................ ................................ .......... 47 Baseline MVCT Dosimetric Uncertainty ................................ ........................... 48 Temporal MVCT Image Variation ................................ ................................ ..... 49 Dosimetric Uncertainty Resulting from Temporal MVCT Image Variation ........ 50 Results ................................ ................................ ................................ .................... 52 Baseline MVCT Dosimetric Uncertainty ................................ ........................... 52 Temporal MVCT Image Variation ................................ ................................ ..... 52 Dosimetric Uncertainty Resulting from Temporal MVCT Image Variation ........ 53 Discussion ................................ ................................ ................................ .............. 55 Conclusion ................................ ................................ ................................ .............. 59 3 THE IMPORTANCE OF DOSE RECALCULATIONS ................................ ............. 69 Materials and Methods ................................ ................................ ............................ 69 Patient Cohort and Image Acquisition ................................ .............................. 69

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7 Dose Recalculation Methodology ................................ ................................ ..... 70 Dose Overlay Methodology ................................ ................................ .............. 71 Deformable Image Registration ................................ ................................ ........ 72 Comparison of the Recalculated and Overlaid Dose Distributions ................... 72 Results ................................ ................................ ................................ .................... 73 Discussion ................................ ................................ ................................ .............. 74 Conclusion ................................ ................................ ................................ .............. 77 4 THE SPATIAL UNCERTAINTY OF DEFORMABLE IMAGE REGISTRATION ....... 83 Materials and Methods ................................ ................................ ............................ 83 Image Acquisition and Patient Selection ................................ .......................... 83 Image Autosegmen tation and Deformation ................................ ...................... 84 Manual Image Deformation ................................ ................................ .............. 85 Deformed Image Post Processing ................................ ................................ .... 86 Virtual Phantom Quality Metrics ................................ ................................ ....... 88 Quantification of DIR Uncertainty ................................ ................................ ..... 89 Results ................................ ................................ ................................ .................... 89 Virtual Phantom Quality Metrics ................................ ................................ ....... 89 Quantification of DIR Uncertainty ................................ ................................ ..... 89 Discussion ................................ ................................ ................................ .............. 90 Conclusion ................................ ................................ ................................ .............. 94 5 THE DOSIMETRIC UNCERTAINTY OF DEFORMABLE IMAGE REGISTRATION ................................ ................................ ................................ ..... 99 Materials and Methods ................................ ................................ .......................... 100 Virtual Phantom Library ................................ ................................ .................. 100 Dose Recalculation ................................ ................................ ........................ 101 Creating and Evaluating DVFs for DIR Dosimetric Error Si mulation .............. 102 DIR Dosimetric Error Simulation ................................ ................................ ..... 104 Results ................................ ................................ ................................ .................. 106 Evaluation of DVF Creation using Random Error Maps ................................ 106 DIR Dosimetric Error Simulation ................................ ................................ ..... 106 Discussion ................................ ................................ ................................ ............ 108 Conclusion ................................ ................................ ................................ ............ 113 6 SUMMARY ................................ ................................ ................................ ........... 123 Result of this Work ................................ ................................ ................................ 123 Opportun ities for Further Development ................................ ................................ 125 Automated Image Calibration ................................ ................................ ......... 125 Graphics Processing Unit Based Dose Calculation ................................ ........ 126 Benchmarking of Deformable Image Registration Algorithms ........................ 127 Development of Additional Virtual Phantoms ................................ ................. 127 Automated Deformable Image Registration Quality Assu rance ...................... 128 Final Thoughts ................................ ................................ ................................ ...... 129

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8 APPENDIX A PRELIMINARY DATA FOR THE DEFORMABLE IMAGE REGISTRATION EVALUATION PROJECT ................................ ................................ ..................... 130 LIST OF REFERENCES ................................ ................................ ............................. 135 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 145

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9 LIST OF TABLES Table page 1 1 Reported geometric and dosimetric target changes during a radiotherapy course ................................ ................................ ................................ ................. 41 1 2 Reported geometric and dosimetric parotid gland changes during a radiotherapy course ................................ ................................ ............................ 42 2 1 Dosimetric endpoints were recalculated on MVCT images of three different phantoms and compared to the endpoints calculated on the initial kVCT plans. ................................ ................................ ................................ .................. 60 2 2 Dosimetric endpoints were calculated over the range of solid water MVCT number variation for six patients and three distinct c linical sites ......................... 61 2 3 Dosimetric endpoints were calculated over the range of solid water MVCT number variation for 10 patients wit h head and neck cancer. ............................. 62 3 1 Mean relative dose difference of the daily dosimetric endpoints for each patient. ................................ ................................ ................................ ................ 78 3 2 Relative dose difference of the accumulated dosimetric endpoints for each plan. ................................ ................................ ................................ .................... 79 3 3 Mean relative dose variations and correlation coefficients for the daily and accumulated dosimetric endpoints. ................................ ................................ .... 80 4 1 Attributes of patients selected for the development of the virtual phantoms. ...... 95 4 2 Virtual phantom quality metrics. ................................ ................................ .......... 96 4 3 Mean spatial error and standard deviation of the means for all 10 virtual phantoms. ................................ ................................ ................................ ........... 96 4 4 Mean and maximum right parotid spatial errors for each virtual phantom. ......... 96 5 1 Attributes of patients selected for the development of the virtual phantoms. .... 114 5 2 Mean error vector magnitude and standard deviation for each phantom ROI. 114 5 3 Attributes of patients selected for DIR error simulation. ................................ .... 11 5 5 4 Mean and maximum differences between using the spatially correlated (baseline) error maps and the non sp atially correlated (random) error maps for the selected ROI endpoints. ................................ ................................ ........ 116

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10 5 5 Median and maximum dosimetric differences of the s imulated DIR errors compared to the non perturbed DVFs for the selected DVH endpoints. ........... 117 A 1 Mean phantom region of interest er ror vector magnitude and standard deviation for Institution 1: Velocity B spline ................................ ...................... 131 A 2 Mean phantom region of interest error vector magnitude and standard deviation for Institution 2: Velocity extended multipass B spline ....................... 131 A 3 Mean phantom region of int erest error vector magnitude and standard deviation for Institution 3: Velocity multipass B spline, no VOI ......................... 132 A 4 Mean phantom r egion of interest error vector magnitude and standard deviation for Institution 3: Velocity multipass B spline, with VOI ....................... 132 A 5 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3: Velocity extended multipass B spline, no VOI ......... 133 A 6 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3: Velocity extended multipass B spline, with VOI ....... 133 A 7 Mean phantom region of interest error vector magnitude and standard deviation for Institution 4: MIM 6.2.2 ................................ ................................ 134

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11 LIST OF FIGURES Figure page 1 1 A typical adaptive radiotherapy (ART) workflow. ................................ ................ 43 1 2 Axial image of a patient with head and neck cancer showing how the left parotid volume has changed during treatment due to weight loss. ..................... 44 1 3 DVHs estimated during the ART dose assessment process. ............................. 45 2 1 Planned dose distributions for each of the phantoms evaluated overlaid on axial kVCT images. ................................ ................................ ............................. 64 2 2 Density histograms for the TomoPhantom image sets. ................................ ...... 65 2 3 Temporal variation of the mean HU va lue of TomoPhantom solid water for two treatment machines. ................................ ................................ .................... 66 2 4 DVH curves calculated for each site. ................................ ................................ .. 67 2 5 Dose difference (cGy) for each evaluated case. ................................ ................. 68 3 1 Recalculated and overlaid daily dosimetric endpoints for Patient 3. ................... 81 3 2 Parotid D 50% data for both parotids. ................................ ................................ .... 82 4 1 Example of image autosegmentation and deformation. ................................ ...... 97 4 2 Example of the manually deformed parotid shrinkage. ................................ ....... 97 4 3 Diagram of the virtual phantom creation process. ................................ .............. 98 5 1 Spatially ...... 118 5 2 Flowchart describing the creation and validation of hypothetical (random) DVFs for DIR error simulation. ................................ ................................ .......... 119 5 3 DVHs generated using the baseline (dashed/blue curve) and random (solid/red curves) error maps for the right parotid of Phantom 5. ...................... 120 5 4 DVHs generated using the non perturbed DVF (dashed/red curve) and the simulated error DVFs (solid/grey curves) for the right parotid of Patient 1. .... 120 5 5 DVHs generated using the non perturbed DVF (dashed/red curve) and the simulated error DVFs (solid/grey curves) for the left parotid of two patients. .. 121 5 6 Coronal slices of Phantom 9 where a 6.3 mm average spatial error was observed in the DIR of the right parotid. ................................ ........................... 122

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12 LIST OF ABBREVIATIONS ART adaptive radiation therapy CC correlation coefficient CT computed tomography CTV clinical target volume DIR deformable image registration DSI Dice similarity index DVF deformation vector field DVH dose volume histogram ED electron density EOT end of treatment FEM finite element modeling FOV field of view GPU graphics processing unit GTV gross tumor volume H&N head and neck HU Hounsfield unit IGRT image guided radiation therapy IMRT intensity modulated radiation therapy IVDT image value to density table kVCBCT kilovoltage cone beam computed tomography kVCT kilovoltage computed tomography MOSFET metal oxide semiconductor field effective transistor MR magnetic resonance MVCBCT megavoltage cone beam computed tomography

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13 MVCT megavoltage computed tomography NCC normalized cross correlation OAR organ at risk PDF probability density function PTV planning target volume QA quality assurance RMSPE root mean square percent error ROI region of interest SEOT simulated end of treatment SID source to imager distance SOT start of treatment TPS thin plate splines UE unbalanced energy

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy UNCERTAINTIES IN ADAPTIVE RADIATION THERAPY FOR PATIENTS WITH CANCERS OF THE HEAD AND NECK By Jason Pukala May 2014 Chair: Frank J. Bova Major: Biomedical Engineering Adaptive radiation therapy (ART) is an emerging area of interest within radiation oncology that aims to estimate the doses actually delivered to patients and adapt thei r treatment plans to mitigate any changes from the planned dose. Recently introduced technologies, including dose recalculation on repeated volumetric patient imaging and deformable image registration (DIR), are required to perform state of the art ART. The inherent uncertainties of these new technologies are not well known, however, undermining the confidence in clinical decisions made using these tools. This work presents a methodology to quantify the uncertainties of ART for the purpose of providing c linicians with a better foundation for making such decisions. To accomplish this goal, this dissertation is divided into four distinct aims: quantify the dosimetric uncertainty of dose recalculations performed on inter fraction volumetric patient images, determine the uncertainty introduced by using a plan dose overlay instead of performing dose recalculation, quantify the uncertainty of DIR, and translate the quanti fied uncertainties into clinically useful tools. The first aim was satisfied by developing a methodology to quantify the uncertainties of dose recalculation using megavoltage CT that could be extended to other imaging modalities. For the

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15 head and neck ca ncer cases examined, it was found that dose recalculation uncertainties could be maintained within 2.5% with minimal additional quality assurance effort. Comparing the plan dose overlay to dose recalculation showed that dose recalculation would be prefer red for the most accurate results, but valuable dosimetric trend data could be still be observed if only the dose overlay were available. A library of ten virtual patient phantoms was developed to quantify the spatial uncertainty of DIR. The phantoms wer e derived from images of head and neck cancer patients and could be used with any DIR algorithm. Finally, a method of translating the spatial uncertainty of DIR into dosimetric uncertainty was developed and validated. Using this method, the dosimetric un certainties for any head and neck patient could be displayed as dose volume histograms useful for making clinical decisions. In conclusion, we have developed quality assurance methods for ART that are clinically relevant and report standard metrics that a re useful for decision making.

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16 CHAPTER 1 INTRODUCTION The Adaptive Radiotherapy Process Yan et al. 1 process where the treatment plan can be modified using a systematic feedback of treatment p arameters, including patient anatomy and positioning, will not vary over therapy course. However, many of the parameters do change resulting in a delivered dose that does not equal the planned dose. Adequate assessment of the delivered dose and the adapt ation of a treatment plan to mitigate negative dosimetric variations is the goal of ART as described in this document. The assessment of the delivered dose is required to make sound treatment decisions and acts as a set of measurements that into the radiotherapy process. One common way to obtain these measurements is through the use of frequent volumetric patient imaging. These images can be used in conjunction with recently developed techniques such as dose recalculation on the newly acqu ired images to quantify the dose distribution specific to that image set, automatic image segmentation to prevent clinic personnel from having to contour several image sets, and dose accumulation to summate the doses delivered over multiple fractions. Aut omatic image segmentation and dose accumulation are made possible by a tool called deformable image registration that will be described in detail later in Chapter 1 A typical ART process is illustrated in Figure 1 1. As an illustration of this process c onsider the example of Figure 1 2. Figure 1 2 shows an axial slice of a patient with head and neck cancer that has lost a noticeable amount of weight during

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17 his radiation therapy treatment course. The image of Figure 1 2 was acquired as part of a volumet Dose was recalculated using this image set to obtain the dose distribution seen in F igure 1 2 was located during the treatment planning phase of the ART process. Generated by automatic image segmentation, the deformed parotid contour shows how the left parotid volume has changed from what was originally planned and moved into a higher dose region due Using dose accumulation, Figure 1 3 illustrates how new a dose volume histogram (DVH) may be estimated for the left parotid gland based on the new anatomy and compared to the original treatment plan. In this case, as would be expected, the DVH of Figure 1 3 shows that the dose to the left parotid has increased compared to the intended plan. With this new information estimated from the ART dose assessment process, a clinician could now decide if the treatment should continu e without any intervention or if a replan should be initiated to reduce the parotid dose. Adaptive Radiotherapy for Head and Neck Cancers It has long been observed that patients undergoing radiotherapy for head and neck cancers may experience significant a natomic changes over the course of their treatment 2 6 These changes may be the result of shrinkage of the tumor, shrinkage of nodal masses, resolution of postoperative changes, or weight loss. Effective ART requires that the magnitude of these changes and their dosimetric impact be assessed in order to pla n an appropriate intervention, if any. The advent of image guided radiation therapy (IGRT) has provided more frequent volumetric images of patients under treatment and facilitated the quantification of anatomic and dosimetric effects.

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18 Many investigators anatomies change throughout a radiotherapy treatment course. The following paragraphs will specifically review how tumor coverage and normal tissue sparing is affected when irradiating head an d neck cancers using standard methods. Table 1 1 shows reported values from several studies of geometric and dosimetric target changes during a radiotherapy course. Although there were variations in the imaging method, imaging frequency, method of image r egistration, and treatment technique in each study, a few conclusions may still be drawn. Shrinking target volumes were consistently observed and this typically had no significant effect on the target dosimetry. The one exception is the investigation by Zhao et al. 7 where a 14.6% decrease in the clinical target volume (CTV) D 95% was observed. This conflicting observation and the variation seen in the magnitude of the target shrinkage may be explained by a lack of standardization in the ini tial target contours and, to a possibly greater extent, disagreement among the researchers concerning the delineation of target structures on the repeated image sets. For example, Hansen et al. 8 chose to maintain the original size of the gross tumor volume (GTV) on the second image set due to the uncertainty that shrinking the GTV might introduce for local regional tumor control. Alternatively, Zhao et al. 7 chose to adapt the GTVs to the anatomy observed on the second scans while maintaining the original size of the CTVs. Despite these differences, one could draw the conclusion that shrinking target volumes in conjunction with adequate margins are sufficient to maintain the prescribed dose to the CTV. While several stu dies have found that doses to other organs at risk (OARs) can change over a course of radiotherapy 7 18 this review will concentrate on the parotid

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19 glands because much of the literature focuses on these organs and they are illustrative of the potential benefits of ART. The parotid glands are essential to preserve salivary flow, have published dose thresholds to maintain function, and are typically located near high dose gradients (see Figure 1 2) 19 20 Therefore, small changes in the size or location of the parotids could result in substantially higher doses than originally planned and negatively impact patient outcomes. Published values for the geometric and dosimetric effects of radiotherapy on the parotid glands are shown in T able 1 2. Again, the change in the vo lume of the parotid glands varies among the authors, but a consistent decrease in volume was observed. Furthermore, the studies reported a medial shift o f the glands of approximately 2 to 3 mm over the course of treatment, especially for ipsilateral struc tures. A medial shift of this magnitude into the high dose region, coupled with a shrinking gland, can potentially escalate the mean dose received by the parotid as shown in T able 1 2. While the overall average parotid dose increase numbers published may seem modest for some studies, a subset of patients saw much larger increases. For example, Lee et al. 21 reported that three out of ten patients received mean parotid dose increases of 33% over the treatment plan while the remaining seven patients received dose increases of 10% or less. Overall, c hanges in shift critical structures into higher dose regions and compromise the sparing of these structures. This evidence shows that anatomical changes frequently occu r during treatment and may result in shrinking tumor volumes and/or increasing doses to OARs. As a means of mitigating these undesirable effects, new patient images may be acquired and

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20 new treatment plans created to adapt to the changing anatomy. Wu et a l. 18 investigated multiple replanning strategies in combination with CTV to planning target volume (PTV) margin reductions. They found that replanning had a minimal effect on doses to the brainstem, cord, and mandible. However, the parot id mean dose was reduced by 3% with the implementation of one replan at midcourse, 5% with two replans, 6% with a weekly replan implemented one week later, and 8% with a weekly replan implemented the same week. Additionally, if the CTV to PTV margins were reduced from 5 mm to 0 mm on the initial plan, parotid sparing improved by 22%. Cumulative CTV coverage was largely unaffected even with the reduced margins, but setup errors were not taken into account in order to solely evaluate the effects of patient deformation. Schwartz and Dong 22 reported results from a prospective ART study of 20 patients. In this study, 3 to 4 mm PTV expansions included in the initial plan were eliminated when adaptive replanning oc curred. 16 patients were replanned once at a median trigger point of the 16 th fraction. Compared to IGRT alone, the replan reduced the mean contralateral parotid dose by 2.8% (0.6 Gy) and the mean ipsilateral parotid dose by 3.9% (1.3 Gy). Four patients were replanned twice at median trigger points of the 11 th and 22 nd fractions. The mean dose to the contralateral parotid was reduced by 3.8% (0.8 Gy) and the ipsilateral parotid was reduced by 9% (4.1 Gy) for these patients. Wang et al. 17 investigated the effects of replanning 28 patients with naspharyngeal carcinoma before the 25 th fraction of intensity modulated radiation therapy (IMRT). This study found that replanning significantly increased the volume of CTV receiving the prescription dose by 4.91% 10.89%. Replanning also significantly reduced the maximum dose to the spinal cord, mean dose to the left parotid, and V 30Gy of the right parotid by 5 9.23 Gy,

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21 4.23 10.03 Gy, and 1 1.47% 18.89%, respectively. Furthermore, 50% of the original treatment plans violated dose constraint criteria of the RTOG0225 protocol at the time of re imaging. None of the replans violated these criteria. Hansen et al. 8 acqui red new CT images after a mean of 19 fractions were delivered. The original beam configuration was applied to the new images and compared to the dosimetric endpoints achieved with a complete replan. The D 95% of the PTV GTV and PTV CTV increased by 2.2 Gy a nd 3 Gy for the remaining fractions, respectively, with a replan when compared to the original treatment plan. Additionally, the D 1cc of the spinal cord and D mean of the right parotid decreased by 3.1 Gy and 2.9 Gy for the remaining fractions, respectivel y. The results of 8 must be evaluated carefully, however, because of a potential patient selection bias caused by selecting patients that experienced substantial anatomic changes and were, theref ore, subject to replanning. Adaptive Radiotherapy Tools Volumetric Image Guided Radiotherapy The adoption of innovative tools in the clinic has brought the possibilities of ART within practical reach. For example, repeat patient imaging is a clear require ment of ART. While these images may be acquired with a traditional CT simulator, the acceptance and implementation of volumetric IGRT have greatly increased the availability and frequency of patient images. Although the current primary use of volumetric IGRT images is for improved patient alignment, they have the additional benefits of providing a means for the assessment of anatomical changes, physical information for dose recalculations and the assessment of dosimetric changes, and a database for the cr eation of new treatment plans. All of these benefits are essential for the effective practice of ART and, thus, a discussion of volumetric IGRT technologies is

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22 warranted. The most common volumetric IGRT technologies currently in use are CT on rails, mega voltage CT (MVCT), kilovoltage cone beam CT (kVCBCT), and megavoltage cone beam CT (MVCBCT). CT on rails employs a conventional CT scanner located in the therapy vault opposite a linear accelerator 23 The treatment couch can be rotated 180 to acquire images while the patient is immobilized in the treatment position. However, instead of the couch translating through a stationary CT gantry as with traditional helical CT scanners, the entire CT gantry is mounted on rails that allow it to move along a stationary couch. After the images are acquired, the couch is rotated 180 again to return the patient to the treatment position. MVCT operates on the same principles as a conventional kilovoltage CT scanner except that a higher energy imaging beam is used. This approach is convenient because it takes advantage of the trea tment beams in the megavoltage energy range generated by linear accelerators. The most common implementation of MVCT has a linear accelerator mounted opposite a xenon filled detector array on a ring gantry 24 25 In this configuration, the linear accelerator produces both the treatment beam and the imaging beam. However, when acquiring imaging data, the x ray beam energy is reduced from a nominal energy of 6 MV to 3.5 MV to improve the imaging characteristics 26 After the patient is setup outside of the gantry, the couch moves into the gantry bore to position the patient correctly for image acquisition or radiation delivery. During image acquisition, the ring gantry rotates around the patient while the linear accelerator produces a 3.5 MV fan beam that is intercepted by the detector array. The quality of the resulting images has been previously described 27 This design allows

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23 imag es of the patient to be acquired using the same equipment and geometry as the planned treatment. Another popular volumetric IGRT method is kVCBCT. kVCBCT takes advantage of the superior contrast that may be achieved with a kV imaging beam compared to a n M V beam. A typical configuration consists of a kV x ray source mounted opposite a flat panel detector 28 29 The source and detector are attached to the linear accelerator by extendable arms such that the direction of the kV imaging beam is perpendicular to the therapy beam and both beams share the same isocenter. A kV cone beam is incident on the detector so that a single rotation of the gantry is capable of producing a volumetric image set by means of filtered back projection. The kVCBCT geometry has an additional consideration when compared to the ring gantries previously mentioned, however. As the linear accelerator gantry rotates, gravity induced flex in the support arms of the kVCBCT system causes slight changes in the positions of the source and detector. This problem can be mitigated by applying flex corrections to the detector data on the order of 2 mm 29 kVCBCT beams have been well characterized using Monte Carlo meth ods and direct measurements 30 MVCBCT and kVCBCT are similar t echnologies outside of the obvious difference that MVCBCT uses a higher energy, megavoltage range beam to acquire image data. nic portal imaging device as the imaging source and detector, respecti vely 31 32 This is an advantage because additional imaging hardware, such as a kV source and detector, is not required and because images are obtained under the same geometric conditions as the treatment delivery. Apart from the differences noted, MVCBCT operation is similar to

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24 that of kVCBCT. Both modalities use a cone beam to acquire volumetric image data in a single arc and both also require flex corrections to account for changes in the relative positions of the source and detector as the gantry rotates. Deformable Image Registrati on Another tool that is greatly enhancing the practicality of ART is deformable image registration (DIR). The aim of DIR is to register two image sets of the same patient that differ substantially enough over time that rigid registration is not adequate o r appropriate. Two typical examples would be a patient that experiences considerable weight loss over a radiotherapy treatment course or lung motion over a breathing cycle. DIR accomplishes this by defining a non rigid spatial transformation from a sourc e image to a target image that best minimizes pre defined differences between the images. One area where DIR is very useful for ART is auto segmentation. Contouring new image sets for ART can be very resource intensive, especially if one considers the am the resources required to segment these image sets by automatically transferring contours from the initial or planning images to all subsequent images through the transf ormation defined by the non rigid registration 33 36 Furthermore, DIR enables the implementation of dose accumulation across multiple image sets 11 18 21 37 For example, each voxel from a d aily volumetric IGRT image may be mapped to a corresponding voxel in the planning image via the non rigid registration. After the dose distribution is recalculated on the daily volumetric IGRT images, the dose to each voxel in the planning image may be ac cumulated by summing the doses to all of its corresponding voxels from the daily images. In this manner, the doses from individual treatment fractions may be accumulated and compared to the treatment plan.

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25 There are many unique approaches to DIR 38 39 However, all of these approaches may be generalized to include two primary components: a similarity metric and a transformation method. Similarity metrics quantify how well two image sets are aligned. These metrics may be classified into point based me thods and intensity based methods. Point based methods minimize the distance between features such as points, curves, or surfaces of corresponding anatomical structures. An advantage of this method is that it allows the user to have some control over the deformable registration by selecting the desired points or surfaces. But, this is also a disadvantage because it requires human interaction which may be unreasonable for large datasets and introduces observer localization uncertainties. Furthermore, a l arge number of points are required to densely sample the deformation field. Intensity based methods do not require human intervention and instead rely on the relationship of voxel intensities to align images. Intensity based metrics include sum of square d differences, cross correlation, and mutual information 40 Sum of squared differences and cross correlation are used to register images of the same modality while mutual information may be used to register images of differing modalities. If each voxel in an imag e were given unlimited freedom to relocate during DIR, many possible and unacceptable solutions would exist. Therefore, transformation methods must be used to constrain the deformation. Transformation methods may be grouped into three categories: spline based techniques, physical techniques, and diffusion techniques. Spline based techniques rely on a set of basis functions, or piecewise polynomials known as splines, to model a deformation. The degrees of freedom of these techniques are defined by contr ol points spaced throughout the image

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26 sets. In the case of the thin plate splines 41 technique, the control points are not restricted to a regular grid but the movement of each control point has a global effect on the registration making it problematic to model local deformations. Additionally, the thin plate splines algorithm suffers from computational difficulties when using a large number of control points to model a complex deformation. The basis (B) splines 42 method uses a regularly spa ced grid of control points where each point only affects the local deformation. Thus, this algorithm overcomes the global deformation and computational restrictions of the thin plate splines algorithm. Physical transformation techniques constrain the defo rmation by using models from continuum mechanics. These techniques primarily include an elastic registration method 43 and a fluid registration method 44 The elastic registration method essential ly draws the anatomy of one image onto a sheet of elastic rubber that can be deformed to match another image. The similarity metrics between two image sets act as external forces on the anatomy of the deforming image. As these external forces are applied the deformation of the image is constrained by the properties of the elastic model. Due to the limitations of this model the elastic registration algorithm performs best when restricted to small deformations. The fluid registration method is very simil ar to the elastic method except that it uses a viscous fluid flow model to better handle large deformations. Both of these techniques are modeled using parti al differential equations that may require substantial computational resources to solve in a reasonable amount of time. Also, real tissue deformations are highly complex and can only be modeled as elastic or visco elastic materials under specific conditions. Therefore, these phy sical techniques may result in unrealistic deformations. Diffusion techniques exploit concepts

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27 45 implementation of this method, there are no constraints on the displacement vectors so the deformation field is regularized by convolution with a Gaussian filter. Lu et al. 46 regularization of the deformation field is accomplished directly within the transformation algorithm by including an objective to maximize the smoo thness of the field instead of indirectly by Gaussian convolution. Diffusion techniques are advantageous because they offer very high degrees of freedom but they suffer in the respect that they are nonphysical and may result in unrealistic deformations. DIR has been studied for images of head and neck cancer patients using the thin plate splines 36 B splines 33 and diffusion 47 50 techniques. Biological Co nsiderations of Dose Accumulation Dose accumulation using DIR makes several simplifying assumptions. One primary assumption, which is also assumed in modern treatment planning, is that a single image volume element (typically a voxel) is small enough to r epresent a differential volume of tissue. Because cell survival is actually a function of the dose delivered to individual cells, ideally, we would be able to track the dose to a single cell. This is not currently practical, however, so the dose to indiv idual cells is assumed to be the same as the dose calculated to an individual image volume element. In the context of DIR and dose accumulation, this assumption is further complicated because volume elements from multiple image sets are linked and dose va lues are interpolated and summed. With multiple image sets and changing patient anatomy, the assumption that the dose to individual cells may be approximated accurately by using larger volume elements becomes more uncertain. Furthermore, as cells die and are removed or

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28 multiply and are added (also referred to as shrinking or growing tissue volumes), accounting for the dose to these cells becomes very difficult. Modern radiation therapy research and practice have not been able to quantify the effects of t his assumption or develop a reasonable alternative however Therefore, for the purposes of this work, we will assume that this approach is valid. Dose accumulation also assumes that estimated doses from multiple treatments may be summed linearly. This assumption was questioned when the dose accumulation model was first published. 51 Conventional r adiation therapy assume s that each image volume element receives the dose that was calculated during treatment planning for every delivered fraction. However, as we have discussed prev iously, the doses to patient tissues likely change over a treatment course. If the fractional dose to a tissue changes, the linear quadratic model should be used to appropriately calculate cell survival fractions. With this in mind, Orban de Xivry et al. 52 investigated if radiobiology must be taken into account when performing inter fraction dose accumulation for head and neck c ancer cases. They concluded that the differences between a dose summation approach that included radiobiological considerations and an approach that consisted of a simple linear sum of the fractional doses were statistically significant but clinically irr elevant. Therefore, this work will assume that a linear summation of fractional doses for dose accumulation is acceptable. Uncertainties in Adaptive Radiotherapy Volumetric Image Guided Radiotherapy While traditional CT simulation and planning have been p resent in the clinic for some time, the relatively recent addition of volumetric IGRT has created new sources of uncertainty that must be analyzed and quantified. Volumetric IGRT has created new

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29 opportunities for ART as previously discussed, but the usefu lness of these new applications will be limited unless the sources and magnitudes of the uncertainties are better understood. There have been many studies exploring the uncertainties inherent in each of the volumetric IGRT modalities which will be discuss ed, in turn, below. CT on rails is perhaps the closest analog to the conventional CT simulator of the IGRT modalities. If the conventional CT simulator is taken as the reference, very few additional sources of uncertainty are evident. The imaging geometr y and beam energy are similar with the primary difference being that the gantry translates over the couch instead of the couch translating through the gantry. This difference is a potential source of positional uncertainty, however. Court et al. 53 examined the mechanical precision of the CT on rails system. That investigation found that the largest single uncertainties were the couch position on the C T side after a 180 couch rotation and the alignment of contours with the CT images. These uncertainties were, to one standard deviation, 0.5 mm in the right left direction for the couch position and 0.4 mm in the inferior superior direction for the conto ur alignment. All other individual sources of uncertainty were less than 0.3 mm. MVCT introduces more potential sources of uncertainty. The imaging geometry is similar to conventional CT, but the imaging beamline and beam energy are quite different. Lan gen et al. 54 investigated the use of MVCT images for dose recomputations. That study found that the MVCT number to physical density calibration curve 55 varied over time. When compared to an image acquired nine months earlier, points on the c alibration curve varied by an average of 20 13 Hounsfield units (HU). There was a maximum variation of 57 HU for the 1.47 g/cc point on the calibration

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30 curve. One potential source of the temporal variation of the calibration curve is electron target de gradation 56 HU measurements of the density calibration plugs were obtained by placing the plugs into a cylindrical solid water phantom and acqu iring MVCT images. Most of the volume of the calibration plugs was surrounded by the solid water phantom, but a fraction of the volume extended into air outside of the phantom. The greatest variation in HU of the calibration plugs was found when comparin g the values measured from the portion of the plug embedded in the phantom to the portion extending into air. The in air measurements showed MVCT numbers that were 50 HU lower and 82 HU higher for the lowest and highest density calibration plugs, respecti vely, than the in phantom measurements. The in air and in phantom calibration curves were used separately to perform dose recalculations on image sets from six clinical sites. Dosimetric endpoints calculated using each of the calibration curves applied t o MVCT images were typically within 2% with a maximum variation of 3%. Dose calculations were also performed on kilovoltage CT (kVCT) images for four phantom plans and compared to dose calculations performed on MVCT images for the same phantom. There was excellent agreement between the kVCT and MV CT dose volume histograms with the D 95% of the target volumes differing by less than 0.5%. Duchateau et al. 57 also investigated the effect of MVCT imaging beam output instabilities on d ose calculation. That study reported an increase of 22 HU in the MVCT number of solid water over a period of three months. If this change was not taken into account in the calibration curve, the D 50% of a phantom target decreased by 3% when calculated o n a MVCT image set as compared to the planning kVCT image set.

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31 kVCBCT uses a similar beam energy to conventional CT but the cone beam geometry creates additional sources of uncertainty. Yoo and Yin 58 examined dose calculations performed on kVCBCT images compared to traditional kVCT treatment plans for a range of phantoms and patient images. That investigation found differences of up to 150 HU i n the peripheral regions of homogeneous phantoms and up to 200 HU in inhomogeneous phantoms between kVCT and kVCBCT images. This translated to a MU/cGy difference of up to 3% in the inhomogeneous phantoms. Yang et al. 59 explored the stability of kVCBCT dose calculation over time and with the introduction of motion artifacts. No significant variation was observed in the kVCBCT cali bration over a period of eight weeks. However, introducing cyclic motion into the acquisition of phantom images caused a maximum discrepancy of 3% in the high dose region of dose calculations performed on kVCBCT images compared to dose calculations perfor med on helical kVCT images. Hatton et al. 60 investigated the effect of phantom scattering volume on kVCBCT based dose calculations. Adding scattering material to a phantom longitudinally, increasing the phantom length from 5 cm to 26 cm, led to a decrease of 260 HU for the high density calibration insert. Adding scattering material radially, increasin g the phantom diameter from 18 cm to 40 cm, resulted in a decrease of 1200 HU for the high density calibration insert. Point doses to bone equivalent material were as much as 22% greater when the HU to electron density (ED) calibration curve for the 40 cm phantom was used for dose calculations on kVCBCT image sets instead of the HU to ED calibration curve for the 18 cm phantom. Rong et al. 61 also considered the effects of phantom size on kVCBCT based dose calculations along with mAs, source to imager distance (SID), and cone angle. Varying mAs resulted in CBCT number

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32 differences of less than 10 HU. Changing the SID also had relatively minor consequences with a maximum HU discrepancy of 66. A difference of 375 HU was measured for the high density calibration insert between a small diameter (18 cm) phant om and a large diameter (28 to 33 cm) phantom. This difference was reduced to 140 HU if a small cone angle was used. Given the HU variation reported as the phantom size increased, Rong et al. 61 showed that dose agreement of approximately 2% could be achieved between kVCBCT based and kVCT based dose calc ulations by using a site specific calibration curve. MVCBCT presents new uncertainties through the use of a high energy imaging beam and a cone beam geometry. These factors contribute to enhancing cupping, or beam hardening, artifacts which have become th e primary concern of authors researching this imaging modality. Morin et al. 62 presented a simple geometric model to perform cupping artifact corrections. Without corrections, dose calculations performed on MVCBCT images of a head sized water phantom res ulted in dosimetric errors of less than 5%. With corrections, the dosimetric errors were reduced to less than 1%. Dose distributions calculated on MVCBCT and kVCT images of a head and neck cancer patient agreed within a gamma criteria of 3%/3mm when the cupping artifact corrections were applied. Aubry et al. 63 reported similar results to the Morin et al. study 62 by using rigid registration of MVCBCT images with kVCT images to obtain correction factors. MVCBCT based dose calculations showed errors within 1% compared to kVCT based calculations for images of phantoms, and within 3% for head and neck patient images. Petit et al. 64 devised a method to correct cupping artifacts without using prior information of the object being imaged. Instead, they used transmission images and an iterative

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33 algorithm to determine the primary photon transmission that would be expected from a mono energetic beam. The calculated primary transmission is then used in the cone beam reconstruction algorithm to produce corrected MVCBCT images. With this method, the study fo und that maximum errors in dose calculations performed on MVCBCT images of homogenous cylindrical phantoms were reduced from 17% to 2%. Deformable Image Registration DIR is also a relatively new technology where the uncertainties of its implementation are not fully understood. The quantification of these uncertainties is comparison between two patient image sets. Therefore, creative scientific approaches s must be devised to measure the uncertainties of DIR. Several researchers have attempted to quantify the uncertainties of DIR using varying methods as described below. Castadot et al. 47 evaluated twelve diffusion based DIR algorithms for their ability to accurately deform pre treatment kVCT images to kVCT images acquired during treatment for five head and neck cancer patients. Contours were delineated on both the pre treatment and during treatment image sets by a physician. The physician drawn contours were compared to contours delineated using DIR throu gh a volume based metric, the Dice similarity index (DSI) 65 and a voxel intensity based metric, the correlation coefficient (CC). The best performing algorithms were able to achieve a median DSI of 0.86 and a median CC of 0.97. Tsuji et al. 66 used a similar a pproach, but took the analysis one step further to investigate the dosimetric uncertainty of DIR. Again, physician drawn contours were compared to automatically drawn contours on pre treatment and mid treatment kVCT image sets of head and neck cancer pati ents. In

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34 this study, however, the manual contours and the automatically drawn contours were used to create two sets of IMRT plans. Dosimetric indices were then calculated for the manual contours by applying separately the dose distributions resulting fro m the manually contoured plans and from the automatically contoured plans. A comparison of the indices showed a statistically significant lower mean coverage of the GTV (V 95% : 89.9 10.1% vs. 98.6 1.9%) and the CTV (V 95% : 89.8 6.2% vs. 98.4 0.8%) for the a utomatic plans vs. the manual plans. Additionally, a higher mean maximum dose to the spinal cord was reported (D 1cc : 42.8 5.4 Gy vs. 39.9 3.7 Gy) for the automatic plans. Brock 67 published a multi institution study investigating a wide range of DIR algorithms and scenarios. Twenty one groups reported results for 4D kVCT image sets of a lung patient, 4D kVCT and magnetic reson ance (MR) image sets at exhale of a liver patient, and repeat MR images of a prostate patient. Anatomic fiducials such as bronchial or vessel bifurcations were identified on the lung and liver image sets, respectively, by an experienced radiation oncologi st and used as markers to determine the true displacement of these points. Implanted gold markers were identified as the fiducials for the prostate case. Each institution performed DIR on the patient cases and the computer predicted results were compared to the observed movement of the fiducials as recorded by the physicians. Mean DIR errors ranged from 0.4 to 6.2 mm. Another approach to quantifying DIR uncertainties is to use deformable phantoms. Kashani et al. 68 developed a deformable lung phantom to simulate breathing motion. The phantom consisted of an anthropomorphic plastic chest wall, a skeleton, and a compressible section made of high density foam embedded with four tumor

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35 simulating spheres. 48 small plastic markers were also e mbedded in the foam to act as fiducials for the characterization of the true phantom deformation. kVCT image sets were acquired of the phantom at simulated inhale and exhale states. The marker coordinates were localized on each of the image sets and then digitally removed from the images. Eight DIR algorithms were tested using the images of the deformed phantom by comparing the computed deformation maps to the known marker displacements. Average errors ranged from 1.5 mm to 3.9 mm, while maximum errors ranged from 5.1 mm to 15.4 mm. Janssens et al. 69 also used deformable phantoms to determine t he accuracy of two different DIR algorithms. However, in this study, eight metal oxide semiconductor field effective transistor (MOSFET) detectors were positioned in a deformable silicon cylindrical phantom to measure the actual dose delivered. MVCBCT im ages of the phantom were acquired, dose calculations were performed on these images, and they were deformably registered to the planning kVCT image set. The deformed dose distributions were then compared to the doses measured with the MOSFET detectors. M edian and maximum dose differences of 1.8% and 33.8%, respectively, were reported. Novel Methods for the Quantification of Uncertainties in Adaptive Radiotherapy The methods for quantifying the uncertainties of DIR for adaptive radiotherapy discussed previ ously suffer from numerous limitations and criticisms. Manually drawn contours have an inherent uncertainty because they are created by imperfect human observers. The assumption that a physician drawn contour flawlessly represents a given structure is su bject to some uncertainty. Furthermore, contours drawn by different physicians, inter observer uncertainty, have been shown to vary 33 34 Errors in the manual creation of contours on either the reference or target images during DIR

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36 evaluati on will affect the reporting of metrics based on those contours. Both contour and marker based DIR assessment methods only evaluate a limited number of points when the entire deformation map should be analyzed. For example, even if the contours of a defo rmed image and a target image are in perfect agreement, the voxels within those contours may not be. The inaccurate movement of voxels within a contour will lead to an increase in the uncertainty of deformable dose accumulation. Similarly, the deformatio n of image markers may be correct in one region of an image but grossly incorrect in another unmarked region. Phantom based DIR evaluation lacks the complete characteristics and complexities of real patient deformations. Finally, while spatial uncertaint y measurements are informative, radiation therapy is ultimately concerned with the dosimetric uncertainty of DIR. Dosimetric uncertainties will be more sensitive to spatial errors in regions with steep dose gradients while large spatial uncertainties may be acceptable in regions with gradual dose gradients 70 In an effort to overcome the limitations cited, several investigators have sug gested innovative methods to analyze the uncertainties of DIR. One such study was published by Zhong et al. 71 In this study, the authors developed a finite element modeling (FEM) deformation technique that relies on the conservation of elastic energy instead of an image similarity metric to deform patient an atomy. This distinction from other DIR approaches allows the FEM technique to create physically and biologically realistic anatomic deformation maps. While the FEM approach has the potential to result in more realistic patient deformations, it currently must be adapted to each unique patient requiring substantial time and resource commitments compared to image similarity metric based techniques. The authors used the FEM model to create a

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37 rmed image and the original image were then used to assess the performance of a diffusion based DIR algorithm and a B spline algorithm. Since the DVF used to create the deformed image by way of the FEM model was known, the DVFs resulting from applying the other algorithms could be compared directly with the FEM DVF to quantify the error in every image voxel. Using this approach, the investigators found that the diffusion based algorithm converged to a mean error of approximately 1.3 mm and that the B spli ne algorithm converged to a mean error of approximately 1.5 mm for the single lung case evaluated. In an earlier study 72 Zhong et al. attempted to develop a practical method of identifying regions of a DVF that exhibit registration errors by using a concept called unbalanced energy (UE). UE is based on the theory that the elastic energy stored in a DVF must be balanced by external work. Therefore, a large UE value for a DVF element should indicate a registration error in that region. The authors found that the UE metric was not exactly correlated with displacement errors, but that it was useful for ide ntifying areas of an image that would require more careful assessment or correction. While a strict correlation with displacement errors was not discovered, UE attempted to overcome the limitations of other DIR analysis methods by proposing an automatic m ethod to evaluate every element in the DVF. Vector calculus methods have also been suggested to perform a complete evaluation of the entire DVF 73 One such approach, the determinant of the Jacobian matrix of a deformation field, identifies local volume changes. A determinant equal to 1 indicates no local volume change, greater than 1 indicates an increase in volume from

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38 the reference image to the target image, and less than 1 indicates a decrease in volume. A zero or negative determinant value indicates an err or in the registration such as a singularity in the DVF or a folding of the image. Jacobian analysis has been applied to DVFs to assess lung ventilation from 4DCT images 74 and parotid shrinkage over a radiation therapy treatment course 75 In an effort to move from spatial DVF uncertainty to an individualized dosimetric uncertainty given a unique dose distribution, Salguero et al. 76 devised two different methods to convert the spatial uncertainty into dosimetric uncertainty. The first method calculates the dosimetric variance of each voxel using a single estimated value of the spatial uncertainty of that voxel. Thus, it is equivalent to considering a sphere around a point of interest which would encompass all probable locations and dose values that the point could be associated with given a specified confidence interval. This approach ignores any directionality of the DVF errors and assumes that the errors are isotropic. The second method takes the directionality of DVF errors into account through the evaluation of the covariance matrix at each point in the target image. The covariance matrix allows for the calculation of a 3D Gaussian probability density function (PDF) that estimates the probability that a given voxel will be mapped to another location. Once a PDF is calculated, it may be used to weight each dose value by t he value of the PDF at its position. In this fashion, both the direction of the DVF error and the unique dose distribution may be considered to estimate the dosimetric uncertainty of a given DVF with a predicted spatial uncertainty. Objectives of this Res earch Adaptive radiotherapy aims to improve radiation delivery by adapting treatment parameters to changing patient anatomy over a course of radiation therapy. In order to

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39 appropriately adapt treatment parameters, the dosimetry of the current treatment plan anatomy. This assessment requires the use of advanced tools including dose recalculation on frequent volumetric patient imaging and DIR However, the inherent uncertainties of these tools are not currently well understood rendering clinical decisions based on these tools difficult. The hypothesis of this work is that the uncertainties of these tools may be quantified using dose recalculation softw are and novel deformation analysis approaches allowing for more effective clinical decision making. The followi ng aims we re proposed to test this hypothesis. 1. Quantify the dosimetric uncertainty of dose recalculations performed on inter fraction volumetric patient images. For a given treatment plan, current dosimetric analysis software allows the recalculation of dose distributions on images acquired during volumetric IGRT. Langen et al. 54 used the same software to investigate and successfully quantify potential sources of dosimetric uncertainty for dose recalculations performed on MVCT images. However, more recent studies have questioned the stability of MVCT imaging over extended periods of time 57 77 Therefore, the purpose of this aim is to solidify the current understanding of the dosimetric uncertainty of dose recalculations performed on MVCT images by quantifying the variability of MVCT images over time and its associated dosimetric impact on clinical cases. Additionally, the successful achievement of this aim would result in a methodology that could be generalized and applied to other imaging modalities. 2. Determine the uncertainty introduced by using a plan dose overlay instead of performing d ose recalculation. Performing a dose recalculation can be time and resource intensive. An alternative solution for ART dose assessment would be to simply overlay the planning dose distribution on newly acquired images of a ll quantify how dosimetry is affected when a dose overlay is used in lieu of a dose recalculation. 3. Quantify the uncertainty of deformable image registration. We propose to develop a library of image pairs, or virtual phantoms where the underlying deforma tion between the image pairs is known. These phantoms will be derived from clinically acquired images and will allow the quantitative evaluation of any DIR algorithm. 4. Translate the quantified ART uncertainties into clinically useful tools. Currently, clinical assessment of changing patient dosimetry is performed by

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40 recalculating dose distributions on volumetric patient images acquired over a radiotherapy treatment course. The dose distributions from each image set are summed through DIR to The dosimetric impact of a ny variability in the imaging or errors in the DIR can only be evaluated qualitatively because quantitative tools are not readily available Given the development of a me thod to quantify the uncertainties of ART these uncertainties must be converted into dosimetric uncertainties, which will likely user in a clinically useful manner. Each of these aims represents a distinct research project. Chapters 2 through 5 of this dissertation each correspond to one of the aims described immediately above. The impact of this work and possible future opportunities for continuing research are discussed in C hapter 6

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41 Tab le 1 1. Reported geometric and dosimetric target changes during a radiotherapy course Author Imaging method Imaging frequency Registration method Target geometric effects Target dosimetric effects Ahn et al (2011) 9 CT After 11, 22, and 33 fractions Rigid GTV: mean volume decrease of 17.2% Castadot et al (2010) 11 CT After mean doses of 14, 25, 35, and 45 Gy Deformable GTV: mean relative shrinkage of 3.2%/day No difference in PTV or CTV coverage Wu et al (2009) 18 CT Weekly Deformable CTV: mean volume decrease of ~5% No differen ce Cheung et al (2009) 12 MVCBCT Daily/Weekly Rigid CTV/GTV: On average, dose difference within 1% over treatment course Vasquez Osorio et al (2008) 16 CT 2 weeks after end of treatm ent Deformable GTV: mean volume decrease of 25% O'Daniel et al (2007) 37 CT on rails Twice weekly Deformable CTV/GTV: no statistical difference Barker et al (2004) 3 CT on rails Three times weekly Rigid GTV: median volume decrease of 69.5% Hansen et al (2006) 8 CT After a mean of 19 fractions Rigid PTV CTV : mean volume decre ase of 7.5% Height et al (2010) 14 CT After a median dose of 43 Gy Rigid GTV: median volume reduction of 49.9% GTV: Continued to receive prescribed dose Zhao et al (2010) 7 CT After a mean of 15 fractions Rigid Nodal GTV: mean volume decrease of 72% CTV: D 95% decrease of 14.6% Note: CT: computed tomograph y MVCBCT: megavoltage cone beam computed tomograph y GTV: gross tumo r volume, CTV: clinical target volume, PTV: planning target volume, D 95% : dose received by 95% of the volume

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42 Table 1 2. Reported geometric and dosimetric parotid gland changes during a radiotherapy course Author Imaging method Imaging frequency Registration method PG geometric effects PG dosimetric effects Schwartz & Dong (2011) 22 CT on rails Daily Deformable Mean volume decrease of 26% Castadot et al (2010) 11 CT After mean doses of 14, 25, 35, and 45 Gy Deformable of 0.9%/day, 3.4 mm medial shift of 1%/day, no medial shift D mean increase from 17.9 Gy to 18.7 Gy Wu et al (2009) 18 CT Weekly Deformable Mean volume decrease of ~15% D mean increase of ~10% Lee et al (2008) 21 34 MVCT Daily Deformable Median volume decrease of 21.3%, median medial migration of 2.63 mm D mean increase greater than 10% for 3 of 10 patients O'Daniel et al (2007) 37 CT on rails Twice weekly Deformable D mean increase of 1 Gy vs. plan dose Barker et al (2004) 3 CT on rails Three times weekly Rigid Median volume decrease of 28.1%, median medial shift of 3.1 mm Hansen et al (2006) 8 CT After a mean of 19 fractions Rigid decrease of 21.5% decrease of 15.6% Robar et al (2007) 15 CT Weekly Rigid 0.7%/day, mean medial shift of 2.6 mm 0.9%/day, mean medial shift of 1.9 mm mean increase of 2.6% over treatment course mean increase of 0.2% over treatment course Bhide et al (2010) CT Weeks 2, 3, 4, and 5 Rigid Mean volume decrease of ~35%, mean medial shift of 2.3 mm mean increase of 7.3% mean increase of 4.1% Note: MVCT: megavoltage computed tomography, CT: computed tomography, PG: parotid gland, IP: ipsilateral, CN: contralateral, Lt: left, Rt: right, D mean : mean dose to the volume

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43 Figure 1 1 A typical adaptive radiotherapy (ART) workflow. The process is broken into three distinct sub processes : tre atment planning (green), treatment delivery (red), and ART dose assessment (blue).

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44 Figure 1 2. Axial image of a patient with head and neck cancer showing how the left parotid volume has changed during treatment due to weight loss. The planning parotid contour depicts where the left parotid gland was located in the original treatment plan. Generated by automatic image segmentation, the deformed parotid gland shows the estimated location of the left parotid during treatment. Note how the displayed isodose lines appear to curve around the original planning parotid contour. This is don e intentionally during the planning process to limit the dose to the parotid and preserve salivary flow.

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45 Figure 1 3. DVHs estimated during the ART dose assessment process. Here, the left parotid gland has migrated medially into a higher dose region as seen in Figure 1 is receiving more dose than originally intended when compared to the

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46 CHAPTER 2 THE UNCERTAINTY OF DOSE RECALCULATIONS As part of the adaptive radiotherapy process, the uncertainties introduced by dose recalculation must be understood in order to perform a dosimetric assessment with confidence. This chapter describes a method to quantify the uncertainty of dose recalculations performed on inter fraction meg avoltage CT (MVCT) image sets. The methods and results described here have been included previously in a published manuscript. 78 Langen et al 54 extensively investigated the use of MVCT images for dose recomputations by examining the stability of the CT number to electron density calibration curve while varying the spatial arrangement of a phantom, acquisition parameters, and tim e between acquisitions. The two calibration curves with the largest observed variation were applied to six clinical MVCT image sets and dose distributions were recalculated. The dosimetric endpoints typically varied by less than 2% with a maximum variati on of 3.1%. The maximum time between image acquisitions in that study was 9 months. Recent studies have questioned the stability of the imaging beam output and, consequently, the stability of the image value to density table (IVDT) over time 57 77 These stability concerns are typically the result of observed changes in the radiation beam characteristics as the target degrades 56 or other major components are replaced. Therefore, in this current investigation the dosimetric uncertainty of MVCT dose recalculations was revisited by examining temporal variations in the MVCT image sets measu red on two clinical machines over a three year time frame. During this time multiple targets were replaced and a variety of service events occurred. In addition, several baseline phantom images were acquired to determine the inherent dosimetric

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47 difference s seen between dose calculations on conventional kilovoltage CT (kVCT) images and MVCT images in the absence of temporal effects. Next, o bserved temporal MVCT image variations were translated into dosimetric variat ions for six patient image sets covering three distinct treatment sites. Finally, because this work, as a whole, focu s es primarily on patients with cancers of the head and neck, the dosimetric uncertainty of dose recalculation due to temporal imaging variations was evaluated for 10 additional he a d and neck cancer patients. Although the method described in this chapter applies specifically to MVCT imaging, it could also be generalized to other imaging modalities. The uncertainty of dose recalculation could be quantified for other modalities by fo llowing a similar procedure of first using phantoms to determine the baseline dosimetric difference between dose calculations performed on kVCT images and the modality of choice. Then, image variations caused by the specific modality could be simulated an d evaluated in a manner similar to the one proposed below. Materials and M ethods Image Acquisition Parameters All kVCT images were acquired using a Philips Brilliance CT system (Philips Medical Systems, Best, The Netherlands). The clinical IVDT for the Ph ilips kVCT system was measured using a commercially available CT calibration phantom. Images of the phantom were acquired using the clinical head and neck, chest, and pelvis protocols. All imaging protocols used a 60 cm field of view 120 140 kVp, and a slice width of 2 from these images and were averaged across the imaging protocols to define the clinical kVCT IVDT. Daily QA is performed on the kVCT IVDT by acquiring images of

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48 anothe r CT calibration phantom. The HU values of density plugs within the QA phantom are compared to those recorded in the kVCT IVDT to ensure consistency. MVCT images were acquired on a TomoTherapy Hi Art II unit (Accuray Inc., Sunnyvale, CA) using a jaw sett ing of 4 mm. Airscan calibrations were performed once daily on each TomoTherapy machine, in the morning, before any images were acquired. The width, respectively. Howev er, the pitch should have little impact on dose recalculations as reported by Langen et al. 54 Baseline MVCT D osimetric U ncertainty A cylindrical water phantom, a thorax phantom (CIRS Model 002LFC, Computerized Imaging Reference Systems Inc., Norfolk, VA, USA) and a head phantom ( CIRS Model 605 Computerized Imaging Reference Systems Inc., Norfolk, VA, USA) were scanned using the same kVCT protocol described earlier to create planning image sets. The clinical IVDT for the kVCT scanner was applied to the image sets and TomoTherapy treatment plans were created. Each treatment plan was optimized to deliver 2 Gy to 95% of a cylindrical target volume. Figure 2 1 shows the planned dose distributions for each phantom in the axial plane. Next, MVCT images of each phantom were acquired on the Hi Art II unit. At the same time, a CT calibration phantom was scanned to obtain the MVCT IVDT 55 The TomoPhantom TomoTherapy was used for MVCT calibration. The TomoPhantom is a cylindrical solid water phantom that has 20 holes to allow the placement of individual density plugs. The mean Hounsfield Unit (HU) value of each density plug was measured on three adjacent axial MVCT slices. The value from each slice was then averaged to obtain the final HU

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49 value assigned to the IVDT. Density plugs with nominal densities of 0.33 g/cc, 0.48 g/cc, 1.561 g/cc, and 1.8 24 g/cc were used to determine the IVDT. Additionally, a plug filled with water was measured in the same fashion and assigned a density of 1 g/cc. Air was measured in a region outside the phantom and assigned a density value of 0.001 g/cc. This geometry was chosen for the measurements to resemble the scatter conditions that would exist when scanning a patient. The measurement of water and air and the exclusion of density plugs from 100 HU to +100 HU are in accordance with the ions. Applying the MVCT IVDT determined as described, dose distributions were recalculated on the MVCT images of each phantom. The dose recalculations were performed assuming the original radiation delivery sinograms. Target dose volume histogram (DVH) c urves were compared to determine the dosimetric difference between the kVCT and MVCT calculations. Temporal MVCT I mage V ariation MVCT images of the TomoPhantom were collected at varying intervals not greater than one month over the course of three years. Data were collected from two clinical Hi Art II units. The mean HU of solid water was measured with a circular region of interest (ROI) located near the cente r of the phantom for each image set. Additionally, the 0.33 g/cc, 0.48 g/cc, 1.561 g/cc, and 1.824 g/cc density plugs were measured along with air and w ater as described in the preceding section, when available. The mean solid water HU values were plotte d with respect to time and major machine component changes were added to these graphs in an attempt to correlate the component changes with HU variations.

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50 Dosimetric U ncertainty R esulting from T emporal MVCT I mage V ariation HU variations can be accounted fo r if they are monitored and the IVDT is updated accordingly. The purpose of this part of the study was to investigate what dosimetric error would arise if HU variations are not monitored and, hence, are not taken into account in MVCT based dose calculatio ns. Ideally, MVCT images that were obtained on days when the imaging system was subject to known HU variations would be used to determine the dosimetric effect of those variations. However, there is an inherent problem with this approach. The anatomical variations that are present in actual MVCT images can also cause perturbations in the dose distributions and those, in turn, may mask the dosimetric variations due to the HU variation. For this reason, a single MVCT image set, called the reference image set, was used and HU variations that would have been present if the images had been acquired at times of imaging system instabilities were artificially introduced by manipulating the IVDT. Figure 2 2 illustrates this process using density histograms of th e TomoPhantom calculated from MVCT images acquired on two different days (day X and Y). For this illustration, image set X will be the reference image set and image set Y will be the target image set. The target image set shows HU variations that we will recreate using the reference images. Between days X and Y the imaging system was unstable and HU variations were introduced. The magnitude of these variations is known from calibration images acquired on days X and Y. Of concern is the clinical scenari o in which the MVCT image acquired on day Y is used in conjunction with the IVDT acquired on day X, i.e. the HU variations are not taken into account. Consequently, the calculated density would be wrong and a dosimetric error would result ( Figure 2 2A). To mimic this scenario using only the reference image set X, an IVDT was derived from the differences between

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51 IVDT X and IVDT Y. The calculation of the derived IVDT is best described with an example. On image set X, the 1.561 g/cc density plug was measur ed to be 400 HU. On image set Y, the same density plug was measured to have a mean MVCT number of 540 HU. If IVDT X were applied to image set Y, the 1.561 g/cc density plug would appear to have a density 1.73 g/cc. Thus, a density of 1.73 g/cc was paire d with 400 HU in the derived IVDT. This process was repeated for all of the measured density plugs to create the complete derived IVDT. The derived IVDT can be applied to the reference image set X such that the error in the density is equal to the error that would result in the aforementioned clinical scenario of Figure 2 2A. Figure 2 2B shows the density histograms for both image sets but, in this case, the derived IVDT was applied to the reference image set. Here, the density peaks overlap indicating that the method was successful in mapping the voxel values of the reference image to mimic the errors in the density distribution. This method allowed the evaluation of the dosimetric error with a single reference image set that was subjected to a range o f derived IVDTs that were calculated from actual measured IVDTs over time. Three different treatment sites were chosen to determine the dosimetric uncertainty introduced by HU variations by subjecting MVCT image sets from each site to the complete range of observed HU variations. Two head and neck, two lung, and two prostate cases were selected for evaluation initially After calculating and applying the derived IVDTs to the reference images for each clinical case, the dose distributions were recalculated. DVH curves for the primary target and organs at risk (OARs) were calculated and compared to quantify the total dosimetric variation associated with the

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52 temporal HU variation. Subsequently, 10 additional head and neck cases were selected and this analysi s was repeated to ensure that the initial results were consistent. Results Baseline MVCT D osimetric U ncertainty The doses to 95%, 50%, and 5% of the target volume (D 95 % D 50 % and D 05 % respectively) were evaluated for each of the baseline phantom DVHs. Table 2 1 shows the difference between the dosimetric endpoints recalculated on the MVCT image sets and the endpoints calculated on the initial kVCT planning images. The endpoints reve al a slight underdose in the recalculated MVCT DVHs for the water and head phantoms when compared to the kVCT calculation. The thorax phantom, however, shows a slight overdose for the recalculated DVH. Based on these endpoints, the head phantom showed th e greatest deviation from the kVCT DVH with 1.4% difference. Temporal MVCT I mage V ariation Figure 2 3 shows the mean HU of the TomoPhantom solid water measurement over the three year period. The MVCT number of solid water varied from a minimum of 5 HU to a maximum of 103 HU for machine #1. The solid water on machine #2 varied from 31 HU to 101 HU. Figure 2 3C shows a subset of the solid water HU data with major component change information added. The mean solid water HU appeared to increase with time an d then decrease sharply following a target change. This observation was consistent across all of the data. For 15 recorded target replacements, the average decrease in the mean MVCT number of solid water was 39.4 HU post target replacement. The effect o f other component changes on the mean HU, however, was less consistent.

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53 While the HU values of individual materials varied over time, the overall shape of the IVDT curve showed little variation over the course of this study. The air measurement was relati vely stable with a maximum variation of only 26 HU. In comparison, the higher density plugs showed a much greater variation over the same time frame with the 1.824 g/cc plug measurement differing by as much as 143 HU. These observations are consistent wi th the IVDT curves observed by Duchateau et al. 57 and Yadav et al. 77 Dosimetric U ncertainty R esulting from T emporal MVCT I mage V ariation Recalculated DVHs that take the temporal MVCT HU var iation into account are shown in Figure 2 4 for each treatment site. These graphs show that as the HU values increased, perceived density values also increased, and doses to the ROIs decreased, as expected. Table 2 2 lists the dosimetric endpoints of the recalculated DVHs for each site over the range of HU variation. In Table 2 2 a point near the middle of the range of total variation, when the MVCT number of solid water was equal to 49 HU, was chosen as the reference point and all other recalculations were compared to this point. Patients 1 and 2 in Table 2 2 were treated for head and neck cancers. D 95% is listed for the primary target while D 50% values are shown for both parotid glands. The greatest dosimetric variation occurs for the PTV of Patien t 2. For that structure, the data show a total variation of 3.5% over the entire range. The total variation for the PTV of Patient 1 is slightly less at 2.5%. Both parotid glands for Patient 1 varied less than the PTV with a total difference not greater than 1.5%. The parotid data for Patient 2 show a different trend, however. In this case, the right parotid gland has a dosimetric variation similar to the PTV while the left parotid gland has an unusual but much smaller deviation. Patient 1 had a centr ally located primary target with similar sparing of both

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54 parotid glands. The primary target for Patient 2 was located just anterior to the right parotid and, therefore, delivered a higher dose to this gland while delivering a much lower dose to the contra lateral (left) parotid. Within 30 HU from the solid water reference, the dosimetric uncertainty within both targets is approximately 1%. Table 2 3 shows the dosimetric variation over the range of HU values for the 10 additional head and neck cases. The results of Table 2 3 were consistent with those found for Patients 1 and 2. For all endpoints, the dosimetric uncertainty was approximately 1% within 30 HU. Patients 3 and 4 were treated for lung cancers. For these cases, the total variations appea r to be comparable for all structures ranging from 3.7% for the D 20 % of Patient 05 % of Patient greater than those seen for the head and neck cases. Again, if the deviation in the HU of solid water is limited to 30 HU, the dosimetric error is limited to approximately 1.5%. Two prostate cancer cases, Patients 5 and 6, are also shown in Table 2 2 Here, again, the total variations are comparable for all structures listed. The total variations for these patients are substantially greater than those seen for the lung cases ranging from 8.2% to 8.6%. However, if the MVCT number of solid water is restricted to 30 HU, the dosimetric error for these endpoints is limited to approximately 2.5%. Finally, Figure 2 5 shows dose difference images for each of the clinical cases investigated. These images were obtained by subtracting the dose distributions calculated when the solid water MVCT number was equal to 5 HU from those calculated when the solid water MVCT number was equal to 103 HU. Therefore, each of these

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55 images shows an example of how the dose distribution differs as the HU values increase. Only one transaxial slice is displayed for each patient. For each case, it can be seen that as the perceiv ed density of an image increases, the calculated dose to the patient decreases due to the increased attenuation of each beam in the patient. The areas of greatest absolute dose difference occur in the primary targets for each treatment plan. Discussion It is important to obtain an estimate of the baseline dosimetric variation between kVCT and MVCT imaging modalities to quantify the uncertainty that exists in the absence of any temporal image changes. This baseline uncertainty likely exists because the res pective kVCT and MVCT IVDTs are unable to perfectly characterize all of the underlying imaging physics. The higher energy photons of the MVCT beam are attenuated primarily through Compton interactions. Since the probability of Compton scattering is effec tively proportional to the electron density of a material, one would expect the MVCT IVDT to be linear with respect to electron density. Previous studies have shown that this is indeed true 55 The MVCT IVDT is described in terms of physical density instead of ele ctron density, however. Hence, if the number of electrons per gram of any given material was constant, then the MVCT IVDT curve should also be nearly linear with respect to physical density. In reality, though, as physical density increases, the number o f electrons per gram tends to decrease. This phenomenon may cause a slight decrease in the slope of the MVCT IVDT curve at higher densities. These physical considerations create non linearities in the IVDT curves that make it difficult to easily characte rize how image values should relate to density values within a given modality and, especially, across imaging modalities. That is why some baseline

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56 uncertainty should be expected when comparing dose distributions calculated on kVCT and MVCT images. Overa ll, the dosimetric uncertainty resulting from dose recalculations on MVCT image sets in the absence of temporal variations was minimal with a range of 1.4% to 0.6%. While any changes to the components of the imaging beamline could potentially impact the b eam characteristics, this study consistently found that the most drastic image variations occurred following a target replacement, corroborating results reported by Yada v et al. 77 Staton et al. 56 reported that, as the target degrades, the treatment beam energy decreases and the lateral edges of the beam profile soften. As suming that similar effects occur in the imaging beam, a gradual decrease in photon energy would explain the gradual increase in the HU of solid water seen in Figure 2 3. As the beam energy decreases, photon attenuation increases and fewer photons reach t he detector. Thus, any material in the imaging beam appears to have a greater density than was measured at the beginning of the target life. This trend should continue until the target is replaced and measured HU values return to lower levels. The MVCT image is essentially measuring total photon attenuation ( and total photon attenuation may be defined as the total mass attenuation coefficient multiplied by density ( Therefore, energy changes in the imaging beam will lead to changes in th e mass attenuation coefficient which should result in changes in the slope of the IVDT curve. This observation is convenient because a measured change to any one point on the IVDT curve could then describe the change to the entire curve. Consequently, IV DT curve tolerances may be specified in terms of a single point, i.e. water or solid water. However, higher density materials will show a greater absolute change in MVCT

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57 number than lower density materials over the same time period, 143 HU for bone like d ensity vs. 26 HU for air in this study. This may be an important consideration for images that contain atypical amounts of high density material. The solid water data over the three years evaluated shows a total variation of 98 HU. This equates to a dens ity change of approximately 0.113 g/cc or 11%. Despite this relatively large density variation, the dosimetric variations were typically less substantial. For the head and neck, lung, and prostate cases evaluated in this study, there was a 3.5%, 5.6%, an d 8.6% maximum change, respectively, in the dosimetric endpoints considered over the entire range of temporal variation. Our data suggest that the dosimetric uncertainty increases as the pathlength of the treatment beams increases, which is consistent wit h simplified physical models. In fact, if a patient is approximated as uniform density with a known or assumed HU variation between image sets, an effective pathlength correction may be applied to percent depth dose data to estimate the dosimetric error. This approach yielded estimates within 1% of the calculated dosimetric errors for the head and neck cancer and prostate cancer targets. If the baseline uncertainty is considered in addition to the temporal uncertainty, a total dosimetric error of approxi mately 5%, 7%, and 10% would be possible in the worst case scenario for the head and neck, lung, and prostate patients, respectively. This scenario would exist if the MVCT calibration image and recalculation image were obtained at the extreme limits of th e potential temporal variation in conjunction with the worst possible baseline error. These uncertainty numbers may seem high compared to other publications. Duchateau et al. 57 reported D 50 differences of only 3% bet ween distributions calculated

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58 on kVCT and MVCT images for a solid water phantom. However, this value was calculated for a maximum solid water MVCT number difference of 22 HU. Yadav et al. 77 reported PTV D 98% differences of just over 3% for dose recalculations performed before and after a target change on images of a prostate patient. When the magnitudes of the image variations in those studies are compared to our observed variation of 98 HU, their values are consistent with tho se reported in this investigation. The disparities in the reported image variations are likely due to the differences in the observation periods. This investigation monitored the MVCT calibration for three years on two machines, allowing the evaluation o f several target life cycles. Duchateau et al. 57 and Yadav et al. 77 measured the stability of MVCT images over periods of four and five months, respectively. The total dosimetric uncertaint ies of 5%, 7%, and 10% cited in this report would exist if the MVCT IVDT were never recalibrated to account for the temporal imaging variations. However, TG 148 79 recommends that monthly HU calibration tests should verify that water equivalent materials vary by less than 30 HU from the calibrated IVDT to maintain a dosimetric uncertainty of 2% or less. The MVCT IVDT should be updated appropriately if the water equ ivalent material is found to vary by more than 30 HU. According to this study, if the MVCT number of solid water were maintained within a 30 HU tolerance, the total dosimetric errors for head and neck, lung, and prostate cancer patients should be within 2.5%, 3%, and 4%, respectively. Over the three years examined, machine #1 would require 7 recalibrations and machine #2 would require 10 recalibrations to maintain the 30 HU tolerance.

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59 Conclusion Uncertainties in the MVCT imaging process do exist, but they may be reduced with little additional clinical effort. If the recommendations of TG 148 are followed, dosimetric errors for head and neck cancers should be within 2.5%, lung cancers should be within 3%, and prostate cancers within 4%. To maintai n this tolerance, commissioned IVDT curves could be verified as part of the monthly machine QA, or, more often, as target degradation is observed. Commissioned IVDT curves should also be checked after changes to any major machine components or image acqui sition parameters.

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60 Table 2 1. Dosimetric endpoints were recalculated on MVCT images of three different phantoms and compared to the endpoints calculated on the initial kVCT plans. Endpoint Water phantom e rror Thorax phantom e rror Head p hantom e rror D 95% 0.3% 0.1% 1.3% D 50% 0.2% 0.6% 1.4% D 05% 0.2% 0.6% 1.3%

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61 Table 2 2. Dosimetric endpoints were calculated over the range of solid water MVCT number variation for six patients and three distinct clinical sites: head and neck cancer, patients 1 and 2; lung cancer, patients 3 and 4; prostate cancer, patients 5 and 6. The dose distribut ion calculated when solid water was equal to 49 HU was assigned as the reference distribution. All other distributions were compared to the reference. Solid water MVCT n umber (HU) Patient Reference d ose (Gy) Endpoint 103 86 80 69 60 49 41 29 20 5 1 2.01 PTV D 95% 1.5% 1.1% 0.9% 0.5% 0.3% 0.0% 0.2% 0.5% 0.7% 1.0% 0.84 Rt Parotid D 50% 0.7% 0.5% 0.5% 0.2% 0.1% 0.0% 0.2% 0.4% 0.5% 0.8% 0.53 Lt Parotid D 50% 0.8% 0.6% 0.5% 0.5% 0.1% 0.0% 0.1% 0.2% 0.2% 0.4% 2 1.98 PTV D 95% 1.9% 1.3% 1.1% 0.7% 0.4% 0.0% 0.3% 0.7% 1.0% 1.6% 1.66 Rt Parotid D 50% 1.9% 1.5% 1.3% 0.7% 0.6% 0.0% 0.5% 0.7% 1.0% 1.7% 0.39 Lt Parotid D 50% 0.6% 0.3% 0.2% 0.4% 0.5% 0.0% 0.1% 0.2% 0.3% 0.5% 3 2.03 PTV D 95% 2.6% 1.8% 1.5% 0.9% 0.5% 0.0% 0.3% 0.8% 1.2% 1.9% 0.78 Lung D 20% 2.0% 1.4% 1.2% 0.7% 0.5% 0.0% 0.3% 0.7% 1.1% 1.7% 1.92 Esophagus D 05% 3.2% 2.2% 1.7% 1.1% 0.6% 0.0% 0.4% 1.0% 1.5% 2.4% 4 1.49 PTV D 95% 2.3% 1.5% 1.3% 0.8% 0.5% 0.0% 0.3% 0.8% 1.2% 1.8% 0.85 Lung D 20% 2.3% 1.6% 1.3% 0.8% 0.5% 0.0% 0.3% 0.8% 1.2% 1.8% 1.51 Esophagus D 05% 2.7% 1.9% 1.5% 1.0% 0.6% 0.0% 0.4% 0.9% 1.5% 2.2% 5 1.98 PTV D 95% 4.6% 3.2% 2.6% 1.6% 0.9% 0.0% 0.7% 1.6% 2.4% 3.6% 1.57 Rectum D 10% 4.6% 3.2% 2.5% 1.7% 1.0% 0.0% 0.7% 1.7% 2.5% 3.9% 1.91 Bladder D 10% 4.5% 3.1% 2.6% 1.6% 0.9% 0.0% 0.6% 1.6% 2.4% 3.7% 6 2.00 PTV D 95% 4.8% 3.3% 2.8% 1.8% 0.9% 0.0% 0.6% 1.6% 2.4% 3.7% 1.53 Rectum D 10% 4.7% 3.2% 2.6% 1.6% 0.9% 0.0% 0.7% 1.8% 2.5% 3.9% 1.71 Bladder D 10% 4.5% 3.1% 2.4% 1.6% 0.9% 0.0% 0.6% 1.8% 2.5% 3.8%

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62 Table 2 3. Dosimetric endpoints were calculated over the range of solid water MVCT number variation for 10 patients with head and neck cancer. The dose distribution calculated when solid water was equal to 50 HU was assigned as the reference distribution. All other distribut ions were compared to the reference. Solid w ater MVCT n umber (HU) Patient Reference d ose (Gy) Endpoint 100 90 80 70 60 50 40 30 20 10 0 1 1.97 PTV D 95% 1.4% 1.1% 0.8% 0.5% 0.2% 0.0% 0.3% 0.5% 0.7% 1.0% 1.2% 0.50 Rt Parotid D 50% 0.7% 0.5% 0.6% 0.4% 0.2% 0.0% 0.0% 0.2% 0.3% 0.5% 0.6% 0.52 Lt Parotid D 50% 0.8% 0.7% 0.5% 0.3% 0.1% 0.0% 0.2% 0.3% 0.5% 0.6% 0.7% 2 1.99 PTV D 95% 1.5% 1.2% 0.9% 0.6% 0.3% 0.0% 0.3% 0.5% 0.8% 1.0% 1.3% 0.85 Rt Parotid D 50% 0.9% 0.7% 0.4% 0.4% 0.2% 0.0% 0.2% 0.4% 0.6% 0.7% 0.9% 0.53 Lt Parotid D 50% 0.3% 0.4% 0.3% 0.4% 0.3% 0.0% 0.1% 0.2% 0.3% 0.4% 0.6% 3 2.02 PTV D 95% 1.7% 1.4% 1.0% 0.7% 0.3% 0.0% 0.3% 0.6% 0.9% 1.2% 1.5% 0.57 Rt Parotid D 50% 0.9% 0.8% 0.5% 0.3% 0.2% 0.0% 0.2% 0.3% 0.6% 0.8% 0.8% 0.59 Lt Parotid D 50% 1.0% 0.7% 0.5% 0.3% 0.2% 0.0% 0.1% 0.2% 0.4% 0.5% 0.6% 4 1.99 PTV D 95% 1.3% 1.0% 0.8% 0.5% 0.2% 0.0% 0.2% 0.5% 0.7% 0.9% 1.1% 1.84 Rt Parotid D 50% 1.2% 1.0% 0.7% 0.5% 0.2% 0.0% 0.2% 0.4% 0.7% 0.9% 1.0% 0.47 Lt Parotid D 50% 0.6% 0.4% 0.3% 0.3% 0.1% 0.0% 0.1% 0.0% 0.0% 0.1% 0.2% 5 2.13 PTV D 95% 1.7% 1.4% 1.1% 0.7% 0.3% 0.0% 0.4% 0.7% 1.0% 1.4% 1.7% 0.53 Rt Parotid D 50% 0.6% 0.5% 0.4% 0.3% 0.1% 0.0% 0.1% 0.3% 0.3% 0.5% 0.7% 0.94 Lt Parotid D 50% 0.9% 0.7% 0.5% 0.2% 0.0% 0.0% 0.5% 0.7% 1.0% 1.2% 1.5% 6 2.13 PTV D 95% 1.8% 1.5% 1.1% 0.7% 0.4% 0.0% 0.3% 0.7% 1.0% 1.4% 1.7% 0.63 Rt Parotid D 50% 1.3% 1.1% 0.8% 0.5% 0.3% 0.0% 0.2% 0.5% 0.7% 0.9% 1.1% 0.58 Lt Parotid D 50% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% 0.2% 0.4% 0.6% 0.7% 0.9%

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6 3 Table 2 3. Continued Solid water MVCT number (HU) Patient Reference d ose (Gy) Endpoint 100 90 80 70 60 50 40 30 20 10 0 7 2.13 PTV D 95% 1.7% 1.4% 1.0% 0.7% 0.4% 0.0% 0.3% 0.6% 1.0% 1.3% 1.6% 0.58 Rt Parotid D 50% 0.9% 0.7% 0.5% 0.3% 0.2% 0.0% 0.2% 0.3% 0.5% 0.6% 0.7% 0.58 Lt Parotid D 50% 0.6% 0.5% 0.3% 0.2% 0.1% 0.0% 0.1% 0.3% 0.4% 0.5% 0.6% 8 2.01 PTV D 95% 1.6% 1.2% 0.9% 0.6% 0.3% 0.0% 0.3% 0.6% 0.9% 1.1% 1.4% 0.54 Rt Parotid D 50% 0.9% 0.7% 0.5% 0.4% 0.2% 0.0% 0.2% 0.3% 0.5% 0.7% 0.8% 0.55 Lt Parotid D 50% 1.0% 0.8% 0.6% 0.3% 0.2% 0.0% 0.2% 0.4% 0.6% 0.7% 0.8% 9 2.12 PTV D 95% 1.6% 1.3% 1.0% 0.7% 0.3% 0.0% 0.3% 0.7% 1.0% 1.3% 1.6% 0.58 Rt Parotid D 50% 0.9% 0.7% 0.5% 0.3% 0.2% 0.0% 0.2% 0.4% 0.5% 0.7% 0.8% 0.48 Lt Parotid D 50% 1.1% 0.9% 0.6% 0.5% 0.2% 0.0% 0.2% 0.5% 0.6% 0.7% 1.0% 10 1.95 PTV D 95% 1.8% 1.4% 1.1% 0.7% 0.3% 0.0% 0.4% 0.7% 1.0% 1.4% 1.7% 0.63 Rt Parotid D 50% 1.2% 1.0% 0.8% 0.5% 0.3% 0.0% 0.3% 0.4% 0.6% 0.7% 1.0% 1.65 Lt Parotid D 50% 1.5% 1.1% 0.8% 0.5% 0.3% 0.0% 0.3% 0.5% 0.8% 1.0% 1.2%

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64 A B C Figure 2 1 Planned dose distributions for each of the phantoms evaluated overlaid on axial kVCT images. The innermost grey line shows the target volume and the white lines show the 90% and 50% of prescription isodose lines. A) Water phantom. B) Thorax phantom. C) Head phantom.

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65 A B Figure 2 2. Density histograms for the TomoPhantom image sets. A) Density histograms resulting from the application of the reference IVDT to the reference TomoPhantom MVCT image set and a subsequent TomoPhantom MVCT image set. HU variations in the second image are unaccounted for and the HU are m apped to incorrect densit ies. B) Density histograms of two TomoPhantom MVCT image sets after IVDT manipulation. The derived IVDT was applied to the reference TomoPhantom MVCT image set to mimic errors in the density distribution that occurred when image set Y was incorrectly map ped using the reference IVDT.

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66 A B C Figure 2 3. Temporal variation of the mean HU value of TomoPhantom solid water for two treatment machines. Measurements preceding target replacement are indicated by a square marker. A) Machine #1. B) M achine #2. (C) Temporal variation of the mean HU value of the TomoPhantom solid water for machine #1 in 2009. Component changes are annotated on F igure 2 3C

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67 Figure 2 4 DVH curves calculated for each site. Solid curves show the DVHs calculated whe n the IVDT that was measured for the lowest HU value of solid water on machine #1 was applied. Dashed curves show the DVHs calculated when the IVDT that was measured for the highest HU value of solid water on machine #1 was applied.

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68 Figure 2 5. Dose di fference (cGy) for each evaluated case. These images were obtained by subtracting the dose distributions calculated when the solid water MVCT number was equal to 5 HU from those calculated when the solid water MVCT number was equal to 103 HU.

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69 CHAP TER 3 THE IMPORTANCE OF DOSE RECALCULATIONS Chapter 2 explored the dosimetric uncertainty of dose recalculations for one imaging modality. However, as discussed in Chapter 1, all of the image guided radiation therapy (IGRT) modalities present challenges f or accurate dose recalculation. Furthermore, implementing dose recalculation into a clinical workflow can be time consuming and resource intensive. Ideally, dose recalculation and accumulation would be performed for every available repeated image set to obtain the best estimate of the delivered dose. Because of the challenges mentioned previously however, dose recalculation may not always be practical. This study aims to investigate the dosimetric difference introduced when using the dose distribution calculated for the initial plan as a substitute for a recalculated dose distribution on each repeated image set for patients with head and neck cancers. This aim is accomplished by simply overlaying the planned dose distribution on the repeated image sets and comparing selected dosimetric endpoints with those obtained using the recalculated dose distributions. If the dosimetric differences between the two approaches are acceptable, the dose overlay technique may reduce the resources required to perform of f line adaptive radiation therapy ( ART ) dose assessment and make on line dose evaluation more viable. Material s and M ethods Patient C ohort and I mage A cquisition As part of an institutional review board approved study, 16 patients with cancers of the head and neck were evaluated in this work. Six of the 16 patients were re plan ned at least once during their treatment course. In total, 24 unique plans were

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70 evaluat ed across the 16 patients. Each patient was treated for 33 35 fractions using a TomoTherapy Hi ART II system (Accuray Inc, Sunnyvale, CA). Prior to each treatment delivery, a helical megavoltage CT ( MVCT ) image set was acquired to verify the sition. These daily MVCT images were used to track the changes to each patient over their treatment course for the purposes of this study. Fractions that included a treatment interruption were excluded for technical reasons, resulting in the evaluation o f 528 total image sets. Dose R ecalculation M ethodology Dose recalculations were performed using the acquired MVCT image sets and a acquired for a 40 cm field of view (FOV) w ith a 512x512 in plane resolution. Slice thicknesses were 4 or 6 mm. Before calculation, the MVCT images were resampled to match the resolution of the planning kilovoltage CT ( kVCT ) and inserted into the planning image set to create a merged image. 54 The merged image incorporates data from the planning kVCT to fill in anatomical information that lies outside of the MVCT FOV and scan range. Patient alignment shifts applied to the pre treatment images by the attending therapists were taken into account during the creation of the merged images by shifting the position that the MVCT images were inserted into the kVCT images. MVCT and kVCT Hounsfield units were converted to density values using separate image value to density table s (IV DT). The MVCT IVDT was created, verified, and maintained according to the procedures outlined in TG 148 to ensure the reliability of the dose recalculations. 79 T he software can then perform a convolution/superposition dose calc ulation using the merged image and the radiation delivery parameters of the treatment plan. 80 The final dose grid resolution was equal to four times the voxel size

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71 of the original kVCT, in plane, and equal to t he kVCT slice thickness (3 mm) in the superior inferior (SI) direction. Therefore, the in plane dose grid resolution depends on the FOV of the planning kVCT but is typically 4 5.5 mm. Dose O verlay M ethodology The planning kVCT image set for each patient was acquired prior to the start of treatment on a Philips Brilliance CT system (Philips Medical Systems, Best, The Netherlands). All kVCT images were acquired with the patient in the simulated treatment position, a 50 70 cm FOV 512x512 in plane resolution, and a 3 mm slice thickness. Per the standard TomoTherapy workflow, t he planning image sets were down sampled to an in plane resolution of 256x256 upon import into the treatment planning system After optimization of the tre atment plan, the final dose grid was dose grid with a resolution of 2x2 voxels in the axial plane and the slice thickness (3 mm) in the SI direction. 79 Thus, the dose grid resolution for the treatment plan was four times the voxel size of the original kVCT, in plane, or approximately 4 5.5 mm. The dose grid resolutions of the recalculated dose distributions and the treatment plan dose dist ributions were the same for each patient. To perform the dose overlay instead of recalculation, the treatment plan dose distribution was simply overlaid on the merged image according to the known treatment isocenter. Anatomical changes and pre treatment patient shifts were represented in the merged images using the dose overlay method. However, changes to the dose distribution that would have resulted from the anatomical changes were not accounted for because the distribution was not recalculated.

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72 Deform able I mage R egistration An intensity based free form deformable image registration ( DIR ) algorithm was used to register the merged images to the planning image sets. 46 81 DIR allowed the propagation of planning contours from the treatment plans to the merged images and the accumulation of dose from the daily images back to the planning images. The automatically propagated contours used in this study were visually inspected by the attending radiation oncologist and were found to represent the intended anatomy. The same deformed contour sets were used with both the recalculated and the overlaid dose distributions. Comparison of the R ecalculated and O verlaid D ose D istributions ART dose assessment may be accomplished by propagating or recreating the planning contours on the daily images and comparing the estimated delivered dose for the new anatomy of that day to the planned dose indep endent of all other fractions. Another ART dose assessment approach would be to accumulate the estimated daily doses to the planning images and compare the result to the expected plan dose. Therefore, in this study, we report the mean relative dose diffe rence between the recalculated and overlaid dose distributions for all 528 fractions as considered independently from all other fractions (daily data) and we report the relative dose difference between the accumulated recalculated and overlaid dose distri butions for each delivered plan (accumulated data) The relative dose difference is calculated according to E quation 3 1: ( 3 1 )

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73 where x overlay is the dosimetric endpoint calculated using the overlaid dose distribution and x recalculate is the dosimetric endpoint calculated using the recalculated dose distribution. To quantify how much the dose varies from the planned value for a given structure over a course of tr eatment, we report the relative dose variation which is calculated as follows: ( 3 2) where x plan is the dosimetric endpoint calculated during the original plan Finally, to show if the recalculated and overlaid dose distributions vary together, each dosimetric endpoint was normalized to the plan value and the correlation coefficient is reported. All of the above metrics are calculated for the following dosimet ric endpoints: PTV D 95% PTV D 05% left parotid D 50% and right parotid D 50% Results Table 3 1 shows the mean relative dose difference statistics for the daily data The mean relative dose difference is reported for each patient and for all 528 fractions. U sing the overlaid planning dose distribution instead of the recalculated distribution never resulted in a dose difference greater than 5% for the PTV endpoints, and, on average, the difference was less than 1% for the PTV D 95% and less than 2% for the PTV D 05% The parotid endpoints did have a maximum difference of almost 12%. However, the greatest mean difference for any patient was just above 5% and the averag e for all fractions, fo r both parotids, was less than 2.5 %. The accumulated statistics for each plan (Table 3 2) are comparable to th e daily statistics ( Table 3 1 ) For both the fraction by fraction (Table 3 1) and the accumulated data (Table 3 2), the

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74 o verlaid dose distribution typically underestimated the PTV endpoints and overestimated the parotid endpoints. Table 3 3 shows the mean relative dose variation and correlation coefficients. The dose variations for the PTV endpoints were all less than 2 %, b ut the dose variations for the left and right parotids were substantially larger with mean values greater than 12% The correlations between the recalculated and overlaid do se distributions were 0.9 9 for both parotids, but were considerably lower for the PTV endpoints. These data show that the parotid doses increased substantially over the treatment course and that both the overlaid and recalculated dose distributions increased together for the parotid D 50% The correlations were much lower for the PTV e ndpoints but so were the variations indicating that although the overlaid and recalculated distributions did not vary together for the target volumes, the dose variations were so small that a suboptimal correlation between the distributions would not likel y have a clinical impact As a graphical example, Figure 3 1 illustrates the daily variation and correlation of the PTV D 05% and left parotid D 50% for P atient 3. Figure 3 2 shows the parotid D 50% data for all 528 fractions. Figure 3 2 further demonstrates both the variation and correlation of the parotid data. Discussion Ultimately, the purpose of this work is to determine the dosimetric uncertainty that may be introduced by using the planning dose distribution instead of recalculating the dose on the changing patient anatomy. For the data presented here, the correlations between the overlaid and recalculated target dosimetry were reasonable for the PTV D 95% and non existent for the PTV D 05% However, the correlations are likely irre levant because the target dosimetry changed very little over the course of treatment,

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75 and, therefore, the differences between the overlaid and recalculated distributions were also minimal. The parotid dosimetry requires a more in depth look. While, on ave rage, the dose difference between the overlaid and recalculat ed distributions was approximately 2.5 %, a single fraction difference could approach 12%. The dose differences were small, however, when compared to the dose variations for both parotids. Coupl ed with the high correlation coefficients for the parotid endpoints, these observations indicate that the parotid doses may vary substantially over a course of treatment but, at the same time, the dose differences between the two distributions remain small because the overlaid and the recalculated parotid doses vary in the same direction. Therefore, for these data, it can be concluded that the variations in the parotid doses may be primarily attributed to changes in the shapes or locations of the parotid g lands instead of changes in the dose distributions themselves. The DIR used in this study accounts for changes in the shapes or locations of ROIs, but changes in the dose distributions due to changing patient anatomies is only taken into account in the re calculated distributions. Consequently overlaying the planning dose distributions instead of performing dose recalculations should be sufficient to identify parotid dosimetry trends because the effects on the dose distributions themselves appear to be sm all in most, but not all, cases. Additionally, as noted earlier, using an overlaid dose distribution instead of a recalculated one typically resulted in the underestimation of the PTV dosimetry and the overestimation of the parotid dosimetry. This is rea ssuring because any clinical decisions to re plan a patient based on these data would err on the conservative side. Considering only the parotid dosimetry, this means that a re plan may be prompted

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76 unnecessarily but also that a parotid overdose would not be missed when using the dose overlay method. Smyth et al. 82 examined a dose distribution overlay technique for the on line verification of CTV coverage during prostate radiotherapy. Multiple verification image sets were acquired over a treatment course for 10 patients using CT on rails. To account for patient shifts and anatomy changes, dose distributions were recalculated on the verification image sets. The 95% isodose lines of the recalculated distributions were compared to the 95% isodose lines of the overlaid planning dose distribution s. That investigation reported that the adequacy of the CTV coverage as determined by the overlaid and recalculated dose distributions were consistent in 80 out of 87 cases. In a recent study, Sharma et al. 83 consider ed the shift and deformation invariance of treatment plans created for patients with prostate cancer. 19 patients with 8 13 CTs/patient were examined. Each image set was shifted by 10 17mm in all directions and the overlaid planning dose distribution was compared to a recalculated distribution for each fraction and applied shift. In this manner, the inter fraction shift and deformation invariance was evaluated simultaneously. The vast majority of root mean square percent errors (RMSPEs) between the dose distributions were within 2% for CTV, rectum, and bladder dosimetric endpoints. Only two patients exhibited RMSPEs greater than 2% in any endpoint examined. Those errors were 3.8% and 4.5% for the bladder D 50% While patients with cancers of the head an d neck have not been previously investigated explicitly, the studies cited above confirm the validity of using a dose overlay technique to estimate the dose delivered to a patient if the resources required to

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77 perform a dose recalculation are not available or practical. The data presented in this study, however, may only be applicable to head and neck cancer patients treated with helical t omo t herapy. Clearly, other treatment sites may be subject to greater dosimetric variations as the patient anatomy chang es. The numerous beamlets and delivery angles of the helical t omo t herapy dose delivery may also render it s dose distributions less sensitive to deforming patient anatomy. Finally, the use of a finer dose grid resolution may affect the data reported above Conclusion While a dose recalculation would ideally be performed on any image sets where a delivered dose assessment were desired, the planning dose overlay technique presented in this work may be acceptable as long as the underlying uncertainties are un derstood. For t he head and neck cancer cases presented here, the target dosimetry is insensitive to patient changes over a treatment course. The parotid dosimetry showed a greater variability, but the high correlation between the overlaid and recalculate d dose distributions in the glands indicates that the dose overlay technique is useful for identifying dosimetric trends even if the uncertainty in the absolute dosimetry were unacceptable. Overall, a greater knowledge of the uncertainties associated with the omission of dose recalculation should contribute to the efficiency and availability of on line or off line ART dose assessment.

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78 Table 3 1. Mean relative dose difference of the daily dosimetric endpoints for each patient. Each dosimetric endpoint is listed as the mean 1 standard deviation. The maximum relative dose difference is displayed in parentheses. Patient PTV D 95% PTV D 05% Left p arotid D 50% Right p arotid D 50% 1 0.8 0.5 ( 1.9)% 1.2 0.6 ( 2.8)% 3.0 1.1 (6.0)% 3.2 1.8 (6.4)% 2 0.7 0.7 ( 2.0)% 1.2 0.7 ( 2.6)% 2.0 0.9 (4.2)% 0.9 0.7 (2.9)% 3 0.9 0.6 ( 2.4)% 1.3 0.6 ( 2.5)% 0.7 1.2 (4.6)% 1.6 1.3 (5.2)% 4 0.3 0.4 ( 1.2)% 1.2 0.3 ( 2.1)% 4.8 1.1 (7.2)% 0.2 0.4 (1.4)% 5 0.5 0.2 ( 1.0)% 1.2 0.2 ( 1.6)% 2.7 1.1 (4.8)% 4.2 1.0 (6.5)% 6 1.6 0.4 ( 2.3)% 2.0 0.4 ( 2.6)% 0.9 1.2 (5.9)% 2.6 0.5 (3.6)% 7 1.0 0.4 ( 1.8)% 3.9 0.4 ( 4.7)% 1.5 0.6 (3.4)% 0.5 0.5 (1.5)% 8 0.0 0.4 (1.0)% 1.2 0.4 ( 1.8)% 2.9 0.9 (4.3)% 3.6 1.0 (6.3)% 9 0.6 0.7 ( 1.9)% 1.9 1.0 ( 3.6)% 3.6 2.0 (8.1)% 0.1 0.5 (1.5)% 10 0.2 0.7 (2.1)% 0.7 0.8 ( 2.0)% 5.2 1.3 (7.5)% 3.9 0.9 (5.6)% 11 0.7 0.6 ( 2.2)% 0.8 0.5 ( 2.1)% 3.1 1.4 (6.0)% 4.1 0.9 (6.0)% 12 0.9 0.4 ( 1.6)% 1.2 0.4 ( 1.9)% 0.0 0.8 (1.7)% 1.6 0.6 (3.3)% 13 0.7 0.4 (1.6)% 1.2 1.0 ( 3.2)% 1.6 0.4 (2.4)% 2.5 1.3 (5.4)% 14 0.0 0.8 ( 2.0)% 0.5 0.7 ( 2.0)% 0.6 0.7 (2.4)% 3.1 2.5 (7.4)% 15 0.7 0.6 ( 2.1)% 1.3 0.8 ( 2.8)% 0.4 1.2 ( 3.0)% 2.4 0.9 (4.7)% 16 0.7 0.7 ( 2.3)% 1.2 0.8 ( 2.6)% 4.3 2.1 (11.8)% 4.4 1.0 (6.2)% Mean a 0.6 1.5 ( 2.4)% 1.4 2.2 ( 4.7)% 2.4 1.5 (11.8)% 2.4 1.2 (7.4)% Note: a The mean data is listed for all 528 fractions.

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79 Table 3 2. Relative dose difference of the accumulated dosimetric endpoints for each plan. Patient (p lan) Fxs a PTV D 95% PTV D 05% Left p arotid D 50% Right p arotid D 50% 1 34 0.9% 1.1% 4.4% 4.1% 2 34 0.7% 1.2% 3.0% 1.2% 3 32 0.9% 1.2% 0.3% 1.0% 4 33 0.4% 1.1% 3.8% 0.3% 5 31 0.6% 1.3% 2.5% 5.4% 6 33 1.5% 1.9% 1.0% 2.3% 7 33 0.7% 3.9% 2.0% 1.2% 8 (1) 24 0.0% 1.3% 3.7% 3.4% 8 (2) 9 0.1% 0.9% 3.4% 3.0% 9 (1) b 4 0.1% 0.4% 5.3% 0.1% 9 (2) 20 1.0% 1.5% 3.7% 0.1% 9 (3) 9 0.7% 1.6% 2.2% 0.1% 10 (1) 20 0.5% 1.0% 4.3% 3.4% 10 (2) 7 0.3% 0.8% 6.0% 3.9% 10 (3) 8 0.8% 0.5% 6.4% 2.8% 11 (1) 21 0.8% 0.6% 2.9% 3.8% 11 (2) 12 0.6% 0.7% 4.9% 4.0% 12 33 0.9% 1.0% 0.1% 1.5% 13 35 0.7% 1.4% 1.8% 0.7% 14 (1) 25 0.0% 0.3% 0.6% 0.7% 14 (2) 8 0.4% 0.8% 0.2% 6.0% 15 30 0.8% 1.1% 0.5% 2.0% 16 (1) 24 0.5% 0.6% 4.6% 4.1% 16 (2) 9 1.3% 2.1% 3.5% 4.0% Weighted m ean c 0.6% 1.3% 2.5% 2.3% Note: a Number of fractions (fxs) accumulated per plan. b Patient 9 was re planned after 4 fractions to account for a change in the tumor volume c The weighted mean was computed by weighting the dosimetric endpoints for each plan by the number of fractions accumulated.

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80 Table 3 3. Mean relative dose variations and correlation coefficients for the daily and accumulated dosimetric endpoints. Daily Data Accumulated Data Endpoint Mean relative d ose v ariation 1 SD Correlation c oefficient Mean relative dose v ariation 1 SD Correlation c oefficient PTV D 95% 0.6 1.3% 0.81 0.2 0.9% 0.83 PTV D 05% 1.3 1.1% 0.29 0.7 0.8% 0.24 Left p arotid D 50% 18.5 19.6% 0.99 17.9 14.5% 0.99 Right p arotid D 50% 12.7 14.3% 0.99 12.3 9.8% 0.99

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81 Figure 3 1. Recalculated and overlaid daily dosimetric endpoints for P atient 3.

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82 Figure 3 2. Parotid D 50% data for both parotids. The D 50% values shown above were normalized to the planned D 50% values to facilitate display. The line shown on the graphs illustrat es where the data points would lie if the recalculated and overlaid values were exactly equal. A) A ll 528 daily fractions B) A ll accumulated plans.

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83 CHAPTER 4 THE SPATIAL UNCERTAINTY OF DEFORMABLE IMAGE REGISTRATION Deformable image registration (DIR) could be a powerful tool in the implementation of adaptive radiation therapy. However, DIR algorithms are complex and difficult to test because the true deformation is unknown in actual patient scenarios. As discussed in Chapter 1, many investigators have attempted to quantify the spatial uncertainty of DIR, but there are numerous limitations to tho se studies. In an attempt to overcome some of those limitations, this study aims to develop a library of clinically releva nt virtual phantoms that may be used to evaluate any deformation algorithm in the context of a radiation therapy treatment course for head and neck ( H&N ) cancer patients These phantoms were derived from actual patient images in an effort to prioritize cl inical relevance. Additionally, they were developed using a combination of biomechanical and human directed models that permit the tracking of the deformation accuracy of every image voxel. 10 of these phantoms were developed from 10 different patient im age sets to allow the assessment of various clinical scenarios and the possible extrapolation of the results to other DIR cases. The methods and results described here have been included in a previously published manuscript. 84 Materials and Methods Image A cquisition and P atient S election Images for this study were acquired as part of an IRB approved prospective adaptive radiothe rapy protocol. All patients were simulated using a Philips Brilliance CT system (Philips Medical Systems, Best, The Netherlands) or a Siemens Biograph 64 PET/CT system (Siemens AG, Munich, Germany). Volumetric images of each patient enrolled in the proto col were re acquired on the same equipment weekly throughout the

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84 course of treatment All images had an in plane resolution of 0.97 to 1.37 mm and a slice thickness of 3 mm. Ten patients were selected from this protocol to represent a reasonable cross sec tion of all H&N cancer patients. Table 4 1 displays the attributes of these 10 patients. The image sets of these 10 patients were used to develop the 10 virtual phantoms presented in this study. For each patient, the planning image set and the final weekly kVCT image set were designated as the s tart of treatment (SOT) and end of treatment (EOT) image sets, respectively. These images formed the basis for the development of the virtual phantoms. Image A utosegmentation and D eformation The goal of the next steps in the development of the virtual pha ntoms was to deform the SOT image s to match the EOT image s as closely as possible. In other words, the SOT images were deformed to create simulated end of treatment (SEOT) images. This objective was important to ensure that the phantom deformations mimic actual patient changes over a treatment course and improve the clinical relevance of the virtual phantoms. With that end in mind, we first used a research version of a biomechanically driven autosegmentation and deformation tool to deform the SOT images. 85 86 This tool uses pre defined atlas data and an adaptive algorithm to map image inte nsity values to tissue types such as bone, fat, muscle, or air. It will also identify and contour key structures such as the skull, mandible, and cervical vertebrae. Using the information obtained from the identification of these structures and tissues, the user can then deform the images in a biologically realistic manner For example, during the application of weight loss, soft tissues are allowed to non rigidly deform according to

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85 pre defined parameters while segmented bony structures are not. Throug h th ese process es this tool allows the user to perform head rotations and translations with six degrees of freedom, mandible translations in any direction and rotation around the lateral axis, and weight loss in the neck region. Following the image defor mation, the user may export the underlying deformation vector field ( DVF ) that defines the transformation. Figure 4 1 shows screenshots of this tool before and after the application of a head rotation about the lateral axis. The image manipulations allowe d by this tool enabled us to perform a first pass image deformation of the SOT images using a biomechanical model. Via this adjusted to match the EOT position. This resul ted in SEOT images that resembled some of the characteristics of the EOT images. Manual I mage D eformation To apply further anatomical deformations to the S E OT images, that could not be taken into account because of the limitations of the biomechanical mode l, the ImSimQA software package (Oncology Systems Limited, Shrewsbury, Shropshire, UK) was used. This software uses a thin plate splines (TPS) algorithm 41 to perform global deformations of volumetric image sets. A detailed overview of the ImSimQA software and its application to DIR validation has been presented previously. 87 Briefly this tool allowed us to designate fixed points and deformation points on the image anatomy. The user may then move the deformation points from the initial position to a desired post deformation position. Using the TPS algorithm, the system calculates a DVF that maps the coordinate transformation of the deformation points while holding the fixed points

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86 stationary. In this manner, a user may create realistic deformations of patient anatomy by defining how selected landmarks deform within that anatomy. Th is procedure allowed us to manually model spine flexion, shoulder position, hyoid movement, tumor/node shrinkage, weight loss, and parotid shrinkage. Each deformation was applied successively and iteratively modified until the S E OT image anatomy was simil ar to the EOT image objective. An example of the modeled parotid shrinkage is shown in F igure 4 2. Deformed I mage P ost P rocessing Once the S E OT image had been satisfactorily deformed to match the EOT image, some post processing was required. First, due t o the use of two distinct deformation algorithms and the iterative nature of the S E OT image deformation, the individual DVFs comprising the complete image transformation had to be combined to create a single DVF that would map the SOT image to the final S E OT state. Because creating this combined DVF required DVF composition techniques involving interpolation of the fields, applying the combined DVF to the original SOT image would not result in the exact same output (deformed) image as applying each individ ual DVF in sequence. The output images in each case should be very similar because the interpolation error is minimal, but they will not be exactly the same. For this reason, the SOT image was deformed using the combined DVF to create a S EOT image that r esembled the actual EOT image. This approach has two primary benefits. First, taken as a pair, the SOT image and the S EOT image form a set of test images, or a virtual phantom, where the tion algorithm had been used to create the virtual phantoms, it would be easier for the same or a similar

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87 algorithm to recreate the image deformation with the same underlying DVF given only the SOT and S EOT test images as inputs. When using the virtual ph antoms to analyze the uncertainty in a deformation algorithm, this would create an unfair bias toward algorithms similar to the one used to create the phantoms. Since multiple algorithms were used in this approach and because they were applied iteratively however, the bias toward any particular algorithm should be minimized. The second piece of image post processing that we implemented involved S EOT noise. In clinical practice, even two images of the same object scanned back to back will have different HU values for the same voxel due to image noise. Since the S EOT image was deformed from the SOT image, the voxel intensity value differences between the two images will not be representative of what would be seen between true inter fra ction images in clinical practice. This characteristic could make the DIR problem unrealistically easy for deformation algorithms that use intensity based similarity metrics. To better represent a true clinical scenario, the following procedure was used t o S EOT images. First, two sets of images of a cylindrical water phantom were acquired on our kVCT simulator back to back. The images were then subtracted from each other to obtain a difference image. A 101x101x101 voxel v olume was selected from the center of the difference image to create a volume of possible noise values. Finally, voxel values were selected at random from this noise volume and added to each voxel in the S EOT image to generate the final S EOT image. The e ntire virtual phantom cre ation process is diagrammed in F igure 4 3.

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88 Virtual P hantom Q uality M etrics To ensure that the virtual phantoms met minimum standards of clinically relevant deformations, two well known DIR metrics were recorded. The normalized cro ss correlation (NCC) was recorded for both the pre deformation SOT image with the EOT image and the post deformation final S EOT image with the actual EOT image. The NCC of two images (A and B) is defined as ( 4 1 ) where A i and B i are the voxel intensities in the overlap region of images A and B at position i, and and are the mean voxel intensities in A and B. A n NCC equal to 1 would indicate that the voxel intensities of the two registered images are perfectly correlated while a n NCC of 0 would indicate no correlation. If the NCC of the S EOT image with the actual EOT image improves over that of the SOT image, th is would indicate that the deformation of the SOT image did increase its similarity to the EOT image. The determinant of the Jacobian matrix (also known as the Jacobian) of each according to Equation 4 2 (4 2) In Equation 4 2, , and are the deformed x, y, and z image coordinates, respectively. The Jacobian is a measure of local volume change throughout the image.

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89 A Jacobian value between 0 and 1 indicates a shrinking volume, while a value greater than 1 indicates a growing volume. Values less than or equal to 0 indicate a singularity or a folding of the image and are typi cally indicative of anatomically unrealistic deformations. For this reason, the minimum Jacobian value within the external contour Quantification of DIR U ncertainty To show the utility of the virt ual phantoms, the final image pair for each phantom was imported into a commercial DIR software package (MIM Software Inc., Cleveland, OH) 88 A deformable registration was performed using MIM and the DVFs were errors are reported for the brainstem, cord, mandible, left parotid, and right parotid. R esults Virtual P hantom Q uality M etrics Table 4 2 shows the virtual ph antom quality metrics. The data show that the NCC improved in all cases. This suggests that the post deformation SEOT images are more similar to the actual EOT images than the SOT images and supports the clinical ditionally, there are no 0 or negative Jacobian values showing that unrealistic deformations that would be identified by the Jacobian have not occurred. Quantification of DIR U ncertainty The mean spatial DIR error s of the algorithm under investigation are reported in Table 4 3 for all 10 phantoms. The errors in the vo xels of the brainstems were, on average, small (< 1 mm) with a mean maximum error of 1.10.6 mm. The errors for the cords were also small with mean errors less than 1mm and a mean maximum err or of

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90 1.30.5 mm. The mandible errors were larger than the brainstem and cord errors almost across the board with a mean error magnitude of 0.90.3 mm. The mean parotid errors and standard deviations (Ta ble 4 3 ) were larger than the other structures exa mined. More specifically, the right parotids showed the largest errors in all metrics. To i nvestigate this further, Table 4 4 shows the mean and maximum errors for the right parotid of each phantom. The multiple virtual phantoms based on distinct patien t cases allows the evaluation of aggr egate data as shown in Table 4 3 or individual data as shown in Table 4 4 The maximum errors for the right parotids rang ed from 2.1 mm to 22.8 mm. While four of the phantoms had mean error magnitudes of 1mm or greate r, the largest errors were contributed by P hantom 9. The errors seen in the right parotid of Phantom 9 would represent a failure of the DIR algorithm. The patient on which this phantom was based rec eived high doses to his parotid glands (Table 4 1 ) and lost almost 17% of his body weight over the treatment course. This resulted in substantial parotid shrinkage. The large change in the parotid coupled with the small voxel intensity gradients of the gland and the surrounding tissues likely made it difficu lt for the algorithm to adequately register this anatomy. The result was a DIR failure and a large algorithm uncertainty for deformations of this nature. Discussion T he above data is reported to demonstrate how the virtual phantoms may be used to benchmar k any given algorithm. Additionally, because the phantom library allows the quantification of the deformation error of every voxel in the image se ts and represents a sample population of 10 unique patients, it is possible to develop statistical spatial un certainty models that may be extrapolated to estimate any evaluated

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91 develop probability distribution functions (PDFs) for the voxels of a given structure or sub volume. These PDFs may then be used to estimate the dosimetric uncertainty of a selected DIR case similar to the work published by Salguero et al. 76 The development of methods to estimate dosimetric uncertainty is the focus of Chapter 5 of this dissertation It should be noted that the data obtained from the virtual phantoms is only applicable to cases in volving the same treatment site and magnitude of anatomical changes For these phantoms, that would include images acquired over a single treatment course with the appropriate immobilization, of patients with cancers of the H&N. Our experience has shown that deformation algorithms may behave very differently depending on the treatment site and magnitude of the transformation For this reason, it can be very difficult to compare deformation accuracy results between studies. This problem is further compl icated by the use of a wide range of metrics to report these results. Despite these difficulties, several studies have attempted to quantify DIR accuracy in H&N cancer cases and would be valuable to review here. Wang et al. 50 used a TPS algorithm to simulate the deformation of an image set obtained from a H&N cancer treatment. Similar to this study, they then compared the DVF calculated using a demons algorithm 45 to the reference DVF created using the TPS error of 0.2 0.6 mm. Recently, Varadhan et al. 87 and Nie et al. 89 both use d ImSimQA to create site specific virtual phantoms. The H&N phantom of the Varadhan study simulated a large neck flexion that would not be representative of typical interfraction variation but,

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92 instead, was intended to imitate a retreatment scenario resul ting in a different neck position. This study reported contour comparison metrics between the contours diffeomorphic demons or a cubic b spline algorithm. The contours generated from the diffeomorphic demons DVF had a mean Dice similarity coefficient 65 mean Hausdorff distance 90 and mean average surface distance of 0.75, 11.2 mm, and 1.9 mm, respectively. The contours generated from the b spline DVF resulted in values of 0.74, 7.9 mm, and 1.7 mm for the same metrics. The H&N phantom of the Nie study attempted to model head rotation about the inferior superior axis, mandible movement, neck flexion, and weight loss in the neck region as was seen in the replanning CT of a patient that lost 40 lbs. during the cour se of treatment. This study compared commercial implementations of a free form deformation algorithm and a B ImSimQA DVF in a region defined by the smallest box that encompassed the target and all ide ntified organs at risk. The free form deformation algorithm resulted in 24.2% of voxels having errors greater than 2 mm, 14.6% greater than 3 mm, and 7% greater than 5 mm. The B spline algorithm resulted in 29.8% of voxels having errors greater than 2 mm 5.1% greater than 3 mm, and 0.1% greater than 5 mm. Due to the limitations of the available tools and time, these investigations were only able to model certain aspects of the H& N deformations that might be seen in clinical scenarios. Only one case was evaluated in each study and only the Nie study attempted to introduce noise into the virtual phantom. For these reasons, it may be difficult to draw conclusions about the applicab ility of the results to other H&N cases.

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93 Furthermore, the diverse approaches and metrics reported in these articles highlight the need for a clinically relevant standard toolset for the benchmarking, comparison, and reporting of DIR algorithms. In additi on to the independent testing of DIR algorithms already mentioned, we have made these phantoms available to the community as a clinically relevant tool to facilitate the comparison of DIR algorithms. The virtual phantoms presented in this study also have i nherent limitations. Although one of the primary goals of this work was to develop clinically relevant phantoms, all of the complexities of the deformation of the human body during a radiotherapy course would be very difficult to model. For example, thes e phantoms do not model sliding interfaces as might be found in the expansion or contraction of the lungs. They also do not model cavities that appear in one image but not the other. An example of this could include a patient that was initially scanned w ith no visible air pockets in the oral cavity. Upon re position creating an air cavity in the image. Care should also be taken when using the phantoms to evaluate DIR uncertainty in the vicinity of im age acquisition artifacts. While the phantoms do include artifacts that would typically be seen in routine clinical practice, such as dental artifacts, the changes that would occur in repeated images due to these artifacts have not been simulated. Theref ore, the DIR results may be biased in these regions. Also, w hile matching the phantoms to actual patient images, ensuring that the NCC increases for the simulated deformations, and checking for negative Jacobian values are necessary conditions for clinica l relevance, they are not sufficient. Clearly, it is not possible to match the S EOT image to the actual EOT image exactly I mages may be unrealistically deformed to artificially increase the NCC, and the Jacobian only tests

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94 for the absence of characterist ics found in unrealistic DVFs but not the presence of clinically relevant ones. Despite this, the nature of the manual deformation process provides for human guidance with the intention of eliminating any unrealistic deformations. Furthermore, although d ifferent users may have created different SEOT images given the same initial images, this is not a source of additional uncertainty. Because the final SEOT image was deformed from the SOT image using the combined DVF, that DVF is the ground truth for the virtual phantom image pair by definition. If another user had created a different combined DVF that resulted in a different SEOT image, that DVF would also be the ground truth for that virtual phantom image pair by definition. Finally, these phantoms can not currently be used to validate multi modality DIR. Conclusion This work provides a description of the construction and characterization of a library of virtual phantoms for the assessment of any DIR algorithm applied to interfraction H&N radiotherapy. The multiple clinically relevant phantoms may provide a standard tool for the comparison of algorithms and the extrapolation of results to H&N cases other than those represented by the phantoms.

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95 Table 4 1. Attributes of patients selected for the de velopment of the virtual phantoms. Patient no. Disease s ite Stage Gender Fxs d elivered Mean right p arotid d ose (Gy) Mean left parotid d ose (Gy) Initial weight/ end of treatment weight (kg ) No. of days between SOT and EOT i mages 1 Base of t ongue T2N2bM0 M 35 25.2 25.7 74.8/70.3 60 2 Base of t ongue T2N2cM0 F 35 34.7 23.2 68.0/62.1 56 3 Tonsil T2N2bM0 M 35 29.4 25.6 96.2/88.5 57 4 Nasopharynx T1N3M0 F 33 26.7 39.5 65.3/61.2 58 5 Unknown T0N2aM0 M 35 24.5 29.0 90.3/81.2 57 6 Supraglottic l arynx T1N1M0 M 33 26.1 21.3 95.3/82.6 43 7 Tonsil T2N2aM0 M 35 14.2 41.7 93.4/86.2 47 8 Tonsil T2N2aM0 F 35 23.5 28.5 106.1/101.6 48 9 Nasopharynx T4N2M0 M 33 55.7 48.7 68.0/56.7 59 10 Base of t ongue T0N2aM0 F 35 21.5 23.4 99.8/81.2 68 Note : Fx: fraction, SOT: start of treatment, EOT: end of treatment.

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96 Table 4 2. Virtual phantom quality metrics. The pre deformation normalized cross correlation (NCC) is reported for the start of treatment (SOT) image with the actual end of treatment (EOT) image. The post deformation NCC is reported for the final simulated end of treatment (SEOT) image with the actual EOT image. Phantom no. Pre deformation NCC Post deformation NCC Minimum J acobian 1 0.935 0.960 0.54 2 0.944 0.959 0.08 3 0.930 0.960 0.20 4 0.946 0.964 0.40 5 0.932 0.968 0.10 6 0.952 0.973 0.45 7 0.948 0.970 0.13 8 0.950 0.974 0.33 9 0.936 0.960 0.13 10 0.940 0.980 0.29 Note: NCC: normalized cross correlation. Table 4 3. Mean spatial error and standard deviation of the means for all 10 virtual phantoms. ROI LAT (mm) AP (mm) SI (mm) Magnitude (mm) Max m agnitude (mm) Brainstem 0.00.1 0.00.0 0.10.3 0.50.2 1.10.6 Cord 0.00.1 0.10.2 0.20.2 0.50.1 1.30.5 Mandible 0.00.3 0.10.3 0.20.1 0.90.3 4.01.3 Left Parotid 0.20.3 0.10.5 0.20.7 1.20.6 5.72.4 Right Parotid 0.30.5 0.11.0 0.71.5 1.51.8 7.26.0 Note: ROI: region of interest, LAT: lateral, AP: anterior/posterior, SI: superior/inferior. Table 4 4. Mean and maximum right parotid spatial errors for each virtual phantom. Phantom no. LAT (mm) AP (mm) SI (mm) Magnitude (mm) Max m agnitude (mm) 1 0.30.5 0.10.4 0.61.1 1.11.0 4.9 2 0.10.3 0.30.4 0.20.5 0.70.4 2.8 3 0.00.2 0.10.2 0.00.5 0.50.3 2.1 4 0.20.5 0.40.7 0.30.8 0.90.9 5.5 5 0.30.6 0.20.9 1.12.1 1.72.0 10.0 6 0.50.7 0.61.1 0.71.4 1.51.6 7.5 7 0.10.4 0.20.5 0.10.9 0.90.8 4.8 8 0.20.4 0.30.7 0.00.4 0.70.6 4.8 9 1.61.6 3.03.3 4.95.1 6.65.6 22.8 10 0.10.3 0.30.9 0.00.5 0.60.9 6.4 Note : LAT: lateral; AP: anterior/posterior; SI: superior/inferior.

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97 Fig ure 4 1. Example of image autosegmentation and deformation. This example shows a head rotation of 5 about the lateral axis. A) Autosegmented original image. B) Original patient position. C) Deformed image simulating a clockwise head rotation about the lateral axis. Fig ure 4 2. Example of the manually deformed parotid shrinkage. A) Original patient image after the application of autosegm entation and head rotation adjustments, but prior to any additional deformations. B) Image with manual parotid deformation applied. C) Actual end of treatment (EOT) patient image.

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98 Figure 4 3. Diagram of the virtual phantom creation process. The proce ss begins with the start of treatment (SOT) image. The SOT image is deformed using two different approaches (autosegmentation and ImSimQA) to create a simulated end of treatment (SEOT) image that resembles the actual end of treatment (EOT) image. Multipl e DVFs are exported from the manual deformation as a result of the iterative process. The resulting deformation vector fields (DVFs) are combined to create a single composite DVF. The combined DVF is then used to deform the original SOT image and re crea te the SEOT image from the single DVF. Simulated image noise is added to the SEOT image to create the final SEOT image. The dashed boxes represent the final image pair that makes up the virtual phantom.

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99 CHAPTER 5 THE DOSIMETRIC UNCERTAINTY OF D EFORMABLE IMAGE REGISTRATION Many studies have attempted to quantify the spatial uncertainty of deformable image registration (DIR) 47 67 68 89 as investigated in Chapter 4 but f ew have attempted to quantify the dosimetric uncertainty. 69 76 91 97 The ideal method for determining the uncertainty of DIR would be clinically relevant, generalizable to other cases and algorithms, and would provide a r esult that would be useful for making clinical decisions. Clinical relevance is very important, but also very difficult to achieve. Because the underlying deformation is unknown in patient anatomy, investigators must use phantoms or surrogate measures of deformation error that have varying degrees of clinical relevance. For example, several authors have used deformable gel, 94 96 polymer, 92 or silicon 69 phantoms to create known deformations. While these phantoms are valuable for making empirical measurements of DIR dosimetric errors, they do not likely represent actual clinical deformatio ns. Generalizability may also be difficult to achieve. Each DIR case has unique anatomy and dose distributions. For this reason, the ideal DIR dose accumulation QA method would be applicable to more than just a single clinical case. While it may be unf easible to extend a given method across treatment sites or scenarios due to vastly different patient deformations, it should be applicable to a range of clinical cases. The method should also not be biased toward any particular DIR algorithm and should ac commodate the comparison of multiple algorithms. In the end, the method should also provide clinicians with results useful for making treatment decisions. QA methods that identify image regions where t he dosimetric uncertainty could be high but do not pr ovide the magnitude of that uncertainty or how the uncertainty might affect the dosimetry of critical structures may

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100 be useful for better understanding the weaknesses of DIR dose accumulation. However, it is difficult to speculate how this information sho uld impact clinical decisions. On the other hand, if clinicians are provided with DIR uncertainty data in the form of dose volume histograms (DVHs), it is easier to see how those results could be applied to clinical decision making. This study presents a method of DIR dose accumulation analysis that attempts to overcome these challenges. The method uses a library of virtual head and neck ( H&N ) phantoms that were derived from actual patient images acquired over a single course of radiotherapy. 84 These virtual phantoms define a clinically relevant simulated deformation with a known deformation vector field (DVF). Because the under lying DVF is known, the phantoms can be used to determine the spatial DIR error using any algorithm. With a sample DIR algorithm, we show how the spatial error distributions determined through the registration and analysis of the phantoms can be applied t o other H&N patients to simulate potential DIR errors. The simulated DIR errors are then used to generate a range of DVHs for each patient that demonstrates how those errors affect dose accumulation. Materials and Methods Virtual P hantom L ibrary A library of 10 virtual phantoms was created from acquired patient images. This process has been described in detail in Chapter 4. 84 Fo r completeness, we will briefly describe this process here. Volumetric images of 10 patients with H&N cancers undergoing radiation therapy using helical tomotherapy (Hi ART, Accuray Inc., Sunnyvale, CA) were acquired before the start of treatment (plannin g image set) and near the end of treatment (EOT image set). All images were acquired using a Philips

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101 Brilliance CT system (Philips Medical Systems, Best, the Netherlands) or a Siemens Biograph 64 PET/CT system (Siemens AG, Munich, Germany). Each image se t had an in plane resolution of 0.97 1.37 mm and a slice thickness of 3 mm. Regions of interest (ROIs) were drawn on the planning images by the attending physician. The planning images for each patient were deformed to represent the anatomy of the EOT im ages using the combination of a biomechanical 85 86 and a human guided thin plate spline s 41 deformation algorithm. The thin plate splines algorithm is part of the ImSimQA software package (Oncology Systems Limited, Shrewsbury, Shropshire, UK) which has been described previously. 87 The deformation of the planning images resulted in a simulated EOT image set for each patient where the underlying deformation was known. Together, the planning and simulated EOT image pairs form a virtual phantom that may be impo rted into a third party DIR software package. The DVF from any third party algorithm may then be compared to the known ground truth DVF to obtain the deformation error for each image voxel. Table 5 1 shows the patient characteristics for each of the virt ual phantoms. These virtual phantoms are available for download as part of the Deformable Image Registration Evaluation Project ( http://sites.google.com/site/dirphantoms ) Table 5 2 shows the spati al registration errors of each phantom and ROI for a sample commercial DIR algorithm (MIM Software Inc., Cleveland, OH). 88 The DVFs calculated using this sample algorithm were used for the rest of this investigation. Dose R ecalculation Dose calculations were performed on the repeated image sets using Each repeated image set was manually registered to the planning image set using three translational degrees of freedom and rotation

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102 about the superior/inferior axis in an attempt to match the planned treatment position. Once a satisfactory registration wa s achieved, dose was recalculated on the new dose resolution of 1.94 2.74 mm, in plane, and 3 mm in the superior/inferior direction. This was the finest dose grid avai lable in the planning software. Creating and E valuating DVFs for DIR D osimetric E rror S imulation One of the aims of this study is to demonstrate a method to estimate the dosimetric error of clinical DIR cases where the ground truth is unknown. For this st udy, we have DVF error maps for each virtual phantom consisting of error vectors calculated by subtracting the third party algorithm vectors from the ground truth vectors. The vectors of these error maps have complex spatial correlations determined by the mathematics of the DIR model. 98 As an example of the spatial correlation, Fig ure 5 1 shows the DVF error map for an axial sli error vectors of any given DVF cannot be assumed to be independent of each other a priori. The problem of applying the known error maps from the virtual phantoms to additional clinical cases becomes difficu lt for the simple reason that the clinical cases have different anatomy than the virtual phantoms. For example, if the error map for a parotid gland is known for one of the virtual phantoms, but the clinical case to be evaluated has a parotid gland twice the size of the phantom (and, therefore, twice the number of voxels), how would one transfer an appropriate DVF error map with the appropriate spatial correlations to this new anatomy? One approach that has been suggested by Murphy et al. 93 to characterize and reproduce the spatial correlations of the error maps is to use principal component an alysis to create hypothetical error maps from known error maps. This approach is not suited to the methods of this study,

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103 however, because it requires a training set that is made up of multiple individual instances of measured DIR errors throughout a regi stered ROI. Only a single instance of measured DIR errors is available for each ROI of each phantom in this study because only a single registration was performed to better mimic what would occur in clinical practice. While multiple instances of measured DIR errors are available for each ROI across the phantom dataset, the work by Murphy et al. 93 states that it can be problematic to combine error maps from a population of subjects into a generic training set. To overcome these difficulties, we propose selecting an error vector at random from the known virtual phantom error maps for each ROI. E rror vectors are selected randomly from the voxels in the known ROI error map and assigned to a voxel in the new anatomy until all of the voxels in the ROI to be evaluated have been assigned an error vector. The result is a new DVF error map, created by selecting error vectors randomly from the known virtual phantom error maps, that coincides with the anatomy to be evaluated. This approach clearly makes the simplistic assumption that each error vector is independent of the other vectors in the error map Therefore, the uncertainty introduced by using this approach was quantified and its use was validated through the following procedure. Dose distributions were calculated on the simulated EOT images of each virtual phantom. Then, the spatially correlat ed error maps for each ROI were added to the third party DVFs calculated by the commercial DIR algorithm. In other words, the ground truth DVFs were recreated for each phantom by adding the spatially correlated error vectors to the third party DVFs. This resulted in a set of baseline DVFs that were created using empirically determined error maps. Using the baseline DVFs,

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104 dose values were deformed to the planning images and DVHs were calculated. The baseline DVFs allowed us to calculate a set of baseline DVHs that were used to quantify how the phantom dosimetry changed when the spatially correlated empirical error maps were used instead of hypothetical error maps created by random error vector selection. Next, random error maps were created for each virt ual phantom by randomly selecting error vectors from the spatially correlated error map of each phantom. The random error maps were then added to the DVFs calculated by the commercial DIR algorithm to create hypothetical DVFs that represent the magnitude and direction of the virtual phantom DIR errors, but lack the spatial correlation. In the same manner as the baseline DVFs, dose values were deformed to the planning images and DVHs were calculated. This process was repeated 10 times to create 10 random error maps for each virtual phantom. To quantify the dosimetric uncertainty introduced by using the random error maps instead of the baseline error maps, DVH endpoints were compared. D 2% values were tabulated for the brainstem, cord, and mandible as a surrogate for the maximum dose. 99 Mean dose (D mean ) values were recorded for the left and right parotid. This process is outlined in the flowchart of Figure 5 2. DIR D osimetric E rror S imulation To demonstrate how DIR spatial errors may translate into dosimetric errors during dose accumulation, 10 clinical patients with H&N cancers treated with helical tom otherapy were selected. Table 5 3 shows the characteristics of these 10 patients. The 10 patients were selected from a cohort of patients that were part of an IRB approved prospective repeated imaging protocol. This is the same protocol from which the original patient images for the development of the virtual phantoms were drawn.

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105 Therefore, 6 of the 10 patient image sets listed in Table 5 3 are the same as th e original patient images that were used to develop the virtual phantoms. Each patient had a planning CT acquired prior to treatment and a CT image set acquired near the EOT. Dose distributions were recalculated on the EOT images and DIRs were performed between the planning and EOT images using the commercial algorithm. This initial registration between the planning and EOT images using the commercial algorithm will be referred to as the non perturbed DVF. Next, random error maps were created from the v irtual phantom error data according to the procedure described above to simulate DIR spatial errors that could potentially occur when using this algorithm. For each patient and ROI, 10 random error maps were created, one from the error data of each virtua l phantom. The error maps were added to the non perturbed DVFs to create deformed to the planning images using the non perturbed and perturbed DVFs. A DVH was calculated f or each ROI and DVF. Finally, DVH endpoints were compared between results obtained using the non perturbed and perturbed DVFs. Again, D 2% values were tabulated for the brainstem, cord, and mandible. D mean values were recorded for the left and right paro tid. Also, the differences, for the evaluated DVH endpoints, between the values calculated using the non perturbed DVFs and the originally planned values were recorded. These differences provide a reference point to compare the observed changes in patien t dosimetry due to changing anatomy to the magnitude of the potential dosimetric errors due to DIR inaccuracies.

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106 Results Evaluation of DVF C reation using R andom E rror M aps Table 5 4 shows the mean and maximum differences between using the spatially correla ted (baseline) error maps and the non spatially correlated (random) error maps for the selected ROI endpoints. On average, the differences, for these DVH endpoints, are less than 1%. In the worst case, there was a maximum difference of 2.1% in the right parotid D mean of Phantom 5. Figure 5 3 displays the right parotid DVHs generated using the baseline error map and the 10 random error maps for Phantom 5. These DVHs show the largest difference of all DVHs examined. Figure 5 3 further demonstrates that t here was little variation among the DVHs calculated using the random error maps. The standard deviation of the random error DVHs never exceeded 0.5% for any of the evaluated endpoints. These data quantify the uncertainty that may be introduced by using n on spatially correlated error maps to simulate potential DIR dosimetric errors. DIR D osimetric E rror S imulation The DVHs obtained using the 10 simulated error maps (one random error map from each of the virtual phantoms) were compared to the DVH obtained u sing the non perturbed DVF determined by the commercial algorithm for each patient. Table 5 5 shows the median and maximum absolute dosimetric differences between using the DVFs perturbed by the simulated error maps and the non perturbed DVFs. The dosime tric differences between the originally planned values for each DVH endpoint and the values calculated by the non perturbed dose accumulations are listed as reference points for comparison with the simulated errors. Some of the plan differences may seem l arger than expected (e.g. Patient 3) due to patient positioning issues when

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107 the EOT images were acquired that made rigid registration with the planning images for dose recalculation difficult. The median dosimetric differences for the brainstem D 2% caused by the simulated DIR errors were 2% or less. However, maximum differences ranged from 0.2% to 6.5%. Because similar error maps were applied to each patient, this range of maximum differences demonstrates the effect that unique patient anatomies and dose distributions may have on DIR dosimetric errors. The median cord endpoint differences were all 0.5% or less with a maximum difference of 1.3% for Patient 6. Even when the differences from the planned values were large as with P atients 3 and 6, the potent ial dosimetric differences due to the simulated errors were small showing that the cord D 2% is likely robust against DIR dosimetric errors for these patients and sample spatial errors. The median mandible D 2% differences were 0.5% or less with a maximum d ifference of 1.1%. The parotid D mean differences are noticeably larger than the brainstem, cord, and mandible endpoints. This is likely to be a result of larger mean spatial errors and steep dose gradients in the parotid ROIs. Median left parotid differences ranged from 0.5% to 4.2%. The maximum dosimetric difference for the simulated left parotid errors was as high as 13%. Median right parotid differences were 1.3% or less. However, maximum differences ranged from 8.4% to 35%. These high maximum differences were the result of a failure of the DIR algorithm to correctly register the right parotid of Phantom 9. The right parotid deformation vectors of Phantom 9 had a mean error of 6.3 mm. When these lar ge errors were simulated in the clinical patient cases, the large dosimetric differences resulted. Figure 5 4 shows the range of DVHs that were generated for the

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108 right parotid of Patient 1. It should be noted from Figure 5 4 that 9 of the 10 simulated er ror DVHs lie close to the non perturbed DVH. The one DVH curve that shows a large overdose of the right parotid gland is the result of simulating the DIR failure seen in Phantom 9. As further examples, Figure 5 5 displays the DVHs for the left parotids o f P atients 5 and 10. Discussion The purpose of this investigation is not to evaluate the acceptability of the DIR algorithm for dose accumulation. The intention of the authors is to present a method for quantifying potential dose accumulation errors in cl inically relevant cases. Any DIR algorithm may be used to register the virtual phantoms and determine DVF error maps for that algorithm. Those error maps may then be applied to similar H&N clinical cases to determine the sensitivity of those cases to dos imetric errors. Our goal for this study is to give an example of how this method may be implemented and the importance of QA for DIR dose accumulation. A limited number of other studies have attempted to quantify the uncertainty of DIR dose accumulation, but the variety of methods and metrics used make comparisons difficult. Direct comparisons of dosimetric uncertainties are problematic for several reasons. First, each investigation makes assumptions about the method used to translate spatial errors into dosimetric errors. Just as this work simplifies the problem of applying known DVF errors to clinical cases where the error map is unknown by assuming a random distribution of those error vectors, other studies must make similar assumptions to generalize the error data to wider range of possible DIR scenarios. For example, Salguero et al. 76 assume d that DVF intrinsic errors are Gaussian distributed, allowing them to create 3 dimensional probability distribution functions (PDFs) of the

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109 DVF spatial errors that were used to generate statistical dosimetric uncertainty maps of assumption of normality was not valid for our data, however, and, among other complicating factors, would make the comparison of data between the studies questionable. Therefore, future investigations should strive to understand how these assumptions mig ht contribute to the uncertainty of the proposed method. Second, because the ground truth is unknown in actual clinical cases, surrogate measures of DVF errors must be used in each study. These surrogate measures may include metrics such as the inverse c onsistency, 76 100 unbalanced energy, 97 or stochastic 91 measures of the DVF. In this work, virtual phantoms were used as a surrogate measure of true DIR error. These metrics may have varying degrees of correlation to actual clinical err ors and clinical relevance further complicating comparisons between studies. Finally, any data reported on the uncertainty of DIR dose accumulation will be dependent on the algorithm used, the treatment site, the treatment modality, and the imaging modali ty. All of these difficulties emphasize the need for a standard set of tools and methods for DIR QA. There are several limitations to using the virtual phantom library for the quantification of DIR dosimetric errors. The first would be that despite the f act that 10 phantoms are available representing a range of clinical H&N cancer cases, this is likely not a large enough sample to create an adequate statistical model of DIR uncertainty for application to all other H&N cases. Ideally, the number of phanto ms would be large enough to generate a PDF that could represent the range of possible DIR errors. One could then sample the PDF in a Monte Carlo approach to create new error maps that could be applied to any clinical H&N case. These new error maps could then be used

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110 to calculate an array of DVHs that would give clinicians a clearer understanding of how DIR errors may impact dose accumulation. This objective remains as an area of future research at our institution. Additional limitations include that the virtual phantom library is only applicable to H&N cancer cases for patients treated over a single course of radiotherapy with similar immobilization and helical CT imaging. DIR algorithms may behave very differently for other treatment sites or imaging m odalities. Finally, the data presented here only represent dose accumulation for a single fraction. While, in practice, dose accumulation would include summing doses from multiple fractions, the assumption in this work is that by selecting the planning a nd EOT images to represent the maximum anatomic changes in each patient the worst case scenario for dose accumulation was presented. Despite these limitations, the method proposed here could be very useful as a standard tool for DIR QA. While the results shown above are only valid for the tested algorithm and tomotherapy dose distributions, this method can be used with any DIR algorithm and IMRT treatment modality making it a valuable tool for benchmarking the dosimetric errors of various algorithms or tre atment modalities. Because DIR dosimetric 70 the ability to ap ply this method to any typical clinical H&N cancer case is also a useful feature. Furthermore, the method presented here allows for the quantification of the uncertainty introduced by the random error map assumption as shown in Table 5 4 This uncertaint y may differ with other DIR algorithms, but the suggested procedure would allow for the estimation of this uncertainty for any algorithm. Also, the virtual phantoms are derived from actual clinical patient images with the intention of enhancing the

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111 clinic al relevance of the simulated deformations as compared to other surrogate measures of DIR errors. Lastly, this method produces DVHs for evaluation and comparison. DVHs are currently the standard tool for ROI dosimetry evaluation. Therefore, for a method of DIR dose accumulation error analysis to be realistically useful in the clinic, it should result in DVHs that would be intuitive for clinicians to review. Several studies have used DIR to report on the dosimetric changes to H&N cancer patients over a co urse of or with replanning during radiotherapy. Castadot et al. 101 evaluated 10 patients with H&N squamous cell carcinomas treated with helical tomotherapy using repeated CT imaging, dose recalculation, and DIR. That study found that, for both parotid glands combined, the D mean increased by 4.4% over the treatment course. There was no statistically significant difference in the D 2% of the spinal cord or the mandible over the treatment course or with replanning. Lee et al. 21 also investigated the dosimetric variations seen in the parotid glands of 10 patients treated with tomotherapy and using daily megavoltage CT, dose recalculation, and DIR. On average, the accumulated mean parotid dose at the end of treatment was 11% greater than planned with a range of 6% to 42%. Wu et al. 18 retrospectively evaluated 11 patients treated with IMRT for dosimetric changes with and without various replanning strategies using weekly repeated CTs, dose recalculation, and DIR. That study reported brainstem, mandible, and cord D 1% changes of less than 3%, on average, without replanning. Mean parotid doses increased by approximately 10%, on average, without replanning. Replanning was able to reduce the mean dose to the parotids by 3% to 8%, on average, depending on the replannin g frequency. These studies are

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112 reviewed here to give the reader an overview of typical dosimetric measurements that have been reported in the literature using DIR. While the algorithms used in each of these studies differ from the one evaluated in this w ork, it should be noted that if the data reported in Table 5 5 were valid for those studies, then some of the measurements from the literature would lie well within the range of potential DIR errors. This observation further highlights the need for compre hensive DIR dose accumulation QA to improve the reliability of ART investigations. There are three implications for the use of DIR for dose accumulation in the clinic based on the data presented here. First, each H&N cancer patient is unique. While the m edian dosimetric differences in Table 5 5 do not vary greatly between patients, the maximum differences can. In the left parotid, for example, where there was not an obvious failure of the registration algorithm, the maximum dosimetric difference ranges f rom 1.8% to 13%. Each patient may have a different sensitivity to DIR dosimetric response. Second, the method proposed in this work would allow clinicians to better underst and the confidence that they should have in DIR results. As an example, consider the dosimetric difference reported for the cord D 2% of Patient 3 in Table 5 5 For this patient, because of poor positioning when her EOT image was acquired, the cord dose w as 17.9% higher than planned according to the DIR. However, the dosimetric error due to DIR was only estimated to be 0.6%, at worst. In this case, a clinician could have more confidence in the DIR results. On the other hand, if the dosimetric endpoint b eing evaluated were on the same order of magnitude as the estimated dosimetric error due to DIR, caution should be used when interpreting the

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113 results. A situation where caution would be warranted is illustrated in Figure 5 5A. For the left parotid of Pat ient 5, the plan DVH lies almost completely within the region bounded by the simulated DIR errors. In that case, it would be difficult to conclude if the change seen in the parotid dosimetry was due to actual dose delivery differences or uncertainty in th e DIR itself. Conversely, Figure 5 5B illustrates the scenario when the uncertainty in the DIR dosimetry is small compared to the estimated change in the parotid dosimetry. Using the data shown in Figure 5 5B, a clinician could be more confident that the dose to the left parotid of Patient 10 has actually increased beyond what was planned. Third, if a DIR algorithm failure occurs, dose accumulation results may be grossly inaccurate. Figure 5 6 shows coronal slices of Phantom 9 where the DIR error averag ed 6.3 mm in the right parotid. Upon a brief visual inspection of the deformed image, a DIR failure is not obvious. Therefore, even errors of this magnitude may go unnoticed resulting in dosimetric errors up to 35%. The frequency of DIR failures is unkn own, but the existence of these types of errors should temper the unrestricted use of DIR for dose accumulation. Conclusion The authors have presented a method for estimating the errors of DIR dose accumulation that is derived from clinically relevant data and provides DVH results for analysis. The sample algorithm evaluated showed how DIR errors could result in dosimetric errors in 10 H&N cancer patient cases. The data presented here reinforce the need for comprehensive DIR QA and caution when using dose accumulation in the clinic.

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114 Table 5 1. Attributes of patients selected for the development of the virtual phantoms. Patient no. Disease s ite Stage Gender Fxs d elivered Mean right p arotid d ose (Gy) Mean left parotid dose (Gy ) Initial weight/ end of treatment weight (kg ) No. of days between SOT and EOT i mages 1 Base of t ongue T2N2bM0 M 35 25.2 25.7 74.8/70.3 60 2 Base of t ongue T2N2cM0 F 35 34.7 23.2 68.0/62.1 56 3 Tonsil T2N2bM0 M 35 29.4 25.6 96.2/88.5 57 4 Nasopharynx T1N3M0 F 33 26.7 39.5 65.3/61.2 58 5 Unknown T0N2aM0 M 35 24.5 29.0 90.3/81.2 57 6 Supraglottic l arynx T1N1M0 M 33 26.1 21.3 95.3/82.6 43 7 Tonsil T2N2aM0 M 35 14.2 41.7 93.4/86.2 47 8 Tonsil T2N2aM0 F 35 23.5 28.5 106.1/101.6 48 9 Nasopharynx T4N2M0 M 33 55.7 48.7 68.0/56.7 59 10 Base of t ongue T0N2aM0 F 35 21.5 23.4 99.8/81.2 68 Note: Fx: fraction, SOT: start of treatment, EOT: end of treatment. Table 5 2. Mean error vector magnitude and standard deviation for each phantom ROI. Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 0.3 0.1 0.3 0.2 0.5 0.5 1.6 1.6 1.1 1.0 2 0.2 0.1 0.4 0.2 0.7 0.5 0.7 0.5 0.7 0.4 3 0.4 0.2 0.7 0.5 1.2 0.9 1.8 1.8 0.4 0.3 4 0.3 0.1 0.4 0.3 0.6 0.6 0.9 0.7 0.9 0.9 5 0.3 0.1 0.4 0.2 0.7 0.6 1.1 1.2 1.7 1.9 6 0.5 0.2 0.5 0.2 0.9 0.6 0.7 0.7 1.5 1.6 7 0.8 0.2 0.5 0.2 1.1 0.7 0.8 0.4 0.8 0.7 8 0.5 0.2 0.5 0.3 0.7 0.6 1.0 1.1 0.7 0.6 9 0.8 0.3 0.5 0.2 1.5 1.2 2.5 1.5 6.3 5.1 10 0.7 0.4 0.5 0.2 0.6 0.4 0.6 0.6 0.6 0.8

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115 Table 5 3. Attributes of patients selected for DIR error simulation. Patient no. Disease site Stage Gender Fxs delivered Mean right parotid dose (Gy) Mean left parotid dose (Gy) Initial weight/ end of treatment weight (kg) No. of days between SOT and EOT images 1 Base of tongue T2N2bM0 M 35 25.2 25.7 74.8/70.3 60 2 Base of tongue T2N2cM0 F 35 34.7 23.2 68.0/62.1 56 3 Nasopharynx T1N2M0 F 33 26.6 25.5 73.0/72.6 44 4 Unknown T0N2aM0 M 35 24.5 29.0 90.3/81.2 57 5 Supraglottic larynx T1N1M0 M 33 26.1 21.3 95.3/82.6 43 6 Nasopharynx T4N2M0 M 33 49.6 56.9 80.7/76.2 59 7 Tonsil T1N2bM0 M 33 24.5 51.7 96.2/87.5 55 8 Tonsil T2N2aM0 F 35 23.5 28.5 106.1/101.6 48 9 Base of tongue T1N2bM0 M 35 45.0 19.0 94 .0 /84.8 50 10 Base of tongue T0N2aM0 F 35 21.5 23.4 99.8/81.2 68 Note: Fx: fraction, SOT: start of treatment, EOT: end of treatment.

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116 Table 5 4 Mean and maximum differences between using the spatially correlated (baseline) error maps and the non spatially correlated (random) error maps for the selected ROI endpoints. ROI Mean difference Max difference Brainstem D 2% 0.7% 1.6% Cord D 2% 0.2% 0.8% Mandible D 2% 0.2% 1.2% Left parotid D mean 0.5% 1.5% Right parotid D mean 0.6% 2.1%

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117 Table 5 5. Median and maximum dosimetric differences of the simulated DIR errors compared to the non perturbed DVFs for the selected DVH endpoints. Plan values list the dosimetric differences of the DVH endpoints for dose accumulation performed with the non perturbed DVFs compared to the origin ally planned values. Brainstem D 2% Cord D 2% Mandible D 2% Left Parotid D mean Right Parotid D mean Patient Median Max Plan Median Max Plan Median Max Plan Median Max Plan Median Max Plan 1 0.3% 0.7% 0.9% 0.3% 0.4% 3.1% 0.1% 0.3% 1.3% 2.1% 7.6% 9.3% 0.7% 35.0% 3.2% 2 2.0% 4.9% 1.3% 0.1% 0.2% 0.9% 0.0% 0.1% 0.7% 4.2% 13.0% 7.6% 1.1% 29.9% 1.0% 3 0.6% 1.2% 16.3% 0.3% 0.6% 17.9% 0.0% 0.3% 0.6% 1.6% 6.8% 19.7% 0.2% 15.1% 45.1% 4 1.0% 1.8% 9.1% 0.0% 0.1% 4.5% 0.2% 0.6% 1.3% 2.1% 7.2% 1.6% 0.8% 22.1% 17.3% 5 0.0% 0.4% 2.4% 0.4% 0.5% 2.6% 0.0% 0.2% 2.7% 3.6% 10.3% 5.9% 1.2% 27.4% 24.3% 6 1.0% 2.0% 7.8% 0.5% 1.3% 36.2% 0.1% 0.2% 0.6% 0.5% 1.8% 3.7% 0.4% 8.4% 1.0% 7 0.1% 0.2% 4.4% 0.1% 0.3% 7.5% 0.0% 0.1% 0.2% 1.3% 3.6% 4.1% 1.3% 24.3% 0.8% 8 2.0% 6.5% 6.2% 0.0% 0.1% 1.7% 0.0% 0.0% 0.7% 2.5% 7.7% 4.5% 1.2% 20.6% 10.5% 9 0.1% 0.3% 3.4% 0.2% 0.2% 6.7% 0.5% 1.1% 3.2% 2.5% 9.0% 15.6% 0.8% 17.1% 11.6% 10 0.3% 1.1% 6.0% 0.0% 0.1% 3.3% 0.0% 0.1% 1.5% 3.4% 9.5% 23.3% 1.0% 30.8% 7.3%

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118 Figure 5 1. Spatially

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119 Figure 5 2. Flowchart describing the creation and validation of hypothetical (random) DVFs for DIR error simulation. The flowchart is divided into three sections by the dashed boxes. The uppermost box defines the process of determining the DIR error using the virtual phantom image pairs. The middle box defines the process of creating the baseline and random DVFs. Th e lowermost box defines the dosimetric comparison process for the baseline and random DVHs.

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120 Fig ure 5 3 DVHs generated using the baseline (dashed/blue curve) and random (solid/red curves) error maps for the right parotid of Phantom 5. The inset shows an enlarged view of the outlined region where the difference between the 10 random error map DVHs is visible Figure 5 4 DVHs generated using the non perturbed DVF (dashed/red curve) and the simulated error DVFs (solid/grey curves) for the right parotid of Patient 1. The plan DVH (dotted/blue curve) is also shown for reference.

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121 Figure 5 5. DVHs generated using the non perturbed DVF (dashed/red curve) and the simulated error DVFs (solid/grey curves) for the left parotid of two patients. The plan DVH (dotted/blue curve) is also shown for reference. (a) Patient 5. (b) Patient 10.

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122 Figure 5 6. Coronal sl ices of Phantom 9 where a 6.3 mm average spatial error was observed in the DIR of the right parotid. (a) simulated EOT image. (b) planning image. (c) Deformed simulated EOT image using the sample DIR algorithm. The ROI outlined in (b) and (c) is the ri ght parotid as drawn by the physician on the original planning image.

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123 CHAPTER 6 SUMMARY Result of this Work One of the primary goals of adaptive radiation therapy (ART) is to determine if the radiation treatment is being delivered as planned. This is of interest especially for patients with cancers of the head and neck (H&N) because the anatomy of these patients tends to vary over a treatment course as discussed at length in Chapter 1. In order to achieve this goal, the current standard process inv olves the use of dose recalculation on repeated patient imaging, deformable image registration (DIR) and deformable dose accumulation. While these to ols have been the subject of much recent research, no comprehensive technique or data have been published to provide a n industry standard validation approach for the ART process and justify its clinical use. This is problematic because if the delivered dose is estimated incorrectly, it could lead to not creating a replan for a patient that could benefit from one or replanning a patient unnecessarily and wasting clinical resources. Therefore, this work aimed to develop a methodology that could be employed to quantify the uncertainties of ART and provide clinicians with better data to assist with decision maki ng The first part of this work presented a methodology for quantifying the uncertainties of dose recalculation using megavoltage CT (MVCT) imaging that could be extended to other imaging modalities. For the H&N cases examined, it was found that dose reca lculation uncertainties could be maintained within 2.5% if the QA recommendations of TG 148 are followed. 79 An uncertainty of this magnitude seems acceptable for ART purposes.

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124 The second part of this work examined the dosimetri c uncertainty that would be introduced if the planning dose distribution were assumed to represent the daily delivered dose in lieu of performing a dose recalculation. The results showed that the target dosimetry varies little over a treatment course so u sing the planning dose distribution would introduce little additional uncertainty into the ART process In contrast, the parotid dosimetry showed substantial variation over the treatment course but the doses estimated by the planning and recalculated dis tributions were highly correlated. Although the difference between the plann ing and recalculated dose distributions approached 12% in the worst case for the left parotid D 50% the high correlation of the two distributions indicated that using the planning dose overlay could help to identify parotid dosimetry trends if not absolute doses. In light of this, dose recalculation would still be preferred where practical, but using the planning dose overlay may be acceptable for some applications as long as the associated uncertainties are taken into account. Another approach could make use of the planning dose overlay for daily or on line dose estimates that would need to be calculated quickly. Then, if adverse dosimetric trends were identified using the plann ing dose overlay, a full dose recalculation could be initiated off line to obtain a more accurate estimate of the delivered dose. The third part of this work described the development of a library of computational phantoms for the purpose of quantifying th e spatial uncertainty of DIR. The phantoms were developed from clinical ly acquired patient images and a combination of deformation algorithms to prioritize their clinical relevance. Ten phantoms were created to represent a variety of possible H&N patient scenarios. A

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125 single DIR algorithm was evaluated to show how the phantoms would be used to determine the spatial uncertainty of the algorithm. Spatial uncertainty statistics were reported for the sample algorithm showing a maximum error in the right parot id of one of the phantoms approaching 23 mm. Errors of that magnitude were atypical, but their existence r eemphasizes the need for a comprehensive method of DIR validation that could be met through the use of the virtual phantom library. While estimating the spatial uncertainty of DIR is a necessary step in understanding how DIR affects the ART process, clinicians are ultimately interested in the dosimetric uncertainty of these algorithms. The final part of this project translated the spa tial errors found in Chapter 4 into clinically useful dosimetric error s. A method of estimating the dosimetric error of DIR dose accumulation for any H&N cancer patient undergoing a typical course of radiotherapy was developed and validated. The dosimetr ic error of the sample DIR algorithm from Chapter 4 was evaluated for 10 H&N cancer patients and reported as dose volume histograms (DVHs) Errors were typically within 2% for the brainstem, cord, and mandible D 2% but parotid D mean errors could be as hig h as 35%. These statistics and their accompanying DVHs provide clinicians with a clinically useful tool for evaluating the suitability of ART decisions made using DIR, or for evaluating if DIR dose accumulation should be used at all. Opportunities for Fur ther Development Automated Image Calibration This work discussed quantifying the uncertainty of dose recalculations using repeated patient imaging. Image correction methods could be developed and automated that could potentially minimize the uncertainty of dose recalculations. For example, Aubry et al. 63 published a method to correct the cupping and missing data

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126 artifacts of megavoltage cone beam CT by match ing the repeated patient images to the original planning image and calculating correction factors. Duchateau et al. 57 also suggested using histogram equalization to crossmatch MVCT image intensity values to the planning image values In response to the published data of Chapter 2 78 and other authors, 54 57 77 Accuray Inc. has implemented an MVCT calibration procedure that autom atically analyzes acquired phantom images and corrects the MVCT image value to density curve to match the expected phantom values. This weekly procedure has effectively eliminated the uncertainty of dose recalculations using MVCT images due to temporal va riations. Graphics Processing Unit Based Dose Calculation The dose calculation algorithms of modern treatment planning systems perform similar calculations many times over to create a complete dose distribution. This characteristic makes the algorithms pr ime candidates for parallel computation. Graphics processing units (GPUs) are designed to perform these types of parallel computations very quickly. Lu 102 developed a dose calculation algorithm for TomoTherapy reduce dose calculation time. For a H&N case, this algorithm is able to reduce dose calculation time from approximately 30 minutes to 30 seconds. In Chapter 3 of this work, we investigated using the planning dose distribution in lieu of recalculating the dose distribution on a repeated patient image set. One of the goals of that investigation was to reduce the resources required to perform ART dose assessment. While substituting the planning dose distribution for the dose recalculation step may reduce the resources required to perform ART dose assessment, it also introduces additional sources of uncertainty. However, if a GPU based dose

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127 r ecalculation were performed, the time required to recalculate dose distributions for a single patient could be reduced from 17.5 hours ( 35 fractions x 30 minutes/fraction) to 17.5 minutes (35 fractions x 30 seconds/fraction). These drastic reductions in t he time required to perform dose recalculations coupled with improvements in the automation of the ART dose assessment workflow could reduce the hardware and human resource requirements of ART making it available to more clinics with limited resources and eliminating the need to find alternatives to dose recalculation. Benchmarking of Deformable Image Registration Algorithms As discussed in Chapter 4, a standard methodology and metrics would be helpful for the benchmarking of DIR algorithms. To this end, a website for the Deformable Image Regist ration Evaluation Project ( https://sites.google.com/site/dirphantoms/ ) was created. The Deformable Image Registration Evaluation Project allows users to download the virtual H&N phantoms developed in this work for use with their own DIR algorithms. Users may then upload their results for comparison with the ground truth deformation vec tor fields (DVFs) Spatial errors are reported on t he website for each algorithm allowing users to compare the results of multiple algorithms This data sharing approach is modeled after the Retrospective Registration Evaluation Project initiated by J. M ichael Fitzpatrick of Vanderbilt University. 103 To date, four institutions have participated in the Deformable Image Registration Project allowing the objective evaluation and comparison of multiple DIR workflows The preliminary data for this proj ect is presented in Appendix A. Development of Additional Virtual Phantoms The results of DIR may vary greatly depending on the clinical scenario being examined. For example, the magnitude of the deformation and the resulting error will

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128 be very different when considering intra fraction lung deformation compared with inter fraction bladder filling. Even for a given clinical site, the anatomic deformations encountered over a single treatment course with controlled patient immobilization may be very differen t than those seen when attempting DIR for a patient retreatment that could be several months or years later. For these reasons, the results reported in this work are only applicable to H&N cancer patients treated over a single radiotherapy course with sim ilar immobilization that match the conditions from which the phantoms were developed. Because the same DIR algorithms are used with various clinical scenarios, additional phantoms would have to be developed to evaluate those algorithms for each site or si tuation. The methodology presented in this dissertation could be used to create the additional phantoms. Automated Deformable Image Registration Quality Assurance Based on the methods outlined in Chapters 4 and 5, one could foreseeably develop a QA software tool that would automatically report the DIR dosimetric uncertainty of given clinical cases to the end user. The tool would first have to be commissioned by performing the DIR of a provided library of v irtual phantoms. The resulting DVFs would be imported into the QA software and compared to ground truth DVFs to create a baseline spatial uncertainty for a selected DIR algorithm. The data (contours, DVF, and dose distribution) from any subsequent clinic al case could then be sent to the tool for analysis. Using the commissioned baseline spatial uncertainty for the selected DIR algorithm, the software could calculate an estimated dosimetric uncertainty for each structure and report the results to the end user as a band of DVHs. Such a tool could be automated, easy to use, and provide clinicians with valuable information for determining how the uncertainty of DIR might affect their decisions.

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129 Final Thoughts The use of the ART dose assessment process is som etimes supported by the argument of it better to hav e uncertain information than the lack of information that igated the two primary sources of uncertainty in the ART dose assessment process: dose recalculation and DIR It was found that the uncertainties of dose recalculation are likely within acceptable limits for the current practice of radiation therapy for p atients with cancers of the H&N, especially with the most recent advances of automated image calibration and GPU based dose calculation. While DIR uncertainties were typically small, much larger errors did occur. The use of DIR for contour propagation is likely acceptable because the deformed contours can be reviewed and modified if any errors occur. On the other hand, errors in dose accumulation can be difficult to identify and even harder to correct. Therefore, DIR dose accumulation should be used wit h caution. Previously, when little or no information was available via dose accumulation, any clinical decisions, such as the decision to retreat a radiation sensitive region, had to be made conservatively. Without adequate QA methods for DIR, its use in the clinic could present problems if the results that dose accumulation generates are not interpreted along with its inherent uncertainties. In other words, if clinical decisions are made with incorrect DIR dose accumulation data, poor patient outcomes c ould result. In light of this, it is very important to develop DIR QA methods that are clinically relevant, easy to use, and report standard metrics that will be useful for clinical decision making. It is our hope that this work is effective in moving re search in this direction.

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130 APPENDIX A PRELIMINARY DATA FOR THE DEFORMABLE IMAGE REGISTRATION EVALUATION PROJECT Tables A 1 through A 7, below represent preliminary data that has been submitted for the Deformable Image Registration Evaluation Projec t (DIREP). Each table shows the mean magnitude of the spatial error calculated for each phantom and region of interest. The spatial error was calculated by comparing the deformation vector fields of the virtual phantom registrations uploaded by each user to the ground truth deformation vector fields. The results may be compared with each other and to the results found at our institution and presented in Table 5 2.

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131 Table A 1 Mean phantom region of interest error vector magnitude and standard devi ation for Institution 1: Velocity B spline Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 1.6 0.1 1.6 0.2 1.8 0.3 2.4 0.7 2.1 0.5 2 1.8 0.2 2.2 0.5 1.4 0.6 1.7 0.4 1.5 0.4 3 0.8 0.1 1.7 0.7 1.0 0.5 2.1 1.3 1.2 0.2 4 0.6 0.2 1.1 0.4 1.0 0.4 2.7 1.3 1.4 0.6 5 0.7 0.1 0.7 0.2 0.8 0.4 2.8 2.1 1.5 0.8 6 0.5 0.2 0.6 0.2 1.0 0.4 2.2 1.2 1.6 0.8 7 0.8 0.2 4.2 3.3 1.5 0.6 1.0 0.2 1.8 0.6 8 0.5 0.1 0.9 0.3 1.2 0.7 2.5 1.3 2.4 1.2 9 2.2 0.2 1.9 0.6 1.7 0.5 1.9 0.8 1.9 1.1 10 0.8 0.2 1.2 0.4 1.3 0.6 2.9 0.8 0.8 0.4 Table A 2. Mean phantom region of interest error vector magnitude and standard deviation for Institution 2: Velocity extended multipass B spline Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 1.5 0.5 1.9 0.5 2.2 0.9 2.5 0.6 2.9 0.8 2 2.0 0.4 1.6 0.4 2.0 0.7 1.9 0.4 1.4 0.6 3 1.1 0.5 1.0 0.4 1.5 0.8 1.9 1.3 1.1 0.3 4 1.5 0.4 1.1 0.3 1.9 0.7 2.1 1.0 2.4 1.3 5 1.2 0.4 1.1 0.3 1.3 0.6 2.3 1.2 1.4 0.9 6 2.2 0.7 1.1 0.5 1.3 0.7 1.7 0.7 1.6 1.0 7 1.5 0.6 1.0 0.4 1.4 0.6 1.3 0.6 1.1 0.4 8 1.8 0.5 1.1 0.4 1.6 0.8 2.2 0.9 2.6 1.1 9 1.7 0.5 1.6 0.4 1.9 0.8 2.2 0.6 1.7 0.6 10 1.6 0.6 0.9 0.3 1.9 0.9 2.3 0.7 1.5 0.7

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132 Table A 3 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3 : Velocity multipass B spline no VOI Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 1.6 0.1 1.7 0.2 1.8 0.3 2.4 0.7 2.2 0.5 2 1.8 0.1 2.2 0.5 1.4 0.6 1.7 0.4 1.5 0.4 3 0.8 0.1 1.8 0.7 1.0 0.5 2.0 1.2 1.3 0.2 4 0.6 0.1 1.1 0.4 1.0 0.4 2.7 1.3 1.4 0.7 5 0.7 0.1 0.7 0.2 0.8 0.4 2.9 2.1 1.6 0.8 6 0.5 0.2 0.6 0.2 1.0 0.3 2.2 1.2 1.7 0.8 7 0.8 0.2 4.1 3.3 1.5 0.6 1.0 0.2 1.7 0.6 8 0.8 0.1 0.9 0.3 1.3 0.8 2.7 1.2 2.4 1.2 9 2.1 0.2 1.9 0.6 1.7 0.5 1.9 0.8 1.8 1.1 10 0.8 0.2 1.2 0.4 1.3 0.6 2.9 0.8 0.9 0.4 Table A 4 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3 : Velocity multipass B spline with VOI Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 2.1 0.1 1.7 0.2 1.9 0.3 1.9 0.6 1.8 0.4 2 0.4 0.2 0.4 0.2 0.8 0.9 1.2 0.9 1.1 0.5 3 0.6 0.2 1.1 0.4 0.7 0.3 1.4 0.9 0.5 0.2 4 0.9 0.1 0.6 0.2 0.6 0.1 1.8 0.9 0.8 0.4 5 0.6 0.1 0.5 0.2 0.7 0.3 2.1 1.5 1.0 0.7 6 0.3 0.1 0.3 0.1 0.3 0.1 0.8 0.4 1.1 0.5 7 0.8 0.2 1.2 0.6 0.7 0.2 0.5 0.2 0.6 0.2 8 1.2 0.2 0.4 0.2 1.0 0.8 1.8 0.8 1.9 1.0 9 2.5 0.3 1.7 0.3 1.5 0.4 1.6 0.5 1.5 0.8 10 1.0 0.1 0.6 0.1 0.9 0.4 1.1 0.5 0.8 0.3

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133 Table A 5 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3 : Velocity extended multipass B spline no VOI Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 2.2 0.3 1.6 0.4 2.1 0.8 2.2 0.6 3.2 0.8 2 2.1 0.4 1.7 0.6 1.6 0.8 2.2 0.6 2.4 1.1 3 1.0 0.3 1.1 0.5 1.4 0.7 1.3 0.8 1.1 0.4 4 1.0 0.4 1.0 0.3 1.4 0.6 1.9 0.8 1.9 0.6 5 0.9 0.3 1.0 0.3 1.4 0.6 2.2 1.0 1.8 1.0 6 1.0 0.3 1.0 0.3 1.4 0.6 1.9 0.6 1.1 0.5 7 1.3 0.4 1.1 0.4 1.2 0.7 1.4 0.8 1.6 0.9 8 1.8 0.4 0.9 0.4 1.8 1.0 2.1 1.0 2.4 1.0 9 2.0 0.4 1.6 0.4 1.7 0.7 2.8 0.7 1.9 0.8 10 1.3 0.3 1.0 0.3 1.7 0.8 2.5 0.7 1.8 0.9 Table A 6 Mean phantom region of interest error vector magnitude and standard deviation for Institution 3 : Velocity extended multipass B spline with VOI Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 2.1 0.4 1.6 0.7 1.8 0.6 2.5 0.4 2.9 0.5 2 1.1 0.4 0.7 0.3 1.0 0.7 1.3 0.4 1.4 0.4 3 1.2 0.4 1.1 0.4 0.9 0.4 1.5 0.7 0.8 0.3 4 1.8 0.3 0.8 0.3 0.9 0.5 2.5 0.7 2.1 0.9 5 0.7 0.3 0.7 0.3 1.1 0.8 2.2 1.2 1.5 0.8 6 0.7 0.3 0.7 0.4 0.8 0.4 0.9 0.5 1.2 0.5 7 1.6 0.4 1.4 0.7 1.0 0.4 1.8 0.5 1.2 0.7 8 2.1 0.5 0.7 0.4 1.2 0.7 3.2 1.7 2.9 1.8 9 2.3 0.6 1.7 0.4 1.9 0.8 2.3 0.7 2.4 1.1 10 1.2 0.5 1.0 0.5 1.5 0.8 1.5 0.6 1.1 0.5

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134 Table A 7 Mean phantom region of interest error vector magnitude and standard deviation for Institution 4 : MIM 6.2.2 Phantom no. Brainstem (mm) Cord (mm) Mandible (mm) Left parotid (mm) Right parotid (mm) 1 0.3 0.1 0.3 0.1 0.7 0.6 1.6 1.6 1.1 0.9 2 0.2 0.1 0.4 0.2 0.7 0.5 0.6 0.5 0.9 0.7 3 0.3 0.1 0.8 0.5 1.1 0.9 1.8 1.4 0.5 0.5 4 0.3 0.1 0.5 0.3 0.9 0.7 1.3 1.1 0.9 0.9 5 0.3 0.2 0.4 0.2 0.5 0.5 1.6 1.8 1.1 1.2 6 0.5 0.2 0.5 0.2 0.8 0.5 0.6 0.5 1.5 1.6 7 0.8 0.2 0.4 0.2 0.6 0.4 0.5 0.3 0.8 0.8 8 0.5 0.2 0.4 0.2 0.7 0.6 1.0 1.0 0.8 0.7 9 0.7 0.3 0.5 0.3 2.5 1.7 2.7 1.6 6.6 5.5 10 0.6 0.3 0.5 0.2 0.7 0.6 0.6 0.5 0.6 0.6

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145 BIOGRAPHICAL SKETCH Jason Pukala was born in Cape Coral, Florida to Thomas and Camille Pukala. He graduated from Cape Coral High School in 2000 and accepted admission to the honors program at the University of Florida. Jason received his B.S. in electrical completed an AAPM Summer Undergraduate Fel lowship under the direction of Dr. Frank Bova in the Radiosurgery/Biology Laboratory at the University of Florida. Instead of pursuing a career in medical physics at that time, Jason went on to study management and received his M.S. degree in 2005. He to ok a position as a consultant with Accenture shortly thereafter. Jason returned to the University of Florida in 2008 to study medical physics with Dr. Bova and received his M.S. in nuclear engineering sciences two years later. He then accepted a research position at what was then MD Anderson Cancer Center Orlando. Jason completed his Ph D in 2014 and will continue as a medical physics resident at UF Health Cancer Center Orlando Health.