UNIVERSITY OF CALGARY. The Effect of Plan Modulation on Dosimetric Effects due to Interplay in Hypofractionated

Transcription

1 UNIVERSITY OF CALGARY The Effect of Plan Modulation on Dosimetric Effects due to Interplay in Hypofractionated Volumetric Modulated Arc Therapy Liver Radiotherapy Treatments By Emily Hubley A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN PHYSICS AND ASTRONOMY CALGARY, ALBERTA SEPTEMBER, 2016 Emily Hubley 2016

2 Abstract When tumours that move with respiration are treated using radiation therapy techniques with dynamic beam intensity modulation, including volumetric modulated arc therapy (VMAT), the interplay between tumour motion and multileaf collimator (MLC) leaf motions may cause differences between the planned and delivered dose distributions. These interplay effects may cause underdosage in the tumour, potentially reducing treatment efficacy. This uncertainty has led to hesitation in using VMAT to treat sites impacted by respiratory motion. These differences may be greater when more MLC leaf modulation is present. To investigate the magnitude of interplay effects in a digital phantom and ten patients, a program was written to simulate respiratory motion in hypofractionated VMAT liver treatment plans with varying amounts of MLC leaf modulation. It was found that highly modulated plans were more susceptible to interplay effects, but these effects were clinically negligible in magnitude due to the hotspot present in hypofractionated treatment plans. ii

3 Acknowledgements I would like to begin by thanking my supervisor Dr. Greg Pierce for taking me on as a graduate student, and for his time, patience, and guidance throughout the entirety of my degree. Greg s enthusiasm and encouragement have been endless and deserve recognition. I have learned a lot working with Greg, and I will continue to carry this knowledge and experience with me in my future endeavours. I would also like to acknowledge the members of my supervisory committee, Dr. Michael Roumeliotis, Dr. Richie Sinha, and Dr. Wendy Smith for sharing their knowledge and experience, and for providing direction and advice throughout this project. Their varied backgrounds and experience have added great value to this project. Dr. Shaun Loewen has also assisted me greatly in providing clinical relevance to my thesis. His expertise and commitment are greatly appreciated. All of the medical physics graduate students that I shared time with at the Tom Baker deserve recognition for making my time as a student an enjoyable and memorable two years. Thanks for all the mentorship, the late nights, the pep talks, the proofreading, the commiseration, the camaraderie, and of course, all the coffee walks. Without all of your support and friendship, this degree would have been a lot more challenging and a lot less fun. Working with all of you has been a hoot. Finally, I would like to acknowledge the continuing support and encouragement from my friends and family. Thanks for helping me get to where I am today. iii

4 Table of Contents Abstract... ii Acknowledgements... iii Table of Contents... iv List of Tables... vi List of Figures and Illustrations... vii List of Symbols, Abbreviations and Nomenclature... xi CHAPTER ONE: INTRODUCTION Liver Cancer Treatments for Liver Cancer Surgery and Liver Transplantation Ablative Therapies Chemotherapy Radiation Therapy Respiratory Motion in Liver Motion Compensation Methods Motion Encompassing Methods Respiratory Gating Breath Hold Real-Time Tumour Tracking Dosimetric Effects of Respiratory Motion in Liver Radiotherapy Dose Blurring Interplay Research Objectives and Thesis Organization...25 CHAPTER TWO: DIGITAL PHANTOM STUDY Overview Materials and Methods Digital Liver Phantom Background on Volumetric Modulated Arc Therapy Optimizer Treatment planning Respiratory Trace Generation Motion Simulation Program Analysis of Dosimetric Effects Results Discussion Conclusion...44 CHAPTER THREE: PATIENT SIMULATIONS Overview Materials and Methods Patient selection Treatment Planning Respiratory Trace Generation Control Point Sampling Resolution...51 iv

5 3.2.5 Motion Simulation Plan Evaluation Combined Effects of Dose Blurring and Interplay Isolating the Effects of Interplay Results Combined Effects of Dose Blurring and Interplay Isolating the Effects of Interplay Discussion Conclusion...69 CHAPTER FOUR: SUMMARY AND FUTURE WORK Summary Future Work...71 REFERENCES...74 v

6 List of Tables Table 1-1: Five-year relative survival ratio for primary liver cancer based on the tumour nodes metastasis (TNM) staging convention. Adapted from the Canadian Cancer Society Table 1-2: The TNM staging classifications are described for primary liver cancer. Adapted from the Canadian Cancer Society Table 1-3: A summary of studies that have been done to characterize the amplitude of respiratory motion in liver including the number of subjects studied and the imaging method used to obtain the data. Motion amplitudes in the liver in the superior-inferior (SI), anterior-posterior (AP), and medial-lateral (ML) directions during normal respiration are reported as mean ± standard deviation and/or (range) Table 3-1: The GTV volume, GTV SI length, target-dome distance, and MFs for both of the patient treatment plans, as discussed in 3.2.2, are listed for each patient. The GTV SI length is measured as the GTV s maximum length in the SI direction. The tumour-dome distance is measured at the minimum SI distance between the GTV and the dome of the liver Table 3-2: The planning criteria used for treatment plans, as outlined in the RAS liver trial Table 3-3: The percentage change in target dose-volume planning constraints for the target volumes between the original treatment plan and the treatment plan with motion simulated using random starting points in the respiratory cycle for each of the three fractions. For each patient, the first row contains data from the low MF plan and the second row contains data from the high MF plan. A positive (negative) value indicates that the constraint increased (decreased) when motion was simulated in the treatment plan. None of the target planning constraints were exceeded in any of the treatment plans. The first three patients had GTVs in direct contact with the dome of the liver. Patients 4-7 and 8-10 had GTVs < 1.8 cm and 1.8 cm from the dome of the liver, respectively. The three groups are separated by horizontal lines Table 3-4: The percentage change in OAR dose-volume planning constraints between the original treatment plan and the treatment plan with motion simulated using random starting points in the respiratory cycle for each of the three fractions. For each patient, the first row contains data from the low MF plan and the second row contains data from the high MF plan. A positive (negative) value indicates that the constraint increased (decreased) when motion was simulated in the treatment plan. None of the OAR planning constraints were exceeded in any of the treatment plans. Horizontal lines group patients by tumour location, as in Table vi

7 List of Figures and Illustrations Figure 1-1: In the case where no CTV margin is used, the ITV can be created by contouring the GTV at end inspiration (blue) and end expiration (yellow) scans, and merging the positions of the GTV margins. The ITV (pink) encompasses the full extent of GTV motion. When a CTV margin is used, the ITV is created by merging the CTV margins Figure 1-2: An example of a typical gating window on the exhale phase of the respiratory cycle. Below, the phases of the 4DCT on which the treatment was planned those where the target is inside the gating window, and the beam is turned on, are indicated with green Figure 1-3: An example of dose blurring is seen for a 5 cm open field delivered to a tumour with a respiratory motion amplitude of 1.6 cm in the direction of the dose profile (xaxis). For a uniform fluence, dose blurring is evident at the edges of the target when respiratory motion is simulated in a treatment plan. The dose profile through the target becomes more spread out with a broader penumbra region Figure 1-4: Illustration of the interplay effect between a tumour in motion and moving MLC leaves during a treatment delivery with dynamic MLC leaves. The solid and open stars represent the tumour motion during two phases of the respiratory cycle (inspiration and expiration). The point in the respiratory cycle in which the beam is turned on relative to the MLC motion can cause the target to receive different doses. (Figure reproduced from Bortfeld et al.) Figure 1-5: Example beam-on timings relative to the respiratory cycle, which could produce the situation illustrated in Figure 1-4, are indicated by solid (beginning of inspiration phase) and open (beginning of expiration phase) stars Figure 1-6: The tumour position at two CPs can be represented with a green and a blue delta function. A profile through the corresponding doses delivered at each of those CPs is given by the green and blue dose profiles Figure 1-7: To calculate the total dose from both CPs, the convolution of static dose profile with target position delta function is performed for each CP, and the resulting total dose profile (purple) is calculated by summing the two CP dose profiles (green and blue) Figure 1-8: The total dose delivered to the moving tumour is calculated using the same method described in Figure 1-7, but using a different tumour position for each CP. The resulting dose profile (purple) is different than the one seen in Figure Figure 1-9: The resulting dose profiles calculated by summing the convolutions of the static delivered dose profiles with the target position delta function are not the same when the target motion is different, for example if a different beam-on timing is used vii

8 Figure 2-1: A) Axial view of digital phantom, B) Coronal view of digital phantom, and C) a 3D view of the digital phantom for which treatment plans were created. The grey, yellow, and cyan cylinders represent the body, liver, and spinal cord contours, respectively. The blue sphere is 4 cm in diameter and represents the GTV. The red ovoid, representing the ITV, is a 0.6 cm superior and inferior extension of the GTV Figure 2-2: Sample beam s eye views of a representative MLC aperture at a single CP for plans with two different amounts of MLC leaf modulation delivering dose to the ITV (red ovoid) of the digital liver phantom. For the higher MF plan, the MLC leaves spend more time blocking the target, thus modulating the fluence, whereas in the low MF plan, the leaves spend more time at the periphery of the target, providing less fluence modulation Figure 2-3: Treatment delivery times for a single 180 arc are plotted for the four MFs, and the six total dose prescriptions. Lowering the total dose prescription forces a decrease in the treatment delivery time for a single arc, until the maximum gantry speed is reached. For a TrueBeam linear accelerator, the maximum gantry speed is 6 /s, so the shortest possible delivery time for a 180 arc is 30 s, which is seen as the plateau for prescriptions of 5 and 10 Gy. All dose prescriptions are delivered in 5 fractions Figure 2-4: The first 120 s of three respiratory traces creating using the Respiratory Trace Generator 82 are plotted. Each trace used in motion simulation in phantom treatment plans has a respiratory period between 3 and 4 s and motion amplitudes between 1.0 and 1.2 cm. Variation in amplitude, period, and baseline position are seen for all traces, to be representative of the patient population Figure 2-5: The first 180 s of a respiratory trace created using the Respiratory Trace Generator 82 with large baseline drift. The respiratory motion period and amplitude are 3 s and 1.0 cm, with some variability of these parameters for each cycle, to be representative of an actual patient Figure 2-6: A description of the process used in simulating respiratory motion. The in-house simulation program reads in a DICOM-RT file, and a respiratory trace file, and shifts the MLC positions, creating a new DICOM-RT file. This new DICOM-RT file is imported into the treatment planning system and the dose is calculated with the new MLC pattern Figure 2-7: The percentage decrease in ITV V 95 coverage that occurs when motion is simulated using a random starting point in the respiratory cycle is plotted for four different MFs and six treatment delivery times corresponding to different dose prescriptions. A larger decrease in ITV coverage is indicative of worse target coverage when motion is simulated. The points with the longest treatment delivery times correspond to the original treatment plans for each MF. Plots a, b, and c come from motion simulated with traces a, b, and c (Figure 2-4), respectively viii

9 Figure 2-8: The data from Figure 2-7 a, b, and c are binned by treatment delivery time and the values for decreases in ITV V 95 coverage are averaged for each bin. Error bars indicate the standard error of the values in each bin Figure 2-9: The percentage decrease in ITV V 95 coverage that occurs when respiratory motion with a baseline drift is simulated using a random starting point in the respiratory cycle is plotted for four different MFs, and five treatment delivery times corresponding to different dose prescriptions. A larger decrease in ITV coverage is indicative of worse target coverage when motion is simulated. The points with the longest treatment delivery times correspond to the original treatment plans for each MF Figure 2-10: The PDFs (target motion kernels) for the first a) 3.3 s, b) 30 s, and c) 163 s of the respiratory trace in Figure 2-4a are shown. The PDFs corresponding to these times displayed are the duration of the first respiratory cycle, the shortest treatment delivery time, and the longest treatment delivery time. Distributions were generated by binning the respiratory motion amplitude value at each time in the respiratory trace (every 0.05 s) into 1 mm-wide bins Figure 3-1: The original GTV contour (green) from all treatment plans was used. The ITV was created by extending the GTV 1.8 cm inferiorly (orange). The example shown is for patient six, belonging to the group with a tumour-dome distance of < 1.8 cm Figure 3-2: The respiratory traces used in fractions 1-3 for motion simulation in all ten patient treatment plans. Traces were created using the Respiratory Trace Generator. 82 The amplitude of motion is 1.6 cm and the respiratory cycle period is 4 s. Small variations in the motion amplitudes and respiratory cycle lengths are visible between fractions Figure 3-3: a) The CPs provided by the VMAT optimizer for a highly modulated plan are shown on the respiratory trace. The respiratory trace is not sampled at a high enough frequency to accurately model respiratory motion. b) With the addition of CPs from two extra arcs, the respiratory trace is sampled much more accurately Figure 3-4: To isolate interplay effects, motion was simulated using four different starting points in the respiratory cycle as beam-on times. The four starting points are indicated by green circles Figure 3-5: Cumulative DVHs for the GTV, ITV, and uninvolved liver (liver minus GTV) for a typical static plan, and the corresponding plan with a random starting phase for each of the three fractions. Patient six s high MF plan is shown. Similar results were seen for both levels of plan modulation in all ten patients Figure 3-6: Cumulative DVHs for the GTVs for treatment plans created when motion is simulated using specific starting points in patient six s highly modulated treatment plan. The DVH of the GTV coverage is very minimally different when motion is simulated using different starting points in the respiratory cycle. Similar results were observed for all treatment plans ix

10 Figure 3-7: Example dose-difference maps on the same slice from a dose subtraction of two plans. Each plan was created by simulating respiratory motion using the same starting point (end-inspiration for one plan and end-expiration for the other) in the respiratory trace for all three fractions. This example is for patient six. The GTV is delineated with a red contour and the liver with an orange contour Figure 3-8: Differential DVHs of the GTV for the six dose subtractions for patient six for a) low and b) high MF plans. The spread of the differential DVHs is quantified by calculating the standard deviation of each of the six histograms and averaging those standard deviations. The mean standard deviation (mean SD) is indicated for each MF Figure 3-9: The standard deviation of the six dose subtractions for low (first box) and high (second box) modulation plans are plotted for each patient. A larger standard deviation indicates more dose differences in the GTV due to interplay effects x

11 List of Symbols, Abbreviations and Nomenclature 4DCT ABC ANOVA AP CBCT cc CERR CP CT CTV D 0.5 cc DICOM-RT DNA DVH FFF GTV Gy HCC IMRT ITV kv Four-Dimensional Computed Tomography Active Breathing Control Analysis of Variance Anterior-Posterior Cone-Beam Computed Tomography Cubic Centimetres A Computational Environment for Radiotherapy Research Control Point Computed Tomography Clinical Target Volume Maximum dose received by 0.5 cubic centimeters of the planning target volume Digital Imaging and Communications in Medicine Radiation Therapy Deoxyribonucleic acid Dose-Volume Histogram Flattening Filter-Free Gross Tumour Volume Gray (unit) Hepatocellular Carcinoma Intensity Modulated Radiation Therapy Internal Target Volume Kilovoltage xi

12 MF ML MLC MLD MRI MSW MU MV OAR PDF PEI PTV RFA RTOG SBRT SI TACE TNM V 20 Gy V 95 VMAT Modulation Factor Medial-Lateral Multileaf Collimator Mean Liver Dose Magnetic Resonance Imaging Meterset Weight Monitor Unit Megavoltage Organ at Risk Probability Distribution Function Percutaneous Ethanol Injection Planning Target Volume Radiofrequency Ablation Radiation Therapy Oncology Group Stereotactic Body Radiation Therapy Superior-Inferior Transarterial Chemoembolization Tumour Nodes Metastasis Volume receiving at least 20 Gy Volume receiving at least 95% of the prescription dose Volumetric Modulated Arc Therapy xii

13 Chapter One: Introduction 1.1 Liver Cancer In Canada, 2200 new cases of primary liver cancer were reported in Liver cancer is one of the deadliest malignancies with a five-year relative survival ratio of 21% or lower, depending on the disease stage, as described in Tables 1-1 and 1-2. Relative survival ratio is the ratio of expected survival in a group with disease compared to the expected survival of a diseasefree group of comparable individuals. The most common primary liver cancer is hepatocellular carcinoma (HCC), which is often associated with cirrhotic liver disease. Overall five-year survival outcomes for patients diagnosed with HCC are reported to be between 30% and 85%. 2 4 Secondary metastasis to liver is more prevalent than primary liver cancer, with hepatic involvement from colorectal cancer as the most common occurrence in clinical practice. The five-year relative survival ratio for patients with colorectal metastases to the liver is 13%. 1 The median overall survival outcomes at 5 years for patients diagnosed with hepatic involvement from colorectal cancer reaches 40% or higher in cases involving partial hepatic resection. 5 Physicians treat primary and secondary liver cancers based on disease type, disease staging, and patient comorbidities. Treatments are often a combination of surgery, chemotherapy, ablative therapies, and radiation therapy. 1

14 Table 1-1: Five-year relative survival ratio for primary liver cancer based on the tumour nodes metastasis (TNM) staging convention. Adapted from the Canadian Cancer Society. 6 Stage TNM Treatment Stage Grouping 5-year Relative Survival I T1N0M0 Localized, resectable 21% II T2N0M0 IIIA T3aN0M0 Locally advanced (regional), IIIB T3bN0M0 6% unresectable IIIC T4N0M0 IVA T(any)N1M0 Advanced 2% IVB T(any)N(any)M1 Table 1-2: The TNM staging classifications are described for primary liver cancer. Adapted from the Canadian Cancer Society. 7 Primary Tumour (T) TX Primary tumour cannot be assessed T0 T1 T2 T3a T3b T4 No evidence of primary tumour A single tumour with no invasion into the blood vessels of the liver A single tumour with invasion into the blood vessels or multiple tumours, none more than 5 cm in size Multiple tumours, with any tumour larger than 5 cm The tumour has grown into either the portal or hepatic vein The tumour has grown into nearby organs (other than the gallbladder) or the tumour has grown into the visceral peritoneum Regional Lymph Nodes (N) NX N0 N1 Regional lymph nodes cannot be assessed No regional lymph node metastasis Regional lymph node metastasis Distant Metastasis (M) M0 M1 No distant metastasis Distant metastasis 2

15 1.2 Treatments for Liver Cancer Surgery and Liver Transplantation Surgical resection has an important role in the management of patients with primary liver cancers or liver metastases. 8, 9 Partial hepatic resection can yield five-year overall survival rates ranging from 40-50% for both HCC and colorectal metastases. Often, patients with liver cancer are asymptomatic until tumour(s) within the liver enlarge to encompass or replace a large volume of normal liver. The volume of functional liver following surgery is a key determinant of the success of the operation and is frequently a limiting factor with regards to eligibility for resection. As a result, fewer than 30% of HCC and liver metastases patient are eligible for hepatic resection Liver transplantation, where the patient s diseased liver is replaced with a healthy donor liver, provides the best survival outcome for HCC patients, but the availability of matched liver donors limits its use. 18 Unfortunately, liver transplantation is not a treatment option for patients with metastatic liver involvement as circulating tumour cells would reseed the liver transplant. Additionally, metastatic disease often progresses more rapidly than HCC, not allowing enough time to identify a matched transplant donor Ablative Therapies For patients ineligible for surgery, local ablative therapies are the recommended treatment option for primary liver lesions less than 3 cm in diameter. 19 The most common ablative therapy for primary and secondary liver tumours is radiofrequency ablation (RFA). A needle is placed in the target under image guidance, and an ablative amount of heat is produced by running a high current through the end of this needle. Five-year overall survival after RFA for the treatment of HCC 20, 21 and for colorectal metastases 10 in the liver is reported to be similar to 3

16 surgical resection for small lesions. When the tumour is located close to large vessels, these vessels can act as a heat sink, cooling the tumour and surrounding area, and reducing the efficacy of the RFA treatments. 22 Another option for inoperable cases is percutaneous ethanol injection (PEI), in which a tumourcidal dose of alcohol is injected directly into the tumour under image guidance. 23 For tumours less than 3cm in diameter, PEI has been shown to yield similar results to RFA, but is inferior for larger lesions Additionally, PEI may require multiple treatment sessions to eliminate the cancer completely. Cryosurgery, where liquid nitrogen or pressurized argon gas is passed through a probe abutting the tumour, presents another method for ablation of small lesions. 27 It is suggested by Adam et al. that cryoablation is an appropriate treatment technique only for lesions less than 6 cm in diameter, as cryotherapy volumes to treat larger lesions cannot be reliably obtained. 28 The five-year overall survival for both HCC 29 and colorectal metastases 30 patients treated with cryosurgery alone is 23% Chemotherapy Chemotherapy is the treatment of cancer with the use of cytotoxic drugs. These drugs can be administered systemically or delivered locally to the target. Generally, patients with metastatic cancers benefit from systemic drug therapy, but tumours may stop responding to chemotherapy drugs or the cumulative toxicity from treatment may limit its continued use. Systemic chemotherapy to treat hepatic lesions is offered with palliative intent, but can improve survival outcomes compared to supportive care alone. 4

17 Hepatocellular carcinoma patients with localized disease can be treated with localized chemotherapy called transarterial chemoembolization (TACE). 31 An interventional radiologist uses a catheter to inject chemotherapy agents bonded to microspheres directly into the hepatic artery to take advantage of the differential blood supply to HCC tumours via the hepatic artery compared to liver hepatocytes that derive their blood supply from the hepatic portal vein. The microspheres occlude the fine tributaries of the hepatic artery to restrict blood supply to the tumour, thereby limiting its growth, and deliver chemotherapy agents locally to the tumour. The difference in blood supply to the tumour versus normal liver tissue leaves the liver relatively unharmed Radiation Therapy Historically, radiation therapy has not been used to treat cancers in the liver due to the low tolerance of large volumes of liver to high doses of radiation. The success of radiation therapy treatments relies on the different radiobiological properties of tumour cells and surrounding healthy cells, and also on the geometric accuracy of the radiation delivery. Most healthy tissues are able to tolerate radiation better than tumour cells when the radiation dose is delivered over the course of many treatment sessions, or fractions, because of the different radiobiological properties of tumour and healthy cells. Cells are most susceptible to deoxyribonucleic acid (DNA) damage from radiation when they are undergoing cell division. Since tumour cells divide more frequently than healthy cells, they experience more damage than healthy cells when exposed to ionizing radiation. Furthermore, healthy cells are better able to repair DNA damage than tumour cells, making any damage from radiation less likely to be lethal. Radiotherapy treatments are typically delivered in fractions, which exploits these 5

18 radiobiological properties of tumour and healthy cells, allowing for higher amounts of tumour cell-kill while limiting damage to healthy tissue. To limit the likelihood of radiation-associated liver injury, the mean liver dose (MLD) is recommended to be less than 28 Gy for primary liver cancer or 32 Gy for liver metastases when dose is delivered in 2 Gy fractions. 32 For comparison, the equivalent 2 Gy per fraction doses required for 90% probability of six-month local control for primary and secondary liver lesions are 84 Gy and 95 Gy, respectively. 33 This is significantly greater than MLD constraints, historically limiting the use of radiation therapy to treat liver lesions. Furthermore, the required number of fractions to delivery this in a conventional 2 Gy per fraction method makes this treatment impractical. Advances in both delivery techniques and image-guidance technology have allowed for greatly increased geometric accuracy in radiation therapy delivery, so treatments are less reliant on the differing radiobiological properties of tumour and healthy cells. This allows lesions in the liver to be treated safely to curative doses without exceeding MLD constraints. Furthermore, the success of radiotherapy does not rely solely on radiobiology, so treatments can be delivered in fewer fractions offering a higher biological equivalent dose and additional proposed mechanism of cell death. For example, 50 Gy in 5 fractions would biologically equivalent to approximately 83 Gy in 2 Gy fractions, assuming an α/β ratio of 10. This fewer-fractions, high-dose approach with high precision delivery is known as stereotactic body radiotherapy (SBRT). Advanced radiation therapy delivery techniques, such as intensity modulated radiation therapy (IMRT) 34 and volumetric modulated arc therapy (VMAT), 35 permit high geometric accuracy and targeted deposition of radiation while minimizing dose to surrounding critical structures. These technologies employ a set of independently movable tungsten leaves, known as 6

19 a multileaf collimator (MLC), to shape the radiation beam and produce highly conformal dose distributions. This allows for the sparing of healthy liver and nearby organs at risk (OARs) while a large dose of radiation is delivered to the tumour. In IMRT treatments, beams of radiation are delivered to the target from a small number of gantry angles while the MLC leaves are stationary (step-and-shoot IMRT) or continuously moving (sliding-window IMRT) to obtain a desired fluence pattern. Volumetric modulated arc therapy treatments involving moving MLC leaves have the added complexities of a continuously rotating gantry, and variable gantry speed and dose rate. In addition to dynamic and precise delivery techniques, image-guidance technology such as kilovoltage (kv) and megavoltage (MV) imaging and cone-beam computed tomography (CBCT) has become increasingly accurate and widely available on medical linear accelerators. These imaging technologies increase the precision of patient setup, allowing for the smaller margins required for SBRT delivery. 1.3 Respiratory Motion in Liver The liver is located in the upper abdomen and is highly affected by respiratory motion. During inspiration, the diaphragm contracts and the liver moves inferiorly. Upon expiration, the liver moves superiorly with the diaphragm. Liver motion due to respiration has been studied extensively and it is consistently reported that the largest extent of liver motion is in the superiorinferior (SI) direction (Table 1-3). Liver motion in the anterior-posterior (AP) and medial-lateral (ML) directions are less contributory. 7

20 Table 1-3: A summary of studies that have been done to characterize the amplitude of respiratory motion in liver including the number of subjects studied and the imaging method used to obtain the data. Motion amplitudes in the liver in the superior-inferior (SI), anterior-posterior (AP), and medial-lateral (ML) directions during normal respiration are reported as mean ± standard deviation and/or (range). Author Year n SI (mm) AP (mm) ML (mm) Method Weiss ± Scintigraphy Harauz Scintigraphy Suramo (10-40) - - Ultrasound Korin MRI Davies (5-17) - - Ultrasound Balter CT Herline ± Surface imaging Shimizu MRI Shimizu ± ± ±1.8 MRI Kitamura ± 5 (2-19) 5 ± 3 (2-12) 4 ± 4 (1-12) Fluoroscopy Rohlfing (12-26) (1-12) (1-3) MRI Brandner DCT Kirilova ( ) 10 ( ) 7.5( ) MRI Park ± ± ± 2.0 4DCT Park ± ± ± 1.6 CBCT During normal respiration the magnitude of SI motion of the liver can be as large as 35 mm, with mean values between 10 mm and 20 mm. Motion amplitudes up to 22 mm and 15 mm are reported for the AP and ML directions, respectively, with mean amplitudes consistently less than 10 mm for both directions. In the case of deep inspiration and expiration, the amplitude of respiratory motion can be much larger than the values reported in Table In addition to translation, the liver deforms during respiration due to the movement of the diaphragm and the physical location of surrounding organs. Liver motion due to respiration hinders imaging verification of target volumes and delivery accuracy of therapeutic radiation, leading to larger treatment volumes that may include healthy tissues. Respiratory motion can be accounted for in a number of different ways during radiation therapy treatment planning and delivery. 8

21 1.4 Motion Compensation Methods Respiratory motion can be accounted for in radiation therapy treatments using a number of techniques, including motion encompassing methods, respiratory gating, breath-hold methods, and real-time tumour tracking. 50 Each of these techniques will be discussed in detail in the following sections Motion Encompassing Methods Respiratory motion can be accounted for by extended margins to encompass tumour motion. Motion encompassing methods require knowledge of the extent of the tumor motion, which can be obtained during the patient s computed tomography (CT) simulation in a number of different ways. First, slow-scanning CT, in which the CT image is acquired over the course of a number of respiratory cycles, yields a CT image where the tumour appears larger than it actually is, showing the full extent of its motion. This technique is limited by the relatively poor image quality and associated lack of precision in target delineation. The second method is achieved by performing two CT scans while the patient is in inspiration and expiration breathhold positions. Examining the tumour position in these two CT images will show the two relative tumour positions due to respiration, but may not provide complete information on the full extent of motion. Additionally, breath holds can be difficult to reproduce, leading to potential errors during treatment and occasionally the need for additional margins to account for this uncertainty. The third option is to perform a four-dimensional CT scan (4DCT). Patients undergo a 4DCT scan under normal or shallow breathing conditions and the CT images are binned based on their position in the respiratory cycle, yielding a number of different CT images, corresponding to different respiratory phases. A 4DCT provides a complete description of the tumour motion, but 9

22 requires consistent and reproducible breathing during simulation and treatment. For a slowscanning CT image, the prescription dose is planned to the visible target volume. For breath-hold and 4DCT scans, the prescription dose is planned to a volume generated by merging the inhale and exhale tumour positions, as seen in Figure 1-1. The volume that encompasses the full extent of tumour motion is known as the internal target volume (ITV). 51 The treatment plan is then designed to deliver the prescription dose of radiation to the ITV, plus an isotropic margin designed to account for patient setup uncertainty, so that this target volume will be covered by the prescribed dose during normal respiration. While the use of an ITV is an effective way to account for organ motion, it increases the amount of healthy tissue being irradiated to high doses. This is especially problematic when the target volume and/or tumour motion amplitude is large. Figure 1-1: In the case where no CTV margin is used, the ITV can be created by contouring the GTV at end inspiration (blue) and end expiration (yellow) scans, and merging the positions of the GTV margins. The ITV (pink) encompasses the full extent of GTV motion. When a CTV margin is used, the ITV is created by merging the CTV margins. Liver patients require a sizable portion of the liver spared from high doses in order to minimize radiation-induced hepatotoxicity after therapy. 52 The recommended minimum critical volume is 700 cc of healthy liver, and it should receive no more than 15 Gy in 3-5 fractions

23 For patients where the liver motion is greater than 1 cm, abdominal compression can be used to minimize this motion. During abdominal compression, a paddle applies force to the anterior surface of the patient s abdomen, which limits the amplitude of respiratory motion by preventing diaphragmatic excursion. When abdominal compression is successful, a smaller ITV can be used that in turn reduces the volume of healthy liver receiving a high dose. Compression can be uncomfortable or intolerable for some patients, and there can be variable effects on how much compression reduces tumour motion between patients The success of abdominal compression relies on the reproducibility of the tumour motion, which is related to the reproducibility of the applied compression force. Fluoroscopy can be used to assess the amount of diaphragm motion in the SI direction with varying degrees of abdominal compression. A balance must be met between the patient comfort and reduction of tumour motion Respiratory Gating Respiratory gating employs imaging technologies to monitor the tumour location in realtime with the goal of reducing the amount of normal tissue irradiated to high doses. The patient undergoes a 4DCT simulation under normal breathing conditions, and the treatment plan is made on one, or a small number, of phases of that CT scan. The target s location on the CT images in the phase(s) on which the plan was made is known as the gating window. During treatment, the radiation beam is turned on only when the target is in the gating window (Figure 1-2). Internal fiducial markers or an external respiratory signal is used as a surrogate for tumour location. A smaller gating window is advantageous because it allows for the use of a smaller ITV margin leading to increased sparing of healthy tissues. However, the use of a smaller gating window will increase the treatment delivery time because the tumour will spend less time inside the gating 11

24 window, and therefore inside the planning target volume (PTV). Regardless of the size of gating window chosen, respiratory gating techniques can greatly reduce the amount of tissue being irradiated to high doses, but will increase the treatment delivery time, but when compared to motion encompassing methods. Respiratory gating has the added disadvantage of being resourceand time-intensive. Gating systems have large upfront costs, require additional commissioning and training, and daily treatments use more clinical resources. Despite these disadvantages, respiratory-gated SBRT may be the only method to deliver radiation safely without exceeding normal tissue dose tolerances. Figure 1-2: An example of a typical gating window on the exhale phase of the respiratory cycle. Below, the phases of the 4DCT on which the treatment was planned those where the target is inside the gating window, and the beam is turned on, are indicated with green Breath Hold Problematic respiratory motion can be eliminated from radiation therapy treatments by performing the CT simulation and treatment delivery while the patient is holding their breath. Breath-holds can be accomplished either voluntarily by the patient or with the aid of an active breathing control (ABC) system. 56 In the case of voluntary breath holds, the patient holds their breath, and attempts are made to accomplish reproducible breath holds through patient coaching 12

25 and/or visual feedback. For abdominal tumours, breath-holds are most frequently done at the end expiration point of the respiratory cycle, as it is the most reproducible breath-hold position and the longest phase of the respiratory cycle, for many patients. 57 Active breathing control systems use spirometry to measure the volume of air exhaled by the patient, making lung volume, and thus breath-hold positions markedly more reproducible than voluntary breath-holds. 58 Using either technique, the treatment plan is made on the breath-hold CT image, and the patient is treated daily under breath-hold conditions. While breath-hold techniques can account for motion effectively, they can be uncomfortable or intolerable for many patients and can increase the length of treatment delivery times. Breath-hold techniques are further limited by reproducibility in the case of voluntary breath-holds, and by cost in the case of ABC Real-Time Tumour Tracking Real-time tumour tracking involves continually repositioning the radiation beam or tumour location to account for tumour motion. This can be done either by changing the location of the beam aperture or by moving the couch to reposition the patient and tumour appropriately. CyberKnife Robotic Radiosurgery System (Accuray Incorporated, Sunnyvale, CA) is capable of real-time tumour-tracking and is currently being used in clinical practice. Tumour tracking 59, 60 using a conventional linear accelerator is an area of active research. 1.5 Dosimetric Effects of Respiratory Motion in Liver Radiotherapy The differences between planned and delivered dose distributions caused by respiratory motion can be separated into two categories: dose blurring effects and interplay effects. 61 These effects are discussed more thoroughly in the following two sections. 13

26 1.5.1 Dose Blurring Dose blurring occurs in both static and dynamic radiotherapy treatments affected by tumour and organ motion. In the case of lesions affected by respiratory motion, including those in the liver, the tumour will move back and forth periodically across the treatment beam profile. This results in the tumour and surrounding tissues experiencing a spread out or smeared fluence profile. 61 For fields that have a flat fluence profile, dose blurring has a pronounced effect in the penumbra region at the edges of the target, as seen in Figure 1-3. Due to the spreading of the dose distribution, the edges of the target do not receive the same dose when respiratory motion is present because a large amount of the prescribed dose is delivered outside the target volume. When the fluence is not flat, dose blurring affects all regions in the target, rather than just the edges. Dose blurring effects can be minimized using motion compensation methods as discussed in section 1.4. Figure 1-3: An example of dose blurring is seen for a 5 cm open field delivered to a tumour with a respiratory motion amplitude of 1.6 cm in the direction of the dose profile (x-axis). For a uniform fluence, dose blurring is evident at the edges of the target when respiratory motion is simulated in a treatment plan. The dose profile through the target becomes more spread out with a broader penumbra region. 14

27 Mathematically, dose blurring is described as the convolution of the static dose distribution with the target motion kernel, or probability density function (PDF) of the target motion. 62 A convolution is the integral of the product of one function with another function that has been flipped and shifted, resulting in a third function that resembles a blurred or smoothed version of the first function. The function resulting from convolving the static dose distribution with the motion kernel is a spread out of smeared version of the static dose distribution, and will be the delivered dose. D d (x, y, z) = D s (x, y, z) p om (z) (1-1) D d (x, y, z) = = D s (x, y, z z ) p om (z ) dz (1-2) In the above equations, D d (x, y, z) is the resultant dose distribution due to respiratory motion blurring that is delivered, D s (x, y, z) is the original dose distribution, and p om (z) is the PDF, or motion kernel of the target position during the respiratory motion. These equations are applicable when the target motion is rigid and exclusively in the z-direction, but can easily be extended to rigid three-dimensional motion. Convolution methods have been applied to model respiratory motion 62, 63 in radiation therapy treatment plans, and the presence of dose blurring effects has been shown. Rosu et al. applied convolution techniques to model patient-specific respiratory motion in conformal radiotherapy plans in liver, and reported hot and cold spots superior and inferior to the target. 64 Monte Carlo calculations were done by Chetty et al., who found similarly blurred distributions in the liver using a fluence convolution technique

28 While dose blurring is known to occur in both static and dynamic treatment types, it can produce a more dramatic effect with VMAT treatments due to highly conformal dose distributions and steep dose gradients. Any blurring of the high-dose region at the edges of the target could be more detrimental to the treatment plan quality Interplay In addition to dose blurring, treatments that involve dynamic fluence modulation such as sliding-window IMRT and VMAT are susceptible to dosimetric differences between planned and delivered treatments caused by the interplay between target motion and MLC leaf motion. Potential dosimetric effects caused by interplay are illustrated by the example shown in Figure 1-4. MLC leaves are moving from left to right with their positions at four time points (t 1 -t 4 ) shown in each of the beam s eye view frames. The two stars are representative of two possible positions of a single point in the tumour that occur due to two different beam-on timings relative to the respiratory cycle. The solid star can represent a situation where the beam was turned on at expiration (Figure 1-5). It can be seen that this point receives no direct dose between times t 1 and t 4 because it is constantly blocked by the MLC leaves. Conversely, if the beam was turned on at inspiration, the target would be represented by the open star and would receive direct dose at all times between t 1 and t 4. This example is theoretical and highly unlikely to occur through several breathing cycles but it illustrates the potential interactions of relative tumour position with respect to motion MLC leaf motion. More specifically, it demonstrates the dependence of interplay effects on beam-on timing relative to the respiratory cycle. 16

29 Figure 1-4: Illustration of the interplay effect between a tumour in motion and moving MLC leaves during a treatment delivery with dynamic MLC leaves. The solid and open stars represent the tumour motion during two phases of the respiratory cycle (inspiration and expiration). The point in the respiratory cycle in which the beam is turned on relative to the MLC motion can cause the target to receive different doses. (Figure reproduced from Bortfeld et al.) 66 Figure 1-5: Example beam-on timings relative to the respiratory cycle, which could produce the situation illustrated in Figure 1-4, are indicated by solid (beginning of inspiration phase) and open (beginning of expiration phase) stars. 17

30 Organ motion can be modelled by convolving the static dose distribution with the PDF of the organ motion, as discussed in section For simplicity, it can be assumed that the dose in VMAT treatment plans is delivered instantaneously at a finite number of control points (CPs). This can be extended later by changing the finite number of CPs to a continuous arc delivery. It is assumed that the dose for each CP is delivered instantaneously and because of this, the organ is in a single position, so the motion PDF of the organ position is modelled by a delta function at each CP. For a case where the organ is located at a point z = a along the axis of motion, the position can be represented by the following function: δ(z) = { +, z = a 0, z a (1-3) For simplicity, it can be assumed that the organ motion is along the z-axis, but this case can be extended to a three-dimensional case. For a single CP, the delivered dose, D d (z), will be the static dose, D s (z), convolved with the motion PDF: D d (z) = D s (z) δ(z) (1-4) The target will have a different delta function at each CP, t, which can be denoted δ t (z). For each CP, the delivered dose, D t d (z), will be the static dose, D t s (z) convolved with the motion PDF, which is δ t (z), based on previously-stated assumptions: D d t (z) = D s t (z) δ t (z) (1-5) To get the total delivered dose for a multi-fraction treatment, Equation 1-5 can be summed for all CPs, t, and over all fractions, k: D d (z) = (D s t,k (z) δ t,k (z)) k t (1-6) 18

31 In this definition, if multiple arcs are used in a single fraction, then each arc should be counted as a separate fraction, because the beam-on time of the second arc is not related to the timing of the first arc. In the case of a static treatment, or one where the fluence is not changing with time, the static dose term will be independent of time. D d (z) = (D k s (z) δ t,k (z)) k t (1-7) Furthermore, if it is assumed that set-up uncertainties are not present, then the static delivered dose will be the same for each fraction. D d (z) = D s (z) δ t,k (z) k t (1-8) The sum of the target positions over all CPs in all fractions is the target s motion PDF, P om (z). Equation 1-8 then becomes: δ t,k (z) = P om (z) (1-9) k t D d (z) = D s (z) P om (z) (1-10) Which is the standard definition of blurred dose due to respiratory motion in the literature. 62 Given the previously-stated assumptions, in the case of dynamic treatments, the fluence is variable with time, and so the static delivered dose will have a different value at each CP. For the single fraction case, the delivered dose will be a sum over n CPs, where n is the total number of CPs in an arc. n D d (z) = (D s t (z) δ t (z)) t=1 (1-11) 19

32 When the beam is turned on at a different point in the respiratory cycle, say a random time, r, later than the first beam-on time, the delivered dose would be: n D d (z) = (D s t (z) δ t+r (z)) t=1 (1-12) Dosimetric differences due to interplay effects, I, can be quantified as the difference in dose delivered when one beam-on time is used, relative to another: n n I = (D t s (z) δ t (z)) (D t s (z) δ t+r (z)) t=1 t=1 (1-13) This can be extended to the multi-fraction case: n n I = (D t,k s (z) δ t,k (z)) (D t,k s (z) δ t+r,k (z)) k t=1 k t=1 (1-14) In the absence of set-up uncertainties, the delivered dose will be the same for each fraction k: n n I = (D t s (z) δ t,k (z)) (D t s (z) δ t+r,k (z)) t=1 k t=1 k (1-15) This cannot be reduced further as it was in the dose blurring case because the interplay effects, I, will depend on the target position when the dose is delivered at each CP. It should be noted that the quantity I will be a 3D matrix of dose differences. As an example, it can be assumed that the dose is delivered in two CPs. The tumour position is indicated in those CPs by the green and blue delta functions in Figure 1-6. A profile through the dose delivered at each CP is given by the green and blue profiles: 20

33 Figure 1-6: The tumour position at two CPs can be represented with a green and a blue delta function. A profile through the corresponding doses delivered at each of those CPs is given by the green and blue dose profiles. For the first case, it can be assumed that the tumour is moving to the right (from the green delta function to the blue delta function) as the two CPs are delivered. As per Equation 1-11, the dose to the tumour is given by convolving the static dose with the tumour position at each CP, and summing over all CPs: Figure 1-7: To calculate the total dose from both CPs, the convolution of static dose profile with target position delta function is performed for each CP, and the resulting total dose profile (purple) is calculated by summing the two CP dose profiles (green and blue). The resulting dose profile is shown in purple. If the tumour was instead moving from right to left (green to blue in Figure 1-8), the following scenario would occur: 21

34 Figure 1-8: The total dose delivered to the moving tumour is calculated using the same method described in Figure 1-7, but using a different tumour position for each CP. The resulting dose profile (purple) is different than the one seen in Figure 1-7. It can be seen that by changing the beam-on timing, or changing whether the tumour is moving from right to left or left to right, the overall delivered dose is changed. The difference between the two dose profiles seen in Figure 1-9 is represented mathematically by Equation Figure 1-9: The resulting dose profiles calculated by summing the convolutions of the static delivered dose profiles with the target position delta function are not the same when the target motion is different, for example if a different beam-on timing is used. In a more realistic example, the tumour could be moving from an inspiration to an expiration position, rather than from left to right. The static dose would also be represented by a 2D fluence plane, rather than a simplified dose profile. This example utilizes an extreme and unrealistic scenario to demonstrate the possible dosimetric effects of interplay. In a realistic 22

35 treatment plan, these effects tend to average out because dose is delivered using more than two CPs, and in multiple fractions. The interplay effect was first studied by Yu et al. for sliding-window IMRT treatments, and it was found that interplay can cause differences in excess of 100% of the desired beam intensity, but that these effects would average out when the prescribed dose was delivered in a conventionally fractioned treatment. 67 The magnitude of interplay effects with IMRT in more recent studies has consistently been reported to be clinically negligible when delivered over the 66, course of a standard fractionation schedule. The interplay effect was studied using convolution methods by Li et al., who looked at intrafraction prostate motion in step-and-shoot IMRT treatments. Instead of convolving the total dose distribution with the motion PDF for the entire treatment, the dose distribution for each segment is convolved with the PDF of motion that occurs during that segment. 71 Extending this technique to IMRT with dynamic MLCs such as sliding-window IMRT or VMAT is challenging as the motion PDFs for each segment, which in the case of a dynamic MLC in these treatments is each MLC position, would need to be convolved with the dose or fluence from each leaf position with interpolation required between known MLC positions. More recently, the interplay effect has been evaluated in VMAT. While VMAT treatments have the added complexity of a continuously rotating gantry, the interplay effects associated with VMAT were negligible in magnitude using a standard fractionation schedule, 72, 73 and similar to data obtained using sliding-window and step-and-shoot IMRT. Unlike conventionally fractionated radiotherapy, SBRT delivers larger doses in fewer fractions and is routinely used to treat lesions in lung and liver. The interplay effect with lung SBRT treatments has been studied and it has been found that despite the lack of interfraction 23

36 averaging seen in conventionally fractionated treatments, interplay effects were also negligible in magnitude Although interplay effects in VMAT lung SBRT has been thoroughly studied, only limited work has been performed with liver SBRT. With lung SBRT, there are few dose-limiting OARs besides the spinal cord and esophagus that require MLC modulation during arc radiation delivery, particularly if the lesion is peripherally located in the lung. In contrast, the liver itself is a dose-limiting critical structure and the liver is surrounded by bowel, spinal cord, kidneys, stomach, esophagus, and heart, all of which are dose-limiting. Because of competing treatment modalities, liver tumours treated with SBRT also tend to be larger in size. RTOG 1112, a phase III clinical trial for HCC patients randomized to Sorafenib alone versus Sorafenib and SBRT, allows radiotherapy treatment of single lesions up to 15 cm in maximal diameter and up to 20 cm if multifocal lesions are present. 80 These characteristics require more MLC leaf modulation to produce more conformal dose distributions. Kuo et al. simulated the interplay effect by sorting the dose delivered during each CP to different CT images corresponding to different phases of the respiratory cycle and calculating the dose accordingly. 73 It was reported that for two patients with hepatic lesions, plans with greater amounts of MLC leaf modulation had more hot and cold spots in the PTV, and that PTV coverage was more affected by interplay when the dose was delivered in a single fraction. The effects of plan modulation could be confounded with the effects caused by the length of the respiratory cycle and the amplitude of tumour motion as a result of the design of this study. The contributions of each of these factors were not explicitly studied in this group s work. The effects of plan modulation were also studied by Ehrbar et al. using a similar technique in VMAT liver plans and it was found that the amount of plan modulation was not correlated to the dose 24

37 differences observed. 79 The definition for modulation factor (MF) used in Ehrbar s work does not take into account the differences in target depth or tissue composition (hepatic, adrenal gland, and lung lesions were studied), so MF does not fully describe the amount of MLC leaf modulation in the treatment plans. Furthermore, the interplay effect was not explicitly isolated from dose blurring effects, but was determined to be negligible in magnitude, if present, due to a lack of cold spots observed in the target. A limitation common to the studies performed by Kuo et al. and Ehrbar et al. is that effects of plan modulation were only investigated on two and three liver patients, respectively. 1.6 Research Objectives and Thesis Organization The work in this thesis aims to more thoroughly investigate the effect of plan modulation on a VMAT liver SBRT treatment plan s susceptibility to dosimetric differences due to interplay. Advantages over previous works include a larger number of patients and a study designed to explicitly isolate the effects of plan modulation from other factors such as target motion amplitude and depth in tissue, and the number of respiratory cycles that occur over the course of a single fraction delivery. Chapters two and three compose the main body of this thesis. Chapter two details the preliminary work completed for this project. A program was developed to simulate respiratory motion from the beam s eye view by moving the MLC leaves to reflect periodic respiratory motion. The roles of plan modulation and treatment delivery time on the magnitude of interplay effects were investigated using VMAT liver SBRT treatment plans created for a homogeneousdensity digital phantom. Chapter three builds off of this phantom study using the existing program to model respiratory motion in VMAT plans created for ten previously treated liver 25

38 patients. In chapter three, interplay effects are explicitly isolated from dose blurring effects, and the investigation is focused on determining whether plans with greater amounts of MLC leaf modulation are more susceptible to interplay effects. Additionally, significant improvements were made to the motion simulation program and are discussed in detail. A summary of the results obtained and potential directions of future research are discussed in chapter four. 26

39 Chapter Two: Digital Phantom Study 2.1 Overview This chapter describes the first stages of work for this thesis. The effects of MF and treatment delivery time on the amount of interplay observed were investigated using VMAT liver SBRT plans. Treatment plans with differing amounts of modulation and varying delivery times were created for a digital phantom. A method to simulate respiratory motion effects by shifting the MLC leaf positions according to a realistic respiratory trace was developed. Dosimetric differences between the static plans and plans with simulated respiratory motion due to dose blurring and interplay effects were quantified through dose-volume histogram (DVH) analysis. 2.2 Materials and Methods Digital Liver Phantom A homogeneous density digital liver phantom (Figure 2-1) created in the Eclipse (Varian Medical Systems, Palo Alto, California) treatment planning system (TPS) (version 11) was used in this study. 81 A large cylinder, 33 cm across in the ML direction, 20 cm in the AP direction, and 31 cm in the SI direction was used to represent the body. A smaller cylinder representing the liver was contoured on the right side of the body. A 4 cm diameter spherical gross tumour volume (GTV) was contoured in the liver, and an ITV was created by extending the GTV by 0.6 cm in the both the superior and inferior directions. This 1.2 cm total extension accounts for a respiratory motion amplitude up to 1.2 cm. No clinical target volume (CTV) was 27

40 used, as it is not used by the planning protocol described in section A PTV margin was not added to the ITV because setup errors were not modelled in the study. Figure 2-1: A) Axial view of digital phantom, B) Coronal view of digital phantom, and C) a 3D view of the digital phantom for which treatment plans were created. The grey, yellow, and cyan cylinders represent the body, liver, and spinal cord contours, respectively. The blue sphere is 4 cm in diameter and represents the GTV. The red ovoid, representing the ITV, is a 0.6 cm superior and inferior extension of the GTV Background on Volumetric Modulated Arc Therapy Optimizer Volumetric modulated arc therapy treatment plans are generated using inverse planning techniques. A CT image, or digital phantom in this case, is imported into the TPS, and all of the involved structures are contoured. The user inputs the plan information such as total dose and the number of fractions into the TPS. In addition, the user indicates the collimator angle for each arc, number of arcs, and angles that those arcs will span. The user must also provide the information that the VMAT optimizer will use to create a treatment plan, including plan objectives, dose constraints, and associated weighting factors. This information is used to create a cost function that is designed to penalize deviations between the planning constraints and the current dose distribution. With this information, the VMAT optimizer iteratively adjusts the MLC positions 28

41 and dose rate during each arc in order to minimize the cost function and develop the best possible treatment plan. The user has the option to increase or decrease objectives, constraints, and weights as the optimizer progresses to exercise some control over the final plan. To efficiently achieve a quality treatment plan, the VMAT optimizer begins with a small number of CPs, sampling the gantry angle extremely coarsely, as the initial step to design an optimal treatment plan. After several iterations, additional CPs are added into the optimization between existing ones, with MLC leaf positions linearly interpolated between the positions at the two adjacent CPs. The leaf positions at the new CPs are adjusted iteratively to minimize the optimization cost function. This increasingly finer sampling decreases the flexibility of the optimization, but allows for increased precision. 35 Once a VMAT plan is complete, the leaf positions and gantry angle for a discrete number of CPs are stored in the DICOM-RT file. Additionally, the fraction of the total arc MUs to be delivered up to each CP, known as the cumulative meterset weight (MSW) is stored. Using the total number of beam MUs, the MSW, and the gantry angle at each CP, the treatment console calculates the speed of gantry rotation and the dose rate for each CP. The number of MUs delivered at the n th CP can be calculated using the MSWs from the n th and (n-1) th CPs and the total number of beam MUs: MUs delivered in CP n = (MSW n MSW n 1 )(total beam MUs) (2-1) From this, the number of MUs per degree of gantry rotation can be calculated: 29

42 MUs per degree n = MUs delivered in CP n Gantry Angle n 1 Gantry Angle n (2-2) The dose rate that would be required to deliver the required number of MUs per degree is calculated using the maximum gantry speed because the treatment console will always deliver a treatment plan at the maximum gantry speed when possible. The maximum gantry speed is 6 /s for a TrueBeam linear accelerator, for which the treatment plans in this study were designed. Dose Rate Required n = (MUs per degree n )(Maximum gantry speed) (2-3) The maximum dose rate for a 6 MV beam with a flattening filter on a TrueBeam is 600 MU/min. If the dose rate required for a CP exceeds 600 MU/min, the dose rate is assigned this maximum value, and the reduced gantry speed for that CP is calculated accordingly. If the required dose rate is physically achievable by the linear accelerator, the gantry speed will be assigned its maximum value of 6 /s, and the dose rate required will be used. Maximum Dose Rate Dose Rate n = { if Dose Rate Required n Dose Rate Required n > 600 MU min if Dose Rate Required n < 600 MU min (2-4) Maximum Dose Rate MUs per Degree n Gantry Speed n = { Maximum Gantry Speed if Dose Rate Required n > 600 MU min if Dose Rate Required n < 600 MU min (2-5) 30

43 2.2.3 Treatment planning Treatment plans with four different MFs delivering 50 Gy to the ITV in 5 fractions, using a 6 MV photon beam with a maximum dose rate of 600 MU/minute, had previously been created for the digital phantom discussed in section All treatment plans delivered the prescribed dose in two 180 arcs spanning from gantry angles 0 to -180 along the phantom s right side. Throughout this study, the following definition is used for MF: MF = Number of Monitor Units per Fraction Dose per Fraction (2-6) For a given geometry, a plan with a higher MF requires more beam-on time, or monitor units (MUs), to deliver the same radiation dose as a lower MF plan. This is because the MLC leaves spend more time in the field, thus blocking more of the radiation from reaching the target. To create treatment plans with lower MFs, few dose constraints were entered in the VMAT optimizer. A 5 mm-thick shell structure was contoured around the ITV, spanning from 5-10 mm from the periphery of the ITV. In order to obtain increasingly complex treatment plans, dose constraints for this shell structure were provided to the optimizer, forcing more MLC leaf modulation by increasing the difficulty of the optimization problem. The dose constraints on the shell structure were increased by trial and error until desired levels of MLC leaf modulation, and thus desired MFs, were obtained. The MFs of the plans for this phantom were 2.1, 2.5, 3.0, and 3.5. Modulation factors around 2.1 are commonly seen in clinical treatment plans at our centre, whereas a MF of 3.5 is 31

44 very highly modulated and is rarely seen. Beam s eye views of example apertures representing the range of plan modulation used in this study can be seen in Figure 2-2. Figure 2-2: Sample beam s eye views of a representative MLC aperture at a single CP for plans with two different amounts of MLC leaf modulation delivering dose to the ITV (red ovoid) of the digital liver phantom. For the higher MF plan, the MLC leaves spend more time blocking the target, thus modulating the fluence, whereas in the low MF plan, the leaves spend more time at the periphery of the target, providing less fluence modulation. In order to study the effects of treatment delivery time, the gantry speed was varied for each of the four different MF plans. As mentioned previously, the gantry speed in a VMAT plan is determined by the number of MUs delivered at each CP. Treatment delivery time is limited by gantry speed defaulting to its maximum value, but can be reduced by lowering the total prescription dose or the number of MUs for each arc. For each of the four MF plans, the total dose prescription was reduced from 50 Gy in 5 fractions to 40, 30, 20, 10, and 5 Gy in 5 fractions, yielding a total of 24 treatment plans. The resultant treatment delivery times are presented graphically in Figure 2-3. Reducing the dose prescription is limited in its ability to 32

45 reduce treatment delivery times because of the maximum gantry speed. This plateau can be seen in Figure 2-3 at treatment delivery times of 30 s. Figure 2-3: Treatment delivery times for a single 180 arc are plotted for the four MFs, and the six total dose prescriptions. Lowering the total dose prescription forces a decrease in the treatment delivery time for a single arc, until the maximum gantry speed is reached. For a TrueBeam linear accelerator, the maximum gantry speed is 6 /s, so the shortest possible delivery time for a 180 arc is 30 s, which is seen as the plateau for prescriptions of 5 and 10 Gy. All dose prescriptions are delivered in 5 fractions Respiratory Trace Generation Realistic respiratory traces were used to simulate respiratory motion in the treatment plans. These traces were created using the population-based library function of a Respiratory Trace Generator. 82 Three traces with respiratory periods between 3 and 4 seconds, and peak-topeak motion amplitudes between 1.0 and 1.2 cm were generated to be used in the motion simulation process (Figure 2-4). The traces used have variability in the respiratory period, motion amplitude, and baseline position, to be reflective of actual patient respiration. 33

46 Figure 2-4: The first 120 s of three respiratory traces creating using the Respiratory Trace Generator 82 are plotted. Each trace used in motion simulation in phantom treatment plans has a respiratory period between 3 and 4 s and motion amplitudes between 1.0 and 1.2 cm. Variation in amplitude, period, and baseline position are seen for all traces, to be representative of the patient population. In addition, a fourth respiratory trace with baseline drift was generated using the same amplitude and period parameters and variability as traces a, b, and c (Figure 2-5). After 40 s, the respiratory motion begins to drift noticeably from the original position, even though the amplitude of each respiratory cycle does not change drastically. This systematic intrafraction motion could be representative of a patient s muscles relaxing or tensing during the course of one fraction, and would introduce dosimetric errors if not accounted for properly. All respiratory traces were exported as a comma-separated value file containing a series of data points (time (s), motion amplitude (mm)), sampling the respiratory trace every 0.05 s. 34

47 Figure 2-5: The first 180 s of a respiratory trace created using the Respiratory Trace Generator 82 with large baseline drift. The respiratory motion period and amplitude are 3 s and 1.0 cm, with some variability of these parameters for each cycle, to be representative of an actual patient Motion Simulation Program An in-house program was written to simulate respiratory motion in the phantom treatment plans. When a patient breathes during a radiation therapy treatment, the target is moving under a stationary beam. This program models the same scenario but by changing the frame of reference; the patient anatomy is kept stationary and the treatment beam is moved. The simulation program incorporates a realistic respiratory trace and introduces this motion as an overall motion pattern on top of the existing VMAT MLC leaf pattern. This model assumes a rigid translation of the liver during respiration. An overview of the process is depicted in Figure

48 Figure 2-6: A description of the process used in simulating respiratory motion. The in-house simulation program reads in a DICOM-RT file, and a respiratory trace file, and shifts the MLC positions, creating a new DICOM-RT file. This new DICOM-RT file is imported into the treatment planning system and the dose is calculated with the new MLC pattern. Once the treatment plan has been created in the treatment planning system, the DICOM- RT file is exported. The shifting program reads in the respiratory trace information as a series of amplitudes corresponding to points in time, spaced every 0.05 s. A continuous function representing the respiratory trace is re-created from this data by performing a linear interpolation between each of the data points. For each fraction, a random starting point is chosen in the first 20 s of the respiratory trace as the beam-on time. The program then reads in the DICOM-RT file, which contains the positions of each MLC leaf at each CP. For each CP, the time that has elapsed since beam-on is calculated. Each active MLC leaf is re-assigned a position that is its original position, plus the amplitude of the respiratory trace at that point in time. This is done for each CP 36

49 in both arcs, for all five fractions. The resulting dynamic MLC pattern will look the same as the original one, but being performed while moving according to the respiratory trace. Once all the MLC leaf positions have been re-assigned, the DICOM-RT is imported into Eclipse and the dose is re-calculated for the new MLC pattern using the Anisotropic Analytical Algorithm (Version ). This was done in all 24 treatment plans using all four respiratory traces Analysis of Dosimetric Effects The effects of respiratory motion were quantified by looking at the changes in dose to the ITV and the GTV after motion had been simulated. A percent difference was calculated for the GTV V 95 and the ITV V 95 with and without motion simulation. The data resulting from simulation with traces a, b, and c were binned according to treatment delivery time and averaged. A two-way repeated-measures analysis of variance (ANOVA) test was performed to test for statistical significance in the trends relating treatment delivery time and MF to degradation of ITV coverage. 2.3 Results The GTV coverage was unaffected in all treatment plans, indicating the ITV margin properly accounted for motion. The decrease in the ITV coverage when motion was simulated with respiratory traces a, b, and c is plotted in Figure

50 Figure 2-7: The percentage decrease in ITV V 95 coverage that occurs when motion is simulated using a random starting point in the respiratory cycle is plotted for four different MFs and six treatment delivery times corresponding to different dose prescriptions. A larger decrease in ITV coverage is indicative of worse target coverage when motion is simulated. The points with the longest treatment delivery times correspond to the original treatment plans for each MF. Plots a, b, and c come from motion simulated with traces a, b, and c (Figure 2-4), respectively. 38

51 The averaged and binned data for ITV coverage decrease when motion was simulated with traces a, b, and c is presented in Figure 2-8. A greater loss of ITV coverage was seen for more highly modulated plans and for plans with shorter delivery times. An ANOVA test indicates that both of these trends are statistically significant (p<0.01). Figure 2-8: The data from Figure 2-7 a, b, and c are binned by treatment delivery time and the values for decreases in ITV V 95 coverage are averaged for each bin. Error bars indicate the standard error of the values in each bin. When the respiratory trace with baseline drift (Figure 2-5) was used to simulate motion, the resultant decrease in ITV coverage was larger than for respiratory motion with no baseline drift. The same trend is seen with MF, but in this case, a longer treatment delivery time yields more dosemetric differences. Both of these trends are statistically significant (ANOVA, p<0.01). 39

52 Figure 2-9: The percentage decrease in ITV V 95 coverage that occurs when respiratory motion with a baseline drift is simulated using a random starting point in the respiratory cycle is plotted for four different MFs, and five treatment delivery times corresponding to different dose prescriptions. A larger decrease in ITV coverage is indicative of worse target coverage when motion is simulated. The points with the longest treatment delivery times correspond to the original treatment plans for each MF. 2.4 Discussion In this work, the dosimetric effects of respiratory motion due to both dose blurring and interplay were demonstrated in VMAT SBRT plans created for a digital liver phantom. The results indicate that when no baseline drift was present, higher MFs and shorter delivery times lead to more dosimetric effects in the ITV. When respiratory motion with a large baseline drift was simulated, a higher MF led to reduced ITV V 95 coverage, but in this case, longer treatment delivery times were detrimental to plan quality. This can be attributed to the baseline drift causing the target to drift further away from the beam, introducing a systematic error. In this case, the motion kernel of the respiratory 40

53 trace would be a broader distribution, and when convolved with the static dose distribution, would cause a greater amount of blurring. These effects seen in the ITV are due to dose blurring and interplay and the contributions from each were not explicitly separated in this study. While dose blurring is known to cause greater dosimetric differences than interplay, it is speculated that some interplay effects are likely present here. The MLC leaves spend more time in the path of the beam during the delivery of treatment plans with higher MFs, leading to more opportunity for certain spatial locations in the target to be blocked by MLC leaves. Depending on the synchrony between the target motion and MLC leaf motions, this blocking of the target has the potential to cause underdosage in the target. The increase in the amount of time that the MLC leaves are in the field is likely the cause of the result indicating that increased MFs lead to more interplay effects observed. The dose blurring effects can be explained mathematically by the convolution of the static dose distribution with the motion kernel of the target. The motion kernels for the first 3.3 s, 30 s, and 163 s of the respiratory trace in Figure 2-4a are shown in Figure The first kernel is the PDF for one respiratory cycle, the second for the shortest delivery times, and the third for the longest delivery time. Differences can be seen between all three of the histograms. The small systematic shift towards higher motion amplitudes seen in Figure 2-4a is reflected in the histogram data. The changes in the histogram shapes can likely be attributed at least partially to the trend of less degradation of target coverage with increased treatment delivery times in Figure 2-6a. This trend cannot be fully attributed to interplay effects. To truly investigate whether treatment delivery time affects the amount of interplay, it would be necessary to use respiratory traces with no baseline drift, so that all of the motion kernel histograms were the same shape. 41

54 Figure 2-10: The PDFs (target motion kernels) for the first a) 3.3 s, b) 30 s, and c) 163 s of the respiratory trace in Figure 2-4a are shown. The PDFs corresponding to these times displayed are the duration of the first respiratory cycle, the shortest treatment delivery time, and the longest treatment delivery time. Distributions were generated by binning the respiratory motion amplitude value at each time in the respiratory trace (every 0.05 s) into 1 mm-wide bins. In the literature, it has been reported that interplay effects average out when the dose is delivered over the course of a conventional number of fractions. 66, 67, 69 While this interfraction averaging is not necessarily present in SBRT plans, there is likely intrafraction averaging. Seco et al. reported that in IMRT treatment plans, greater interplay effects were present when segments of fewer MUs were delivered because the beam-on times were so short. 83 The opposite case is present here; SBRT VMAT plans can be thought of as extremely long IMRT segments with many MUs, leading to intrafraction averaging. That is, each part of the tumour is irradiated many times during a VMAT SBRT arc, so it is less likely that any interplay between part of the target and an MLC leaf would be repeated in exactly the same way enough times for dosimetric effects to accumulate to non-negligible levels. This is supported by the observation of greater 42

55 dosimetric effects for plans with shorter delivery times in this study. The data was plotted according to treatment delivery time to account for this intrafraction averaging. It should be noted that intrafraction averaging in SBRT arcs is due to a long beam-on time, and not due to the large amount of dose delivered. This means that when a treatment is delivered with a higher dose rate, which is possible with a flattening filter-free (FFF) beam, this intrafraction averaging may not be present. One assumption that is made in this work is that the respiratory motion can be accurately represented by a rigid translation exclusively in the SI direction. While it has been reported that liver motion is predominantly in the SI direction, 40, 46, 48 it is known that a rigid translation is not an accurate representation, especially at the periphery of the organ. 46 Although rigid motion may not be an accurate model for respiratory motion in liver, 84, 85 the effects of heterogeneities that yield dosimetric errors when assuming rigid translation are not applicable when motion is simulated in a homogeneous phantom, as done in this study. An additional source of error relates to the shape of the tumour present in patients. Patient treatment plans are different than those created for a homogeneous phantom. Patient target volumes are often non-spherical or multifocal and can be close to OARs. This can lead to highly conformal and asymmetric dose distributions with extremely sharp dose gradients, which were not fully explored in this study. It should be noted that the program developed for simulating respiratory motion is limited in its ability to accurately introduce motion because of the nature of the DICOM-RT file. The positional information for the MLC leaves only exists at CPs. Furthermore, the dose is only calculated by the TPS at CPs. For plans that are highly modulated and/or deliver a lot of dose, the delivery time is quite long, so more time elapses between CPs, resulting in coarser sampling 43

56 of the respiratory trace. This leads to dose calculations that may not accurately represent the MLC leaf patterns with respiratory motion. A solution to this limitation is described in detail in section Conclusion A method was developed to simulate rigid SI respiratory motion in VMAT SBRT plans created for a digital liver phantom. For these plans, more dosimetric differences were observed in the ITV for plans with more MLC leaf modulation. For plans with no baseline drift, greater degradation to the ITV coverage was seen for shorter delivery times. The converse is true when baseline drift is present. This investigation modeled both dose blurring and interplay effects. While dose differences due to interplay are not isolated from those due to dose blurring, it is assumed that the differences in ITV coverage can be partially attributed to interplay. Further investigation is required before these conclusions are applied to patient anatomies, and additional work is required to identify the magnitude of dose differences that can be attributed to interplay and the clinical significance of these dose differences. 44

57 Chapter Three: Patient Simulations 3.1 Overview Chapter two concluded that in VMAT liver SBRT plans created for a digital phantom, an increased amount of plan modulation caused more dosimetric effects that are likely due to interplay. The results and limitations from the phantom study led into the work reported in this chapter. This project aimed to determine whether the relationship between MF and interplay holds true for patient treatment plans. In contrast to the digital phantom, patients have the added complexity of tissue heterogeneities, OARs close to lesions, and often non-spherical tumours. These geometrical factors cause the VMAT optimizer to make different treatment plans for every patient anatomy that will provide a more complete picture of clinical treatment plans. Furthermore, the assumption that respiratory motion can be accurately modelled as a rigid translation in the liver may become less accurate with the presence of tissue heterogeneities. This chapter also addresses the issue of the combined effects of dose blurring and interplay. Unlike in chapter two, here interplay effects are isolated from the larger effects of dose blurring. The relationship between treatment delivery time and interplay effects is not pursued in this chapter. While interesting, it lacks clinical relevance as the increasing delivery time to minimize interplay effects is not practical in the clinical setting. 3.2 Materials and Methods Patient selection Ten patients previously treated for single lesions in the liver were selected for this study. The clinical treatment plans for these patients had been made as per the SBRT dose 45

58 specifications outlined in RTOG 1112 clinical trial. 80 This protocol prescribes 50 Gy in 5 fractions, and if the mean liver dose (MLD) or an OAR dose constraint cannot be met, the dose prescription is reduced by 5 Gy increments to a lower limit of 30 Gy in 5 fractions. Only patients that could be planned to the highest prescription dose were included in this study. This excluded patients with lesions that were extremely large, multifocal, and/or that were directly abutting, or extremely close to, OARs. Ten patients selected for study had tumours ranging from cm 3. Patients were grouped by the minimum distance from the superior edge of the tumour to the dome of the liver. Patients were categorized as having lesions in direct contact with the liver dome, < 1.8 cm from the dome but not in contact with the dome, or 1.8 cm from the dome. The tumour-dome distance of 1.8 cm was selected because this was the maximum amplitude of target motion used in motion simulation. For patients where this distance is 1.8 cm, the target volume is moved into the lung tissue when motion was simulated. Selected tumour and planning characteristics from the ten study patients are listed in Table

59 Table 3-1: The GTV volume, GTV SI length, target-dome distance, and MFs for both of the patient treatment plans, as discussed in 3.2.2, are listed for each patient. The GTV SI length is measured as the GTV s maximum length in the SI direction. The tumour-dome distance is measured at the minimum SI distance between the GTV and the dome of the liver. Patient GTV Volume GTV SI length Tumour-Dome (cm 3 ) (cm) Distance (cm) Low MF High MF < < < < Treatment Planning Two VMAT plans with low and high amounts of modulation were created for each patient as outlined in Table 3-1. The MF was increased by increasing the severity of the planning constraints on artificial shell structures, as discussed in section The mean percent increase in MF from the low to high modulation plans was 14%, and at least 5% for all patients. All plans were delivered using two 180 arcs spanning gantry angles from 0 to -180, along the patient s right side with a 6 MV photon treatment beam at a maximum dose rate of 600 MU/minute. The GTV from the original patient treatment plans was used and a 1.8 cm inferior extension of the GTV was made to create the ITV (Figure 3-1). This simulated a scenario where the GTV was contoured on, and the treatment plan was made on an end-expiration CT scan. A motion amplitude, and therefore ITV margin, of 1.8 cm was chosen based on the mean values for SI liver motion reported in the literature (Table 1-3). The same amplitude of motion was used for each patient to isolate the effects of interplay by excluding the effect of variable tumour motion 47

60 on dosimetric outcomes. No PTV margin was used as set-up errors were not modelled in this study. Treatment plans were made to deliver 54 Gy in 3 fractions to the ITV, and followed the planning criteria outlined in the RAS liver trial protocol. 86 All treatment plans were made such that 100% of the ITV was covered by at least 95% of the prescription dose and 98% of the ITV was covered by 100% of the prescription dose. The MLD was kept below 15 Gy and at least 700 cc of the uninvolved liver was spared to 15 Gy. The full list of planning constraints is provided in Table 3-2. Figure 3-1: The original GTV contour (green) from all treatment plans was used. The ITV was created by extending the GTV 1.8 cm inferiorly (orange). The example shown is for patient six, belonging to the group with a tumour-dome distance of < 1.8 cm. 48

61 Table 3-2: The planning criteria used for treatment plans, as outlined in the RAS liver trial. 86 Structure Planning Constraint V 100 > 98% ITV V 95 > 100% D max < 133% Non-ITV D max < 120% Liver minus GTV MLD < 15 Gy V <15 Gy > 700 cc Stomach Duodenum Esophagus D 0.5 cc < 21Gy Small Bowel Large Bowel Chest Wall D 0.5 cc < 50 Gy Gallbladder D 0.5 cc < 55 Gy Heart D 1 cc < 30 Gy Kidneys Bilateral mean dose < 10 Gy Ipsilateral Lung V 20 Gy < 10% of total lung volume V 13 Gy < 1000 cc As mentioned previously, two plans were made for each patient with different amounts of modulation. The MF used here is the same as the one defined in chapter 2: MF = Number of Monitor Units per Fraction Dose per Fraction (3-1) This definition of MF describes the amount of MLC leaf modulation using only on the number of MUs required to deliver a specific dose. In reality, the number of MUs required to deliver a specific dose does not depend only on the amount on plan modulation, but on two patientspecific factors as well. First, the depth of the target in the patient and the type of tissue that the beam must pass through to reach the target will affect the number of MUs required to deliver a prescribed dose, and will therefore affect the MF if this definition is used. Secondly, the number 49

62 of MUs will be dependent on the field sizes used in a treatment. For targets that are small, the MLC leaves will generally create smaller apertures, and the amounts of phantom scatter and collimator scatter will be smaller, meaning more MUs will be required to achieve a desired dose. This will also affect this definition of MF. These two factors, target size and target depth, will vary between patients, but will not vary for a single patient anatomy. The same MF will describe different levels of MLC leaf modulation for different patients, so MFs are compared only for the same patient, and not used to draw inter-patient comparisons. Because of this, no effort was made to plan all patients to similar MFs; plans were constructed such that each patient had two plans with relatively lower and higher amounts of MLC leaf modulation Respiratory Trace Generation Three respiratory traces were created using the custom feature in the Respiratory Trace Generator. 82 The period and amplitude were set to 4 s and 1.6 cm with some variability introduced to more closely replicate typical breathing patterns in patients. The amplitude was allowed to vary up to 1.8 cm, such that the ITV would encompass the full extent of target motion. No baseline drift was used as the effects of this phenomenon were not modelled in this study. A different respiratory trace was used in each of the three fractions. Small variations in amplitude and respiratory cycle length for different fractions are seen in Figure

63 Figure 3-2: The respiratory traces used in fractions 1-3 for motion simulation in all ten patient treatment plans. Traces were created using the Respiratory Trace Generator. 82 The amplitude of motion is 1.6 cm and the respiratory cycle period is 4 s. Small variations in the motion amplitudes and respiratory cycle lengths are visible between fractions Control Point Sampling Resolution It was identified in chapter two that the motion simulation program was limited in its ability to sample respiratory traces, especially for highly modulated plans, because of the long times between CPs that occur as a result of their coarse angular spacing. To overcome this limitation, once the optimization was complete and a treatment plan was finalized, each original arc (denoted arc a) in the VMAT treatment plan was triplicated, creating arcs denoted b and c. The gantry angles of the CPs for arcs b and c were then shifted such that they occurred at onethird and two-thirds of the time between consecutive CPs in the original arc, a. This was done by calculating the time that elapses between two consecutive CPs, CP n and CP n+1, in the first arc, arc a, and assigning times to the CPs in arcs b and c: 51

64 t( bcpn) = 1 (t( CP 3 a n+1) t( acpn)) (3-2) t( ccpn) = 2 (t( CP 3 a n+1) t( acpn)) (3-3) The gantry angles corresponding to the new times for the CPs in arcs b and c were then calculated using the information in the DICOM-RT file about the gantry speed and dose rate for acpn and acpn+1, as described in section The original and adjusted sampling can be seen in Figure 3-3. Figure 3-3: a) The CPs provided by the VMAT optimizer for a highly modulated plan are shown on the respiratory trace. The respiratory trace is not sampled at a high enough frequency to accurately model respiratory motion. b) With the addition of CPs from two extra arcs, the respiratory trace is sampled much more accurately. 52

65 This process effectively triples the number of CPs in each arc and triples the amount of dose delivered. The dose for each arc was not reduced by a factor of three to account for this because this would have changed the treatment delivery times and dose rates for each arc. Instead, the dose was re-calculated with the shifted MLC patterns, and the dose distribution was scaled appropriately afterwards Motion Simulation Once the new CPs had been assigned appropriate gantry angles and times, the MLC positions at each CP in each arc were shifted by the amplitude of the respiratory trace, as described in section This was done in two ways. First, to represent a realistic scenario, a different starting point in the respiratory cycle was randomly selected for each of the three treatment fractions. This simulates a clinical situation, where the beam would be turned on at a random point in the patient s respiratory cycle for each fraction. In this scenario, when comparing plans with motion simulated to the original plans, dosimetric effects are attributed to dose blurring and interplay. Second, to isolate the interplay effects from dose blurring effects, motion was simulated using four different specified starting points, or beam-on times, in the respiratory cycle (Figure 3-4). Simulating motion using different starting points in the respiratory cycles leads to different interactions between the target and MLC leaves, making dosimetric effects due to interplay visible. When comparing treatment plans with motion simulated using different starting points in the respiratory cycle, dosimetric differences between these plans are attributed exclusively to interplay effects. To simulate a worst-case scenario, and to make the effects of interplay more prominent, the same starting point was used in each of the three fractions. 53

66 Figure 3-4: To isolate interplay effects, motion was simulated using four different starting points in the respiratory cycle as beam-on times. The four starting points are indicated by green circles. After motion simulation, the treatment plans were then re-imported into Eclipse and the dose was re-calculated for the new MLC patterns. It should be noted that Eclipse calculates the dose at each CP, and not for MLC positions in between CPs, so although each arc does not sample consecutive CPs, the simulation should yield the same results as it would if one arc sampled all of the CPs consecutively. This process was repeated for both of the VMAT plans for each of the ten patients Plan Evaluation Combined Effects of Dose Blurring and Interplay In order to evaluate the combined dosimetric effects of dose blurring and interplay, the static plans were compared to plans with respiratory motion simulated using a random starting point in the respiratory cycle for each fraction. These plans are representative of a realistic scenario and were used to evaluate overall plan quality. The target coverage was evaluated by 54

67 ensuring that the GTV met at least the minimum ITV planning constraints outlined in Table 3-2. After motion simulation, the GTV moved within the ITV. Because the ITV was created to account for GTV motion of 1.8 cm, any dosimetric differences in the GTV would be caused by interplay effects. The ITV margin accounts for dose blurring at the superior and inferior target edges. In addition, the MLD, which is measured using the liver volume minus the GTV volume, was measured to ensure that it did not exceed 15 Gy. Liver dose was further evaluated by ensuring that at least 700 cc of liver was spared to 15 Gy. All other planning constraints listed in Table 3-2 were also examined to evaluate plan quality Isolating the Effects of Interplay In order to isolate interplay effects from dose blurring effects, the dosimetric differences caused by using different beam-on timings was examined. For each treatment plan, motion was simulated using four different specified starting points in the respiratory cycle and the same beam-on time was used for all three fractions. Each of these four resultant dose distributions were subtracted from each other using A Computational Environment for Radiotherapy Research (CERR), 87 yielding six dose-difference maps. These dose differences are due to interplay effects caused by using beam-on timings at different phases of the respiratory cycle. The dose differences inside the GTV on the dose-difference maps were evaluated by plotting a differential dose-difference volume histogram for the GTV. The spread of these histograms was quantified by calculating the standard deviation. A more spread out histogram, or one with a larger standard deviation, is representative of dose differences in the GTV that are more prevalent and larger in magnitude. The medians of the six standard deviations were compared between the low 55

68 modulation plans and the high modulation plans using a Wilcoxon signed-rank test to determine if the relationship between MF and dose difference due to interplay was statistically significant. 3.3 Results Combined Effects of Dose Blurring and Interplay The overall plan quality, including dosimetric effects caused by dose blurring and interplay, was examined through DVH analysis. The dose to the uninvolved liver (liver minus GTV) did not exceed MLD tolerance of 15 Gy, and the volume of liver spared to 15 Gy was greater than 700 cc in all plans. For patients where the GTV was in direct contact with the dome of the liver, or was less than 1.8 cm inferior to the dome of the liver, the MLD decreased when respiratory motion was introduced. An overall decrease in liver dose, and therefore lower MLD, can be seen in the DVH for patient six in Figure 3-5. The MLD increased for all patients with lesions greater than 1.8 cm inferior to the dome of the liver, but did not exceed the planning constraint of 15 Gy in any of the ten patients. 56

69 Figure 3-5: Cumulative DVHs for the GTV, ITV, and uninvolved liver (liver minus GTV) for a typical static plan, and the corresponding plan with a random starting phase for each of the three fractions. Patient six s high MF plan is shown. Similar results were seen for both levels of plan modulation in all ten patients. The dose to the ITV decreased for all treatment plans, as was expected due to dose blurring (Figure 3-5). The GTV coverage was deemed acceptable after respiratory motion simulation in all treatment plans because the GTV coverage met or exceeded the original ITV planning criteria. The changes in planning constraints for each plan caused by dose blurring and interplay are listed in Tables 3-3 and

70 Patient Table 3-3: The percentage change in target dose-volume planning constraints for the target volumes between the original treatment plan and the treatment plan with motion simulated using random starting points in the respiratory cycle for each of the three fractions. For each patient, the first row contains data from the low MF plan and the second row contains data from the high MF plan. A positive (negative) value indicates that the constraint increased (decreased) when motion was simulated in the treatment plan. None of the target planning constraints were exceeded in any of the treatment plans. The first three patients had GTVs in direct contact with the dome of the liver. Patients 4-7 and 8-10 had GTVs < 1.8 cm and 1.8 cm from the dome of the liver, respectively. The three groups are separated by horizontal lines. Target Volume GTV ITV Constraint V 100 V 95 D max V 100 V 95 D max 1 0.7% 0.0% 0.7% -22.4% -19.4% 0.7% 2.0% 0.1% 0.9% -21.9% -19.5% 0.6% 2 0.6% 0.0% 3.9% -18.4% -16.5% 3.9% 0.6% 0.0% 3.6% -18.4% -16.5% 3.6% 3-0.2% 0.0% -0.5% -21.4% -17.1% -0.5% 0.9% 0.0% -0.5% -20.8% -17.8% -0.5% 4 1.3% 0.1% -0.5% -17.7% -15.7% -0.5% 1.2% 0.1% 0.1% -16.6% -14.8% -0.6% 5 1.2% 0.0% 2.6% -27.9% -25.3% 2.6% 0.4% 0.0% 0.8% -28.4% -26.1% 0.3% 6 1.6% 0.1% 1.5% -23.2% -21.5% 1.4% 1.6% 0.0% 1.2% -23.1% -21.1% 1.0% 7 1.6% 0.3% -6.6% -20.9% -18.4% -8.4% 0.9% 0.1% -0.8% -23.2% -20.6% -0.8% 8 2.1% 0.7% -4.8% -31.8% -29.4% -6.4% 3.3% 0.4% -4.5% -31.7% -29.8% -5.8% 9 1.2% 0.0% 1.1% -31.4% -28.8% 1.1% 1.3% 0.0% -0.3% -32.2% -30.2% -0.3% % 0.0% 4.9% -21.3% -19.3% 4.9% 1.5% 0.1% 5.6% -23.0% -20.5% 4.0% 58

71 Patient Ipsilateral Lung Kidneys Heart Gall Bladder Chest Wall Large Bowel Small Bowel Esophagus Duodenum Stomach Liver- GTV Table 3-4: The percentage change in OAR dose-volume planning constraints between the original treatment plan and the treatment plan with motion simulated using random starting points in the respiratory cycle for each of the three fractions. For each patient, the first row contains data from the low MF plan and the second row contains data from the high MF plan. A positive (negative) value indicates that the constraint increased (decreased) when motion was simulated in the treatment plan. None of the OAR planning constraints were exceeded in any of the treatment plans. Horizontal lines group patients by tumour location, as in Table 3-3. OAR Constraint Mean V<15Gy D 0.5 cc D 1 cc Mean V 13 Gy V 20 Gy % 4.0% -5.2% 57.2% 70.2% -12.8% 4.1% -4.4% 57.0% 68.1% 2-7.8% 3.8% -28.0% 10.5% -34.0% 96.7% 69.3% 80.6% -7.8% 3.9% -28.3% 6.0% -37.7% 99.5% 73.9% 82.7% % 5.0% % % % % -99.9% % % -20.9% 68.1% 84.3% -17.6% 4.9% -8.6% -18.7% 7.6% -29.9% 2.3% -21.6% 36.5% -20.8% 69.9% 82.5% 4-1.3% 0.5% 7.9% 18.1% -14.1% -1.2% 0.4% 5.6% 22.9% 36.8% % 0.9% -7.5% -22.9% -7.7% -70.0% -28.4% 64.3% -12.8% 0.9% -8.2% -22.7% -8.1% -67.0% -27.0% 60.5% % 1.3% 4.4% 6.7% 24.2% 103.9% 117.0% -15.9% 1.3% 1.5% 2.5% 24.0% 103.4% 127.6% 7-4.5% 1.2% 5.1% -27.0% 19.3% -31.3% -10.4% 0.9% -56.1% 33.5% -27.7% 111.6% 106.6% -4.8% 1.1% -7.7% -29.6% 9.4% -40.5% -21.2% -3.1% -59.2% 37.9% -22.2% 122.9% 163.5% 8 6.8% -1.1% 40.0% -40.4% 105.1% -39.4% -26.3% 367.3% 28.4% -53.5% 7.8% -1.0% 39.2% -45.6% 89.7% -34.6% -21.2% 372.2% 27.1% -50.7% % -0.4% -3.8% -52.3% 25.2% -49.3% 3.1% -44.5% 27.1% -12.5% 10.4% -0.3% -6.4% -56.9% 23.0% -49.7% 9.2% -47.7% 26.3% -13.7% % -3.6% 25.0% -43.5% 111.7% 106.4% 6.4% -3.8% 26.3% -43.5% 120.3% 92.1% 59

72 3.3.2 Isolating the Effects of Interplay For all treatment plans, the GTV coverage was nearly identical after respiratory motion was simulated with four different starting times. An example of this is seen in Figure 3-6 for a highly modulated treatment plan. Some variation is visible between the DVHs of the GTV for different starting points in the respiratory cycle, indicating the presence of some interplay effects. To ensure plan quality was acceptable when motion was simulated for the same beam-on timing for each fraction, the GTV coverage was examined and it was found that the GTV coverage was not degraded below the ITV planning constraints in any of the treatment plans for any starting point. Figure 3-6: Cumulative DVHs for the GTVs for treatment plans created when motion is simulated using specific starting points in patient six s highly modulated treatment plan. The DVH of the GTV coverage is very minimally different when motion is simulated using different starting points in the respiratory cycle. Similar results were observed for all treatment plans. 60

73 An example of a dose-difference map that results when two dose maps created using two different beam-on timings were subtracted from each other is shown in Figure 3-7. It can be seen qualitatively that there are more, and larger, dose differences in the GTV and surrounding liver for the more highly modulated plan than for the less modulated plan. Figure 3-7: Example dose-difference maps on the same slice from a dose subtraction of two plans. Each plan was created by simulating respiratory motion using the same starting point (endinspiration for one plan and end-expiration for the other) in the respiratory trace for all three fractions. This example is for patient six. The GTV is delineated with a red contour and the liver with an orange contour. Figure 3-8 shows the differential dose-difference volume histograms of the GTV for the six dose-difference maps for patient six s treatment plans. The histograms for the more highly modulated plan are more spread out, indicating the presence of larger dose variation in the GTV 61