UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A four dimensional volumetric modulated arc therapy planning system for stereotactic body radiation therapy… Chin, Erika Ming Yee 2013

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2013_spring_chin_erika.pdf [ 3.32MB ]
Metadata
JSON: 24-1.0073633.json
JSON-LD: 24-1.0073633-ld.json
RDF/XML (Pretty): 24-1.0073633-rdf.xml
RDF/JSON: 24-1.0073633-rdf.json
Turtle: 24-1.0073633-turtle.txt
N-Triples: 24-1.0073633-rdf-ntriples.txt
Original Record: 24-1.0073633-source.json
Full Text
24-1.0073633-fulltext.txt
Citation
24-1.0073633.ris

Full Text

A Four Dimensional Volumetric Modulated Arc Therapy Planning System for Stereotactic Body Radiation Therapy in Lung Cancers by Erika Ming Yee Chin B.Sc., University of British Columbia, 2005 M.Sc., McGill University, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES (Physics)  The University of British Columbia (Vancouver) March 2013  © Erika Ming Yee Chin, 2013  Abstract A novel 4D volumetric modulated arc therapy (4D VMAT) planning system is presented where radiation sparing of organs at risk (OARs) is enhanced by exploiting relative target and healthy tissue motion induced by patient respiration. In conventional radiation therapy, a motion encompassing margin is normally added to the clinical target volume (CTV) to ensure the tumour receives the planned treatment dose. For lung tumours which display large displacements due to patient breathing, this results in a substantial increase in dose to the OARs.  These wider margins are incompatible with the growing clinical use of  stereotactic body radiation therapy (SBRT) in lung cancer treatment. The ablative dose fractions of SBRT are correlated to significantly better survival rates but also increase the risk of serious normal tissue injury. The 4D VMAT system aims to reduce OAR dose by incorporating 4D CT information on volumetric target and OAR motions directly into the optimization process. The resulting treatment plans have respiratory phase-optimized radiation beam apertures whose deliveries are synchronized to the patient’s respiratory cycle. The performance of the 4D VMAT system was evaluated by comparing against other tumour motion compensation techniques such as 3D VMAT, gated VMAT and tracked VMAT for a range of tumour motions in both phantom simulations and on SBRT eligible patient 4D CT data. Results showed that 4D VMAT's ability to spare healthy tissue is superior to 3D VMAT and tracked VMAT. 4D VMAT treatment plan quality relative to gated VMAT is similar and in certain cases, depending on the spatial relationship between anatomical structures, it can be superior. Further dose escalation is possible with 4D VMAT and gated VMAT, but 4D VMAT has the advantage of faster treatment times which are only 11-25% longer than 3D VMAT, whereas gated VMAT are 77-148% longer. Lastly, although 4D VMAT is a ii  respiration synchronized technique, preliminary tests showed that treatment plan quality can be robust to some desynchronization delivery errors caused by irregular patient breathing. This thesis concludes with a detailed discussion on the subsequent investigative tasks that must be conducted to bring 4D VMAT nearer to clinical implementation.  iii  Preface The work in Chapter 4 has been published as:   E. Chin and K. Otto, “Investigation of a novel algorithm for true 4D-VMAT planning with comparison to tracked, gated and static delivery,” Med. Phys. 38:2698-2707 (2011).  I am the first and corresponding author of this publication. I completed the work with guidance provided by Dr. Otto. This publication was specially featured in:    J. Hewett, "Including motion optimizes VMAT plans," Medical Physics Web, June 27, 2011. http://medicalphysicsweb.org/cws/article/research/46353    U. Lula, "A novel 4D-VMAT planning algorithm: a simulation study," IPEM SCOPE (UK), vol. 20, issue 3, Sep 2011. http://www.ipem.ac.uk/SiteCollectionDocuments/Publications/ESCOPE%20full%20versions/Sept%202011.pdf  The work in Chapter 5 has been published as a featured article in:   E. Chin, S. Loewen, A. Nichol and K. Otto, "4D VMAT, gated VMAT, and 3D VMAT for stereotactic body radiation therapy in lung," Phys. Med. Biol. 58:749-70 (2013).  I am the first and corresponding author of this publication. I completed the majority of the work. Dr. Otto provided advice and sample code of 1D path length correction for tissue inhomogeneity. Dr. Loewen and Dr. Nichol provided clinical expertise on lung cancer treatment and aided in the contouring of structures in 4D CT data. This publication was specially featured in:  iv    J. Dineley, "4D VMAT spares tissue, speeds treatment," Medical Physics Web, Feb 26, 2013. http://medicalphysicsweb.org/cws/article/research/52508  v  Table of Contents Abstract ................................................................................................................................... ii Preface .................................................................................................................................... iv Table of Contents ................................................................................................................... vi List of Tables ........................................................................................................................... x List of Figures ........................................................................................................................ xi Glossary .............................................................................................................................. xviii Acknowledgements .............................................................................................................. xxi 1 Overview of Thesis.............................................................................................................. 1 2 Introduction to Radiation Therapy................................................................................... 5 2.1 Ionizing Radiation ......................................................................................................... 5 2.2 Photon Interactions ........................................................................................................ 6 2.2.1 Photoelectric Effect ................................................................................................ 7 2.2.2 Compton Scattering ................................................................................................ 8 2.2.3 Pair Production ....................................................................................................... 9 2.2.4 Atomic Shell Vacancies ........................................................................................ 10 2.3 Electron Interactions .................................................................................................... 10 2.4 Radiation Biology ........................................................................................................ 11 2.4.1 Linear Energy Transfer ......................................................................................... 11 2.4.2 Direct and Indirect Action .................................................................................... 11 2.4.3 DNA Damage from Ionizing Radiation ................................................................ 12 2.4.4 Therapeutic Ratio of Radiation Therapy .............................................................. 13 vi  2.5 Treatment Delivery Equipment ................................................................................... 14 2.5.1 Linear Accelerator & Photon Beams .................................................................... 15 2.5.2 Integrated Treatment/Imaging Systems ................................................................ 17 2.6 Radiation Treatment Planning ..................................................................................... 18 2.6.1 Planning Volumes ................................................................................................. 19 2.6.2 Plan Delivery Schedule: Conventional Fractionation........................................... 20 2.6.3 Plan Evaluation: Dose Volume Histograms ......................................................... 21 2.7 Intensity-Modulated Radiation Therapy ...................................................................... 22 2.7.1 Dose-Volume Constraints..................................................................................... 24 2.7.2 Objective Function................................................................................................ 25 2.7.3 Optimization Algorithms ...................................................................................... 28 2.7.4 Treatment Parameters ........................................................................................... 31 2.7.5 Dose Calculation: Pencil-Beam Algorithm .......................................................... 34 3 Lung Cancer & Motion Management Strategies ........................................................... 36 3.1 Lung Cancer................................................................................................................. 36 3.2 Stereotactic Body Radiation Therapy .......................................................................... 37 3.2.1 SBRT Mechanism of Action ................................................................................ 38 3.3 Lung Tumour Motion .................................................................................................. 39 3.3.1 Effect of Motion on Dose Distribution ................................................................. 40 3.3.2 4D Dose Calculation ............................................................................................. 41 3.4 Management of Respiratory Motion ............................................................................ 42 3.4.1 Motion Encompassing Methods ........................................................................... 42 3.4.2 Forced Shallow-Breathing Method....................................................................... 44 3.4.3 Breath-Hold Techniques ....................................................................................... 44 3.4.4 Respiratory Gated Techniques .............................................................................. 46 3.4.5 Respiration Synchronized Techniques ................................................................. 47 4 Implementation and Evaluation of 4D VMAT for Periodically Moving Tumours .... 52 4.1 Introduction to VMAT ................................................................................................. 52 4.2 Development of VMAT ............................................................................................... 53 4.2.1 Forward Planning.................................................................................................. 54 vii  4.2.2 Inverse Planning ................................................................................................... 56 4.3 VMAT Algorithm ........................................................................................................ 59 4.3.1 Angle Dependent Optimization Constraints ......................................................... 59 4.3.2 Progressive Beam Sampling ................................................................................. 62 4.4 4D VMAT System ....................................................................................................... 65 4.5 The Potential for Healthy Tissue Sparing in 4D VMAT ............................................. 68 4.5.1 Motivation............................................................................................................. 68 4.5.2 Methods ................................................................................................................ 69 4.5.3 Results .................................................................................................................. 73 4.5.4 Discussion ............................................................................................................. 80 4.5.5 Conclusion ............................................................................................................ 84 5 4D VMAT, Gated VMAT and 3D VMAT for SBRT in Lung Cancers ....................... 85 5.1 4D Treatment Planning Incorporating 4D CT Patient Data ........................................ 85 5.1.1 Image Registration ................................................................................................ 85 5.1.2 Tissue Inhomogeneity Correction ........................................................................ 87 5.1.3 Monte Carlo Dose Calculation ............................................................................. 89 5.2 Motivation.................................................................................................................... 91 5.3 Methods ....................................................................................................................... 92 5.3.1 Patient Data ........................................................................................................... 92 5.3.2 Dose Calculation ................................................................................................... 94 5.3.3 Treatment Planning Process ................................................................................. 96 5.3.4 CT Phase Bias in 4D VMAT Optimization ........................................................ 100 5.3.5 4D VMAT Treatment Delivery Time ................................................................. 103 5.3.6 Robustness of 4D VMAT Delivery to Desynchronization ................................. 106 5.4 Results ....................................................................................................................... 108 5.4.1 4D VMAT, Gated VMAT and 3D VMAT Treatment Plans .............................. 108 5.4.2 CT Phase Bias in 4D VMAT Optimization ........................................................ 113 5.4.3 Treatment Delivery Times .................................................................................. 114 5.4.4 Robustness of 4D VMAT Delivery to Desynchronization ................................. 117 5.5 Discussion .................................................................................................................. 119 5.6 Conclusion ................................................................................................................. 122 viii  6 Conclusions and Future Work ...................................................................................... 124 6.1 Conclusions ............................................................................................................... 124 6.2 Future Work ............................................................................................................... 127 Bibliography ........................................................................................................................ 131  ix  List of Tables Table 5.1: List of tissue inhomogeneity corrections algorithms categorized by level of anatomy sampled (1D or 3D) and inclusion or exclusion of electron transport. Methods are listed in increasing order of complexity, accuracy and computational time (adapted from [121]). ................................................ 88 Table 5.2: Sample of SBRT dose constraints used in lung treatment planning (48 Gy in 4 fractions). ...................................................................................................... 97 Table 5.3: 4D VMAT optimization parameters for treatment of NSCLC patients with SBRT prescription of 48 Gy in 4 fractions. 4D CT data was divided into 10 respiratory phases. ..................................................................................... 106 Table 5.4: Factors that affect the length of time random delivery errors can occur before being detected and corrected by an on-line imaging system. ............. 107 Table 5.5: Lung doses for patients A, B, and C treated with gated VMAT, 4D VMAT, and 3D VMAT. .............................................................................................. 111 Table 5.6: Treatment times for 3D VMAT, 4D VMAT and gated VMAT to deliver a 12 Gy fraction. Note that 3D VMAT and gated VMAT treatment times are not dependent on the patient's respiratory period..................................... 115 Table 5.7: Robustness of 4D VMAT to random treatment delivery errors. Beam aperture deliveries were randomly desynchronized from their intended respiratory phases. .......................................................................................... 118 Table 5.8: Listing of the treatment technique characteristics that can improve plan quality when highly mobile tumours are present. .......................................... 119  x  List of Figures Figure 2.1: The relative predominance of the photoelectric effect, Compton scattering and pair production as a function of atomic number Z and photon energy. ...... 6 Figure 2.2: Compton scattering schematic diagram. Incident photon interacts with loosely bound orbital electron. Part of the photon energy is transferred to the electron ejecting it from the atom and a scattered photon with lower energy is created................................................................................................. 8 Figure 2.3: The therapeutic ratio for radiation therapy where the relationship between the tumour control dose-response and the normal tissue tolerance curves are (a) optimal, (b) unacceptable and (c) acceptable (adapted from [46]). ...... 14 Figure 2.4: Schematic of the various components in a linear accelerator used for creating photon and electron beams. ................................................................ 16 Figure 2.5: (a) Schematic of the components in the linac treatment head. (b) Beam's eye view through the MLC (Image courtesy of Varian Medical Systems Inc., All rights reserved). ................................................................................. 17 Figure 2.6: (a) Linac equipped with an EPID.  (b) Linac equipped with an OBI.  (Images courtesy of Varian Medical Systems Inc., All rights reserved) ......... 18 Figure 2.7: (a) Illustration of in-room stereoscopic X-ray imaging. (b) Illustration of in-room infrared tracking of reflective markers on a patient surface. (Images courtesy of Brainlab, All rights reserved) .......................................... 18 Figure 2.8: Illustration of the planning volumes in radiation therapy. ................................ 20 Figure 2.9: (a) Ideal cumulative DVH. (b) Realistic cumulative DVH. ............................. 22 Figure 2.10: Simplified illustration of the cross-section of a rectangular radiation field that has been subdivided into beamlets of (a) varying intensities or (b) uniform intensities. .......................................................................................... 23 xi  Figure 2.11: Schematic of IMRT optimization. Starting with non-optimal treatment parameters, x, the resultant dose distribution is calculated and evaluated using the objective function. If the value of the objective function has converged to a minimum, the loop is exited; otherwise new treatment parameters are found using the optimization algorithm and the whole process is repeated (Adapted from [52]). ......................................................... 24 Figure 2.12: (a) Example of a maximum dose-volume constraint on an OAR. (b) Example of a minimum and maximum dose-volume constraint on the target (adapted from [51]). ............................................................................... 25 Figure 2.13: Example of a DVH where the critical structure has 2 maximal dosevolume constraints (red triangles) while the target has 1 maximal and 1 minimal (blue triangle) dose-volume constraint. Shaded green and blue areas indicate portions of the structures that do not meet the desired constraints. ....................................................................................................... 27 Figure 2.14: DVHs of an OAR where the dose constraint is represented by the shaded area.  The likelihood of optimization achieving the desired constraint  depends on the magnitude of the relative constraint weight. (a) Constraint was not met. (b) Constraint was met (adapted from [51]). .............................. 28 Figure 2.15: Simplified illustrations of a 1-D (a) convex and (b) non-convex objective function. ........................................................................................................... 29 Figure 2.16: Example of a fluence map decomposed into 3 MLC apertures of equal weights. ............................................................................................................ 33 Figure 3.1: Examples of (a) an asymmetric sinusoidal trace of a respiratory motion and (b) lung tumour trajectory with hysteresis. ...................................................... 40 Figure 3.2: A simple 1D dose profile from an open field at a set depth in water. Blue represents the static plan where points within a radius of 35 mm receive 100% of the dose. As motion increases, the radius of the field receiving 100% of the dose decreases and the beam penumbra increases (red dashed and dotted lines). .............................................................................................. 41  xii  Figure 3.3: Illustration of the motion encompassing method. The red sphere represents the tumour. The expanded blue surrounding is the PTV. (a) Static PTV (b) Enlarged PTV that encompasses the left/right motion of the tumour. ....... 43 Figure 3.4: Illustration of gated radiation delivery. The beam is only turned on when the tumour position is within the gating window. ............................................ 46 Figure 3.5: Diagram of the workflow when tumour tracking is performed (a) prior to treatment or (b) in real-time during treatment (adapted from [89]). ................ 50 Figure 4.1: Illustration of VMAT delivery.  Gantry rotates continuously during  radiation treatment. (Image from varian.mediaroom.com, image courtesy of Varian Medical Systems Inc., All rights reserved) ...................................... 53 Figure 4.2: Diagram showing different VMAT optimization strategies. For simplicity only 3 apertures are shown per control point. (a) Method where each sequenced beam aperture for a control point is delivered in a separate arc. (b) Method where all beam apertures of a control point are delivered in a single arc by spreading them out to other angles. (c) Method where several control points are grouped together and only 1 aperture from each control point is delivered. None of the delivered apertures in a group can have the same beam intensity........................................................................... 54 Figure 4.3: An illustrative explanation for (a) the beam MU weight change notation and (b) the linac dose rate notation. ................................................................. 60 Figure 4.4: Modeling of a continuous gantry arc using a progressive sampling of static beam angles. (a) At the start of optimization, the gantry range is coarsely sampled. (b) After a given amount of time, a new sample is added between two pre-existing samples.  (c)-(e) Further additions of beam  sample apertures to the optimizable set follow the illustrated pattern until the desired sampling frequency is attained. ..................................................... 63  xiii  Figure 4.5: (a) A schematic showing segmentation of the patient's respiratory cycle into multiple phases. Colours represent specific CT phases 1 through 6. (b) At the start of treatment plan optimization, the arc is coarsely sampled with few beam apertures. (c) As optimization progresses, more beams are inserted.  Numbers represent the order in which beam apertures are  introduced into the optimization process. (d) By the end of optimization, the arc is fully sampled and sequentially delivered beams correlate to sequential CT phases. The 4D CT data is sampled multiple times over the arc. Note that (a) - (d) are simplified illustrations. Real plan optimizations uses 4D CT data with 10 respiratory phases,  arcs, at least 177 beam  apertures per arc, and 1-3 arcs. ........................................................................ 66 Figure 4.6: Simulations were performed using phantom A (a) or phantom B (b). In phantom A, a cylindrical target was surrounded by a half-ring OAR. In phantom B, a spherical target was surrounded by a half-cup OAR. Surface contours (not shown) formed an elliptic cylinder body (semimajor axis 17.5 cm, semi-minor axis 12.5 cm) with a thickness of 15 cm. The target was centred in the middle of the body. ........................................... 70 Figure 4.7: The 2D-sagittal view of the simulated target motions for simulation set 1 (a), set 2 (b) and set 3 (c). Note that only half of the motion cycle is shown. .............................................................................................................. 70 Figure 4.8: DVH results for simulation set 1. Individual simulation plan constraints are set such that all simulations in the set achieve a similar PTV coverage (a). (b) and (c) display the DVHs for the OAR when motion amplitude of the cylindrical PTV was 1 cm and 2 cm respectively. 4D VMAT and DMLC ideal-tracking VMAT plans for PTV motion amplitude of 2 cm have almost identical OAR DVHs when collimator angle is 90° (d). ...................... 75 Figure 4.9: DVH results for simulation set 2 when motion amplitude of the cylindrical PTV was 1 cm (a) and 2 cm (b). ...................................................................... 76 Figure 4.10: DVH results for simulation set 3 when motion amplitude of the spherical PTV was 1 cm (a) and 2 cm (b). ...................................................................... 77  xiv  Figure 4.11: 4D VMAT DVHs for the OAR in simulation set 1 (a), set 2 (b) and set 3 (c) for PTV motions ranging from 0.5-2 cm. (d) DMLC ideal-tracking VMAT DVHs for the OAR in simulation set 3 for PTV motions ranging from 0.5-2 cm. .................................................................................................. 78 Figure 4.12: Illustration of the spatial relationship between the rotation of the linac beam and the target motion along (a) the anterior/posterior axis and (b) the superior/inferior axis. For target motion in the AP direction, the radiation beam will still pass through the target and OAR regardless of respiratory phase during a good portion of the arc. ............................................................ 79 Figure 5.1: CT data of NSCLC patients at max-exhale. (a) Patient A: stage IIA, 1.4 cm CC motion, gated duty cycle 40%. (b) Patient B: stage IB, 1.8 cm CC motion, gated duty cycle 60%. (c) Patient C: Stage IIA, 3.4 cm CC motion, gated duty cycle 50%. ......................................................................... 93 Figure 5.2: Visual verification of image registration results with the target image in green and the transformed source image in red. The yellow images are the result of superimposing the red and green images and reveal areas affected by registration errors. First, second and third rows correspond to patients A, B and C. ....................................................................................................... 94 Figure 5.3: DVHs for VMAT plans created on the max-exhale phase of (a) patient A and (b) patient C. Solid lines are for pencil-beam based dose calculations with electronic path length correction. Dashed lines are for rescaled MC based dose calculations. ................................................................................... 96 Figure 5.4: DVHs for patient C. (a) 4D dose calculation after 3D VMAT plan optimization showed that true dose to the target (4D GTV) was greater than expected (3D GTV). (b) 4D DVHs showing difference in dose distribution between 3D VMAT planned with D95 of 3D PTV receiving 100% of prescribed dose (dashed lines) and 3D VMAT planned with 4D GTV receiving the same target coverage as in 4D VMAT and gated VMAT (solid lines). ......................................................................................... 99  xv  Figure 5.5: (a) to (d) is the same as Figure 4.5 and is reproduced here to illustrate the contrast between the original beam insertion method and the balanced setup method (e). In the balanced setup, the new beam aperture insertion schedule more evenly employs the CTs from all respiratory phases during 4D VMAT treatment plan optimization. Note that the figure is highly simplified for visual clarity. Real plan optimizations used 4D CT data with 10 respiratory phases,  arcs, 177 beam apertures per arc and the  shift in selected beam position was only  . ............................................... 102  Figure 5.6: (a) Old plan optimization and (b) new plan optimization workflow for 4D VMAT. ........................................................................................................... 105 Figure 5.7: 4D DVH of selected OARs for patient A (motion 1.4 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT................. 109 Figure 5.8: 4D DVH of selected OARs for patient B (motion 1.8 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT................. 109 Figure 5.9: 4D DVH of selected OARs for patient C (motion 3.4 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT................. 110 Figure 5.10: 4D VMAT treatment apertures for patient A. Aperture weights are scaled by the mean weight. ....................................................................................... 111 Figure 5.11: 4D VMAT treatment apertures for patient B. Aperture weights are scaled by the mean weight. ....................................................................................... 112 Figure 5.12: 4D VMAT treatment apertures for patient C. Aperture weights are scaled by the mean weight. ....................................................................................... 112 Figure 5.13: 4D DVH for patient A (motion 1.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b). ..................................................... 113 Figure 5.14: 4D DVH for patient B (motion 1.8 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b). ..................................................... 114 Figure 5.15: 4D DVH for patient C (motion 3.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b). ..................................................... 114 xvi  Figure 5.16: 4D DVH for patient A (motion 1.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the  constraint for a patient respiratory  period of 3 s (a) and 6 s (b). ........................................................................... 116 Figure 5.17: 4D DVH for patient B (motion 1.8 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the  constraint for a patient respiratory  period of 3 s (a) and 6 s (b). ........................................................................... 116 Figure 5.18: 4D DVH for patient C (motion 3.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the  constraint for a patient respiratory  period of 3 s (a) and 6 s (b). ........................................................................... 117 Figure 5.19: (a) Example of 4D VMAT DVH for systematic error: patient B, respiratory period 3s and patient breathing lagging behind treatment delivery by 2 respiratory phases for the entire treatment. (b) Example of 4D VMAT DVH affected by random error: patient A, respiratory period 6 s and 15% of beams delivered incorrectly to patient breathing by a lag or advance of 2 respiratory phases. Solid lines represent the original errorfree delivery and dashed lines represent the error-prone delivery. ................ 118 Figure 6.1: Diagram of the various components required for 4D VMAT to be implemented clinically. .................................................................................. 128 Figure 6.2: Illustration of the various methods for deformable 4D dose calculation (adapted from [163, 164]). ............................................................................. 130  xvii  Glossary AAPM: American Association of Physicists in Medicine, 42 ABC: Active-breathing control, 44 AMCBT: Arc-modulated cone beam therapy, 58 AMRT: Arc-modulated radiation therapy, 57 AP: Anterior/posterior, 39 BCCA: British Columbia Cancer Agency, 36 BED: Biological effective dose, 108 BEV: Beam's eye view, 33 CBCT: Cone-beam computed tomography, 17 CC: Cranial/caudal, 39 CIMO: Continuous-intensity-map-optimization, 56 COM: Centre of mass, 128 CT: Computed tomography, 19 CTV: Clinical tumour volume, 19 DAO: Direct aperture optimization, 33 DIBH: Deep-inspiration breath-hold, 44 DMLC: Dynamic multi-leaf collimator, 48 DNA: Deoxyribonucleic acid, 12 DSB: Double-strand break, 12 DVH: Dose volume histogram, 21 EGSnrc: Electron gamma shower, 91 EPID: Electronic portal imaging device, 17 EUD: Equivalent uniform dose, 128 FFF: Flattening filter-free, 15 xviii  FSB: Forced shallow breathing, 44 GEANT4: Geometry and Tracking, 91 GTV: Gross tumour volume, 19 Gy: Gray, 12 IGRT: Image-guided radiation therapy, 13 IM: Internal margin, 19 IMAT: Intensity-modulated arc therapy, 53 IMRT: Intensity-modulated radiation therapy, 13, 22 ITV: Internal target volume, 19 LET: Linear energy transfer, 11 LLL: Left lower lobe, 92 LR: Left/right, 39 MC: Monte Carlo, 89 MCNP: Monte Carlo N-particle, 91 MLC: Multi-leaf collimator, 15 MU: Monitor unit, 15 NSCLC: Non-small cell lung cancer, 36 NTCP: Normal tissue complication probability, 13 OAR: Organ at risk, 19 OBI: On-board imager, 17 PB: Pencil-beam, 34 PDF: Probability distribution function, 41 PENELOPE: Penetration and energy loss of positrons and electrons in matter, 91 PRV: Planning organ at risk volume, 19 PTV: Planning target volume, 19 RLL: Right lower lobe, 92 RPM: Real-time position management, 45 SBRT: Stereotactic body radiation therapy, 37 SCLC: Small cell lung cancer, 36 SM: Setup margin, 19 SSB: Single-strand break, 12 xix  SWAT: Sweeping-window arc therapy, 57 TCP: Tumour control probability, 13 TERMA: Total energy released per unit mass, 87 VMAT: Volumetric modulated arc therapy, 52  xx  Acknowledgements I would like to express my appreciation for the help and guidance I received from my PhD supervisor, Dr. Karl Otto. I am grateful for his generous patience with me as I muddled through the early years of my project. I admire his sharp understanding of both the research and clinical aspects of the medical physics field which allows him to shrewdly identify and rapidly solve clinically relevant problems. Dr. Otto's humorous and witty, yet always honest observations of our field has brought a little fun and entertainment to the PhD process. This thesis would also never have been completed without the contributions from a host of people. My PhD committee of Dr. Alan Nichol, Dr. Alex Mackay and Dr. Stefan Reinsberg were always ready to provide assistance whenever I asked. Dr. Shaun Loewen is gratefully acknowledge for his aid in contouring all the anatomical structures in the 4D CT patient data provided by Dr. Wilko Verbakel of the VUmc in Amsterdam. Dr. Gregory Sharp and the Plastimatch group from Harvard were invaluable for making their image registration software publicly available and providing active guidance and support for its use. Dr. Emily Heath from Ryerson University shared her expertise on image registration methods.  Dr. Tony Popescu and John Lucido of the BCCA Vancouver Centre were  instrumental for the Monte Carlo VMAT simulations. Fellow graduate students Dr. Lingshu Yin, Dr. Tony Teke, Dr. Tony Mestrovic and Robert Kosztyla as well as many more medical physicists, radiation therapists and physics assistants of the BCCA have all shared their time and knowledge. This work has been supported in part by the Natural Sciences and Engineering Research Council of Canada's Alexander Graham Bell Canada Graduate Scholarship and in part by funds from the BCCA's medical physics department headed by Dr. Cheryl Duzenli.  xxi  Finally to my family and friends, thank you for all your love and care and good-natured ribbing of my seemingly never-ending student status. It was a great motivator to get this work done.  xxii  Chapter 1  Overview of Thesis Radiation therapy is the treatment of disease, primarily cancer, using ionizing radiation. Successful and safe clinical application of radiation therapy is based on the integration of detailed knowledge of both physics and radiobiology.  Chapter 2 provides a brief  introduction to some of the important concepts of radiation therapy. The basic physics of relevant particle interactions and radiobiology are explained. Linear accelerators, which are the most common mode employed to deliver external beam radiation therapy, are also described along with select options for in-room imaging systems that are used to help guide and verify treatment accuracy. Properly designing radiation delivery plans and predicting dose deposition within the patient are central pillars of radiation therapy. The principles, procedures and algorithms developed for radiation treatment planning that are pertinent to this thesis are discussed. Treatment plan delivery is complicated by patient tumour and organ motion which reduce the precision of radiation therapy [1]. Radiation therapy treatment plans include treatment margins to account for various uncertainties such as patient setup errors and patient motion [2-4]. The patient motion margin, also known as the internal margin (IM), can account for such factors as respiration, variation in the filling of the bladder and rectum, swallowing, heartbeat and movement of the bowels. The motion margin ensures that dose coverage of the tumour is preserved but results in larger volumes of healthy tissue being irradiated [5].  1  With the development of sophisticated imaging techniques that provide information on tumour motion and deformation over time such as 4D CT [6-8], 4D CBCT [9-11] and MRI [12-15], research into using this data to improve radiation treatment plans has become an active field of inquiry. Much of this focus has been on lung tumours where margins in the cranial/caudal axis can be as large as 1 cm due to respiratory motion [5]. Minimizing these margins is important as mean lung dose and V20 (% total lung volume receiving ≥20 Gy) have been shown to correlate with lung complications such as radiation pneumonitis and pulmonary fibrosis [16-19]. Additionally, dose escalation could potentially improve cancer control rates [20-24], but is currently limited by normal tissue toxicity within the margin [2527]. Globally, lung cancer is the leading cause of cancer deaths accounting for approximately 1 in 5 deaths and there is considerable opportunity to improve lung radiation therapy. Chapter 3 gives a short description of lung cancer, introduces a new promising treatment called stereotactic body radiation therapy (SBRT) and outlines the main motion compensation techniques that have been developed to date.  SBRT is essentially an  escalation of dose fraction. In SBRT, the full course of radiation is delivered in a period of 2 weeks or less rather than the 6-7 weeks for conventional radiation therapy. This means that the doses per treatment in SBRT are substantially higher by a factor of 2.5-10 times the conventional dose of 2 Gy. Resulting 5 year survival rates for SBRT are 60-70% versus 20% for conventional radiation therapy [28], but the high SBRT fraction doses increase the danger of normal tissue injury. Consequently, motion management techniques that can reduce treatment margins are a priority for SBRT. Two of the most advanced radiation treatment techniques that attempt to minimize the conventional tumour motion encompassing margin are respiratory-gated radiation therapy and dynamic multi-leaf collimator (DMLC) tracking radiation therapy.  Both of these  techniques have been shown to reduce the volume of healthy tissue exposed to high doses of radiation [29-32]. However, these treatment plans are normally based on static 3D CT images of the patient. Thus, the system does not fully exploit the anatomical information available in the temporal dimension. For example: If the 4D information was also included during the planning stage, critical structures such as the heart, spinal cord and esophagus 2  could be further spared if higher radiation doses are delivered to the tumour when it moves farther away from these structures. Extending this idea further, it is not unreasonable to hypothesize that the time dimension might be exploited to reduce dose to healthy tissue further than what might be achieved for a motionless patient. This idea of creating respiratory phase-optimized 4D treatment plans has already been proposed for tomotherapy, intensity-modulated radiation therapy (IMRT) and radiosurgery [33-37]. Delivering these treatment plans is technically challenging requiring tumour motion be anticipated so that the optimal radiation beam apertures are delivered to their corresponding respiratory phases. The benefit, however, is that the reduction in healthy tissue doses compared to even the ideal 3D static plan with no motion margin is possible [36].  These results support the concept that instead of tumour motion always being  detrimental to treatment plan quality; it may in certain cases become an advantage. In this thesis we propose an implementation of a respiratory phase-optimized 4D treatment planning algorithm for volumetric modulated arc therapy (4D VMAT) [38]. VMAT delivers radiation to the tumour volume during one or more continuous rotational arcs of a linac gantry [39-43]. The choice of VMAT for 4D treatment planning has multiple advantages. By increasing the degree of freedom in beam angles, VMAT can achieve better target dose conformality and increased sparing of healthy tissues over conventional multibeam static-gantry IMRT. VMAT has also been shown to have shorter treatment times compared to IMRT and tomotherapy [39, 41, 42]. While tomotherapy also uses a continuous 360° arc of beam directions, it is less efficient because radiation is delivered in a two dimensional slice-by-slice fashion requiring many rotations compared to VMAT’s normally one or two arc delivery of the entire 3D dose volume. As well, the use of aperture based optimization in our VMAT system results in fewer monitor units (MU) required to deliver the treatment plan when compared to IMRT optimized using fluence based methods [44, 45]. Chapter 4 gives an in depth description of the development and details of the VMAT system used in this work. The design of the new 4D VMAT system is outlined and its treatment planning performance is analyzed relative to gated VMAT, tracked VMAT and 3D VMAT based on results of initial motion simulations. Chapter 5 continues the investigation of 4D VMAT treatment planning using 4D CT data from SBRT eligible patients with non3  small cell lung cancer (NSCLC). The problem of 4D CT phase bias during optimization is explored and a few issues related to the practical clinical implementation of 4D VMAT treatments are addressed. These include the formulation of a strategy to ensure efficient treatment delivery times and a study on the robustness of the 4D VMAT respiratorysynchronized plans to desynchronization delivery errors caused by irregular patient breathing. Finally, Chapter 6 summarizes the main findings of this thesis and lists an array for future works that are required before the 4D VMAT treatment technique can become clinically available.  4  Chapter 2  Introduction to Radiation Therapy 2.1 Ionizing Radiation Ionizing radiation can be categorized as either directly ionizing or indirectly ionizing radiation.  Directly ionizing radiation refers to charged particles, such as electrons and  protons, that deposit their energy through direct Coulomb interactions with the orbital electrons of atoms in the surrounding medium. Indirectly ionizing radiation refers to neutral particles, such as photons and neutrons. They deposit their energy in a 2-step process where in the first step, the interaction of the neutral particles with the medium releases charged particles. Subsequent energy deposition in the medium then occurs via Coulomb interactions of the charged particles. The majority of radiation therapy treatments involve photons. Electrons are used less frequently and mainly target superficial tumours at depths of less than 5 cm. Particles such as protons, neutrons, heavy ions and negative  mesons have also been used, but are  available to only a few select centres globally. These latter infrequently used particles will not be discussed in this work.  5  2.2 Photon Interactions As a photon beam travels through tissue, it becomes attenuated due to interactions with either free orbital electrons, nuclei, or entire atoms of the surrounding medium. A given photon may be completely absorbed and disappear, or it may scatter (coherently or incoherently). Only the three photon interactions of major importance to radiation therapy will be briefly presented: 1) photoelectric effect, 2) Compton (incoherent) scattering and 3) pair production. Other interactions do exist, such as Rayleigh (coherent) scattering, Thompson scattering and photonuclear reactions, but are of moderate to minor importance. The probability of a given interaction's occurrence depends on the energy of the photon and the atomic number Z of the attenuating medium. The relative predominance of the three major interactions for a range of energies and Z values is shown in Figure 2.1.  The  photoelectric effect has the greatest contribution to photon beam attenuation at low energies while Compton scattering predominates at intermediate energies and pair production predominates at high energies.  100  Atomic number Z  75 Pair production dominant  Photoelectric effect dominant 50 Compton scattering dominant 25  0 0.01  1  0.1  10  100  Photon energy (MeV)  Figure 2.1: The relative predominance of the photoelectric effect, Compton scattering and pair production as a function of atomic number Z and photon energy. 6  2.2.1 Photoelectric Effect In the photoelectric effect, the photon interacts with a tightly bound orbital electron. The photon is completely absorbed and disappears, ejecting the orbital electron. A portion of the photon's momentum is absorbed by the atom as a whole but the atomic recoil energy is negligible due to the relatively large nuclear mass. Thus, the kinetic energy, Ek, of the ejected photoelectron is calculated as  (2.1)  where hv is the energy of the incident photon and EB is the binding energy of the electron. Most often the ejected photoelectron leaves a vacancy in the K-shell. This vacancy is filled with an upper shell electron and the transition energy is emitted either as a characteristic (fluorescent) photon or transferred to another orbital electron that is then ejected as an Auger electron. The mean energy transferred to all electrons produced from a photoelectric effect,  ,will therefore be between Ek and hv and dependent on the amount of  energy lost to characteristic radiation.  (2.2)  PK is the fraction of photoelectric interactions that occur in the K-shell, wK is the K-shell yield for characteristic radiation and  is the K-shell weighted mean of all possible  fluorescent transition energies.  7  2.2.2 Compton Scattering In Compton scattering, the photon interacts with a free (i.e. loosely bound) orbital electron. The photon is scattered away from its originally trajectory by an angle  after transferring  part of its kinetic energy to the recoil electron which is ejected at an angle  (Figure 2.2).  y Recoil electron  Incident photon  x  Scattered photon  Figure 2.2: Compton scattering schematic diagram. Incident photon interacts with loosely bound orbital electron. Part of the photon energy is transferred to the electron ejecting it from the atom and a scattered photon with lower energy is created.  If the energy of the incident photon is hv, then the energy of the scattered photon is  (2.3)  and the kinetic energy of the recoil electron, Ek, is  8  (2.4)  where scattering angle  and  is the electron mass. The relationship between the photon's  and recoil electron angle  is given by the following equation  (2.5)  Although the value of  can range from  to + , at low values of , the probabilities of  forward and backscattering are equal and twice as large as the probability of side scattering. As the photon energy increases, the probability of photon back scattering decreases resulting in more forward peaked scatter.  2.2.3 Pair Production In pair production, photon interaction with an atom of the absorbing medium will result in the disappearance of the photon and the creation of an electron-positron pair.  For  conservation of momentum, a portion of the photon's momentum is absorbed by the atom. If the momentum is absorbed by the atomic nucleus, the recoil energy is negligible and only the electron-positron pair leaves the site of interaction. This is the standard pair production. Conversely, if the photon interacts with an orbital electron transferring a portion of its momentum, the recoil energy of the orbital electron may be substantial. This is termed triplet production since the orbital electron is ejected and leaves the site of interaction along with the newly created electron-positron pair. The newly released positron will travel a short distance before annihilating with another orbital electron in the medium. Most often the annihilation will produce two photons, each with energy  MeV, travelling in opposing directions (~180º).  However,  approximately 2% of annihilations happen before the positron has lost all its kinetic energy. 9  These are known as annihilations-in-flight and can produce a photon with energy greater than 0.511 MeV. Unlike the previously presented photon interactions (photoelectric effect and Compton scattering), pair production requires the incident photon's energy to be above a certain threshold energy to occur. For standard pair production, this energy is and for triplet production, the threshold energy is  .  transferred to the released particles in pair production,  The total kinetic energy  , is  .  (2.6)  2.2.4 Atomic Shell Vacancies The photoelectric effect, Compton scattering and triplet production create atomic shell vacancies by ejecting orbital electrons usually from inner shells of the absorbing medium. Inner shell vacancies are unstable and will prompt a series of characteristic X-ray and Auger electron emissions that propagate to the outer shell of the atom. Afterward, the positively charged atom will attract an electron from its surroundings and return to its stable neutral form.  2.3 Electron Interactions An energetic electron will undergo thousands of Coulomb interactions with surrounding atoms before expending all its energy. The scattering angle of the incident electron may be significant due to the relatively small electron mass. Elastic and inelastic collisions occur with either the absorbing medium's orbital electrons or nuclei. Collision with an orbital electron can result in excitation or ionization. Up to 50% of the incident electron's energy can be transferred to an orbital electron. Collision with an atomic nucleus can cause the incident electron to rapidly decelerate and emit a portion of it energy as a bremsstrahlung  10  photon. Excitations and ionizations are more prevalent in media with low atomic numbers, such as water and tissues, while the probability of bremsstrahlung radiation increases with electron energy and high atomic numbers (e.g. lead).  2.4 Radiation Biology 2.4.1 Linear Energy Transfer Biological damage occurs when ionizing radiation deposits energy to the surrounding tissues. The quality of the radiation can be quantified by the linear energy transfer (LET) which measures the average energy locally imparted to the medium per unit length traversed by the radiation particles. As the LET value increases, the efficiency of radiation in mammalian cell killing increases until approximately 100 keV/ m, whereafter any extra biological damage is redundant. X-rays and  rays have low LET values below 10 keV/ m and are  considered sparsely ionizing radiation. Particles with LET values greater than 10 keV/ m, such as protons, neutrons and heavy charged particles, are considered densely ionizing radiation (high LET).  2.4.2 Direct and Indirect Action High energy charged particles from directly ionizing radiation, or generated from indirectly ionizing radiation can deposit their energy into the surrounding medium by Coulomb interactions with the medium's orbital electrons. Atoms and molecules become excited or ionized leading to disruption of chemical bonds and formation of new chemical arrangements. These events can be categorized either as direct action or indirect action in cell damage by radiation. In direct action, the ionizing radiation directly excites or ionizes the critical target of the cell, such as the DNA, to produce biological damage.  In indirect action, the ionizing  radiation interacts with other molecules creating free radicals that damage the critical targets. The intermediate molecule is typically water as it constitutes approximately 80% of a cell. 11  Three important free radicals produced by the irradiation of water are e-aq (aqueous electron), H• (hydrogen radical) and OH• (hydroxyl radical). The free radicals are highly reactive and create a cascade of chemical reactions within the cell. For sparsely ionizing radiation, approximately 2/3 of biological damage is due to indirect action.  The OH• radical is  considered the most damaging radical species.  2.4.3 DNA Damage from Ionizing Radiation Ionizing radiation inactivates cells primarily by damaging the deoxyribonucleic acid (DNA) molecules in the nuclei of cells. The DNA molecule is composed of two complementary strands of nucleotides that intertwine to form a double helical structure. Each nucleotide is composed of a sugar, a phosphate and one of four possible nitrogen bases (adenine, guanine, cytosine, thymine). The alternating sugars and phosphates are oriented outwards to create the backbone of the double helix while in between the strands, hydrogen bonds connect the nitrogen bases of each nucleotide to their complement on the opposing strand. The sequence of nitrogen bases encodes all genetic information critical to the function and development of the cell. Thus, damage to the DNA structure caused by ionizing radiation, if not correctly repaired, may lead to cell death. The types of structural damage to the DNA molecule include single-strand breaks (SSB), double strand breaks (DSB), DNA interstrand crosslinks, crosslinks between DNA and protein, and damage to the sugars and nitrogen bases. Of these lesions, DSBs are most likely to result in lethality. Multiple cellular mechanisms exist to repair DNA damage. These include base excision repair, nucleotide excision repair, homologous recombination and nonhomologous end-joining. Energy deposition from ionizing radiation occurs in short random bursts known as spurs, blobs and short tracks which can create multiply damaged sites along the DNA structure and overwhelm the repair mechanisms of the cell. These closely spaced lesions explain the high toxicity of ionizing radiation. The mean energy imparted to a given mass of medium is defined as the absorbed dose. The unit of measure for absorbed dose, or simply dose, is the gray (Gy) which is defined as 1 J/kg. 12  2.4.4 Therapeutic Ratio of Radiation Therapy In radiation therapy, the therapeutic ratio is a method to compare the tumour control rates against the normal tissue complication rates as a function of radiation doses.  Ideally,  sufficient radiation to the tumour is delivered to eradicate it without exposing the normal tissue to a dose that will cause serious complications (e.g. ulceration, pericarditis, pneumonitis, rib fracture). While there are multiple methods to calculate the therapeutic ratio, the main concepts are illustrated in Figure 2.3. The red curves represent the tumour control probability (TCP) and the green curves show the normal tissue complication probability (NTCP). Figure 2.3(a) displays the optimal situation where the TCP curve is far enough to the left of the NTCP curve such that tumour control is easily achieved without inducing unacceptable tissue injury. Conversely, Figure 2.3(b) illustrates a disadvantageous situation where the NTCP curve is to the left of the TCP curve and irradiation of the tumour will likely cause treatment complications. Several factors can affect the shape of the TCP and NTCP curves such as tumour type, dose rate, fractionation scheme and LET. As well, methods that improve the conformity of radiation deposition to the tumour while avoiding healthy tissues such as intensity-modulated radiation therapy (IMRT), or methods that improve precision of radiation delivery like image-guided radiation therapy (IGRT) can enhance the therapeutic ratio. Figure 2.3(c) displays a realistic example of the clinical trade-off between TCP and NTCP curves.  13  Desirable probability of tumour control  95%  Optimal therapeutic ratio  Probability of effect  Probability of effect  95%  50% Tumour control 5%  Normal tissue complication  Unacceptable therapeutic ratio 50% Normal tissue complication 5%  Acceptable risk of normal tissue complication  Desirable probability of tumour control  Acceptable risk of normal tissue complication  Total dose (Gy)  Total dose (Gy)  (b)  (a) 95% Probability of effect  Tumour control  Desirable probability of tumour control  Acceptable therapeutic ratio 50% Tumour control 5%  Normal tissue complication  Acceptable risk of normal tissue complication  Total dose (Gy)  (c)  Figure 2.3: The therapeutic ratio for radiation therapy where the relationship between the tumour control dose-response and the normal tissue tolerance curves are (a) optimal, (b) unacceptable and (c) acceptable (adapted from [46]).  2.5 Treatment Delivery Equipment The most common method for radiation treatment delivery is the use of high energy photons generated externally to a patient. The research focus of this work was tailored specifically to high energy photon beams produced by linear accelerators. The integration of imaging systems into the treatment room is another essential component of radiation therapy. Inroom imaging systems are used for pre-treatment verification of patient setup, incorporated into motion management strategies during treatment and utilized in post-treatment checks of radiation delivery accuracy. A few select imaging systems relevant to lung imaging will be briefly presented.  14  2.5.1 Linear Accelerator & Photon Beams A clinical linear accelerator (linac) can produce photons beams of energy 6-18 MV (Figure 2.4). This is accomplished by using microwave RF fields, usually with a frequency of 2856 MHz, to accelerate electrons to high kinetic energies (e.g. 6-18 MeV). Briefly, an electron gun provides electrons to the system through thermionic emission of a heated cathode. The emitted electrons then enter the evacuated accelerating waveguide where electric fields, set up by the transmission of microwaves, increase the kinetic energy of the electrons. An electron transport system then guides the electron beam to strike a special metallic target. Most of the kinetic energy of the electrons is lost as thermal energy in the target, but a small portion is emitted as bremsstrahlung X-rays. Electron collision with target orbital electrons can also create atomic shell vacancies that evoke characteristic X-ray emission, but their contribution to the resultant photon beam is negligible for electron energies in the megavoltage range. Bremsstrahlung photons exiting the target are forward peaked. Components in the linac treatment head help shape and control the radiation that is delivered to the patient (Figure 2.5(a)). The primary collimator defines a maximum circular field. Immediately below is the flattening filter. It is designed to preferentially attenuate photons at the centre of the forward peaked incident beam such that the dose deposition profile at a certain depth (e.g. 10 cm) in water is uniform. The dual ionization chamber monitors the radiation output as well as the beam flatness. Radiation output is measured in monitor units (MU). The linac is typically calibrated such that 1 MU corresponds to a dose of 1 cGy measured at the depth of maximum dose and under a set of standard conditions. The maximum dose rate in most linacs is 600 MU/min. In recent years, manufacturers have developed linacs with higher dose rates (14002400 MU/min) by removing the flattening filter [47, 48]. The characterization of flattening filter-free (FFF) radiation beams is still under investigation. The linac also has adjustable upper and lower jaws that further collimate the radiation beam into rectangular fields. The maximum field dimensions are 40x40 cm2. Finally, the multi-leaf collimator (MLC) can create irregular fields that conform to tumour target shape, or allows for complex beam intensity modulation (Section 2.7). The MLC consists of opposing tungsten leaf pairs (Figure 2.5(b)). In the axis parallel to the radiation beam, the 15  leaves have a height of 6 cm. In the perpendicular axis, the width of the central 40 leaves projected at isocentre is 0.5 cm while the outer 10 leaves on each end project an isocentre width of 1 cm. Each leaf is individually computer controlled with its own motors and circuits. The linac provides a flexible range of delivery orientations. The radiation beam delivery system is mounted within a gantry that can rotate 360º around a patient lying on a treatment couch. Both the couch and the MLC can each independently rotate 180º about the beam axis.  Electron gun  Electron beam transport  Accelerating waveguide  Target Stand  Linac treatment head Isocentre  Treatment couch  Gantry RF power generator  Gantry axis  Couch axis  Figure 2.4: Schematic of the various components in a linear accelerator used for creating photon and electron beams.  16  X-rays from target  Primary collimator Flattening filter Dual ionization chamber  Linac treatment head  Upper jaws Lower jaws MLC Towards patient  (a)  (b)  Figure 2.5: (a) Schematic of the components in the linac treatment head. (b) Beam's eye view through the MLC (Image courtesy of Varian Medical Systems Inc., All rights reserved).  2.5.2 Integrated Treatment/Imaging Systems One or more imaging systems are generally available during a radiation treatment session. Figure 2.6(a) displays a flat panel electronic portal imaging device (EPID) which consists of a matrix of amorphous silicon detectors. Its position, mounted on the end opposite to the linac head, allows it to detect the megavoltage treatment radiation resulting in images of both the beam portals and patient anatomy. A linac can also be equipped with an on-board imager (OBI) that provides kV imaging (Figure 2.6(b)). kV imaging gives better image quality than the MV imaging of the EPID. The OBI can provide 2D radiographs, fluoroscopic images, or 3D cone-beam computed tomography (CBCT) images. Non-linac mounted imaging options include stereoscopic X-ray imaging (Figure 2.7(a)) and tracking of reflective body surface markers using an infrared tracking camera (Figure 2.7(b)).  17  (a)  (b)  Figure 2.6: (a) Linac equipped with an EPID. (b) Linac equipped with an OBI. (Images courtesy of Varian Medical Systems Inc., All rights reserved)  (a)  (b)  Figure 2.7: (a) Illustration of in-room stereoscopic X-ray imaging. (b) Illustration of inroom infrared tracking of reflective markers on a patient surface. (Images courtesy of Brainlab, All rights reserved)  2.6 Radiation Treatment Planning Once images of patient anatomy have been acquired, radiation treatment planning consists of the following steps: 1) identify the planning volumes, 2) determine the dose fractionation 18  schedule, 3) create a treatment plan and 4) evaluate the plan. Steps 1, 2 and 4 will be described in the following three subsections (2.6.1-2.6.3). Creation of treatment plan (step 3), however, is treatment technique dependent.  The treatment technique of intensity  modulated radiation therapy (IMRT) along with its method for plan creation will be presented separately in section 2.7.  2.6.1 Planning Volumes 3D planning structures (volumes) are required for both the tumour target and surrounding critical structures known as organs at risk (OAR). Visualization of patient anatomy is most commonly provided by 3-dimensional computed tomography (3D CT).  For the target  volumes, a radiation oncologist will delineate gross tumour volume (GTV) and clinical target volume (CTV) (Figure 2.8). GTV refers to the visible extent of the tumour growth. The CTV contains the GTV as well as extra tissue in the adjacent surroundings that may contain subclinical microscopic malignant disease. An internal margin (IM) is then added to the CTV to create the internal target volume (ITV). The IM is required to account for variation in tumour position caused by physiologic movements, such as respiration, variation in filling of the bladder and rectum, swallowing, heartbeat and bowel movements. Additionally, the IM compensates for tumour shape changes that may occur over the course of treatment. The IM is often asymmetric. Another margin, known as the setup margin (SM), is added to the ITV to produce the planning target volume (PTV). The SM accounts for uncertainties in both the positioning of the patient and alignment of the treatment fields. The dose coverage of the PTV is often used as one of the objectives in treatment planning. For example, dose within the PTV should be within +7% and -5% of the prescribed dose. OARs will also be contoured by a radiation oncologist. Occasionally, the motion of an OAR (e.g. esophagus) may periodically bring it to within dangerous proximity of the PTV leading to unexpected overexposure of the OAR. In such cases, an additional motion margin is added around the OAR creating a planning organ at risk volume (PRV). Once a treatment plan has been generated, the volume enclosed by an isodose surface capable of achieving tumour control is identified as the treated volume. Ideally, the treated 19  volume coincides precisely to the PTV, but this is often not possible due to limitations in treatment techniques. The volume of normal tissues receiving doses that are relatively large in comparison to their radiation tolerance levels are defined as the irradiated volume.  Internal margin (IM) Gross tumour volume (GTV) Internal target volume (ITV)  Clinical target volume (CTV) Planning target volume (PTV)  Combined internal margin and set-up margin  Treated volume Irradiated volume  Figure 2.8: Illustration of the planning volumes in radiation therapy.  2.6.2 Plan Delivery Schedule: Conventional Fractionation Based on the size and location of the planning volumes, a radiation oncologist will prescribe a dose to the tumour. The dose is delivered in multiple fractions over several weeks rather than in a single large dose. This choice is based on over 80 years of empirical clinical experience that shows fractionation can deliver effective tumour control while providing better sparing of normal tissues from radiation damage (i.e. improved therapeutic ratio). In conventional fractionation schemes, the number of daily fractions can range from 30-40 with approximately 2.0 Gy delivered per fraction. Five factors that influence conventionally fractionated treatments are: 1) radiosensitivity, 2) repair, 3) repopulation, 4) redistribution and 5) reoxygenation. Radiosensitivity of normal tissue limits the dose that can be administered in radiation therapy. The different tissues in the body have a range of radiosensitivities (e.g. skin, 20  intestine lining, lungs, bone marrow). Sparing of normal tissues is aided by repair of sublethal damage and cell repopulation in the interval between treatment fractions. While malignant cells also undergo repair and repopulation, repair may be compromised by mutations and appreciable repopulation is prevented by limiting the size of the fractionation interval. Damage to malignant cells is increased by redistribution and reoxygenation. Redistribution is related to the cell cycle phases which have variations in radiosensitivity. After irradiation, cells from more resistant phases have a higher probability of survival. The interval between dose fractions allows the surviving cells to progress through the cell cycle such that some will have redistributed to radiosensitive phases by the next scheduled treatment. Reoxygenation is related to the vasculature around a tumour. Tumour cells distant from blood vessels tend to be hypoxic. Hypoxic cells are radioresistant to particles with low LET such as photons. After a treatment fraction, oxic cells killed by the radiation are removed allowing tumour shrinkage. This allows for closer proximity between the surviving cells and the vasculature and thus oxygenation of the hypoxic regions of the tumour.  2.6.3 Plan Evaluation: Dose Volume Histograms A dose volume histogram (DVH) is one of the main tools used to evaluate radiation therapy treatment plans. It summarizes the radiation dose distribution within the patient volume. The patient volume is typically segmented into sub-volumes for specific critical organs and tumour targets. A distinct DVH curve will characterize each structure's radiation exposure. Two types of DVHs exist: differential (or direct) DVHs and cumulative (or integral) DVHs. A cumulative DVH quantifies the volume of a structure that receives at least a given dose. For example, if the prescribed target dose is 48 Gy, in an ideal situation 100% of the target will receive at least 48 Gy while 100% of the critical structure will receive no more than 0 Gy (Figure 2.9 (a)). In a realistic DVH (Figure 2.9 (b)), critical structures near the target will be unavoidably irradiated and dose in the target will not be perfectly homogeneous. Only  21  cumulative DVH will be discussed in this work as it is the type most used for treatment plan evaluation. All subsequent references to it will be shortened to DVH.  (a)  (b)  Figure 2.9: (a) Ideal cumulative DVH. (b) Realistic cumulative DVH.  2.7 Intensity-Modulated Radiation Therapy Intensity-modulated radiation therapy (IMRT) is a complex treatment technique that modulates the energy fluence ('intensity') of multiple incoming radiation beams. Each beam portal is conceptually divided into 102-103 independently modulated beamlets.  Figure  2.10(a) shows a simplified example of a single modulated radiation beam's cross-sectional energy fluence (i.e. fluence/intensity map). Darker shades correspond to beamlets with greater intensities. The flexibility in modulating the beam intensity allows IMRT to achieve a higher degree of dose conformality around the target and thus a lower dose to critical structures than would be possible with beams of uniform intensity (Figure 2.10(b)). Multiple beams of heterogeneous intensity (7-9 beams) are designed in conjunction such that their superimposition will result in a fairly homogeneous dose distribution within the target [49, 50].  22  (a)  (b)  Figure 2.10: Simplified illustration of the cross-section of a rectangular radiation field that has been subdivided into beamlets of (a) varying intensities or (b) uniform intensities.  The derivation of the IMRT treatment plan is referred to as an inverse planning problem. A desired outcome, such as achieving a prescribed target coverage, is first specified and then the method to achieve the outcome is determined (i.e. finding the fluence maps). The inverse problem of IMRT has no exact solution because it is not possible to deliver the full prescription dose to the target without also irradiating healthy tissue. Radiation beams with negative intensity are not physically possible [51]. Therefore, the IMRT inverse problem is formulated as an optimization process that iteratively searches for treatment parameters that minimize the dose difference between a realistic plan and the desired plan (Figure 2.9). Greater detail on IMRT optimization is provided in subsequent sections (Figure 2.11). In brief, optimization starts with the planner specifying a set of treatment goals (section 2.7.1) that will be used to construct the objective function (section 2.7.2). Dose calculated (section 2.7.5) from some initial treatment parameter settings, x, is used to compute the objective function.  If the value of the objective function converges, usually to a minimum,  optimization exits and the optimized treatment parameters are saved as xopt. Otherwise, the optimization algorithm (section 2.7.3) helps select a new set of treatment parameters (section 2.7.4) and the process is repeated. Depending on the complexity of the problem and the choice of optimization algorithm, the number of iterations can range from approximately a dozen to hundreds of thousands. 23  The reliance on the optimization algorithm to select treatment parameters is in contrast to the method used in the past known as forward planning. In forward planning, it is the treatment planner that manually and iteratively adjusts the treatment parameters to obtain the desired dose distribution. Plans created in this manner are unable to match the level of dose conformity around the target and sparing of healthy tissues achievable in IMRT plans because the complex fluence patterns required are nearly impossible to derive intuitively through manual adjustments.  x' Dose calculation (x)  Objective function (x)  Treatment parameters (x)  Convergence  no  Optimization algorithm (x)  yes Clinical experience  xopt Figure 2.11: Schematic of IMRT optimization. Starting with non-optimal treatment parameters, x, the resultant dose distribution is calculated and evaluated using the objective function. If the value of the objective function has converged to a minimum, the loop is exited; otherwise new treatment parameters are found using the optimization algorithm and the whole process is repeated (Adapted from [52]).  2.7.1 Dose-Volume Constraints Before the IMRT problem can be solved, treatment planning goals must be quantified into clinically meaningful optimization objectives and constraints. A common option is the use of dose-volume constraints [51] that can be defined for both OARs and target volumes. For OARs, a maximal dose-volume constraint is defined by two values, Vmax% and Dmax. The meaning is that no more than Vmax% of the volume should receive more than a dose of Dmax. Figure 2.12(a) represents this constraint as a shaded region in the DVH. Setting multiple 24  maximal constraints on an OAR can provide some control over the dose distribution in its volume. For target volumes, a maximal and a minimal dose-volume constraint can be defined to control target coverage and target dose inhomogeneity (Figure 2.12(b)). The Vmin% and Dmin values of the minimal DVH constraint are interpreted as Vmin% of the target  Volume  Volume  volume should receive at least a dose of Dmin.  Vmax  Dmax  Dose  Dmin  (a)  Dmax Dose (b)  Figure 2.12: (a) Example of a maximum dose-volume constraint on an OAR. (b) Example of a minimum and maximum dose-volume constraint on the target (adapted from [51]).  2.7.2 Objective Function The objective function, also known as the cost function, is used to guide the IMRT optimization. One of the most common objective functions in IMRT treatment planning is the minimization of the mean square deviation between the actual dose distribution and treatment planning goals represented by the dose-volume constraints. The total objective function, f, is defined as the sum of the objective functions of the OARs (fOAR) and the target (ftarget).  (2.7)  25  Each OAR can have more than one maximal dose-volume constraint, f  max  . Thus, for a  given OAR, fOAR is  (2.8)  Each maximal dose-volume constraint, f max, is calculated as follows:  ( 2.9)  and (2.10)  wmax is the weight of the maximal constraint, Dmax is the maximum dose in the constraint, Dj is the dose in the jth voxel and N is the total number of voxels in the structure.  is the  dose that corresponds to the point of intersection between Vmax and the DVH curve (Figure 2.13). The two step functions act together to enforce the maximal dose-volume constraint. Both functions have non-zero values only for voxels where the constraint is exceeded. These voxels are represented by the shaded green areas in Figure 2.13. The maximal dose-volume constraints are denoted by red arrows. For the target, its objective function is composed of both maximal and minimal dosevolume constraints although frequently only one of each is employed.  (2.11)  f max is the same as defined in Equation 2.9 and f min is 26  (2.12)  wmin is the weight of the minimal constraint, Dmin is the minimal dose in the constraint and is the dose that corresponds to the point of intersection between Vmin and the DVH curve (Figure 2.13). Analogous to Equation 2.9, the two step functions in Equation 2.12 penalize the objective function only for voxels that violate the minimal dose-volume constraint (Figure 2.13, shaded blue area).  Vmin  Vmax  Dmax  Dmin  Figure 2.13: Example of a DVH where the critical structure has 2 maximal dose-volume constraints (red triangles) while the target has 1 maximal and 1 minimal (blue triangle) dose-volume constraint. Shaded green and blue areas indicate portions of the structures that do not meet the desired constraints.  All constraint weights are manually chosen and the importance of any particular constraint is determined by its value relative to other weights. For example, if a weight is of low relative value, then the solution to the optimization may exceed the dose-volume constraints (Figure 2.14(a)). In contrast, if it is critical that the constraint be met (Figure 2.14(b)), then the weight must be set to a large relative value. All constraints are normalized  27  by their respective number of voxels, N, to prevent structures of large volumes from  Volume  Volume  dominating the optimization.  Dmax  Dose  Dmax  (a)  Dose  (b)  Figure 2.14: DVHs of an OAR where the dose constraint is represented by the shaded area. The likelihood of optimization achieving the desired constraint depends on the magnitude of the relative constraint weight. (a) Constraint was not met. (b) Constraint was met (adapted from [51]).  2.7.3 Optimization Algorithms Optimization algorithms help navigate the solution space of the objective function. The solution space can be thought of as a multi-dimensional surface whose coordinates are given in terms of the treatment parameters, x, which control dose deposition. The algorithms are categorized as either deterministic or stochastic.  Deterministic algorithms are usually  applied when the objective function is convex (i.e. only a global minimum exists) (Figure 2.15(a)); otherwise, they may become trapped in a local minimum. An example of a convex objective function is one based on dose constraints. Such a function would be similar to Equations 2.9 and 2.12 except for the omission of the second step function. Stochastic algorithms, such as simulated annealing, are applied to find the global minimum when the objective function has multiple minima (non-convex) (Figure 2.15(b)). Objective functions involving dose-volume constraints are non-convex.  While stochastic algorithms allow  escape from local minima, their optimization time is much longer relative to deterministic algorithms.  28  Objective function  Objective function  Climb hill Tunnel  local min.  x1 x0  x0  x  x  global min. global min. (a)  (b)  Figure 2.15: Simplified illustrations of a 1-D (a) convex and (b) non-convex objective function.  I. Deterministic Algorithm: Gradient Methods Examples of deterministic algorithms are those using gradient methods such as steepest descent and conjugated gradient approach [53, 54]. The set of variable treatment parameters, x, are adjusted in iterative steps towards an optimal solution according to the following equation  ( 2.13)  where i is the index of the step,  is the size of the step and d(i) is the change in direction of  the step. The simplest form of Equation 2.13 is the steepest descent where  is a constant and the  direction of the step is the negative of the steepest slope of the objective function, f, found by taking its first derivative.  (2.14)  29  The disadvantage of the steepest descent method is that convergence to an minimal objective function is slow because the gain of moving closer to the solution in one step may be partially lost in the next step. This drawback is avoided by using the conjugated gradient approach which calculates the new direction using both the current gradient and the previous direction.  (2.15)  (2.16)  II. Stochastic Algorithm: Simulated Annealing An example of a stochastic algorithm is simulated annealing [55]. Simulated annealing involves two parts. The first is the determination of the iterative step size, displacement distribution,  , from a  , where i represents the iteration number.  As  optimization progresses, the width of the displacement distribution will decrease such that smaller steps are taken when nearing the objective function's global minimum. The second part of simulated annealing involves determining whether the change to the treatment parameters moved the optimization closer to the optimal solution. If the objective function's value decreases (Equation 2.7), the change is always accepted. On the other hand, if the difference in the objective function's value,  , is positive, the change may still be accepted  but with a probability of P(i).  (2.17)  T(i) is the temperature and will decrease over the course of the optimization.  By  occasionally allowing the value of the objective function to increase, the optimization is able  30  to 'climb' out of a local minimum (Figure 2.15(b)). Escape by 'tunneling' can also occur if the step size is sufficiently large. For the determination of the step size, two common simulated annealing algorithms are Boltzmann annealing and fast simulated annealing.  In Boltzmann annealing, the  displacement distribution is a Gaussian given by  (2.18)  where N is the number of treatment parameters and the temperature T(i) is  (2.19)  In fast simulated annealing, the step size is sampled from a Cauchy distribution  (2.20)  and the temperature T reduces more quickly,  (2.21)  2.7.4 Treatment Parameters The choice of treatment parameters is dependent on the method of IMRT delivery. Most commonly, IMRT is delivered on a linac with beam modulation provided by the mechanical movements of the MLC. Therefore, example parameters would be beam angles, MLC settings and monitor units. In general, the treatment parameters that are chosen prior to 31  optimization are radiation type, beam energy and beam entry angles. Two common methods using distinctly different treatment parameters for IMRT optimization are fluence optimization and direct aperture optimization.  I. Fluence optimization In fluence optimization, the beam portals are discretized into uniform rectangular beamlets, or bixels (Figure 2.10(a)). Dimensions of bixels commonly used range from 0.2x0.2 cm2 to 1.0x1.0 cm2. The fluence through each bixel is the only type of treatment parameter used in the optimization and is described by a set of fluence amplitudes x = {xj}, where j is the index of a bixel. The dose distribution to each volume element (voxel) in the patient from a bixel can be pre-calculated as a discrete kernel and is nearly linear to the bixel's energy fluence. The use of a single set of treatment parameters, x, with a direct relationship to dose is advantageous to IMRT optimization as it simplifies its mathematical formulation. A gradient search method can be used for fluence optimization even though the objective function based on dose-volume constraints creates a non-convex problem. While local minima may exist in the solution space, the likelihood of being trapped in a poor solution far from the global minimum is low [56, 57]. The disadvantage of fluence optimization is that the output fluence maps are 'idealized'. In other words, after optimization the fluence maps must be converted into deliverable MLC leaf motion sequences. Figure 2.16 shows a simple fluence map that is easily decomposed into 3 MLC apertures of equal intensity, but realistic maps are often far more complex and can only be approximately recreated by the MLC. The actual MLC delivered treatment will be degraded from the planned treatment due to multiple factors not accounted for during fluence optimization: conversion of continuous fluence into a discrete number of intensity levels, linac radiation head scatter, MLC transmission, MLC mechanical constraints (leaf widths, leaf speed, interdigitation), and dosimetry inaccuracies with small off-axis fields or with low MU.  32  = +  +  Figure 2.16: Example of a fluence map decomposed into 3 MLC apertures of equal weights.  II. Direct Aperture Optimization In direct aperture optimization (DAO), the shapes and weights of the MLC apertures are directly optimized in the planning process thus avoiding the necessity of the complex MLC leaf sequencing step seen after fluence optimization [58]. A general implementation of DAO will be described, but other forms also exist [59]. Prior to DAO, each beam angle is assigned a set number of apertures. The number of apertures, n, determines the number of intensity levels available (2n-1) [44] and unlike fluence optimization, they can vary continuously. For most cases, 5 apertures/beam provide sufficient flexibility in intensity modulation. All aperture shapes are initialized to conform to the beam's eye view (BEV) of the target. BEV is defined as the 2D projection of the structure onto a virtual plane at the treatment isocentre from the view point of the radiation beam. Optimizing MLC leaf positions, which are far from the dose points in the patient, has a weaker influence on dose than fluence optimization. DAO is mathematically more difficult 33  and creates a non-convex problem. Thus, the optimization algorithm utilizes simulated annealing. At each iteration, a treatment variable (any MLC leaf position or any beam weight) is randomly selected for change.  The size of the change is sampled from a  probability distribution (e.g. Gaussian) whose width gradually decreases over the course of the optimization. Any MLC or beam weight constraint is easily incorporated at this point by verifying the selected change does not violate any of the user chosen limits. If the selected change is within allowed boundaries, the objective function is calculated. All changes that improve the objective function are immediately accepted, whereas changes that increase the objective function are accepted with a probability P(i) (Equation 2.17). DAO requires more time to create a treatment plan than fluence-based optimization, but there is no degradation in the delivered plan quality because the MLC leaf sequencing step is avoided. In addition, it has been shown that DAO plans can be delivered with a fewer number of total apertures and total MU than fluence-optimized plans [44].  Therefore,  resulting treatment times are faster and the patient is exposed to less leakage radiation that could induce secondary cancers [60, 61].  2.7.5 Dose Calculation: Pencil-Beam Algorithm During optimization, dose deposited in the patient must be recomputed each time a treatment parameter is altered to calculate the new value of the objective function (Equation 2.7). This process is a major limiting factor affecting the overall optimization time and generally a balance must be found between dose calculation efficiency and dose calculation accuracy. Pencil-beam (PB) algorithms are the most commonly used algorithms in IMRT optimization due to their fast calculation speed [52]. The fluence map for each beam is subdivided into small beamlets, usually of dimensions 0.25x0.25 cm2. The beamlets are small enough that the intensity within each beamlet is uniform. The radiation passing through a beamlet is referred to as a 'pencil-beam'. At a given depth d in water, the spatial dose distribution in a plane perpendicular to the beam axis from a single pencil-beam can be modelled as a 2D dose kernel. The shape of the kernel changes with depth as it is influenced by depth dependent variables such as the photon energy spectrum and the distribution of 34  secondary electrons. The kernel can be derived from measured beam data which is fitted to a double exponential function [62]  (2.22)  r is the radial distance from the interaction point of the radiation. To compute the dose to a voxel within the patient at coordinates x, y and depth d, the dose contributions from all the pencil-beams must be summed using the equation  (2.23)  where dref = user defined reference depth SSD = Source-to-surface distance F(x', y') = Photon fluence map P(x', y', d) = Primary beam off-axis intensity profile shaped by the linac's flattening filter. The squared terms in front of the integrals are to account for the beam divergence. The major disadvantage of PB algorithms is that they are based on dose to water measurements. Corrections for the presence of non-water materials can be applied using 1-D radiological path length scaling in the axis parallel to the beam, but changes in electron lateral scatter are ignored. This can result in treatment plan errors, such as underdosage in lung tumours. 35  Chapter 3  Lung Cancer & Motion Management Strategies 3.1 Lung Cancer Globally, lung cancer is the leading cause of cancer death. In Canada it accounts for 27% of all cancer mortalities [63]. Lung cancer can be divided into two types. Approximately 85% are categorized as non-small cell lung cancer (NSCLC) and the remaining 15% are small-cell lung cancer (SCLC). Lung cancer treatment options include surgical removal, radiation therapy and chemotherapy. The role of radiation therapy is most prominent in early stage (I & II) NSCLC. Generally surgery is the preferred option with reported 5 year survival rates of 60-70% [28]. Approximately 20% of the cases referred to the British Columbia Cancer Agency (BCCA) are for stage I or II NSCLC. Of these patients, approximately 25% refuse surgery or are deemed medically inoperable due to co-morbidities, such as poor pulmonary function, or recent myocardial infarction, and therefore receive radiation therapy. These patients are treated with a conventional fractionation scheme of 60-66 Gy in 30-33 fractions (section 2.6.2).  Relative to surgical resection, the 5 year survival rate of radiation therapy is  significantly poorer and ranges from 13-31% [64, 65].  36  To improve the outcomes of radiation therapy in NSCLC, a method that moves away from the conventionally fractionated regimen, known as stereotactic body radiation therapy, has been under increasingly active investigation over the past decade.  3.2 Stereotactic Body Radiation Therapy Stereotactic body radiation therapy (SBRT) irradiates tumours in fewer fractions (hypofractionated) and to a higher dose per fraction than conventional treatment. High dose per fraction entails an increased risk of toxicity to normal tissues. Therefore, a stringent requirement of SBRT is precise localization of tumour position and knowledge of its motion. Radiation delivery techniques that conform radiation dose more tightly to the tumour and away from critical structures are another necessity. Advancements over the last decade in imaging (e.g. 4D CT, CBCT, near real-time imaging) and in treatment planning and delivery (e.g. IMRT, VMAT) have allowed SBRT delivery with acceptable risk to normal tissues. SBRT is a continually evolving technique but has already been used to treat tumours in the lungs, liver, around the spine and in the genitourinary system (e.g. prostate and renal cancer) with promising results. For lung cancer, the use of SBRT is growing because its outcomes rival those of surgical resection [66]. A meta-analysis of 34 lung cancer SBRT studies involving 2587 patients reported 3-year local control rates of 87% for tumours measuring greater than 3 cm [67]. As of yet, there is no standard fractionation scheme for SBRT lung treatments. Current dose schedules under study include 18 Gy x 3, 12 Gy x 4, 11 Gy x 5, 7.5 Gy x 8 and 5 Gy x 10. A higher dose per fraction is preferred but in many cases, adjacent OARs are the limiting factor. For example, centrally located tumours have higher associated toxicity compared to peripherally located lung tumours in 3-fraction SBRT [68]. At the BC Cancer Agency, the current SBRT protocol prescribes the 12 Gy x 4 regimen for peripheral tumours and 5 Gy x 10 for central tumours.  37  3.2.1 SBRT Mechanism of Action SBRT and conventionally fractionated radiation therapy can both seriously damage tumour DNA leading directly to cell death. SBRT delivers 48-60 Gy in fewer fractions (3-10 fractions) than conventional radiation therapy (60 Gy in 30 fractions). The basis for SBRT's superior outcomes relative to conventionally fractionated radiation therapy is not yet fully understood. Current research suggests that the factors of reoxygenation, repair, redistribution and repopulation, that contributed to the effectiveness of conventional fractionation schemes, are not applicable to SBRT, or are of lesser importance. Instead, the higher dose per fraction in SBRT appears to induce indirect cell death in addition to the direct lethality of DNA damage. A major component of indirect cell death is thought to be the substantial damage to tumour vasculature at SBRT doses greater than 10 Gy. Tumour blood vessels are necessary to the survival and proliferation of tumour cells. Blood vessels are serial structures and any damage blocking blood flow at a point can then catalyze a downstream cascade of cell death, including those of hypoxic cells. Tumour stem cells, which are located near blood vessels, will also be killed as factors that maintain their self-renewing and undifferentiated state can no longer be delivered. The stem cells are normally radioresistant and a source for cancer relapse after radiation. Their destruction contributes to the effectiveness of SBRT in tumour control. Additionally, other factors that enhance indirect tumour cell death may include an immune response and interference with ATP production and protein synthesis triggered by the higher dose per fraction. The reduced importance of reoxygenation, repair, redistribution and repopulation in SBRT can be explained as follows [69]: 1) Reoxygenation of hypoxic cells after a SBRT fraction is inhibited by tumour vascular damage. 2) Repair of tumour cells is either impeded by the nutrient deficient environment resulting from blood vessel injuries or the damage from ablative doses are too extensive to repair.  38  3) Redistribution of surviving tumour cells over the phases of the cell cycle may not occur. Rather than being transiently arrested in a phase, cells are indefinitely arrested after SBRT and can subsequently undergo apoptosis or necrosis. 4) Repopulation is minimized as the entire SBRT prescription is delivered in less than 2 weeks. Tumour repopulation typically commences after 3-4 weeks. Therefore, SBRT needs to kill fewer tumour cells than in conventionally fractionated treatment which requires 6 weeks to deliver.  3.3 Lung Tumour Motion Targeting of lung tumours in radiation therapy is complicated by motion induced by patient respiration.  Respiration can cause the tumours to move in one to all three axes:  cranial/caudal (CC), anterior/posterior (AP) and left/right (LR).  In most cases, the  predominant motion is along the CC axis [70] and can be as large as 3 cm [71] leading to large dose delivery errors if not accounted for during treatment planning. Motion of lung tumours is often modelled as a sinusoid [72].  (3.1)  zo is the tumour position at maximum exhalation (max-exhale), b is the extent of motion, t is the time in seconds,  is the period of a respiratory cycle,  is the starting phase and n  determines the asymmetry of the model (e.g. n = 1,2,3) (Figure 3.1(a)). Typically, the tumour spends more time at the max-exhale phase than at maximum inhalation (max-inhale) and the path taken by the tumour from max-exhale to max-inhale is often distinct from the return path of max-inhale to max-exhale. This is known as motion hysteresis (Figure 3.1(b)). Each patient's respiratory pattern is unique and under free-breathing conditions, the breathing model is often not stable or reproducible. Specifically, the values for zo, b and with time.  39  will change  Exhale CC (cm) inhale AP (cm)  LR (cm)  Figure 3.1: Examples of (a) an asymmetric sinusoidal trace of a respiratory motion and (b) lung tumour trajectory with hysteresis.  3.3.1 Effect of Motion on Dose Distribution Treatment plans in radiation therapy are usually based on a static 3D CT reference image of the patient. Breathing motions during treatment will result in dose difference errors between the planned and delivered dose distribution. Dose errors can be large (>20%) if only 1 treatment beam or fraction is considered, but tends to average out when all beams and fractions are involved [73, 74]. The outcome is a blurring or averaging of the planned dose distribution. The beam penumbra at the field edges are enlarged resulting in a reduction in the dose conformality around the tumour (Figure 3.2). The larger the motion, the greater the blurring in the dose distribution.  40  Figure 3.2: A simple 1D dose profile from an open field at a set depth in water. Blue represents the static plan where points within a radius of 35 mm receive 100% of the dose. As motion increases, the radius of the field receiving 100% of the dose decreases and the beam penumbra increases (red dashed and dotted lines).  The dose blurring can be mathematically modelled as a convolution of the static dose distribution with the probability distribution function (PDF) of the tumour displacement. The PDF will tend towards a Gaussian distribution after multiple fractions such as in conventionally fractionated treatments (~30 fractions).  In some treatment planning  algorithms, motion is incorporated into the optimization by convolving the pencil-beam (section 2.7.5) with the PDF [5]. For SBRT treatments with a small number of fractions, the assumption of Gaussian blurring may no longer be valid and more sophisticated techniques employing computationally intensive 4D dose calculations are necessary.  3.3.2 4D Dose Calculation 4D dose calculation has been made possible with the development of time-resolved volumetric imaging such as 4D CT/respiration-correlated CT [6-8]. 4D CT captures multiple 3D CT images of the patient corresponding to various phases over 1 full respiratory cycle. Typically, the respiratory cycle is divided into 10 phases. Voxels are first identified in one reference 3D CT. Deformable image registration (section 5.1.1) is then used to obtain the 41  voxel displacement vectors from the reference phase to any other respiratory phase allowing for voxels to be continuously tracked. With knowledge of the radiation fields delivered to each phase, dose distributions on each 3D CT data set can be calculated and summed onto the reference 3D CT using the voxel displacement vectors to give the 4D dose distribution. The 4D dose distribution gives the true dose delivered to each voxel of tissue and can be used to calculate the 4D DVH for plan quality evaluation.  3.4 Management of Respiratory Motion Various methods to compensate for lung tumour motion and to ensure that the target is irradiated to its full prescription dose are topics of active research due to the prevalence of the disease and the magnitudes of the induced motions. The following sections provide an overview of the respiratory motion measurement and management techniques that have been explored to date in order of simplest to most sophisticated implementation. The American Association of Physicists in Medicine (AAPM) recommends in Task Group 76 that some form of motion compensation strategy be employed in radiation therapy for tumour movements greater than 5 mm [71].  3.4.1 Motion Encompassing Methods The motion encompassing strategy is the easiest and most commonly used method to account for lung tumour motion. First, the displacement range of the tumour is estimated from CT imaging and then the treatment margins or planning volumes (section 2.6.1) are expanded accordingly (Figure 3.3).  42  (b)  (a)  Figure 3.3: Illustration of the motion encompassing method. The red sphere represents the tumour. The expanded blue surrounding is the PTV. (a) Static PTV (b) Enlarged PTV that encompasses the left/right motion of the tumour.  For the motion encompassing method, CT imaging of the lungs can be approached in three different ways. First in slow CT scanning, the acquisition time is long allowing multiple respiratory cycles to be captured.  The resulting 3D image gives the average  representation of the patient and yields a tumour-encompassing volume. Slow CT scanning has the lightest workload, but is only recommended where there is high-contrast between the tumour and its surroundings (i.e. not near mediastinum or chest wall).  The loss of  anatomical resolution due to CT averaging may also lead to errors in tumour and OAR delineations by the radiation oncologist. The second method is to acquire both max-inhale and max-exhale gated or breath-hold CT scans and to fuse the two images together to obtain the expanded target volume. This methods results in reduced blurring compared to slow CT scanning. Finally, the third method is 4D CT imaging and it has the highest workload. By capturing several (e.g. 10) temporally separated images of the patient breathing, it not only provides the best anatomical resolution but also gives information on the tumour trajectory in relation to OARs and to any fiducial markers used to track respiration. The obvious disadvantage of using a motion-encompassing technique to create the PTV is that a larger volume of healthy tissue is irradiated [5]. This is in direct conflict with SBRT's requirement to minimize healthy tissue exposure by conforming dose to as small a treatment volume as possible. The larger dose per fraction in SBRT can increase the probability and severity of toxicity in adjacent OARs. If the volume of normal tissue exposed to radiation  43  can not be reduced, lower dose per fraction SBRT regimes may be required which would reduce the benefit and limit the applicability of SBRT.  3.4.2 Forced Shallow-Breathing Method Forced shallow breathing (FSB) is one option to minimize intrafraction motion due to respiration. A pressure plate is applied to the patient's abdomen with enough force such that the motion of the diaphragm is limited. Patient breathing becomes shallower causing a reduction in tumour motion range. Negoro et al [75] reported in a study with 18 patients that tumour motion was reduced from 8-20 mm (12.3 mm mean) to 2-11 mm (7.0 mm mean) with abdominal compression. Reproducing the exact compression setup for each treatment fraction can be challenging and requires verification either through CT images or from visualization of implanted fiducials in radiographs. While FSB was originally developed for SBRT of the lung and liver cancers, it is not universally implemented due to patient discomfort.  3.4.3 Breath-Hold Techniques In breath-hold techniques, breath is preferably held at or near maximum inspiration because the expansion of the lung volume tends to increase the separation between the target and OARs and minimizes the volume of the irradiated lung. The breath-hold techniques also require patients to have the ability to follow verbal coaching to produce a controlled respiratory pattern in preparation for breath-holds lasting at least 10-30 s. Breath-holds are always followed by recovery periods and hence for conventional fractionation, treatment times can be longer than motion-encompassing methods by 5-10 min. The implementation of breath-holding has been approached in multiple ways. In deepinspiration breath-hold (DIBH), the patient's breathing is monitored using a spirometer and the therapist is responsible for turning the beam on during breath-hold and turning the beam off when the patient resumes respiration [76]. In active-breathing control (ABC), a balloon  44  valve attached to the spirometer is inflated with an air compressor during breath-hold to help suspend the patient's respiration [77]. The use of a spirometer can cause patient discomfort. One method that does not use a spirometer is the held-breath self-gating technique [78]. In this technique, the patient is given a switch to depress when breath holding begins. This clears an interlock allowing the therapist to begin irradiation. The beam is later turned off either by the therapist or when the patient releases the switch.  This method is heavily reliant on the patient's ability to  simultaneously cooperate with breathing instructions and operate the switch. Also while some patients believe that they are holding their breath, it has been observed that internal anatomical motions, such as in the diaphragm, can still occur. An alternative to the spirometer in respiratory monitoring is to use optical infrared tracking (section 2.5.2) such as in the Varian Medical System's real-time position management (RPM) system. In the RPM system, a box with reflective markers is placed on the patient's abdomen. An in-room infrared tracking camera detects motion of the reflective markers which is maximal in the AP direction during respiration. The patient respiratory pattern is constantly monitored and beam-on and beam-holds can automatically be triggered according to preset thresholds [79]. The respiratory phase is indirectly inferred from the external measurement of the patient's abdominal motion and its correspondence must be properly verified prior to treatment using some form of x-ray imaging. The main disadvantage of breath-holding techniques in lung cancer is that many patients are too ill to reproducibly perform breath-holding multiple times during a treatment fraction. In one study performed at the Memorial Sloan-Kettering Cancer Center, 60% of patients were unable to comply [76].  Generally for a 2 Gy fraction delivered using IMRT, a  minimum of 10-15 breath-holds are required. In SBRT, dose fraction sizes range from 5-18 Gy and would place even further physical strain on patients.  45  3.4.4 Respiratory Gated Techniques Respiratory gated techniques allow the patient to breathe freely and the treatment volume is minimized by irradiating the tumour only when it is within a given location known as the gating window (Figure 3.4) [29, 30, 80, 81]. The selection of the location and width of the gating window is a compromise between treatment delivery efficiency and healthy tissue sparing. For example, both a wider window and treating the tumour near max-exhale allows the radiation beam to be active for a greater fraction of the respiratory cycle, hence benefitting treatment times. The exhale portion of the respiratory cycle usually lasts longer and has more stable tumour positions than the inhale portion. However, a wider gating window contains more residual tumour motion.  Also, it can be more dosimetrically  advantageous to treat the tumour near max-inhale when the lung volume has expanded.  Inhale  Exhale  Gating window  Beam on Beam off Time (s)  Figure 3.4: Illustration of gated radiation delivery. The beam is only turned on when the tumour position is within the gating window.  To gate the radiation beam, continuous monitoring of the patient's breathing motion is required via either an external respiratory signal or an internal fiducial marker. Radiation delivery will automatically be triggered on or cut off when the patient's breathing enters or exits the gating window. Options for an external respiratory signal include patient surface markers tracked with an infrared camera (e.g. RPM system), a strain gauge within a belt 46  wrapped about the patient's mid-section, or a 3D video camera that monitors the patient's ventral surface. Internal signals can be provided by implanting radiopaque fiducials in or near the tumour. These fiducial markers can then be detected by a stereoscopic x-ray imaging system, or by the linac's EPID or OBI systems (section 2.5.2). Internal fiducials are needed because imaging lung tumours alone seldom provides enough contrast from surrounding tissues to permit automatic segmentation and image registration. The benefits of measuring external signals are that data acquisition and processing times are fast and the patient receives no extra radiation exposure. The disadvantage is that the correlation between the surrogate signal and the tumour position is not as robust as an internal signal and can drift over time [82]. For the internal signal acquisition, aside from the added radiation dose to the patient, implantation of fiducial markers is invasive and carries the risk of pneumothorax [83]. The discontinuous delivery of radiation in respiratory gated techniques results in longer treatment times. The fraction of the respiratory cycle where the beam is enabled is referred to as the duty cycle and its value depends on the patient's breathing pattern. Generally, duty cycles can range from 30-50% [71] which translates to treatment times that are at least 2-3 times longer than plans delivered using a motion encompassing method. Considering SBRT treatments are already longer than conventionally fractionated treatments due to the higher dose per fraction, gating SBRT will further extend treatment times. Patients may experience greater discomfort leading to an increased risk of patient movement and dose delivery errors. Patient throughput will also decrease.  3.4.5 Respiration Synchronized Techniques In respiration synchronized techniques, the radiation beam dynamically tracks the tumour motion as the patient breathes freely. This allows treatment margins to remain small while simultaneously maintaining continuous radiation delivery (i.e. 100% duty cycle). Respiration synchronized techniques are the most complex to implement. They require realtime imaging of tumour position, the ability to predict future tumour positions to compensate for delays in the treatment system's response time and a method to reposition the beam. 47  The options for real-time imaging of tumour position are the same as discussed in the previous section on respiratory gated techniques. Frequently, a hybrid imaging system that combines both internal and external respiratory acquisition methods is used. For example, continuous tracking of the respiratory cycle can be provided through infrared imaging of patient surface markers while periodic x-rays are taken to verify or update the correlation between the external surrogate and the internal tumour motion [84].  To ensure the  synchronicity between the radiation beam and the tumour trajectory is not affected by system delays, heuristic learning algorithms such as Neural networks are used to predict future tumour positions [85-87]. For linacs, the most common option for realigning the treatment field to the tumour trajectory is via continuous motion of the MLC leaves. Leaf response times have been estimated to range from 100-200 ms or more. The methods used to create respiratory synchronized treatment plans and to calculate final dose distributions can be categorized into 2 approaches based on how knowledge of the tumour movement is integrated into the treatment planning process. In the first approach, plans are optimized on a 3D CT of the patient that captures one respiratory phase and then altered post-optimization to match tumour trajectory. In the second approach, all patient motion is directly incorporated into the plan optimization stage by using a 4D CT of the patient.  I. 3D CT Plan Optimization The respiration synchronized technique that creates treatment plans on a static 3D CT representation of the patient is commonly referred to as dynamic multi-leaf collimator (DMLC) tracking radiation therapy [88-92] or tracking for short. In tracking, a 3D CT representing one respiratory phase is chosen from the 4D CT planning data set.  Plan  optimization is performed on the selected 3D CT image as if the patient was immobile (i.e. no motion encompassing margins) creating a 3D plan. Tumour trajectory information is only used to alter the treatment plan post-optimization. Essentially, the MLC apertures sequenced from the static plan are translated according to the displacement of the tumour centroid. The goal is to reproduce the planned dose distribution as closely as possible.  48  The modification of planned MLC apertures can be done either prior to treatment delivery using the 4D CT planning data set (Figure 3.5 (a)) or during the delivery using data acquired from the real-time imaging system (Figure 3.5 (b) using the static plan as the start plan). In the first option, by adapting the MLC leaves to motion before plan delivery, it can be verified that MLC mechanical constraints, such as leaf speed, will not compromise the motion tracking capabilities. Also, a post-optimization 4D dose calculation (section 3.3.2) can be performed to check that changing the 3D plan into a tracking plan did not create any unintended radiation hot spots in the OARs. The disadvantage of pre-treatment tracking is that the patient must then reproduce the same respiratory pattern seen in the planning 4D CTs during treatment delivery. A patient respiratory guidance system would be required since it is well known that there is variability in patient breathing from cycle to cycle [70, 93]. The second option of translating MLC leaf positions based on real-time free-breathing patterns during delivery completely removes the burden of treatment compliance from the patient. Instead, the focus is on the challenging task of designing a system that can image and process tumour location, calculate new MLC leaf positions, and reposition MLCs in realtime without sacrificing treatment accuracy. The entire system response latency period must be minimized to avoid large errors in the motion prediction algorithm. The drawback of realtime tracking is that periods where the mechanical limits of the MLC leaves prevent accurate tracking can not be anticipated and accidental creation of hot spots will not be discovered until a post-delivery 4D dose calculation. Suh et al [89] proposed combining both pre-treatment and intra-treatment tracking by using the pre-treatment motion tracking plan as input for the intra-treatment tracking (Figure 3.5 (a) and (b)). The motion tracking plan would give a better estimate of the delivered dose than the static plan on a reference 3D CT and potential problems with MLC deliverability or radiation hot spots can be identified prior to treatment. Additionally, the patient breathing pattern during treatment can diverge from the planned pattern as intra-treatment tracking would compensate for the difference. Naturally, this method is still based on the assumption that the breathing pattern seen during treatment does not substantially diverge from the breathing pattern in the 4D CT planning data set.  49  BEFORE TREATMENT TRACKING 4D CT planning data set  DURING TREATMENT TRACKING  Static plan on reference 3D CT  Starting plan  Real-time imaging system  DMLC algorithm modifies MLCs  DMLC algorithm modifies MLCs  Motion prediction algorithm  Motion tracking plan  New MLC positions  (a)  (b)  Figure 3.5: Diagram of the workflow when tumour tracking is performed (a) prior to treatment or (b) in real-time during treatment (adapted from [89]).  II. 4D CT Plan Optimization Optimizing treatment plans on 4D CT data addresses 2 limitations of tracking plans created on 3D CT data. The first issue is that tracking will never precisely reproduce the static planned distribution.  There will always be residual dose errors because shifting beam  apertures can not fully account for tissue density changes during respiration, differential tissue motion along a ray path and tissue motions perpendicular to the leaf motion [36]. The second more important issue is that tracking does not fully exploit tissue motion information to improve healthy tissue sparing. Tracking only alters the shape of the radiation field based on tumour trajectory. Neither the field shape nor its intensity is modified to account for the relative motion between the target and nearby healthy tissues [89]. For example, if the 4D information is also included during the plan optimization stage, critical structures such as the heart, spinal cord, and esophagus could be further spared if higher radiation doses are delivered to the tumor at instances when it has moved further away from these structures.  50  Previous studies have already shown that the changing anatomy of the entire patient can result in superior OAR sparing in certain respiratory phases over others [5, 89, 94]. To address these limitations, the temporal information of the patient's anatomy contained in 4D CT data should be fully incorporated into the treatment plan optimization stage. This will be referred to as 4D treatment planning. The term "4D treatment planning" has been associated with several treatment planning strategies including the use of a motion encompassing margin, gating and tracking so long as the 4D CT data was used in some postoptimization capacity either to recalculate the delivered dose or to modify the treatment fields. For clarity, the use of "4D treatment planning" in this study will refer only to the instances where 4D CT data is directly integrated into the plan optimization. At present, breathing synchronized 4D optimized treatment plans are the most advanced form of respiratory management for radiation therapy. Plans are generated based on true voxel doses because 4D dose calculations are performed within the optimization rather than after. Sparing of OARs should be superior to tracked plans. Unlike breath-holding and forced shallow-breathing plans, patients are not overly strained because they are allowed to breathe naturally.  Treatment times are not prolonged extensively by frequent beam  interruptions as in gating. Motion encompassing margins are avoided by the inclusion of 4D CT in the optimization which should inherently result in beam apertures that follow tumour trajectory. The goal of this thesis was to develop a 4D treatment planning system for volumetric modulated arc therapy (4D VMAT). VMAT is a linac-based technique that is able to deliver highly conformal treatment plans in a very time efficient manner making it highly suitable for SBRT in lung cancer [95-98]. The details of 4D VMAT, its implementation and the evaluation of its plan qualities and treatment times are presented in chapters 4 and 5.  51  Chapter 4  Implementation and Evaluation of 4D VMAT for Periodically Moving Tumours 4.1 Introduction to VMAT The linac-based rotational form of IMRT is most commonly referred to as volumetric modulated arc therapy (VMAT). Rather than using 7-9 intensity modulated beams at static gantry angles as in conventional IMRT, VMAT delivers modulated radiation in a continuously moving arc around the patient via gantry rotation of the linac (Figure 4.1). Current clinical systems provide fluence modulation not only by the motion of the MLC leaves but also by the variation in the dose rate and gantry speed of the linac. A VMAT treatment plan can consist of one or more full or partial gantry arcs with optional static or dynamic MLC rotation and/or couch translation/rotation. The additional flexibility provided by multiple beam directions allows the creation of more highly conformal treatment plans with lower average dose to normal tissues due to spreading of the irradiation over a greater volume. Also, VMAT's ability to deliver the entire treatment fraction in an uninterrupted fashion substantially improves the time efficiency relative to static-gantry/conventional IMRT. However, the development of VMAT optimization algorithms capable of fully exploiting all the new variables to create high quality time efficient treatment plans has, until recently, been unsuccessful. The VMAT optimization problem is far more complex than that  52  of static-gantry IMRT and some of VMAT's plan flexibility is lost due to extra mechanical constraints required to ensure seamless rotational delivery.  Figure 4.1: Illustration of VMAT delivery. Gantry rotates continuously during radiation treatment. (Image from varian.mediaroom.com, image courtesy of Varian Medical Systems Inc., All rights reserved)  4.2 Development of VMAT Rotational fluence-modulated arc therapy delivered on a linac was first proposed by Yu in 1995 [99] under the name intensity-modulated arc therapy (IMAT). In the initial study, the dynamic arc was approximated by 55 static beams (control points) spaced 5º apart and their respective intensity maps were determined via fluence optimization. Post-optimization, a conventional IMRT MLC leaf sequencer translated intensity maps into sets of beam apertures. The more modulated an intensity map, the greater the number of apertures in a set.  Figure 4.2(a) shows a simplified example of the fluence map at gantry angle 0º  segmented into a set of 3 apertures. Each aperture in a set was delivered in a separate arc. To ensure that the MLC leaves could smoothly morph their aperture from one beam angle to the next, a second specialized MLC leaf sequencer was developed to account for the limits on MLC leaf displacement per degree. 53  The work by Yu (1995) was a feasibility study and was never adopted clinically due to inefficiencies in treatment time and plan quality degradation [100]. Up to 13 full and partial arcs were required to deliver a treatment of 250 MU in 14.5 min. In general, 8-10 arcs could only achieve 3 levels of intensity [101]. Additionally, the deliverable fluence maps were degraded from the optimized ideal fluence maps as they were processed through two separate MLC leaf sequencers. In the years following the initial proposal of IMAT, various forward planning and inverse planning strategies were explored in an attempt to create VMAT plans that were superior to static-gantry IMRT plans in both target dose conformality and treatment time efficiency.  Segmented Segmented & delivered in 3 arcs  3 2 1  3  3A  3B  3C  2  2A  2B  2C  1A  1B  1C  1A  2B  3C  Segmented  1  Delivered in 1 arc  2  1  3  Delivered in 1 arc  Adjacent control point  (a)  (b)  (c)  Figure 4.2: Diagram showing different VMAT optimization strategies. For simplicity only 3 apertures are shown per control point. (a) Method where each sequenced beam aperture for a control point is delivered in a separate arc. (b) Method where all beam apertures of a control point are delivered in a single arc by spreading them out to other angles. (c) Method where several control points are grouped together and only 1 aperture from each control point is delivered. None of the delivered apertures in a group can have the same beam intensity.  4.2.1 Forward Planning Forward planning simplifies the process of creating VMAT treatment plans by removing some of the flexibility in the treatment parameters. Generally, a user specifies the MLC leaves to conform to the beam's eye view (BEV) of the target in one arc. Additional arcs are 54  added for each OAR that overlaps with the target. In these extra arcs, the MLC leaves conform to the target's BEV minus the OAR overlapped area. Arc weights are also manually adjusted by the user.  For treatment planning, a moving arc of radiation is generally  approximated by beams spaced every 10º and MLC positions at all other gantry angles are found by interpolation. In the forward planning IMAT work by Yu et al [102], 2-5 arc plans were created to treat 50 patients with cancers of the central nervous system, head and neck, and prostate. Plan qualities in comparison to static-gantry IMRT had mixed results and the average treatment time was 7.5 min [100]. The approximation of the dynamic arc as a series of beams spaced every 10º was accurate for high dose levels near the target but was inaccurate for lower isodose areas. It was found that for accurate dose calculation, a spacing of at most 3º was necessary. Similar forward planning IMAT work was also investigated by Wong et al [103] who also showed 2-5 arcs were required for plan delivery. Other researchers incorporated both forward planning and inverse planning into the IMAT treatment planning process [104, 105]. Forward planning was used for determining the number of arcs and MLC leaf positions as described earlier while inverse optimization was used to calculate the arc weights. Forward planning improved the treatment delivery efficiency over the original IMAT but the difference relative to IMRT treatment times was not significant. Forward planning also had many other disadvantages.  The quality of plans were strongly correlated to the  experience and skill of the treatment planner and planning times ranged from 1-2 hours vs. the 20-60 min for IMRT [105]. The plan quality for forward planned IMAT was shown to be comparable to IMRT in some simple cases such as prostate, but could fail for more complicated sites such as head and neck cancers where multiple targets were prescribed to different doses [41]. Finally, forward planning is site specific and not generalizable to all tumour sizes and locations. Inverse planning is needed to fully explore the potential of IMRT arc delivery.  55  4.2.2 Inverse Planning Research on inverse planning for rotational IMRT has explored both DAO methods and fluence optimization methods. The previously described advantages of DAO over fluence optimization, such as fewer apertures and MUs (section 2.7.4), are of even greater importance in rotational IMRT. The requirement of beam shape interconnectedness from angle to angle is easier to enforce when there are fewer apertures and the limits can be directly incorporated into the DAO algorithm. Fluence optimization, on the other hand, only handles the limits on leaf travel distance between gantry angles post-optimization. The addition of this angular dependent MLC limit to the set of conventional limits (section 2.7.4) further inhibits the ability of the MLC leaf sequencers to replicate the optimal intensity maps. In contrast, the advantage of fluence optimization over DAO is the faster convergence to a solution which can be even more important in rotational IMRT due to the large increase of treatment parameters. Earl et al [101] attempted to improve on the original IMAT technique by using DAO instead of fluence optimization. Arcs were modelled as 36 static beams spaced 10º apart and initial apertures conformed to the BEV of the target. While demonstrating the feasibility of DAO for IMAT, convergence to a solution was longer than an hour [100] and a large number of arcs (6-10) were still needed to deliver the treatment in 10-20 min. Shepard et al [100] continued the use of fluence optimization for IMAT, but developed an improved IMAT MLC leaf sequencer called continuous-intensity-map-optimization (CIMO). CIMO used simulated annealing to simultaneous optimize the deliverable aperture shapes and weights while minimizing the sum of absolute differences between the optimized and delivered intensities.  With CIMO, the delivered dose distributions were nearer to the  planned dose distribution, but plans still required 4.6-16 arcs to deliver the treatment in 5-15 min. The study also showed that when delivered dose was calculated at a finer beam resolution (1 beam/2º) rather than at the planned resolution of 1 beam/10º, there would be discrepancies in the PTV dose coverage. The high number of gantry arcs in the previous studies prevented IMAT from shortening treatment times. Multiple overlapping arcs were required because it was assumed that linac 56  dose rate and gantry rotation were constant within an arc. Linacs by different manufacturers have varying capabilities. By allowing dose rate and/or gantry rotation to vary within an arc, beams of different weights could all be delivered together in a single arc potentially improving treatment delivery efficiency. In general, for single-arc IMRT plans created from fluence optimization, the optimal intensity maps were segmented into apertures which were then spread out to adjacent angles (Figure 4.2(b)). In arc-modulated radiation therapy (AMRT) [40], graph algorithms were used to sequence the MLC leaves from intensity maps optimized at 10º intervals. In a VMAT algorithm by Cao et al [41], the CIMO algorithm was used to sequence intensity maps spaced 10º-30º apart. By delivering the entire treatment fraction in a single arc, treatment times in both studies (2.5-4.5 min) were only a third to a half of static-gantry IMRT times. Delivered plan quality degradation from the optimal plan still existed. A concern with spreading out apertures that have been optimized at one angle to other angles is the fact that the beam's eye view of the OARs vary with gantry angle. Therefore, the dispersed apertures will not properly account for the relative shift between the normal tissues and the radiation beam. Many factors can influence the size of the resulting dose error, but Webb and McQuaid have suggested the angle shift be no larger than 5º [106]. To avoid the issues associated with fanning out apertures, Bedford proposed a VMAT algorithm that combined both fluence optimization and DAO methods [107]. First, intensity maps were created at every 5º and then sequenced into apertures sets. Aperture sets within 10º of each other were grouped together. It was assumed that adjacent aperture sets were fairly similar to each other. Consequently, one aperture from each beam angle in a group was selected for delivery and the rest were discarded (Figure 4.2(c)). The apertures chosen for delivery represented different intensity levels. To recover any plan degradation caused by the segmentation, a second optimization on MLC positions and weights was performed using DAO. This VMAT algorithm had difficulty handling cancers requiring complex modulation leading to treatment times that were inferior to static-gantry IMRT. Single-arc IMRT algorithms based only on DAO have been proposed such as sweepingwindow arc therapy (SWAT) by Cameron [108] and arc-modulated cone beam therapy 57  (AMCBT) by Ulrich et al [42]. Unlike DAO for static-gantry IMRT, only one aperture is allowed per beam angle per arc due to gantry rotation. In SWAT, the starting beam apertures were initialized in a manner that causes the MLC leaves to sweep back and forth over the target during gantry rotation and final leaf positions were determined using simulated annealing while optimal beam weights were calculated analytically. Only 24 beams spaced 15º apart were used to model each arc and convergence to a solution was slow. In AMCBT, the initial beam apertures were anatomy-based in that they considered both the target and OARs positions. Final fields shapes were found using a tabu search algorithm [109] while beam weights were optimized using a gradient algorithm. The tabu search algorithm is an iterative neighbourhood method that avoids oscillating between a few solutions by maintaining a 'taboo' list of already visited solutions.  AMCBT gantry rotation was  approximated by 36 beams and maximum MLC leaf travel distance between beam angles was not considered.  Both SWAT and AMCBT encountered issues with insufficient  computer memory due to the greater number of beams in rotational therapy. For a VMAT algorithm to be successfully implemented in the clinic, it would require the following characteristics: 1) High-resolution sampling of the treatment arc during plan optimization for accurate dose calculation (interval < 5°) 2) Flexible optimization allowing creation of highly conformal and time efficient treatment plans despite tight restrictions placed on beam modulation/degree due to requirement #1 3) Quick convergence of the optimization to a solution despite tight restrictions placed on beam modulation/degree due to requirement #1 Such a VMAT algorithm was finally developed by Otto [39] and was quickly commercialized as RapidArc® by Varian Medical Systems in 2008. All subsequent work presented was based largely on the VMAT algorithm by Otto (section 4.3) prior to its commercialization.  58  4.3 VMAT Algorithm The VMAT algorithm by Otto is a DAO based method. MLC leaf positions and beam weights are used as optimization parameters.  The dynamic 360° arc of the linac is  approximated by a minimum of 177 static beams. To reach an acceptable plan solution, the optimization is guided by a cost function based on dose-volume constraints as described by Bortfeld et al [51, 110] (section 2.7.1). Multiple maximum dose-volume constraints may be set for each target or healthy tissue structure. Targets may also be subject to minimum dosevolume constraints.  The cost of each constraint is calculated using a quadratic dose  difference function multiplied by a priority value. The total plan cost equals the sum of the individual constraint costs (section 2.7.2). The algorithm will hereafter be referred to as 3D VMAT to distinguish it from the 4D VMAT system that will be introduced in section 4.4.  4.3.1 Angle Dependent Optimization Constraints DAO algorithms normally incorporate constraints for MLC leaf widths, maximum leaf speed and maximum dose rate. To ensure smooth rotational delivery, 3D VMAT has additional gantry angle dependent constraints for the MLC leaves and beam weights:  (4.1) and (4.2)  MU,  and x are the MU beam weight, gantry angle and MLC leaf position, respectively.  For Equation 4.1,  can be calculated as follows:  59  (4.3)  The  notation represents the maximum MU beam weight change over time  and should not be confused with  which is the notation for the maximum dose rate in  a conventional linac (e.g. 600 MU/min). To illustrate the difference, a continuous radiation beam moving at a constant rotational speed around a target can be approximated by 60 evenly distributed beams. Each beam can have a weight of 10 MUs resulting in the target receiving a total of 600 MU (Figure 4.3(a)). In contrast, a dose of 600 MU can be delivered if a single beam irradiates the target at 600 MU/min for 1 min (Figure 4.3(b)). The single beam has an MU weight of 600 MU.  Dose at patient reference point  Beam weight MU  MU  600 10  Beam # (a)  60  60  Time (s) (b)  Figure 4.3: An illustrative explanation for (a) the beam MU weight change notation and (b) the linac dose rate notation.  is the linac's gantry rotation speed. For Varian linacs, the gantry requires a minimum of 60 s to complete a 360° arc  .  if it is desired that treatment is completed as quickly as possible. Conversely, by allowing gantry speed to decrease within an arc, there is a greater range in the value of and dose can be more closely sculpted around the tumour. To balance the  60  trade-off between shorter treatment times vs. better plan quality, the 3D VMAT algorithm allows  to fluctuate during delivery and uses a flexible constraint of  (4.4)  instead of Equation 4.3.  is the average MU of all the beam weights present in the  optimization at a given point in time, t. To prevent over modulation of the radiation beam, an absolute cap on the total MU weight that any given beam aperture can have is set to  .  (4.5)  This value is considered large and will not negatively constrain the optimization. For Equation 4.2,  is calculated as follows  (4.6)  In a Varian Millennium 120 leaf MLC, the maximum leaf speed is  .  is used to guarantee that excessive leaf motions do not compromise treatment delivery efficiency. Furthermore,  can not be too large or else the assumption  that dose calculations for static beams are an accurate approximation of dynamic radiation delivery will fail.  61  4.3.2 Progressive Beam Sampling The key feature of the 3D VMAT algorithm that separates it from previously proposed VMAT algorithms is the progressive sampling of the static gantry beam angles over the course of the optimization to approximate a continuous arc of radiation. As shown in Figure 4.4(a), optimization begins with a coarse sample of evenly distributed beams (e.g. 5-13 beams) whose apertures conform to the BEV of the target. Changes to MU beam weights and MLC leaf positions are randomly sampled from uniform distributions and  .  and  are functions of the angular spacing,  , between the  beam aperture being optimized and its nearest neighbours.  (4.7)  (4.8)  After a period of time involving many MLC leaf and beam weight changes, a new beam sample is added to the set of optimizable apertures (Figure 4.4(b)). The new beam sample is inserted mid-way between two existing beams and its MLC leaf positions are linearly interpolated from the MLC positions of adjacent beams. The MU weight of the new sample is based on a redistribution of weights from its immediate neighbours according to the equations: (4.9)  (4.10)  and  62  (4.11)  S is the sample index of the new beam sample. MUnew is the new MU weight and MUold is the MU weight prior to the addition of the new sample. Optimization continues and further beam samples are added successively to the optimizable set following the pattern in Figure 4.4(c) to (e) until a desired sampling frequency is reached.  Initial Arc Samples (a) l Arc Gantry Samples Range  3 (b)  1  (c) 2  4  (d)  1  5  (e)  6  st  1 New Sample  Nsamples = Ninit = 6 Nsamples = Ninit +1= 7  Nsamples = Ninit +5=11  Nsamples = Ninit +6=12  Nsamples = Ninit +10=21  Figure 4.4: Modeling of a continuous gantry arc using a progressive sampling of static beam angles. (a) At the start of optimization, the gantry range is coarsely sampled. (b) After a given amount of time, a new sample is added between two pre-existing samples. (c)-(e) Further additions of beam sample apertures to the optimizable set follow the illustrated pattern until the desired sampling frequency is attained.  The use of progressive beam sampling is the key to 3D VMAT's success. It allows 3D VMAT to smoothly balance the competing demands of high-resolution beam sampling for dose calculation accuracy against flexible optimization parameters needed to easily reach the optimal solution. Near the beginning of optimization, when sample spacing  is wide and  treatment parameters are far from the best solution, optimization flexibility is high because the iteration steps sizes are allowed to be large (Equations 4.7 and 4.8). Dose calculation accuracy is sacrificed to more quickly reach the optimal plan. As more beams are added to the arc and optimization nears a solution, optimization flexibility diminishes because the value of  decreases leading to proportionally smaller iteration step sizes, but the accuracy  of dose calculation increases due to finer sampling of the arc. The end result is a plan that is both of high quality and high dose accuracy. 63  Progressive sampling also allows rapid convergence of the optimization to the solution. In 3D VMAT, changes to MLC leaf position and beam weight are only accepted if the objective function decreases. However, the DAO problem is non-convex. Rather than relying on a time consuming simulated annealing algorithm, escape from local minima is accomplished by the addition of each new beam sample which generally perturbs the value of the objective function.  The size of the perturbation will be greater at the start of  optimization when few beams represent the treatment arc. This is beneficial because the objective function will also be far from the global minimum. As the gantry range between beams decreases and the objective function approaches the global minimum, insertion of new beam samples will naturally cause a smaller disturbance. To compensate for the changing magnitude of the perturbation, the interval between each new beam sample addition (e.g. CPU time or number of successful iterations) follows the form of a decreasing exponential. As a result, at the start when there are fewer beam samples and greater perturbations, it is balanced out by exponentially more iterations. Conversely, when the arc is more closely sampled and the optimal solution is near, exponentially fewer iterations occur. In the work by Otto, the effectiveness of progressive beam sampling was demonstrated by 3D VMAT's creation of a treatment plan superior to static-gantry IMRT for a difficult head and neck cancer. The treatment plan had three separate targets all prescribed to different dose levels. Optimization time was 1 hour and gantry sample spacing of no more than 2° was necessary to maintain dose modeling accuracy. In comparison, it was estimated that a VMAT algorithm incorporating all the finely sampled beams right from the start of a simulated annealing based optimization would require nearly a month to converge to a solution. If given only 1 hour, the objective function value was at least a magnitude greater than 3D VMAT. Treatment time of 3D VMAT's head and neck plan was 1.8 min for delivery of a 2 Gy fraction using a maximum dose rate of 600 MU/min.  This is  approximately only a quarter of the static-gantry IMRT time. For simpler treatment sites, 3D VMAT can converge to a solution in as little as 10 min. The general technique of moving from coarse to finer parameter space sampling when searching for a solution is known as multi-resolution optimization. Shortly after its use in VMAT optimization was demonstrated by Otto, Bzdusek et al [111] proposed another form 64  of multi-resolution optimization. In their work, VMAT begins with fluence optimization on beams samples spaced every 24° in an arc. Resulting apertures from fluence optimization are then spread out to produce beam intervals of 8° and a second optimization using DAO is performed. Final dose calculation is performed at a beam spacing of 4°. The authors speculate that plan quality can be further improved for complex cases if optimization is performed using a higher arc sampling rate of 2°. This version of VMAT is marketed as SmartArcTM by Philips Medical Systems, Inc.  4.4 4D VMAT System The 4D VMAT optimization system implemented in MATLAB®, is an extension of the 3D VMAT algorithm by Otto [39]. The key characteristic of the 4D VMAT system is that while other radiation therapy techniques, such as gated VMAT and 3D VMAT, rely on a static representation of the patient based on 3D CT data, 4D VMAT integrates the patient's 4D CT data into the optimization process.  This is achieved by correlating consecutive beam  apertures to consecutive CT phases (Figure 4.5). Only one CT phase is assigned per beam, generating treatment plans with respiratory phase-optimized apertures whose deliveries are synchronized to the patient's breathing motion. As explained in section 3.4.5 part II, by exploiting patient 4D CT motion information during optimization, the ability of resulting plans to spare healthy tissue should be superior to plans created on 3D CT data.  65  Tumour motion  CT 1  CT 2  CT 3  CT 4  CT 5  CT 6  (a) tphase  Time  Figure 4.5: (a) A schematic showing segmentation of the patient's respiratory cycle into multiple phases. Colours represent specific CT phases 1 through 6. (b) At the start of treatment plan optimization, the arc is coarsely sampled with few beam apertures. (c) As optimization progresses, more beams are inserted. Numbers represent the order in which beam apertures are introduced into the optimization process. (d) By the end of optimization, the arc is fully sampled and sequentially delivered beams correlate to sequential CT phases. The 4D CT data is sampled multiple times over the arc. Note that (a) - (d) are simplified illustrations. Real plan optimizations uses 4D CT data with 10 respiratory phases, arcs, at least 177 beam apertures per arc, and 1-3 arcs.  The synchronization of radiation delivery to respiratory phases of equal periods results in a constant gantry rotation [35, 38]. The time required for one arc rotation, tarc, is calculated by  ( 4.12)  66  where Nbeams is the number of beam apertures in one arc, and tphase is the duration of one respiratory CT phase (Figure 4.5(a)). While the above equation is simple, it is highly dependent on the complex synchronization between the mechanical constraints of the linac and the patient’s breathing pattern. For example, radiation delivery times may be reduced by minimizing the product of Nbeams and tphase with the caveat that the time for a single arc must not go below 60 seconds due to the maximum gantry rotation speed. An excessively small tphase value will also compromise plan quality because as each beam aperture in an arc is correlated to a respiratory phase, tphase also represents the time allowed for MLC movement and radiation dose deposition per aperture. A short tphase combined with the constraints on the MLC leaf velocity (3 cm/s) and the radiation dose rate (  600 MU/min) will  reduce the flexibility in modulating and shaping the radiation aperture. Conversely, a tphase too large will not only increase treatment time but also poorly sample the tumour motion and hence reduce the capacity of the 4D VMAT system to boost healthy tissue sparing by modulating radiation according to tumour trajectory. The value of Nbeams is influenced by several factors. Nbeams must be approximately 180 or greater to accurately model a 360° dynamic arc [39]. A greater number of beams in an arc can increase the flexibility in beam modulation without increasing the value of tphase. However, for simple treatment plans greater flexibility in beam modulation may be superfluous and unnecessarily prolong treatment times. A more thorough study on 4D VMAT treatment times will be presented in chapter 5. The new 4D VMAT MATLAB code retains its 3D VMAT optimization capabilities and has been expanded to also perform gated VMAT optimization. In addition, a function capable of converting beam apertures from a static 3D VMAT plan into a tracked VMAT plan post-optimization based on tumour centroid motion was also implemented.  67  4.5 The Potential for Healthy Tissue Sparing in 4D VMAT 4.5.1 Motivation The primary goal of the following study was to evaluate, under a range of controlled conditions, the difference in healthy tissue sparing of 4 different radiation therapy motion management strategies: 1) 4D VMAT, 2) tracked VMAT, 3) gated VMAT and 4) 3D VMAT.  Completely new code capable of treatment plan optimization and 4D dose  calculation for all the techniques was written in MATLAB. The secondary goal was to experiment with different combinations of Nbeams and tphase values to better understand their interaction. As explained in section 4.4, the values of these 2 optimization parameters strongly influence the delivery time and plan quality of 4D VMAT. The product of Nbeams and tphase sets the gantry rotation period (Equation 4.12). Gantry rotation speed is then fixed to  (4.13)  By restricting gantry speed to a constant value, the flexible constraint on the amount of radiation that can be delivered per beam aperture (Equation 4.5) will be replaced by a significantly lower value.  (4.14)  Nfx is the number of treatment fractions. The switch to a tighter constraint on will have a negative impact on the ability of the 4D VMAT optimization algorithm to spare healthy tissue. This in turn conflicts with the primary goal of the study. To avoid any interference of the secondary goal with the primary goal, all 4D VMAT optimizations were performed with the flexible constraint for  68  (Equation 4.5) so  that the maximum potential of OAR sparing in 4D VMAT could be obtained. optimization, the restrictive constraint for  Post-  (Equation 4.14) was applied to the  treatment plans. If MU weights of some beams were greater than the absolute constraint, the excess radiation would be delivered in a subsequent second, third, or multiple gantry arcs. Total treatment time, T, was then  (4.15)  where Narcs was the number of gantry arcs required to deliver the full radiation dose of the beam aperture with the largest optimized MU weight,  . The extension in 4D  VMAT delivery times over 3D VMAT times can provide a sense of how to better balance the values for Nbeams and tphase.  4.5.2 Methods To investigate the performance of the 4D VMAT system, 3 different sets of simulations were performed using two separate water equivalent phantoms (Phantom A and Phantom B). These phantoms are illustrated in Figure 4.6 with each target centered at the treatment isocentre. The static position shown in Figure 4.6 was considered the reference phase. Simulation sets 1 and 2 both used phantom A where a cylindrical target 4 cm in diameter and 2 cm in length was surrounded by a half-ring OAR. However, set 1 simulated target motion in the superior/inferior direction (Figure 4.7(a)) while set 2 simulated anterior/posterior motion (Figure 4.7(b)). Simulation set 3 used phantom B where a spherical target of radius 1.5 cm was encompassed by a half-cup OAR. The spherical target motion was in the superior/inferior direction (Figure 4.7(c)).  69  (a)  (b)  Figure 4.6: Simulations were performed using phantom A (a) or phantom B (b). In phantom A, a cylindrical target was surrounded by a half-ring OAR. In phantom B, a spherical target was surrounded by a half-cup OAR. Surface contours (not shown) formed an elliptic cylinder body (semi-major axis 17.5 cm, semi-minor axis 12.5 cm) with a thickness of 15 cm. The target was centred in the middle of the body.  Tumour motions: 2D-sagittal view Phantom A  Phantom A  (a)  (b)  Phantom B  Sup  Post  Ant  Inf  Time  (c)  Figure 4.7: The 2D-sagittal view of the simulated target motions for simulation set 1 (a), set 2 (b) and set 3 (c). Note that only half of the motion cycle is shown.  70  For all 3 simulation sets, the OAR was static and the target prescription dose was 60 Gy. The simulated amplitudes of the target’s motion, dpeak-to-trough, were 0.5, 1, 1.5 and 2 cm. For these 4D VMAT simulations, no extra margins for patient setup uncertainty or motion were specified. Therefore, the PTV was identical to the moving target with different phase dependent PTVs linked to each beam aperture. Respiratory periods, trespiration, were 2.5-5.5 s. MLC collimator rotation was 45°. As described in the previous section 4.4, 4D VMAT requires that the breathing cycle be divided into equal periods of tphase. The choice of tphase affects both the plan quality and treatment time. To gauge the impact of a range of tphase values, this study assumed a uniform target motion, dphase, of 0.5 cm between respiratory phases. Thus the number of phases in a respiratory cycle, Nphases, was calculated by:  (4.16)  And the time per respiration phase, tphase, was  (4.17)  In order to evaluate how 4D VMAT planning performs relative to other techniques, DVHs generated from the 4D VMAT optimizations were compared to those from 3D VMAT, optimal-gated VMAT, suboptimal-gated VMAT and DMLC ideal-tracking VMAT. In 3D VMAT, plan optimization was performed on a motion encompassing contour of the reference phase PTV. For optimal and suboptimal-gated VMAT, simulations were purely theoretical and did not consider the practicalities of clinical treatment plan delivery. A gating window of 0.5 cm was used for motion amplitudes of 0.5 and 1 cm (duty cycles of 50% and 25%) while a gating window of 1 cm was used for motion amplitudes of 1.5 and 2 cm (duty cycles of 33% and 25%). Optimal-gated consisted of delivering radiation when the distance between the PTV and OAR was greatest whereas suboptimal-gated consisted of 71  delivering radiation when the PTV and OAR were closest together. The DVHs from these two gating options will show the potential range of gating plan qualities as it is not always possible to gate on the optimal phases. Asymmetry in actual patient breathing patterns means that often the duration of the optimal phases (e.g. inhale) is too brief and the resulting extension in gated treatment time is not clinically acceptable. Note that for simulation set 1 where the PTV moves parallel to the OAR, there is no distinction between optimal and suboptimal-gated. Finally, DMLC ideal-tracking VMAT plans were generated on the static reference phase PTV. Dose deposition on the moving phantom was calculated by precisely translating the optimized apertures to follow PTV motion while disregarding the restrictions imposed by the collimator rotation and the MLC leaf widths. Plan constraints for each individual simulation were chosen such that in a given simulation set all simulations produced near identical PTV DVHs. Standardizing the target coverage ensured an objective comparison of the OAR DVHs from the five different radiation therapy approaches. An example of a PTV minimum and maximum dose-volume constraint may be 100% of the PTV volume receiving at least 58 Gy but no more than 64 Gy. Priority values on constraints were adjustable. Once matching DVHs for the PTV were achieved, the maximum dose-volume constraints on the OAR (e.g. at 5, 10, 15, 20, 25 Gy) were iteratively challenged by decreasing the Vmax% or by increasing the priority value of the constraint. This continued until just before the PTV DVH curve lost target coverage. Only the results from the treatment plans with the most demanding OAR constraints are presented. The calculation of 4D radiation deposition in the phantom was performed using a pencilbeam based algorithm [62, 112]. Dose on the reference phase was accumulated by mapping the voxels as they moved from phase to phase. No deformable registration method was required as target motion was rigid and dose was only calculated in the PTV and OAR.  72  4.5.3 Results I. Pre-Simulation Study of 4D VMAT Optimization Starting Parameters Prior to the simulations in this study, selection of reasonable 4D VMAT optimization starting parameters was necessary. Of primary interest was the effect of the interplay between Nbeams and tphase on treatment delivery time. Tested Nbeams values ranged from 193 to 769 beams per arc while the target motion amplitudes and respiratory periods were 0.5-3.5 cm and 2.5-5.5 s respectively.  In general, a lower value for Nbeams was preferable.  tphase values were  calculated from Equations 4.16 and 4.17 based on target motion of dphase = 0.5 cm between respiratory phases. Although a dphase value of 0.25 cm could have resulted in better treatment plans due to the finer sampling of target motion, the resultant decrease in tphase value overly restricted the allowed fluence modulation per beam for some of the motion patterns tested. The radiation beam on times for fractions of 2 Gy, 15 Gy and 20 Gy ranged from 2.8-8.9 min, 16.1-26.8 min and 20.9-36.0 min respectively depending on the respiratory pattern and assuming a maximum dose rate of 1000 MU/min. Multiple identical arc treatments were generally required to deliver a single fraction. For fractions of 15 and 20 Gy, a maximum dose rate of 2000 MU/min would have been preferable to minimize the treatment time and reduce the number of arcs/fraction. From these initial tests, simulations in this paper were performed using an average Nbeams value of 385 as results showed that the choice of Nbeams value did not greatly impact the DVHs.  The fastest treatment times of the preliminary 4D VMAT system were  approximately 2 to 3 times greater than those for 3D VMAT as a greater number of arcs were required to deliver the full MU of a few heavily weighted beam apertures. Strategies to refine the 4D VMAT system to improve treatment delivery efficiency were reserved for future studies.  II. Simulation Set 1: Cylindrical PTV Moving Parallel to the OAR (Sup/Inf Axis) DVH results for simulation set 1 are displayed in Figure 4.8. Figure 4.8(a) shows how PTV coverage across the different VMAT techniques was virtually identical thereby permitting 73  independent comparison of OAR sparing. Figure 4.8(b) and (c) show the DVHs for the OAR when the PTV motion amplitude was 1 cm and 2 cm respectively.  For both motion  amplitudes and at all dose levels, the 3D VMAT treatment plans had the poorest performance by irradiating a larger volume of the OAR. For gating VMAT plans, they were most successful at minimizing the irradiated OAR volume at doses below 6-7 Gy. However at higher doses, the performance of 4D VMAT and DMLC ideal-tracking VMAT plans were superior to the gating VMAT plans resulting overall in mean OAR doses that were 0.3-1.3 Gy lower (11.6-12.0 Gy ± 0.1 Gy). Similar conclusions were found for motion amplitudes of 0.5 and 1.5 cm. 4D VMAT and DMLC ideal-tracking VMAT performed equally well in sparing the OAR except for the PTV motion of 2 cm (Figure 4.8(c)). However, as described in section 4.5.2, DMLC ideal-tracking VMAT results are for the best case scenario as no restrictions on MLC leaf mobility were considered when superimposing the static VMAT plan onto the moving phantom. In contrast, 4D VMAT does account for leaf constraints. When simulations were redone with collimator at 90° rather than 45° to align the MLC leaf motion parallel to that of the PTV motion, the OAR DVHs generated by the 4D VMAT and DMLC ideal-tracking VMAT plans were almost identical (Figure 4.8(d)). Thus in future 4D VMAT simulation studies, collimator alignment in relation to tumour motion must be carefully considered.  74  Figure 4.8: DVH results for simulation set 1. Individual simulation plan constraints are set such that all simulations in the set achieve a similar PTV coverage (a). (b) and (c) display the DVHs for the OAR when motion amplitude of the cylindrical PTV was 1 cm and 2 cm respectively. 4D VMAT and DMLC ideal-tracking VMAT plans for PTV motion amplitude of 2 cm have almost identical OAR DVHs when collimator angle is 90° (d).  III. Simulation Set 2: Cylindrical PTV Moving In and Out of the OAR (Ant/Post Axis) The OAR DVH results for simulation set 2 for PTV motion of 1 cm and 2 cm are shown in Figure 4.9(a) and (b) respectively. 4D VMAT and optimal-gated VMAT performed equally well in sparing the OAR and were superior to other treatment techniques such as DMLC ideal-tracking VMAT. Suboptimal-gated VMAT and 3D VMAT performed the poorest and 75  produced similar DVHs for the OAR. Results for PTV motions of 0.5 cm and 1.5 cm generated equivalent observations and are not shown.  Figure 4.9: DVH results for simulation set 2 when motion amplitude of the cylindrical PTV was 1 cm (a) and 2 cm (b).  IV. Simulation Set 3: Spherical PTV Moving In and Out of the OAR (Sup/Inf Axis) The OAR DVH results of simulation set 3 for the spherical PTV motion of 1 and 2 cm are displayed in Figure 4.10(a) and (b) respectively. As in the previous simulation sets, PTV coverage was identical across all the simulations. The 3D VMAT and suboptimal-gated VMAT plans were the least capable of sparing the OAR. DMLC ideal-tracking VMAT was able to substantially reduce dose to the OAR but not as greatly as 4D VMAT and optimalgated VMAT. Optimal-gated VMAT was the best at reducing volume of the OAR exposed to doses below approximately 12-13 Gy. However, for doses greater than 12-13 Gy and PTV motion amplitudes of 1.5 cm and 2 cm (Figure 4.10(b)), 4D VMAT performed better than optimal-gated VMAT.  76  Figure 4.10: DVH results for simulation set 3 when motion amplitude of the spherical PTV was 1 cm (a) and 2 cm (b).  V. Effect of the PTV Motion Range on the OAR DVHs in 4D VMAT When the magnitude of tumour motion expands in conventional radiation therapy, the volume of the OAR exposed to different levels of radiation increases due to the enlarged motion margin in the PTV (section 3.4.1). This does not occur for 4D VMAT. The variation in dose deposited in the OAR with changing magnitude of the PTV motion for 4D VMAT plans is displayed in Figure 4.11(a) - (c). For superior/inferior PTV motion (simulation set 1 and 3, Figure 4.11(a) and (c)), there was a shift in OAR dose distribution with the OAR volume exposed to low doses (<~10 Gy) increasing while the OAR volume exposed to higher doses (>~10 Gy) decreasing. Two factors contributed to this shift. The first was the redistribution of the delivered dose over the entire path of the respiratory cycle causing a blurring of the OAR dose distribution. This characteristic is not unique to 4D VMAT. DMLC ideal-tracking VMAT also blurs OAR dose in this manner. The second factor contributing to the OAR dose shift was 4D VMAT’s ability to time larger MU deliveries to phases where the relative distance between the PTV and OAR was maximized thus enhancing OAR sparing. Simulation set 1 results were only affected by the first factor since in this phantom the distance between the PTV and OAR remained constant (Figure 4.11(a)). Blurring in this 77  case did not cause the mean OAR dose to vary substantially over the range of motion. For both 4D VMAT and DMLC ideal-tracking VMAT, the mean OAR dose was 11.7 ± 0.2 Gy. In contrast, simulation set 3 results were affected by both factors leading to a significant difference in the OAR DVHs of 4D VMAT and DMLC ideal-tracking VMAT (Figure 4.11(c) and (d)). As the target motion increased, mean OAR dose for 4D VMAT treatment plans decreased from 9.1 Gy to 8.3 Gy (± 0.1 Gy) while the mean OAR dose from DMLC ideal-tracking VMAT increased from 9.7 Gy to 10.2 Gy (± 0.1 Gy).  Figure 4.11: 4D VMAT DVHs for the OAR in simulation set 1 (a), set 2 (b) and set 3 (c) for PTV motions ranging from 0.5-2 cm. (d) DMLC ideal-tracking VMAT DVHs for the OAR in simulation set 3 for PTV motions ranging from 0.5-2 cm. 78  Finally, for simulation set 2 where PTV motion was along the anterior/posterior axis, there was no substantial change in the dose deposited to the OAR as the magnitude of PTV motion increased (Figure 4.11 8(b)). The cause was the spatial relationship between the linac’s beam axis and the anterior/posterior motion of the PTV. Both the effects of OAR dose blurring over the tumour path and the selective phase-timed delivery of MUs were minimized because regardless of respiratory phase, irradiating significant portions of the OAR over the course of treatment was unavoidable. Specifically, the PTV motion axis and OAR were aligned, or nearly aligned with the beam axis for a large fraction of the plan delivery (Figure 4.12(a)) unlike in simulation set 3 where tumour motion was always perpendicular to the beam axis and the beam's eye view of the PTV and OAR continually changed with target motion (Figure 4.12 (b)).  Tumour motions: 2D-sagittal view Phantom B  Phantom A  Ant Gantry arc Sup  Gantry arc  Inf Post  (b)  (a)  Figure 4.12: Illustration of the spatial relationship between the rotation of the linac beam and the target motion along (a) the anterior/posterior axis and (b) the superior/inferior axis. For target motion in the AP direction, the radiation beam will still pass through the target and OAR regardless of respiratory phase during a good portion of the arc.  79  4.5.4 Discussion The goal of the 4D VMAT system was to improve radiation sparing of the OAR by integrating temporal information on patient anatomy and tumour motion into treatment planning. The algorithm exploited three key methods for reducing dose to healthy tissues: 1) motion margin reduction, 2) dose redistribution and 3) selective respiratory phase optimization. Dose redistribution is the concept of spreading the dose delivery over a larger volume to reduce the maximum dose delivered to healthy tissues. In conventional radiation therapy, this is normally accomplished by using multiple treatment fields. However, for any form of tracking radiation therapy and 4D VMAT, maximum dose to the OARs is also reduced by redistributing the dose over multiple phases of the respiratory motion cycle. For selective respiratory phase optimization, the concept is to time larger dose contributions (MU) to respiratory phases where greater separations between the target and OAR occur. Gating radiation therapy is a limited form of selective respiratory phase optimization by limiting the gating window to a few favorable phases.  In contrast, the 4D VMAT  optimization algorithm has an enlarged search space by incorporating all respiratory phases. The performance of the 4D VMAT system was compared against optimal/suboptimalgated VMAT and DMLC ideal-tracking VMAT using their respective DVHs. Both these alternative radiation therapies only utilize two dose reduction methods. Gating employs both motion margin reduction and selective respiratory phase optimization. Tracking also reduces the motion margin and allows for dose redistribution. Only 4D VMAT takes advantage of all 3 dose reduction methods. However, this does not imply that for all clinical cases 4D VMAT will always produce the superior treatment plan. The potential of 4D VMAT can only be maximized when the combination of factors such as phantom geometry, tumour motion range and the axis of the motion allow the 4D VMAT system to fully exploit its combined advantages of dose redistribution and selective respiratory phase optimization. Therefore, for an initial 4D VMAT feasibility study, geometrical phantoms rather than 4D CT data were used to systematically analyze the 4D VMAT performance under different motion scenarios in 3 simulation sets. In simulation set 1, cylindrical target motion in the superior/inferior axis was parallel to the half-ring OAR. The important factor is that the parallel motion did not change the 80  relative distance between the target and the OAR and hence provided no advantage to optimizing on a particular phase but did allow for dose redistribution. This explains the similarity in treatment plan qualities between 4D VMAT and DMLC ideal-tracking VMAT. Should structures be replaced with a cylindrical OAR (spine or esophagus) and a spherical tumour, plan qualities would still agree due to the unchanging distance between the structures. The current implementation of the 4D VMAT system produces treatment plans requiring approximately 25% more MUs than DMLC ideal-tracking VMAT. Therefore, in the case of rigid target and OAR motion, DMLC ideal-tracking VMAT is the preferred treatment technique when the distance between the tumour and OAR is constant. If the OAR in simulation set 1 is viewed as a serial organ where high doses to any point are forbidden, the gating VMAT technique is inferior to 4D VMAT and DMLC idealtracking VMAT. Gating VMAT provided the greatest sparing of the OAR at doses lower than 6-7 Gy (Figure 4.8) by restricting radiation delivery to limited positions in the tumour motion pathway. However, this came at the expense of doses higher than 6-7 Gy being allowed to detrimentally accumulate in larger volumes of the OAR and ultimately higher mean OAR doses. When the distance between tumour and OAR changes periodically in time (simulation set 2 and 3), 4D VMAT’s ability to spare the OAR through selective respiratory phase optimization is maximized and the quality of the generated treatment plans is superior to that of DMLC ideal-tracking VMAT (Figure 4.9 and Figure 4.10). Conclusions regarding 4D VMAT’s performance relative to optimal-gated VMAT are more complex and depends on the axis of the tumour motion.  For tumour motion along the anterior/posterior axis  (simulation set 2), the best plan qualities were achieved with 4D VMAT and optimal-gated VMAT with negligible difference between the two. While optimal-gated VMAT has the advantage of irradiating the tumour only when the distance between the tumour and OAR is maximized, this effect is reduced by the fact that for anterior/posterior motion, the radiation beam from the linac must in general pass through the same portion of the OAR regardless of the respiratory phase or treatment technique (Figure 4.12(a)). To balance the advantage of optimal-gated VMAT, 4D VMAT optimizes dose delivery over the full respiratory cycle.  81  Due to the lower duty cycle of gating, 4D VMAT would be the preferred treatment technique for simulation set 2. When the tumour is moving along the superior/inferior axis causing the distance to the OAR to change (simulation set 3), optimal-gated VMAT has the potential to completely avoid irradiating the OAR and hence no other treatment technique matched its sparing of the OAR for doses below 12-13 Gy (Figure 4.10). For doses greater than 12-13 Gy, the situation is reversed with 4D VMAT’s sparing of the OAR either equalling (1 cm motion, Figure 4.10(a)) or bettering (1.5 and 2 cm motion, Figure 4.10(b)) that of optimal-gated VMAT. As the spherical target never fully exited the half-cup OAR, 4D VMAT’s flexibility in optimizing beam apertures according to the entire set of respiration phases can be more advantageous than only restrictively gating on a few phases. Where this may prove useful clinically is for stereotactic arc treatments of the lung [113]. The half-cup OAR can be representative of the bronchial tree where symptoms of bronchial toxicity include dyspnea, hypoxia, pleural effusion and pleuritic pain. The internal anatomy of a lung cancer patient is more complicated than the basic simulated phantoms in this study and future investigations using 4D CT lung patient data is required to assess 4D VMAT’s potential clinical impact. The value of this study is that the resulting observations can be used as building blocks to analyze more complex geometries and hence guide the selection of 4D CT data by identifying lung cancer patients most likely to benefit from 4D VMAT treatment. As well, the preliminary test data gathered on the effect of a range of Nbeams and tphase values on treatment time and plan quality will aid in planning and refining the 4D VMAT optimization algorithm on clinical data. Further investigation of 4D VMAT vs. 3D VMAT is also required on relevant patient data. 4D VMAT enhances OAR sparing by exploiting large tumour motions. Therefore, for smaller tumour motions (e.g. <1 cm), 4D VMAT may be unnecessary as 3D VMAT could likely achieve a similar level of OAR sparing if margins smaller than the motion encompassing margins, as suggested by van Herk et al. [114], are used to generate the PTV. For tumour motions greater than 1 cm where 4D VMAT could improve plan quality, 3D VMAT treatment plan deliveries are still 2-3 times faster than the current implementation of 4D VMAT and improvements to the algorithm are necessary. 82  The lower efficiency of 4D VMAT is a result of the speed of gantry rotation being affected by the patient’s respiratory period. The consequence of a set gantry rotation period (Equation 4.12) is that the maximum MU deliverable per beam aperture in a single rotation is also set (  ). Concurrently, the basis of 4D VMAT is its phase-optimized apertures  that encourage large fluctuations in MUs between apertures to enhance the OAR sparing. This promotes treatment plans with aperture weights ranging from zero to those exceeding the limit on  . The delivery of the full dose would necessitate multiple gantry  rotations and hence an extension of the treatment time. Strategies to decrease treatment time include aligning the collimator such that leaf motion is parallel to tumour motion. Other work has shown that this decreases total plan MU [31] but may detrimentally affect the algorithm’s intensity modulation flexibility in the axis perpendicular to tumour motion. Stricter beam weight constraints can be added to the 4D VMAT optimization algorithm to limit excessive beam modulation. Finally, development of a hybrid 4D VMAT gating radiation therapy system where gating is performed only on apertures with doses exceeding the  limit is a viable option. For the larger  fractions required in stereotactic radiation therapy, single-arc delivery is unlikely and the option of 4D VMAT optimization on consecutive clockwise and counterclockwise arcs should be pursued. The planning and delivery of 4D VMAT treatment requires regular and reproducible tumour motion. Studies of free breathing patients have shown that large variations in the motion pattern can occur from fraction to fraction and cycle to cycle [70].  These  perturbations in breathing motion can degrade the final 4D VMAT DVH. To help regulate tumour motion, clinical implementation of 4D VMAT will require tumour motion modeling [93, 115] during treatment planning and an audiovisual patient respiratory guidance and feedback system [116] during treatment delivery. To further ensure accurate plan delivery, an imaging system [117, 118] capable of providing real-time tumour location is needed along with a tumour motion prediction algorithm [119, 120] to compensate for latency in the radiation delivery system.  83  4.5.5 Conclusion A 4D VMAT optimization algorithm that integrates temporal information on patient anatomy and tumour motion directly into the planning process to enhance OAR sparing was developed. Preliminary simulations evaluating treatment plan qualities of 4D VMAT against gating VMAT and DMLC ideal-tracking VMAT show that 4D VMAT has the potential to improve radiation therapy delivery but only in a situation where the relative distance between the tumour and OAR are periodically changing over time.  Other important factors  influencing 4D VMAT’s relative performance are the axis of tumour motion and the magnitude of the tumour displacement. Future study of the 4D VMAT system on clinical 4D CT lung cancer patient data is necessary. As well, strategies to increase the treatment delivery efficiency of 4D VMAT need to be pursued. These topics are studied in detail in the following chapter.  84  Chapter 5  4D VMAT, Gated VMAT and 3D VMAT for SBRT in Lung Cancers 5.1 4D Treatment Planning Incorporating 4D CT Patient Data The 4D VMAT treatment plans created in chapter 4 were for known simulated tumour motions in water-equivalent geometric phantoms. For the 4D VMAT system to be applied to 4D CT lung patient data, completion of several additional tasks were required. First, to enable 4D dose calculations, deformable registration of all the 3D CT images in the 4D CT data set to a reference image was necessary (section 5.1.1). Second, when dealing with tumours surrounded by significant amounts of non-water-equivalent tissues such as in lung cancer (e.g. lung tissue, ribs), dose calculations require corrections for the tissue inhomogeneity (section 5.1.2). Lastly, because the dose calculation algorithms used in plan optimizations favour speed over accuracy, particularly in cases of considerable tissue heterogeneity, a final dose calculation should be performed post-optimization using more accurate methods such as Monte Carlo (section 5.1.3).  5.1.1 Image Registration Image registration is the process of determining the spatial transformation that relates coordinates in one image to corresponding coordinates in another image. Typically, one 85  image remains static and is used as the target/reference image while the image registration algorithm finds the transformation/deformation field that will warp the source image to match the static image. Image registration can be classified as either rigid (translation, rotation, scaling, shearing) or non-rigid/deformable.  For patient images, rigid image  registrations can be used for brain images when there is little change in shape or position, but for the majority of tissues in the body, deformable image registration is required. Image registration can be divided into 3 components: 1. Similarity metric: Also known as the objective or cost function, it measures how well the transformed source image matches the target image. 2. Transformation model: Defines the allowable deformations that the source image can undergo to match the target image. 3. Optimization algorithm: Determines how the transformation parameters are iteratively selected to maximize the alignment of the images. All image registrations performed in this chapter used Plastimatch, an open source software for image computing (http://plastimatch.org/index.html). A variety of deformable image registration algorithms such as B-spline, Demons and landmark-based methods are implemented in Plastimatch. For the purposes of this study, Plastimatch input files were written that selected the mean squared difference as the similarity metric, B-spline as the transformation model and L-BFGS-B as the optimization algorithm. Mean squared difference is a voxel intensity-based metric suitable for mono-modal image registration. It is defined as  (5.1)  N is the number of voxels in the region of overlap between the two images. T(x) is the intensity of the target image at position x and S(t(x)) is the intensity at the corresponding point in the source image transformed by t(x). 86  In the B-spline based model, a sparse deformation field is defined on a lattice of control points. Displacements vectors for all other points in the image are interpolated using Bspline basis functions. The control points in the B-spline model are said to have local influence. Perturbing the position of one control point will only affect the transformation in the immediate surrounding region. The computational time required for B-spline image registration depends on the number and spacing of the control points. More points with finer spacings increase the calculation time but allow for more complex deformations to be recovered. All Plastimatch input files were therefore setup to perform image registration as a 2-step multi-resolution process. Finally, L-BFGS-B refers to the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm.  It is a quasi-Newton optimizer that is suitable for optimization problems  involving a large number of variables.  5.1.2 Tissue Inhomogeneity Correction Dosimetric data for treatment planning are derived mainly from measurements in water due to the near water-equivalent nature of most tissues. Many dose calculation algorithms such as pencil-beam (PB) (section 2.7.5) calculate radiation deposition in the patient as if the entire patient was composed of water.  Development of methods to correct for tissue  inhomogeneities has been aided by two factors: 1) The availability of patient-specific anatomical geometries and densities from CT images and 2) The on-going increase in computer speed and memory. Table 5.1 provides a listing of some of the tissue inhomogeneity correction algorithms in order of increasing complexity, accuracy and computational time. Correction algorithms are classified according to whether they handle only the total energy released per unit mass (TERMA) by the photon energy fluence or if they additionally handle the dose deposited by the scattered primary electrons. Correction algorithms also differ in whether the patient density information is sampled only along the 1D primary ray paths or in all three dimensions. Category 1 and 2 algorithms are not suitable for photon beams with energies 6 MV or greater as they rely on an assumption of electron equilibrium in the radiation field. 87  Category 4 algorithms provide the highest accuracy but their computational times are too long to be practical for treatment plan optimization. These algorithms are generally reserved for final dose calculations after plan creation.  Table 5.1: List of tissue inhomogeneity corrections algorithms categorized by level of anatomy sampled (1D or 3D) and inclusion or exclusion of electron transport. Methods are listed in increasing order of complexity, accuracy and computational time (adapted from [121]). TERMA DOSE Local energy deposition Non-local energy deposition (No electron transport) (Electron transport) 1D Category 1 Category 3 - Linear attenuation - Convolution (pencil-beam) - Effective attenuation coefficient - FFT techniques (Equivalent path length) - Ratio of TAR (effective SSD, isodose shift) - Batho power law 3D Category 2 Category 4 - Equivalent TAR (ETAR) - Superposition/Convolution - Differential SAR (DSAR) - Monte Carlo - Delta volume (DVOL) - Differential TAR (dTAR) - 3D beam subtraction method  The convolution method of category 3 was implemented in the 4D VMAT system. The equation for the pencil-beam dose calculation was similar to Equation 2.23 from section 2.7.5 except that 1D equivalent path length scaling, deqv, was used to find the values for the primary beam off-axis intensity profile, P(x', y', deqv) and the dose kernel, K(x - x', y - y', deqv). deqv is defined as  (5.2)  88  where  are the thicknesses of all the different tissues lying above the calculation point and  are their electron densities relative to water obtained from CT data. The equation for dose calculation then becomes  (5.3)  5.1.3 Monte Carlo Dose Calculation In radiation therapy, Monte Carlo (MC) methods provide the most accurate dose calculation in heterogeneous patient tissues.  MC techniques can simulate the random transport of  individual photons and electrons from the linear accelerator all the way to dose deposition within the patient based on stochastic sampling of the known probability distributions governing photon and electron interactions in matter. For the photon megavoltage energy range in linacs, interactions can be divided into four processes: 1) photoelectric effect, 2) Compton scattering, 3) pair production and 4) Rayleigh scattering. Only the first three processes transfer energy from the photon to charged particles. MC simulations will track both the initial photons and all particles created from the photon interactions. However, unlike tracking of photons, simulation of each individual charged particle interaction does not occur as it would be impractical to simulate the high number of interactions they undergo before final absorption in the surrounding medium. Instead, charged particle interactions are grouped into a few condensed history steps. This is a valid approximation as it has been observed that the majority of charged particle interactions result in only minor changes in the particle's energy and direction [122]. MC simulation of particle transport is divided into 4 steps that are continuously repeated until all original and secondary particles leave the volume of interest or are absorbed in the medium. The steps are:  89  1) Distance to the next interaction is selected. 2) Particle is transported to the interaction location while accounting for patient geometry 3) The type of interaction is chosen. 4) The chosen interaction is simulated. In step 1, the probability that a particle interacts in an interval dr at a distance r from its current position is given by  (5.4)  where  is the linear attenuation coefficient. The inverse transform method can be used to  randomly sample the interaction distance, r. It equates the cumulative probability of p(r) with a uniformly distributed random number, , ranging from 0 to 1.  (5.5)  In step 2, basic ray tracing is performed to transport the particle. Patient geometry information such as the type of medium, the mass density and the distance to the next tissue boundary are needed. For step 3, the inverse transform method is used again to randomly select the particle interaction.  Assuming that there are n possible interactions whose  respective cross sections are denoted by  , the total cross section is  (5.6)  A random number .  is generated. Interaction 1 occurs if  . Interaction 2 occurs if  This pattern continues through to interaction n occurring if . 90  Finally in step 4, particle energy and direction changes are sampled from the differential cross section of the chosen interaction. The most common strategies employed can be found in various reports [123-126]. The trajectory simulation of a single particle, including all generated secondary particles, is referred to as the particle's history. The accumulation of histories from a multitude of particles allows the calculation of quantities of interest, which in treatment planning is the dose deposited in the patient. Multiple general purpose codes for MC simulations exist such as PENELOPE, MCNP, GEANT4 and EGSnrc. The PENELOPE is an abbreviation for PENetration and Energy LOss of Positrons and Electrons in matter (photon simulation was added later) and is released by the Organization for Economic Co-operation and Development's (OECD) Nuclear Energy Agency. It has comprehensive cross sections for low-energy transport and can accommodate detailed simulations of linear accelerators. MCNP (Monte Carlo NParticle) is maintained by the Los Alamos National Laboratory and was originally created to simulate neutron-photon transport in nuclear reactors.  GEANT4 (GEomentry ANd  Tracking) was developed by Centre Européen de la Recherche Nucléaire (CERN) for particle physics and can handle a range of particles including neutrons, protons and pions. EGSnrc (Electron Gamma Shower) is the result of a collaboration between the National Research Council of Canada and the Stanford Linear Accelerator Centre. It is the most commonly used MC code in medical physics. This study used a special version of EGSnrc capable of modelling continuously varying beams that was recently developed at the BC Cancer Agency [127] to perform a set of 3D VMAT dose verification calculations.  5.2 Motivation The main objective of the following study was to assess the potential for healthy tissue sparing of 4D VMAT relative to gated VMAT and 3D VMAT on real 4D CT patient data when equivalent tumour coverage across all techniques was achieved. Previous 4D VMAT work by Ma et al (2010) [38] was a feasibility study limited to one lung and one pancreas case using a digital phantom. In the work by Chin and Otto (2011) in chapter 4 [128], the different relative motions between a target and an OAR were explored to identify cases 91  where 4D VMAT planning can be more advantageous than tracked or gated VMAT. These studies neither used 4D CT patient data, nor investigated the additional mechanical constraints and their subsequent impact on treatment time caused by the synchronization of the radiation delivery to the patient's breathing. In this study, 4D CT data from three patients with non-small cell lung cancer (NSCLC) were used to generate SBRT treatment plans for 4D VMAT, gated VMAT and conventional 3D VMAT. Additionally, a strategy to manage the impact of breathing-correlated plans on treatment delivery times was developed and its consequence on plan quality was tested. Delivery times from all VMAT techniques were compared. Finally, exploratory tests of 4D VMAT plan robustness to patient breathing phase irregularities that would desynchronize the radiation delivery from the planned respiratory pattern was also performed.  5.3 Methods 5.3.1 Patient Data 4D CT data for three NSCLC patients was obtained from the VU University Medical Centre in Amsterdam (Figure 5.1). All 4D CT data were divided into 10 respiratory phases. The locations and tumour stages were left lower lobe (LLL) stage IIA for patient A, LLL stage IB for patient B, and right lower lobe (RLL) stage IIA for patient C. Contours of relevant targets and OARs were drawn by a radiation oncologist on the max-exhale phase in EclipseTM from Varian Medical Systems. The GTV volumes on the max-exhale phase for patients A, B, and C were 83.9 cm3, 27.4 cm3, and 44.3 cm3, respectively. A B-spline algorithm was used for deformable image registration on the CTs of the 9 other respiratory phases to the max-exhale phase [129]. Registration results were visually inspected and no major errors were detected. Figure 5.2 displays examples of the registered images where the first, second and third rows correspond to Patients A, B and C. In green are the target images of the max-exhale reference phase. In red are the source images of the max-inhale phase that were transformed to match the max-exhale phase. The images in yellow are the result of superimposing the green target images with the red transformed 92  source images. Regions where red and green colours remain visible indicate registration errors. Image registration errors are unavoidable because features in the source image may not have a unique matching counterpart in the target image. This can be caused by image noise, change in voxel intensities or the presence of anatomy in one image but not the other due to tissue motion or fluid flow. As well, 4D CT images can contain artifacts due to excessive motion during a breathing gate, irregular patient breathing or errors in binning the projection data to the appropriate respiratory phase. For this study, as long as registration errors were small, there was no effect on the simulation outcomes. The reason was the comparative nature of the investigation. All target and OAR volumes irradiated by 4D VMAT, gated VMAT and 3D VMAT were created using the same image registration results and therefore there was no unwarranted bias favouring one treatment over another. Motion of the target was quantified by the displacement of the GTV's geometric centre. GTV motion was primarily observed in the cranial caudal (CC) axis and was 1.4 cm (patient A), 1.8 cm (patient B) and 3.4 cm (patient C). Motion of the GTV in the other axes ranged from 0.3 cm to 0.5 cm.  (a)  (b)  (c)  Figure 5.1: CT data of NSCLC patients at max-exhale. (a) Patient A: stage IIA, 1.4 cm CC motion, gated duty cycle 40%. (b) Patient B: stage IB, 1.8 cm CC motion, gated duty cycle 60%. (c) Patient C: Stage IIA, 3.4 cm CC motion, gated duty cycle 50%.  93  Figure 5.2: Visual verification of image registration results with the target image in green and the transformed source image in red. The yellow images are the result of superimposing the red and green images and reveal areas affected by registration errors. First, second and third rows correspond to patients A, B and C.  5.3.2 Dose Calculation 4D VMAT optimization currently uses a pencil-beam based dose calculation algorithm [62, 112] and electronic path length scaling is used for inhomogeneity corrections. This method is generally not recommended for SBRT lung dose calculations [130] as it does not model changes in lateral transport of electrons.  However, pencil-beams allow for fast plan  optimization which is particularly essential for large-scale problems such as 4D VMAT  94  where the number of beams/arc ranges from 177-289. In these cases after plan optimization, a final dose calculation using more accurate techniques is usually performed. To assess the impact of pencil-beam based VMAT optimization on DVHs, 3D VMAT test treatment plans for SBRT prescribed to 48 Gy in 4 fractions were created on the max-exhale 3D CTs of patients A, B, and C (plan constraints in section 5.3.3, Table 5.2).  Dose  distributions were recalculated by 3D VMAT Monte Carlo (MC) using source 20 of DOSXYZnrc code [127]. As expected, pencil-beams overestimated target coverage [131, 132]. Recalculation with MC found that D95 of the PTV (dose received by 95% of the volume) was lower than the prescribed value by 13-15% which is within the range found by Schuring and Hurkmans (2008). Minimum dose coverage of the GTV could be recovered if the plan MUs were increased by 8.7% for patient A, 7.6% for patient B, and 10% for patient C. Examples with the largest dose differences for the pencil-beam derived DVHs vs. the rescaled MC DVHs are displayed in Figure 5.3. The rescaled MC DVHs show slightly higher dose to the OARs, but otherwise closely followed the form of the pencil-beam DVHs. The main goal of this study was to compare the relative performance of 4D VMAT, gated VMAT and 3D VMAT in sparing of OARs. The results that will be subsequently presented are not invalidated due to the use of pencil-beams in the plan optimization as Figure 5.3 demonstrates that only small shifts in the rescaled MC DVH curves occurred. These shifts will affect all techniques equally. It is inferred that the close agreement in DVH form between pencil-beam and rescaled MC will carry over to 4D dose calculations. Work on a 4D VMAT MC dose calculation algorithm using 4D CTs is pending. The reported MUs and treatment times in this study should be viewed from a perspective of relative comparison between the tested treatment techniques. These values will inevitably change once faster and more accurate dose calculation algorithms for plan optimization are employed [133-135] along with the higher dose rates used in flattening filter-free beams [95].  95  (a) (b) Figure 5.3: DVHs for VMAT plans created on the max-exhale phase of (a) patient A and (b) patient C. Solid lines are for pencil-beam based dose calculations with electronic path length correction. Dashed lines are for rescaled MC based dose calculations.  5.3.3 Treatment Planning Process As mentioned in section 5.3.1, 4D VMAT incorporates all 10 4D CT phases into the optimization. For both gated VMAT and 3D VMAT, the 3D treatment planning CT and structures were created by merging and averaging the CTs from the relevant phases of the 4D CT data to create an average 3D CT (gated VMAT: 4-6 phases, 3D VMAT: 10 phases). All 4D CT image processing, registration and deformation were performed using the Plastimatch software (http://plastimatch.org/).  For gated VMAT, the gating window was set by  constraining residual tumour motion to 3 mm or less resulting in duty cycles of 40% for patient A, 60% for patient B, and 50% for patient C. The max-exhale phase was always within the gating window. Gating at phases closer to max-inhale was not selected because for the chosen gating window, duty cycles would have been 20% for patient A and 10% for patients B and C. Following the SBRT lung protocol at the Vancouver Cancer Centre, an experienced treatment planner created VMAT SBRT treatment plans for all three patients on the maxexhale phase with instructions to maximize OAR sparing. SBRT schedule was 48 Gy in 4 fractions with a minimum of 95% of the PTV volume receiving the prescribed dose. No 96  margin was added to the GTV to create the CTV. The PTV was created by a 5 mm isotropic expansion around the GTV. Table 5.2 gives a sampling of some of the protocol's dose constraints.  All constraints were strict constraints except for the ribs and chest wall.  Exceeding any strict constraint rendered the plan clinically unacceptable. MLC collimator rotation was 45°. Plans were exported from Eclipse and into the 4D VMAT software. The treatment planner's optimized dose-volume constraints on the max-exhale phase were used as starting points for the 4D VMAT, gated VMAT and 3D VMAT optimizations of this study.  Table 5.2: Sample of SBRT dose constraints fractions). OAR Constraint (Gy) Skin Skin < 10 cm3 Heart Heart < 15cm3 Great vessels Great vessels < 10 cm3 Esophagus Esophagus < 5 cm3 Chest wall < 30 cm3  used in lung treatment planning (48 Gy in 4 OAR Spinal cord Spinal cord < 0.35 cm3 Spinal cord < 1.2 cm3 Bronchus Bronchus < 4 cm3 Stomach Stomach < 10 cm3 Ribs Ribs < 1 cm3  Constraint (Gy)  All results from the treatment plan optimizations were evaluated using a 4D dose volume histogram (4D DVH). 4D DVHs were generated by calculating dose on each phase of the 4D CT image set and then summing the doses onto the reference max-exhale phase using the deformable transformation matrix (section 5.3.1). For 4D VMAT, calculation of 4D DVHs occurs naturally since delivery of beam apertures are synchronized to specific patient respiratory phases and hence can occur within treatment plan optimization.  For gated  VMAT and 3D VMAT, where the exact correlation between beam aperture delivery and tumour position is unknown and plan optimization uses 3D CTs, the 4D DVH calculation must be performed post-optimization.  When optimization was completed, the entire  treatment plan dose was individually calculated on each relevant CT phase (gated VMAT: 46 phases, 3D VMAT: 10 phases), summed onto the reference CT, and then averaged by the number of CTs.  97  To ensure that the 4D DVH comparison between 4D VMAT, gated VMAT and 3D VMAT was fair, care was required in specifying the target coverage used during plan optimization. Uniformly requiring all techniques to achieve a 95% coverage of the PTV volume (D95) by the prescribed dose would have unfairly biased the results of one treatment over another because the PTVs were defined differently in each technique. In 3D VMAT and gated VMAT, an internal target volume (ITV) was formed from merging the GTVs of the applicable CT phases. Expanding the ITV by a 5 mm margin created the merged PTV. For 4D VMAT, there were multiple individual PTVs. The reference PTV was created from a 5 mm expansion around the max-exhale GTV. The PTVs on the other phases were found by deforming the reference max-exhale PTV with the transformation matrix. The problem with using the merged PTV of 3D VMAT is that multiple studies have already demonstrated that the ITV concept for motion compensation results in a higher than expected dose to the 4D GTV. In other words, margins were larger than needed leading to unnecessary irradiation of greater volumes [136, 137]. Our own preliminary 3D VMAT test simulations using similar clinical margins also confirmed these findings.  Figure 5.4(a)  shows an example of an increase in the minimum GTV dose (+2.6 Gy) when the 3D VMAT plan was recalculated using 4D methods. Regarding 4D VMAT PTVs, as the patient cycles from exhale to inhale, tumour and lung volumes can expand in an anisotropic fashion. Consequently, the transformation matrix's deformation of the 5 mm margin used to define the reference PTV on max-exhale would likely create larger margins at phases closer to max-inhale resulting in an over estimation of PTV sizes at those phases.  98  (a) (b) Figure 5.4: DVHs for patient C. (a) 4D dose calculation after 3D VMAT plan optimization showed that true dose to the target (4D GTV) was greater than expected (3D GTV). (b) 4D DVHs showing difference in dose distribution between 3D VMAT planned with D95 of 3D PTV receiving 100% of prescribed dose (dashed lines) and 3D VMAT planned with 4D GTV receiving the same target coverage as in 4D VMAT and gated VMAT (solid lines).  The gated VMAT's merged PTV was less likely to exhibit the problems of 3D VMAT's merged PTV to the same magnitude because our gating window minimized target motion. Therefore, for the purposes of a comparative study, gated VMAT's target coverage was chosen as the common plan objective for all 3 treatment techniques. Prescription was 48 Gy in 4 fractions with at least 95% of the gated merged PTV receiving the prescribed dose. After a clinically acceptable gated plan was created on gated VMAT's 3D CT, a 4D dose calculation using 4D CTs was performed post-optimization onto the max-exhale phase as described previously. The gated 4D results for the minimum GTV dose and percentage of the PTV receiving 48 Gy on the max-exhale phase then had to be achieved in the 4D VMAT and 3D VMAT plan optimizations. This was straight forward to accomplish in 4D VMAT because 4D dose calculation on the max-exhale phase occurs within the optimization. However, 3D VMAT, like gated VMAT, optimized on 3D CT data and required a postoptimization 4D dose calculation on 4D CTs. Target coverage of 3D VMAT's merged PTV was never used as a plan objective.  99  Only by matching the 4D calculated max-exhale target coverage for all treatment techniques could an unbiased comparison be made of the OAR sparing results. Figure 5.4(b) shows an example of the OAR dose differences that can occur in 3D VMAT plans if the issue of target coverage is not carefully handled.  Greater emphasis was placed on  maintaining the max-exhale's minimum GTV dose with values for all three treatment techniques required to fall within a 0.5 Gy range. For the percentage of the max-exhale PTV covered by 48 Gy, the range in values was within a few percent (90-94%). This latter criterion had greater flexibility as it was more challenging to control dose fall off without compromising minimum GTV dose due to the disparate nature in technique delivery. Specifically, gated VMAT's irradiation of the tumour only in a set position resulted in lower 4D calculated max-exhale PTV coverage (90-91%). In contrast, 4D VMAT and 3D VMAT's irradiation of the tumour along its entire trajectory led to a greater spread in deposited dose and thus slightly greater max-exhale PTV coverage (92-94%). To ensure that the OAR sparing was maximized for each treatment technique, the creation of treatment plans for 4D VMAT, gated VMAT and 3D VMAT required an iterative process. As OAR sparing was improved in one technique, treatment plans were re-optimized with stricter dose-volume constraints for other techniques in an attempt to match the improvement. Target coverage was maintained and all plans met the strict constraints in Table 5.2. For all three techniques in this section, a single arc of 177 beam apertures was used. Maximum dose rate was 600 MU/min.  5.3.4 CT Phase Bias in 4D VMAT Optimization As treatment plan optimization progresses, the 4D VMAT system gradually adds more beam apertures exactly in between existing beams (section 4.4). A consequence of this design is that during a given step of the optimization, the CT phases are not equally represented. Figure 5.5 gives a simplified illustration of this problem. From Figure 5.5 (b) to (c), plan optimization occurs on the odd numbered CT phases (red, yellow and blue). The even numbered CT phases (orange, green and purple) are not included until Figure 5.5 (d). For 4D VMAT simulations in section 5.3.3 with 10 CT phases and 177 beam apertures, the result 100  was that the first half of the optimization (89 beams) involved odd numbered CT phases and the next 88 beams inserted into the optimization related to even numbered CT phases. To test whether this phase bias affected the 4D DVH results, 4D VMAT optimizations from section 5.3.3 were repeated with two different setups. In the first setup, if the original plan started with odd numbered CTs, then the new optimization started with even numbered CTs or vice versa. This setup was called the reciprocal bias setup. In the second setup, the order of beam aperture introduction was altered slightly. Instead of choosing to add a beam that was precisely between two existing ones, the beam immediately adjacent to original insertion point (  shift) was chosen in such a fashion that CTs from all phases were more  evenly represented throughout the entire optimization (Figure 5.5(e)). This was known as the balanced setup.  101  Tumour motion  CT 1  CT 2  CT 3  CT 4  CT 5  CT 6  (a) tphase  Time  (e)  Figure 5.5: (a) to (d) is the same as Figure 4.5 and is reproduced here to illustrate the contrast between the original beam insertion method and the balanced setup method (e). In the balanced setup, the new beam aperture insertion schedule more evenly employs the CTs from all respiratory phases during 4D VMAT treatment plan optimization. Note that the figure is highly simplified for visual clarity. Real plan optimizations used 4D CT data with 10 respiratory phases, arcs, 177 beam apertures per arc and the shift in selected beam position was only .  102  5.3.5 4D VMAT Treatment Delivery Time In section 5.3.3, gated VMAT, 4D VMAT and 3D VMAT all used the same optimization constraint on MUs (Equations 4.4 and 4.5). Similar to chapter 4, this was done so that all techniques were given the same optimization flexibility and their respective maximum OAR sparing potential could be compared. However, as was explained in sections 4.4 and 4.5.1, 4D VMAT has a constant gantry rotation speed given by Equation 4.13 which limits the absolute MU beam weight (  ) that can be assigned to any aperture (Equation  4.14). 3D VMAT and gated VMAT are not subject to this constraint as their deliveries allow gantry rotation speed to accelerate or decelerate depending on beam MUs. If the absolute MU constraint is not incorporated into the treatment plan optimization, the consequence is a wide range of treatment times whose magnitudes are dependent on the specific respiratory pattern and the arbitrary value of  that is generated by the stochastic algorithm  (Equation 4.15 and section 4.5.3 part I). Such random fluctuations in treatment time, ranging from  = 6-16 min depending on dose fraction size, would not be clinically practical as it  would prevent predictable scheduling of patients. In addition, the 4D VMAT treatment delivery would be inefficient with even the fastest treatment times from chapter 4 being 2-3 times those of 3D VMAT. To improve 4D VMAT treatment efficiency and to better control delivery times, a new workflow for 4D VMAT optimization was developed. In the old workflow used in chapter 4 (Figure 5.6(a)), optimization parameters Nbeams and tphase were chosen and 4D VMAT optimization was subsequently run to create the treatment plans.  Limits on the MUs  deliverable per aperture were only factored in post-optimization to calculate total treatment time. In the new 4D VMAT workflow (Figure 5.6(b)), planning starts with setting the desired total treatment time, T. Lookup tables generated using Equation 4.15 contain T values for all valid combinations of Nbeams, Narcs and tphase . Values for Nbeams and Narcs are chosen such that the T value is close to the corresponding 3D VMAT treatment plan time while minimizing computational memory. The tphase value is set by Equation 4.17 based on the fact that 4D CT data generally have 10 respiratory phases. The constraint on the maximum deliverable MU per beam aperture,  103  is then defined as  (5.7)  where  is the maximum dose rate (600 MU/min) and Nfx is the number of treatment  fractions. The 4D VMAT system has the ability to optimize for multiple unique arcs, but this study was restricted to identical arcs due to limits on computational memory. It is for this reason that Equation 5.7 contains the extra term  . The new equation for  replaces the loose constraint given by Equation 4.5 in the 4D VMAT system and plan optimization is run.  104  (a) Old Workflow  (b) New Workflow  Select optimization parameters  Estimate total treatment time T based on 3D VMAT  (Nbeams & tphase)  Run 4D VMAT optimization  Use look up table to find optimization parameters (Narcs, Nbeams)  Calculate Calculate  Calculate total treatment time Run 4D VMAT optimization  Figure 5.6: (a) Old plan optimization and (b) new plan optimization workflow for 4D VMAT.  4D VMAT optimizations from section 5.3.3 were repeated with the new workflow and the tighter  constraint (Equation 5.7).  The resulting 4D DVHs were compared  against the original 4D DVHs to determine whether the decrease in optimization flexibility degraded plan quality. The breathing periods tested were 3 s and 6 s as this covers the commonly reported respiratory range [70, 138]. To compensate for the negative effect of the new  constraint on optimization flexibility, the value of Nbeams can be increased,  but at the cost of increased treatment time. Final optimization parameters are shown in Table 5.3. 105  Table 5.3: 4D VMAT optimization parameters for treatment of NSCLC patients with SBRT prescription of 48 Gy in 4 fractions. 4D CT data was divided into 10 respiratory phases.  Patient A B&C  Respiratory period (s) 3 6 3 6  tphase (s) 0.3 0.6 0.3 0.6  Parameters T (min) Nbeams 3.86 3.86 4.34 4.18  257 193 289 209  Narc 3 2 3 2  36 48 36 48  5.3.6 Robustness of 4D VMAT Delivery to Desynchronization 4D VMAT is a respiratory correlated technique. In other words, treatment plans are tailored to specific patient respiratory motions given by 4D CT data.  Thus, during treatment  delivery, the patient must breathe in a similar fashion as during planning 4D CT. Unfortunately, respiratory motion of free-breathing patients can show variability from cycle to cycle [70, 93], which could degrade the final 4D VMAT DVH. Tumour motion would need to be modelled to achieve a regular and reproducible respiratory pattern [115, 139] and audiovisual respiratory guidance would be required during the radiation delivery [93, 116]. Monitoring of tumour location throughout treatment would require a real-time imaging system [117, 118] and a motion prediction algorithm would need to be incorporated to compensate for latency in the radiation delivery system's response time [119, 120]. Despite methods used to regulate and predict patient breathing, desynchronization delivery errors can still occur. To assess the robustness of 4D VMAT to these errors, the plans created in section 5.3.5 were tested for both systematic and random desynchronization delivery errors. For systematic desynchronization error, two different simulations were performed. The delivery of all beam apertures was offset from their correlated respiratory phases by either a lag or an advance of 2 phases. This offset size was deemed to be sufficiently challenging to plan quality and any shift greater than this was expected to be detected by an online imaging system.  106  For random desynchronization error, it was assumed that when patient breathing irregularity occurs, it is unavoidable for beam apertures to be delivered to the incorrect respiratory phases for short segments of time due to: 1) the imaging frequency of the realtime imaging system, 2) the processing time of the tumour motion prediction algorithm, 3) the hardware response time, and 4) the undetectable phase shifts in the respiratory pattern due to lack of tumour motion at certain phases (e.g. near exhale). For factors 1) to 3), a total system response time of 0.6 s (Table 5.4, columns 4 and 5) was assumed based on a range of values given in literature [15, 119, 120]. In regards to 4), the phase to phase tumour centroid displacement was examined for each patient. Based on a desynchronization delivery error of 2 phases, the number of phases where such an offset would alter the tumour's position by less than 2 mm (Table 5.4, column 6) was determined. The ability to track tumour motion typically has an uncertainty of 2 mm or better [29, 117, 140]. The total period of consecutive desynchronized beam aperture delivery was conservatively estimated to be the sum of all four listed factors (Table 5.4, column 7 and 8).  Table 5.4: Factors that affect the length of time random delivery errors can occur before being detected and corrected by an on-line imaging system.  Patient A&C B  Respiratory tphase period (s) (s) 3 0.3 6 0.6 3 0.3 6 0.6  System response time (s) 0.6 0.6 0.6 0.6  System response time (phases) 2 1 2 1  Period for undetected errors (phases) 2 2 3 3  # of consecutive incorrectly delivered beams 4 3 5 4  Period of 1 incorrect delivery (s) 1.2 1.8 1.5 2.4  To assess 4D VMAT's robustness to random desynchronization delivery errors, short periods of incorrect delivery calculated in Table 5.4 were randomly introduced throughout the treatment arc. The direction (lag or advance) of each error period's 2-phase offset was also randomized. The more periods of delivery errors that could be inserted into the plan without negatively impacting plan quality, the greater the robustness to desynchronization. For the sake of simplicity, plan quality was defined as maintained if neither the minimum 107  dose to the GTV decreased by more than 1 Gy, nor the maximum dose to any OAR increased by more than 1 Gy.  Gauging desynchronization robustness was therefore an iterative  simulation process with more and more delivery errors inserted until plan quality could no longer be maintained. For a given number of delivery errors, plan quality was considered unaffected if the above limits for its maintenance could not be breached for three repeated simulations. Conversely, only one simulation violating the limits was required to conclude plan quality had degraded.  5.4 Results 5.4.1 4D VMAT, Gated VMAT and 3D VMAT Treatment Plans Figure 5.7 to Figure 5.9 display the 4D DVH results comparing 4D VMAT, gated VMAT and 3D VMAT for patients A, B and C. If evaluation is based solely on the constraints listed in Table 5.2, gated VMAT plans had the better OAR sparing overall, although 4D VMAT's sparing of a few OARs, such as the heart in patient A (Figure 5.7) and the spinal cord in patient B (Figure 5.8), was slightly superior. Doses to the ribs and chest wall were always greater than the desired constraints due to their overlap with the target. Considering the difference in the range of tumour motions treated by 4D VMAT (1.4-3.4 cm) vs. gated VMAT (0.3 cm), the treatment plan qualities between the two techniques were not widely dissimilar with the majority of the differences in mean OAR dose remaining below 0.5 Gy. 3D VMAT had the poorest plan qualities for all patients. The differences in mean OAR doses between 3D VMAT and gated VMAT in many cases were at least 1 Gy and was as large as 3.5 Gy for the liver in patient C (Figure 5.9). For patient A, none of the OARs with strict constraints were in the immediate vicinity of the tumour; thus, all the treatment plans easily met the requirements of Table 5.2 (Figure 5.7). While 3D VMAT would have a higher probability of chest wall pain and rib fracture, an SBRT fractionation schedule with a higher biological effective dose (BED) could be considered for all three techniques. In the 3D VMAT treatment plan for patient B (Figure 5.8), the strict constraints on the spinal cord and bronchi were barely achieved. Thus, dose 108  escalation with 3D VMAT would be much harder to achieve than with 4D VMAT or gated VMAT. In addition, an extra 16.2 - 22.4 cm3 of chest wall was exposed to doses above 30 Gy in 3D VMAT vs. 4D VMAT and gated VMAT. Similarly for patient C (Figure 5.9), dose escalation using the 3D VMAT delivery would entail a higher risk of complications than 4D VMAT or gated VMAT due to radiation exposure of the esophagus, ribs and chest wall.  (a) (b) Figure 5.7: 4D DVH of selected OARs for patient A (motion 1.4 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT.  (a) (b) Figure 5.8: 4D DVH of selected OARs for patient B (motion 1.8 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT.  109  (a) (b) Figure 5.9: 4D DVH of selected OARs for patient C (motion 3.4 cm). Solid line is 4D VMAT. Dashed line is gated VMAT. Dotted line is 3D VMAT.  Table 5.5 contains the percentage of the lung volume exposed to 5 and 20 Gy (V5 and V20) as well as the mean lung dose for all three patients. In general, gated VMAT tended to have the lowest values followed by 4D VMAT and then 3D VMAT. VMAT produces plans with highly conformal dose distributions and therefore, for all three techniques, the values for V5 and V20 were within a few percent of each other and mean lung dose differences were below 1 Gy. The exception was patient B where the differences between gated VMAT and 3D VMAT were 10.2% for V5 and 1.8 Gy for the mean lung dose. This was likely due to a combination of 2 factors: 1) patient B had the smallest GTV volume (27.4 cm3) yet a fairly large tumour displacement (1.8 cm), and 2) the GTV in patient B was surrounded by lung tissue whereas in patient A and C, lung tissue was above the GTV and the diaphragm was immediately below. Table 5.5 also contains the percent difference in plan MUs of gated VMAT and 4D VMAT relative to 3D VMAT. The 3D VMAT plans required 7548 MUs for patient A, 9063 MUs for patient B, and 8189 MUs for patient C. The number of MUs were inversely related to the volume of the GTVs. Gated VMAT and 4D VMAT plans required more MUs than 3D VMAT because beam aperture sizes were smaller. The exception was for patient A with gated VMAT where 1.0% fewer MUs was required, but this is within MU variability during plan generation. 4D VMAT also required more MUs than gated VMAT and 3D VMAT 110  because to better shape dose distribution around the moving target, more complex fluence modulation was necessary. Figure 5.10-Figure 5.12 show the 4D VMAT treatment apertures for patients A, B and C.  Table 5.5: Lung doses for patients A, B, and C treated with gated VMAT, 4D VMAT, and 3D VMAT. Patient A Patient B Patient C Metric V5 (%) V20 (%) Mean dose (Gy)  Gated 20.7 9.4 5.6 -1.0  4D 22.7 9.1 5.5 +4.7  3D 22.3 11.2 6.2 N/A  Gated 23.6 4.3 4.1 +6.2  4D 25.6 5.2 4.6 +12.3  3D 33.8 7.0 5.9 N/A  Gated 32.0 8.8 6.4 +10.5  4D 33.0 9.4 6.6 +16.7  3D 35.0 9.9 6.9 N/A  Figure 5.10: 4D VMAT treatment apertures for patient A. Aperture weights are scaled by the mean weight.  111  Figure 5.11: 4D VMAT treatment apertures for patient B. Aperture weights are scaled by the mean weight.  Figure 5.12: 4D VMAT treatment apertures for patient C. Aperture weights are scaled by the mean weight.  112  5.4.2 CT Phase Bias in 4D VMAT Optimization CT phase bias in the 4D VMAT optimization did not have a major affect on treatment plan quality. For both the reciprocal biased and the balanced setups tested and across all three patients, the largest decrease in minimum GTV dose was less than 0.7 Gy and the greatest increase in mean OAR dose was 0.4 Gy. For the investigation of phase bias, dose-volume constraints were not altered from those used in section 5.4.1, but they would only have required minor adjustments to maintain the original minimum GTV dose. Figure 5.13-Figure 5.15 show the 4D DVH results for patients A, B and C. There was no major difference between the 4D DVH curves of the original simulations (section 5.4.1, solid line) and those of the altered setups (dashed lines). In fact, the small observable differences did not favour one setup over another.  (a)  (b)  Figure 5.13: 4D DVH for patient A (motion 1.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b).  113  (a)  (b)  Figure 5.14: 4D DVH for patient B (motion 1.8 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b).  (a)  (b)  Figure 5.15: 4D DVH for patient C (motion 3.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for the reciprocal biased setup (a) or the balanced setup (b).  5.4.3 Treatment Delivery Times Table 5.6 displays the calculated estimates of treatment delivery times for 3D VMAT, 4D VMAT and gated VMAT. The fastest plan deliveries were for 3D VMAT (3.17-3.78 min) followed closely by 4D VMAT (3.86-4.34 min). Gated VMAT had the longest treatment times (6.68-7.85 min). The treatment times for gated VMAT were calculated based on the 114  duty cycles of 40% for patient A, 60% for patient B and 50% for patient C. However, in actual clinical delivery of gated VMAT, beam interruptions involve the gantry slowing down to a complete stop followed by a reversal of the gantry rotation until it reaches a position just before the gate-close signal was triggered.  This could further increase gated VMAT  treatment times from a few percent to 25% and is highly dependent on the patient respiratory pattern [81]. 4D VMAT treatment delivery times were longer than those for 3D VMAT for two reasons. First, as explained in section 5.4.1, the total plan MUs for 4D VMAT were always greater than 3D VMAT. Second, to compensate for the reduced optimization flexibility caused by the  constraint (Equation 5.7), the number of beams in an arc (Nbeams)  were increased which resulted in longer treatment times (Equation 4.15). To avoid greatly extending treatment times, the values for Nbeams chosen in this study did not fully offset the negative effects of  and therefore, there was some minor degradation in plan  quality. Figure 5.16-Figure 5.18 compare the 4D DVHs of the 4D VMAT treatment plan optimizations with (dashed lines) and without (solid lines, section 5.4.1) the constraint for patients A, B and C. Patient C had the largest tumour motion (3.4 cm) and the greatest degradation in plan quality. The  constrained plans were all clinically  acceptable and the largest increase in mean OAR dose was limited to 0.5 Gy.  Table 5.6: Treatment times for 3D VMAT, 4D VMAT and gated VMAT to deliver a 12 Gy fraction. Note that 3D VMAT and gated VMAT treatment times are not dependent on the patient's respiratory period. Treatment time (min) Respiratory # Gated beam Patient period (s) 3D VMAT 4D VMATa Gated VMATb interruptions A 3 3.86 157 3.17 7.85 6 3.86 79 B 3 4.34 134 3.78 6.68 6 4.18 67 C 3 4.34 152 3.47 7.58 6 4.18 76 a  Treatment times for 4D VMAT assumed reproducible tumour motion. Treatment times for gated VMAT only accounted for the duty cycle. Temporal consequences of beam interruptions on gantry rotation were ignored. b  115  (a)  (b)  Figure 5.16: 4D DVH for patient A (motion 1.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the constraint for a patient respiratory period of 3 s (a) and 6 s (b).  (a)  (b)  Figure 5.17: 4D DVH for patient B (motion 1.8 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the constraint for a patient respiratory period of 3 s (a) and 6 s (b).  116  (a)  (b)  Figure 5.18: 4D DVH for patient C (motion 3.4 cm). Solid lines are the original 4D VMAT results from section 5.4.1. Dashed lines are for treatment plan optimizations using the constraint for a patient respiratory period of 3 s (a) and 6 s (b).  5.4.4 Robustness of 4D VMAT Delivery to Desynchronization Figure 5.19 displays examples of the effects of systematic and random 4D VMAT treatment desynchronization delivery errors on 4D DVH curves. The solid lines are the original errorfree delivered plans from section 5.4.3 optimized with the strict  constraint while  the dashed lines represent the same plans compromised by delivery errors.  For the  systematic error, the greatest degradation in plan quality occurred for patient B where the respiratory pattern lagged the beam aperture delivery by 2 phases (Figure 5.19(a)). Only a few OARs are shown for better clarity.  The primary impact of the systematic  desynchronization error was the loss of GTV coverage. For all simulations tested, minimum GTV dose decreased anywhere from 2.0 Gy to 5.5 Gy. Overall impact on the OARs was negligible. Increases in mean OAR doses remained below 0.1 Gy. There was potential for some OARs, such as the bronchi, to see an increase in their maximum dose by several Gy but under our current SBRT protocol, no strict constraints ever came close to being violated. Figure 5.19(b) shows an example of a 4D DVH curve affected by random treatment desynchronization delivery errors for patient A with respiratory period of 6 s. The minimum GTV dose decreased by 0.9 Gy while the bronchi had the greatest increase in maximum dose 117  at 0.9 Gy. Table 5.7 summarizes the total percentage of beam apertures for the various plans that could be delivered incorrectly without degrading plan quality below the set limit. These values ranged from 10-20% and were inversely proportional to the theoretical system response time.  (a) (b) Figure 5.19: (a) Example of 4D VMAT DVH for systematic error: patient B, respiratory period 3s and patient breathing lagging behind treatment delivery by 2 respiratory phases for the entire treatment. (b) Example of 4D VMAT DVH affected by random error: patient A, respiratory period 6 s and 15% of beams delivered incorrectly to patient breathing by a lag or advance of 2 respiratory phases. Solid lines represent the original error-free delivery and dashed lines represent the error-prone delivery.  Table 5.7: Robustness of 4D VMAT to random treatment delivery errors. Beam aperture deliveries were randomly desynchronized from their intended respiratory phases. Respiratory Period of 1 incorrect Total % of allowed Patient period (s) delivery (s) incorrectly delivered beams A 3 1.2 20% 6 1.8 15% B 3 1.5 10% 6 2.4 10% C 3 1.2 20% 6 1.8 10%  118  5.5 Discussion In this study, the treatment plan quality of 4D VMAT was investigated in comparison to gated VMAT and 3D VMAT for SBRT treatment of highly mobile lung tumours. When tumour motion is involved in radiation therapy, there are three primary strategies available to reduce dose to healthy tissues.  The first is to eliminate or minimize the motion  encompassing margin used to ensure target coverage. The second is to temporally spread the instantaneous dose delivered to the tumour over its motion trajectory similar to how multiple beams are spatially used to prevent hot spots. The third is to optimize greater radiation dose delivery to respiratory phases that maximize the relative distance between the target and OARs. Table 5.8 provides a summary of the applicability of these three strategies to the treatment techniques of 3D VMAT, gated VMAT, and 4D VMAT.  For a complete  overview, characteristics of tracked VMAT were also included in Table 5.8.  Table 5.8: Listing of the treatment technique characteristics that can improve plan quality when highly mobile tumours are present. VMAT Reduce motion Temporally Sync high MU to larger technique margin spread out dose target/OAR distance    3D   Gated a    Tracked    4D a  Gating at max-inhale is often not clinically feasible due to low duty cycle.  Gated VMAT can maximize the separation between target and OARs if the gating window occurs around max-inhale. However, for the majority of patients, this would lead to excessively extended treatment times. This study did not gate at max-inhale because it would have reduced the duty cycle from 40% to 20% for patient A, 60% to 10% for patient B and 50% to 10% for patient C. Despite planning near max-exhale, gated VMAT's ability to spare the majority of the OARs was the greatest (section 5.4.1). 4D VMAT treated the tumour over its entire trajectory, but plan qualities were only slightly below those of gated VMAT because 4D VMAT was the only treatment technique that could exploit all three 119  primary strategies (Table 5.8). In fact, this study (section 5.4.1) and previous work by Chin and Otto (2011) showed that for certain anatomical deformations, 4D VMAT's sparing of some OARs can be superior to other treatment deliveries such as gated VMAT. For 3D VMAT, despite the care in maximizing the sparing of healthy tissues by avoiding the ITV margin concept, plan quality was the poorest for all three patients. Under the current SBRT protocol of 48 Gy in 4 fractions, all generated plans were clinically acceptable, including those by 3D VMAT. As a result from a practical perspective, 3D VMAT would be the treatment of choice because its delivery was the fastest and the simplest to execute. However, if OAR sparing was prioritized above all else or the clinician chose to escalate the dose, then the preferred treatment options would have been gated VMAT or 4D VMAT. Future improvements in the understanding of the radiobiological consequences of different dose distributions [141] may also alter the SBRT protocol to favor more complex treatments. This study was limited to three patients with large tumour motions (1.4-3.4 cm). The benefits of gated VMAT or 4D VMAT are less likely to be observed for tumour motions below 1 cm as expansion of treatment margins may only be in the range of a few millimetres [136, 142]. The main advantage of 4D VMAT was that while plan quality was similar to gated VMAT, treatment delivery time was less than a minute longer than 3D VMAT. There was some degradation in 4D VMAT plan quality when the  constraint was enforced  to ensure efficient delivery, but this problem can easily be solved with the higher dose rates of 1400 - 2400 MU/min available in flattening filter-free (FFF) beams [95]. With a higher dose rate, the relative difference in treatment times between 3D VMAT and 4D VMAT would be eliminated. Gated VMAT treatment times would also decrease but the frequent stops and starts of the gantry rotation would still be mechanically challenging for the linac. Ideally, this study would have also included a comparison with tracked VMAT. Unfortunately, test simulations of a rigid DMLC tracked VMAT algorithm tended to lose target coverage because they did not account for the deformation of the GTV. This loss of target coverage in rigid tracking algorithms has also been found by others [89, 90, 143]. Tracked test simulations with slightly larger treatment margins obtained satisfactory GTV dose coverage, but OAR sparing was not competitive. A possible solution would be to create 120  a deformable DMLC tracking algorithm [90, 144, 145], but that was beyond the scope of this work. Previous work by Chin and Otto (2011) did demonstrate that 4D VMAT was superior to tracked VMAT but was only verified in rigidly moving phantoms.  Relative to  comparisons with 3D VMAT and gated VMAT, comparing 4D VMAT to tracked VMAT was of lower importance because both are respiratory correlated techniques whose deliveries require a similar level of time, complexity and workload. 4D VMAT simply offers the possibility of better healthy tissue sparing by planning on 4D CT data instead of 3D CT data. The strength and weakness of 4D VMAT treatment planning is the integration of a priori patient motion information into the plan optimization. The advantage is higher quality treatment plans as all tissue motion is accounted for, but the disadvantage is the requirement that beam aperture delivery be synchronized to patient breathing and that the breathing pattern be reproducible.  The robustness of 4D VMAT treatment plans to treatment  desynchronization delivery errors was tested using an artificial setup. While it may not have mimicked the full range of breathing variability in real patients, a few important conclusions can still be made. First, 4D VMAT can be insensitive to some delivery errors. Of the total beam apertures, 10-20% could be delivered out of synchronization by a shift of 2 phases from their correlated phase without violating the threshold on plan quality. Second, the shorter the system latency in responding to treatment delivery errors, the more frequently the errors could occur. In Table 5.7, the percentage of beams with delivery errors could be as much as 20% with a 1.2 s response time but only allowed 10% with a 2.4 s response time. This information may be useful for future designs of online image guidance systems. The 4D VMAT plans were robust to some desynchronization delivery errors due to the limits placed on beam weight and MLC motion. The strict  constraint prevented  major variation of MUs between beam apertures and was comparable to the robust technique of Nohadani et al (2010) [146]. The 4D VMAT system also constrained the amount of allowed MLC leaf motion between beam apertures [39] to avoid large changes in aperture shape and could be considered analogous to the robust strategy employed by Alasti et al (2006) [147]. Despite these constraints, the 4D VMAT plan qualities still compared well to the gated VMAT plans.  121  For future work, there are many possible avenues of investigation. With only 4D CT data, robustness testing of 4D VMAT plans was limited to desynchronization delivery errors in this study. Irregularities in tumour motion amplitude or shifts in tumour baseline position could not be investigated. Complete and realistic testing of the robustness of 4D VMAT treatment plans to all possible deviations requires the creation of a dynamic virtual patient model [139, 145, 148-150]. Not all deviations will have a meaningful effect on plan quality; therefore, action thresholds should also be established. The magnitude of these action thresholds will likely depend on the specific patient geometry and treatment plan [151, 152]. Another consideration is that perfectly regular breathing motion may not actually be necessary for 4D VMAT delivery. The current implementation of 4D VMAT did not allow for changing gantry speeds only because the dose rate of 600 MU/min is too low to deliver the full MU of some beam apertures should the patient breathing accelerate. This is less likely to be a concern with the higher dose rates of FFF beams. The gantry rotation may then be allowed to change speeds to track patients with moderately irregular respiratory periods in a concept similar to MLC tracking for irregular breathing by Yi et al (2008) [153]. Lastly but most importantly, the 4D VMAT optimization must be updated with a faster and more accurate dose calculation algorithm. Promising options are GPU-based MC or GPU-based finite-size pencil-beams with 3D density corrections [133, 134].  5.6 Conclusion A breathing synchronized 4D VMAT treatment technique incorporating patient motion information from 4D CT data directly into the optimization algorithm was used to generate SBRT treatment plans on three patients with NSCLC. Healthy tissue sparing of 4D VMAT plans were comparable to gated VMAT plans but with treatment delivery efficiencies closer to 3D VMAT. The current implementation of 4D VMAT requires treatment synchronization to reproducible patient motion but preliminary tests showed robustness to random and systematic desynchronized delivery errors. Future developments in respiratory tracking have the potential to adapt 4D VMAT to irregular patient breathing. 4D VMAT is a viable  122  alternative to gated VMAT. It can allow for further dose escalation in SBRT lung treatments without the negative consequence of gated VMAT's extended treatment time.  123  Chapter 6  Conclusions and Future Work 6.1 Conclusions The objective of this thesis was to develop a new 4D treatment planning system for volumetric modulated arc therapy (4D VMAT) that could target moving tumours in the lung while minimizing dose to normal tissues. This 4D system incorporates lung cancer patient anatomical motion information from 4D CT data to create radiation treatment plans whose beam aperture shapes and weights are modulated according to the changing patient respiratory phase. It was hypothesized that such a respiration synchronized technique would be capable of tightly sculpting dose to mobile tumour targets while improving the sparing of healthy tissues relative to conventional 3D VMAT plans. This would be beneficial to SBRT treatments of lung cancer as the large ablative fraction doses carry a higher risk of normal tissue complications. The 4D VMAT system was based on the 3D VMAT algorithm by Otto (2008), but was completely recoded from the beginning in MATLAB as a large percentage of variables had to be restructured and many new variables created to handle the additional time dimension and the 4D CT data. The original pencil-beam dose calculation algorithm was updated with a function to correct for tissue inhomogeneities that are significant in the thorax and 4D dose calculation capabilities that incorporated 4D CT deformable image registration results were also included. Finally, to evaluate the treatment plan qualities of 4D VMAT in comparison 124  to other lung motion management strategies, the new 4D VMAT MATLAB program retained its original capacity for 3D VMAT optimization and was also augmented with functions to handle gated VMAT and tracked VMAT techniques. Initial testing of the 4D VMAT system focused on creating treatment plans for rigid uniform target motions in simulated water-equivalent phantoms for a range of motion amplitudes (0.5-2 cm) and directions (superior/inferior and anterior/posterior). 4D VMAT plan qualities were compared against those of 3D VMAT, gated VMAT and tracked VMAT. In all cases, 3D VMAT irradiated the largest volume of healthy tissue.  Several other  conclusions include: 1) 4D VMAT and tracked VMAT are advantageous in the case of serial organ structures (e.g. cord, esophagus) as they can avoid hot spots by spreading out the dose over the tumour's trajectory. 2) If relative motion between the tumour and OAR exists, 4D VMAT is better at sparing the OAR than tracked VMAT 3) Gated VMAT provides the best sparing of OARs only if irradiation in the gating window avoids most of the OAR; otherwise, 4D VMAT has the capacity to be superior to gated VMAT. 4) 4D VMAT's ability to minimize OAR dose is greatest if the primary axis of tumour motion is along the patient's cranial/caudal direction. These conclusions were used to help select the 4D CT data of patients with NSCLC. When 4D VMAT was applied to clinical patient data, its ability to spare healthy tissue was nearly as great as gated VMAT even though 4D VMAT had to account for tumour motions of up to 3.4 cm while gated VMAT only had to handle motions less than 0.3 cm. The superiority in healthy tissue sparing of both 4D VMAT and gated VMAT over conventional 3D VMAT makes further dose fraction escalation (> 12 Gy) in SBRT a possibility.  125  The primary advantage for a clinician to choose 4D VMAT over gated VMAT for SBRT lung cancer treatment is supposed to be the shorter delivery times. The duty cycle for 4D VMAT is potentially 100% while gated VMAT is much lower at 30-50% and can require over a hundred start/stop/reverse motions of the linac gantry rotation.  However, the  respiratory synchronized nature of 4D VMAT treatment plan delivery subjects it to a strict optimization constraint on  (Equation 5.7) that can affect plan quality. This  constraint was not implemented into the optimization algorithm for initial simulations (Chapter 4) as it was not known how large the impact on optimization flexibility would be nor the extent of the increase in treatment time (Equation 4.15). Chapter 4 results showed that without the strict  constraint, 4D VMAT  treatment delivery times were at best 2-3 times those of 3D VMAT making them similar to gated VMAT times or longer. Consequently, to improve 4D VMAT treatment efficiency, it was essential to include the strict  constraint during plan optimization.  Unfortunately, the treatment planning experience gained from chapter 4 (particularly in section 4.5.3 part I) did not reveal any coherent pattern on how best to select the optimization parameters of  Narcs and Nbeams that would perfectly balance the trade-off  between optimization flexibility and the extension of treatment time. This was the main motivating factor for reversing the 4D VMAT optimization workflow (Figure 5.6(b)) to preselect the desired treatment time at the beginning of optimization. Once the treatment time is set, the values of  Narcs and Nbeams can be derived from Equations 4.15 and 5.7.  The new workflow was successful in shortening 4D VMAT delivery times to just 11-25% longer than 3D VMAT times. The strict  constraint did slightly degrade 4D  VMAT treatment plan quality, but this effect will likely disappear once linacs with higher dose rates (1400-2400 MU/min) are implemented clinically. In conclusion, the new 4D VMAT system is a viable motion compensation technique that produces treatment plans of similar quality to gated VMAT without greatly increasing treatment times over conventional 3D VMAT. The concern that the respiratory phase bias in the 4D VMAT system (section 5.4.2) would negatively influence optimization results was found to be unnecessary. The robustness of 4D VMAT plans to desynchronization delivery  126  errors of up to 20% of beams suggests that clinical implementation is feasible despite known irregularities in patient breathing patterns over time.  6.2 Future Work The work in this thesis focused on the development and implementation of the 4D VMAT planning system.  Treatment planning simulations on phantoms and 4D CT data were  performed to evaluate 4D VMAT's capacity for healthy tissue sparing and its feasibility for clinical implementation in terms of treatment time and robustness to desynchronization delivery errors. Before further investigations can continue, it is of primary importance that the pencil-beam dose calculation algorithm with 1D path length scaling for tissue inhomogeneity correction be replaced with a more accurate category 4 (Table 5.1) technique such as Monte Carlo (MC). Work on fast MC for radiation therapy include the PEREGRINE project [154], the VMC++ code [155], the DPM code [156] and the MCDOSE code [157]. With increasing computing power provided by GPUs, treatment planning with Monte Carlo will soon become standard practice. Once 4D VMAT has been updated with a more sophisticated dose calculation algorithm, the next stage of the investigation would be to export plans to a linac and verify their deliverability on a deformable lung phantom capable of measuring radiation deposition [158]. If a database of patient respiratory traces is available, a more realistic test of 4D VMAT plan robustness to irregular patient breathing can also be performed by programming the phantom to move according to different measured breathing patterns. The respiratory synchronized nature of 4D VMAT plans greatly increases the complexity of treatment delivery. To ensure the correlation between patient breathing and radiation beam modulation is maintained throughout treatment, several extra components must be integrated into 4D VMAT delivery before clinical testing is possible. These components have already been discussed in sections 5.3.6 and 5.5, but are visually summarized again in Figure 6.1.  A real-time 3D imaging system combined with an audio-visual patient  respiratory guidance and feedback system is needed to monitor and regulate patient breathing  127  during radiation treatment. Multiple studies have shown that patient breath coaching via audio-visual respiratory guidance can reduce variation in the breathing pattern [116, 159, 160]. One method for visual guidance includes a display screen with a guiding waveform and a moving ball to show the current respiratory position. Another method would be a bar model where the height of the bar is proportional to phase of inhalation/exhalation. Audio guidance for inhalation/exhalation may be verbal commands or ascending and descending musical tones.  A tumour motion prediction algorithm is also required to account for  latencies in the system response time and tumour motion modelling is necessary for both plan optimization and the prediction algorithm. Lastly, action thresholds must be established to determine when a beam interlock must be triggered as not all treatment delivery errors necessarily translate to meaningful dose delivery errors. For example, sudden coughing or sneezing by the patient will undoubtedly cause large disruptions in the dose delivery and treatment should immediately be halted until patient breathing renormalizes.  In contrast, slow minor random fluctuations in patient  breathing pattern from the planned trajectory may have little influence on the 4D VMAT plan quality and treatment interruptions would be unnecessary. The magnitude of the action thresholds will depend on the complexity of the 4D VMAT plan and thus would need to be tailored specifically to each patient.  Figure 6.1: Diagram of the various components required for 4D VMAT to be implemented clinically. 128  There are many other aspects of 4D VMAT available for investigation: 1) Increasing the number of lung cancer patients in the 4D VMAT study would be desirable. 2) Expanding the pool of available gantry angles through non-coplanar arcs may further improve radiation sparing of OARs. This thesis only explored coplanar arcs. 3) Rather than focusing only on the physical dose deposition of radiation, the 4D VMAT system could be enhanced with objectives used in biologically guided radiation therapy such as TCP, NTCP, BED and equivalent uniform dose (EUD) [161, 162]. 4) Update the voxel tracking method used in 4D dose calculations to a more sophisticated technique. Current code uses a simple centre of mass (COM) tracking method that assumes a one-to-one correspondence between undeformed voxels [163] (Figure 6.2(a)). This assumption can fail in the lungs since lung volume can change by as much as 20% during respiration [7]. A more accurate voxel tracking method is trilinear remapping [94, 164] (Figure 6.2(b)) where dose is obtained by trilinear interpolation of dose from voxels around the transformed reference voxel's COM. A further refinement of trilinear remapping is to divide the original reference voxel into octants and then apply trilinear remapping to each [165] (Figure 6.2(c)). All 4D dose calculations that rely on interpolation will likely have errors in regions of sharp dose gradients.  They also ignore changes in the deforming voxel's density and they  disregard the maintenance of tissue type on a voxel-by-voxel level. To address these issues, the most sophisticated dose warping method for 4D dose calculations is the direct deformable voxel tracking method [166] (Figure 6.2(d)). For this thesis, the use of COM tracking is unlikely to affect our results due to the comparative nature of the study. Moreover, DVHs were used as our evaluation metric. DVHs are a measure of dose to the entire volume of the structure and the impact of dose errors in a small percentage of voxels will be negligible. However, due to the large ablative dose fractions and highly conformal dose depositions related to 4D VMAT SBRT, the deformable dose tracking method should be improved prior to clinical implementation. 129  (a) Centre of mass tracking  (b) Trilinear remapping  (c) Trilinear remapping with octant subdivision  (d) Direct deformable voxel tracking  Figure 6.2: Illustration of the various methods for deformable 4D dose calculation (adapted from [165, 166]).  130  Bibliography [1] T. Bortfeld, S. B. Jiang and E. Rietzel, "Effects of motion on the total dose distribution," Semin. Radiat. Oncol., 14:41-51 (2004). [2] A. L. McKenzie, M. van Herk and B. Mijnheer, "The width of margins in radiotherapy treatment plans," Phys. Med. Biol., 45:3331-42 (2000). [3] M. van Herk, "Errors and margins in radiotherapy," Semin. Radiat. Oncol., 14:52-64 (2004). [4] G. D. Hugo, D. Yan and J. Liang, "Population and patient-specific target margins for 4D adaptive radiotherapy to account for intra- and inter-fraction variation in lung tumour position," Phys. Med. Biol., 52:257-74 (2007). [5] A. Trofimov et al., "Temporo-spatial IMRT optimization: concepts, implementation and initial results," Phys. Med. Biol., 50:2779-98 (2005). [6] E. C. Ford et al., "Respiration-correlated spiral CT: A method of measuring respiratoryinduced anatomic motion for radiation treatment planning," Med. Phys., 30:88-97 (2003). [7] P. J. Keall et al., "Acquiring 4D thoracic CT scans using a multislice helical method," Phys. Med. Biol., 49:2053-67 (2004). [8] U. W. Langner and P. J. Keall, "Accuracy in the localization of thoracic and abdominal tumors using respiratory displacement, velocity, and phase," Med. Phys., 36:386-93 (2009). [9] J. J. Sonke et al., "Respiratory correlated cone beam CT," Med. Phys., 32:1176-86 (2005). [10] L. Dietrich et al., "Linac-integrated 4D cone beam CT: first experimental results," Phys. Med. Biol., 51:2939-52 (2006).  131  [11] T. F. Li et al., "Four-dimensional cone-beam computed tomography using an on-board imager," Med. Phys., 33:3825-33 (2006). [12] C. Plathow et al., "Therapy monitoring using dynamic MRI: Analysis of lung motion and intrathoracic tumor mobility before and after radiotherapy," Eur. Radiol., 16:1942-50 (2006). [13] H. H. Liu et al., "Evaluation of internal lung motion for respiratory-gated radiotherapy using MRI: Part II - Margin reduction of internal target volume," Int. J. Radiat. Oncol. Biol. Phys., 60:1473-83 (2004). [14] J. M. Blackall et al., "MRI-based measurements of respiratory motion variability and assessment of imaging strategies for radiotherapy planning," Phys. Med. Biol., 51:4147-69 (2006). [15] L. I. Cervino, J. D. and S. B. Jiang, "MRI-guided tumor tracking in lung cancer radiotherapy," Phys. Med. Biol., 56:3773-85 (2011). [16] S. L. S. Kwa et al., "Radiation pneumonitis as a function of mean lung dose: An analysis of pooled data of 540 patients," Int. J. Radiat. Oncol., Biol., Phys., 42:1-9 (1998). [17] V. Mehta, "Radiation pneumonitis and pulmonary fibrosis in non-small-cell lung cancer: Pulmonary function, prediction, and prevention," Int. J. Radiat. Oncol. Biol. Phys., 63:524 (2005). [18] Y. Seppenwoolde et al., "Comparing different NTCP models that predict the incidence of radiation pneumonitis," Int. J. Radiat. Oncol., Biol., Phys., 55:724-35 (2003). [19] E. D. Yorke et al., "Dose-volume factors contributing to the incidence of radiation pneumonitis in non-small-cell lung cancer patients treated with three-dimensional conformal radiation therapy," Int. J. Radiat. Oncol. Biol. Phys., 54:329-39 (2002). [20] F. M. Kong et al., "High-dose radiation improved local tumor control and overall survival in patients with inoperable/unresectable non-small-cell lung cancer: Long-term results of a radiation dose escalation study," Int. J. Radiat. Oncol., Biol., Phys., 63:324-33 (2005). [21] M. K. Martel et al., "Estimation of tumor control probability model parameters from 3D dose distributions of non-small cell lung cancer patients," Lung Cancer, 24:31-7 (1999). [22] R. C. McGarry et al., "Stereotactic body radiation therapy of early-stage non-small-cell lung carcinoma: Phase I study," Int. J. Radiat. Oncol., Biol., Phys., 63:1010-5 (2005). 132  [23] A. J. Fakiris et al., "Stereotactic Body Radiation Therapy for Early-Stage Non-SmallCell Lung Carcinoma: Four-Year Results of a Prospective Phase II Study," Int. J. Radiat. Oncol., Biol., Phys., 75:677-82 (2009). [24] J. Wulf et al., "Dose-response in stereotactic irradiation of lung tumors," Radiother. Oncol., 77:83-7 (2005). [25] J. D. Bradley et al., "Gross tumor volume, critical prognostic factor in patients treated with three-dimensional conformal radiation therapy for non-small-cell lung carcinoma," Int. J. Radiat. Oncol., Biol., Phys., 52:49-57 (2002). [26] D. Etiz et al., "Influence of tumor volume on survival in patients irradiated for nonsmall-cell lung cancer," Int. J. Radiat. Oncol., Biol., Phys., 53:835-46 (2002). [27] J. Willner et al., "Dose, volume, and tumor control predictions in primary radiotherapy of non-small-cell lung cancer," Int. J. Radiat. Oncol., Biol., Phys., 52:382-9 (2002). [28] C. R. Lund, "Protocol Guidelines for Stereotactic Body Radiotherapy (SBRT) for Primary Early Stage NSCLC in British Columbia," (2011). [29] H. Shirato et al., "Physical aspects of a real-time tumor-tracking system for gated radiotherapy," Int. J. Radiat. Oncol. Biol. Phys., 48:1187-95 (2000). [30] S. S. Vedam et al., "Determining parameters for respiration-gated radiotherapy," Med. Phys., 28:2139-46 (2001). [31] A. Sawant et al., "Management of three-dimensional intrafraction motion through realtime DMLC tracking," Med. Phys., 35:2050-61 (2008). [32] T. Neicu et al., "Synchronized moving aperture radiation therapy (SMART): average tumour trajectory for lung patients," Phys. Med. Biol., 48:587-98 (2003). [33] L. Lee et al., "Conceptual formulation on four-dimensional inverse planning for intensity modulated radiation therapy," Phys. Med. Biol., 54:N255-66 (2009). [34] T. Z. Zhang et al., "Treatment plan optimization incorporating respiratory motion," Med. Phys., 31:1576-86 (2004). [35] T. Z. Zhang et al., "Breathing-synchronized delivery: A potential four-dimensional tomotherapy treatment technique," Int. J. Radiat. Oncol. Biol. Phys., 68:1572-8 (2007).  133  [36] D. McQuaid and S. Webb, "Target-tracking deliveries using conventional multileaf collimators planned with 4D direct-aperture optimization," Phys. Med. Biol., 53:4013-29 (2008). [37] A. Schlaefer et al., "Feasibility of four-dimensional conformal planning for robotic radiosurgery," Med. Phys., 32:3786-92 (2005). [38] Y. Ma et al., "Inverse planning for four-dimensional (4D) volumetric modulated arc therapy," Med. Phys., 37:5627-33 (2010). [39] K. Otto, "Volumetric modulated arc therapy: IMRT in a single gantry arc," Med. Phys., 35:310-7 (2008). [40] C. Wang et al., "Arc-modulated radiation therapy (AMRT): a single-arc form of intensity-modulated arc therapy," Phys. Med. Biol., 53:6291-303 (2008). [41] D. L. Cao et al., "A generalized inverse planning tool for volumetric-modulated arc therapy," Phys. Med. Biol., 54:6725-38 (2009). [42] S. Ulrich, S. Nill and U. Oelfke, "Development of an optimization concept for arcmodulated cone beam therapy," Phys. Med. Biol., 52:4099-119 (2007). [43] S. M. Crooks et al., "Aperture modulated arc therapy," Phys. Med. Biol., 48:1333-44 (2003). [44] D. M. Shepard et al., "Direct aperture optimization: A turnkey solution for step-andshoot IMRT," Med. Phys., 29:1007-18 (2002). [45] M. P. Milette and K. Otto, "Maximizing the potential of direct aperture optimization through collimator rotation," Med. Phys., 34:1431-8 (2007). [46] A. E. Chang et al., editors, Oncology, an evidence-based approach, 1st ed. (Springer, United States of America, 2005). [47] O. N. Vassiliev et al., "Dosimetric properties of photon beams from a flattening filter free clinical accelerator," Phys. Med. Biol., 51:1907-17 (2006). [48] G. Kragl et al., "Dosimetric characteristics of 6 and 10 MV unflattened photon beams," Radiother. Oncol., 93:141-6 (2009). [49] T. Bortfeld and W. Schlegel, "Optimization of Beam Orientations in Radiation-Therapy - some Theoretical Considerations," Phys. Med. Biol., 38:291-304 (1993). 134  [50] J. Stein et al., "Number and orientations of beams in intensity-modulated radiation treatments," Med. Phys., 24:149-60 (1997). [51] T. Bortfeld, "Optimized planning using physical objectives and constraints," Semin. Radiat. Oncol., 9:20-34 (1999). [52] T. Bortfeld et al., editors, Image-guided IMRT, 1st ed. (Springer-Verlag, Germany, 2006). [53] S. V. Spirou and C. S. Chui, "A gradient inverse planning algorithm with dose-volume constraints," Med. Phys., 25:321-33 (1998). [54] X. D. Zhang et al., "Speed and convergence properties of gradient algorithms for optimization of IMRT," Med. Phys., 31:1141-52 (2004). [55] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, "Optimization by Simulated Annealing," Science, 220:671-80 (1983). [56] Q. W. Wu and R. Mohan, "Multiple local minima in IMRT optimization based on dosevolume criteria," Med. Phys., 29:1514-27 (2002). [57] J. Llacer et al., "Absence of multiple local minima effects in intensity modulated optimization with dose-volume constraints," Phys. Med. Biol., 48:183-210 (2003). [58] W. De Gersem et al., "Leaf position optimization for step-and-shoot IMRT," Int. J. Radiat. Oncol. Biol. Phys., 51:1371-88 (2001). [59] B. Hårdemark et al., "Direct machine parameter optimization with RayMachine in Pinnacle," RaySearch White Paper, (2003). [60] E. J. Hall, "Intensity-modulated radiation therapy, protons, and the risk of second cancers," Int. J. Radiat. Oncol. Biol. Phys., 65:1-7 (2006). [61] X. G. Xu, B. Bednarz and H. Paganetti, "A review of dosimetry studies on externalbeam radiation treatment with respect to second cancer induction," Phys. Med. Biol., 53:R193-241 (2008). [62] P. R. M. Storchi, L. J. van Battum and E. Woudstra, "Calculation of a pencil beam kernel from measured photon beam data," Phys. Med. Biol., 44:2917-28 (1999). [63] Canadian Cancer Society’s Steering Committee on Cancer Statistics, "Canadian Cancer Statistics 2012," (2012). 135  [64] C. A. Perez et al., "Impact of Irradiation Technique and Tumor Extent in Tumor-Control and Survival of Patients with Unresectable Non-Oat Cell-Carcinoma of the Lung - Report by the Radiation-Therapy Oncology Group," Cancer, 50:1091-9 (1982). [65] L. Kaskowitz et al., "Radiation-Therapy Alone for Stage-i Nonsmall Cell LungCancer," Int. J. Radiat. Oncol. Biol. Phys., 27:517-23 (1993). [66] D. Palma et al., "Impact of Introducing Stereotactic Lung Radiotherapy for Elderly Patients With Stage I Non-Small-Cell Lung Cancer: A Population-Based Time-Trend Analysis," J. Clin. Oncol., 28:5153-9 (2010). [67] J. Zhang et al., "Which is the optimal biologically effective dose of stereotactic body radiotherapy for Stage I non-small-cell lung cancer? A meta-analysis." Int. J. Radiat. Oncol. Biol. Phys., 81:E305-16 (2011). [68] R. Timmerman et al., "Excessive toxicity when treating central tumors in a phase II study of stereotactic body radiation therapy for medically inoperable early-stage lung cancer," J. Clin. Oncol., 24:4833-9 (2006). [69] S. H. Levitt et al., editors, Technical Basis of Radiation Therapy: Practical Clinical Applications, 5th ed. (Springer-Verlag Berlin, Heidelberg, 2012). [70] Y. Suh et al., "An analysis of thoracic and abdominal tumour motion for stereotactic body radiotherapy patients," Phys. Med. Biol., 53:3623-40 (2008). [71] P. Keall et al., "The management of respiratory motion in radiation oncology report of AAPM Task Group 76," Med. Phys., 33:3874-900 (2006). [72] A. E. Lujan et al., "A method for incorporating organ motion due to breathing into 3D dose calculations," Med. Phys., 26:715-20 (1999). [73] T. Bortfeld et al., "Effects of intra-fraction motion on IMRT dose delivery: statistical analysis and simulation," Phys. Med. Biol., 47:2203-20 (2002). [74] C. S. Chui, E. Yorke and L. Hong, "The effects of intra-fraction organ motion on the delivery of intensity-modulated field with a multileaf collimator," Med. Phys., 30:1736-46 (2003). [75] Y. Negoro et al., "The effectiveness of an immobilization device in conformal radiotherapy for lung tumor: Reduction of respiratory tumor movement and evaluation of the daily setup accuracy," Int. J. Radiat. Oncol. Biol. Phys., 50:889-98 (2001).  136  [76] K. E. Rosenzweig et al., "The deep inspiration breath-hold technique in the treatment of inoperable non-small-cell lung cancer," Int. J. Radiat. Oncol. Biol. Phys., 48:81-7 (2000). [77] J. W. Wong et al., "The use of active breathing control (ABC) to reduce margin for breathing motion," Int. J. Radiat. Oncol. Biol. Phys., 44:911-9 (1999). [78] E. A. Barnes et al., "Dosimetric evaluation of lung tumor immobilization using breath hold at deep inspiration," Int. J. Radiat. Oncol. Biol. Phys., 50:1091-8 (2001). [79] A. M. Berson et al., "Clinical experience using respiratory gated radiation therapy: Comparison of free-breathing and breath-hold techniques," Int. J. Radiat. Oncol. Biol. Phys., 60:419-26 (2004). [80] G. Nicolini et al., "Pre-clinical evaluation of respiratory-gated delivery of volumetric modulated arc therapy with RapidArc," Phys. Med. Biol., 55:N347-57 (2010). [81] J. Qian et al., "Dose verification for respiratory-gated volumetric modulated arc therapy," Phys. Med. Biol., 56:4827-38 (2011). [82] D. Ionascu et al., "Internal-external correlation investigations of respiratory induced motion of lung tumors," Med. Phys., 34:3893-903 (2007). [83] N. Kothary et al., "Safety and Efficacy of Percutaneous Fiducial Marker Implantation for Image-guided Radiation Therapy," J. Vasc. Interv. Radiol., 20:235-9 (2009). [84] A. Schweikard, H. Shiomi and J. Adler, "Respiration tracking in radiosurgery," Med.Phys., 31:2738-41 (2004). [85] G. C. Sharp et al., "Prediction of respiratory tumour motion for real-time image-guided radiotherapy," Phys. Med. Biol., 49:425-40 (2004). [86] M. Isaksson, J. Jalden and M. J. Murphy, "On using an adaptive neural network to predict lung tumor motion during respiration for radiotherapy applications," Med.Phys., 32:3801-9 (2005). [87] M. J. Murphy and S. Dieterich, "Comparative performance of linear and nonlinear neural networks to predict irregular breathing," Phys. Med. Biol., 51:5903-14 (2006). [88] J. Xu et al., "Synchronized moving aperture radiation therapy (SMART): superimposing tumor motion on IMRT MLC leaf sequences under realistic delivery conditions," Phys. Med. Biol., 54:4993-5007 (2009).  137  [89] Y. Suh et al., "Four-dimensional IMRT treatment planning using a DMLC motiontracking algorithm," Phys. Med. Biol., 54:3821-35 (2009). [90] M. Gui et al., "Four-dimensional intensity-modulated radiation therapy planning for dynamic tracking using a direct aperture deformation (DAD) method," Med. Phys., 37:1966-75 (2010). [91] M. Falk et al., "Real-time dynamic MLC tracking for inversely optimized arc radiotherapy," Radiother. Oncol., 94:218-23 (2010). [92] B. Sun et al., "Target tracking using DMLC for volumetric modulated arc therapy: A simulation study," Med. Phys., 37:6116-24 (2010). [93] R. George et al., "The application of the sinusoidal model to lung cancer patient respiratory motion," Med. Phys., 32:2850-61 (2005). [94] P. J. Keall et al., "Monte Carlo as a four-dimensional radiotherapy treatment-planning tool to account for respiratory motion," Phys. Med. Biol., 49:3639-48 (2004). [95] C. L. Ong et al., "Fast Arc Delivery for Stereotactic Body Radiotherapy of Vertebral and Lung Tumors," Int. J. Radiat. Oncol. Biol. Phys., 83:E137-43 (2012). [96] A. Holt et al., "Volumetric-Modulated Arc Therapy for Stereotactic Body Radiotherapy of Lung Tumors: a Comparison with Intensity-Modulated Radiotherapy Techniques," Int. J. Radiat. Oncol. Biol. Phys., 81:1560-5 (2011). [97] J. Brock et al., "Optimising Stereotactic Body Radiotherapy for Non-small Cell Lung Cancer with Volumetric Intensity-modulated Arc Therapy-A Planning Study," Clin. Oncol., 24:68-75 (2012). [98] C. L. Ong et al., "Stereotactic radiotherapy for peripheral lung tumors: A comparison of volumetric modulated arc therapy with 3 other delivery techniques," Radiother. Oncol., 97:437-42 (2010). [99] C. X. Yu, "Intensity-modulated arc therapy with dynamic multileaf collimation: an alternative to tomotherapy," Phys. Med. Biol., 40:1435-49 (1995). [100] D. M. Shepard et al., "An arc-sequencing algorithm for intensity modulated arc therapy," Med. Phys., 34:464-70 (2007). [101] M. A. Earl et al., "Inverse planning for intensity-modulated arc therapy using direct aperture optimization," Phys. Med. Biol., 48:1075-89 (2003). 138  [102] C. X. Yu et al., "Clinical implementation of intensity-modulated arc therapy," Int. J. Radiat. Oncol., Biol., Phys., 53:453-63 (2002). [103] E. Wong, J. Z. Chen and J. Greenland, "Intensity-modulated arc therapy simplified," Int. J. Radiat. Oncol. Biol. Phys., 53:222-35 (2002). [104] C. Cotrutz, C. Kappas and S. Webb, "Intensity modulated arc therapy (IMAT) with centrally blocked rotational fields," Phys. Med. Biol., 45:2185-206 (2000). [105] L. J. Ma et al., "Optimized intensity-modulated arc therapy for prostate cancer treatment," Int. J. Cancer, 96:379-84 (2001). [106] S. Webb and D. McQuaid, "Some considerations concerning volume-modulated arc therapy: a stepping stone towards a general theory," Phys. Med. Biol., 54:4345-60 (2009). [107] J. L. Bedford, "Treatment planning for volumetric modulated arc therapy," Med. Phys., 36:5128-38 (2009). [108] C. Cameron, "Sweeping-window arc therapy: an implementation of rotational IMRT with automatic beam-weight calculation," Phys. Med. Biol., 50:4317-36 (2005). [109] F. Glover, "Tabu Search - a Tutorial," Interfaces, 20:74-94 (1990). [110] T. Bortfeld, J. Stein and K. Preiser, "Clinically relevant intensity modulation optimization using physical criteria," in XIIth International Conference on the Use of Computers in Radiation Therapy, Salt Lake City, UT, 1-4 (1997). [111] K. Bzdusek et al., "Development and evaluation of an efficient approach to volumetric arc therapy planning," Med. Phys., 36:2328-39 (2009). [112] P. Storchi and E. Woudstra, "Calculation of the absorbed dose distribution due to irregularly shaped photon beams using pencil beam kernels derived from basic beam data," Phys. Med. Biol., 41:637-56 (1996). [113] W. F. A. R. Verbakel et al., "Rapid delivery of stereotactic radiotherapy for peripheral lung tumors using volumetric intensity-modulated arcs," Radiother.Oncol., 93:122-4 (2009). [114] M. van Herk et al., "Biologic and physical fractionation effects of random geometric errors," International Journal of Radiation Oncology Biology Physics, 57:1460-71 (2003).  139  [115] J. R. McClelland et al., "A continuous 4D motion model from multiple respiratory cycles for use in lung radiotherapy," Med. Phys., 33:3348-58 (2006). [116] R. B. Venkat et al., "Development and preliminary evaluation of a prototype audiovisual biofeedback device incorporating a patient-specific guiding waveform," Phys. Med. Biol., 53:N197-208 (2008). [117] W. Liu et al., "Real-time 3D internal marker tracking during arc radiotherapy by the use of combined MV-kV imaging," Phys. Med. Biol., 53:7197-213 (2008). [118] B. Fallone et al., "Development of a Linac-MRI system for real-time ART," Med. Phys., 34:2547 (2007). [119] Q. Ren et al., "Adaptive prediction of respiratory motion for motion compensation radiotherapy," Phys. Med. Biol., 52:6651-61 (2007). [120] N. Riaz et al., "Predicting respiratory tumor motion with multi-dimensional adaptive filters and support vector regression," Phys. Med. Biol., 54:5735-48 (2009). [121] N. Papanikolaou et al., "Tissue inhomogeneity corrections for megavoltage photon beams," Report of Task Group No. 65 of the Radiation Therapy Committee of the AAPM, Report No. 85 (2004). [122] M. J. Berger, Methods in Computational Physics, edited by S. Fernbach, B. Alder and M. Rothenberg, (Academic, New York, 1963) Vol. 1. [123] J. Baro et al., "Penelope - an Algorithm for Monte-Carlo Simulation of the Penetration and Energy-Loss of Electrons and Positrons in Matter," Nucl. Instrum. Methods Phys. Res. A, 100:31-46 (1995). [124] I. Kawrakow and D. W. O. Rogers, "The EGSnrc code system: Monte Carlo simulation of electron and photon transport," edited by Anonymous Technical Report PIRS-701, National Research Council of Canada, Ottawa, Ontario, 2000. [125] F. B. Brown, "MCNP — A general Monte Carlo-particle transport code, version 5," edited by Anonymous Report LA-UR-03-1987, Los Alamos National Laboratory, Los Alamos, NM, 2003. [126] S. Agostinelli et al., "GEANT4-a simulation toolkit," Nucl. Instrum. Methods Phys. Res. A, 506:250-303 (2003).  140  [127] J. Lobo and I. A. Popescu, "Two new DOSXYZnrc sources for 4D Monte Carlo simulations of continuously variable beam configurations, with applications to RapidArc, VMAT, TomoTherapy and CyberKnife," Phys. Med. Biol., 55:4431-43 (2010). [128] E. Chin and K. Otto, "Investigation of a novel algorithm for true 4D-VMAT planning with comparison to tracked, gated and static delivery," Med. Phys., 38:2698-707 (2011). [129] J. A. Shackleford, N. Kandasamy and G. C. Sharp, "On developing B-spline registration algorithms for multi-core processors," Phys. Med. Biol., 55:6329-51 (2010). [130] S. H. Benedict et al., "Stereotactic body radiation therapy: The report of AAPM Task Group 101," Med. Phys., 37:4078-101 (2010). [131] C. Scholz, S. Nill and U. Oelfke, "Comparison of IMRT optimization based on a pencil beam and a superposition algorithm," Med. Phys., 30:1909-13 (2003). [132] D. Schuring and C. W. Hurkmans, "Developing and evaluating stereotactic lung RT trials: what we should know about the influence of inhomogeneity corrections on dose," Radiat. Oncol., 3:21 (2008). [133] X. Gu et al., "A GPU-based finite-size pencil beam algorithm with 3D-density correction for radiotherapy dose calculation," Phys. Med. Biol., 56:3337-50 (2011). [134] X. Jia et al., "GPU-based fast Monte Carlo simulation for radiotherapy dose calculation," Phys. Med. Biol., 56:7017-31 (2011). [135] F. Peng et al., "A new column-generation-based algorithm for VMAT treatment plan optimization," Phys. Med. Biol., 57:4569-88 (2012). [136] M. Guckenberger et al., "A novel respiratory motion compensation strategy combining gated beam delivery and mean target position concept - A compromise between small safety margins and long duty cycles," Radiother. Oncol., 98:317-22 (2011). [137] M. Baker et al., "Isotoxic Dose Escalation in the Treatment of Lung Cancer by Means of Heterogeneous Dose Distributions in the Presence of Respiratory Motion," Int. J. Radiat. Oncol. Biol. Phys., 81:849-55 (2011). [138] Y. Seppenwoolde et al., "Precise and real-time measurement of 3D tumor motion in lung due to breathing and heartbeat, measured during radiotherapy," Int. J. Radiat. Oncol. Biol. Phys., 53:822-34 (2002).  141  [139] D. A. Low et al., "Novel breathing motion model for radiotherapy," Int. J. Radiat. Oncol. Biol. Phys., 63:921-9 (2005). [140] B. Cho et al., "A monoscopic method for real-time tumour tracking using combined occasional x-ray imaging and continuous respiratory monitoring," Phys. Med. Biol., 53:2837-55 (2008). [141] X. Allen Li et al., "The use and QA of biologically related models for treatment planning: Short report of the TG-166 of the therapy physics committee of the AAPM(a)," Med. Phys., 39:1386-409 (2012). [142] M. Guckenberger et al., "Potential of image-guidance, gating and real-time tracking to improve accuracy in pulmonary stereotactic body radiotherapy," Radiother. Oncol., 91:288-95 (2009). [143] Y. Suh et al., "A deliverable four-dimensional intensity-modulated radiation therapyplanning method for dynamic multileaf collimator tumor tracking delivery," Int. J. Radiat. Oncol. Biol. Phys., 71:1526-36 (2008). [144] L. Papiez, D. Rangaraj and P. Keall, "Real-time DMLC IMRT delivery for mobile and deforming targets," Med. Phys., 32:3037-48 (2005). [145] B. Guo, X. G. Xu and C. Shi, "Real time 4D IMRT treatment planning based on a dynamic virtual patient model: Proof of concept," Med. Phys., 38:2639-50 (2011). [146] O. Nohadani, J. Seco and T. Bortfeld, "Motion management with phase-adapted 4Doptimization," Phys. Med. Biol., 55:5189-202 (2010). [147] H. Alasti et al., "A novel four-dimensional radiotherapy method for lung cancer: imaging, treatment planning and delivery," Phys. Med. Biol., 51:3251-67 (2006). [148] J. Eom et al., "Predictive modeling of lung motion over the entire respiratory cycle using measured pressure-volume data, 4DCT images, and finite-element analysis," Med. Phys., 37:4389-400 (2010). [149] R. McGurk et al., "Extension of the NCAT phantom for the investigation of intrafraction respiratory motion in IMRT using 4D Monte Carlo," Phys. Med. Biol., 55:147590 (2010). [150] D. Yang et al., "4D-CT motion estimation using deformable image registration and 5D respiratory motion modeling," Med. Phys., 35:4577-90 (2008).  142  [151] P. Zhang et al., "Determination of action thresholds for electromagnetic tracking system-guided hypofractionated prostate radiotherapy using volumetric modulated arc therapy," Med. Phys., 38:4001-8 (2011). [152] P. Zhang et al., "Incorporation of treatment plan spatial and temporal dose patterns into a prostate intrafractional motion management strategy." Med. Phys., 39:5429-36 (2012). [153] B. Y. Yi et al., "Real-time tumor tracking with preprogrammed dynamic multileafcollimator motion and adaptive dose-rate regulation," Med. Phys., 35:3955-62 (2008). [154] C. L. H. Siantar et al., "Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom." Med. Phys., 28:1322-7 (2001). [155] I. Kawrakow, "VMC++, electron and photon Monte Carlo calculations optimized for radiation treatment planning," , edited by Kling, A Barao, F Nakagawa, M Tavora, L Vaz,P., Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications: Proc. Monte Carlo 2000 Meeting (Lisbon) ed. Springer, Berlin, 2001 pp. 229-236. [156] J. Sempau, S. J. Wilderman and A. F. Bielajew, "DPM, a fast, accurate Monte Carlo code optimized for photon and electron radiotherapy treatment planning dose calculations," Phys. Med. Biol., 45:2291 (2000). [157] C. M. Ma et al., "A Monte Carlo dose calculation tool for radiotherapy treatment planning," Phys. Med. Biol., 47:1671-89 (2002). [158] M. Margeanu et al., "A deformable phantom for quality assurance in 4D radiotherapy," Radiother. Oncol., 84:S80-1 (2007). [159] T. Kim et al., "Audiovisual biofeedback improves diaphragm motion reproducibility in MRI," Med. Phys., 39:6921-8 (2012). [160] T. Neicu et al., "Synchronized moving aperture radiation therapy (SMART): improvement of breathing pattern reproducibility using respiratory coaching," Phys. Med. Biol., 51:617-36 (2006). [161] R. D. Stewart and X. A. Li, "BGRT: Biologically guided radiation therapy - The future is fast approaching!" Med. Phys., 34:3739-51 (2007). [162] Q. Diot et al., "Biological-based optimization and volumetric modulated arc therapy delivery for stereotactic body radiation therapy," Med. Phys., 39:237-45 (2012). 143  [163] S. Flampouri et al., "Estimation of the delivered patient dose in lung IMRT treatment based on deformable registration of 4D-CT data and Monte Carlo simulations," Phys.Med.Biol., 51:2763-79 (2006). [164] B. Schaly et al., "Tracking the dose distribution in radiation therapy by accounting for variable anatomy," Phys. Med. Biol., 49:791-805 (2004). [165] M. Rosu et al., "Dose reconstruction in deforming lung anatomy: Dose grid size effects and clinical implications," Med. Phys., 32:2487-95 (2005). [166] E. Heath and J. Seuntjens, "A direct voxel tracking method for four-dimensional Monte Carlo dose calculations in deforming anatomy," Med. Phys., 33:434-45 (2006).  144  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0073633/manifest

Comment

Related Items