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Direct optimization of 3D dose distributions using collimator rotation Milette, Marie-Pierre 2008

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DIRECT OPTIMIZATION OF 3D DOSE DISTRIBUTIONS USING COLLIMATOR ROTATION by  MARIE-PIERRE MILETTE B.Sc., Universit´e du Qu´ebec `a Montr´eal, 2000 M.Sc., Universit´e du Qu´ebec `a Montr´eal, 2002  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE STUDIES  (Physics)  THE UNIVERSITY OF BRITISH COLUMBIA January 2008 c Marie-Pierre Milette, 2008  Abstract The primary goal of this thesis is to improve the precision and efficiency of radiation therapy treatment. This goal is achieved by developing and implementing a direct aperture optimization (DAO) platform where the multileaf collimator (MLC) is rotated between each aperture. The approach is referred to as rotating aperture optimization (RAO). A series of tests is performed to evaluate how a final optimized plan depends on MLC parameters. Imposing constraints on the leaf sequence results in increased efficiency and a simplification of the treatment plan without compromising the quality of the dose distribution. It is also shown that an arrangement of equispaced collimator angles takes full advantage of the flexibility associated with collimator rotation. A study including ten recurring nasopharynx cancer patients is used to evaluate the capabilities of RAO compared to other optimization techniques. It is shown that RAO plans require significantly less linac radiation output (monitor units or MU) while maintaining equivalent dose distribution quality compared to plans generated with the conventional fluence based approach. Furthermore with an improved collimator rotation speed, the RAO plans should be executable in the same or less time than plans generated with the fluence-based approach. For the second part of the study it is shown that plans generated with RAO are as good as or better than plans generated with standard fixed collimator DAO. Film and ion chamber measurements indicate that RAO plans can be delivered more accurately than DAO plans. Additional applications of DAO were investigated through collaboration with two PhD students. First, Monte Carlo was used to generate pencil beam dose distributions for DAO inverse treatment planning (MC-DAO). The MC-DAO technique correctly models traditionally difficult treatment geometries such as small fields and tissue inhomogeneities. The MC-DAO also takes advantage of the improved MU efficiency associated with the DAO technique. Secondly DAO is proposed for adaptive radiation therapy. The results show that plan re-adaptation can be performed more quickly ii  Abstract than complete plan regeneration thereby minimizing the time the patient has to spend in the treatment room and reducing the potential for geometric errors in treatment delivery.  iii  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  List of Tables  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  viii  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 1.3 1.4 1.5  Tumour and Healthy Tissues Response . . . . . . . CT/MR Imaging . . . . . . . . . . . . . . . . . . . Radiation Delivery with a Linear Accelerator . . . Dose Deposition . . . . . . . . . . . . . . . . . . .  1.6  1.7  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  2 3 4 6  1.5.1 Photon Interactions with Matter . . . . . 1.5.2 Kerma and Absorbed Dose . . . . . . . . Dose Calculation Algorithms . . . . . . . . . . . 1.6.1 Single Pencil Beam Convolution Algorithm 1.6.2 Inhomogeneity Corrections . . . . . . . .  . . . . . . . . . . . . . . . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  6 12 14 14 17  1.6.3 Monte Carlo Simulations . . Radiation Delivery Techniques . . . 1.7.1 Multiple Fields . . . . . . . . 1.7.2 Field Shaping . . . . . . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  20 20 21 22  . . . . . . . . . . . . . . . . . . . . . . . .  23  1.7.3  Forward Planning  iv  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  1 1  . . . .  . . . .  Table of Contents . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  24 27 28 28  . . . . . . . . . . . . . . . . . . . . . Agreement . . . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  30 31 31 32 32  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33  2 Intensity Modulated Radiation Therapy . . . . . . . . . . . . . . . . 2.1 IMRT Delivery with a Multileaf Collimator . . . . . . . . . . . . . .  36 37  1.8  1.9  1.7.4 Intensity Modulated Radiation Therapy 1.7.5 Adaptive Radiation Therapy . . . . . . Dose Measurement . . . . . . . . . . . . . . . . 1.8.1 Absolute Dosimeters . . . . . . . . . . . 1.8.2 Relative Dosimeters . . . . . . 2D Dose Distribution Comparison . . 1.9.1 Qualitative Analysis . . . . . . 1.9.2 Dose Difference and Distance to 1.9.3 The Gamma Factor . . . . . .  1.10 Thesis Objectives  2.2  Inverse Treatment Planning . . 2.2.1 Dose Volume Histogram 2.2.2 Physical Dose Objective 2.2.3 Biological Objective . .  2.3  . . . .  . . . .  . . . .  39 40 41 43  IMRT Optimization Techniques . . . . . . . . . . . 2.3.1 Fluence Based Optimization . . . . . . . . 2.3.2 Aperture Based Optimization . . . . . . . . 2.3.3 Direct Aperture Optimization . . . . . . . . Direct Aperture Optimization versus Fluence Based  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization  . . . . .  . . . . .  44 45 47 48 49  2.4.1 2.4.2 2.4.3 2.4.4  . . . .  . . . .  . . . .  49 51 53 56  3 Rotating Aperture Optimization . . . . . . . . . . . . . . . . . . . . 3.1 Advantages of Collimator Rotation . . . . . . . . . . . . . . . . . . . 3.1.1 Interleaf Effects . . . . . . . . . . . . . . . . . . . . . . . . .  57 58 58  2.4  3.2 3.3 3.4  Plan degradation . Efficiency . . . . . Tongue-and-Groove Applications . . .  . . . .  . . . . . . . . Effect . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  3.1.2 Spatial Resolution . . . . . . . Radiation Delivery with MLC rotation Rotating Aperture Optimization . . . Dose Calculation . . . . . . . . . . . . v  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  59 60 61 64  Table of Contents  3.5  3.4.1 Pre-calculated Pencil Beam Dose Distribution . . . . . . . . . 3.4.2 Single Pencil Beam Dose Calculation . . . . . . . . . . . . . . MLC Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . .  4 Characterization of the Rotating Aperture 4.1 Patients Description . . . . . . . . . . . . 4.1.1 C-Shape Target . . . . . . . . . . 4.1.2 Prostate Patient . . . . . . . . . . 4.2  4.1.3 Multiple PTV Nasopharynx Cancer Methods . . . . . . . . . . . . . . . . . . 4.2.1 Consistency . . . . . . . . . . . . . 4.2.2 Number of Apertures per Beam . . 4.2.3 Minimum Aperture Size . . . . . . 4.2.4 Collimator Angles . Results . . . . . . . . . . . 4.3.1 Consistency . . . . . 4.3.2 Number of Apertures  69 69 69 70  . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  73 74 74 75 76  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  77 78 78 83  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  87 92 93 95  5 Rotating Aperture Optimization Evaluation . . . . . . . 5.1 Patients Description . . . . . . . . . . . . . . . . . . . . . 5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 RAO vs Conventional Fluence Based Optimization  . . . .  . . . .  . . . .  . . . .  . . . .  . 96 . 96 . 100 . 100  5.2.2 RAO vs Direct Aperture Optimization . . . . . . . 5.2.3 Delivery accuracy . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . 5.3.1 RAO vs Conventional Fluence Based Optimization  . . . .  . . . .  . . . .  . . . .  . . . .  . . . .  4.3  4.4 4.5  5.3  5.4  4.3.3 Minimum Aperture 4.3.4 Collimator angles Discussion . . . . . . . . Conclusion . . . . . . . .  . . . . . . . . . . . . . . . . . . per Beam  Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  64 67 68  Size . . . . . . . . .  . . . .  . . . .  . . . .  . . . .  102 103 106 106  5.3.2 RAO vs Direct Aperture Optimization . . . . . . . . . . . . . 113 5.3.3 Delivery Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 120 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 137  vi  Table of Contents 6 Novel applications of DAO . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Direct Aperture Optimization Using Monte Carlo Generated Beamlets 6.1.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . 6.1.2 Monte Carlo DAO Description . . . . . . . . . . . . . . . . .  6.2  6.1.3 Methods . . . . . . . . . . 6.1.4 Results . . . . . . . . . . . 6.1.5 Discussion and Conclusion Adaptive Radiation Therapy (ART) 6.2.1 Methods . . . . . . . . . . 6.2.2 6.2.3  7 Conclusion 7.1  . . . . . . . . . with . . .  . . . . . . . . . . . . DAO . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  141 141 142 144 145 146 151 151 152  Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159  Future Work  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167  Appendices A Steps involved in generating a RAO plan . . . . . . . . . . . . . . . 178 B Comparison of RAO and fluence based optimization for patients 310 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 C Comparison of RAO and direct aperture optimization for patients 3-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183  vii  List of Tables 4.1 4.2 4.3 4.4  5.1 5.2 5.3  5.4  5.5  5.6 5.7  Summary of the treatment goals for the hypothetical c-shaped target. Summary of the treatment goals for the prostate patient. . . . . . . . Summary of the treatment goals for the multiple PTV nasopharynx  70 71  patient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The optimization times (minutes) for the plans with 2,4,6,8 and 10 apertures per beam. Results are shown for two types of MLC: the Millennium 80 (1 cm leaf width MLC) and the Millennium 120 (5 mm leaf width MLC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73  86  Summary of the re-treatment goals for 10 nasopharynx cancer cases. . 98 Comparison between Eclipse SMLC, DMLC and RAO. Results are derived from dose volume histograms for all 10 patients. . . . . . . . 108 Patient 1: Dose-volume indices for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC. 6 apertures per beam were used optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . Patient 2: Dose-volume indices for DAO with 1cm and 5mm and RAO with the 1 cm MLC. 6 apertures per beam were used optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . .  in the . . . . 115 MLC, in the . . . . 118  Summary of the measurements for the c-shape target. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Summary of the ion chamber measurements for the c-shape target. . . 127 Summary of the delivery times for the c-shape target. The plans were delivered with a dose rate of 400 MU/min. . . . . . . . . . . . . . . . 127  viii  List of Tables 5.8  5.9  Summary of the measurements for patient 1. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Summary of the ion chamber measurements for the nasopharynx cancer  patient 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.10 Summary of the measurements for patient 2. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.11 Summary of the ion chamber measurements for the nasopharynx cancer patient 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.1 6.2 7.1  Summary of the treatment goals for the hypothetical c-shaped target located near an air cavity. . . . . . . . . . . . . . . . . . . . . . . . . 146 Summary of the treatment goals for the prostate model . . . . . . . . 154 Summary of the delivery parameters on an Elekta linac for a prostate patient and the RPC head and neck phantom. . . . . . . . . . . . . . 165  ix  List of Figures 1.1  3  1.2  (a) Classical dose-response curve. (b) A more realistic dose-response curve for both tumour and normal tissues . . . . . . . . . . . . . . . (a) CT and (b) MRI of a patient with a brain tumour. Note that the  1.3 1.4 1.5  tumour volume is more clearly seen on the MR image, where the target has been contoured and superimposed on the CT. . . . . . . . . . . . Schematic diagram of a typical medical linear accelerator. . . . . . . . Relative importance of the three major types of photon interactions. . Photoelectric effect: (a) Incident photon hν interacts with a bound  4 6 8  1.6  electron. (b) The electron is ejected from the atom with energy Etr = hν − BE where BE is the binding energy of the electron. In the case shown BE = EK where EK is the binding energy of the K shell. . . . (a) The hole left in the shell after photoelectric effect is filled and  1.7  1.8 1.9  9  characteristic radiation is emitted. In this case the photon energy is hν = EK − EL where EK and EL are the energies of the K and L shell respectively. (b) The hole in the shell is filled and the extra energy of the excited atom is carried away by an Auger electron. . . . . . . . .  10  Compton effect: (a) Incident photon (hν) interacts with a loosely bound electron. (b) The electron is ejected and the photon is scattered with a reduced energy hν . . . . . . . . . . . . . . . . . . . . . . (a) Pair production and (b) triplet production. . . . . . . . . . . . . . Relationship between KERMA and dose. . . . . . . . . . . . . . . . .  11 12 13  1.10 (a) The beam is divided into 5 mm × 2.5 mm beamlets or pencil beams. (b) The pencil beam is projected onto a water phantom and dose is deposited in and around the point of interaction. (c) The dose deposited by the pencil beam is modeled with a depth dependent pencil beam kernel K(x, y, z) (here shown for depth z = 10 cm). . . . . . . . x  15  List of Figures 1.11 The pencil beam model of dose deposition. (a) With multiple pencil beams the total dose is the sum of all pencil beam kernels (PBK). (b) In the limit as the number of pencil beams approaches infinity the calculation becomes a convolution of the incident fluence by the PBK. 1.12 Illustration of the definition of tissue-air ratio. . . . . . . . . . . . . . 1.13 Photon beam incident on a water phantom (density ρw ) containing an inhomogeneity (density ρ2 ). . . . . . . . . . . . . . . . . . . . . . . . 1.14 (a) A percent depth dose curve for a 6 MV photon beam. The maximum dose deposited is at a depth of 1.5 cm. . . . . . . . . . . . . . . 1.15 The linac rotates around the isocenter allowing delivery from different gantry angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.16 (a) Two sets of independently moving jaws are used to create a rectangular field. A field shape conforming more closely to the planning target volume (PTV) may be obtained with (b) custom made blocks or (c) a multileaf collimator. . . . . . . . . . . . . . . . . . . . . . . . 1.17 Typical dose distribution for a prostate patient using the forward planning technique. Two pairs of opposing conformal beams were used. . 1.18 (a) Open beam dose distribution for a wedge shaped surface. (b) Dose distribution for the same surface when a wedge is added to modulate the fluence. Note that the isodoses are more flat and that the dose across the structure is more uniform with the wedge. . . . . . . . . . 1.19 (a)-(c) Three MLC apertures delivered sequentially. (d)-(f) The corresponding fluence builds up with each aperture resulting in a twodimensionally varying fluence . . . . . . . . . . . . . . . . . . . . . . 1.20 Resulting dose distribution for five intensity modulated beams. . . . . 1.21 A simple example to illustrate the adaptive radiation therapy process.  16 18 19 21 22  23 24  25  26 27  (a) The patient is imaged before treatment and an MLC shape is conformed to the beam’s eye view of the PTV. (b) Image during treatment shows that the PTV has expanded and that the MLC does not cover the whole PTV. (b) The MLC shape is adapted based on the new image. 28 1.22 Cross section of a Farmer type ion chamber. . . . . . . . . . . . . . . 29 1.23 A typical sensitometric curve for radiographic film. . . . . . . . . . .  xi  31  List of Figures 2.1 2.2 2.3  2.4  2.5 2.6  2.7 2.8  Beam’s eye view of (a) the Varian Millennium 80 MLC and (b) the Varian Millennium 120 MLC. . . . . . . . . . . . . . . . . . . . . . . 37 (a) Cross sectional view of a multileaf collimator and (b) end on diagram of the tongue-and-groove design of the Varian Millennium MLCs. 38 (a) In the static mode the leaves move to their position while the beam is off. (b) In dynamic mode each leaf pair moves continuously from one side of the beam to the other while the beam is on. . . . . . . . . . . Dose Volume Histograms for two treatment plans. The dashed line shows a poor plan with non-uniform tumour coverage and high dose  39  to the critical structure. The solid line represents a superior plan with better tumour uniformity and reduced dose to the critical structure. . 41 Ideally 100% of a target would receive the prescribed dose. Generally a minimum and maximum dose constraint are specified for each target. 42 Illustration of how dose-volume constraints are taken into account in the objective function. The dose-volume constraint is specified as the volume receiving a dose greater than D1 should be less than V1 . Only the points receiving a dose between D1 and D2 are penalized by the objective function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluence maps are divided into beamlets of width w and length l. Note that the beamlet width w is limited by the leaf width. . . . . . . . . . In aperture based optimization the apertures for each beam are defined to conform to the PTV and/or cover the critical structures. Example apertures for a prostate patient are shown for one beam. (a) The MLC conforms to the PTV. The MLC conforms to the PTV and (b) covers the rectum, (c) covers the bladder and (d) covers the rectum and the bladder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Flowchart of the conventional fluence based optimization approach versus the direct aperture optimization technique. . . . . . . . . . . . . . 2.10 Comparison of the optimal (solid line) and actual (dashed line) DVHs for the conventional fluence based optimization approach. . . . . . . . 2.11 (a)-(c) Three aperture shapes and (d) corresponding fluence map (7  43 46  48  2.9  intensity levels) for one beam direction. . . . . . . . . . . . . . . . . .  xii  50 50 52  List of Figures 2.12 The tongue-and-groove effect is illustrated by considering an open field delivered with the two adjacent segments shown in (a) and (b). The sum of both profiles should ideally result in a constant fluence across both leaves, but the sum of (a) and (b) results in an underdosage located at the tongue-and-groove interface (shown in (c)). . . . . . . . 2.13 Tongue-and-groove effect as measured on a Varian CL21EX with a Millennium 120 MLC. (a) Open field fluence delivered in one segment, and (b) the same open field fluence is delivered in two segments. In this case the sum of the two segments does not equal the open field fluence in (a): a line of underdosage due to the tongue-and-groove shape of the leaf is observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 (a) MLC aperture which does not violate the interdigitation constraint. (b) In this case the central leaf on the left bank is extended past the adjacent leaves of the opposite bank: the interdigitation constraint is violated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.15 Comparison of the DVHs for a treatment plan optimized with (dashed line) and without (solid line) interdigitation constraint. . . . . . . . .  3.3  (a) Conventional IMRT delivery: the collimator remains fixed (e.g. 0o ). (c) IMRT delivery with collimator rotation. . . . . . . . . . . . . . . When the collimator is rotated between each aperture the location of the leaf edges changes thereby reducing interleaf effects. . . . . . . . . (a) With conventional delivery the spatial resolution is limited by the  3.4  leaf width. (b) When the collimator is rotated between each aperture the spatial resolution is approximated by a circle with a diameter equal to the minimum leaf displacement. . . . . . . . . . . . . . . . . . . . (a), (b), (c) The initial rotated apertures outline the target beam’s eye  3.1 3.2  3.5 3.6  view. (d), (e), (f) Final optimized rotated leaf sequence. One beam is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The concept of local minima is illustrated with an objective function. A pre-calculated pencil beam dose distribution (PBDD) establish the relationship between a fluence pixel (or beamlet) and the dose to the patient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xiii  53  54  55 56  58 59  60  63 64  65  List of Figures 3.7  3.8  4.1 4.2  4.3 4.4 4.5 4.6  (a) For an MLC aperture shape without rotation, the minimum beamlet size is 5 mm x 2.5 mm. Each beamlet is either completely covered (beamlet intensity equal to zero) or completely uncovered (beamlet intensity equal to one). (b) When the entire MLC is rotated the subsampled beamlet dimensions are 2.5 mm x 2.5 mm. In this situation, one leaf could partially block one or more beamlets. The corresponding beamlet intensity is scaled by the area uncovered by the MLC. . . . . Dose volume histograms calculated with (1) full scatter conditions, (2) PBDD contribution within a 1 cm truncation radius, and (3) PBDD  66  contribution within a 2 cm truncation radius. . . . . . . . . . . . . .  67  Hypothetical c-shaped target with a centrally located aorgan at risk (OAR) (a) axial view and beam configuration and (b) 3D view. . . . Prostate patient: (a) axial view and beam arrangement, (b) coronal  70  view and (c) sagittal view . Structures are numbered as follows: (1) PTV, (2) rectum, (3) bladder and (4) femoral heads. . . . . . . . . . Multiple PTV nasopahrynx patient (a) axial view and beam configuration, (b) coronal view and (c) sagittal view. . . . . . . . . . . . . . At the beginning of the optimization the collimator angles are set so that there is an equal angle between each aperture. . . . . . . . . . . (a) The cost value versus the number of iterations. (b) Dose volume histograms after 25 000 and 100 000 iterations. . . . . . . . . . . . . . Optimization was run 100 times for each patient. All patient plans  72 74 77 78  were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the cost values are shown for (a) the c-shape target, (b) prostate patient and (d) the multi-PTV nasopharynx patient. The mean value (µ) and the standard deviation 4.7  (σ) are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resulting DVHs for (a) the c-shaped target, (b) the prostate patient and (c) the multi-PTV nasopharynx patient showing the best and worst results of the consistency test. The optimization constraints are also shown for each structure. . . . . . . . . . . . . . . . . . . . . . . . . .  xiv  80  81  List of Figures 4.8  4.9  Optimization was run 100 times for each patient. All patient plans were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the number of MU are shown for (a) the c-shape target, (b) prostate patient and (c) the multi-PTV nasopharynx patient. The mean value (µ) and the standard deviation (σ) are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Final normalized cost for different number of apertures per beam for (a) the c-shape target, (b) the prostate patient and (c) the multiple PTV nasopharynx cancer patient. Results are shown for RAO with  the Varian Millenium 120 (5mm leaf width for the central 40 leaves). 4.10 DVHs for the C-shaped target (left) and the OAR (right) for plans with 2, 4, 6, 8 and 10 apertures per beam angle. . . . . . . . . . . . . 4.11 DVHs for the planning target volume (left) and the rectum and bladder (right) for plans with 2, 4, 6, 8 and 10 apertures per beam angle. . . . 4.12 DVHs for the three clinical target volume (left) and the left parotid (right) of the multi-PTV nasopharynx patient for plans with 2, 6 and 10 apertures per beam angle. . . . . . . . . . . . . . . . . . . . . . . .  82  84 85 85  86  4.13 The final cost and the number of MU for different aperture size. All other optimization parameters kept constant and 6 apertures per beam angle were used. Results are shown for (a) the prostate patient, (b) the c-shaped target and (c) the multi-PTV nasopharynx cancer patient. 88 4.14 Prostate patient DVHs for 6 rotated aperture per beam and minimum aperture size equal to 0%, 80%, 90% and 100% of the target BEV. . . 4.15 Leaf sequence for the prostate patient with no constraints on the minimum aperture size set during the optimization. . . . . . . . . . . . . 4.16 Leaf sequence for the prostate patient with a minimum aperture size  89 90  set to 80% of the target beam’s eye view. . . . . . . . . . . . . . . . . 4.17 Prostate dose distribution for 6 rotated apertures per beam and a minimum aperture size equal to 80% of the BEV. The PTV is outlined in white, the femoral heads are outlined with the solid black line and the rectum is outlined with the dashed black line. The dose is normalized  90  to the prescribed dose (70 Gy). . . . . . . . . . . . . . . . . . . . . .  91  xv  List of Figures 4.18 C-shaped target DVHs for 6 rotated aperture per beam and minimum aperture size equal to 0%, 40%, 50% and 60% of the target BEV. . . 91 4.19 Multiple PTV patient DVHs for 6 rotated aperture per beam and minimum aperture size equal of 0%, 40%, 50% and 60% of the target BEV. 92 4.20 Optimization was run 50 times for each patient with random nonequispaced collimator angles. All patient plans were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the cost values are shown for (a) the c-shape target, (b) the prostate patient and (c) the multi-PTV nasopharynx patient.  5.1  5.2  5.3 5.4 5.5 5.6 5.7  The results of the consistency test (with equispaced collimator angles) are shown for comparison. The mean value (µ) and the standard deviation (σ) are also shown (in parentheses for the equispaced collimator angles). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  93  Patient 1 structures. (a) Axial (b) sagittal and (c) coronal views. Structures are numbered as follow: (1) PTV, (2) brainstem, (3) spinal cord, (4) left temporal lobe, (5) right temporal lobe. The beam geometry is shown in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . .  99  Patient 2 structures. (a) Axial (b) sagittal and (c) coronal views. Structures are numbered as follow: (1) PTV, (2) brainstem, (3) spinal cord, (4) left temporal lobe, (5) right temporal lobe, (6) brain and (7) optical apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Summary of the planning process . . . . . . . . . . . . . . . . . . . . 102 The AVID IMRT verification phantom is mounted on the treatment couch with the localizer box used to set up the phantom. . . . . . . . 104 Percent depth dose calibration film for (a) low dose, (b) medium dose and (c) high dose. (d) A calibration curve converts pixel value into dose.105 Patient 1: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 109 Patient 2: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 109  xvi  List of Figures 5.8  5.9  Patient 2: Isodose distributions for (a) the Eclipse fluence based technique (DMLC) and (b) the Rotating Aperture Optimization technique. Doses are given as the percentage of the prescribed dose (60 Gy). The PTV is outlined in white, the brainstem in dashed black and the temporal lobes in dashed white. . . . . . . . . . . . . . . . . . . . . . . . 110 Number of apertures required for the 10 patients included in the study. Results are shown for plans generated with Eclipse using static (SMLC) delivery and plans generated with the Rotating Aperture Optimization (RAO) technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111  5.10 Number of MU required for the 10 patients included in the study. Results are shown for plans generated with Eclipse using dynamic (DMLC) and static (SMLC) delivery, as well as plans generated with the Rotating Aperture Optimization (RAO) technique. . . . . . . . . 112 5.11 Treatment times for the 10 patients included in the study. Results are shown for plans generated with Eclipse using dynamic (DMLC) and static (SMLC) delivery, as well as plans generated with the Rotating Aperture Optimization (RAO) technique. Estimate of treatment times for a collimator rotating through 1800 in 10 seconds are also shown (*RAO). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.12 Final normalized cost value for different number of apertures per beam for patient 1. Results are shown for DAO and RAO with two types of MLC: Varian Millenium 80 (1cm leaf width) and Millenium 120 (5mm leaf width for the central 40 leaves). . . . . . . . . . . . . . . . . . . . 114 5.13 Patient 1: DVHs for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC are shown. 6 apertures per beam were used in the optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.14 Patient 1: Number of MU required for DAO and RAO with 1cm and 5mm MLC. 6 apertures per beam were used in the optimization. . . . 116 5.15 Patient 1: (a) DAO and (b) RAO optimized dose distribution for 1 cm leaf width MLC with 6 apertures per beam. The PTV is outlined with a solid white line, and the critical structures (temporal lobes and brainstem) are outlined with dashed white lines. . . . . . . . . . . . . 116  xvii  List of Figures 5.16 Final normalized cost value for different number of apertures per beam for patient 2. Results are shown for DAO and RAO with two types of MLC: Varian Millenium 80 (1cm leaf width) and Millenium 120 (5mm leaf width for the central 40 leaves). . . . . . . . . . . . . . . . . . . . 117 5.17 Patient 2: DVHs for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC are shown. 6 apertures per beam were used in the optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.18 Patient 2: Number of MU required for DAO and RAO with 1cm and 5mm MLC. 6 apertures per beam were used in the optimization. . . . 118 5.19 Patients 3-7: (a) Final cost and (b) number of MU for RAO and DAO with the 5 mm leaf width MLC and the 1 cm leaf width MLC. 6 apertures per beam were used in the optimization. . . . . . . . . . . . 119 5.20 C-shape target optimized dose distribution in the transverse plane for (a) DAO and (b) RAO. Both plans were optimized with 6 apertures per beam angle and the 5 mm MLC. The c-shape target and the centrally located sensitive structure are outlined in white. . . . . . . . . . . . . 120 5.21 (a) DVH and (b) number of MU comparison of RAO and DAO for the c shape target. For each case, 6 apertures per beam angle were used. 5.22 (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for C-shape target. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. Arrows show tongue and groove effect. (c) Corresponding  121  gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.23 (a) Calculated and (b) measured dose distribution of the DAO plan in the axial plane for C-shape target. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . 124  xviii  List of Figures 5.24 (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for C-shape target. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.25 (a) Calculated and (b) measured dose distribution of the RAO plan in the axial plane for C-shape target. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.26 (a) Calculated and (b) measured dose distribution of the FBO Eclipse plan in the coronal plane for nasopharynx patient 1. This plan was generated with collimator at 0◦ for each beam, 5 mm MLC in dynamic mode. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . 129 5.27 (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for nasopharynx patient 1. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . 130 5.28 (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for nasopharynx patient 1. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.29 (a) Calculated and (b) measured dose distribution of the FBO Eclipse plan in the coronal plane for nasopharynx patient 2. This plan was generated with collimator at 0◦ for each beam, 5 mm MLC in dynamic mode. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . 134  xix  List of Figures 5.30 (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for nasopharynx patient 2. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . 135 5.31 (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for nasopharynx patient 2. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6.1 6.2  The linac model used in Monte Carlo simulations. . . . . . . . . . . . 144 Water equivalent AVID phantom with a 5 cm thick air cavity. The c-shaped PTV and a spinal-cord like structure (OAR) are shown. . . 146  6.3  Monte Carlo DAO example for a c-shape target with a nearby critical structure. (a) Eclipse TPS IMRT plan employing a PBK dose algorithm (solid line) is recalculated using Monte Carlo (dashed line). (b) MC-DAO plan (solid line) compared to Eclipse optimized/MC for-  6.4  6.5  ward calculation (same dashed line in (a)). Dose is normalized to the prescribed dose (60 Gy). . . . . . . . . . . . . . . . . . . . . . . . . . 148 3D representation of the 95% isodose line covering the c-shape target. (a) IMRT plan employing a PBK dose algorithm for the optimization and the final dose caluclation. (b) The PBK plan is recalculated using Monte Carlo. (c) MC-DAO plan using 6 apertures per beam. Note: wireframe box indicates location of air cavity. . . . . . . . . . . . . . 149 Results of the coronal dose measurement for the MC-DAO plan. (a) film measurement (left) and Monte Carlo caluclated dose (right). The arrows show the effect. Dose profiles taken along the (b) the x axis and (c) the y axis. (d) Cropped film plane. (e) Corresponding dose difference (DD=3%)/distance-to-agreement (DTA=3 mm) map. The dark areas correspond to pixels that pass the DTA or the DD criteria. The white pixels failed DD/DTA criteria. . . . . . . . . . . . . . . . . 150  6.6  A model simulating a prostate case. . . . . . . . . . . . . . . . . . . . 153  xx  List of Figures 6.7 6.8  6.9  Four deformed anatomies are created by systematically deforming the original prostate model. . . . . . . . . . . . . . . . . . . . . . . . . . 153 The search space during plan adaptation is reduced by (a) restraining the maximum step size, (b) restraining the allowed leaf range and (c) predefining an optimization order for the parameters. . . . . . . . . . 155 DVHs for the non-adapted original treatment plan and the adapted plan. The DVHs for the plan generated by the complete plan regeneration and the plans generated by the treatment plan adaptation are indistinguishable, so the DVHs for original plan adaptation are shown. 156  6.10 The average times needed for the complete plan regeneration and the original treatment plan adaptation. The error bars shown represent one standard deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.1  An axial slice of the RPC patient. PTV 66 Gy is outline in red, PTV 54 Gy is outlined in magenta and the spinal cord like structure is outlined in yellow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165  B.1 Patient 4: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 179 B.2 Patient 5: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 180 B.3 Patient 6: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 180 B.4 Patient 7: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 181 B.5 Patient 8: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 181 B.6 Patient 9: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . . . . . . . 182 B.7 Patient 10: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO). . . . . . . . . 182 C.1 Patient 3: DVHs for DAO and RAO with the 1 cm leaf width MLC. . 183 C.2 Patient 4: DVHs for DAO and RAO with the 1 cm leaf width MLC. . 184  xxi  List of Figures C.3 C.4 C.5 C.6  Patient Patient Patient Patient  5: 6: 7: 8:  DVHs DVHs DVHs DVHs  for for for for  DAO DAO DAO DAO  and and and and  RAO RAO RAO RAO  with with with with  the the the the  1 1 1 1  cm cm cm cm  leaf leaf leaf leaf  width width width width  MLC. MLC. MLC. MLC.  . . . .  184 185 185 186  C.7 Patient 9: DVHs for DAO and RAO with the 1 cm leaf width MLC. . 186 C.8 Patient 10: DVHs for DAO and RAO with the 1 cm leaf width MLC. 187  xxii  List of Abbreviations 3DCRT  Three-Dimensional Conformal Radiation Therapy  ART  Adaptive Radiation Therapy  BEV  Beam’s Eye View  CT  Computed Tomography  DAO  Direct Aperture Optimization  DMLC  Dynamic Multileaf Collimator  DTA  Distance To Agreement  DVH  Dose-Volume Histogram  FBO  Fluence Based Optimization  IMRT  Intensity Modulated Radiation Therapy  MC  Monte Carlo  MLC  Multileaf Collimator  MU  Monitor Unit  OAR  Organ At Risk  PBDD  Pencil Beam Dose Distribution  PBK  Pencil Beam Kernel  PTV  Planning Target Volume  RAO  Rotating Aperture Optimization  RF  Radio-Frequency  SMLC  Static Multileaf Collimator  TPS  Treatment Planning System  xxiii  Acknowledgements Firstly, I would like to thank my research supervisor, Dr. Karl Otto, for his guidance and support during the duration of my PhD. I would also like to thank my cosupervisor, Dr. Brenda Clark, for her advices and encouragements. I would also like to acknowledge the other members of my thesis committee, Dr. Alex MacKay, Dr. Andre Marziali and Dr. Michael McKenzie, for their input throughout the years. I would also like to express my gratitude to the group I had the chance to work with for the nasopharynx cancer study: Dr. Martin Rolles, Dr. Jonn Wu, Rosie Vellani and Margaret Welsh. I would also like to thank Emily Vollans for her help at the beginning of the study. Thanks to my fellow students Alanah Bergman, Tony Mestrovic, Moira Schmuland and Nick Chng for their help and comments on many practice presentations. Thanks to Alanah and Tony for giving me the opportunity to work on interesting projects, and for providing most of the figures included in chapter 6. Thanks also to Moira who spent some time to show me how to do measurements. I would like to acknowledge the financial support I received from Varian Medical System during my PhD. Thanks to my family for their constant support. Finally thanks to Tony Teke for his love and patience during these last five years. Thank you for always being there when I need it the most.  xxiv  Chapter 1 Introduction Radiation therapy is a method of treating a disease through the delivery of radiation. Radiation oncology is the clinical speciality which uses radiation to treat cancer. The goal of radiation therapy is to kill the cancer cells and to avoid further proliferation by the use of ionizing radiation. Cancerous tissues are destroyed primarily through damage to DNA caused by ionizing radiation [1]. X-rays and electrons are the most common form of ionizing radiation used to treat cancerous tumours but external beam radiotherapy can also be carried out with heavier particles such as protons and neutrons. However, the equipment necessary to produce protons and neutrons is considerably more expensive and is used only in a few specialized centers. There is only one proton therapy facility in Canada, which is located at TRIUMF, University of British Columbia. In this chapter an introduction to various radiation therapy concepts relevant to this thesis are presented.  1.1  Historical Background  After the discovery of x-rays in 1895 by Wilhelm R¨oentgen and the development of medicinal use of radioactivity in 1896 by Henri Becquerel and Marie Curie, it was soon realized that the penetrating and non-invasive characteristics of x-rays could be exploited to acquire images of internal structures in the body and that higher energy photons could be used to treat malignant tumours. In 1899 the first patient to be cured by radiation was reported[2]. In the early days radiation therapy was used to treat superficial malignancies. In 1913 Coolidge developed the first x-ray tube and by 1922 tubes were able to generate a photon spectrum with a maximum energy of 200 keV. Higher energy particle accelerators, with peak energies in the MeV range, were introduced in the 1940’s. In 1951 a patient was treated with 60 Co gamma-rays for the first time. With  1  Chapter 1. Introduction a high specific activity, a half life of 5.26 years and average photon energy of 1.25 MeV 60 Co became a popular method of radiation treatment and is still used in many cancer centers. One of the most important developments in modern radiation therapy has been the development of linear accelerators (linacs) in the 1960s. Today the linac is the most common equipment used to generate megavoltage photon and electron beams for cancer treatment.  1.2  Tumour and Healthy Tissues Response  The response of different cell types to radiation is complex. The radiation beam usually needs to go through healthy tissues in order to reach the tumour. This can result in normal tissues complication. Therefore there is a need to balance between tumour control and normal tissue complication as it is impossible to irradiate cancer cells without irradiating normal tissues. Ideally the tumour would be more sensitive to radiation than normal tissues as illustrated in figure 1.1 (a)[3]. This simple model is characterized by a sigmoidal doseresponse curve. After a certain threshold there is an increase in tumour response with increasing dose. After this steep increase the tumour response asymptotically reaches 100%. In this ideal situation the normal tissue has the same sigmoidal shape but is shifted to higher dose indicating that it is less sensitive to radiation. A more realistic tumour/healthy tissue dose response is shown in figure 1.1 (b)[3]. The first difference with (a) is that the tumour response curve is shallower compared to normal tissues and in some case never reaches the 100% tumour control as a result of microscopic or metastatic spread of the disease beyond the primary tumour site. Secondly, the healthy tissues curve is now located to the left of the tumour curve, indicating that healthy tissues are more sensitive to radiation. The radiation dose tolerance depends on the structure considered (a summary of radiation dose tolerance for different tissues can be found in Emami et al.[4]). Appropriate treatment planning is therefore necessary to keep the dose to normal tissue lower than doses to the tumour.  2  100  100  80  80  Normal Tissue  Tumor  60  Relative Response (%)  Relative Response (%)  Chapter 1. Introduction  40 20 0  0  20  40 60 Dose (Gy)  80  (a)  Tumor  40 20 0  100  Normal Tissue  60  0  20  40 60 Dose (Gy)  80  100  (b)  Figure 1.1: (a) Classical dose-response curve. (b) A more realistic dose-response curve for both tumour and normal tissues  1.3  CT/MR Imaging  As mentioned in the previous section it is essential to generate a uniform dose distribution in a target volume while minimizing dose to surrounding healthy tissues. Therefore accurate localization of tumours and adjacent critical structures (such as the spinal cord, optic nerves, parotids, lungs, etc) is essential to radiation therapy. One of the advantages of radiation therapy is that it is relatively non-invasive. This benefit can only be achieved if the tumour can be located with a non-invasive procedure. In the late 1970s computed tomography (CT) was introduced and is now used for accurate treatment planning. CT uses radiographic projections obtained at different angles around the patient to digitally reconstruct a 3D distribution of the physical density inside the patient. Based on this information the radiation oncologist delineates the tumor (target) and the critical structures on each CT slice. Adequate target information is not always provided on the CT image, therefore magnetic resonance imaging (MRI) or positron emission tomography (PET) can also be performed. For example, soft tissue contrast with MRI is superior to CT in some areas such as the brain (see figure 1.2). However, MRI/PET can not be used alone for radiation therapy planning because it does not provide the electron density information necessary for 3  Chapter 1. Introduction accurate radiation dosimetry in treatment planning. Many treatment planning systems are able to fuse or register different image studies, thereby combining accurate volume definition of MRI with electron density information provided by CT.  (a)  (b)  Figure 1.2: (a) CT and (b) MRI of a patient with a brain tumour. Note that the tumour volume is more clearly seen on the MR image, where the target has been contoured and superimposed on the CT.  1.4  Radiation Delivery with a Linear Accelerator  A schematic diagram of a typical medical linear accelerator is shown in figure 1.3. Medical linear accelerators are designed to accelerate electrons to kinetic energies from 4 to 25 MeV using microwave radio-frequency (RF) fields. Most linacs operate in the ”S” band, or at a frequency of 2856 MHz. The injection system is the source of electrons called an electron gun. Electrons are thermionically emitted from a heated cathode and focused into a pencil beam by a curved focusing electrode. Microwave radiation is used in the accelerating waveguide to accelerate electrons 4  Chapter 1. Introduction to the desired kinetic energy. The RF power generation system consists of the RF power source and a pulsed modulator. The RF power source is either a magnetron or klystron, which are both devices that use electron acceleration and deceleration in vacuum to produce the high power RF fields. The modulator emits high-voltage pulses at rates between 30 and 300 Hz. These pulses are required to ensure the synchronicity between the arrival of the electrons and microwaves to the accelerating waveguide. There are two types of accelerating waveguide: standing wave and traveling wave. Electrons are accelerated in the accelerating waveguide by means of an energy transfer from the high power RF fields. The length of the waveguide depends on the final kinetic energy of electrons and ranges from 30 cm at 4 Mev to 150 cm at 25 MeV. In the traveling wave guide the microwaves enter the waveguide at the gun side and propagate to the end where they are absorbed without reflection. With this configuration only one out of four cavities, at a given moment, provides an electric field in the direction of propagation necessary for electron acceleration. In the standing waveguide the microwaves are reflected at both ends on the accelerating structure resulting in a buildup of standing waves in the waveguide. With this configuration every second cavity does not provide energy gain for the electrons since they carry no electric field. These cavities can be moved to the side of the waveguide thereby shortening the overall structure by 50%. Once the electrons have been accelerated they are directed to the target. For low energy linacs there is no need for a beam electron transport system, as the target can be embedded into the accelerating waveguide and mounted parallel to the beam axis. For linacs operating at energies above 6 MeV, the accelerating structure is longer and must be mounted perpendicular to the beam axis. A bending magnet is used to redirect the electrons to the target, as illustrated in figure 1.3. Bremsstrahlung x-rays are produced when the electrons strike a target made of high Z material such as tungsten. Between the target and the patient there are several beam modifiers such as the flattening filter (to flatten the profile of the forward peaked beam), the primary collimators, an ion chamber (to monitor the dose delivered to the patient), secondary collimating jaws that move independently (used to create rectangular fields) and finally an optional tertiary collimation system such as a multileaf collimator. 5  Chapter 1. Introduction The output of linear accelerators must be calibrated to deliver dose precisely to the patient. Since the output of the linac is not stable with time, Monitor Units (or MU), which are related to the charge collected in ion chamber located in the head on the linac, are used. At the Vancouver Cancer Centre, linacs are adjusted so that 1 MU will deliver 1 cGy of dose to water at a depth of maximum dose (dmax = 1.5 cm for a 6MV beam) at a source axis distance (SAD) of 100 cm for a 10 cm × 10 cm field size.  Figure 1.3: Schematic diagram of a typical medical linear accelerator.  1.5 1.5.1  Dose Deposition Photon Interactions with Matter  Photons incident on matter have a probability of interacting with the atoms contained within. If a monoenergetic beam with N0 photons is incident on a slab of thickness  6  Chapter 1. Introduction x, then the number of remaining photons is given by N = N0 e−µx  (1.1)  where µ is the linear attenuation coefficient. µ depends on the type and density of the absorbing material and on the energy of the incident photons. µ is often normalized by the material density which gives the mass attenuation coefficient µ/ρ. Six basic types of interactions can occur in the 0-25 MeV energy range produced by clinical linear accelerators: • Rayleigh scattering (or coherent scattering) • Compton effect (or incoherent scattering) • Photoelectric effect • Pair production • Triplet production • Nuclear photodisintegration Rayleigh, or coherent, scattering is elastic and therefore no energy is transferred to the medium. Nuclear disintegration is important only for high photon energy (> 10 MeV). The photoelectric effect (τ ), Compton effect (σincoherent ) and pair production (κ) occur with the greatest probability in the 0-25 MeV energy range. The relative importance of these three interactions is depicted in figure 1.4[5].  7  Chapter 1. Introduction 100  Z of absorber  80  Photoelectric effect dominant  Pair production dominant  60 40  Compton effect dominant  20 0 0.01  0.1  1 10 Photon energy (MeV)  100  Figure 1.4: Relative importance of the three major types of photon interactions. Photoelectric effect The photoelectric effect is a phenomenon in which a photon interacts with an atom and ejects one of the bound electrons. A diagram of the photoelectric process is shown in figure 1.5. The energy transferred (Etr ) to the electron is given by: Etr = hν − BE  (1.2)  where hν is the energy of the incident photon and BE is the binding energy of the shell from which the electron is ejected. The atom is left in an excited state and emits characteristic radiation (illustrated in figure 1.6 (a)) and Auger electrons (illustrated in figure 1.6 (b)) as it returns to the ground state. In general the mass attenuation coefficient for photoelectric effect is proportional to Z 3 /(hν)3 where Z is the atomic number of the material and hν is the energy of the incident photon. The probability of ejecting a bound electron is maximum when the photon has just enough energy to knock the electron out of the shell, therefore the plot of the mass attenuation coefficient vs energy shows sharp discontinuities when hν equals the binding energy of a particular shell.  8  Chapter 1. Introduction  Figure 1.5: Photoelectric effect: (a) Incident photon hν interacts with a bound electron. (b) The electron is ejected from the atom with energy Etr = hν − BE where BE is the binding energy of the electron. In the case shown BE = EK where EK is the binding energy of the K shell.  9  Chapter 1. Introduction  Figure 1.6: (a) The hole left in the shell after photoelectric effect is filled and characteristic radiation is emitted. In this case the photon energy is hν = EK − EL where EK and EL are the energies of the K and L shell respectively. (b) The hole in the shell is filled and the extra energy of the excited atom is carried away by an Auger electron. Compton scattering In Compton interaction a photon interacts with a loosely bound or free electron. The electron absorbs some of the photon energy while the photon is scattered with a reduced energy as shown in figure 1.7. The energy transferred to the electron is given by: Etr = hν − hν  (1.3)  where hν is the energy of the incident photon and hν is the energy of the scattered photon.  10  Chapter 1. Introduction  Figure 1.7: Compton effect: (a) Incident photon (hν) interacts with a loosely bound electron. (b) The electron is ejected and the photon is scattered with a reduced energy hν . Pair Production Pair production occurs when a photon interacts with the electromagnetic field of an atomic nucleus to create an electron (e−) and positron (e+) pair. The threshold energy for pair production to occur is 2me c2 = 1.022 M eV . For energies above this threshold the mass attenuation coefficient κ/ρ increases rapidly with hν and is proportional to Z. The effect is referred to as triplet production when the incident photon interacts with the field of an orbital electron, as shown in figure 1.8 (b). The threshold energy for triplet production is 4me c2 .  11  Chapter 1. Introduction  Figure 1.8: (a) Pair production and (b) triplet production.  1.5.2  Kerma and Absorbed Dose  The transfer of energy from a photon beam to a medium takes place in two stages. In the first step photons interacts with an atom and set electrons in motion as described in the previous section. In the second step these electrons deposit energy to the medium through excitation and ionization. The initial transfer of energy to a point in the medium is known as KERMA or Kinetic Energy Released in the Medium, and is defined as K=  dEtr dm  (1.4)  where dEtr is the kinetic energy transferred from photons to electrons per unit mass dm. The unit of kerma is joule per kilogram (J/kg) or Gray, where 1 Gy = 1 J/kg  (1.5)  In the second step energy is transferred from the electrons to the atoms in the  12  Chapter 1. Introduction surrounding medium, resulting in absorbed dose which is defined as D=  dEab dm  (1.6)  where dEab is the energy imparted by the ionizing radiation to a mass dm of matter. Since the electrons travel in the medium and deposit energy along their tracks, this absorption of energy does not take place at the same location as the transfer of energy described by kerma. The relationship between kerma and absorbed dose is illustrated in figure 1.9. The kerma decreases continually due to the attenuation of the beam. The absorbed dose first increases since electronic equilibrium (i.e. when the number of electrons entering a region of interest is equal to the number of electrons leaving this region) has not yet been achieved and the dose is primarily deposited downstream of where the interaction occurs. This region is known as the build-up region. At a depth equal to the mean interaction distance of the photon, the electronic equilibrium is reached. After this point both the dose and kerma decrease but the absorbed dose is always above the kerma curve. This is because the absorbed dose after the peak is due to the kerma further upstream.  Relative energy per unit mass  Dose  Buildup region  KERMA  Charged particle equilibrium  Depth in medium  Figure 1.9: Relationship between KERMA and dose.  13  Chapter 1. Introduction  1.6 1.6.1  Dose Calculation Algorithms Single Pencil Beam Convolution Algorithm  The single pencil beam algorithm is the dose calculation method used by the commercial treatment planning system (Eclipse) at the Vancouver Cancer Center. Each photon beam is first divided into a finite number of beamlets or pencil beams (e.g. 2.5 mm × 5 mm, see figure 1.10(a)). The pencil beam is projected onto a water phantom (along the beam axis, z) and dose is deposited in and around the point of interaction due to photon scatter and electron transport (figure 1.10(b)). In this pencil beam model, the resulting dose in water is modeled with a symmetric function referred to as the pencil beam kernel (PBK, figure 1.10(c)). The total dose contribution to a point in the phantom is obtained by convolving the photon fluence with the depth dependent pencil beam kernel (figure 1.11): D(x, y, z) =  (f + zref )2 (f + z)2  +∞ −∞  +∞ −∞  F (x , y )Pint (x , y , z)K(x − x , y − y , z)dx dy(1.7)  where • f is the Source-to-Surface Distance (SSD) • z is the depth of dose calculation • zref is the reference depth • F (x , y ) is the photon fluence • Pint (x , y , z) is the primary beam off-axis intensity profile which accounts for the presence of the flattening filter • K(x − x , y − y , z) is the depth dependent PBK  14  Chapter 1. Introduction  (a)  Kernel Value  10  10  1  −2  −5  10 −30 (b)  −15 0 15 Position (mm)  30  (c) t  Figure 1.10: (a) The beam is divided into 5 mm × 2.5 mm beamlets or pencil beams. (b) The pencil beam is projected onto a water phantom and dose is deposited in and around the point of interaction. (c) The dose deposited by the pencil beam is modeled with a depth dependent pencil beam kernel K(x, y, z) (here shown for depth z = 10 cm).  15  Chapter 1. Introduction  Multiple pencil beams  Photon beam  PBK convolution  Dose profile  (a)  (b)  Figure 1.11: The pencil beam model of dose deposition. (a) With multiple pencil beams the total dose is the sum of all pencil beam kernels (PBK). (b) In the limit as the number of pencil beams approaches infinity the calculation becomes a convolution of the incident fluence by the PBK. It has been demonstrated that PBK can be derived from measured beam data[6, 7]. It has been shown that higher resolution dosimeters (e.g. film, diodes) are necessary to generate more accurate dose kernels and that sharper dose kernels improve dose calculation accuracy[8–10]. It was also demonstrated that further improvements to the dose calculation accuracy can be achieved by iteratively modifying the shape of the PBK[11]. The main advantage on the pencil beam convolution algorithm is that it is fast and accurate for most clinical situations. The main disadvantage of this algorithm is that the kernel assumes that the patient is water equivalent but the patient is obviously more complex as it has air cavities (e.g. lungs) and bones, which will affect the dose distribution. The pencil beam convolution algorithm can not model the effects introduced by these inhomogeneities. For this reason the algorithm first calculates the dose to water and then applies a correction factor to the regions affected by the inhomogeneity.  16  Chapter 1. Introduction  1.6.2  Inhomogeneity Corrections  For the pencil beam dose calculation algorithm described in the previous section, the patient is considered equivalent to water. Correction factors must be calculated to take into account the inhomogeneities in the patient (such as lungs, bones). Two common inhomogeneity correction methods will be described in this section. Tissue-Air Ratio Method The tissue-air ratio (TAR) method is a simple technique used to correct for inhomogeneity[12]. The TAR concept is illustrated in figure 1.12 and is defined by the following equation: T AR(d, A, E) =  Dwater (d, SAD, A, E) Dair (SAD, A, E)  (1.8)  where • Dwater is the dose in water and Dair is the dose in air, as illustrated in figure 1.12 • d is the depth in water • SAD is the source-axis distance • E is the energy of the beam • A is the field size projected at calculation point  17  Chapter 1. Introduction  Figure 1.12: Illustration of the definition of tissue-air ratio. When an inhomogeneity is introduced in a water phantom (as shown in figure 1.13) the following correction factor applies to the dose at point P : CF =  T AR(def f , A) T AR(d, A)  (1.9)  where • d is the actual depth of P from the surface • def f is the effective (or water equivalent) depth obtained by scaling the depth by the inhomogeneity density: d = d1 + ρρw2 d2 + d3 • A is the field size projected at point P This correction method does not take into account the position of the inhomogeneity relative to point P and the lateral extent of the inhomogeneity is not considered. Points adjacent to an inhomogeneity (e.g. point Q in figure 1.13) are not considered. 18  Chapter 1. Introduction  Figure 1.13: Photon beam incident on a water phantom (density ρw ) containing an inhomogeneity (density ρ2 ). Modified Batho Method Batho[13], with corrections by Sontag[14], have proposed a method in which the ratio of the tissue-air ratios is raised to a power. Referring again to figure 1.13, the correction factor at point P is given by: CF =  T AR(d2 + d3 , A)(ρ3 −ρ2 ) T AR(d3 , A)(1−ρ2 )  (1.10)  where • ρ3 is the density in which point P lies (ρ3 = ρw in figure 1.13) • ρ2 is the density of the overlying material • A is the field size projected at point P With this method the position of the dose calculation point relative to the tissue inhomogeneity is considered. The lateral extent of the inhomogeneity and points adjacent to an inhomogeneity (e.g. point Q in figure 1.13) are not considered.  19  Chapter 1. Introduction  1.6.3  Monte Carlo Simulations  Monte Carlo is a stochastic method used to simulate fundamental interaction of particles with matter based on well known laws of nature. In medical physics Monte Carlo simulations are used to simulate radiation beams from a medical linear accelerator and to simulate dose deposited in media (e.g. tissue or water equivalent phantom). Each photon and its secondary particles are tracked as they interact with the medium, and dose is recorded for each voxel. The type of interaction is selected randomly but weighted by a probability distribution which refers to the different cross sections for photons and electrons interactions which occurs in the patient/phantom. Millions of photons histories are scored to ultimately reveal the dose deposited in the medium. Monte Carlo simulations are often considered as the “gold standard” for dose calculation accuracy since patient anatomy (including inhomogeneities) and the geometry of the linear accelerator are inherently modeled with this method. The current limitation of the Monte Carlo method is the calculation time needed to calculate the large number of histories required to reduce the statistical uncertainties to an acceptable level.  1.7  Radiation Delivery Techniques  Treatment planning is generally performed in a commercial 3D treatment planning system (TPS). CT images are imported in the TPS where the oncologist contours the target and critical structures. The treatment dose, number of fractions given and dose constraints to the target and critical structures are specified by the oncologist. Dose is calculated to the patient with a dose calculation such as described in section 1.6. Generally, the goal is to generate a uniform dose to the tumour while minimizing the dose to the surrounding healthy tissues. Several techniques can be used to achieve this goal ranging from simple combination of multiple rectangular beams to delivery of complex intensity modulated radiation beams. These techniques are described in the following sections.  20  Chapter 1. Introduction  1.7.1  Multiple Fields  A plot of the dose as a function of the depth for a single 6 MV photon beam (as a percent of maximum dose) is shown in figure 1.14 (a). At a depth of 1.5 cm the maximum dose is achieved and is followed by a dose decrease. This depth is dependent on the energy of the beam: higher energy beams are more penetrating and the location of maximum dose will be deeper in the tissue. Since the dose decreases with depth it is difficult to obtain a uniform dose to a tumour with a single beam. As shown in figure 1.15 the linac is mounted on a gantry that rotates around the patient. To achieve a uniform dose in a target volume a combination of beams with different gantry angles and appropriate energies can be used. It is possible to choose different energies for each gantry angle depending on the patient geometry.  Relative Dose (%)  100 80 60 40 20 0  0  5  10 Depth (cm)  15  20  (a)  Figure 1.14: (a) A percent depth dose curve for a 6 MV photon beam. The maximum dose deposited is at a depth of 1.5 cm.  21  Chapter 1. Introduction  Figure 1.15: The linac rotates around the isocenter allowing delivery from different gantry angles.  1.7.2  Field Shaping  As mentioned in section 1.4 the photon beam is defined by two pairs of secondary jaws located in the treatment head. Field sizes defined by the jaws are limited to rectangular shapes (up to 40 cm x 40 cm), as shown in figure 1.16 (a). One technique used to improve the conformity of the beam to the different tumour shapes is the use of custom made metal blocks that match the shape of the tumour, as shown in figure 1.16 (b). Because the projection of the tumour is different for different gantry angles, a different set of blocks needs to be built for each gantry angle. This process is cumbersome as it is specific to each patient. Field shaping to the tumour can also be achieved with a multileaf collimator (MLC) as shown in figure 1.16. An MLC consists of a series of tungsten alloy leaves that move parallel to each other in and out of the field. Each leaf is controlled by its own motor allowing the leaves to move independently and conform to different tumour shapes. A more detailed discussion of MLC characteristics is included in  22  Chapter 1. Introduction chapter 2.  Figure 1.16: (a) Two sets of independently moving jaws are used to create a rectangular field. A field shape conforming more closely to the planning target volume (PTV) may be obtained with (b) custom made blocks or (c) a multileaf collimator.  1.7.3  Forward Planning  Treatment plans are usually generated with the “forward planning” approach. First the beam configuration is specified by the user and the treatment planning system calculates the resulting dose distribution. This dose distribution is compared to the desired dose prescribed by the radiation oncologist. If the desired dose distribution is not met, the beam directions, weights (i.e. the dose contribution of a beam to a point) and shapes are manually adjusted, and the resulting dose distribution is recalculated. This process is repeated until the dose distribution is accepted by the radiation oncologist. A typical dose distribution for a prostate patient planned with the forward technique is shown in figure 1.17.  23  Chapter 1. Introduction  Figure 1.17: Typical dose distribution for a prostate patient using the forward planning technique. Two pairs of opposing conformal beams were used.  1.7.4  Intensity Modulated Radiation Therapy  The goal in Intensity Modulated Radiation Therapy (IMRT) is to generate a high uniform dose in the target while reducing the dose as much as possible to critical structures and other healthy tissues. This is achieved by modulating the fluence across a plane perpendicular to the beam axis. In the strictest sense wedges and compensators can be used to modulate fluence. Wedges are often made of brass and designed with different angles (e.g. 15o , 30o , 60o ). The photon beam is attenuated preferentially in the thicker end of the wedge. For example wedges can be used to compensate for missing tissues on wedge-shaped patient surface (e.g. breast) as illustrated in figure 1.18. For more irregular surfaces custom-made compensators can be used to modulate the beam fluence. They are similar to wedges in that the photon beam attenuation depends on the thickness of the compensator. However, they are labor-intensive and the therapist has to enter the treatment room between each field which prolongs the treatment time. IMRT is typically associated with more complex fluences as generated with a 24  Chapter 1. Introduction  (a)  (b)  Figure 1.18: (a) Open beam dose distribution for a wedge shaped surface. (b) Dose distribution for the same surface when a wedge is added to modulate the fluence. Note that the isodoses are more flat and that the dose across the structure is more uniform with the wedge.  25  Chapter 1. Introduction multileaf collimator. A multileaf collimator (MLC) can be used to modulate the fluence by summing the contribution of MLC defined apertures. An example of fluence modulation using an MLC is shown in figure 1.19. In practice, the forward planning technique can be applied to IMRT and works well for simple target shapes without numerous surrounding critical structures. However due to the large number of parameters introduced (i.e. leaf positions and weights), sophisticated optimization techniques are usually used to generate IMRT plans. An example of such an IMRT plan is shown in figure 1.20. By modulating the fluence of each beam a highly conformal dose to the target can be achieved. Since IMRT optimization is the focus of this thesis a detailed description, including planning and optimization methods is provided in chapter 2.  (a) Aperture 1  (b) Aperture 2  (c) Aperture 3  (d) Fluence 1  (e) Fluence 1+2  (f) Fluence 1+2+3  Figure 1.19: (a)-(c) Three MLC apertures delivered sequentially. (d)-(f) The corresponding fluence builds up with each aperture resulting in a two-dimensionally varying fluence  26  Chapter 1. Introduction  Figure 1.20: Resulting dose distribution for five intensity modulated beams.  1.7.5  Adaptive Radiation Therapy  Intensity modulated radiation therapy allows higher dose gradients and tighter margins than what is possible with conventional radiotherapy techniques. The patient is imaged before treatment and a treatment plan based on this “fixed” image is generated. The resulting treatment is delivered to the patient in multiple fractions. However, the patient anatomy such as tumour shape, weight loss, change in rectal and bladder content have been found to change significantly during the course of the treatment[15, 16]. Image guided strategies can be employed to minimize the impact of interfraction changes. Before treatment the patient is imaged and can be repositioned to minimize errors. This strategy is adequate if the patient anatomy does not change significantly during the course of the treatment. To overcome the impact of interfraction changes in the patient anatomy a new form of radiation therapy called Adaptive Radiation Therapy (ART) has recently emerged[17, 18]. The ART process can be summarized as follows (also illustrated in figure 1.21): 1. Acquire high-quality treatment verification images prior to treatment delivery, 27  Chapter 1. Introduction e.g. cone-beam CT 2. Register and contour CT datasets quickly and reliably using registration methods[19, 20] 3. Based on patient’s anatomy deformation the original treatment plan is adapted and delivered to the patient. If all of these steps are performed on-line, i.e. while the patient is in the treatment room, it is important that all these steps be performed quickly to minimize time the patient has to spend on the couch.  (a)  (b)  (c)  Figure 1.21: A simple example to illustrate the adaptive radiation therapy process. (a) The patient is imaged before treatment and an MLC shape is conformed to the beam’s eye view of the PTV. (b) Image during treatment shows that the PTV has expanded and that the MLC does not cover the whole PTV. (b) The MLC shape is adapted based on the new image.  1.8  Dose Measurement  1.8.1  Absolute Dosimeters  An absolute dosimeter refers to a dosimeter for which the measured quantity can be related to dose with well understood physics principles. Different types of absolute dosimeters are available including calorimeters, chemical dosimeters and ionization chambers. Ion chambers are used in this thesis for point dose measurements and will be discussed in more details. 28  Chapter 1. Introduction Ion Chambers Ionization chambers are routinely used in clinics for point dose verification. It is made of a conductive outer wall surrounding an air cavity which has a central collecting electrode, as illustrated in figure 1.22. An electrometer is used to measure the charge collected in the chamber Q which can be related to the absorbed dose in air: Dair =  Q Wair ( ) mair e  (1.11)  where • mair is the air mass in the cavity • (Wair /e) = 33.97eV /ionpair is the energy required to produce an ion pair in air per unit charge. Based on Bragg-Gray cavity theory the dose to air Dair can be converted to dose to medium, which is usually water. For more details about the cavity theory the reader is referred to standard textbooks[5, 21]. Ionization chambers can also be used as a relative dosimeter by measuring the chamber response in a calibrated radiation field.  Figure 1.22: Cross section of a Farmer type ion chamber.  29  Chapter 1. Introduction  1.8.2  Relative Dosimeters  In the case of relative dosimeters a reference dose measurement must be performed to relate the measured quantity to dose. Radiographic films are used in this thesis. Other relative dosimeters include radiochromic film, thermoluminescent dosimeters, gel dosimeters and silicon diodes detectors. Radiographic Film Radiographic film is the most common relative dosimeter used to verify 2D dose distributions. It has a high degree of spatial resolution which is only limited by the resolution of the scanner of digitizer used. Radiographic film consist of a clear polyester base that is coated on one or both sides with a radiosensitive emulsion. The emulsion consists of microscopic grains of silver bromide (AgBr) embedded in a gelatin layer. When an x-ray photon is incident on the radiographic film, the absorption of ionizing radiation causes the following chemical reactions: γ + Br− ⇒ Br + e− e− + Ag + ⇒ Ag  (1.12) (1.13)  A latent image is formed by the accumulation of elemental silver. This latent image is revealed during development of the film. Once the film has been exposed to radiation and developed it is usually scanned with an optical scanner or a densitometer to measure the transmission of light, or optical density, through the film. In order to establish the relationship between optical density and dose, a calibration curve is required. A calibration curve is obtained by measuring the optical density for a number of known doses. Several factors such as the film batch and the processing conditions can vary from day to day. For this reason a calibration curve is generated for each set of measurements. For clinical use it is important to choose the appropriate film that will have a linear response for the desired dose range. A typical sensitometric curve is shown in figure 1.23. Note that at low relative exposures the film shows very small changes in dose response, this is called the ”toe” of the curve. At high relative exposure  30  Chapter 1. Introduction the film begins to saturate. There is a range, specific to each film type, where the film response is linear. For example Kodak EDR2 films (which are used for IMRT verification in this thesis) have a dose-responsive range between 25 and 400 cGy and does not saturate until 700 cGy. Kodak EDR2 films are therefore useful to verify IMRT plans for which the doses are usually between 150 and 250 cGy. For lower doses (e.g. single field measurements) Kodak XV films would be more appropriate since the linear range is between 5 and 50 cGy. 6 Shoulder  Optical Density  5 4 Linear  3 2 1 0 0 10  Toe 1  2  10 10 Exposure (arb. units)  3  10  Figure 1.23: A typical sensitometric curve for radiographic film.  1.9  2D Dose Distribution Comparison  In order to evaluate the delivery accuracy of a treatment plan it is verified through a quality assurance procedure. Several tools are available to compare measured dose distributions with the planned dose distribution and will be described briefly here.  1.9.1  Qualitative Analysis  A simple way to visually assess the agreement between calculated and measured dose distributions is to plot orthogonal profiles at various location in the dose distribution. With this technique, geometric and dosimetric shifts can be easily located. A qualitative assessment can be done using this method, but the pass/fail outcome is highly subjective. 31  Chapter 1. Introduction  1.9.2  Dose Difference and Distance to Agreement  Van Dyk et al.[22] subdivide the dose distribution comparisons into regions of high and low dose gradients, each with different acceptance criterion. In low gradient regions, the doses are compared directly by displaying a dose-difference distribution. Regions where the calculated dose distribution disagrees with the measured dose distribution can be identified on the dose-difference distribution. In high-dose gradient region (for example at the field edge), a small spatial error can result in a large dose difference. In these regions, poor dose-difference agreement is not a good indicator of the overall agreement between measured and calculated distribution. The concept of distance-toagreement (DTA) is therefore introduced to determine the acceptability of the plan. The DTA is the distance between a measured data point and the nearest point in the calculated dose distribution that exhibits the same dose. The dose-difference and DTA evaluations complement each other when comparing dose distributions.  1.9.3  The Gamma Factor  The gamma (γ) factor analysis is a quantitative technique commonly used to compare two dose distributions [23–25]. The γ factor analysis uses a pass/fail criteria combining both the dose-difference and DTA. This analysis requires the user to set an acceptability criteria for the dose difference and DTA. The dose difference criteria is referred to as ∆DM and the DTA criteria is referred to as ∆dM . Van Dyk et al. suggest an acceptability criteria of a ∆DM = 3% dose-difference and ∆dM = 3mm DTA. In this work a tighter criteria of 2%/2 mm was used. The γ factor analysis can be applied to any n-dimensional dose distributions.  Γ(re , rr ) =  r2 (re , rr ) δ 2 (re , rr ) + 2 ∆d2M ∆DM  γ(rr ) = min{Γ(re , rr )}∀re  (1.14)  (1.15)  where • r is the distance between the calculated (rr ) and the measured (re ) points 32  Chapter 1. Introduction  • ∆dM is the DTA acceptability criteria  • δ(rm , rc ) is the dose difference between the measured data point and the calculated data point  • ∆DM is the dose-difference acceptability criteria  1.10  Thesis Objectives  Intensity Modulated Radiation Therapy (IMRT) is recognized as a powerful tool to increase target coverage while sparing surrounding critical structures. The conventional approach to inverse planning for intensity-modulated radiation therapy is divided into a two-step process. First, fluence maps from prespecified gantry angles are divided into finite size pencil beams (beamlets). The beamlet weights are updated iteratively under the constraints of a cost function until an optimal dose distribution is obtained[26, 27]. The next step is to derive the MLC aperture shapes required to generate the optimal fluence maps using a leaf sequencing algorithm[28–30]. The main limitation of this method is that the optimization step does not take into account delivery constraints imposed by the MLC. Therefore the deliverable fluence maps differ from the optimized fluence maps due to physical and mechanical constraints of the MLC. It may also produce a leaf sequence that is generally inefficient and requires a large number of apertures and number of MU. Inefficient leaf sequences may compromise the accuracy of the delivered dose due to approximations applied that attempt to take into account MLC characteristics[31]. As compared to 3D conformal radiation therapy, IMRT also results in a considerable increase in the plan complexity. Because IMRT techniques use some form of photon attenuation to modulate the beam, they require a substantial increase in monitor units (MU), or beam-on time, with respect to conventional treatment techniques to deliver equivalent target doses. As a result there is an increase of the whole-body dose to the patient due to leakage and scattering of photons through the collimation and treatment head of the linear accelerator. 33  Chapter 1. Introduction Various investigators[32–35], and most recently Hall[36], have expressed concern that the increase in whole body scatter with IMRT will lead to a greater probability of cancer induction. Several techniques have been proposed to simplify IMRT plans. For the fluence based approach this can be achieved by smoothing intensity maps or improved leaf sequencing algorithms[37–39]. An alternative approach to fluence based optimization is to optimize directly the leaf positions and weights of the segmented fields[40–42]. This approach is gaining popularity and is referred to as Direct Aperture Optimization (DAO). One of the advantages is that it eliminates the leaf sequencing step. MLC constraints are included in the optimization ensuring that the plan is always deliverable. It also allows the user to control the complexity of the optimized plan. For example, it has been shown that DAO results in a significant decrease in the number of MU and apertures[40, 43] required for delivery without sacrificing the quality of the dose distribution. Recently, a new method of delivering IMRT was proposed in which the entire MLC is rotated between each segment field[30]. It was shown that including collimator rotation with leaf sequencing has several advantages over conventional techniques including higher fluence spatial resolution, less interleaf systematic error and more flexibility in the generation of aperture shapes. In this thesis an extension of DAO where the MLC is rotated between each aperture is proposed. This approach is referred to as Rotating Aperture Optimization (RAO). The remainder of this thesis is organized as follows. First the fluence based and direct aperture optimization approaches are described in more details in chapter 2. The rotating aperture optimization technique is described in chapter 3. This chapter also includes a discussion of the delivery characteristics associated with collimator rotation. In chapter 4 a series of experiments are performed to investigate the dependence of the RAO on various parameters such as the cooling schedule, the number of apertures per beam, the minimum aperture size and the collimator rotation range. To evaluate the RAO technique, treatment plans were generated for ten recurring nasopharynx cancer patients with varying levels of complexity. Comparison plans were generated with the fluence based IMRT approach and with the standard fixed collimator DAO technique. The results of this study, including an analysis of dose volume histograms (DVH), dose distributions and MU efficiency, are presented in 34  Chapter 1. Introduction chapter 5. The accuracy of treatment delivery with RAO is also verified. As part of this thesis a collaboration with two PhD students was initiated. The DAO algorithm developed in this thesis (employing a non-rotating collimator) is used in two different contexts. The first project involves Monte Carlo calculated beamlet dose distribution matrices which are input to the DAO algorithm and compared to standard pencil beam convolution matrices. For the second project DAO is used for on-line adaptive radiation therapy applications. These two DAO applications are discussed in Chapter 6.  35  Chapter 2 Intensity Modulated Radiation Therapy The goal of intensity modulated radiation therapy (IMRT) is to generate highly conformal dose to the tumour while reducing the dose as much as possible to surrounding critical structures and healthy tissue. These highly conformal dose distributions are achieved by modulating the photon fluence across a plane perpendicular to the beam axis. It has been shown that IMRT represents a significant improvement over three dimensional conformal radiation therapy in terms of target coverage and critical structure sparing for many tumour sites[44–47]. The IMRT treatment planning process is generally more complex than the conventional forward treatment planning described in chapter 1. The process begins with the patient undergoing a treatment simulation involving a CT scan, and if necessary an MRI and/or PET scan in the treatment position. The three dimensional CT scan is then transferred to the treatment planning system where the radiation oncologist contours the target(s) and surrounding critical structures (e.g. spinal cord, optic nerves, etc). The radiation oncologist also specifies the desired (or prescribed) dose to these structures. The gantry angles and energy of each beam also need to be specified at that point. Most IMRT treatment plans are generated in an inverse planning process where optimization techniques are used. As mentioned in the previous chapter, IMRT is generally associated with the multileaf collimator (MLC). In this chapter IMRT delivery with an MLC will first be described. The inverse treatment planning process and different optimization techniques will be discussed in more detail in the following sections.  36  Chapter 2. Intensity Modulated Radiation Therapy  2.1  IMRT Delivery with a Multileaf Collimator  As mentioned previously, IMRT is often synonymous with the multileaf collimator. The design of the MLC in each linear accelerator differs from one manufacturer to another. This has an impact on IMRT delivery and therefore it is essential to understand the characteristics of a particular MLC to implement MLC based IMRT. In this thesis Varian linacs are used with two types of MLC: Varian Millennium 80 and Millennium 120. The characteristics for the Millennium MLCs are discussed below. The MLC leaves are made of 6 cm thick tungsten alloy and are designed to block more than 95% of incoming photons[48]. The Millennium 80, shown in figure 2.1(a), is made of two banks of 40 leaves and each leaf has a width of 1 cm at isocenter. The Millennium 120, shown in figure 2.1(b), is made of two banks of 60 leaves. The 40 central leaves have a 5 mm leaf width at isocenter and the outer 20 leaves have a 1 cm leaf width at isocenter. The maximum leaf speed is 3.0 cm/sec at the isocenter and the distance between the most protruding leaf and the most retracted leaf from the same bank is limited to 15.0 cm.  1 cm  leaf                     1 cm      width     5      mm  leaf    width   leaf     width                         1 cm   leaf  width (a)  (b)  Figure 2.1: Beam’s eye view of (a) the Varian Millennium 80 MLC and (b) the Varian Millennium 120 MLC.  37  Chapter 2. Intensity Modulated Radiation Therapy Radiation beams are divergent in both x (parallel to the leaf motion) and y (perpendicular to the leaf motion) direction. For Millennium MLCs the leaves travel linearly in a plane perpendicular to the central axis of the beam. However, due to the divergence of the beam radiation transmission through the leaf end varies as a function of leaf position. To minimize this effect each leaf has a rounded leaf end design such that the leaf end transmission is approximately the same independent of leaf position. The rounded end corresponds to a radius of 80 mm. The cross sectional view of the leaves is shown in figure 2.2 (a). The rounded end significantly reduces the leaf thickness at the tip of the leaf, causing a large radiation leakage between two opposing leaves when they are in closed position. To reduce this leakage the closed leaves are moved under the jaws whenever possible. To reduce the leakage through the small gap between two adjacent leaves (interleaf leakage) the side of adjacent MLC leaves are coupled so that the side of one leaf has a 0.4 mm extended portion called the“tongue” and the adjacent leaf has a corresponding indented portion called the“groove” as shown in figure 2.2 (b).  groove →  (a)  ← tongue  (b)  Figure 2.2: (a) Cross sectional view of a multileaf collimator and (b) end on diagram of the tongue-and-groove design of the Varian Millennium MLCs.  38  Chapter 2. Intensity Modulated Radiation Therapy MLC based IMRT delivery can be divided in two types: static, or step-and-shoot, delivery (SMLC) and dynamic delivery (DMLC). In the SMLC mode, illustrated in figure 2.3(a), the delivery sequence consists of a number of steps in which the leaves move to their designated positions while the beam is off. The next step is to shoot where the leaves remain stationary while the beam is on. In the dynamic delivery mode (DMLC), the radiation beam is on for the entire delivery while the MLC leaves moves continuously across the field (shown in figure 2.3(b)). The leaves move at a variable speed to obtain the desired fluence distribution.  Figure 2.3: (a) In the static mode the leaves move to their position while the beam is off. (b) In dynamic mode each leaf pair moves continuously from one side of the beam to the other while the beam is on.  2.2  Inverse Treatment Planning  Although intensity modulation can be achieved through forward planning, the large number of parameters (i.e. the leaf positions and aperture weights) renders the task difficult, especially for complex cases where several PTVs with different prescribed doses are located near several sensitive structures. Inverse treatment planning was developed to take advantage of the intensity modulation flexibility offered by the MLC. With inverse treatment planning the desired dose distribution or the biological 39  Chapter 2. Intensity Modulated Radiation Therapy end points are used to specify the treatment goals. Based on these treatment goals an algorithm is used to optimize the plan parameters. In order to optimize the dose distributions, an objective function or cost function is defined. The objective function basically reduces the treatment plan to one single number, which is related to the plan quality. It relates the current dose distribution to a desirable dose distribution. The two most common types of objective function are physical dose objectives, which are based on the physical dose distribution, and biological objectives, which are based on a model of the biological effect of the dose distribution.  2.2.1  Dose Volume Histogram  Cumulative dose-volume histograms (DVHs) are commonly used to evaluate the quality of a 3D dose distribution. A DVH for a specified tissue structure reports the fraction of volume which receives at least a particular dose. Ideally 100% of the tumour (or target volume) would receive a prescribed dose specified by the radiation oncologist. Similarly 100% of a critical structure (for example spinal cord, optic nerves) would ideally receive a dose of 0 Gy. An example of poor DVHs is shown as a dashed line in figure 2.4. In this case, the critical structure receives a high dose and the tumour a non-uniform dose. For the DVHs shown with a solid line, the dose to the critical structure is reduced and the dose to the tumour is more uniform (steep DVH curve). Therefore the solid line DVHs are considered superior to the dashed line DVHs.  40  Chapter 2. Intensity Modulated Radiation Therapy Poor  Superior  100  Volume (%)  80 60 ←Target 40 20 Critical→ structure 0  0  20  40 Dose (Gy)  60  80  Figure 2.4: Dose Volume Histograms for two treatment plans. The dashed line shows a poor plan with non-uniform tumour coverage and high dose to the critical structure. The solid line represents a superior plan with better tumour uniformity and reduced dose to the critical structure.  2.2.2  Physical Dose Objective  A physical dose objective is a criterion that can be expressed in terms of measurable and well-defined physical quantities such as dose and volume. The most simple form for the physical objective is a least square equation: f=  1 N  N  (Di − D)2  (2.1)  i=1  where • Di is the total dose to a point or voxel i • D is the desired or prescribed dose • N the number of points or voxels in the structure. The objective is normalized by N to avoid having big structures dominate the optimization. Strict fulfillment of a constraint is often too restrictive, especially when a critical structure is immediately adjacent to the target volume. Therefore a weighting factor,  41  Chapter 2. Intensity Modulated Radiation Therapy also called a penalty factor, can be added to determine the relative importance of a particular constraint. Generally a minimum and maximum dose (Dmin and Dmax ) with priorities (wtmin and wtmax ) are specified for the target volume. The form of the objective function for these constraints is defined as ft  wtmin Nt (Di − Dmin )2 H(Dmin − Di ) = Nt i=1 +  (2.2)  wtmax Nt (Di − Dmax )2 H(Di − Dmax ) Nt i=1  where H(x) is the Heavyside function and is given by   1 H(x) =  0  x≥0 x<0  Volume (%)  100  Dmin→  50  0  0  20  40 60 Dose (Gy)  ← Dmax  80  100  Figure 2.5: Ideally 100% of a target would receive the prescribed dose. Generally a minimum and maximum dose constraint are specified for each target. Although a strict maximum dose constraint can be used on critical structures, it is also useful to specify a volume value. This is because some specific clinical outcomes are known to result from some dose-volume endpoints. For example, in patients with lung cancer radiation-induced pneumonitis has been associated with the volume of 42  Chapter 2. Intensity Modulated Radiation Therapy the lung receiving a dose of 20 Gy, or V20 [49–51]. Dose-volume constraints can also be added on the critical structures. Figure 2.6 illustrates how the dose-volume constraints work, as suggested by Bortfeld et al.[52]. The dose volume constraint is specified as: the volume receiving a dose greater than D1 should be less than V1 . To implement this constraint in the objective function, another dose D2 is defined so that V (D2 ) = V1 in the actual DVH. The objective function is then given by fS =  wS N · (Di − D1 )2 · H(Di − D1 ) · H(D2 − Di ) NS i=1  (2.3)  so that only the voxels receiving a dose between D1 and D2 are penalized. An unlimited number of dose-volume constraints can be specified.  Volume  100 Dose−Volume Constraint  V2 50 V1  0  0  D1  D2 40 Dose  80  Figure 2.6: Illustration of how dose-volume constraints are taken into account in the objective function. The dose-volume constraint is specified as the volume receiving a dose greater than D1 should be less than V1 . Only the points receiving a dose between D1 and D2 are penalized by the objective function.  2.2.3  Biological Objective  Most optimization systems use dose and/or dose-volume based objective functions but it can be argued that they do not adequately represents the nonlinear response of tumours or normal critical structures to dose. Therefore it has been suggested that IMRT optimization should be based on the biological effects of dose to tissues[53–55]. 43  Chapter 2. Intensity Modulated Radiation Therapy The most common biological models calculate tumour control probability (TCP) and normal tissue complication probability (NTCP). The goal is to maximize TCP and minimize NTCP. TCP depends on tumour type, stage, size, etc. NTCP depends on organ type and clinical complication endpoint. The concept of equivalent uniform dose (EUD) is also commonly used for biological modeling[56]. The equivalent uniform dose for tumours is defined as the biologically equivalent dose that, if given uniformly, will lead to the same cell kill in the tumour volume as the actual non-uniform dose distribution. For normal tissues it represents the uniform dose which leads to the same probability of injury as the corresponding inhomogeneous dose distribution. Objective functions based on the EUD have been proposed by other investigators[57]. The EUD formulation is based on the power law dependence of the response of a complex biological system to dose and is given by the following equation for both tumours and normal tissues: EU D =  1 N  Dia  1 a  (2.4)  i  where • N is the number of voxels in the structure of interest. • Di is the dose to the ith voxel. • a is the tumor or normal tissue specific parameter. This factor can be determined empirically by fitting published dose-volume data (e.g. Emami et al.[4]). It is usually negative for tumors and positive for critical structures. For organs with parallel behavior (i.e. mean dose is more important) a is generally small and close to 1. For organs with serial behavior (i.e. maximum dose is more important) a is large.  2.3  IMRT Optimization Techniques  Inverse treatment planning can be divided into three categories: 1. Fluence based optimization  44  Chapter 2. Intensity Modulated Radiation Therapy 2. Aperture based optimization 3. Direct aperture optimization The difference between these three types of optimization are the treatment parameters to be optimized (optimization variables). In fluence based optimization each beam is divided into beamlets and the weights of these beamlet are optimized. After optimization each fluence map is converted into a set of deliverable MLC shapes. This step is generally called ”leaf sequencing”. In the aperture based optimization approach MLC apertures are predefined by the user based on the patient anatomy, and the weight of each aperture is optimized. In direct aperture optimization the MLC leaf positions and aperture weights are directly optimized. Leaf sequencing is not required as the optimized plan is ready to deliver. The following sections describe in more detail the three types of optimization algorithms.  2.3.1  Fluence Based Optimization  Fluence based optimization (FBO) is divided into a two-step process. First, fluence maps from pre-specified gantry angles are divided into finite size pencil beams (see figure 2.7). The width of these beamlets is generally equal to the MLC leaf width. The length of each beamlet is parallel to the direction of leaf travel and is typically predetermined by the treatment planning system. Zhang et al. [58] have studied the relationship between pencil beam step size and plan quality using beamlet stepsizes of 1, 2, 5 and 10 mm. They observed a continuous improvement in target dose conformity and surrounding critical structure sparing with smaller step-size. However there are some computational limitations in clinical practice and a 2.5 mm beamlet length is generally used.  45  Chapter 2. Intensity Modulated Radiation Therapy  Figure 2.7: Fluence maps are divided into beamlets of width w and length l. Note that the beamlet width w is limited by the leaf width. The beamlet weights are updated iteratively under the constraints of a cost function until an optimal dose distribution is obtained. In gradient based algorithm the direction of optimization is determined by a vector derived from the objective function The most simple implementation of gradient based optimization is the steepest descent method which iteratively updates the beamlet weights according to: wjk+1 = wjk − λ ·  ∂f ∂wj  (2.5)  where • f is the cost function • wj are the weights of each individual beamlet • λ is the step size Other gradient based algorithms include Newton’s method[27] and the conjugate gradient technique[26]. Other algorithms used for fluence based optimization include simulated annealing[59],genetic algorithms[60] and linear programming[61, 62].  46  Chapter 2. Intensity Modulated Radiation Therapy After the optimization a set of optimal fluence maps (one per beam direction or gantry angle) has been determined. The next step is to derive the MLC aperture shapes required to generate the optimal fluence maps using a leaf sequencing algorithm. After leaf sequencing a set of deliverable MLC shapes that matches the optimal fluence map as closely as possible are obtained. Several leaf sequencing algorithms have been proposed with both dynamic (DMLC)[63, 64] delivery and step-and-shoot (SMLC)[28, 29, 41] delivery.  2.3.2  Aperture Based Optimization  Aperture based optimization can be considered as an intermediate step between forward and inverse planning. In this approach MLC apertures are predefined by the user based on the patient anatomy and optimized[65, 66]. For each beam the apertures are generated based on the beam’s eye view (BEV) of the target and the critical structures. In the prostate example shown in figure 2.8 the first aperture is chosen to conform to the target’s BEV plus a margin. A second aperture blocking the rectum is defined, i.e. an aperture that conforms to the BEV of the PTV minus the rectum. A third aperture blocking the bladder and a fourth aperture blocking the bladder and rectum are also defined. Once the apertures are defined for each beam the computer optimizes the weight of each aperture. This approach has been reported to produce relatively simple plans with low number of apertures and monitor units. In addition, the resulting fluence patterns are more intuitive as they reflect the target and critical structures BEVs. It is generally effective for simple treatment sites, like breast and prostate.  47  Chapter 2. Intensity Modulated Radiation Therapy  (a)  (b)  (c)  (d)  Figure 2.8: In aperture based optimization the apertures for each beam are defined to conform to the PTV and/or cover the critical structures. Example apertures for a prostate patient are shown for one beam. (a) The MLC conforms to the PTV. The MLC conforms to the PTV and (b) covers the rectum, (c) covers the bladder and (d) covers the rectum and the bladder.  2.3.3  Direct Aperture Optimization  Direct Aperture Optimization (DAO) has been proposed recently as an alternative approach to conventional fluence based optimization[40–42, 67]. With this approach the MLC shapes and weights are optimized directly, therefore there is no need for a separate leaf sequencing step. The approach proposed by Shepard et al. uses a simulated annealing algorithm[68] to minimize a cost function. Simulated annealing  48  Chapter 2. Intensity Modulated Radiation Therapy is a stochastic optimization technique which mimics a thermalized system reaching its ground state as the temperature slowly decreases. It generally requires more iterations than gradient based algorithm but has the capability to escape local minima. Genetic algorithms were also proposed to optimize directly the MLC shapes and positions[42]. With DAO the user defines the beam geometry and energy. The user also needs to specify the number of apertures per beam that will be used to generate the stepand-shoot leaf sequence. All apertures are initialized to outline the target beam’s eye view plus a margin (typically 5 mm). During the optimization the algorithm cycles randomly through the variables to be optimized: leaf positions for each aperture and aperture weights. At the beginning of the optimization the random changes applied to the variables are relatively large and decrease as the optimization get closer to a solution.  2.4  Direct Aperture Optimization versus Fluence Based Optimization  2.4.1  Plan degradation  A flowchart of the conventional fluence based optimization approach versus the direct aperture optimization technique is shown in figure 2.9. One of the advantages of DAO is that it eliminates the leaf sequencing step. Although it has been shown that conventional fluence based IMRT represents a significant improvement over 3DCRT in terms of target coverage and critical organ sparing for many tumour sites[44–47, 69], there are some limitations associated with the conventional fluence based IMRT technique. First, fluence maps are optimized prior to leaf sequencing, which may cause a degradation of the plan once physical and mechanical constraints of the MLC are introduced[70]. Although the leaves are 6 cm thick, there is some radiation transmitted through the MLC. For a 6 MV beam the average transmission is 1.6%. The plan degradation resulting from leaf sequencing is illustrated in figure 2.10. Note the degradation of the PTV coverage and the increase in the maximum dose for all critical structures for the final dose distribution. With DAO, MLC characteristics, such as MLC transmission and interdigitation constraints, are included in the optimization ensuring that the plan is always deliverable. 49  Chapter 2. Intensity Modulated Radiation Therapy  Figure 2.9: Flowchart of the conventional fluence based optimization approach versus the direct aperture optimization technique.  100 PTV →  Volume (%)  80 60  ← Right Temp. Lobe  40  ← Left Temp. Lobe  20 0  ← Brainstem 0  20  40  60 80 Dose (%)  100  120  Figure 2.10: Comparison of the optimal (solid line) and actual (dashed line) DVHs for the conventional fluence based optimization approach.  50  Chapter 2. Intensity Modulated Radiation Therapy  2.4.2  Efficiency  With DAO, the user has control over the complexity of the optimized plan. The most obvious parameter is the number of apertures per beam direction. A small number of apertures per beam can create a complex intensity pattern. The number of intensity levels (N ) that can be created by n apertures per beam (with distinct weights) is given by the relation:  N = 2n − 1  (2.6)  For example it is possible to generate 7 intensity levels with only three apertures per beam direction (figure 2.11). The number of intensity levels increase quickly with the number of apertures per beam. For example 63 intensity levels can be created using six apertures per beam with different weights. Therefore complex intensity patterns can be created with a small number of apertures. Jiang et al. have shown that for most cases, only modest improvements in the objective function and the corresponding DVHs are seen beyond 5-9 apertures per beam angle. This indicates that step-and-shoot IMRT plans can be simplified without sacrificing the quality of the dose distributions. Any other MLC constraint, such as a minimum aperture size and minimum number of MU, can be included. This helps avoid inefficient fields. With the fluence based approach these constraints are only taken after optimization, and any additional constraints result in the degradation of the actual fluence maps compared to the optimal fluence maps.  51  Chapter 2. Intensity Modulated Radiation Therapy  (a)  (b)  (c)  4 3 2 1 0  (d)  Figure 2.11: (a)-(c) Three aperture shapes and (d) corresponding fluence map (7 intensity levels) for one beam direction. IMRT allows for better tumour conformity while sparing the surrounding healthy tissues. However, IMRT also results in a considerable increase in the plan complexity. Since MLC constraints are not taken into account during the dose optimization for the fluence based approach, the leaf sequence is generally inefficient, requiring a large number of segments and MU. Several techniques have been proposed to simplify IMRT plans. For the fluence based approach this can be achieved by smoothing intensity maps or improved leaf sequencing algorithms[38, 39, 71]. A side effect of simplifying IMRT plans with DAO is the reduction in the number of MU[40, 67]. Improved MU efficiency has the benefit of less total body scatter and less MLC transmission. Other investigators have argued that the high number of MU associated with IMRT results in an increased probability of long term complications, including secondary malignancies, when compared to conventional three dimensional conformal radiotherapy techniques (3DCRT)[32–36].  52  Chapter 2. Intensity Modulated Radiation Therapy  2.4.3  Tongue-and-Groove Effect  The tongue-and-groove design of the MLC leaves (as shown in figure 2.2) gives rise to a phenomenon called the tongue-and-groove effect which is illustrated in figure 2.12. The tongue-and-groove effect is an artifact which appears as a line of underdosage parallel to the leaf motion. This effect is particularly noticeable in the situation illustrated in figure 2.12 where an open field is delivered with two adjacent segments. In this case the sum of the two segments does not equal the open field fluence: a line of underdosage is observed. This occurs because this small region is always covered by either the tongue or the groove, i.e. it never receives a completely open fluence. This effect was measured on a Varian CL21EX linac with the Millennium 120 MLC and results are shown in figure 2.13. It is shown that tongue-and-groove underdosage can be up to 22% for a 6MV beam and Varian MLC which is in agreement with results obtained by Huq et al.[72] (a)  (b)  (c)  Fluence  Fluence  Fluence  Tongue and groove artifact ↓  Figure 2.12: The tongue-and-groove effect is illustrated by considering an open field delivered with the two adjacent segments shown in (a) and (b). The sum of both profiles should ideally result in a constant fluence across both leaves, but the sum of (a) and (b) results in an underdosage located at the tongue-and-groove interface (shown in (c)).  53  Chapter 2. Intensity Modulated Radiation Therapy  Calculated  Measured 100  100  80  80  60  60  40  40  20  20  (a)  (b)  Calculated  Measured  Dose (cGy)  80 60 40 20 0  −100  0 Position (mm)  100  (c)  Figure 2.13: Tongue-and-groove effect as measured on a Varian CL21EX with a Millennium 120 MLC. (a) Open field fluence delivered in one segment, and (b) the same open field fluence is delivered in two segments. In this case the sum of the two segments does not equal the open field fluence in (a): a line of underdosage due to the tongue-and-groove shape of the leaf is observed. Inefficient leaf sequences may compromise the accuracy of the delivered dose due to approximations applied that attempt to account for MLC characteristics such as the rounded leaf end, the tongue-and-groove MLC shape and the leaf transmission[31]. Inefficient MLC delivery also results in longer treatment times, which could increase geometric errors due to patient motion. However, DAO can be more sensitive to tongue-and-groove effects than FBO since restrictions are generally not applied to individual leaf positions[73, 74]. Some constraints can be added in DAO to control 54  Chapter 2. Intensity Modulated Radiation Therapy protrusions. For example Bedford et al.[75] proposed a specialized DAO algorithm with constrained segments shapes. This algorithm was designed to provide a minimum of simple and regular apertures. In this case the TPS can reliably calculate the dose distribution and measurements should then agree more closely with the predicted dose. However, this limits considerably the search space. Xia et al. have also shown that interdigitation constraint (shown in figure 2.14) is a necessary condition to eliminate the tongue-and-groove effect. This constraint can be included in DAO but it also limits considerably the search space as the algorithm will reject all changes that violate the interdigitation constraint. An example of a DAO plan optimized with and without interdigitation is shown in figure 2.15. The plan with the interdigitation constraint is clearly inferior with higher dose to critical structure and slight underdosage to the target. With the fluence based approach it was shown that the interdigitation constraint provides a means to reduce the tongue-and-groove effect at the expense of approximately 25% more segments[29].  Figure 2.14: (a) MLC aperture which does not violate the interdigitation constraint. (b) In this case the central leaf on the left bank is extended past the adjacent leaves of the opposite bank: the interdigitation constraint is violated.  55  Chapter 2. Intensity Modulated Radiation Therapy 100  Volume (%)  80 PTV →  60 ← OAR  40 20 0  0  20  40 Dose (Gy)  60  Figure 2.15: Comparison of the DVHs for a treatment plan optimized with (dashed line) and without (solid line) interdigitation constraint.  2.4.4  Applications  Recently DAO has been gaining popularity for breast IMRT. Breast cancer patients do not usually require highly modulated beams and the need for fluence modulation comes from the variation in separation thickness around the breast. It was shown that for this site there is improvements in both target dose uniformity and critical organ sparing when compared to fluence based IMRT[76–78]. Another application of DAO is “jaws-only” IMRT[79, 80]. Although this offers less flexibility than MLC IMRT, jaws-only IMRT has been proposed as an interesting option for clinics where MLCs are not available. In this case the jaws are used to defined rectangular apertures. It was shown that plans can be created that are comparable to MLC IMRT and better than 3D-CRT for a simple treatment site like prostate.  56  Chapter 3 Rotating Aperture Optimization In the last chapter, the advantages of direct aperture optimization versus the conventional fluence based approach were discussed. However, direct aperture optimization (DAO) can be more sensitive to tongue-and-groove effects than fluence based optimization (FBO) since restrictions are generally not applied to individual leaf positions. Recently, a new method of delivering IMRT was proposed in which the entire MLC is rotated during treatment[30]. Figure 3.1 (a) shows the conventional delivery method described in chapter 2 where the MLC leaves moves in and out of the field and the collimator remains fixed. In figure 3.1 (b) an extra degree of freedom is added to MLC delivery by rotating the collimator between each aperture. It was shown that including collimator rotation with leaf sequencing has several advantages including less interleaf systematic error, higher fluence spatial resolution and more flexibility in the generation of aperture shapes. These characteristics are discussed in more detail in this chapter. Next an extension of DAO in which the collimator is rotated between each aperture is introduced thereby combining the advantages of both techniques.  57  Chapter 3. Rotating Aperture Optimization  (a)  (b)  Figure 3.1: (a) Conventional IMRT delivery: the collimator remains fixed (e.g. 0o ). (c) IMRT delivery with collimator rotation.  3.1 3.1.1  Advantages of Collimator Rotation Interleaf Effects  For conventional IMRT delivery, the leaf movement in and out of the radiation field occurs at a fixed collimator angle. Because of this restriction, the adjacent leaf edges for a given field are always at the same location relative to the patient. Therefore interleaf radiation leakage and tongue-and-groove artifacts will cumulate and be enhanced under these interfaces. These effects can be minimized by introducing collimator rotation (figure 3.2). Since the leaf edges are at different location for each aperture, the maximum interleaf error is only a fraction of the error associated with conventional IMRT delivery.  58  Chapter 3. Rotating Aperture Optimization  Aperture 1  Aperture 2  Figure 3.2: When the collimator is rotated between each aperture the location of the leaf edges changes thereby reducing interleaf effects.  3.1.2  Spatial Resolution  Treatment planning for IMRT begins by dividing each beam’s-eye-view of the target into small beamlets, as shown in figure 3.3. The length of each beamlet is defined parallel to the direction of leaf motion and is typically set to 2.5 mm. The beamlet width is oriented perpendicular to the leaf motion and is limited by the physical width of each MLC leaf (typical 5 mm or 10 mm). It has been shown that beamlet length affects plan quality and that smaller beamlets improve target conformality and reduce dose to adjacent critical structures[58]. However, the width of each beamlet is limited by the physical construction of the MLC and larger leaf widths reduce the plan quality. Different approaches have been suggested to improve the spatial resolution limitation associated with larger leaf widths. One approach requires the use of two orthogonal fields [81–83]. Another approach involves the superposition of two fields having a relative isocenter shift offset by half a leaf width[84]. Finally another approach is the use of a specialized six-bank multi-leaf collimation system[85, 86]. 59  Chapter 3. Rotating Aperture Optimization The improvement in spatial resolution with collimator rotation can be visualized by illustrating the minimum beamlet size delivered by the linac. Conventional IMRT delivery is illustrated in figure 3.3 (a). In this case the MLC leaves move in a single plane, in and out of the treatment field. Although the leaves can move in small increments (less than 1 mm) the width of the beamlet is limited by the leaf width (5 mm or 1 cm depending on the MLC model). With the rotational delivery, the direction of leaf motion changes for each collimator angle as seen in figure 3.3 (b). Therefore, the minimum beamlet size is not limited by the leaf width but is more closely approximated by a circle with a diameter equal to the minimum leaf displacement. Minimum beamlet size (a) Conventional delivery  Minimum beamlet size  (b) Rotational delivery  Figure 3.3: (a) With conventional delivery the spatial resolution is limited by the leaf width. (b) When the collimator is rotated between each aperture the spatial resolution is approximated by a circle with a diameter equal to the minimum leaf displacement.  3.2  Radiation Delivery with MLC rotation  The Varian CL21EX linac was used for all measurements performed in this thesis. Control of the rotating MLC aperture is performed using specialized software called the Dynamic Beam Delivery (DBD) toolbox. The DBD toolbox can control a variety of motions dynamically including collimator and gantry rotation, as well as couch 60  Chapter 3. Rotating Aperture Optimization and jaw motion. In this work the collimator rotation feature is used. The accuracy and reproducibility of the DBD toolbox has been validated during commissioning and quality assurance testing. It was shown that the DBD toolbox can accurately rotate the MLC to its intended collimator angle to within 0.5o . This result is within the limitations specified by the manufacturer. For more details on radiation delivery accuracy using the DBD toolbox to control the collimator rotation, the reader is referred to M. Schmuland’s thesis[87].  3.3  Rotating Aperture Optimization  The leaf positions and the aperture weights are optimized using a simulated annealing algorithm[68]. The beam arrangement, MLC specifications (such as the MLC leaf width) and dose constraints of the PTV and critical structures are specified by the user and are input to the algorithm. The user also have control over the complexity of the plan by specifying the number of apertures per beam to be used in the optimization. The RAO technique differs from other DAO techniques in that the MLC is rotated between each aperture. After the user specifies the number of apertures per beam, the collimator angles of each beam are initialized so that there is an equal angle between each aperture (range from 270o to 90o ). The leaf positions are set so that the MLC aperture conforms to the beam’s eye view of the target plus a margin. An example of an initial rotated leaf sequence is shown in figure 3.4. During the optimization the leaves cannot move outside this beam’s eye view. The aperture weights are initially set to the same value so that the mean dose to the PTV is equal to the prescribed dose. The first step is to calculate the dose and cost function for the initial rotated leaf sequences. This cost function is defined by the constraints placed on the target and surrounding healthy tissue structures. The algorithm then cycles through the variables that are to be optimized (i.e. the MLC leaf positions and aperture weights). The optimization begins with the random selection of either an MLC leaf or an aperture weight. Next, a random sized change is applied to that variable. The maximum change decreases according to the following schedule  W (nsucc ) =  W0 1  (1 + nsucc ) R 61  (3.1)  Chapter 3. Rotating Aperture Optimization where R defines the rate at which the change decreases and nsucc is the number of changes already accepted by the algorithm. If the selected variable is a leaf position then W0 is the initial maximum leaf step size. If the selected variable is an aperture weight then W0 is the initial maximum weight change. The selected change must not violate the mechanical and physical constraints of the MLC. Also, negative aperture weights are rejected. Constraints on the minimum aperture size and on the minimum number of monitor units (MU) for each aperture can also be added. This helps avoid inefficient segments. If the selected change violates a constraint, it is automatically rejected. If it meets all the constraints the cost function is calculated. If the change results in a lower cost, it means that the change corresponds to an improvement in the dose distribution and it is accepted. If the change results in an increase of the cost function, the change is not automatically rejected. It may still be accepted with a probability given by  P = exp  −∆f T  (3.2)  where ∆f is the change in the cost function and T is a ”temperature” parameter. The probability of retaining a solution with a higher cost function decreases as the temperature of the system decreases. The temperature is reduced according to the following cooling schedule[88]  T (nsucc ) =  T0 1  (1 + nsucc ) RT  (3.3)  where T0 is the initial temperature, RT defines the rate of cooling and nsucc is the number of successful changes. The RAO algorithm uses a dose-volume objective which is known to contain multiple local minima ([89, 90]) (illustrated in figure 3.5). At the beginning of the optimization the objective values “jumps” between local minima because the “temperature” is high and the maximum step allowed is large. As the “temperature” cools down and the step size get smaller there is a decreased probability of escaping a local minima. If the cooling schedule decreases very slowly it will have a better chance to find the global minimum but the optimization time will be 62  Chapter 3. Rotating Aperture Optimization long which is not clinically practical. Alternatively if the temperature decreases too fast the optimization time will be very short but there will be an increase probability of being “stuck” in a local minimum. Therefore an appropriate cooling schedule will find a balance between optimization time and avoidance of local minima. The schedule also needs to be flexible enough for use on any kind of patient.  (a) collimator=3300  (b) collimator=300  (c) collimator=900  (d) collimator=3300  (e) collimator=300  (f) collimator=900  Figure 3.4: (a), (b), (c) The initial rotated apertures outline the target beam’s eye view. (d), (e), (f) Final optimized rotated leaf sequence. One beam is shown.  63  Chapter 3. Rotating Aperture Optimization 25 Local minima Objective Value  20 15 10 5 0  Global minimum 0  20 40 60 80 Optimization variable  100  Figure 3.5: The concept of local minima is illustrated with an objective function.  3.4  Dose Calculation  Two versions of the RAO algorithm have been implemented. These two versions are different in the way the dose is calculated during the optimization. The first version uses pre-calculated pencil beam dose distributions (PBDD). These pencil beam doses are stored in a large matrix and provide a link between the pencil beam location and the dose to the patient. The second version uses a single pencil beam dose calculation and does not require a permanent storage PBDD matrix. These two algorithms are discussed in more details in the following sections.  3.4.1  Pre-calculated Pencil Beam Dose Distribution  The first version of the RAO algorithm uses the Varian Cadplan Helios inverse treatment planning system (version 6.27) for dose calculation and plan evaluation. A plan is first created in Cadplan where the beam angles and energies are selected by the user. The TPS distributes dose calculation points quasi-randomly in each structure of interest (e.g. PTV, spinal cord) according to a density specified by the user [91]. Each beam is segmented into 2.5 mm x 2.5 mm beamlets. For each structure included in the optimization, Cadplan calculates the dose contribution of each beamlet to every point within a pre-specified radius (typically 1 cm), as shown in figure 3.6. Dose 64  Chapter 3. Rotating Aperture Optimization contribution to points outside this radius is considered to be negligible. For a given field the total dose to a point i is given by the following equation: N  Di =  aij xj  (3.4)  j=1  where aij is the dose contribution to a point i from a beamlet j having a weight xj . This aij matrix is also referred to as the pencil beam dose distribution (PBDD). The PBDD are then exported to Matlab (Natick, MA) where the RAO optimization occurs. After the optimization the optimized MLC apertures are converted into fluence maps, which are reimported into Cadplan for a final dose calculation with full scatter conditions.  Figure 3.6: A pre-calculated pencil beam dose distribution (PBDD) establish the relationship between a fluence pixel (or beamlet) and the dose to the patient. In conventional IMRT delivery (no MLC rotation) the beamlet size is limited by the width of the MLC leaf (typically 5 or 10 mm). For a 5 mm leaf width MLC with a minimum step size along the direction of leaf motion of 2.5 mm, the minimum beamlet size would be 5 mm × 2.5 mm. Since the MLC angle is the same for each segment, any beamlet is either completely covered or completely uncovered by a leaf (see figure 3.7a). By moving one leaf by one position, only one beamlet will be affected. With RAO the MLC is rotated between each segment and the beamlet size is not 65  Chapter 3. Rotating Aperture Optimization limited by the leaf width. Since the entire MLC is rotated between each segment, one leaf could partially block one or more beamlets. To account for this effect we use a smaller beamlet size of 2.5 mm × 2.5 mm (minimum beamlet size allowed by Cadplan) and we introduce sub-sampling. In figure 3.7 (b), the MLC is rotated with respect to the fluence grid and each beamlet intensity is scaled by the area uncovered by the MLC. The rotated positions and sub-sampling of MLC leaves with respect to the beamlets of the fluence map are precalculated for all possible leaf positions at each collimator angle. This calculation is performed only once. The precalculated rotated positions are loaded into memory each time the RAO algorithm is started.  Figure 3.7: (a) For an MLC aperture shape without rotation, the minimum beamlet size is 5 mm x 2.5 mm. Each beamlet is either completely covered (beamlet intensity equal to zero) or completely uncovered (beamlet intensity equal to one). (b) When the entire MLC is rotated the sub-sampled beamlet dimensions are 2.5 mm x 2.5 mm. In this situation, one leaf could partially block one or more beamlets. The corresponding beamlet intensity is scaled by the area uncovered by the MLC. 66  Chapter 3. Rotating Aperture Optimization The advantage of pre-calculating the PBDD is that the optimization algorithm is independent of the dose calculation method. In this thesis a pencil beam dose calculation is used, but a more accurate dose calculation, like Monte Carlo, could also be used. This will be discussed further in section chapter 6. There are some disadvantages associated with the PBDD approach. First, the truncated pencil beam kernel will neglect the residual scatter contributions to points located outside the truncation radius, possibly resulting in a dose calculation error (figure 3.8). Second the approximation with sub-sampling could result in inaccuracies in the dose distribution. 100  Volume (%)  80 60  Full Scatter Trunc. 1 cm Trunc. 2 cm  PTV→ 40 ← Spinal cord 20 0  ← Brainstem 0  20  40 Dose (Gy)  60  80  Figure 3.8: Dose volume histograms calculated with (1) full scatter conditions, (2) PBDD contribution within a 1 cm truncation radius, and (3) PBDD contribution within a 2 cm truncation radius.  3.4.2  Single Pencil Beam Dose Calculation  In order to overcome the disadvantages associated with the pre-calculated pencil beam dose distributions, a second version of the RAO algorithm has been developed in which the dose is calculated at each iteration. This version is interfaced with the Varian Eclipse treatment planning system (version 6.5) and was also implemented in Matlab (Natick, MA). Patient contours (representing various structures of interest such as PTV and spinal cord) are first generated in Eclipse and exported into Matlab using a standard DICOM RT data formatting protocol. Points are then uniformly distributed in each structure of interest that is to be included in the optimization. The typical dose resolution grid is set to 2.5 mm. For larger structures, the dose 67  Chapter 3. Rotating Aperture Optimization grid resolution can be reduced (i.e. fewer dose calculation points) to speed up the optimization. In this case a random point sampling is used [91]. The novel feature of our algorithm is in the dose calculation method. Other DAO algorithms typically precalculate the pencil beam dose distributions (PBDD) before the optimization (as described in section 3.4.1). With this approach one usually needs to truncate the PBDD dose calculation radius or use a poorer voxel resolution. For the RAO technique, a single pencil beam dose calculation algorithm [7] (described in section 1.6.1) with full scatter conditions is used therefore eliminating the pre-calculation step. Since the apertures of a leaf sequence (for a particular beam) have a different collimator angle, each aperture is treated separately for the dose calculation. Variable beamlet sizes are used to speed up the process. After optimizing the MLC apertures the final plan can be exported back to Eclipse where a final dose calculation is performed. This final dose calculation confirms that the dose calculated by the MATLAB dose calculation algorithm is accurate.  3.5  MLC Specifications  The characteristics of any type of MLC can be included in the RAO algorithm. Two types of MLC were studied in this thesis: a Varian Millennium 120 MLC with a 5 mm leaf width at isocenter for the central 40 leaves, and a Varian Millennium 80 MLC with a 1 cm leaf width at isocenter (detailed characteristics of each MLC are provided in section 2.1). An average MLC photon transmission through the closed MLC leaves of 1.6% was measured for a 6 MV beam and was accounted for in both models. The MLC leaves are also constrained to protrude a maximum of 14.5 cm into the open radiation field as defined by the secondary jaws. Additional constraints, such as interdigitation of opposing leaves, which is currently impossible for Siemens and Elekta MLCs, could also be included.  68  Chapter 4 Characterization of the Rotating Aperture Optimization Algorithm In the previous chapter the rotating aperture optimization (RAO) algorithm was introduced. With direct optimization of MLC leaf sequence, the user has control over several MLC parameters. In this chapter a series of tests were performed to evaluate how the final optimized plan depends on these parameters. Three test patients with different levels of complexity were selected: a complex c-shaped target, a prostate patient and a nasopharynx patient with multiple planning target volumes (PTV). The cooling schedule, the number of apertures per beam, the minimum aperture size and the choice of collimator angles were considered.  4.1 4.1.1  Patients Description C-Shape Target  The RAO algorithm was first tested with a 25.6 × 25.6 × 28cm3 water equivalent AVID phantom (MDX Medical, Vancouver,BC) which was scanned with a 3 mm slice thickness. A hypothetical c-shape target surrounding a centrally located sensitive structure (spinal cord like) was contoured on the phantom CT scan. Seven equispaced 6 MV beams were placed around the phantom. The beam configuration and the structures are shown in figure 4.1. The prescribed dose to the c-shaped target is 60 Gy in 30 fractions and dose constraints are applied to the centrally located organ at risk (OAR) and to surrounding “healthy tissue”. These constraints are summarized in table 4.1.  69  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  (a)  (b)  Figure 4.1: Hypothetical c-shaped target with a centrally located aorgan at risk (OAR) (a) axial view and beam configuration and (b) 3D view.  Table 4.1: Summary of the treatment goals for the hypothetical c-shaped target. Case C-Shaped target  Structure Target Centrally located OAR  4.1.2  Goals V57 Gy > 95% V66 Gy < 5% Reduce max. dose  Prostate Patient  One patient with prostate cancer was selected. The CT was acquired with the patient in the supine position (slice thickness of 3 mm). The relevant critical structures (bladder, rectum and femoral heads) were contoured in accordance with ICRU (International Commission on Radiation Units and Measurements) report 50[92]. The prescription dose to the planning target volume (PTV) is 70 Gy delivered in 28 fractions. The dose-volume constraints for the PTV and critical structures were established according to literature data on acute and late toxicity after 3D conformal radiotherapy[93, 94] and are summarized in table 4.2. Five 6 MV photon beams were used with gantry angles 0◦ − 75◦ − 135◦ − 225◦ − 285◦ . The PTV, critical structures and beam arrangement are shown in figure 4.2.  70  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm Table 4.2: Summary of the treatment goals for the prostate patient. Case Structure Prostate patient PTV Bladder Rectum  Femoral heads  71  Goals V70 Gy > 98% V74.9 Gy < 2cc V40 Gy < 25% V20 Gy < 50% V70 Gy < 5% V40 Gy < 25% V20 Gy < 50% V40 Gy < 5%  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  (a)  (b)  (c)  Figure 4.2: Prostate patient: (a) axial view and beam arrangement, (b) coronal view and (c) sagittal view . Structures are numbered as follows: (1) PTV, (2) rectum, (3) bladder and (4) femoral heads.  72  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  4.1.3  Multiple PTV Nasopharynx Cancer  Treatment planning is particularly complex for this patient since there were 3 different planning target volumes (PTV) each having a different dose prescription. The PTVs are surrounded by numerous critical structures: optic nerves, chiasm, parotids, brainstem, spinal cord and brain. The planning goals are summarized in table 4.3. This patient also required bigger field sizes (greater than 15 × 15 cm2 ). Seven equispaced 6 MV beams were used. The PTVs, critical structures and beam arrangement are shown in figure 4.3. Table 4.3: Summary of the treatment goals for the multiple PTV nasopharynx patient. Case Multiple PTV Nasopharynx  Structure PTV1 PTV2 PTV3 Lt Parotid Rt Parotid Brainstem Spinal Cord Brain Chiasm Optic Nerves Eyes  73  Goals V70 Gy > 95% V80 Gy < 5% V63 Gy > 95% V75 Gy < 5% V56 Gy > 95% V70 Gy = 0% V20 Gy < 20% V25 Gy < 40% V54 Gy = 0% V45 Gy = 0% V60 Gy < 5cc V50 Gy = 0% V25 Gy = 0% V20 Gy = 0%  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  (a)  (b)  (c)  Figure 4.3: Multiple PTV nasopahrynx patient (a) axial view and beam configuration, (b) coronal view and (c) sagittal view.  4.2 4.2.1  Methods Consistency  The RAO algorithm uses a simulated annealing algorithm, which implies that the results of the optimization may vary depending on the random seed input at the  74  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm beginning of each optimization. It is therefore necessary to verify that an appropriate cooling schedule is used in order to give a certain consistency if the plan is re-optimized several times with the same optimization parameters. It would not be practical if the optimization would give a significantly better (or worse) answer when the same plan is optimized twice. The cooling schedule is defined by the step size (equation 3.1) and the “temperature” (equation 3.3). To test the consistency of the cooling schedule the three cases described in section 4.1 (c-shaped target, prostate patient and multi-PTV nasopharynx cancer patient) were tested. First the number of iterations need to be specified for the algorithm to reach convergence. For each case, the convergence was confirmed by comparing DVHs and cost with an optimized plan for which a large number of iterations (100000) was specified. The consistency test was performed as follows: for each case the optimization was repeated 100 times using a different random seed but keeping all optimization parameters constant. The optimization parameters include the cooling schedule, the dose-volume constraints, the beam configuration, the MLC type (1 cm or 5 mm leaf width) and the number of apertures per beam. For each case six rotated apertures per beam and a 5 mm leaf width MLC were specified at the beginning of the optimization. The cost and the number of MU were analyzed for consistency.  4.2.2  Number of Apertures per Beam  At the beginning of the optimization the user needs to specify the number of apertures per beam to be used in the optimization which controls the complexity of the resulting plan. A plan with a small number of apertures could be extremely simple to deliver, but would defeat the purpose of IMRT if the target is not covered properly or if the sparing of the critical structures is compromised. The extent to which the plan quality is affected by the number of apertures was considered in this section. Plans for the c-shaped target, the prostate patient and the multi-PTV nasopharynx cancer patient were created with a 5 mm leaf width MLC. For each patient, a series of optimizations with 2, 4, 6, 8 and 10 apertures per beam were performed. For each case the gantry angles and the optimization constraints were kept constant while the number of apertures was varied. Each optimization was terminated once the  75  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm algorithm reached convergence. The effects of the number of apertures per beam angle was analyzed based on their final cost values, DVHs and number of MU. The optimization time was also considered for each plan. The optimization time will be shorter for a 1 cm leaf width MLC than a 5 mm leaf width MLC since there are less optimization parameters. For example with the 5 mm width MLC the number of optimization parameters (N5mm ) for a 10 cm x 10 cm field is N = (20 leaves ∗ 2 banks + 1 aperture weight) ∗6 apertures per beam ∗ 7 beams = 1722  (4.1) (4.2)  For a 1 cm width MLC and the same field size the number of optimization parameters is reduced to N = (10 leaves ∗ 2 banks + 1 aperture weight) ∗6 apertures per beam ∗ 7 beams = 882  4.2.3  (4.3) (4.4)  Minimum Aperture Size  The direct aperture optimization approach provides control on the complexity of a treatment plan by allowing the user to specify the number of apertures per beam. It is also possible to specify other constraints in order to further simplify IMRT plans. For example specifying a minimum aperture size would result in bigger, more regular aperture shapes. The advantage of treatment plans with simple apertures is that the treatment planning system can calculate dose distributions more reliably. A test was therefore designed to determine how the quality of the dose distribution and MU efficiency are affected by the minimum aperture size. The minimum aperture size was defined as a fraction of the target beam’s eye view (BEV) as this corresponds to the maximum aperture size that would ever be required. This test was repeated for the prostate patient, the c-shape target and the multi-PTV nasopharynx cancer patient. For each case the gantry angles and the optimization constraints were kept constant while the minimum size of each aperture was varied from 0% (i.e. no constraint) to 100% of the BEV by increments of 10%. Each optimization was terminated once the algorithm reached convergence. The effects of the minimum size of each aperture was 76  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm analyzed based on their final cost values, DVHs and number of MU.  4.2.4  Collimator Angles  One of the advantages of the RAO algorithm is the increased flexibility in the generation of aperture shapes introduced with MLC rotation. The initial collimator angles for each beam are initialized so that there is an equal angle between each aperture and they remain fixed during the optimization (figure 4.4). To test this equispaced angle approach treatment plans with non-equispaced collimator angle were generated and compared to the equispaced collimator angle plan for the c-shape target, the prostate patient and the nasopharynx cancer patient. For each patient 50 different plans were generated by randomly selecting the collimator angle arrangement for each beam (i.e. a different collimator angles selection for each plan). The test was performed with six apertures per beam direction. It is assumed that if there is an optimal collimator angle arrangement (significantly better than the equispaced angle arrangement), a better solution will be found with this approach (a solution closer to the optimal solution). This is because although a treatment plan can be sensitive to the collimator angles chosen it is not as sensitive as the collimator angle precision. For example it is unlikely that a change of 1o or 2o will have a significant impact on the resulting treatment plan, therefore reducing the search space considerably.  Figure 4.4: At the beginning of the optimization the collimator angles are set so that there is an equal angle between each aperture.  77  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  4.3  Results  4.3.1  Consistency  First the number of iterations was determined for each test case with the procedure described in section 4.2.1. An example of the resulting cost as a function of the number of iterations for the c-shaped target is shown in figure 4.5 (a). It can be seen that the cost does not change significantly for more than 25000 iterations. The corresponding DVHs after 25000 and 100000 iterations are shown in figure 4.5. As seen for the cost function, there is no significant difference in the dose-volume histograms. Therefore the optimization was stopped after 25000 iterations for the c-shaped target consistency test. The number of iterations for the prostate patients and the multiPTV nasopharynx patient was determined using the same procedure.  500  100  400  80 Volume (%)  Cost value  100 000 iterations 25 000 iterations  300 200 100 0  Shell →  60  ← PTV  ← OAR  40 20  0  2  4 6 # iterations  8  10 4  x 10  (a)  0  0  20  40 Dose (Gy)  60  80  (b)  Figure 4.5: (a) The cost value versus the number of iterations. (b) Dose volume histograms after 25 000 and 100 000 iterations.  78  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm The resulting histograms of the consistency test are shown in figure 4.6. Since the range of cost values appears to be relatively large ( 100 to 200 for the prostate patient) it is important to look at the corresponding DVHs to evaluate the consistency of the treatment plans. The corresponding DVHs for the two extremes, that is the plan with the best (lowest) and worst (highest) cost values, are shown in figure 4.7. Only minor differences between the two extremes are observed for the three test cases. This indicates that the cooling schedule is consistent and that all plans with a final cost value between the two extrema do not exhibit any significant difference. The constraints used in the optimization are also shown in figure 4.7. The resulting number of MU for the 100 plans are shown in figure 4.8. The results are also consistent, with standard deviations of 12 MU or less. The cooling schedule is therefore satisfying in terms of consistency.  79  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  25 20 15 10 5 0  µ = 144.2 σ = 25.1  20  Nplans  Nplans  25  µ = 12.6 σ = 1.9  15 10 5  5  10  15 Final Cost  20  0 50  25  100  (a)  150 Final Cost  200  250  (b)  20  µ = 912.6 σ = 54.4  Nplans  15  10  5  0 700  800  900 1000 Final Cost  1100  (c)  Figure 4.6: Optimization was run 100 times for each patient. All patient plans were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the cost values are shown for (a) the c-shape target, (b) prostate patient and (d) the multi-PTV nasopharynx patient. The mean value (µ) and the standard deviation (σ) are also shown.  80  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  Best  Worst  Best  100  100 ← PTV Shell →  60 40  ← OAR  20 0  20  ← PTV  80 Volume (%)  Volume (%)  80  0  Worst  60 40  ← Bladder  20  40 Dose (Gy)  60  0  80  Rectum→ 0  20  (a)  40 60 Dose (Gy)  80  100  (b)  Best  Worst  100 PTV3 →  Volume (%)  80 60  ← Brain  40  ← PTV2  ← Lt. Parotid  20 0  ← PTV1  0  20  40 60 Dose (Gy)  80  100  (c)  Figure 4.7: Resulting DVHs for (a) the c-shaped target, (b) the prostate patient and (c) the multi-PTV nasopharynx patient showing the best and worst results of the consistency test. The optimization constraints are also shown for each structure.  81  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  20  25  µ = 738.0 σ = 12.1  20  Nplans  Nplans  15  10  5  0 700  µ = 533.2 σ = 9.9  15 10 5  720  740 760 Number of MU  0 500  780  (a)  520 540 Number of MU  560  (b)  30 µ = 581.2 σ = 9.1  25  Nplans  20 15 10 5 0  560  580 600 Number of MU  620  (c)  Figure 4.8: Optimization was run 100 times for each patient. All patient plans were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the number of MU are shown for (a) the c-shape target, (b) prostate patient and (c) the multi-PTV nasopharynx patient. The mean value (µ) and the standard deviation (σ) are also shown.  82  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  4.3.2  Number of Apertures per Beam  Each case was optimized with 2, 4, 6, 8 and 10 apertures per beam angle in order to determine how the plan quality and efficiency are affected by the number of apertures for plans including collimator rotation. The final normalized cost value as a function of the number of apertures per beam and the number of MU for the corresponding plans are shown in figure 4.9. As the number of apertures increases the degrees of freedom provided to the optimization increase. This results in a decrease in the cost value. However this decrease in the cost value reaches a plateau beyond which there is only a small benefit in increasing the number of apertures per beam. For the three cases presented in figure 4.9 this plateau starts around 6 apertures per beam angle. By increasing the number of apertures per beam there is also an increase in the complexity of the plan. There is therefore a tendency for the number of monitor units (MU) to increase, as shown in figure 4.9. For the prostate patient the plan with 6 apertures per beam is more efficient (50 MU) than the plan with 10 apertures per beam, but the cost function does not change significantly. In figure 4.10, 4.11 and 4.12 the resulting DVHs for the plans with 2, 6 and 10 apertures per beam are compared. In all three cases the PTV coverage is compromised (i.e. it does not meet the planning goals) for the plans with 2 apertures per beam angle. For example the volume of the c-shaped target receiving 57 Gy is equal to 86.6% and the treatment goal is V57 Gy = 95%. As for the cost value there is no clinically significant improvement between the plans with 6 and 10 apertures per beam. Since 6 apertures per beam angle was found to be the optimal value, this was used for the other tests performed in the following sections. Finally the optimization times are listed in table 4.4. As expected the optimization times are longer for the plans with larger number of optimization parameters. Firstly for higher number of apertures per beam the number of optimization parameters, and therefore the optimization time, increases. Secondly the choice of MLC also affects the optimization time: the Millennium 120 MLC includes more leaves, and therefore more optimization parameters, than the Millennium 80 MLC. Finally the optimization time is longer for the nasopharynx cancer patient. This is because there is three relatively large PTVs and the optimization also includes a big structure (the brain) that contains a large number of voxels.  83  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  1  800  1  0.6  550  0.4 0.2  2  4 6 8 Number of apertures  600 10  0  500  2  4 6 8 Number of apertures  Final cost  (a)  10  (b)  1  650  0.5  550  0  2  4 6 8 Number of apertures  MU  0  MU  700  Final cost  0.5  MU  Final cost  0.8  450 10  (c)  Figure 4.9: Final normalized cost for different number of apertures per beam for (a) the c-shape target, (b) the prostate patient and (c) the multiple PTV nasopharynx cancer patient. Results are shown for RAO with the Varian Millenium 120 (5mm leaf width for the central 40 leaves).  84  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  80  80 Volume (%)  100  Volume (%)  100  60 PTV→ 40 20 0 50  2 apertures 4 apertures 6 apertures  60 40 ← OAR 20  55  60 Dose (Gy)  65  0  70  0  10  20 30 Dose (Gy)  40  100  100  80  80 Volume (%)  Volume (%)  Figure 4.10: DVHs for the C-shaped target (left) and the OAR (right) for plans with 2, 4, 6, 8 and 10 apertures per beam angle.  60 PTV→ 40 20 0 65  2 apertures 6 apertures 10 apertures  60 40 ← Bladder  20  70 75 Dose (Gy)  80  0  0  20  ← Rectum  40 Dose (Gy)  60  80  Figure 4.11: DVHs for the planning target volume (left) and the rectum and bladder (right) for plans with 2, 4, 6, 8 and 10 apertures per beam angle.  85  100  100  80  80 Volume (%)  Volume (%)  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  60 40 20 0 50  2 apertures 6 apertures 10 apertures  60 40 20  60  70 Dose (Gy)  0  80  0  10  20 30 Dose (Gy)  40  Figure 4.12: DVHs for the three clinical target volume (left) and the left parotid (right) of the multi-PTV nasopharynx patient for plans with 2, 6 and 10 apertures per beam angle.  Table 4.4: The optimization times (minutes) for the plans with 2,4,6,8 and 10 apertures per beam. Results are shown for two types of MLC: the Millennium 80 (1 cm leaf width MLC) and the Millennium 120 (5 mm leaf width MLC). Number of apertures per beam 2 4 6 8 10  C shaped target 1 cm 5 mm MLC MLC 1.8 2.2 2.8 4.8 3.9 6.8 5.6 8.8 5.8 9.9  Prostate 1 cm 5 mm MLC MLC 1.4 2.1 2.7 3.9 3.5 6.4 5.2 6.8 6.8 10.0  86  Multiple PTV 1 cm 5 mm MLC MLC 7.6 8.7 12.4 15.7 16.1 20.8 18.2 22.9 20.8 27.0  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  4.3.3  Minimum Aperture Size  The extent to which an IMRT plan can be further simplified was studied by imposing an additional constraint on the minimum aperture size during the optimization. The cost function and the number of MU required for plans constrained to a minimum aperture size from 0% (i.e. no constraint) to 100% of the target beam’s eye view (BEV) are plotted in figure 4.13. For each case there is a plateau region for which the increase in the minimum aperture size have a negligible effect on the cost value. For the c-shaped target and the nasopharynx cancer patient, the plateau extends up to 40% of the target BEV. For the more simple prostate case this region covers up to 80% of the target BEV. For each case in figure 4.13, the plateau region for the cost value is associated with an initial slow decrease in the number of MU. As the minimum aperture size reaches the end of the cost plateau region the number of MU decreases faster. A better understanding of the relation between plan quality/efficiency can be shown by looking at the dose-volume histograms. The DVHs for the prostate patient and the plans with a minimum aperture size of 0%, 80%, 90% and 100% of the BEV are shown in figure 4.14. When comparing the plans with a minimum aperture area of 0% and 80% of the target BEV for this patient, the DVHs for all structures are indistinguishable but the number of MU decreases by 14% (65 MU). The 100% plan is clearly unacceptable as it is not meeting the treatment goals for the target (V70/Gy = 79%) and the rectum (V40 Gy = 29.7%). The optimized dose distribution for the plan with a minimum aperture size of 80% is shown in figure 4.17. With only 6 segments per beam angle, the 95% isodose encompasses the target, while sparing the rectum and the bladder. The DVH results for the c-shaped target are shown in figure 4.18. Contrary to the prostate patient, plan degradation begins for a minimum aperture size of 50%. The 40% plan is virtually identical to the unconstrained plan, but with a 15.3% (97 MU) reduction in the number of MU. The DVH results for the multiple PTV patient are shown in figure 4.19. Similar to the c-shaped target, plan degradation begins for a minimum aperture size of 50%. The 40% plan is virtually identical to the unconstrained plan, but with a 13.2% (65 MU) reduction in the number of MU.  87  0.5  475  0  400 0 50 100 Min. aperture size (% of target BEV)  1  800  0.5  600  0  0 20 40 60 Min. aperture size (% of target BEV)  400  (b)  1  600  0.5  450  0  0 20 40 60 Min. aperture size (% of target BEV)  MU  Final cost  (a)  MU  550  Final cost  1  MU  Final cost  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  300  (c)  Figure 4.13: The final cost and the number of MU for different aperture size. All other optimization parameters kept constant and 6 apertures per beam angle were used. Results are shown for (a) the prostate patient, (b) the c-shaped target and (c) the multi-PTV nasopharynx cancer patient.  88  100  100  80  80 Volume (%)  Volume (%)  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  60 PTV→ 40 20  60 ← Rectum  40 20  0 65  70 75 Dose (Gy)  0  80  100  100  80  80 Volume (%)  Volume (%)  0% 80% 90% 100%  60 40  ← L.Femur  Bladder → 0  20  40 Dose (Gy)  60  80  0% 80% 90% 100%  60 40  20  20  0  0  R. Femur→ 0  10  20 Dose (Gy)  30  40  0  10  20 Dose (Gy)  30  40  Figure 4.14: Prostate patient DVHs for 6 rotated aperture per beam and minimum aperture size equal to 0%, 80%, 90% and 100% of the target BEV.  89  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  Figure 4.15: Leaf sequence for the prostate patient with no constraints on the minimum aperture size set during the optimization.  Figure 4.16: Leaf sequence for the prostate patient with a minimum aperture size set to 80% of the target beam’s eye view.  90  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm 105 90  60 45  Dose (%)  75  30 15  100  100  80  80 Volume (%)  Volume (%)  Figure 4.17: Prostate dose distribution for 6 rotated apertures per beam and a minimum aperture size equal to 80% of the BEV. The PTV is outlined in white, the femoral heads are outlined with the solid black line and the rectum is outlined with the dashed black line. The dose is normalized to the prescribed dose (70 Gy).  60 PTV→ 40 20 0 50  0% 40% 50% 60%  60 40 ← OAR 20  55  60 Dose (Gy)  65  70  0  0  10  20 Dose (Gy)  30  40  Figure 4.18: C-shaped target DVHs for 6 rotated aperture per beam and minimum aperture size equal to 0%, 40%, 50% and 60% of the target BEV.  91  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  100  100 ← PTV1  80 Volume (%)  Volume (%)  80 60 PTV3 →  0% 40% 50% 60%  ← PTV2  40 20  60 ← Lt. Parotid  40 20  0 50  60 70 Dose (Gy)  80  0  0  10  20 30 Dose (Gy)  40  50  Figure 4.19: Multiple PTV patient DVHs for 6 rotated aperture per beam and minimum aperture size equal of 0%, 40%, 50% and 60% of the target BEV.  4.3.4  Collimator angles  The effect of the choice of collimator angles for each aperture is studied by comparing an equispaced and 50 different randomly distributed collimator angle arrangement. Histogram distributions of the cost values obtained with random collimator angles are shown in figure 4.20. It can be seen that these distributions are fairly similar to the results of the consistency test (for equispaced collimator angles arrangement) presented in section 4.3.1 and also shown in figure 4.20. For example, for the c-shaped target and the random collimator angles arrangement, the mean and the standard deviation of the cost value are 13.0 and 3.4 respectively compared to 12.6 and 1.9 for the equispaced collimator arrangements. A collimator angles arrangement giving significantly better results than the equispaced plans was not found for any of the cases presented. As discussed in the section 4.2.4 this indicates that the equispaced collimator angles arrangement is a choice that will fully take advantage of the flexibility associated with collimator rotation.  92  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm  Random 30  Equispaced  Random 30  µ=13.0 (12.6) σ=3.4 (1.9)  25  σ=26.1 (25.1)  20 Nplans  Nplans  µ=152.7 (144.2)  25  20 15  15  10  10  5  5  0  Equispaced  10  15 Final Cost  0  20  100  150 Final Cost  (a)  200  (b) Random 20  Equispaced µ=922.3 (912.6) σ=52.9 (54.4)  Nplans  15  10  5  0 800  850  900 950 Final Cost  1000  1050  (c)  Figure 4.20: Optimization was run 50 times for each patient with random nonequispaced collimator angles. All patient plans were optimized with 6 rotated apertures per beam and the Millenium 120 MLC (5 mm leaf width). Results for the cost values are shown for (a) the c-shape target, (b) the prostate patient and (c) the multi-PTV nasopharynx patient. The results of the consistency test (with equispaced collimator angles) are shown for comparison. The mean value (µ) and the standard deviation (σ) are also shown (in parentheses for the equispaced collimator angles).  4.4  Discussion  A series of tests were presented to characterize the rotating aperture optimization algorithm. Three different cases with varying level of complexity were used for each  93  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm test. The first element to be tested was the consistency of the cooling schedule. Because RAO uses a simulated annealing algorithm, changes applied during the optimization are chosen randomly. The choice of an appropriate cooling schedule is therefore critical to make sure that the optimization does not get trapped in a local minimum. Based on the three cases presented for the analysis the cooling schedule was found to be consistent in terms of the cost value, the number of MU and the dose volume histograms. This cooling schedule will therefore be used for the remainder of this thesis. Parameters defining a leaf sequence can be directly controlled by the user. The effect of the number of apertures per beam angle was tested by generating plans with 2, 4, 6, 8 and 10 apertures per beam. The results show that for more than 6 apertures per beam there is very little improvement in the cost value and therefore the quality of the dose distribution. Jiang et al. found similar results for a direct aperture optimization algorithm that does not include collimator rotation[43]. The complexity of an IMRT treatment plan was further reduced by adding a constraint on the minimum aperture size. For a simple prostate patient case, treatment plan with a minimum aperture of 80% of the target BEV was shown to be dosimetrically equivalent to a plan without any constraint. For the the two other cases (c-shape and nasopharynx cancer) a degradation in the dose distribution is observed at smaller aperture sizes. This is most likely due to the increased complexity associated with these cases. It is more complex to generate a treatment plan for the c-shaped target and the nasopharynx cancer patient because the dose constraints are more stringent and also because of the relative location of the critical structures with respect to the target. Complex cases generally require more complex fluence modulation and consequently more flexibility in aperture shaping. For all three cases it was found that an indirect benefit associated with specifying a minimum aperture size is a reduction in the number of monitor units necessary to deliver the IMRT plan (up to 15 %). Another way of simplifying the aperture shapes is to restrain the relative position difference between two adjacent leaves to prevent large protrusions of a leaf into an open beam. Bedford et al.[75] have proposed aperture shape constraints (a cubic function is used to smooth MLC shapes) which are designed to create simple and regular segments. Their method was shown to provide efficient and simple IMRT plans. 94  Chapter 4. Characterization of the Rotating Aperture Optimization Algorithm Finally, a test was designed to test the equispaced collimator angles arrangement. Wang et al. have shown that for standard fixed collimator IMRT an optimal collimator angle can be found that favors efficiency in IMRT[95]. It could then be argued that there would be an advantage to optimize the collimator angles. The optimization of leaf sequences with randomly chosen collimator angles did not result in a better cost value. This suggests that the equispaced collimator angles arrangement takes full advantage of the flexibility associated with collimator rotation and that there should be no significant benefit in including the collimator angles as optimization parameters.  4.5  Conclusion  In conclusion, some optimization parameters were found to affect RAO IMRT treatment plans. For each of these parameters a “threshold” value can generally be found for which there is an increased efficiency and/or a simplification of the treatment plan without compromising the quality of the resulting dose distribution. More efficient leaf sequences have the benefit of shorter treatment times and less total body scatter. Other investigators have argued that the high number of MU associated with IMRT results in an increased probability of long term complications, including secondary malignancies[32–36]. More simple and regular aperture shapes in the leaf sequences are also beneficial as they will be calculated more accurately by the treatment planning system.  95  Chapter 5 Rotating Aperture Optimization Evaluation This chapter describes a series of tests designed to evaluate the capabilities of RAO compared to other optimization techniques. First a study was designed to compare RAO with a commercial treatment planning system using the conventional two-step IMRT approach, or fluence based optimization (FBO). Ten nasopharynx cancer recurrence patients were selected for the study. For all ten patients two aspects of the treatment plans were compared: the quality of the dose distribution (target coverage and critical structure sparing) and the delivery efficiency. Next, comparison plans were generated with the standard fixed collimator DAO technique. An analysis including comparison of dose-volume histograms, dose distribution and MU efficiency is included in order to provide a comprehensive evaluation of the capabilities of RAO compared to DAO. The effects of spatial resolution were also explored by repeating the same tests for both the Millenium 120 (5 mm leaf width for the central 40 leaves) and the Millenium 80 (1 cm leaf width) MLCs. The results of this study are published in Medical Physics [96]. Finally, the dosimetric accuracy of treatment delivery was verified. Measurements of treatment plans for the three different optimization techniques (FBO, DAO and RAO) were performed using radiographic film and ion chamber. The film measurements were analyzed using the gamma factor.  5.1  Patients Description  Ten patients with recurrent nasopharyngeal carcinoma (rNPC) were selected to evaluate the RAO technique. rNPC presents a special radiotherapeutic challenge as these tumours are generally deep-seated, and close to vulnerable structures which have been  96  Chapter 5. Rotating Aperture Optimization Evaluation treated close to tolerance during primary radiotherapy. These cases presented a wide range of complexity as the planning target volumes (PTV) varied in volume (mean: 143 cm3 , range: 37 cm3 to 421 cm3 ), shape, and proximity to critical structures (brainstem, spinal cord, temporal lobes, brain, visual pathways). CT Simulation scans with the patient immobilized in the treatment position were acquired for all cases. Scan slice thickness was 3 mm. The CT dataset included a margin of at least 5 cm superior and inferior to the PTVs. The definition of volumes was in accordance with the ICRU Report 50[92]. All volumes of interest were contoured on all CT slices in which the structures existed. All contours were drawn by a single radiation oncologist according to the study definitions to ensure consistency between cases. Seven isocentric 6MV beams weighted towards the anterior aspect of the patients (gantry angles =0◦ −38◦ −76◦ −114◦ −246◦ −284◦ − 322◦ shown in figure 5.1) and the Varian Millennium 120 MLC were used. The dose prescribed to the PTV was 60 Gy in 30 fractions. Many critical structures are located in the head and neck region. For this study the brainstem, spinal cord, temporal lobes, brain and visual pathways were given the highest priority. Planning goals specified by the radiation oncologist are summarized in table 5.1. The dose-volume constraints were based on clinical experience, and on well established conventions for individual tissue tolerance[4], assuming that all cases had received a similar, homogeneous dose close to tissue tolerance during the primary treatment. The dose-volume constraints were set up in order to give consistency across the series, and to give a critical structure dose as low as reasonably possible given the volume prioritization. In clinical practice the dose constraints and prioritization of the critical structures are individualized on a case-by-case basis for re-treatment. This is because the dosimetry will inevitably vary depending on a number of factors integral to the primary treatment e.g. the proximity of the PTV to the critical structures, the treatment technique and the dose per fraction schedule. In addition, the time between primary treatment and recurrence is likely to have some effect on critical structures tolerance to re-treatment[97]. It should also be noted that these were taken as guidelines to generate the plan, since in some cases it was impossible to reach these goals for some structures. Two example patients (patient 1 and 2) representing different level of complexity are shown in figure 5.1 and 5.2. Patient 1 is one of the most simple of the 10 patients. The optical apparatus is 21 mm above the PTV and was therefore not included in 97  Chapter 5. Rotating Aperture Optimization Evaluation the optimization. For patient 2, several critical structures are in close proximity to the PTV, which made treatment planning more complex. As can be seen on the axial view, the brainstem and temporal lobes are surrounding the PTV. The mean distance between the brainstem and the PTV is 5mm and both temporal lobes are overlapping with the PTV. Table 5.1: Summary of the re-treatment goals for 10 nasopharynx cancer cases. Case Nasopharynx Recurrence (10 patients)  Structure PTV Brainstem, Spinal Cord Temporal Lobes Chiasm Optic Nerves  98  Goals V57 Gy > 95% V66 Gy < 5% V20 Gy < 2% V15 Gy < 2% V15 Gy < 2% V15 Gy < 2%  Chapter 5. Rotating Aperture Optimization Evaluation  (a)  (b)  (c)  Figure 5.1: Patient 1 structures. (a) Axial (b) sagittal and (c) coronal views. Structures are numbered as follow: (1) PTV, (2) brainstem, (3) spinal cord, (4) left temporal lobe, (5) right temporal lobe. The beam geometry is shown in (a).  99  Chapter 5. Rotating Aperture Optimization Evaluation  (a)  (b)  (c)  Figure 5.2: Patient 2 structures. (a) Axial (b) sagittal and (c) coronal views. Structures are numbered as follow: (1) PTV, (2) brainstem, (3) spinal cord, (4) left temporal lobe, (5) right temporal lobe, (6) brain and (7) optical apparatus.  5.2 5.2.1  Methods RAO vs Conventional Fluence Based Optimization  The planning process was designed to resemble the usual IMRT planning protocol at the Vancouver Cancer Centre (summarized in figure 5.3). The 10 nasopharynx cancer recurrence patients described in section 5.1 were used for this study. Each patient was planned with the conventional fluence based optimization and the rotating 100  Chapter 5. Rotating Aperture Optimization Evaluation aperture optimization techniques. Conventional FBO IMRT plans were generated using the Varian Eclipse treatment planning system (version 7.3.10). In Eclipse, two delivery techniques can be selected: a dynamic (DMLC) or step-and-shoot (SMLC) method. Previous authors have shown that a relatively low number of intensity levels are sufficient to generate SMLC plans that are comparable to those obtainable with the DMLC technique[46, 70, 98]. Plans were generated using DMLC delivery along with plans using SMLC delivery and 10 intensity levels. For the RAO technique six apertures per beam are used for each patient. The choice of six apertures per beam is based on the results obtained in chapter 4 and observations made by Jiang et al. [43]. After optimization the final RAO plan was exported back to Eclipse where the dose was recalculated in order to confirm that the dose calculated by the RAO algorithm is accurate. This has the benefit of (1) using a fully commissioned treatment planning system and (2) the comparison of RAO and Eclipse is done with the same dose calculation algorithm. The dose calculation resolution was set to 2.5 mm. The first and most important planning priority was the dose constraints for the PTV. The OARs were then prioritized according to the list in table 5.1. When the dose-volume constraint was met (or as close as possible) for a structure, then the next structure on the list was optimized, without compromising the DVH of any of the preceding structures. For each patient two independent teams generated RAO and Eclipse plans in parallel based on the written planning objectives described above. These plans were then reviewed on the Eclipse treatment planning system jointly by two radiation oncologists. At this point, the oncologists indicated patient-specific desirable and undesirable characteristics of each plan to both teams at the same time. Each team then generated a final plan based on the information given by the oncologists. Both teams had access to the previously generated plans. After both teams submitted their final plan, the radiation oncologists evaluated the plans sideby-side on the Eclipse TPS using DVH constraints stated in table 5.1, mean doses (for all critical structures) and axial isodoses. The radiation oncologists were blinded to the technique for the final evaluation. The oncologists decided if (a) one plan was significantly better than the other, or (b) the plans were equivalent (no significant clinical difference). If the decision was made that one plan was clearly superior to the other, the team with the inferior plan had the opportunity to resubmit the final 101  Chapter 5. Rotating Aperture Optimization Evaluation plan. This team had access to the other team’s superior plan for the resubmission. A numerical analysis was also performed for all patients. For each patient, the set of parameters used by the radiation oncologist to evaluate the plans was calculated. These parameters include the dose-volume goals stated in table 5.1, as well as mean doses for all critical structures. Differences between techniques were tested with a Student’s paired t-test with two tails. Both the number of MU necessary to deliver each plan, and the treatment times were used to evaluate the efficiency for DMLC, SMLC and RAO. To evaluate treatment times, treatment plans were delivered using a Varian CL21EX linear accelerator with a Millenium120 MLC and a dose rate of 300 MU/min. Differences between techniques were tested through a two-tails, paired Student’s t-test.  Figure 5.3: Summary of the planning process  5.2.2  RAO vs Direct Aperture Optimization  In order to evaluate the capabilities of RAO compared to standard fixed collimator angle DAO, treatment plans were generated using both techniques for 10 nasopharynx recurrence patients described in section 5.1. Plans with 2, 4, 6, 8 and 10 apertures per beam were generated using DAO and RAO. For DAO, the collimator angle was set at 0◦ for each aperture. This test was designed to evaluate how the quality of the dose distribution is affected by the number of apertures per beam for RAO and DAO. To explore the effects of spatial resolution the optimization was repeated with 102  Chapter 5. Rotating Aperture Optimization Evaluation the 1 cm and 5 mm leaf width MLCs. Final cost values were normalized to the cost of the DAO plan with 1 cm MLC and 2 apertures per beam.  5.2.3  Delivery accuracy  AVID IMRT phantom The AVID IMRT verification phantom was used for all dosimetric verifications presented in this section. It can be used to perform ion chamber measurements as well as radiographic film measurements. The AVID phantom is a 18.5 cm cube made of solid water-equivalent material. The phantom is placed on the treatment couch with a localizer box, as shown in figure 5.4. Cross hair drawn on the top, left and right side of the localizer box allow the phantom to be accurately aligned using the isocenter lasers in the linac vault. An ion chamber can be inserted in the phantom so that the measurement point is exactly at the center of the phantom. Ion chamber measurements were performed with a Victoreen 0.01 cc NAC mini chamber and a Victoreen Precision Electrometer/Dosimeter (model 530). Another 18.5 cm cube is used for film measurements. The cube contains removable solid water spacers between which film can be inserted. The phantom can be placed so that the film is irradiated in either the coronal, axial or sagittal plane. The AVID phantom was imaged on a CT scanner with a 3 mm slice spacing. The scan was imported in the Eclipse TPS and each IMRT verification plan, including gantry angles, MLC shapes and weights, and beam energy, was transferred to the phantom for dose calculation. The isocenter of each beam was set at the center of the phantom. This dose distribution was then used for comparison with measurements (film and ion chamber).  103  Chapter 5. Rotating Aperture Optimization Evaluation  Figure 5.4: The AVID IMRT verification phantom is mounted on the treatment couch with the localizer box used to set up the phantom. Film Measurements and Calibration Film requires calibration in order to convert optical density (OD) values into dose values. In order to establish the relationship between optical density and dose, a separate irradiation using known doses must be performed. In this work, percent depth dose (PDD) curves are used. A film (Kodak EDR2) is placed in the axial plane of the AVID phantom with the beam axis parallel to the film. A 6 MV beam with 5x5 cm2 field size was used to irradiate three Kodak EDR2 film with different number of MU. The number of MU for each film is chosen to cover the dose range of the IMRT plans to be delivered and so that dose values overlap between all three films. In this case, if there are any problems due to calibration errors or film processing, it can be easily detected as the three curves would not overlap. After the film has been exposed and processed, the amount of dose deposited is related to the optical density at that point. The point doses used for the calibration curve are calculated in the Eclipse TPS. Optical density is determined by measuring the transmission of collimated light source through the film. The films were scanned with a Vidar DosimetryPRO film scanner using a resolution of 71 pixels per inch and 104  Chapter 5. Rotating Aperture Optimization Evaluation a 16 bit depth. Finally the data is fitted to a 3rd order polynomial for easy conversion of pixel values to dose. An example of three PDD films is shown in figure 5.5(a)-(c). The corresponding calibration curve is shown in figure 5.5(d).  (a)  (b)  (c)  4  3.5  x 10  3 Pixel value  2.5 2 1.5 1 0.5 0  0  50  100  150 200 Dose (cGy)  250  300  (d)  Figure 5.5: Percent depth dose calibration film for (a) low dose, (b) medium dose and (c) high dose. (d) A calibration curve converts pixel value into dose. Plan Delivery The accuracy of RAO delivery was first tested with the hypothetical c-shape target described in the previous chapter (section 4.1.1). Seven equispaced 6MV beams with 6 apertures per beam were used for the optimization. Dose constraints were applied to the centrally located sensitive structure and to surrounding ”healthy tissue” (summa105  Chapter 5. Rotating Aperture Optimization Evaluation rized in table 4.1). Two plans, using the same optimization constraints, were created: one with collimator rotation (RAO plan) and one without collimator rotation (DAO plan with collimator angle set to 0◦ for each aperture). The 5 mm leaf width MLC was used for both optimizations. The RAO and DAO c-shape plans were delivered to the AVID IMRT Phantom with Kodak EDR2 film inserted in the coronal and axial planes. The measured values were compared to the calculated values in Eclipse. The delivery accuracy was also tested for two nasopharynx cancer recurrence patients. The DAO and RAO plans were delivered to the AVID IMRT phantom with Kodak EDR2 film inserted in the coronal plane. For comparison, the conventional IMRT plans (generated with the Eclipse treatment planning system) were also delivered to the AVID phantom. In all cases, the measured values were compared to the calculated values in Eclipse. A γ factor analysis (% dose difference = 2%, DTA = 2 mm) was also performed for each treatment plan.  5.3 5.3.1  Results and Discussion RAO vs Conventional Fluence Based Optimization  Dose analysis Based on the blinded evaluation of the radiation oncologists, SMLC, DMLC and RAO are considered dosimetrically equivalent for all 10 patients. Table 5.4 summarizes numerical results for the three techniques. Results are reported as an average over the 10 patients. No statistically significant difference is found between each technique. Two example cases are discussed in more details. DVHs for patients 3-10 can be found in appendix B. Patient 1: Structures for this patient are outlined in figure 5.1. This case is one of the least challenging of the 10 patients. The optical apparatus is 21 mm above the PTV and was therefore not included in the optimization. Final DVHs for this patient are shown in figure 5.6 for both RAO and Eclipse DMLC. DVHs for Eclipse SMLC are omitted for clarity. Similar PTV coverage is obtained for all three techniques. For example, V57Gy = 97.0%, 97.9% and 98.4% and V66Gy = 5.0%, 3.3% and 4.8% 106  Chapter 5. Rotating Aperture Optimization Evaluation for SMLC, DMLC and RAO respectively. For all three techniques, the planning goals are met for all critical structures except the left temporal lobe. In this case the mean dose is 3.2 Gy, 3.3 Gy and 3.6 Gy and V15Gy = 3.8%, 3.9% and 3.7% for SMLC, DMLC and RAO respectively. Patient 2: Contours for this patient are shown in figure 5.2. Several critical structures are in close proximity to the PTV, which made planning fairly complex. As can be seen on the axial view, the brainstem and temporal lobes are surrounding the PTV. The mean distance between the brainstem and the PTV is 5mm. Both temporal lobes are overlapping with the PTV. The resulting DVHs for RAO and Eclipse (DMLC) are shown in figure 5.7. Similar results are obtained for the other critical structures. Corresponding dose distributions are shown in Figure 8. Comparable PTV coverage is obtained for RAO and Eclipse DMLC, SMLC. V57Gy = 95.5% for the three techniques. The three techniques obtain similar results although the planning goals were impossible to meet for several critical structures (brainstem, temporal lobes, right optic nerve and retinas). For the brainstem V20Gy = 21%, 21.9% and 21.4%, and the mean dose is 14.4 Gy, 14.8 Gy and 14.8 Gy for SMLC, DMLC and RAO respectively.  107  Chapter 5. Rotating Aperture Optimization Evaluation Table 5.2: Comparison between Eclipse SMLC, DMLC and RAO. Results are derived from dose volume histograms for all 10 patients. Structure  Parameter  PTV  V54Gy (%) V57Gy (%) V66Gy (%) V69Gy (%) V20Gy (%) Mean Dose V20Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose V15Gy (%) Mean Dose  Brainstem Spinal Cord Left Temporal Lobe Right Temporal Lobe Brain Chiasm Left Optic Nerve Right Optic Nerve Left Retina Right Retina  108  (Gy) (Gy) (Gy) (Gy) (Gy) (Gy) (Gy) (Gy) (Gy) (Gy)  Eclipse SMLC 99.0 96.3 4.7 0.2 4.7 9.0 2.5 4.2 11.6 7.4 20.7 9.4 1.1 1.6 12.6 7.9 6.2 4.0 4.2 4.1 3.1 3.4 0.5 3.0  Eclipse DMLC 99.1 97.3 3.7 0.2 5.2 9.3 2.9 4.4 11.9 7.5 21.4 9.5 1.1 1.7 12.7 8.0 7.4 4.1 5.0 4.2 3.0 3.4 0.7 3.1  RAO 99.1 97.0 3.2 0.0 4.7 9.6 2.6 4.4 12.2 7.5 20.8 9.7 1.2 1.9 12.8 8.5 7.0 4.2 4.4 4.4 2.4 3.4 0.1 3.1  Chapter 5. Rotating Aperture Optimization Evaluation 100  100 80 Volume (%)  Volume (%)  80 PTV →  60 40  ← Brainstem  60 40 ← Spinal Cord  20  20 ← Left Temporal Lobe 0  DMLC RAO  0  20  40 Dose (Gy)  0 60  ← 0  Brain 20  40 Dose (Gy)  60  100  100  80  80  60 ← Left Retina 40  Volume (%)  Volume (%)  Figure 5.6: Patient 1: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  PTV →  ← Brainstem  20  DMLC RAO ← Right Temp. Lobe  60 40  ← Left Temp. Lobe  20 ← Left Optic Nerve  0  0  20  40 Dose (Gy)  0  60  0  20  40 Dose (Gy)  60  Figure 5.7: Patient 2: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  109  Chapter 5. Rotating Aperture Optimization Evaluation  105  (a) Eclipse (DMLC)  (b) RAO  90  Dose (%)  75 60 45 30 15  Figure 5.8: Patient 2: Isodose distributions for (a) the Eclipse fluence based technique (DMLC) and (b) the Rotating Aperture Optimization technique. Doses are given as the percentage of the prescribed dose (60 Gy). The PTV is outlined in white, the brainstem in dashed black and the temporal lobes in dashed white. Efficiency analysis The number of apertures required to deliver the step-and-shoot plans (SMLC and RAO) is shown in figure 5.9. The SMLC technique requires on average twice the number of apertures required for RAO (p < 0.0001). The patient specific number of MUs required to deliver plans for the three techniques is shown in Figure 5.10. The mean number of MU is 1031, 964 and 547 for DMLC, SMLC and RAO respectively. Both SMLC and RAO show a decrease of 6.5% and 46.9% in the number of MU when compared with DMLC. These results were statistically significant (p < 0.0001) in both cases. There is also a significant decrease of 43.3% (p < 0.0001) when comparing the number of MU for RAO and SMLC. Eclipse plans show more variation in the number of MU (between patients) with a standard deviation of 15.5%, 14.6% for DMLC and SMLC respectively, compared to a standard deviation of 4.9% for RAO. This is most likely because the delivery constraints are not taken into account during the optimization, leading to more complex fluence patterns, and therefore larger number of MU, depending on the patient geometry[31]. With RAO the number of apertures per beam is fixed at the beginning of the optimization, 110  Chapter 5. Rotating Aperture Optimization Evaluation thereby ensuring that the final plan is not unnecessarily complex. Treatment times for DMLC, SMLC and RAO are shown in figure 5.11. Although the number of MU is consistently lower for SMLC, treatment times for SMLC are consistently higher than DMLC. This increase is statistically significant, but relatively small (6%, p < 0.0001). The main limitation of our RAO technique is the current rotation speed of the MLC. The Varian CL21EX linac that we used to deliver our IMRT plans takes 45 seconds to rotate through 1800 . RAO results in a 96.6% average increase in treatment times compared with DMLC (85.2% when compared to SMLC). An estimate of treatment times for a collimator rotating over 1800 in 10 seconds (labeled *RAO) is also shown in figure 5.11. It is interesting to note that the *RAO treatment times drop drastically to a mean value of 4.64 minutes compared to 4.44 minutes for DMLC and 4.71 minutes for SMLC. SMLC  RAO  4  8  # apertures  150  100  50  0  1  2  3  5 6 7 Patient #  9 10  Figure 5.9: Number of apertures required for the 10 patients included in the study. Results are shown for plans generated with Eclipse using static (SMLC) delivery and plans generated with the Rotating Aperture Optimization (RAO) technique.  111  Chapter 5. Rotating Aperture Optimization Evaluation DMLC  SMLC  RAO  1500  # MU  1000  500  0  1  2  3  4  5 6 7 Patient #  8  9 10  Figure 5.10: Number of MU required for the 10 patients included in the study. Results are shown for plans generated with Eclipse using dynamic (DMLC) and static (SMLC) delivery, as well as plans generated with the Rotating Aperture Optimization (RAO) technique.  DMLC SMLC RAO *RAO  treatment time (min.)  10 8 6 4 2 0  1  2  3  4  5 6 7 Patient #  8  9 10  Figure 5.11: Treatment times for the 10 patients included in the study. Results are shown for plans generated with Eclipse using dynamic (DMLC) and static (SMLC) delivery, as well as plans generated with the Rotating Aperture Optimization (RAO) technique. Estimate of treatment times for a collimator rotating through 1800 in 10 seconds are also shown (*RAO).  112  Chapter 5. Rotating Aperture Optimization Evaluation  5.3.2  RAO vs Direct Aperture Optimization  Nasopharynx Patient 1 The final normalized cost value (which is related to the plan quality) is plotted as a function of the number of apertures for plans associated with patient 1 in figure 5.12. The final cost decreases as the number of apertures increases, but little improvement (less than 8%) is seen with more than 6 apertures per beam for the 4 techniques shown (DAO 1cm, RAO 1cm, DAO 5mm and RAO 5mm). This result is in agreement with observations made by Jiang et al. [43]. The same trend is observed with DAO and RAO. For the plans with 6 apertures per beam and 5 mm MLC, RAO and DAO plans result in similar final cost, but RAO has the lowest final cost. However for the 1 cm MLC the final cost for DAO is considerably higher (54%) than RAO. To illustrate how the difference in the final cost value is reflected on the dose distribution, the DVHs for DAO and RAO using 6 apertures per beam are plotted in figure 5.13. The DVH for RAO with the 5 mm MLC is almost identical to the DAO 5 mm MLC and is omitted for clarity. A summary of the relevant dose-volume indices is shown in table 5.3. Even with a larger 1 cm MLC RAO results in similar DVHs to DAO with 5 mm MLC. When compared with DAO 1 cm, RAO 1cm and DAO 5mm plans are able to reduce the maximum and mean dose to both optic nerves. For the 1cm MLC, there is a reduction of 6.2 Gy in maximum doses using RAO for the left and right optic nerves. There is also a reduction in the mean dose of 1.8 Gy and 3.6 Gy for the left and right optic nerves respectively. Similar results are obtained for the other critical structures. The number of MU required to deliver all plans optimized with 6 apertures per beam is shown in figure 5.14. RAO 5mm is the plan requiring the less number of MU, 7.5 % less than DAO 5 mm. The optimized dose distributions for RAO and DAO plans with 1cm MLC are shown in figure 5.15. The 90% and 75% isodose line conforms more tightly to the PTV for RAO. This allows better sparing of the critical structures and surrounding healthy tissues.  113  Final Cost (norm.)  Chapter 5. Rotating Aperture Optimization Evaluation  DAO 1cm RAO 1cm DAO 5mm RAO 5mm  1.2 1 0.8 0.6 0.4 0.2 0  2  4 6 8 # apertures per beam  10  Figure 5.12: Final normalized cost value for different number of apertures per beam for patient 1. Results are shown for DAO and RAO with two types of MLC: Varian Millenium 80 (1cm leaf width) and Millenium 120 (5mm leaf width for the central 40 leaves).  100  100  (a)  80  60  PTV →  40  ← Right Optic Nerve  Volume (%)  Volume (%)  80  0  60 ← Brainstem  40 20  20  0 0  20  40 Dose (Gy)  60  (b)  DAO 1cm RAO 1cm DAO 5mm  ← Left Optic Nerve 0  20  40 Dose (Gy)  60  Figure 5.13: Patient 1: DVHs for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC are shown. 6 apertures per beam were used in the optimization.  114  Chapter 5. Rotating Aperture Optimization Evaluation  Table 5.3: Patient 1: Dose-volume indices for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC. 6 apertures per beam were used in the optimization. Structure PTV  Parameter V57Gy (%) V66Gy (%)  DAO 1cm 94.4 6.6  Brainstem  V20Gy (%) Max. (Gy) Mean (Gy)  33.6 52.9 19.4  26.7 48.0 16.9  27.5 47.3 17.4  Left optic nerve  V15Gy (%) Max. (Gy) Mean (Gy)  2.3 20.5 7.7  0 14.3 5.9  0 13.0 4.5  Right optic nerve  V15Gy (%) Max. (Gy) Mean (Gy)  42.5 53.6 17.3  32.0 47.4 13.7  30.4 44.1 14.2  115  RAO 1cm 95.4 2.4  DAO 5mm 95.5 3.7  Chapter 5. Rotating Aperture Optimization Evaluation 500  # MU  400 300  DAO 1cm RAO 1cm DAO 5mm RAO 5mm  200 100 0  Figure 5.14: Patient 1: Number of MU required for DAO and RAO with 1cm and 5mm MLC. 6 apertures per beam were used in the optimization.  105  (a) DAO (1 cm)  (b) RAO (1 cm)  90  Dose (%)  75 60 45 30 15  Figure 5.15: Patient 1: (a) DAO and (b) RAO optimized dose distribution for 1 cm leaf width MLC with 6 apertures per beam. The PTV is outlined with a solid white line, and the critical structures (temporal lobes and brainstem) are outlined with dashed white lines.  116  Chapter 5. Rotating Aperture Optimization Evaluation Nasopharynx Patient 2 The final normalized cost value is plotted as a function of the number of apertures for plans associated with patient 2 in figure 5.16. Results similar to patient 1 are obtained for the final cost value as a function of the number of apertures per beam. The DVHs for the PTV and the left temporal lobe for the plans using 6 apertures per beam are shown in figure 5.17. The DVHs for RAO with the 5 mm MLC are omitted for clarity. A summary of the relevant dose-volume indices is shown in table 5.4. Only small differences are observed between RAO 1 cm and DAO 5 mm. For example, both meet the treatment goal of 95% isodose coverage to 95% of the PTV. In contrast, DAO 1 cm failed to meet that goal with a 93.6% dose coverage to 95% of the PTV. Sparing of the left temporal lobe is also compromised with DAO 1 cm: V15 Gy is 2.6% higher than RAO 1 cm. The number of MU required to deliver all plans optimized with 6 apertures per beam is shown in figure 5.18. Even if only small differences are observed between RAO with the 1 cm MLC and DAO with the 5 mm MLC, RAO 1 cm requires 11% less MU than DAO 5 mm. DAO 1cm RAO 1cm DAO 5mm RAO 5mm  Final cost (norm.)  1.2 1 0.8 0.6 0.4 0.2 0  2  4 6 8 # apertures per beam  10  Figure 5.16: Final normalized cost value for different number of apertures per beam for patient 2. Results are shown for DAO and RAO with two types of MLC: Varian Millenium 80 (1cm leaf width) and Millenium 120 (5mm leaf width for the central 40 leaves).  117  Chapter 5. Rotating Aperture Optimization Evaluation 100 DAO 1cm RAO 1cm DAO 5mm  Volume (%)  80  PTV →  60 40  ← Left Temporal Lobe  20 0  0  20  40 Dose (Gy)  60  Figure 5.17: Patient 2: DVHs for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC are shown. 6 apertures per beam were used in the optimization.  Table 5.4: Patient 2: Dose-volume indices for DAO with 1cm and 5mm MLC, and RAO with the 1 cm MLC. 6 apertures per beam were used in the optimization. Structure PTV  Parameter V57Gy (%) V66Gy (%)  Left Temporal Lobe  V15Gy (%) Mean (Gy)  DAO 1cm 93.6 3.9 6.3 4.1  RAO 1cm 96.3 3.6 3.7 3.5  DAO 5mm 97.4 2.9 3.2 3.2  600 500  # MU  400  DAO 1cm RAO 1cm DAO 5mm RAO 5mm  300 200 100 0  Figure 5.18: Patient 2: Number of MU required for DAO and RAO with 1cm and 5mm MLC. 6 apertures per beam were used in the optimization. 118  Chapter 5. Rotating Aperture Optimization Evaluation Nasopharynx Patients 3-10 The results for the 7 remaining patient plans optimized with 6 apertures per beam are summarized in figure 5.19. The corresponding DVHs are presented in appendix C. The lowest final cost value is obtained with RAO and the 5 mm MLC for all five patients. RAO with 1 cm MLC final costs are smaller than DAO 1 cm except for patient 3. For this patient the final normalized cost is increase by only 1.2%. For patients 4-7 the decrease in the final normalized cost was between 15.2% and 54.5%. For the 1 cm leaf MLC, RAO results in a better final cost value without increasing substantially the number of MU. The maximum increase in the number of MU is 5%. There is also a decrease in the number of MU of 20% for patient 3. For the 5 mm MLC the five RAO plans result in a decrease in the number of MU compared to DAO. The minimum and maximum decrease was 5% and 20% respectively. DAO 1cm RAO 1cm DAO 5mm RAO 5mm  DAO 1cm RAO 1cm DAO 5mm RAO 5mm 700 600  0.8  500 0.6  #MU  Final Cost (norm.)  1  0.4  400 300 200  0.2 0  100 3  4  5  6 7 Patient #  8  9  0  10  (a)  3  4  5  6 7 8 Patient #  9  10  (b)  Figure 5.19: Patients 3-7: (a) Final cost and (b) number of MU for RAO and DAO with the 5 mm leaf width MLC and the 1 cm leaf width MLC. 6 apertures per beam were used in the optimization.  119  Chapter 5. Rotating Aperture Optimization Evaluation  5.3.3  Delivery Accuracy  C-Shape Target The optimized dose distributions for the DAO and the RAO plans are shown in figure 5.20. The corresponding dose-volume histograms along with the total number of MU required to deliver each plan are shown in figure 5.21. RAO and DAO provides similar target coverage. Although RAO reduces slightly the maximum and mean doses to the critical structure by 1.1 and 2.3 Gy respectively, there is a 28% reduction in the number of MU. Dose(cGy) 50  100  150  (a)  200  250  (b)  Figure 5.20: C-shape target optimized dose distribution in the transverse plane for (a) DAO and (b) RAO. Both plans were optimized with 6 apertures per beam angle and the 5 mm MLC. The c-shape target and the centrally located sensitive structure are outlined in white.  120  Chapter 5. Rotating Aperture Optimization Evaluation 1200  (a)  DAO RAO  Volume (%)  80  PTV →  60 ← OAR  40  (b)  1000  DAO RAO  800 # MU  100  600 400  20 200 0  0  20  40 Dose (Gy)  60  0  Figure 5.21: (a) DVH and (b) number of MU comparison of RAO and DAO for the c shape target. For each case, 6 apertures per beam angle were used. DAO Plan: The calculated (Eclipse TPS) and measured (film) dose distributions in the coronal plane for DAO are shown in figure 5.22 (a) and (b) respectively. The two dose distributions shown the same dose pattern. However lines of underdosage located at the edge of the MLC leaves in the direction of leaf motion can be seen. This is most likely due to the effect which is not currently modeled in Eclipse. The magnitude of the disagreement can be seen in the γ factor analysis, shown in figure 5.22 (c). In this figure, a pixel satisfying the γ ≤ 1 criteria (dose difference of 2% and DTA 2 mm) is shown in black. Any pixel with γ > 1 is plotted according to the γ index scale. The maximum γ value of 5.3 is located along a center leaf edge. 85.4% of the pixels in the region of interest pass the γ ≤ 1 criteria. The majority of pixels not satisfying the γ ≤ 1 are found along the leaf edges in the target area. Orthogonal profiles along the x and y axes are shown in figure 5.22 (d) and (e). The profiles were chosen in one of the worst part of the γ map (dashed lines indicated on the dose distributions and γ map). The error is obvious in both profiles. Almost every point in the measured x-profile shows a severe underdosage when compared to the calculated dose distributions. An underdosage of 11.4% is observed at x = −11mm.. The results for the measurements in the axial plane are shown in figure 5.23. The tongue and groove underdosage is important since this plane is aligned with a leaf edge. Only 57.5% of the pixels pass the γ ≤ 1 criteria which is clinically unacceptable. Most of the pixels with γ > 1 are located in the target area.  121  Chapter 5. Rotating Aperture Optimization Evaluation RAO Plan: The calculated and measured dose distributions in the coronal plane for RAO are shown in figure 5.24 (a) and (b) respectively. Lines of underdosage are not observed, most likely because this effect is blurred out with collimator rotation (i.e. the maximum overall error is reduced). A γ distribution is shown in figure 5.24(c), with the same scale that was used for the DAO plan (for easier comparison). Although some discrepancies are still observed, they are no longer located at the leaves edges. The orthogonal profiles (dashed lines indicated on the dose distributions) shown in figure 5.24 (d) and (e) also indicates good agreement between calculated and measured dose. Small portions of overdosage are observed in the target: the maximum overdosage in the x-profile is 5.9% at x = −5.5mm. The results for the measurements in the axial plane are shown in figure 5.25. 93.5% of the pixels pass the γ ≤ 1 criteria. The orthogonal profiles also indicate an excellent agreement. Summary: A summary of the γ values for the DAO and RAO plans are shown in table 5.5. The maximum γ value for the RAO plan is lower than the DAO plan and more pixels pass the γ ≤ 1 criteria. A summary of the ion chamber measurements is shown in table 5.6. Similar results are obtained for the two plans. Based on the γ and dose profiles analysis, it is clear that the RAO plan was delivered more accurately than the DAO plan. The DAO plan took 3.69 minutes to deliver and the RAO plan took 8.39 minutes to deliver with a dose rate of 400 MU/min. This is about 2.3 times longer than the corresponding DAO plan. The treatment times for DAO and RAO are summarized in table 5.7.  122  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 300  240  240  Dose (cGy)  Dose (cGy)  (a) Calculated 300  180 120 60  180 120 60  (c) Gamma Distribution 5 Gamma index  4 3 2 1 0 (d) x−profile  (e) y−profile  300  300 Dose (cGy)  Dose (cGy)  250 200 150 Calculated Measured  100 50  −40  −20  0 x (mm)  20  200 100 Calculated Measured 0  40  −20  0 y (mm)  20  Figure 5.22: (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for C-shape target. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. Arrows show tongue and groove effect. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  123  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 300  240  240 Dose (cGy)  Dose (cGy)  (a) Calculated 300  180 120 60  180 120 60  (c) Gamma Distribution 5  Gamma index  4 3 2 1 0 (d) x−profile  (e) y−profile 300 250  200  Dose (cGy)  Dose (cGy)  250  150 100 50 −40  200 150 Calculated Measured  100 −20  0 x (mm)  20  50  40  −20  0 y (mm)  20  Figure 5.23: (a) Calculated and (b) measured dose distribution of the DAO plan in the axial plane for C-shape target. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  124  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 300  240  240  Dose (cGy)  Dose (cGy)  (a) Calculated 300  180 120 60  180 120 60  (c) Gamma Distribution 5 Gamma index  4 3 2 1 0 (d) x−profile  (e) y−profile 300  250  Dose (cGy)  Dose (cGy)  300  200 150 100  Calculated Measured −40  −20  0 x (mm)  20  200 100 Calculated Measured 0  40  −20  0 y (mm)  20  Figure 5.24: (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for C-shape target. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  125  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 300  240  240 Dose (cGy)  Dose (cGy)  (a) Calculated 300  180 120 60  180 120 60  (c) Gamma Distribution 5  Gamma index  4 3 2 1 0 (d) x−profile  (e) y−profile 300  250  Dose (cGy)  Dose (cGy)  300  200 150 100 −40  Calculated Measured −20  0 x (mm)  20  200 100  0  40  −20  0 y (mm)  20  Figure 5.25: (a) Calculated and (b) measured dose distribution of the RAO plan in the axial plane for C-shape target. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  126  Chapter 5. Rotating Aperture Optimization Evaluation Table 5.5: Summary of the measurements for the c-shape target. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. Optimization(min) technique DAO (coronal) DAO (axial) RAO (coronal) RAO (axial)  % of pixels passing γ < 1 85.3% 57.5% 90.0% 93.5%  Maximum γ 5.3 4.6 3.9 3.1  Table 5.6: Summary of the ion chamber measurements for the c-shape target. Optimization Ion chamber technique dose (cGy) DAO 244.7 RAO 243.8  Calculated dose (cGy) 244.9 243.4  Absolute difference(%) 0.1 0.2  Table 5.7: Summary of the delivery times for the c-shape target. The plans were delivered with a dose rate of 400 MU/min. Optimization technique DAO RAO  Delivery time (min) 3.69 8.39  Nasopharynx Recurrence Cancer Patient 1 Eclipse Plan Results for the Eclipse plan are shown in figure 5.26. In general a good agreement exists between calculated and measured dose, although some tongue and groove underdosage is observed in the superior part of the target. 93.5% of the pixels in the ROI pass the γ ≤ 1 criteria, and the maximum γ value is 2.5. Two orthogonal profiles taken in the superior part of the target are shown in figure 5.26 (d) and (e). DAO Plan Results for the DAO plan are shown in figure 5.27. Underdosage located at the leaf edges of the MLC is observe across the target. The maximum γ value is 127  Chapter 5. Rotating Aperture Optimization Evaluation 3.8 and only 84.6% of the pixels in the ROI pass the γ ≤ 1 criteria. Two orthogonal profiles are shown in figure 5.27 (d) and (e). RAO Plan The calculated and measured dose distributions for the RAO plan are shown in figure 5.28 (a) and (b). The corresponding γ distribution is shown in figure 5.28 (c). The maximum γ value is 2.5 and 91.8% of the pixels in the ROI pass the γ ≤ 1 criteria. Two orthogonal profiles are shown in figure 5.28 (d) and (e). Summary A summary of the γ values for the three optimization techniques is shown in table 5.8. RAO and Eclipse obtain similar results. DAO shows a degradation of the delivery accuracy: less than 90% of the pixels pass the γ ≤ 1 criteria and the maximum γ value is higher than Eclipse and RAO. The ion chamber results are shown in table 5.9. The Eclipse plan has the best agreement and RAO has a slightly worse error than DAO and Eclipse.  128  Chapter 5. Rotating Aperture Optimization Evaluation  Measured 250  200  200  Dose (cGy)  Dose (cGy)  Calculated 250  150 100  150 100 50  250  250  200  200 Dose (cGy)  Dose (cGy)  50  150 100 Calculated Measured  50 0  −50  0 x (mm)  150 100 Calculated Measured  50 0  50  −20  0 y (mm)  20  Gamma Distribution  Gamma index  5 4 3 2 1 0  Figure 5.26: (a) Calculated and (b) measured dose distribution of the FBO Eclipse plan in the coronal plane for nasopharynx patient 1. This plan was generated with collimator at 0◦ for each beam, 5 mm MLC in dynamic mode. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  129  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 250  200  200  Dose (cGy)  Dose (cGy)  (a) Calculated 250  150 100  150 100  50  50  (c) Gamma Distribution  Gamma index  5 4 3 2 1 0 (e) y−profile 250  200  200 Dose (cGy)  Dose (cGy)  (d) x−profile 250  150 100 Calculated Measured  50 0  −50  0 x (mm)  150 100 Calculated Measured  50 0  50  −20  0 y (mm)  20  Figure 5.27: (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for nasopharynx patient 1. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  130  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 250  200  200  Dose (cGy)  Dose (cGy)  (a) Calculated 250  150 100  150 100  50  50  (c) Gamma Distribution  Gamma index  5 4 3 2 1 0 (e) y−profile 250  200  200 Dose (cGy)  Dose (cGy)  (d) x−profile 250  150 100 Calculated Measured  50 0  −50  0 x (mm)  150 100 Calculated Measured  50 0  50  −20  0 y (mm)  20  Figure 5.28: (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for nasopharynx patient 1. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  131  Chapter 5. Rotating Aperture Optimization Evaluation Table 5.8: Summary of the measurements for patient 1. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. Optimization technique DAO RAO FBO (Eclipse)  % of pixels passing γ < 1 84.6% 91.8% 93.9%  Maximum γ 3.8 2.5 2.5  Table 5.9: Summary of the ion chamber measurements for the nasopharynx cancer patient 1. Optimization Ion chamber technique dose (cGy) Eclipse 192.7 DAO 180.0 RAO 184.0  Calculated dose (cGy) 194.1 185.4 190.7  Absolute difference(%) 2.2 3.0 3.5  Nasopharynx Recurrence Cancer Patient 2 Eclipse Plan: The calculated and measured dose distributions for the Eclipse plan are shown in figure 5.29 (a) and (b) respectively. A few lines of underdosage are observed. The γ map analysis shown in figure 5.29 (c) indicate that a majority of pixels pass the γ ≤ 1. A small part located in the middle-left part of the target shows a higher γ value. The maximum γ value is 3.3. The orthogonal profiles shown in figure 5.29 (d) and (e) indicate that this correspond to a mild underdosage of about 7% from x = −29mm to x = 0mm. DAO Plan: The calculated and measured dose distributions for the DAO plan are shown in figure 5.30 (a) and (b) respectively. The underdosage is clearly observed in the measured dose distribution. The magnitude of this underdosage is illustrated in the γ distribution shown in figure 5.30 (c). 84.6% of the pixels pass the γ ≤ 1 criteria, and the maximum γ value is 4.0. Two orthogonal profiles, corresponding to the worst part of the γ map, are shown in figure 5.30 (d) and (e). The x-profile shows an underdosage in the target area (from x = −20.5mm to x = 28.5mm) of about 8.3%. 132  Chapter 5. Rotating Aperture Optimization Evaluation RAO Plan: The calculated and measured dose distributions for the RAO plan are shown in figure 5.31 (a) and (b) respectively. The corresponding γ distribution shown in figure 5.31 (c) indicate an excellent agreement. Two orthogonal profiles (indicated by the dashed white line on the calculated and measured distributions) are shown in figure 5.31 (d) and (e). Although these profiles were take in the worst part of the γ distribution, a good agreement exists between calculated and measured dose. For example there is a small underdosage of 3.6% at x = −18mm. Summary: A summary of the γ values is shown in table 5.10. The results for the DAO plan indicate a degradation of the agreement between calculated and measured dose compared to the Eclipse and the RAO plans. A summary of the ion chamber measurements is shown in table 5.11. The Eclipse and the RAO plans obtain acceptable results. However the DAO plan shows an 8.6% underdosage. This is probably because the measurement point is located at a lead edge, and therefore the effect was important at that point.  133  Chapter 5. Rotating Aperture Optimization Evaluation  Measured 250  200  200 Dose (cGy)  Dose (cGy)  Calculated 250  150 100  150 100  50  50  Gamma Distribution 5  Gamma index  4 3 2 1  250  250  200  200 Dose (cGy)  Dose (cGy)  0  150 100 50 0 −50  Calculated Measured 0 x (mm)  150 100 Calculated Measured  50 0  50  −20  −10  0 10 y (mm)  20  Figure 5.29: (a) Calculated and (b) measured dose distribution of the FBO Eclipse plan in the coronal plane for nasopharynx patient 2. This plan was generated with collimator at 0◦ for each beam, 5 mm MLC in dynamic mode. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  134  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 250  200  200 Dose (cGy)  Dose (cGy)  (a) Calculated 250  150 100  150 100  50  50  (c) Gamma Distribution 5  Gamma index  4 3 2 1 0 (e) y−profile 250  200  200 Dose (cGy)  Dose (cGy)  (d) x−profile 250  150 100 50 0 −50  Calculated Measured 0 x (mm)  150 100 Calculated Measured  50 0  50  −20  −10  0 10 y (mm)  20  Figure 5.30: (a) Calculated and (b) measured dose distribution of the DAO plan in the coronal plane for nasopharynx patient 2. This plan was generated with 6 apertures (collimator at 0◦ for each aperture) per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  135  Chapter 5. Rotating Aperture Optimization Evaluation  (b) Measured 250  200  200 Dose (cGy)  Dose (cGy)  (a) Calculated 250  150 100  150 100  50  50  (c) Gamma Distribution 5  Gamma index  4 3 2 1 0 (e) y−profile 250  200  200 Dose (cGy)  Dose (cGy)  (d) x−profile 250  150 100 50 0 −50  Calculated Measured 0 x (mm)  150 100 Calculated Measured  50 0  50  −20  −10  0 10 y (mm)  20  Figure 5.31: (a) Calculated and (b) measured dose distribution of the RAO plan in the coronal plane for nasopharynx patient 2. This plan was generated with 6 rotated apertures per gantry angle and the 5 mm MLC. (c) Corresponding gamma distribution. Dose profile taken along (d) the x axis and (e) the y axis.  136  Chapter 5. Rotating Aperture Optimization Evaluation Table 5.10: Summary of the measurements for patient 2. The percentage of pixels passing the γ < 1 and the maximum γ value are listed for RAO, DAO and FBO. Optimization technique DAO RAO FBO (Eclipse)  % of pixels passing γ < 1 86.6% 93.7% 92.9%  Maximum γ 4.0 1.8 3.3  Table 5.11: Summary of the ion chamber measurements for the nasopharynx cancer patient 2. Optimization Ion chamber technique dose (cGy) Eclipse 185.6 DAO 177.6 RAO 182.0  5.4  Calculated dose (cGy) 185.9 194.4 187.5  Absolute difference(%) 0.2 8.6 2.9  Discussion and Conclusion  Two studies were presented in this chapter to provide a comprehensive evaluation of the capabilities of the rotating aperture optimization technique. In both cases ten nasopharynx recurrence patients were chosen as they present a wide range of complexity as the PTVs vary in volume (mean: 143 cm3 , range: 37 cm3 to 421 cm3 ), shape, and proximity to critical structures. For the first part of the study, the focus was to provide a robust comparison of the rotating aperture optimization technique with plans generated with the conventional two-step fluence based optimization approach used by the commercial Eclipse treatment planning system. For each patient two aspects of the treatment plans were compared: the dose distributions (target coverage and critical structure sparing) and the delivery efficiency (number of apertures and monitor units and treatment delivery time). Interest has grown recently in using DAO for simple treatment sites such as breast patients[76, 77]. Breast IMRT does not usually require highly modulated fluence maps. Here it was shown that the RAO technique can be applied successfully to a more complex treatment site in which highly modulated beams are required. Based on a blinded evaluation and statistical analysis, RAO plans and Eclipse plans 137  Chapter 5. Rotating Aperture Optimization Evaluation (after final evaluation) were considered dosimetrically equivalent. This equivalence was based on (1) the radiation oncologists’ blinded evaluation of DVHs and axial isodoses distribution as well as (2) numerical comparison of dose-volume constraints on target and critical structures. With respect to delivery efficiency, two parameters were evaluated: the number of MU and the treatment time required to deliver each plan. It was shown that RAO plans required significantly fewer MU than both DMLC and SMLC plans. RAO requires an average of 43.3% less MU when compared with SMLC, and 46.9% when compared with DMLC. Improved MU efficiency has the benefit of less total body scatter and less MLC transmission. Other investigators have argued that the high number of MU associated with IMRT results in an increased probability of long term complications, including secondary malignancies[32–36]. It is also interesting to note that the RAO plans were more consistent in terms of MU efficiency between patients. There is a larger MU variation (standard deviation up to 15.5%) associated with the conventional two-step approach. This is most likely because the delivery constraints are not taken into account during the optimization, leading to more complex fluence patterns, and therefore larger number of MU, depending on the patient geometry. With RAO the number of apertures per beam is fixed at the beginning of the optimization, thereby ensuring that the final plan is not unnecessarily complex. The main limitation of the RAO technique is the current rotation speed of the MLC. The Varian CL21EX linac used to deliver the IMRT plans takes 45 seconds to rotate through 180o . It should be noted that this is a mechanical constraint that could be overcome by the manufacturer. An estimate of treatment times (*RAO) for a collimator rotating over 180o in 10 seconds is shown in figure 5.11. With this collimator rotation speed, *RAO treatment times would drop drastically to a mean value of 4.64 minutes compared to 4.44 minutes for DMLC and 4.71 minutes for SMLC. Also the delivery process is such that, between each aperture, the collimator rotates before the leaves can move from one position to the next. Clearly it would be more efficient if they were to move simultaneously. Since this limitation was not considered in the *RAO estimate, it is reasonable to expect that RAO would be faster to deliver than DMLC and SMLC if this constraint was eliminated. With these simple modifications RAO will take advantage of the delivery efficiency associated with DAO while providing the improved delivery accuracy associated with collimator rotation. 138  Chapter 5. Rotating Aperture Optimization Evaluation For the second part of the RAO evaluation, the ten nasopharynx cases were used to provide a comprehensive comparison with a fixed collimator angle DAO. Results indicate that plans generated with RAO are as good as or better than DAO. For the 1 cm leaf width MLC this benefit was achieved for most of the patients. This is most likely due to the increased spatial resolution associated with collimator rotation. Other investigators have shown that increasing the fluence map spatial resolution results in a substantial increase in the number of MU[31]. Here we show plans with increased spatial resolution while maintaining a small number of apertures and MU. In some cases RAO plans are more efficient. For example, RAO with a 1 cm leaf width MLC can generate better plans than DAO with the same MLC and plans that are equivalent to DAO with the smaller 5 mm leaf width MLC. Although for some cases there was only a minor improvement in the quality of the dose distribution, there tended to be a greater reduction (up to 28% for the complex c-shape target) in the number of MU. With the 5 mm leaf width MLC there were smaller improvements in DVHs and dose distributions when comparing RAO to DAO. However, this could be due to the voxel resolution that we used for our dose calculations. Bortfeld et al.[99] estimate that improvements should be observable for MLCs with leaf widths as small as 2 mm. Based on the fact that similar results are obtained for RAO with 1 cm MLC and DAO with 5 mm MLC, it is reasonable to expect some improvements when comparing RAO with a 5 mm MLC to a non-rotating DAO with 3 mm MLC. A higher dose grid resolution and a smaller CT slice spacing would be required in this case[100]. This could have important implications for stereotactic radiosurgery where so-called micro-MLCs are recommended. SRS patients would particularly benefit from collimator rotation since collimator rotation is associated with a better spatial resolution. Furthermore the collimator speed limitations will be relatively less important for these cases since SRS patients require much higher MU (due to high fractional dose). Finally the delivery accuracy was tested. The shape of the MLC leaves can lead to some underdosage at the leaf edges. With DAO, leaf positions are not restricted during the optimization, therefore some leaves may protrude into the beam, which can make DAO more sensitive to effects than the conventional fluence based optimization (Eclipse). Measurements of one c-shaped target plan and two nasopharynx recurrence plans show a clear underdosage at the leaf edges for DAO plans with collimator angle 139  Chapter 5. Rotating Aperture Optimization Evaluation set to 00 . This effect was also observed by Earl et al.[74]. Setting to a different collimator angle, 900 for example, would probably help to reduce the error for DAO plans. However with RAO the leaf edges are at different locations for each aperture thereby further minimizing this error. For the three cases presented in this chapter, a γ analysis indicate that the delivery accuracy is better with RAO than DAO. It was also shown that the RAO delivery accuracy is comparable to plans generated in Eclipse. Bedford et al.[75] proposed a constrained shape algorithm that results in more regular shapes to reduce effects, however this technique does not take advantage of higher spatial resolution. Based on the results obtain for the two studies, it appears that RAO could be particularly beneficial for Elekta linacs. Elekta MLCs offer a faster collimator rotation speed. Also, these wider leaf MLCs (1 cm at isocenter) will take advantage of the higher spatial resolution associated with collimator rotation. Finally, there is an interdigitation constraint for the Elekta MLCs which can be included directly in the rotating aperture optimization algorithm.  140  Chapter 6 Novel applications of DAO As part of this thesis, a collaboration with two PhD students was initiated. It was recognized that the advantages provided by the direct aperture optimization (DAO) approach could be extended to other IMRT related situations. The algorithm developed in this thesis (employing a non-rotating collimator) is used in two different contexts: 1. Beamlet dose distribution matrices generated from Monte Carlo and pencil beam convolution dose calculation algorithms are input into the DAO algorithm and compared. 2. DAO is applied to on-line Adaptive Radiation Therapy (ART). These two projects are described in the following sections. The reader is referred to A. Bergman’s thesis for more details regarding the Monte-Carlo DAO project[101]. This work was also published in Medical Physics[73]. For more details about DAO for on-line ART, the reader is referred to Mestrovic et al.[102]’s article in Medical Physics.  6.1  Direct Aperture Optimization Using Monte Carlo Generated Beamlets  Monte Carlo (MC) is a stochastic method used to simulate fundamental interactions of particles with matter based on well known laws of physics. In medical physics, Monte Carlo simulations are used to simulate radiation beams from a medical linear accelerator and to simulate dose deposited in media (e.g. tissue or water equivalent phantom). The patient anatomy (including inhomogeneities) and the geometry of the linear accelerator are inherently modeled with this method. MC is recognized as the most accurate dose calculation tool for radiation therapy planning particularly 141  Chapter 6. Novel applications of DAO in regions of electronic disequilibrium[103, 104]. It has been shown that the presence of small fields or inhomogeneities can lead to dose calculation errors for algorithms that are unable to model lateral electronic disequilibrium (such as the pencil beam convolution algorithm)[103, 105, 106]. This can have a substantial impact on IMRT treatment plans since the nature of IMRT is to sum a number of small fields and treatment beams often pass through inhomogeneities to reach the target volume (e.g. air cavities located in the head and neck region). When dose perturbations caused by tissue inhomogeneities are not modeled properly, systematic errors are introduced into the optimization process which will converge to a suboptimal solution. Including Monte Carlo modeling in the optimization process will allow for accurate dose calculation and the possibility to compensate for the dose perturbation introduced by inhomogeneities. The goal of this project was to introduce Monte Carlo dose calculation in a direct aperture optimization algorithm and to assess if this combination will improve the dose accuracy and treatment efficiency of IMRT treatment plans. As mentioned in section 3.4.1, the DAO algorithm optimizes pre-calculated doses thus is independent of the dose calculation used. For Monte Carlo DAO (MC-DAO) the PBDD is calculated using DOSXYZnrc (NRC, Ottawa, Canada)[107], which is a radiation dose calculation application of the EGSnrc (Electron Gamma Shower - National Research Council) particle transport simulation algorithm.  6.1.1  Monte Carlo Simulation  Several Monte Carlo implementations are available. In this work the Monte Carlo simulations are based on the EGSnrc particle transport code. EGSnrc is a public MC program used to simulate electron and photon interactions with matter. The first step of a Monte Carlo simulation involves the modeling of the linear accelerator, in this case a Varian CL21EX with a 6 MV beam. The following components (shown in figure 6.1) are defined and modeled with the BEAMnrc source simulation code: • target and primary collimator • flattening filter  142  Chapter 6. Novel applications of DAO • monitor chamber • mylar mirror • secondary collimating jaws • tertiary collimating system (e.g. MLC, blocks) (optional) • compensators (e.g. wedges) (optional) Phase spaces are virtual counting planes perpendicular to the beam axis located at a user-specified distance from the source. Information of the phase space is recorded: traversing particles’ position, energy, direction, charge, weight and point of origin. They are often located at the end of a fixed chain of components (e.g before the moving secondary jaws). Phase spaces are also found at the very end of a chain of components(e.g. after the MLC in figure 6.1). BEAMnrc is used to model the Millennium 120 MLC with a method developed by Keall and Siebers [108] at the Virginia Commonwealth University. With this method the open field phase space is transported very rapidly through the MLC by making some simplifying assumptions about the MLC geometry and the physical interactions between incident photons/electrons and the tungsten material. Once the beam has been transported through all the components of the linac dose is calculated to the patient using DOSXYZnrc (an EGSnrc based MC simulation package). Each photon and its secondary particles are tracked as they interact with the medium, and dose is recorded for each voxel in the patient. The type of interaction is selected randomly but weighted by a probability distribution which refers to the different cross sections for photon and electron interactions with the patient/phantom. Millions of photon histories are scored to ultimately reveal the dose deposited in the medium. Benchmarking tests have demonstrated that the model can accurately model the Varian CL21EX linac with the MLC for a 6 MV beam[101]. It is able to model accurately the tongue and groove effect which is not modeled in the commercial Eclipse treatment planning system.  143  Chapter 6. Novel applications of DAO  Figure 6.1: The linac model used in Monte Carlo simulations.  6.1.2  Monte Carlo DAO Description  The open phase space located below the secondary jaws of the linear accelerator is sub-divided into 5 mm x 2.5 mm beamlets using an in-house software [109]. The open field is thus converted into n phase space files, where n = the number of beamlets. Each beamlet is then projected onto the patient or phantom where the dose can be calculated using DOSXYZnrc. A pencil beam dose distribution (PBDD) matrix can then be constructed by determining the contribution of each beamlet to each voxel located in a structure of interest. The beamlet dose contribution is calculated under full scatter conditions. Once the pencil beam dose distribution is calculated, the optimization is performed using a simulated annealing algorithm as described in section 3.3. As mentioned in section 3.4.1 the DAO algorithm using pre-calculated PBDD is independent of the dose calculation method selected to generate the PBDD matrix, but a number of 144  Chapter 6. Novel applications of DAO modifications to the original algorithm were necessary to make it compatible with the Monte Carlo output. First, the original RAO algorithm uses 2.5 mm × 2.5 mm beamlets due to the higher spatial resolution necessary with collimator rotation. The Monte Carlo code was written for a fixed collimator PBDD, and therefore the spatial resolution in the direction parallel to the leaf motion is limited by the leaf width (figure 3.7). A beamlet size of 5 mm × 2.5 mm is therefore sufficient and reduces significantly the size of the PDBB matrix. Next, the coordinate system used in the RAO algorithm was different than the MC coordinate system so the coordinate system used by the RAO algorithm was adapted. Finally the procedure to calculate the number of monitor units (MU) is different. The raw DOSXYZnrc doses are in relative units. In order to convert to absolute dose, the number of MU assigned to each beam must be known, but the optimized MU cannot be determined until the optimization is completed. For this reason an initialization value of 100 MU is arbitrarily assigned to each field. The final number of MU are obtained by applying the optimized weighting factor. It should be noted that the MLC leaf tip and shape are not modeled in the PBDD matrix. After the optimization, the MC-DAO plan undergoes a full forward calculation using Monte Carlo simulation. The MLC characteristics are fully modeled in this forward dose calculation step.  6.1.3  Methods  The following example illustrates the problem encountered when tissue inhomogeneity is not adequately modeled during dose calculation (e.g. pencil beam kernel convolution). A c-shape PTV surrounding a centrally located organ at risk (OAR) were contoured on the CT dataset of a water equivalent AVID phantom (MDX Medical, Vancouver,BC). A 5.0 cm thick air cavity is introduced into the phantom and the c-shaped target is located 2.0 mm below the air cavity (see figure 6.2). Seven equispaced 6 MV beams were placed around the phantom. The prescribed dose to the PTV was 60 Gy and dose constraints were applied to the centrally located sensitive structure, and to surrounding “healthy tissue” (summarized in table 6.1). An IMRT plan was generated using the Varian Eclipse treatment planning system. Eclipse uses a fluence based optimization algorithm with a pencil beam kernel (PBK) convolution  145  Chapter 6. Novel applications of DAO dose calculation. Tissue inhomogeneities are corrected for using a standard modified Batho heterogeneity correction[13, 14].  Figure 6.2: Water equivalent AVID phantom with a 5 cm thick air cavity. The c-shaped PTV and a spinal-cord like structure (OAR) are shown.  Table 6.1: Summary of the treatment goals for the hypothetical c-shaped target located near an air cavity. Case Structure C-Shape Target PTV Centrally located structure “Healthy tissues”  6.1.4  Goals V57 Gy > 95% V66 Gy < 5% V30 Gy < 5% V66 Gy < 5%  Results  The resulting plan dose-volume histograms (DVHs) are shown in figure 6.3 (a). Also shown in figure 6.3 (a) are the DVHs for the same plan recalculated using Monte Carlo simulation. The mean planning target volume (PTV) dose is 3% higher for the Eclipse optimized/MC calculated plan, but the 95% isodose coverage is compromised. In addition, the mean dose to the OAR is 5% higher when calculated with MC. Figure 6.3 (a) reveals dose calculation errors introduced by the PBK algorithm. The reason 146  Chapter 6. Novel applications of DAO for the failure is related to the lack of modeling of electron lateral spread within the air cavity, which is simulated accurately with MC. In figure 6.3 (b) the plan is reoptimized using the MC-DAO method. In this case the 95% PTV coverage meets the planning goal and the maximum dose to the critical structure has been reduced. The corresponding representations of the 3D dose distributions are shown in figure 6.4. The problem introduced by the air cavity is clearly revealed in figure 6.4 (b) by the systematic clipping of the PTV by the 95% isodose surface. On the other hand the MC-DAO plan accurately models the effect of the air cavity during the optimization and can attempt to provide appropriate coverage in this region. The MC plan also takes advantage of the efficiency associated with DAO. Only 1040 MU was required to deliver this plan compared to 1519 MU for the Eclipse fluence-based optimized plan. The MC-DAO planned dose was verified using film inserted in the coronal plane of the AVID phantom. The film measurement was identical to the procedure described in section 5.2.3. Results are shown in figure 6.5. The Monte Carlo calculated dose and the film measurement show excellent agreement and MC was able to model accurately the effect. When comparing the two plans with the dose difference (3%) and distance-to-agreement (3 mm) method, only 1.8% of the pixels fail the criteria.  147  Chapter 6. Novel applications of DAO  MC opt/MC final calc. PBK opt/MC final calc.  100  100  80  80 Volume (%)  Volume (%)  PBK opt/PBK final calc. PBK opt/MC final calc.  60 PTV → 40 ← OAR  20 0  0  20  40  60 80 Dose (%)  60 PTV → 40 ← OAR  20  100  0  120  (a)  0  20  40  60 80 Dose (%)  100  120  (b)  Figure 6.3: Monte Carlo DAO example for a c-shape target with a nearby critical structure. (a) Eclipse TPS IMRT plan employing a PBK dose algorithm (solid line) is recalculated using Monte Carlo (dashed line). (b) MC-DAO plan (solid line) compared to Eclipse optimized/MC forward calculation (same dashed line in (a)). Dose is normalized to the prescribed dose (60 Gy).  148  Chapter 6. Novel applications of DAO  (a)  (b)  (c)  Figure 6.4: 3D representation of the 95% isodose line covering the c-shape target. (a) IMRT plan employing a PBK dose algorithm for the optimization and the final dose caluclation. (b) The PBK plan is recalculated using Monte Carlo. (c) MC-DAO plan using 6 apertures per beam. Note: wireframe box indicates location of air cavity.  149  Chapter 6. Novel applications of DAO  (a)  (b)  (c)  (d)  (e)  Figure 6.5: Results of the coronal dose measurement for the MC-DAO plan. (a) film measurement (left) and Monte Carlo caluclated dose (right). The arrows show the effect. Dose profiles taken along the (b) the x axis and (c) the y axis. (d) Cropped film plane. (e) Corresponding dose difference (DD=3%)/distance-to-agreement (DTA=3 mm) map. The dark areas correspond to pixels that pass the DTA or the DD criteria. The white pixels failed DD/DTA criteria.  150  Chapter 6. Novel applications of DAO  6.1.5  Discussion and Conclusion  For this project Monte Carlo was used to generate pencil beam dose distributions for direct aperture optimization IMRT inverse treatment planning. The MC-DAO technique offers a clear benefit by properly modeling traditionally difficult treatment geometries such as small fields and tissue inhomogeneities. The MC-DAO also takes advantage of the improved MU efficiency associated with the DAO technique with a 31.5% reduction for the c-shaped target example. The MLC characteristics, such as interleaf leakage and the leaf tip shape, are not included during the MC optimization. This is because the MC calculated PBDD are generated by segmenting an open field phase space. As shown in chapter 5 the inclusion of collimator rotation results in less interleaf systematic error. It would therefore be beneficial to include collimator rotation in a Monte Carlo rotating aperture optimization algorithm. The current limitation of the Monte Carlo method is the computation time needed to simulate the large number of histories required to reduce the statistical uncertainties to an acceptable level. The time involved in the generation of a treatment plan for the c-shaped target example presented here is as follows: • Preprocessing time including the generation of the pencil beam dose distribution is about 2.8 hours. This step only needs to be performed once. • Optimization time is about 5 to 10 minutes for each generated plan. • Final forward dose calculation is about 3.5 hours per plan. Simulations are performed on a cluster comprised of 30 Sun Fire 2100 Opteron processors (2.8 GHz).  6.2  Adaptive Radiation Therapy (ART) with DAO  Intensity modulated radiation therapy allows higher dose gradients and tighter margins than what is possible with conventional radiotherapy techniques. The patient is  151  Chapter 6. Novel applications of DAO imaged before treatment and a treatment plan based on this “fixed” image is generated. The resulting treatment is delivered to the patient in multiple fractions. To overcome the impact of interfraction changes in the patient anatomy a new form of radiation therapy called Adaptive Radiation Therapy (ART) has recently emerged[17, 18]. In the ART process high-quality treatment verification images are acquired prior to treatment delivery. Next, CT datasets must be registered and contoured quickly and reliably using registration methods[19, 20]. Based on patient’s anatomy deformation the original treatment plan is adapted and delivered to the patient. If all of these steps are performed on-line, i.e. while the patient is in the treatment room, it is important that all these steps be performed quickly to minimize time the patient has to spend on the couch. The DAO approach offers several advantages over the traditional fluence based approach for conventional IMRT planning. In addition DAO offers additional benefits which makes it suitable for online ART: • Direct optimization of the leaf sequence parameters allows for better control over plan adaptation, therefore offering the possibility of accelerating the plan adaptation. • There is no need for a leaf sequencing step which accelerates plan adaptation. The use of DAO for on-line adaptive radiation therapy was investigated.  6.2.1  Methods  A geometrical model, shown in figure 6.6(a), representing the anatomy of a typical prostate patient was created. The anatomy was deformed systematically to simulate inter-fractional deformations of the organs as shown in figure 6.6. A DAO plan with 6 apertures per beam was generated for the original geometry based on the treatment goals stated in table 6.2. The prescribed dose to the PTV and the dose-volume constraints for the bladder and rectum are based on the RTOG 0415 IMRT prostate protocol (reference). Seven beams were used with gantry angles of 40, 80, 110, 250, 280, 310 and 355 degrees.  152  Chapter 6. Novel applications of DAO  Figure 6.6: A model simulating a prostate case.  Figure 6.7: Four deformed anatomies are created by systematically deforming the original prostate model.  153  Chapter 6. Novel applications of DAO Table 6.2: Summary of the treatment goals for the prostate model Structure Bladder  Rectum  Bladder  Goals V85 Gy < 5% V80 Gy < 15% V75 Gy < 25% V70 Gy < 35% V85 Gy < 5% V80 Gy < 15% V70 Gy < 25% V65 Gy < 35% V83.8 Gy > 98% Max. Dose (no variations)=89.7 Gy Max. Dose (minor variations)=92.2 Gy Max. Dose (major variations)>92.2 Gy  For each deformed anatomy the original treatment plan is adapted using the DAO algorithm. For the original treatment the MLC shapes were initialized to outline the target beam’s eye view. For plan adaptation the original treatment plan is used as the starting point for the optimization. The hypothesis is that after introducing anatomical deformations the original treatment plan corresponds to a relatively small displacement on the objective function curve, i.e. that the original treatment plan is still in close proximity to the objective function minimum. In this case the original treatment plan can be quickly adapted in order to return to its optimal value. To test this hypothesis the time to adapt the original treatment plan is compared to the time necessary for a complete plan regeneration. Different methods for reducing the search space by adding different constraints to the MLC were also investigated. The hypothesis is that this approach would allow plan adaptation acceleration. The three different methods tested are illustrated in figure 6.8. These include: • restriction of the maximum step size • restriction of the allowed leaf range • predefinition of an optimization order of the parameters  154  Chapter 6. Novel applications of DAO  Figure 6.8: The search space during plan adaptation is reduced by (a) restraining the maximum step size, (b) restraining the allowed leaf range and (c) predefining an optimization order for the parameters.  6.2.2  Results  A treatment plan was first generated using the DAO algorithm for the original plan anatomy. The resulting DVHs are shown in figure 6.9. Using the DAO algorithm the original treatment plan is adapted to correct for the deterioration of dose distribution quality caused by anatomical deformation. As an example the results for the 0.75 cm deformation are shown in figure 6.9. As expected the non-adapted plan shows a deterioration compared to the original treatment plan. For example, the minimum dose to the PTV decreases from 83 Gy to 61 Gy for the 0.75 cm deformation shown in figure 6.9. For the other deformed anatomies the minimum PTV dose decreases to 80 Gy(0.25 cm deformation), 72 Gy (0.5 cm deformation) and 41 Gy (1.0 cm deformation). With the adapted plan, target coverage is recovered and the rectum is spared. The average time needed for the complete plan regeneration is compared to the plan adaptation in figure 6.10. For all four deformed anatomy the original plan adaptation is faster than the complete plan regeneration. It was found the average time needed for the original plan adaptation is roughly half the time needed for a complete plan regeneration. A series of techniques used to reduce the optimization search space were also tested. For the 0.25 cm deformation the plan adaptation is accelerated by a factor of about 6 compared to the complete plan regeneration. For the 0.5 cm and 0.75 cm deformations this factor is about 3. The 1.0 cm deformation demonstrates the 155  Chapter 6. Novel applications of DAO limit of the reduction of the optimization search space as it does not result in any adaptation acceleration. 100  100 Adapted Non−adapted  80 Volume (%)  Volume (%)  80 60  PTV→ 40 ← Bladder 20 0  60 Shell→ 40 ← Rectum  20  0  20  40 60 Dose (Gy)  80  100  (a)  0  0  20  40 60 Dose (Gy)  80  100  (b)  Figure 6.9: DVHs for the non-adapted original treatment plan and the adapted plan. The DVHs for the plan generated by the complete plan regeneration and the plans generated by the treatment plan adaptation are indistinguishable, so the DVHs for original plan adaptation are shown.  156  Chapter 6. Novel applications of DAO  Figure 6.10: The average times needed for the complete plan regeneration and the original treatment plan adaptation. The error bars shown represent one standard deviation.  6.2.3  Discussion  Including adaptive radiation therapy in the IMRT process has the potential of improving dose distributions delivered to the patient. However, to exploit the full benefit of online ART it is essential to be able to perform the plan adaptation (optimization) quickly in order to minimize the additional time the patient has to spend on the treatment couch. In this work DAO is proposed as an alternative approach to conventional fluence based adaptation. Direct optimization of MLC shapes and weight has the potential to rapidly and efficiently re-optimize the original treatment plan. This approach was tested with a prostate deformation model. The results show that the plan re-adaptation can be performed more quickly than a complete plan regeneration thereby minimizing the time the patient has to spend in the treatment room. Adaptive radiation therapy is another application where collimator rotation has not been exploited. In the work presented here original treatment plans are adapted through modifications of the DAO algorithm to correct for the deterioration of dose 157  Chapter 6. Novel applications of DAO distribution quality caused by anatomical deformations. The use of collimator rotation was not exploited. Without collimator rotation it is certainly more difficult to correct for deformations that occurs in a direction other than the direction of leaf travel. By including collimator rotation in the original treatment plan, these deformations could be more easily corrected for.  158  Chapter 7 Conclusion The primary goal of this thesis was to develop a treatment planning and delivery technique for high precision and high efficiency radiation therapy. An extension of a direct aperture optimization (DAO) algorithm where the collimator is rotated between each aperture was introduced thereby combining the advantages of both techniques. Including collimator rotation with leaf sequencing has several advantages including less interleaf systematic error, higher fluence spatial resolution and more flexibility in the generation of aperture shapes. A series of tests were presented to characterize the rotating aperture optimization algorithm. From these tests certain parameters, such as the number of apertures per beam and the minimum aperture size, were found to affect IMRT treatment plans. For the tested parameters a “threshold” value can generally be found for which there is an increased efficiency and/or a simplification of the treatment plan without compromising the quality of the resulting dose distribution. More efficient leaf sequences have the benefit of shorter treatment times and less total body scatter. Other investigators have argued that the high number of MU associated with IMRT results in an increased probability of long term complications, including secondary malignancies[32–36]. More simple and regular aperture shapes in the leaf sequences are also beneficial as they will be calculated more accurately by the treatment planning system. More specifically it was shown that a highly conformal dose distribution can be generated with only 6 apertures per beam. The complexity of an IMRT treatment plan was further reduced by adding a constraint on the minimum aperture size. For a simple prostate patient case, treatment plan with a minimum aperture of 80% of the target BEV was shown to be dosimetrically equivalent to a plan without this constraint. For the the two other cases (c-shape and nasopharynx cancer) a degradation in the dose distribution was observed at smaller aperture sizes (i.e. 40% of the target BEV). This is most likely due to the increased complexity associated with these cases. It is more complex to generate a treatment plan for the c-shaped target 159  Chapter 7. Conclusion and the nasopharynx cancer patient because the dose constraints are more stringent and also because of the relative location of the critical structures with respect to the target. Complex cases generally require more complex fluence modulation and consequently more flexibility in aperture shaping. The specification of a minimum aperture size was also associated with a reduction in the number of monitor units necessary to deliver the IMRT plan (up to 15 %). This constraint could be applied easily to a clinical situation. Once a satisfactory unconstrained plan is obtained the optimization can be repeated with minimum aperture sizes varying from 0% to 100%. The resulting plans can then be easily assessed to determine if a more simple and efficient plan exists. A test was also designed to evaluate the equispaced collimator angle arrangement proposed in this thesis. Wang et al. have shown that for standard fixed collimator IMRT an optimal collimator angle can be found that favors delivery efficiency [95]. It could then be argued that there would be an advantage to optimize the collimator angles. For this reason optimization of leaf sequences were performed with randomly chosen collimator angles. These treatment plans did not result in a better cost value, suggesting that the equispaced collimator angle arrangement takes full advantage of the flexibility associated with collimator rotation and that there should be no significant benefit in including the collimator angles as optimization parameters. A study was presented to provide a comprehensive evaluation of the capabilities of the rotating aperture optimization technique. Ten nasopharynx recurrence patients were chosen as they present a wide range of complexity with PTVs varying in volume (mean: 143 cm3 , range: 37 cm3 to 421 cm3 ), shape, and proximity to critical structures. For the first part of the study, the focus was to provide a robust comparison of the rotating aperture optimization technique with plans generated with the conventional two-step fluence based optimization approach used by the commercial Eclipse treatment planning system. Interest has grown recently in using DAO for simple treatment sites such as breast patients[76, 77]. Breast IMRT does not usually require highly modulated fluence maps. Here it was shown that the RAO technique can be applied successfully to a more complex treatment site in which highly modulated beams are required. This equivalence was based on (1) the radiation oncologists’ blinded evaluation of DVHs and axial isodoses distribution and (2) numerical com160  Chapter 7. Conclusion parison of dose-volume constraints on target and critical structures as well as mean dose of all critical structures. With respect to delivery efficiency, it was shown that RAO plans required significantly fewer MU than the plans generated with the fluence based approach. Improved MU efficiency has the benefit of less total body scatter and less MLC transmission, reducing the probability of long term complications and secondary malignancies. It was also noted that the RAO plans are more consistent in terms of MU efficiency between patients. This is most likely because the delivery constraints are not taken into account during the fluence based optimization, leading to more complex fluence patterns, and therefore larger number of MU, depending on the patient geometry. With RAO the number of apertures per beam is fixed at the beginning of the optimization, thereby ensuring that the final plan is not unnecessarily complex. The main limitation of the RAO technique is the current rotation speed of the MLC. The Varian CL21EX linac used to deliver the IMRT plans takes 45 seconds to rotate through 180o . It should be noted that this is a mechanical constraint that could be overcome by the manufacturer. Also the delivery process is such that, between each aperture, the collimator rotates before the leaves can move from one position to the next. Clearly it would be more efficient if they were to move simultaneously. It is reasonable to expect that RAO would be faster to deliver than the plans generated with the fluence based approach if these constraints were eliminated. With these simple modifications RAO will take advantage of the delivery efficiency associated with DAO while providing the improved delivery accuracy associated with collimator rotation. For the second part of the RAO evaluation, ten nasopharynx cases were used to provide a comprehensive comparison with a fixed collimator angle DAO. Results indicate that plans generated with collimator rotation are as good or better than fixed collimator plans. This benefit was generally more important for the 1 cm leaf width MLC. This is most likely due to the increased spatial resolution associated with collimator rotation. Although for some cases there was only a minor improvement in the quality of the dose distribution, there tended to be a greater reduction (up to 28% for the complex c-shape target) in the number of MU. With the 5 mm leaf width MLC there were smaller improvements in DVHs and dose distributions when comparing RAO to DAO. However, this could be due to the voxel resolution used for 161  Chapter 7. Conclusion dose calculations. Bortfeld et al.[99] estimate that improvements should be observable for MLCs with leaf widths as small as 2 mm. Based on the fact that similar results are obtained for RAO with 1 cm MLC and DAO with 5 mm MLC, it is reasonable to expect some improvements when comparing RAO with a 5 mm MLC to a nonrotating DAO with 3 mm MLC. A higher dose grid resolution and a smaller CT slice spacing would be required in this case[100]. This could have important implications for stereotactic radiosurgery where so-called micro-MLCs are recommended. SRS patients would particularly benefit from collimator rotation since collimator rotation does provide better spatial resolution. Furthermore, the collimator speed limitations will be relatively less important for these cases since SRS patients require much higher MU (due to high fractional dose). The shape of the MLC leaves can lead to some underdosage at the leaf edges. With DAO, leaf positions are not restricted during the optimization, therefore some leaves may protrude into the beam, which can make DAO more sensitive to effects than the conventional fluence based optimization (Eclipse). Measurements of one cshaped target plan and two nasopharynx recurrence plans show a clear underdosage at the leaf edges for DAO plans with collimator angle set to 00 . Setting to a different collimator angle, 900 for example, would probably help to reduce the error for DAO plans. However with RAO the leaf edges are at different locations for each aperture thereby further minimizing this error. For the three cases presented in chapter 5, a γ analysis indicate that the delivery accuracy is better with RAO than DAO. It was also shown that the RAO delivery accuracy is comparable to plans generated in Eclipse. As part of this thesis a collaboration with two PhD students was initiated. For the first project Monte Carlo was used to generate pencil beam dose distributions for direct aperture optimization IMRT inverse treatment planning. The MC-DAO technique offers a clear benefit by properly modeling traditionally difficult treatment geometries such as small fields and tissue inhomogeneities. The MC-DAO also take advantage of the improved MU efficiency associated with the DAO technique with a 31.5% reduction for the c-shaped target example. The current limitation of the Monte Carlo method is the calculation time needed to calculate the large number of histories required to reduce the statistical uncertainties to an acceptable level. For the second project DAO is proposed for online adaptive radiation therapy 162  Chapter 7. Conclusion (ART). Including ART in the IMRT process has the potential of improving dose distributions delivered to the patient. However, to exploit the full benefit of online ART it is essential that the plan adaptation (optimization) be performed quickly in order to minimize the additional time the patient has to spend on the treatment couch. In this work DAO is proposed as an alternative approach to the conventional fluence based optimization approach to adaptation. Direct optimization of MLC shapes and weights has the potential to rapidly and efficiently re-optimize the original treatment plan. This approach was tested with a prostate deformation model. The results show that the plan re-adaption can be performed more quickly than a complete plan regeneration thereby minimizing the time the patient has to spend in the treatment room.  7.1  Future Work  Modifications could be included to improve the RAO algorithm. For example, the inclusion of a more accurate MLC model (tongue and groove, rounded leaf end) could improve further the delivery accuracy. This would allow the optimization to provide some compensation for perturbations introduced by the leaf design. Without collimator rotation the effect can not be compensated for since it occurs at the leaf edge which is always located at the same place. Also, the number of apertures per beam is fixed at the beginning of the optimization. Li et al.[110] have shown that varying the number of apertures from beam to beam results in a better dose conformity to the target and lower dose to critical structures. It was also shown that assigning suitable number of apertures to different beams according to their complexity results in a decrease in the total number of MU. The results shown in chapter 5 tend to show that RAO would be ideal for Elekta linacs for the following reasons: 1. Elekta’s MLC leaf width is 1 cm and therefore would benefit from the higher spatial resolution offered with collimator rotation. 2. The collimator rotation speed is faster than a Varian linac and the leaves can moves as the collimator rotates. This will overcome the longer treatment times.  163  Chapter 7. Conclusion 3. There is an interdigitation constraint for the Elekta MLCs which can be included directly in the optimization. 4. It was found that the output of the linac may be unstable at low MU. This constraint can be included in the optimization, e.g. a minimum of 3 MUs is specified for each aperture. Preliminary tests were performed on a SL20 Elekta linac which is used for IMRT treatment delivery at the Cancer Center for the Southern Interior (Kelowna, BC). Two treatment plans, i.e. an Eclipse generated plan and a RAO plan, were generated for a prostate patient and the RPC (Radiological Physics Center) head and neck phantom which is designed to test IMRT techniques. This phantom contains two PTVs with different prescriptions (66 Gy and 54 Gy) and a spinal cord like critical structure (shown in figure 7.1). For the prostate patient, treatment plans were generated using the treatment goals specified in section 4.1.2. For the RPC patient the treatment plans were generated with the RPC guidelines. The number of MU and apertures as well as the treatment delivery times for each plan are summarized in table 7.1. These plans take advantage of the benefits associated with collimator rotation without increasing the treatment time. There is actually a decrease in the treatment time associated with the low number of MU and apertures.  164  Chapter 7. Conclusion  Figure 7.1: An axial slice of the RPC patient. PTV 66 Gy is outline in red, PTV 54 Gy is outlined in magenta and the spinal cord like structure is outlined in yellow.  Prostate patient RPC phantom  MU total # apertures treatment time MU total # apertures treatment time  RAO 470 25 ∼6 min. 373 42 ∼8 min.  Eclipse 576 75 ∼10 min. 664 125 ∼12 min.  Table 7.1: Summary of the delivery parameters on an Elekta linac for a prostate patient and the RPC head and neck phantom. The two projects presented in chapter 6 would also benefit from the inclusion of collimator rotation. The MLC characteristics, such as interleaf leakage and the leaf tip shape, are not included during the Monte Carlo optimization. This is because the Monte Carlo calculated pencil beam dose distributions are generated by segmenting an open field phase space. 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Generate the patient contours (representing various structures of interest) in the Varian Eclipse treatment planning system and export to Matlab using a standard DICOM RT data formatting protocol. 2. Uniformly distribute dose calculation points in each structure to be included in the optimization (typical dose resolution grid is set to 2.5 mm). 3. Define the beam arrangement (number of beams, gantry angles, beam energy). 4. Select number of apertures per beam and initialize the leaf sequence for each beam: (a) Initialize the collimator angles so that there is an equal angle between each aperture. (b) Initialize the MLC aperture shapes to outline the target BEV. 5. Define the dose-volume constraints for each structure to be included in the optimization. 6. Calculate the initial dose distribution using the single pencil beam algorithm (full scatter conditions). 7. Optimize the MLC aperture shapes and weights using a simulated annealing algorithm. 8. Import the optimized MLC apertures and weights into Eclipse (using DICOM RT) for a final forward dose calculation.  178  Appendix B Comparison of RAO and fluence based optimization for patients 3-10 DMLC  RAO  100  Volume (%)  80 PTV →  60 ← Brainstem  40  Left Temp. Lobe ↓  20 0  0  20  40 Dose (Gy)  60  Figure B.1: Patient 4: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  179  Appendix B. Comparison of RAO and fluence based optimization for patients 3-10  DMLC  RAO  100  Volume (%)  80 60 PTV Brainstem L.Lobe  40 20 0  0  20  40 Dose (Gy)  60  Figure B.2: Patient 5: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  DMLC  RAO  100  Volume (%)  80 PTV →  60 ← L.Temp.Lobe  40 20 0  ← Chiasm 0  20  40 Dose (Gy)  60  Figure B.3: Patient 6: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  180  Appendix B. Comparison of RAO and fluence based optimization for patients 3-10  DMLC  RAO  100  Volume (%)  80 60 PTV Brainstem L.Lobe R.Optic Nerve  40 20 0  0  20  40 Dose (Gy)  60  Figure B.4: Patient 7: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  DMLC  RAO  100  Volume (%)  80 PTV →  60  ← R.Lobe  40 ← L.Lobe  20 0  0  20  40 Dose (Gy)  60  Figure B.5: Patient 8: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  181  Appendix B. Comparison of RAO and fluence based optimization for patients 3-10  DMLC  RAO  100  Volume (%)  80 60 PTV Chiasm R.Optic Nerve  40 20 0  0  20  40 Dose (Gy)  60  Figure B.6: Patient 9: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  DMLC  RAO  100  Volume (%)  80 60 PTV Brainstem L.Lobe  40 20 0  0  20  40 Dose (Gy)  60  Figure B.7: Patient 10: DVHs for Eclipse using the dynamic delivery method (DMLC) and Rotating Aperture Optimization (RAO).  182  Appendix C Comparison of RAO and direct aperture optimization for patients 3-10 DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV Brainstem Spinal Cord  40 20 0  0  20  40 Dose (Gy)  60  Figure C.1: Patient 3: DVHs for DAO and RAO with the 1 cm leaf width MLC.  183  Appendix C. Comparison of RAO and direct aperture optimization for patients 3-10  DAO 1cm  RAO 1cm  100  Volume (%)  80 60  PTV →  ← Brainstem  40 20 0  Left Temp. Lobe ↓ 0  20  40 Dose (Gy)  60  Figure C.2: Patient 4: DVHs for DAO and RAO with the 1 cm leaf width MLC.  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV Brainstem L.Lobe  40 20 0  0  20  40 Dose (Gy)  60  Figure C.3: Patient 5: DVHs for DAO and RAO with the 1 cm leaf width MLC.  184  Appendix C. Comparison of RAO and direct aperture optimization for patients 3-10  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV L.Lobe Chiasm  40 20 0  0  20  40 Dose (Gy)  60  Figure C.4: Patient 6: DVHs for DAO and RAO with the 1 cm leaf width MLC.  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV Brainstem R.Lobe R.Optic Nerve  40 20 0  0  20  40 Dose (Gy)  60  Figure C.5: Patient 7: DVHs for DAO and RAO with the 1 cm leaf width MLC.  185  Appendix C. Comparison of RAO and direct aperture optimization for patients 3-10  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV L.Lobe R.Lobe  40 20 0  0  20  40 Dose (Gy)  60  Figure C.6: Patient 8: DVHs for DAO and RAO with the 1 cm leaf width MLC.  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV Chiasm R.Optic Nerve  40 20 0  0  20  40 Dose (Gy)  60  Figure C.7: Patient 9: DVHs for DAO and RAO with the 1 cm leaf width MLC.  186  Appendix C. Comparison of RAO and direct aperture optimization for patients 3-10  DAO 1cm  RAO 1cm  100  Volume (%)  80 60 PTV Brainstem  40 20 0  0  20  40 Dose (Gy)  60  Figure C.8: Patient 10: DVHs for DAO and RAO with the 1 cm leaf width MLC.  187  

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