Optimization methods for high dose rate brachytherapy treatment planning. Elodie R. Mok Tsze Chung

Transcription

1 Optimization methods for high dose rate brachytherapy treatment planning by Elodie R. Mok Tsze Chung A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto Copyright c 2016 by Elodie R. Mok Tsze Chung

2 Abstract Optimization methods for high dose rate brachytherapy treatment planning Elodie R. Mok Tsze Chung Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto 2016 Optimization approaches for treatment planning in two novel high-dose-rate (HDR) brachytherapy techniques, direction-modulation brachytherapy (DMBT) and energymodulated brachytherapy (EMBT), are investigated for cervical cancer and prostate cancer. Brachytherapy is a form of radiation therapy where a radioactive source is placed inside the body to irradiate the tumour internally. Conventionally, only one source is used and it is unshielded, thus providing an isotropic dose distribution. DMBT makes use of a new shielded applicator that is capable of delivering highly directional radiation distributions. In EMBT, three HDR sources, 192 Ir, 60 Co, and 169 Yb, are used in combination to provide variety in dose profiles. To investigate the benefit of these two new techniques over conventional brachytherapy, we use an inverse planning approach to generate the treatment plans. We model the treatment planning problem as a quadratic program and use an interior point constraint generation algorithm to generate the treatment plans. ii

3 Acknowledgements First and foremost, I would like to thank my two supervisors and mentors, Dr. Dionne Aleman and Dr. William Song for patiently guiding and encouraging me throughout my entire research. This work would not have been possible without their support and expertise. I am grateful to my colleagues and friends from the Medical Operations Research Laboratory and Sunnybrook Health Sciences Centre for their guidance as I embarked on my journey at U of T, as well as their insightful ideas and helpful discussions about my research work. They have helped me overcome many obstacles and I have learned so much from them. Lastly, my biggest thanks go to my family for their everlasting love and support from halfway across the globe. Without them, I would not be the person I am today. As hard as it was to be away from them, their words of encouragement cheered me through the hardships of my degree. I would also like to thank Cole for being my rock over the last two years. iii

4 Contents 1 Introduction Brachytherapy Inverse planning Contributions Publications and presentations Methodology Treatment plan evaluation Optimization model Interior point constraint generation algorithm Direction-modulated brachytherapy DMBT optimization model Results Discussion Conclusion Energy-modulated brachytherapy EMBT optimization model Results Discussion iv

5 4.4 Conclusion Conclusion 49 Bibliography 51 v

6 List of Tables 3.1 Patient information for cervical cancer cancer Plan quality comparison between conventional BT and DMBT Homogeneity index and conformal index for cervical cancer plans Computation time for cervical cancer plans HDR source information Patient information for prostate cancer Clinical protocols for prostate cancer Plan quality summary for the target volume Plan quality summary for the OARs Homogeneity index for the prostate cancer plans Conformal index for the prostate cancer plans Comparison of source combinations to 192 Ir plan Treatment time for prostate cancer plans Breakdown of TRAK for prostate cancer plans Computation time for prostate cancer plans vi

7 List of Figures 1.1 HDR brachytherapy treatment DTO penalty function Linear approximations of a convex function mordirect evaluation window Tandem and ring applicator DMBT tandem Comparison of tandem design Comparison of conventional BT and DMBT plans Comparison of plan quality for a representative cervical case Computation time for DMBT Radial dose functions of 192 Ir, 60 Co, and 169 Yb Depth dose functions of 192 Ir, 60 Co, and 169 Yb Comparison of source combinations to 192 Ir plan Comparison of plan quality for a representative prostate case without DILs Comparison of plan quality for a representative prostate case with DILs Computation time for EMBT vii

8 Chapter 1 Introduction Cancer is the leading cause of death in Canada [9]. In 2015, the Canadian Cancer Society estimated 196,900 new cancer diagnoses and 78,000 deaths [10]. There are several ways to treat cancer, including radiation therapy, chemotherapy, and surgery. In radiation therapy, high energy radiation is directed to the tumour to kill the cancerous cells. The goal is to deliver enough radiation to the tumour while minimizing the dose delivered to the healthy tissues and critical structures surrounding the tumour, known as organs-atrisk (OARs). Radiation therapy can be performed externally or internally. In external beam radiation therapy (EBRT), a machine directs beams of radiation from different directions outside the patient towards the tumour. The radiation must travel through the skin and healthy tissues before reaching the tumour. In internal radiation therapy, also known as brachytherapy, radioactive sources are placed inside the body to deliver radiation to the tumour internally. 1.1 Brachytherapy Different types of brachytherapy can be defined according to three characteristics. The first characteristic is the source placement. In intracavitary brachytherapy, the appli- 1

9 Chapter 1. Introduction 2 cators and the source are placed inside a body cavity near the tumour. This type of brachytherapy is usually used for the treatment of cervical cancer, where the source is placed in the vagina. In interstitial brachytherapy, the applicators in which the source travels are inserted directly into the tumour tissue. Interstitial brachytherapy is commonly used to treat prostate or breast cancer. Other types include intralumenal and intravascular brachytherapy, where the applicators are inserted inside a body lumen (a tubular-shaped structure) and an artery, respectively. The second characteristic is the duration of dose delivery. In temporary brachytherapy, radioactive sources are temporarily implanted inside the body. The time can range from a few minutes to several days. On the other hand, in permanent brachytherapy, small low dose rate radioactive seeds or pellets are permanently placed inside the body and are left to decay. The radiation will decrease with time until it is insignificant and the seeds are safe to remain in the body. The third characteristic is the dose rate, which depends on the energy of the source being used. Brachytherapy is divided into three modalities: high-dose-rate (HDR), lowdose-rate (LDR), and pulse-dose-rate (PDR). HDR brachytherapy sources have a dose rate greater than 12 Gray per hour (Gy/h), while LDR sources have a dose rate smaller than 2 Gy/h. HDR brachytherapy treatments typically lasts for a few minutes and are done in one or several sessions, called fractions. In LDR brachytherapy, the radioactive sources (seeds) are implanted inside the tumour for a few days or permanently. Finally, in PDR brachytherapy, the treatment is delivered in shorter pulses. HDR brachytherapy offers many advantages. Due to the high dose rate of the source, the treatment time is very short and can be mainly carried out on an outpatient basis. Furthermore, it is minimally invasive compared to other treatment types such as surgery. Unlike EBRT, HDR brachytherapy, as well as LDR and PDR brachytherapy, has the advantage of reducing the dose delivered outside the tumour. Hence, it allows for higher amounts of radiation to be prescribed to the tumour with limited exposure of the OARs.

10 Chapter 1. Introduction 3 HDR brachytherapy is also robust to tumour movement inside the body; since the source is placed inside or near the tumour, its position relative to the tumour is generally maintained. Due to the high radioactivity of the source, usually the isotope Iridum-192 ( 192 Ir), treatment cannot be done manually and is instead delivered through a technique called remote afterloading. After the applicators are inserted into the patient (Figure 1.1a), they are connected to a computer-controlled machine, called an afterloader, using guiding tubes (Figure 1.1b). The source is mounted at the end of a wire which is stored in a shielded safe within the afterloader. Once the clinical staff leaves the room, the afterloader is programmed to first send a dummy wire through the applicators to ensure that the path is unobstructed (Figure 1.1c) and then send the HDR source through the guiding tubes to pre-determined points in the applicator known as dwell positions (Figure 1.1d). The source sequentially stays at these dwell positions for a pre-specified amount of time (Figures 1.1e, 1.1f, and 1.1g), known as the dwell time, after which it is pulled out and returned to the shielded safe (Figure 1.1h). The treatment potential of two novel HDR brachytherapy techniques are explored using optimization methods to develop treatment plans. Conventionally, only one HDR source is used during treatment and it is unshielded. The dose distribution about the source is thus isotropic. The first technique is called direction modulated brachytherapy (DMBT) and makes use of a shielded applicator to produce anisotropic dose distributions. The second technique, called energy modulated brachytherapy (EMBT), makes use of three HDR sources, 192 Ir, Cobalt-60 ( 60 Co), and Ytterbium-169 ( 169 Yb), in combination. 1.2 Inverse planning In radiation therapy, including brachytherapy, radiation kills both cancerous and healthy cells. Therefore, treatments must be designed carefully for each patient to achieve an

11 4 Chapter 1. Introduction (a) Applicators inserted in tumour (b) Applicators connected to afterloader (c) Dummy wire sent through applicators (d) Dwell positions along catheters (e) HDR source at the first dwell position (f) HDR source at another dwell position (g) HDR source at the last dwell position (h) HDR source sent back to afterloader Figure 1.1: HDR brachytherapy treatment procedure (Source: com/watch?v=myxl4heccn4)

12 Chapter 1. Introduction 5 accurate treatment plan and a successful outcome. In brachytherapy, the amount of radiation delivered by the source from a dwell position is determined by the corresponding dwell time. Therefore, the selection of dwell positions and dwell times, known as treatment planning, is a critical part of HDR brachytherapy. Treatment plans are typically generated manually, called forward planning. That is, the dwell positions and dwell times are iteratively changed until the desired dose distribution is achieved. The trial-and-error nature of forward planning is time-consuming and the quality of the treatment plans is heavily dependent on the experience and skill of the planner. Alternatively, inverse planning optimization can be used to develop treatment plans to ensure that the best set of dwell positions and dwell times are selected. Inverse planning starts with a set of dosimetric criteria and the anatomical information of the patient obtained from ultrasound (US), computed tomography (CT) or magnetic resonance (MR) images, and then uses optimization techniques to find the optimal set of dwell positions and dwell times that satisfies the clinical objectives. Inverse treatment planning has gained popularity over the last decade [13]. Several mathematical models and solution techniques have been proposed to optimize brachytherapy treatment plans. The optimization techniques can be classified as heuristics or exact methods. Heuristics produce a solution that is assumed to be good enough but cannot be guaranteed to be optimal. Conversely, exact methods provide certainty in the optimality of the solution, but may be computationally intensive. Linear and integer programming are often used to model the brachytherapy treatment planning problem as they can be solved by exact techniques. Linear programming is usually used to optimize the dwell times given fixed dwell positions [5, 27, 28, 35]. They are typically solved using the simplex method [5, 35] or commercial softwares, such as CPLEX [27, 28]. For interstitial brachytherapy, the need to determine the insertion or non-insertion of an applicator requires the use of integer programs to model the treatment

13 Chapter 1. Introduction 6 planning problem. Integer programs and mixed integer programs for brachytherapy have been solved using branch-and-bound algorithms [41, 42, 76] and commercial softwares [17, 23]. While these models can be solved exactly to produce an optimal solution, they become increasingly hard to solve as the problem increases in size, especially with integer programs [75]. As an alternative, heuristics can be used in HDR brachytherapy optimization. They can further be broken down into stochastic or deterministic categories. Stochastic heuristics used in brachytherapy include simulated annealing [15, 30, 32, 37, 43, 44, 74, 77], evolutionary algorithms [38 40, 52, 53, 70], and harmony search [58]. Deterministic heuristics include gradient methods, such as the projected gradient algorithm [25, 81, 82, 85], the Broyden-Fletcher-Goldberg-Shanno algorithm [54], or the Fletcher-Reeves-Polak-Ribiere algorithm [54]. Non-gradient methods include the modified Powell algorithm [54] and an attraction-repulsion model [79]. To combine the guaranteed optimality of an exact method with the speed of a heuristic, we adapt the sector duration optimization (SDO) problem for stereotactic radiosurgery (SRS) [4, 14, 18 20, 56] for our brachytherapy treatment planning problem. This model is similar to the fluence map optimization (FMO) problem for intensity-modulated radiation therapy (IMRT) [1 4, 51, 67 69]. We model the problem as a quadratic program and solve it using an interior point constraint generation (IPCG) algorithm, which was successfully implemented on a SRS inverse planning problem [56]. In SRS, beams of radiation are directed to a point in the tumour, called an isocenter. Meanwhile in brachytherapy, radiation diverges from the source at a dwell position. Dwell positions and dwell times are therefore similar to isocenters and the time of radiation delivery from the beams in SRS, respectively. Since brachytherapy and SRS are analogous, we expect the IPCG algorithm to perform well on brachytherapy inverse planning problems.

14 Chapter 1. Introduction Contributions We contribute to the field of brachytherapy by exploring two new forms of treatment delivery: DMBT for cervical cancer and EMBT for prostate cancer. We show that the DMBT applicator, with its modulating capacity to produce anisotropic dose profiles, allows for superior treatment plans compared to conventional brachytherapy. DMBT especially proves useful in cases where the tumour is asymmetric or extends laterally. Additionally, we demonstrate that the combination of different HDR sources in EMBT allows for better OAR sparing without compromising target coverage. With the introduction of afterloaders equipped with additional wires (i.e., capable of handling a second HDR source) in the market, EMBT is now clinically viable. We also contribute to the literature on HDR brachytherapy inverse planning. We use an exact algorithm to solve a dwell time optimization problem to ɛ-optimality in a finite number of iterations. This algorithm is able to handle large-scale convex problems, which is desirable since the DMBT and EMBT problems are more complex than their conventional counterparts. 1.4 Publications and presentations The following contributions were made to the literature. Publications 1. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman, W. Song. Evaluation of 192 Ir, 60 Co, and 169 Yb sources for high dose rate prostate brachytherapy inverse planning using an interior point constraint generation algorithm. Work in progress. Presentations The underlined text indicate the presenter(s) of the work.

15 Chapter 1. Introduction 8 1. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman, W. Song. Evaluation of 192 Ir, 60 Co, and 169 Yb sources for HDR prostate brachytherapy using an interior point constraint generation algorithm. INFORMS Annual Conference, Nashville, TN, November E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman, W. Song. Evaluation of 192 Ir, 60 Co, and 169 Yb sources for high dose rate prostate brachytherapy inverse planning using an interior point constraint generation algorithm. AAPM Annual Conference, Washington DC. August E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman, W. Song. Evaluation of 192 Ir, 60 Co, and 169 Yb sources for high dose rate prostate brachytherapy inverse planning using an interior point constraint generation algorithm. Mechanical and Industrial Engineering Graduate Research Symposium. University of Toronto, Canada. June 2016.

16 Chapter 2 Methodology In our optimization model, we consider every dwell position along the applicator(s) as a dwell position to be used, thereby ensuring the best possible treatment quality (though potentially at the expense of treatment time). We then use a dwell time optimization (DTO) model to optimize the dwell times of each dwell position so that the final dose distribution meets the clinical objectives as much as possible. Then, we assess the treatment plan quality with common evaluation metrics to determine whether the plans are clinically acceptable or not. 2.1 Treatment plan evaluation Once a patient is diagnosed and scheduled for HDR brachytherapy, s/he is imaged using US, CT or MRI scanners. After the images are obtained, the structures (tumour volume and surrounding OARs) are contoured by a radiation oncologist. The prescription dose and the dose thresholds are obtained from the radiation therapist. The structure volumes are then broken down into 3D pixels, called voxels. Voxels have a size of 1 mm x 1 mm x 1 mm, which depends on the image resolution. The applicators are inserted in the patient and contoured on the planning scans, after which the location of the dwell positions relative to the structures are obtained. The corresponding dwell times can then 9

17 Chapter 2. Methodology 10 be optimized. The most common method to evaluate a treatment plan is to use the cumulative dose-volume histogram (DVH) [62]. A DVH shows the percentage of a structure volume that receives a certain amount of dose or more. The structures can be the target or the OARs. From the DVH curve, clinically relevant DVH parameters are obtained: (1) V x, the structure volume that receives x% of the prescription dose, and (2) D x, the dose received by x% of the structure volume. Ideally, 100% of the tumour volume should receive 100% of the prescription dose (V 100 = 100%), while 100% of the OARS should receive no dose at all. Isodose lines, which are curved lines joining points that receive the same amount of radiation through the target volume overlaid on structure images, are also used to assess the plan quality. There are also a variety of dosimetric indices to assess the quality of a treatment plan. To measure how well the isodose corresponding to the prescription dose covers the target volume, we use the conformal index (COIN) [8]. We also use the homogeneity index (HI) to describe the homogeneity of the dose delivered to the target volume [84]. Both COIN and HI have an ideal value of 1, with values less than 1 indicating worse conformity and homogeneity, respectively. COIN and HI are calculated using the following formulas: COIN = PTV ref PTV PTV ref BV ref HI = V 100 V 150 V 100 where PTV ref is the target volume that is covered by the prescription dose (100% isodose line), and BV ref is the body volume that receives the prescription dose. The treatment time is an important factor to consider in evaluating a treatment plan, since longer treatment times mean that the patient needs to stay in the brachytherapy unit and under anaesthesia for longer. Treatment time is assumed to be a linear sum of the individual dwell times. This definition is not entirely accurate because transition

18 Chapter 2. Methodology 11 time between dwell positions is not accounted for. However, the dwell positions are evenly spaced and hence the transition time should remain constant across plans, and can therefore be ignored for comparison purposes. 2.2 Optimization model Similar to existing optimization models for IMRT [1 4, 51, 67 69] and SRS [4, 14, 18 20, 56], we formulate the brachytherapy treatment planning problem as a quadratic program that minimizes the sum of penalties incurred by deviating from the desired dose per voxel. The only constraints are that the dwell times must be non-negative and bounded. Quadratic programs generally reflect clinical attitudes towards overdose and underdose, i.e., small deviations are more acceptable than large deviations [3, 69]. The DTO model is a basic formulation for brachytherapy treatments using conventional applicators and only one HDR source. Define P as the set of all possible dwell positions along the applicator(s), S as the set of structures, and V s as the voxels in structure s S. The set S consists of the target(s) and all or a subset of the OARs surrounding the target. The decision variables are x i, the dwell time at dwell position i P. The dose delivered to voxel j in structure s, z js, is calculated as z js = i P D ijs x i j V s, s S (2.1) where D ijs is the amount of dose delivered from dwell position i to voxel j in structure s per unit time. These dose coefficients were obtained using the Monte Carlo N-Particle (MCNP) code [22] to simulate the dose distributions around the source in water. All recommendations of the AAPM TG-43 [55, 66] and AAPM-ESTRO [60] reports for HDR brachytherapy sources were considered in the simulation. Each voxel is assigned a penalty for any overdose or underdose it receives. The

19 Chapter 2. Methodology 12 F s (z js ) T_u T_o zjs Figure 2.1: The penalty function of the DTO problem is convex and non-smooth. Note that no penalty is incurred between the lower and upper dose thresholds, T u and T o. penalties are weighted according to the structure to which the voxel belongs so that some structures have a higher priority than others. Additionally, some structures may benefit from an underdose but not an overdose. For example, the penalty weight for underdosing an OAR could be zero. To this end, the penalties for an underdose may be different from the penalties for an overdose. The penalty function for voxel j in structure s is F s (z js ) = 1 V s [w s(z js T s ) w s (T s z js ) 2 +] (2.2) where ( ) + is max{0, }; w s and w s are the overdose and underdose penalties for structure s S, respectively; and T s and T s are the upper and lower dose thresholds for structure s S, respectively. These dose thresholds provide flexibility to the model: If z js lies between T s and T s, then there is no penalty. The penalty function is normalized with respect to the number of voxels in the structure to remove any bias towards structure size. Figure 2.1 illustrates the shape of F s.

20 Chapter 2. Methodology 13 The DTO model is then to minimize the total penalty over all voxels: minimize s S j V s F s (z js ) (DTO) subject to z js = i P D ijs x i j V s, s S 0 x i t max i P where t max is the upper bound on the dwell times. Since the penalty functions F s are convex, the DTO model can be reformulated as a semi-infinite linear optimization (SILO) problem and solved using an interior point constraint generation (IPCG) algorithm developed by Oskoorouchi et al. [56]. A SILO problem is an optimization problem in which there is an infinite number of variables or an infinite number of constraints, but not both. Our DTO-SILO problem has a linear objective and infinitely many linear constraints: minimize δ (DTO-SILO) subject to F s (z js ) δ s S j V s z js = D ijs x i i P j V s, s S 0 x i t max i P The infinite number of constraints come from the constraints used to approximate the convex functions F s (z js ), as shown in Figure 2.2. A graphical user interface (GUI) called mordirect (the Medical Operations Reseach Laboratory s Display for Ranking and Evaluating Customized Treatments) [65] was used to generate treatment plans with ranges of parameter values automatically (Figure 2.3). The best plan was then chosen for each patient according to target coverage and OAR

21 Chapter 2. Methodology 14 Figure 2.2: Linear approximations (blue) of a convex function (black) sparing. mordirect is a multi-criteria decision support system that allows the decisionmaker to easily generate and choose a high-quality plan without the iterative process of identifying suitable model parameters, which is a common characteristic of inverse treatment planning in brachytherapy. 2.3 Interior point constraint generation algorithm The IPCG algorithm was developed to solve a similar model for a SRS inverse planning problem [4, 14, 56]. The algorithm is guaranteed to find an ɛ-optimal solution, unlike heuristics and gradient descent methods, and it was shown to converge to an ɛ-optimal solution in a finite number of iterations. For simplicity, we only present the main idea of the IPCG algorithm. The theoretical aspects and mathematical proofs behind the algorithm can be found in Oskoorouchi et al. [56]. We start with a simpler version of the original problem that only considers a small subset of the constraints, called the reduced problem. An optimal solution to the reduced problem is found and multiple constraints violated by that optimal solution are identified.

22 Chapter 2. Methodology 15 Figure 2.3: mordirect s evaluation window These constraints are added to the reduced problem and at the same time, the barrier function is updated by reducing the barrier parameter. The feasibility of the solution is then recovered, and an optimal solution is found for the new reduced problem. The process is repeated until the duality gap is within ɛ distance, that is, the solution is ɛ-optimal.

23 Chapter 3 Direction-modulated brachytherapy Using conventional intracavitary applicators, such as the tandem and ring applicator (Figure 3.1), with isotropic sources limits the maximal dose delivered to the tumour, especially in cases where the target volume is laterally extended or non-symmetric. To prevent the overdose of OARs, parts of the target volume must be underdosed, leading to less conformal plans. To address the lack of shielded intrauterine tandem applicators for cervical cancer brachytherapy and build on the concept of anisotropic dose profiles [15], a novel tandem applicator, called the DMBT tandem (Figure 3.2), was proposed that is able to produce anisotropic dose distributions [25]. The tandem can generate directional radiation dose profiles through its intelligent shielding design to achieve superior target coverage (Figure 3.3). DMBT was theoretically studied on rectal cancer [81, 82], breast cancer [83], and cervical cancer [25, 26, 71 73]. The DMBT tandem is symmetric along the transverse and longitudinal axes. It has six peripheral holes of width 1.3 mm grooved along a non-magnetic tungsten alloy (95% tungsten, 3.5% nickel, and 1.5% copper, ρ = 18 g/cm 3 ), enclosed in a 0.3 mm thick plastic sheath. The DMBT tandem diameter is no larger than 6 mm, the dimension of a conventional tandem. Thus, it can be readily used with existing tandem-and-ring 16

24 Chapter 3. Direction-modulated brachytherapy 17 Tandem Interstitial/needles (optional) Ring Figure 3.1: Tandem and ring applicator. The HDR source can travel through the ring and the tandem. (Adapted from Viswanathan et al. [80]) Figure 3.2: DMBT tandem (Source: Han et al. [26]) applicators. Furthermore, the paramagnetic tungsten alloy renders the DMBT tandem MRI-safe. The high density of the tungsten alloy allows the rod to be used as a shield to block part of the radiation. With the grooves equally spaced at 60, highly directional beams of radiation can be delivered in six different directions, which is a sharp contrast to the near-circular, or isotropic, dose distribution obtained from a conventional tandem that has no shielding. To evaluate the modulating capacity of the DMBT tandem, we use our inverse planning approach to develop treatment plans for both conventional brachytherapy (conven-

25 Chapter 3. Direction-modulated brachytherapy mm 6.0 mm (a) Conventional tandem 6.0 mm (b) DMBT tandem (c) Isotropic dose distribution from conventional tandem (d) Anisotropic dose distribution from DMBT tandem Figure 3.3: Cross-sections of conventional and DMBT tandems

26 Chapter 3. Direction-modulated brachytherapy 19 tional BT) and DMBT for cervical cancer, and then compare the plan quality. We use the DTO formulation to model the conventional BT problem and then solve it using the IPCG algorithm. 3.1 DMBT optimization model The optimization model for DMBT is a slight modification of the DTO model. In addition to the parameters previously defined, let C be the set of channels grooved along the tandem applicator, where C = 6. The dwell positions (in the ring and in the tandem) are fixed to the positions used in the clinical treatments. The decision variables for DMBT-DTO are x ic, the dwell time at dwell position i P in channel c C, as opposed to x i for conventional brachytherapy. The dose delivered to voxel j in structure s, z js, is calculated as z js = D icjs x ic j V s, s S (3.1) c C i P where D icjs is the amount of dose delivered from dwell position i to voxel j in structure s per unit time along channel c. Using the same penalty function F s (z js ) (Equation 2.2), the DMBT-DTO problem is then minimize subject to s S j V s F s (z js ) z js = c C D icjs x ic i P j V s, s S (DMBT-DTO) 0 x ic t max i P, c C where t max is the upper bound on the dwell times.

27 Chapter 3. Direction-modulated brachytherapy Results Twenty-seven clinical cervical cancer cases obtained from Aarhus University Hospital (Aarhus, Denmark) are studied retrospectively. The target volume and the OARs (bladder, rectum, and sigmoid) were contoured on T2w MR images and treatment plans were generated using the BrachyVision TM (Varian Medical Systems, Palo Alto, CA, USA) treatment planning system. The prescription dose was 15 Gy or 17.5 Gy. All patients were treated using a tandem and ring applicator and an 192 Ir pulsed-dose-rate source, with source strength normalized to one Curie (Ci). The results can be converted back to match a 10 Ci source, which is typical in HDR brachytherapy. The clinical details of the cases are shown in Table 3.1. To ensure that any improvement solely resulted from the modulating capacity of the DMBT tandem, the ring was left untouched in both the conventional BT and DMBT setup and only the tandem was replaced. To evaluate the quality of treatment plans, all plans were normalized to receive their respective clinical target volume D 90 values. D 2cc, the dose to the hottest 2 cm 3 of the structure volume, was calculated for the three OARs, as well as COIN and HI. On average, DMBT improved the sparing of all three OARs (Table 3.2). The percent improvement in OAR D 2cc is illustrated in Figure 3.4. The dose delivered to the bladder, rectum, and sigmoid was reduced by 6.4%, 12.5%, and 2.6%, respectively. The corresponding maximum decrease was 17.2%, 43.3%, and 16.7%, respectively. In 23 out of 27 cases (85%), DMBT plans were superior to the conventional BT plans for all three OARs. The COIN and HI values are shown in Table 3.3. In terms of conformity, 25 of 27 (92.5%) DMBT plans are more conformal than the conventional BT plans. The mean COIN values for conventional BT and DMBT plans were 0.47 ± 0.07 (mean ± standard deviation) and 0.55 ± 0.08, respectively. With regards to homogeneity, the DMBT plans and conventional BT plans exhibit no clear relationship, but they are comparable on

28 Chapter 3. Direction-modulated brachytherapy 21 Table 3.1: Patient information Number of dwell positions Patient ID Target vol. (cc) Conventional BT DMBT Rx dose (Gy) Mean Stdev

29 Chapter 3. Direction-modulated brachytherapy 22 Table 3.2: OAR dose metrics for the conventional BT plans and the DMBT plans. A negative value (shaded) means that the DMBT plan improves on the conventional BT plan. The maximum decrease is bolded. D 2cc Bladder (Gy) D 2cc Rectum (Gy) D 2cc Sigmoid (Gy) Patient Conventional Conventional Conventional DMBT % Diff DMBT % Diff DMBT ID BT BT BT % Diff Mean Stdev

30 Chapter 3. Direction-modulated brachytherapy Percent change Bladder Rectum Sigmoid Case number Figure 3.4: Pairwise difference between the conventional BT and DMBT plans for all 27 cases. average. The mean HI was of 0.31 ± 0.08 for the conventional BT plans and 0.30 ± 0.06 for the DMBT plans. The DVH and isodose lines for a representative case (Patient 4) are shown in Figure 3.5 to illustrate the benefits of the DMBT tandem. The DVHs (Figure 3.5a) show that the target receives the required prescription dose in both plans while the dose to the three OARs decreases in the DMBT plans. The corresponding slices (Figure 3.5b) further illustrate the OAR sparing, as well as the superior conformity of the DMBT plans. The average IPCG computation time for conventional BT plans was 0.4 min for a mean of 31 dwell positions and 1.1 min for a mean of 89 dwell positions for DMBT plans (Table 3.4). As expected, the DMBT computation times are consistently longer than their corresponding conventional BT times since the number of variables increases when the DMBT tandem applicator is used. Figure 3.6 shows that the computation time is quadratic with the number of dwell positions, despite the exponential complexity of the algorithm [18].

31 Chapter 3. Direction-modulated brachytherapy 24 Table 3.3: Homogeneity index and conformal index. The better index value is shaded. HI COIN Patient ID Conventional Conventional DMBT BT BT DMBT Mean Stdev

32 Chapter 3. Direction-modulated brachytherapy HRCTV Bladder Rectum Sigmoid 70 Percent volume (%) Percent dose (%) (a) Dose-volume histogram (b) Slices with 100% and 50% isodose lines Figure 3.5: Comparison between a conventional BT plan (dashed lines) and a DMBT plan (solid lines) for a representative case.

33 Chapter 3. Direction-modulated brachytherapy 26 Table 3.4: Computation time in minutes for the conventional BT and DMBT plans Conventional BT DMBT Patient ID # dwell positions Comp. time # dwell positions Comp. time Mean Stdev

34 Chapter 3. Direction-modulated brachytherapy Conventional BT DMBT Best fit: Quadratic Computation time (min) Number of dwell positions Figure 3.6: Computation time for DMBT as a function of number of dwell positions. 3.3 Discussion Treatment planning for cervical cancer can be challenging, especially with the presence of asymmetric or bulky tumours. We have shown that the DMBT tandem, with its ability to generate highly directional beams of radiation, allows for clinically significant reduction in dose to the OARs without compromising the target coverage. Furthermore, the results are independent of the tumour size. The dose homogeneity is maintained from the conventional BT plans to the DMBT plans, while conformity is significantly improved clinically in the DMBT plans. Since a prototype has already been constructed, the next step is to obtain approval for DMBT clinical trials. Our results also indicate that the inverse planning approach used in SRS [4, 14, 56] can be successfully implemented in HDR brachytherapy. High quality treatment plans were obtained in less than two minutes. While these times are comparable to, say, simulated annealing run times previously used in brachytherapy inverse planning [43], we are able to guarantee the optimality of our results. If the planner is not satisfied

35 Chapter 3. Direction-modulated brachytherapy 28 with the plan obtained, new plans can be quickly generated within a few minutes. To avoid such situations, we used mordirect [65] as a complementary tool to choose the best treatment plans according to our criteria. The short computation time of the IPCG algorithm is advantageous when running several trials through mordirect. 3.4 Conclusion We investigated the dosimetric benefits of DMBT on 27 cervical cancer cases with different tumour sizes. The DMBT plans achieved lower OAR doses than the conventional BT plans while maintaining similar target coverage. An alternative interpretation of these results is that for the same OAR exposure to radiation, the dose to the target can be safely escalated, thus potentially improving tumour control and treatment outcome. In terms of algorithm performance, we showed that a quadratic penalty optimization approach combined with IPCG [56], similar to approaches in radiosurgery inverse planning [4, 14, 18 20, 56], performs well for HDR brachytherapy inverse planning problems. Good quality treatment plans were generated within a few minutes of run time. Additionally, the treatment time obtained were all clinically acceptable.

36 Chapter 4 Energy-modulated brachytherapy The radionuclides 192 Ir and 60 Co are commonly used as sources in HDR brachytherapy, but other nuclides, such as 169 Yb, have also been previously used as HDR sources [50]. While the use of these individual radionuclides as HDR sources has been studied, the use of two or more radionuclides in combination, or EMBT, has yet to be investigated on prostate cancer. If used together, the different dose profiles of these radioactive sources can potentially improve OAR sparing. The dosimetric benefits of EMBT were successfully investigated on cervical cancer using 192 Ir, 60 Co, and 169 Yb [71, 73]. A quadratic penalty model (with same penalty for overdose and underdose of a structure) and a projected gradient algorithm [25] were used to develop the treatment plans for single- and dualsource combinations and only the DMBT tandem was used (instead of the conventional tandem). Since the DMBT tandem alone allows for superior plan quality, we assess the potential advantages of EMBT only on prostate cancer. Furthermore, we also consider using all three sources in combination. Recently, in addition to irradiating the whole prostate gland, regions of the prostate with the highest tumour concentration have been prescribed higher doses [29]. These regions are called dominant intraprostatic lesions (DILs) and they are now a new focus of HDR prostate brachytherapy [29]. The expectation is that recurrence is less likely to 29

37 Chapter 4. Energy-modulated brachytherapy 30 happen when DILs are identified and boosted [33]. EMBT may allow safer dose escalation to the DILs while limiting the dose to the OARs. 192 Ir is the most common radioactive source for HDR brachytherapy [64, 78]. Due to its high specific activity, which is defined as the rate at which unstable nuclei decay per unit mass, the radioactive source can be made small enough to be inserted in the body while keeping a significantly high activity, which is essential for HDR purposes. However, the source has a short half-life of 74 days, which means that it needs to be replaced every three to four months to maintain acceptable treatment times. 60 Co sources are now commercially available in the same geometric dimensions as 192 Ir, and are comparable with 192 Ir with respect to clinical aspects for HDR prostate brachytherapy [31, 64, 78]. However, 60 Co s longer half-life of approximately five years means that it does not need to be replaced frequently, leading to fewer source exchanges. Thus, 60 Co has a lower operating cost, and can be a cheaper alternative for developing countries [7, 64]. 169 Yb, with a half-life of 32 days, has also been investigated as a potential HDR source [11, 47, 59]. It has been shown to be at least equivalent to 192 Ir in terms of dosimetry [36, 45, 46], with reduced radiation protection and shielding requirements due to its lower energy [24]. Afterloaders that can handle two sources, such as the Multisource R afterloader from Eckert & Ziegler BEBIG [16], have already been introduced on the market. However, such afterloaders cannot handle both sources at the same time [57]. Recently, a new afterloader capable of handling two different sources simultaneously was proposed by Elekta (Flexitron R, Elekta Brachytherapy, Veenendaal, The Netherlands). Furthermore, the machine is equipped to handle 192 Ir, 60 Co, or 169 Yb. We therefore investigate the dosimetric benefits of EMBT for every possible combination of 192 Ir, 60 Co, and 169 Yb, and then compare treatment quality to the 192 Ir-only plan. The DTO model is used in combination with the IPCG algorithm to generate the single-source plans.

38 Chapter 4. Energy-modulated brachytherapy 31 Table 4.1: HDR source information Length Diameter Energy Activity Half-life Source Model Manufacturer (mm) (mm) (kev) (Ci) (days) microselectron 192 Ir Nucletron v2 60 Co Co0.A Yb 4140 Eckert & Ziegler BEBIG Implant Sciences Corporation EMBT optimization model Based on the DTO model, we formulate the EMBT-DTO problem as follows. In addition to the previously defined parameters, let R be the set of sources, where R = 3 in our study. The dwell positions, evenly spaced at intervals (which vary per case), are fixed to the positions used in the clinical treatments.the decision variables are x ir, the dwell time of source r R at dwell position i P. The dose delivered to voxel j in structure s, z js, is calculated as z js = r R D irjs x ir j V s, s S (4.1) i P where D irjs is the amount of dose delivered from dwell position i to voxel j in structure s per unit time from source r. Details about the sources are shown in Table 4.1. Their radial and depth dose functions are plotted against the distance from the middle of each source in Figures 4.1 and 4.2, respectively.

39 Chapter 4. Energy-modulated brachytherapy Ir 192 Co 60 Yb 169 Radial dose function Distance (cm) Figure 4.1: Radial dose function of 192 Ir, 60 Co, and 169 Yb normalized at 1 cm Ir 192 Co 60 Yb 169 Depth dose Distance (cm) Figure 4.2: Depth dose function of 192 Ir, 60 Co, and 169 Yb normalized at 1 cm.

40 Chapter 4. Energy-modulated brachytherapy 33 Using the same penalty function F s (z js ) (Equation 2.2), the EMBT-DTO problem is minimize subject to s S j V s F s (z js ) z js = r R D irjs x ir j V s, s S (EMBT-DTO) i P 0 x ir t max i P, r R where t max is the upper bound on the dwell times. 4.2 Results We test our approach retrospectively on 12 anonymized HDR prostate cases treated at the Odette Cancer Centre, Sunnybrook Health Sciences Centre (Toronto, ON, Canada) (Table 4.2). The structures (prostate, DILs, urethra, and rectum) were contoured on the planning scans and treatment plans were generated using the Oncentra Brachy R (Nucletron, Veenendaal, The Netherlands) treatment planning system. For planning purposes, the cases were separated into two groups: Group A patients have the prostate as the main target volume, while Group B patients have DILs as secondary targets in addition to the prostate. DILs are prescribed 150% of the prescription dose. All patients were treated with the Nucletron microselectron HDR-version 2 (mhdr-v2) 192 Ir source and followed the clinical protocol shown in Table 4.3. The plans were separated into three categories: (1) single-source with Co, Ir, and Yb individually; (2) double-source with the pairs Co-Ir, Co-Yb, and Ir-Yb; and (3) triplesource with Co-Ir-Yb (assuming future developments in afterloader technology allows for triple-source delivery). There were a total of seven treatment plans per patient. For fair comparison, all plans were normalized to the clinical prostate V 100 and where applicable, the clinical DIL V 150. In addition to reporting the DVH parameters presented in Table 4.3, COIN and HI are also calculated.

41 Chapter 4. Energy-modulated brachytherapy 34 Table 4.2: Patient information. Group A patients have the prostate as main target volume, and Group B patients have DILs as secondary targets. Group A Patient ID Target vol. # # Dwell Rx dose (cc) Applicators positions (Gy) Mean 38.1 Stdev 11.4 B Mean 30.6 Stdev 8.5 Table 4.3: Clinical protocols Target DILs Urethra Rectum V % V 150 = 100 % D max 130 % D max 90 % V 150 < 35 % - D % V cc V 200 < 12 % - - -

42 Chapter 4. Energy-modulated brachytherapy 35 Table 4.4: Average values ± standard deviation of target DVH parameters and indices. Group A patients have the prostate as main target volume, and Group B patients have DILs as secondary targets. Group Plan V 150 (%) V 200 (%) HI COIN A B Clinical 37.6 ± ± ± ± 0.04 Ir 27.3 ± ± ± ± 0.03 Co 29.1 ± ± ± ± 0.03 Yb 24.8 ± ± ± ± 0.03 Co-Ir 29.8 ± ± ± ± 0.03 Co-Yb 29.0 ± ± ± ± 0.03 Ir-Yb 26.7 ± ± ± ± 0.04 Co-Ir-Yb 28.6 ± ± ± ± 0.02 Clinical 34.1 ± ± ± ± 0.04 Ir 32.1 ± ± ± ± 0.06 Co 33.7 ± ± ± ± 0.05 Yb 30.9 ± ± ± ± 0.06 Co-Ir 33.9 ± ± ± ± 0.06 Co-Yb 33.9 ± ± ± ± 0.06 Ir-Yb 31.9 ± ± ± ± 0.06 Co-Ir-Yb 33.5 ± ± ± ± 0.05 On average, treatment plans generated from all combinations achieve the clinical objectives for both targets (Table 4.4) and OARs (Table 4.5). As expected, Group B patients have higher V 150 and V 200 values than Group A patients due to the presence of DILs. Additionally, source combinations that include 60 Co generate plans with higher V 150 and V 200 values than the conventional Ir-only plans, due to the higher energy of 60 Co. Yb-only plans have the lowest V 150 and V 200 values since 169 Yb has the lowest energy. The HI and COIN values are presented in Tables 4.6 and 4.7, respectively. The column with the heading Clinical 192 Ir shows the clinical treatment values. With the exception of Patient 12, all optimized Ir-only plans have better HI values than the clinical Ir plans. Source combinations that include 60 Co generate plans that are slightly less homogeneous