Beam Angle Optimization Problem Research Articles

TBS-BAO: fully automated beam angle optimization for IMRT guided by a total-beam-space reference plan

Properly selected beam angles contribute to the quality of radiotherapy treatment plans. However, the beam angle optimization (BAO) problem is difficult to solve to optimality due to its non-convex discrete nature with many local minima. In this study, we propose TBS-BAO, a novel approach for solving the BAO problem, and test it for non-coplanar robotic CyberKnife radiotherapy for prostate cancer. First, an ideal Pareto-optimal reference dose distribution is automatically generated using a priori multi-criterial fluence map optimization (FMO) to generate a plan that includes all candidate beams (total-beam-space, TBS). Then, this ideal dose distribution is reproduced as closely as possible in a subsequent segmentation/beam angle optimization step (SEG/BAO), while limiting the number of allowed beams to a user-selectable preset value. SEG/BAO aims at a close reproduction of the ideal dose distribution. For each of 33 prostate SBRT patients, 18 treatment plans with different pre-set numbers of allowed beams were automatically generated with the proposed TBS-BAO. For each patient, the TBS-BAO plans were then compared to a plan that was automatically generated with an alternative BAO method (Erasmus-iCycle) and to a high-quality manually generated plan. TBS-BAO was able to automatically generate plans with clinically feasible numbers of beams (∼25), with a quality highly similar to corresponding 91-beam ideal reference plans. Compared to the alternative Erasmus-iCycle BAO approach, similar plan quality was obtained for 25-beam segmented plans, while computation times were reduced from 10.7 hours to 4.8/1.5 hours, depending on the applied pencil-beam resolution in TBS-BAO. 25-beam TBS-BAO plans had similar quality as manually generated plans with on average 48 beams, while delivery times reduced from 22.3 to 18.4/18.1 min. TBS reference plans could effectively steer the discrete non-convex BAO.

Beam angle optimization in IMRT: are we really optimizing what matters?

AbstractIntensity‐modulated radiation therapy (IMRT) is a modern radiotherapy modality that uses a multileaf collimator to enable the irradiation of the patient with nonuniform maps of radiation from a set of distinct beam irradiation directions. The aim of IMRT is to eradicate all cancerous cells by irradiating the tumor with a prescribed dose while simultaneously sparing, as much as possible, the neighboring tissues and organs. The optimal choice of beam irradiation directions—beam angle optimization (BAO)—can play an important role in IMRT treatment planning by improving organ sparing and tumor coverage, increasing the treatment plan quality. Typically, the BAO search is guided by the optimal value of the fluence map optimization (FMO)—the problem of obtaining the most appropriate radiation intensities for each beam direction. In this paper, a new score to guide the BAO search is introduced and embedded in a parallel multistart derivative‐free optimization framework that is detailed for the extremely challenging continuous BAO problem. For the set of 10 clinical nasopharyngeal tumor cases considered, treatment plans obtained for optimized beam directions clearly outperform the benchmark treatment plans obtained considering equidistant beam directions typically used in clinical practice. Furthermore, treatment plans obtained considering the proposed score clearly improve the quality of the plans resulting from the use of the optimal value of the FMO problem to guide the BAO search.

A matheuristic approach to solve the multiobjective beam angle optimization problem in intensity‐modulated radiation therapy

AbstractSelecting a suitable set of beam angles is an important but difficult task in intensity‐modulated radiation therapy (IMRT) for cancer treatment. From a single objective point of view, this problem, known as the beam angle optimization (BAO) problem, is solved by finding a beam angle configuration (BAC) that leads to the best dose distribution, according to some objective function. As there exists a trade‐off between the main goals in IMRT (to irradiate the tumor according to some prescription and to avoid surrounding healthy tissue), it makes sense to solve this problem from a multiobjective (MO) point of view. When doing so, a solution of the BAO problem is no longer a single BAC, but instead a set of BACs that lead to a set of dose distributions that, depending on both dose prescription and physician preferences, can be selected as the preferred treatment. We solve this MO problem using a two‐phase strategy. During the first phase, a deterministic local search algorithm is used for selecting a set of locally optimal BACs, according to a single‐objective function. During this search, an optimal dose distribution for each BAC, with respect to the single‐objective function, is calculated using an exact nonlinear programming algorithm. During the second phase, a set of nondominated points is generated for each promising locally optimal BAC and a dominance analysis among them is performed. The output of the procedure is a set of (approximately) efficient BACs that lead to good dose distributions. To demonstrate the viability of the method, the two‐phase strategy is applied to a prostate case.

Noncoplanar beam angle optimization in IMRT treatment planning using pattern search methods

Radiation therapy is used to treat localized cancers, aiming to deliver a dose of radiation to the tumor volume to sterilize all cancer cells while minimizing the collateral effects on the surrounding healthy organs and tissues. The planning of radiation therapy treatments requires decisions regarding the angles used for radiation incidence, the fluence intensities and, if multileaf collimators are used, the definition of the leaf sequencing. The beam angle optimization problem consists in finding the optimal number and incidence directions of the irradiation beams. The selection of appropriate radiation incidence directions is important for the quality of the treatment. However, the possibility of improving the quality of treatment plans by an optimized selection of the beam incidences is seldom done in the clinical practice. Adding the possibility for noncoplanar incidences is even more rarely used. Nevertheless, the advantage of noncoplanar beams is well known. The optimization of noncoplanar beam incidences may further allow the reduction of the number of beams needed to reach a clinically acceptable plan. In this paper we present the benefits of using pattern search methods for the optimization of the highly non-convex noncoplanar beam angle optimization problem.

SU‐F‐BRD‐08: Guaranteed Epsilon‐Optimal Treatment Plans with Minimum Number of Beams for SBRT Using RayStation

Purpose:To efficiently find quality‐guaranteed treatment plans with the minimum number of beams for stereotactic body radiation therapy using RayStation.Methods:For a pre‐specified pool of candidate beams we use RayStation (a treatment planning software for clinical use) to identify the deliverable plan which uses all the beams with the minimum dose to organs at risk (OARs) and dose to the tumor and other structures in specified ranges. Then use the dose matrix information for the generated apertures from RayStation to solve a linear program to find the ideal plan with the same objective and constraints allowing use of all beams. Finally we solve a mixed integer programming formulation of the beam angle optimization problem (BAO) with the objective of minimizing the number of beams while remaining in a predetermined epsilon‐optimality of the ideal plan with respect to the dose to OARs. Since the treatment plan optimization is a multicriteria optimization problem, the planner can exploit the multicriteria optimization capability of RayStation to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing quality. For the numerical experiments two liver cases and one lung case with 33 non‐coplanar beams are considered.Results:The ideal plan uses an impractically large number of beams. The proposed technique reduces the number of beams to the range of practical application (5 to 9 beams) while remaining in the epsilon‐optimal range of 1% to 5% optimality gap.Conclusion:The proposed method can be integrated into a general algorithm for fast navigation of the ideal dose distribution Pareto surface and finding the treatment plan with the minimum number of beams, which corresponds to the delivery time, in epsilon‐optimality range of the desired ideal plan.The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and partially by RaySearch Laboratories.

Pattern search methods framework for beam angle optimization in radiotherapy design

The selection of appropriate beam directions is decisive for the quality of the treatment, both for maximizing tumor doses and for organs sparing. However, the beam angle optimization (BAO) problem is still an open problem and, most of the time, beam directions continue to be manually selected in clinical practice which requires many trial and error iterations between selecting beam angles and computing fluence patterns until a suitable treatment is achieved. The goal of BAO is to improve the quality of the directions used and, at the same time, release the treatment planner for other tasks. The objective of this paper is to introduce a new approach for the resolution of the BAO problem, using pattern search methods to tackle this highly non-convex optimization problem. Pattern search methods are derivative-free optimization methods with the ability to avoid local entrapment. Moreover, they require few function value evaluations to progress and converge. These two characteristics gathered together make pattern search methods suited to address the BAO problem. A set of clinical examples of head-and-neck cases is used to discuss the benefits of using pattern search methods in the optimization of the BAO problem.

MO‐A‐137‐03: Effective Heuristic Cuts for Beam Angle Optimization in Radiation Therapy

Purpose: To improve the solution efficiency (i.e., reducing computation time while obtaining high‐quality treatment plans) for the beam angle optimization problem (BAO) in radiation therapy treatment planning. Methods: We formulate BAO as a mixed integer programming problem (MIP) whose solution gives the optimal beam orientation as well as optimal beam intensity map. We then incorporate a family of heuristic cuts into the resultant MIP based on the observation that the number of candidate beams is usually much larger than the number of beams used in the treatment plan, and therefore, it is less likely that adjacent beams are simultaneously used in the optimal treatment plan. The proposed cuts, referred to as ((neighbor cuts)), force the optimization system to choose one or a few beams from any set of adjacent beams. As a Result, the search space and the computation time are reduced considerably. The neighbor cuts can be added to any MIP formulation for BAO including the cases of coplanar/noncoplanar beams for intensity modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT). For the numerical experiments a liver case (both IMRT and SBRT) with 34 and a head and neck case (only IMRT) with 36 coplanar beams were considered. Each beam was divided into 109‐144 beamlets of size 1*1 cm2. Results: We first solved the corresponding MIP without the neighbor cuts and recorded the optimal solution and the computation time. Then we incorporated the neighbor cuts into the MIP and resolved it. Our results show that incorporating the neighbor cuts into the MIP reduces the computation time considerably and results in solutions with negligible optimality gaps. Conclusion: This research incorporates the observation that optimal beam configurations are typically a sparse set of well‐spaced beams to improve the efficiency of the solution technique drastically. The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and also partially by RaySearch laboratories.

TH-A-116-08: Guaranteed Epsilon-Optimal Treatment Plans with Minimum Number of Beams for Stereotactic Body Radiation Therapy

Purpose: To efficiently find quality‐guaranteed treatment plans with the minimum number of beams for stereotactic body radiation therapy (SBRT). Methods: We formulate the beam angle optimization problem (BAO) as a mixed integer programming problem (MIP) whose solution gives the optimal beam orientation as well as optimal beam intensity. We first allow use of all candidate beams and find the ' 'ideal plan' ' with the objective of minimizing dose to organs at risk (OARs) while keeping the dose to the tumor and other structures in specified ranges. Then we resolve the MIP with the objective of minimizing the number of beams while remaining in a predetermined epsilon‐optimality of the ideal plan with respect to the dose to OARs. Since the treatment plan optimization is a multicriteria optimization problem, the planner can navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing epsilon‐optimality. To reduce the computation time, we use a family of heuristic cuts, known as ((neighbor cuts)) while preserving epsilon‐optimality. For the numerical experiments a liver case with 34 and a lung case with 36 coplanar beams were considered. Results: The ideal plan uses an impractically large number of beams. The proposed technique reduced the number of beams to the range of practical application (5 to 9 beams) while remaining in the epsilon‐optimal range of 1% to 5% optimality gap. Adding the neighbor cuts reduced the computation time considerably. Conclusion: The proposed method can be integrated into a general algorithm for fast navigation of the ideal dose distribution Pareto surface and finding the treatment plan with the minimum number of beams, which corresponds to the delivery time, in epsilon‐optimality range of the desired ideal plan. The project was supported by the Federal Share of program income earned by Massachusetts; General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and also partially by RaySearch laboratories.

Beam angle optimization for intensity-modulated radiation therapy using a guided pattern search method

Generally, the inverse planning of radiation therapy consists mainly of the fluence optimization. The beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) consists of selecting appropriate radiation incidence directions and may influence the quality of the IMRT plans, both to enhance better organ sparing and to improve tumor coverage. However, in clinical practice, most of the time, beam directions continue to be manually selected by the treatment planner without objective and rigorous criteria. The goal of this paper is to introduce a novel approach that uses beam’s-eye-view dose ray tracing metrics within a pattern search method framework in the optimization of the highly non-convex BAO problem. Pattern search methods are derivative-free optimization methods that require a few function evaluations to progress and converge and have the ability to better avoid local entrapment. The pattern search method framework is composed of a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and ensures the convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Beam’s-eye-view dose metrics assign a score to each radiation beam direction and can be used within the pattern search framework furnishing a priori knowledge of the problem so that directions with larger dosimetric scores are tested first. A set of clinical cases of head-and-neck tumors treated at the Portuguese Institute of Oncology of Coimbra is used to discuss the potential of this approach in the optimization of the BAO problem.

Selection of intensity modulated radiation therapy treatment beam directions using radial basis functions within a pattern search methods framework

The selection of appropriate radiation incidence directions in radiation therapy treatment planning is important for the quality of the treatment plan, both for appropriate tumor coverage and for better organ sparing. The objective of this paper is to discuss the benefits of using radial basis functions within a pattern search methods framework in the optimization of the highly non-convex beam angle optimization (BAO) problem. Pattern search methods are derivative-free optimization methods that require few function value evaluations to converge and have the ability to avoid local entrapment. These two characteristics gathered together make pattern search methods suited to address the BAO problem. The pattern search methods framework is composed by a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and assures convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Radial basis functions are used and tested in this step both to influence the quality of the local minimizer found by the method and to obtain a better coverage of the search space in amplitude. A set of retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of using this approach in the optimization of the BAO problem.

A Feasible Solution to the Beam-Angle-Optimization Problem in Radiotherapy Planning With a DNA-Based Genetic Algorithm

Intensity-modulated radiotherapy (IMRT) is now becoming a powerful clinical technique to improve the therapeutic radio for cancer treatment. It has been demonstrated that selection of suitable beam angles is quite valuable for most of the treatment plans, especially for the complicated tumor cases and when limited number of beams is used. However, beam-angle optimization (BAO) remains a challenging inverse problem mainly due to the huge computation time. This paper introduced a DNA genetic algorithm (DNA-GA) to solve the BAO problem aiming to improve the optimization efficiency. A feasible mapping was constructed between the universal DNA-GA algorithm and the specified engineering problem of BAO. Specifically, a triplet code was used to represent a beam angle, and the angles of several beams in a plan composed a DNA individual. A bit-mutation strategy was designed to set different segments in DNA individuals with different mutation probabilities; and also, the dynamic probability of structure mutation operations was designed to further improve the evolutionary process. The results on simulated and clinical cases showed that DNA-GA is feasible and effective for the BAO problem in IMRT planning, and to some extent, is faster to obtain the optimized results than GA.

A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning

Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated.