Beam angle optimization for proton therapy via group‐sparsity based angle generation method

Abstract

Background: In treatment planning, beam angle optimization (BAO) refers to the selection of a subset with a given number of beam angles from all available angles that provides the best plan quality. BAO is a NP-hard combinatorial problem. Although exhaustive search (ES) can exactly solve BAO by exploring all possible combinations, ES is very time-consuming and practically infeasible. Purpose: To the best of our knowledge, (1) no optimization method has been demonstrated that can provide the exact solution to BAO,and (2) no study has validated an optimization method for solving BAO by benchmarking with the optimal BAO solution (e.g., via ES), both of which will be addressed by this work. Methods: This work considers BAO for proton therapy,for example,the selection of 2-4 beam angles for IMPT. The optimal BAO solution is obtained via ES and serves as the ground truth. A new BAO algorithm, namely angle generation (AG) method, is proposed, and demonstrated to provide nearly-exact solutions for BAO in reference to the ES solution. AG iteratively optimizes the angular set via group-sparsity (GS) regularization, until the planning objective does not decrease further. Results: Since GS alone can also solve BAO, AG was validated and compared with GS for 2-angle brain, 3-angle lung, and 4-angle brain cases, in reference to the optimal BAO solutions obtained by ES: the AG solution had the rank (1/276, 1/2024, 4/10 626), while the GS solution had the rank (42/276, 279/2024, 4328/10 626). Conclusions: A new BAO algorithm called AG is proposed and shown to provide substantially improved accuracy for BAO from current methods with nearly-exact solutions to BAO, in reference to the ground truth of optimal BAO solution via ES.

Biological optimization for hybrid proton-photon radiotherapy

“…On the other hand, beam angle optimization (BAO) methods could be explored in a future work to improve the optimality for treatment planning, e.g. our recently developed BAO method (Shen et al 2023).…”

“…However, it should be noted that the ICR and ADMM can handle the nonlinear and nonconvex constraints and objectives from direct aperture optimization of VMAT, which has been shown to work for complex treatment planning scenarios (Gao et al 2020b, 2022, 2023c. Additionally, with IMRT, beam angles optimized via BAO (Shen et al 2023) could be performed to further improve Photon or the photon component of Hybrid. The replacement of IMPT by proton ARC (Zhang et al 2022(Zhang et al , 2023a) could potentially further improve Proton or the proton component of Hybrid.…”

A treatment plan optimization method with direct minimization of number of energy jumps for proton arc therapy

“…The IMPT brain plan had four angles, starting with a clinical template of the 'X' shape (i.e. 45°, 135°, 225°, and 315°) and then optimized to 45°,75°,165°and 315°via a beam angle optimization algorithm (Shen et al 2022). The comparison results of IMPT and NEW are presented in table C1, which shows that NEW had better plan quality than IMPT, in terms of improved target coverage (i.e.…”

An orthogonal matching pursuit optimization method for solving minimum‐monitor‐unit problems: Applications to proton IMPT, ARC and FLASH

“…11,12,19,22,24 For example, a post-processing method 9 with simple thresholding of proton spots was used by Varian Eclipse treatment planning system; the spot-reduction method 8,42,43 was proposed to solve the MMU problem, which heuristically handles the MMU constraint by iteratively removing small-weight spots, that is, the smallest m% spot weights are set to 0 every n iterations during a total of N iterations; a mathematically rigorous optimization approach was developed to solve the MMU problem, using alternating direction method of multipliers (ADMM) 7,10,15,22,24,37 ;very recently,a so-called stochastic coordinate descent (SCD) 7 method was proposed to solve the MMU problem with relatively large g. 31 However, the MMU problem with large g remains challenging, as it becomes increasingly difficult to maintain the plan quality (e.g., the conformal dose coverage for tumor target and the low dose for normal tissue) for large value of g. Note that although some methods can have better plan quality than others, this observation of deteriorated plan quality for the MMU problem with large g is intrinsic to the MMU problem, and not specific to an optimization method. To demonstrate this point, we will also compare with another popular optimization algorithm called proximal gradient descent (PGD) method (a generalization of proximal forward-backward splitting or FISTA method) 6,14,20,28,29,33,[38][39][40] that can be used to solve the MMU problem.…”

“…Note that although some methods can have better plan quality than others, this observation of deteriorated plan quality for the MMU problem with large g is intrinsic to the MMU problem, and not specific to an optimization method. To demonstrate this point, we will also compare with another popular optimization algorithm called proximal gradient descent (PGD) method (a generalization of proximal forward‐backward splitting or FISTA method) 6,14,20,28,29,33,38–40 that can be used to solve the MMU problem.…”