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

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.

Energy layer optimization via energy matrix regularization for proton spot-scanning arc therapy.

PURPOSE: Spot-scanning arc therapy (SPArc) is an emerging proton modality that can potentially offer a combination of advantages in plan quality and delivery efficiency, compared with traditional IMPT of a few beam angles. Unlike IMPT, frequent low-to-high energy layer switching (so called switch-up (SU)) can degrade delivery efficiency for SPArc. However, it is a tradeoff between the minimization of SU times and the optimization of plan quality. This work will consider the energy layer optimization (ELO) problem for SPArc and develop a new ELO method via energy matrix (EM) regularization to improve plan quality and delivery efficiency. METHODS: The major innovation of EM method for ELO is to design an EM that encourages desirable energy-layer map with minimal SU during SPArc, and then incorporate this EM into the SPArc treatment planning to simultaneously minimize the number of SU and optimize plan quality. The EM method is solved by the fast iterative shrinkage-thresholding algorithm and validated in comparison with a state-of-the-art method, so-called energy sequencing (ES). RESULTS: EM is validated and compared with ES using representative clinical cases. In terms of delivery efficiency, EM had fewer SU than ES with an average of 35% reduction of SU. In terms of plan quality, compared with ES, EM had smaller optimization objective values and better target dose conformality, and generally lower dose to organs-at-risk and lower integral dose to body. In terms of computational efficiency, EM was substantially more efficient than ES by at least 10-fold. CONCLUSION: We have developed a new ELO method for SPArc using EM regularization and shown that this new method EM can improve both delivery efficiency and plan quality, with substantially reduced computational time, compared with ES.