An Effective Dose Rate Optimization Algorithm for Efficient Conventional-Dose-Rate Proton Therapy and Ultra-High-Dose-Rate FLASH Proton Therapy

Abstract

The treatment delivery with high dose rate is desirable for efficient conventional-dose-rate proton therapy (IMPT and proton ARC) and essential for achieving biological sparing effect to normal tissues for ultra-high-dose-rate FLASH proton therapy. The minimum-monitor-unit (MMU) problem is mathematically fundamental to these high-dose-rate proton therapy problems, since the dose rate is proportionally associated with the MMU threshold. However, the MMU problem is nonconvex and larger MMU threshold that leads to higher dose rate makes the nonconvex problem more difficult to solve, for which the conventional optimization methods (e.g., alternating direction method of multipliers (ADMM) or proximal gradient descent (PGD) usually cannot satisfactorily solve. This work will develop an effective dose rate optimization algorithm for the MMU problem. The new method is based on orthogonal matching pursuit (OMP), and consists of two essential components. First, the iterative convex relaxation method is used to determine the active sets for dose-volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non-zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non-zero spots localized via OMP will be adaptively added to or removed from the optimization objective. The new method via OMP is validated in comparison with conventional methods (ADMM and PGD) and a recently proposed new method (called stochastic coordinate descent (SCD) method) for high-dose-rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). A brain case is provided in the table: compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. A new dose rate optimization algorithm via OMP is developed to solve the MMU problem with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from conventional methods (ADMM and PGD) and a recently proposed new method SCD.