Flash proton radiation therapy via a stochastic three-operator splitting method

Abstract The inverse radiation therapy planning problem is crucial in achieving tumoricidal doses while minimizing radiation-induced normal-tissue toxicity. Compared to conventional radiation therapy (with conventional dose rates), flash proton radiation therapy (with ultra-high dose rates) can provide additional normal tissue sparing. However, this groundbreaking advancement in radiation oncology introduces a challenging nonconvex and nonsmooth optimization problem. In this paper, we propose a stochastic three-operator splitting (STOS) algorithm to address the flash proton radiation therapy problem. We establish the convergence and convergence rates of the STOS algorithm under the nonconvex framework for both unbiased gradient estimators and variance-reduced gradient estimators. These stochastic gradient estimators include the most popular ones, such as SGD, SAGA, SARAH, and SAG, among others. Experimental results demonstrate that the flash proton radiation therapy plans obtained by the STOS algorithm can effectively kill tumors while better protecting normal tissues.