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BackgroundSpatially fractionated radiotherapy (SFRT) intentionally creates spatially-modulated peak-valley dose patterns for improving the tumor control or/and the sparing of organs at risk, compared to conventional radiotherapy (CONV). Evaluating non-uniform dose distributions using conventional physical dose does not fully account for the biological effectiveness of SFRT. In this study, we adopt the equivalent uniform dose (EUD) as a surrogate metric to evaluate non-uniform dose distributions.PurposeThis work will develop a SFRT treatment planning method with EUD optimization, which is the first-of-its-kind to the best of our knowledge.MethodsThe SFRT scenario of proton GRID with uniform target dose is considered in this work for dose-only optimization (DO) and joint dose and peak-valley-dose-ratio (PVDR) optimization (JDPO) respectively. In addition to dose and PVDR optimization, SFRT treatment planning also optimizes the EUD. The EUD used in this work is based on cell survival as modeled by the linear-quadratic model. The EUD optimization problem is solved by: (1) iterative convex relaxation to decouple the nonconvex dose-volume-histogram constraint; (2) linearized alternating direction method of multiplier to efficiently handle the nonconvex minimum-monitor-unit constraint and nonlinear EUD objective.ResultsEUD optimization reduced the EUD and increased survival fraction. For example, for a head-and-neck patient, EUD optimization decreased the brainstem EUD from 5.52% to 3.86% for DO, and from 5.78% to 4.82% for JDPO, and increased the brainstem survival fraction from 72.9% to 81.6% for DO, and from 71.5% to 76.6% for JDPO. Furthermore, EUD optimization preserved PVDR from DO or JDPO.ConclusionsA novel EUD optimization method is proposed for SFRT that can reduce the EUD and increase the survival fraction.