Simultaneous dose and dose rate optimization (SDDRO) for FLASH proton therapy

Purpose: FLASH radiotherapy (RT) can potentially reduce normal tissue toxicity while preserving tumoricidal effectiveness to improve the therapeutic ratio. The key of FLASH for sparing normal tissues is to irradiate tissues with an ultra-high dose rate (i.e., >= 40 Gy/s), for which proton RT can be used. However, currently available treatment plan optimization method only optimizes the dose distribution and does not directly optimize the dose rate. The contribution of this work to FLASH proton RT is the development of a novel treatment optimization method, that is, simultaneous dose and dose rate optimization (SDDRO), to optimize tissue-receiving dose rate distribution as well as dose distribution. Methods: Distinguished from existing methods, SDDRO accounts for dose rate constraint and optimizes dose rate distribution. In terms of mathematical formulation, SDDRO is a constrained optimization problem with dose-volume constraint on dose distribution, minimum dose rate constraint on dose-averaged tissue-receiving dose rates, minimum monitor unit constraint on spot weight, and maximum intensity constraint on beam intensity. In terms of optimization algorithm, SDDRO is solved by iterative convex relaxation and alternating direction method of multipliers. SDDRO algorithms are presented for both scenarios with either constant or variable beam intensity. Results: SDDRO was compared with intensity modulated proton therapy (IMPT) (dose optimization alone, and no dose rate optimization) using three lung cases. SDDRO substantially improved the dose rate distribution compared to IMPT, for example, increasing of the region-of-interest (ROI) volume (ROI = CTV_10mm: the ring sandwiched by 10 mm outer and inner expansion of CTV boundary) receiving at least 40 Gy/s from similar to 30-50% to at least 98%, and the lung volume receiving at least 40 Gy/s from similar to 30-40% to similar to 70-90%. Moreover, both dose and dose rate distributions from SDDRO were further considerably improved via the combined use of hypofractionation and multiple beams. Conclusions: We have developed a joint dose and dose rate optimization method for FLASH proton RT, namely SDDRO, which is first-of-its-kind to the best of our knowledge. The results suggest that (a) SDDRO can substantially improve the FLASH-dose rate coverage (e.g., in terms of dose rate volume histogram) compared to IMPT for the purpose of normal tissue sparing while preserving the dose distribution and (b) the combination of hypofractionation and multiple beams can further considerably improve the SDDRO plan quality in terms of both dose and dose rate distribution. (c) 2020 American Association of Physicists in Medicine [https://doi.org/10.1002/mp.14531]