Mitigating the impact of FLASH-model uncertainties through personalized FLASH optimization functions for delivery pattern optimization for lung IMPT

<i>Objective.</i>It is generally assumed that the FLASH effect is triggered at dose rates (DRs) of at least 40 Gy s^-1, while recent studies indicate that this threshold is not binary but follows a sigmoid across samples. Some patients may thus already experience the FLASH effect at lower DRs, while the current FLASH models do not account for this. We propose a method that aims to maximally exploit the FLASH effect over a wider dose-rate range through dose-rate-dependent FLASH delivery pattern optimization (DPO) functions while maintaining the FLASH effect at the currently accepted binary dose-rate threshold of 40 Gy s^-1.<i>Approach.</i>We optimized and evaluated FLASH-weighted dose (FWD) distributions for 1397 FLASH optimization functions. All FLASH optimization functions were used to optimize the FWD distribution using DPO. The generated FWD distributions were evaluated in case FLASH is triggered at DRs ranging from 10 to 60 Gy s^-1and compared to the FWD distribution that was optimized under the assumption that FLASH is only and maximally triggered at 40 Gy s^-1.<i>Main results.</i>(i) Substantial improvements in FWD distributions were obtained using FLASH optimization functions. (ii) The optimal FLASH optimization function differs both per patient and per beam. (iii) FLASH optimization function class solutions can also lead to an overall improvement of FWD distributions.<i>Significance.</i>We demonstrated that substantial improvements in FWD distributions can be achieved by using FLASH optimization functions that exploit the FLASH effect over a wider dose-rate range.