An in-silico study of conventional and FLASH radiotherapy iso-effectiveness: potential impact of radiolytic oxygen depletion on tumor growth curves and tumor control probability.

Objective. This work aims to investigate the iso-effectiveness of conventional and FLASH radiotherapy on tumors through in-silico mathematical models. We focused on the role of radiolytic oxygen depletion (ROD), which has been argued as a possible factor to explain the FLASH effect.Approach. We used a spatiotemporal reaction-diffusion model, including ROD, to simulate tumor oxygenation and response. From those oxygen distributions we obtained surviving fractions (SFs) using the linear-quadratic (LQ) model with the oxygen enhancement ratios (OERs). We then employed the calculated SFs to describe the evolution of preclinical tumor volumes through a mathematical model of tumor response, and we also extrapolated those results to calculate tumor control probabilities (TCPs) using the Poisson-LQ approach.Main results. Our study suggests that the ROD effect may cause differences in SF between FLASH and conventional radiotherapy, especially in lowα/βandpoorly oxygenatedcells. However, a statistical analysis showed that these changes in SF generally do not result in significant differences in the evolution of preclinical tumor growth curves when the sample size is small, because such differences in SF may not be noticeable in the heterogeneity of the population of animals. Nonetheless, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH radiotherapy). When analyzing the response of tumors with heterogeneous oxygenations, differences in TCP are more important forwell oxygenatedtumors. This apparent contradiction with the results obtained for homogeneously oxygenated cells is explained by the complex interplay between the heterogeneity of tumor oxygenation, the OER effect, and the ROD effect.Significance. This study supports the experimentally observed iso-effectiveness of FLASH and conventional radiotherapy when analyzing the volume evolution of preclinical tumors (that are far from control). However, this study also hints that tumor growth curves may be less sensitive to small variations in SF than tumor control probability: ROD may lead to increased SF in FLASH radiotherapy, which while not large enough to cause significant differences in tumor growth curves, could lead to important differences in clinical TCPs. Nonetheless, it cannot be discarded that other effects not modeled in this work, like radiation-induced immune effects, can contribute to tumor control and maintain the iso-effectiveness of FLASH radiotherapy. The study of tumor growth curves may not be the ideal experiment to test the iso-effectiveness of FLASH, and experiments reporting TCP orD₅₀may be preferred.