The radical-mediated linear-exponential (RMLE) model: integrating radical recombination and oxygen depletion for FLASH radiotherapy.

Objective.The conventional linear-quadratic (LQ) model is the standard tool for radiotherapy but lacks dose-rate dependence, limiting its application in ultra-high dose rate (UHDR) regimes. This study proposes the radical-mediated linear-exponential (RMLE) model to quantitatively describe biological effects as a function of dose rate and oxygen concentration, aiming to model the FLASH sparing effect and identify underlying physicochemical mechanisms.Approach.The RMLE model formulates cell survival as a function of dose, dose rate, and oxygen partial pressure. It incorporates a saturation term for lethal damage at high doses, alongside a dose-rate dependent radical survival probability (Ps) and an oxygen-dependent damage fixation probability (Px). The model was validated usingin vitroprostate cancer cell survival under varying dose rates (FLASH vs CONV) and oxygenation conditions (normoxia vs hypoxia). A hierarchical regression strategy was employed to decouplePsandPx, and physical feasibility was evaluated using track-track interaction simulations.Main results.The RMLE model successfully reproduced the dose-response curves across all experimental conditions, resolving the high-dose overestimation issue of the standard LQ model. Analysis indicated that the FLASH sparing effect-notably more pronounced under hypoxic conditions-cannot be explained by oxygen depletion alone. Instead, the present analysis supports a synergistic interaction between radical recombination (reducedPs) and oxygen depletion (reducedPx). Furthermore, track structure simulations revealed that achieving necessary physical recombination at 600 Gy s-1requires a microsecond-scale interaction time (τ∼10-100μs), suggesting mediation by long-lived secondary chemical species.Significance.The RMLE model provides a mathematically tractable diagnostic framework to evaluate biological responses in the UHDR regime. The results suggest that thein vitroFLASH phenomenon arises from the interplay of microsecond-scale physical track overlap and chemical oxygen depletion. This model serves as a potential tool for exploring the fundamental mechanisms and informing future investigations into clinical FLASH protocols.