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 using in vitro prostate cancer cell survival under varying dose rates (FLASH vs. CONV) and oxygenation conditions (normoxia vs. hypoxia). A hierarchical regression strategy was employed to decouple Ps and Px, 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 (reduced Ps) and oxygen depletion (reduced Px). Furthermore, Track structure simulations revealed that achieving necessary physical recombination at 600 Gy/s requires a microsecond-scale interaction time (τ ~10 - 100 μs), 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 the in vitro FLASH 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.