Analytical framework for LET- and oxygen-dependent transport of hydroxyl radicals under irradiation

The biological effectiveness of ionizing radiation depends not only on absorbed dose but also on radiation quality and microenvironmental factors, particularly linear energy transfer (LET) and oxygenation. Although Monte Carlo track-structure simulations can describe radiation–matter interactions in detail, such complexity often obscures the individual roles played by governing parameters. We present here a closed-form, analytical transport–reaction model of the indirect chemical stage of radiation action. The model introduces an LET-dependent source term for hydroxyl radical production based on experimentally and computationally established G-value trends and combines it with an analytical transport equation formulated using a directional Boltzmann-P₁ approximation. Macroscopic reaction rates incorporate the presence of oxygen and background scavengers, leading to an explicit, steady-state expression for hydroxyl radical density independent of biological response functions. The model systematically replicates suppression of indirect chemical activity with increasing LET and predicts the natural emergence of smoothly varying radiochemical regimes corresponding to production-limited, scavenging-limited, and track-structure-dominated behavior. These regimes emerge from first-principles considerations rather than imposed thresholds. The framework is not designed to predict biological damage or clinical outcomes but provides a physically transparent and analytically tractable description of the chemical stage of radiation action, one suitable for incorporation into multiscale models of heterogeneous irradiation.