A closed‑form reaction‑kinetics model for LET‑ and oxygen‑dependent hydroxyl radical availability 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 reaction-kinetics model for 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 a balance equation derived from a directional Boltzmann-P₁ approximation under spatial averaging. 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 naturally from the model structure and the interplay between production, scavenging, and track‑density effects. 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.