A modified lethal-potentially lethal model for oxygen-mediated FLASH sparing in stem cell niches

Ultra-high dose rate (FLASH) irradiation can reduce normal-tissue toxicity while preserving tumor control, but a mechanistic explanation consistent with classical radiobiology remains incomplete. In particular, oxygen-depletion arguments based solely on bulk tissue oxygenation can appear inconsistent with clinically relevant fraction sizes, motivating a DNA-target-level oxygen formulation.

To develop a theory-based mechanistic extension of the Lethal and Potentially Lethal (LPL) model that explains oxygen-mediated FLASH trends without prescribing dose rate-dependent radiosensitivity, and to identify the baseline nuclear oxygen window in which sparing is expected to be largest.

We introduce an explicit Precursor Lesion population whose fate is governed by competing chemical restitution/repair versus oxygen-dependent fixation into potentially lethal and lethal lesion channels. Fixation kinetics are coupled to a time-varying nuclear oxygen tension, $p{O}_2\left(t\right)$ , which decreases via radiolytic depletion during irradiation and recovers toward a baseline via reduced-order reoxygenation kinetics. To address the oxygen paradox, we distinguish bulk vascular oxygenation from a lower effective DNA target-level oxygenation that may arise in regulated stem-cell niches because of niche hypoxia and intracellular oxygen consumption. Oxygen modulation is implemented through a mechanistic exponential OER formulation parameterized by an oxygen-fixation rate constant, while retaining classical LPL behavior in the conventional low-dose-rate limit.

The model predicts that oxygen-mediated FLASH sparing is largest when baseline nuclear oxygenation lies in an intermediate physiologic-hypoxia regime, corresponding to the steep oxygen-responsive portion of the OER curve. In the reference parameter set, a quiescent normal-tissue niche with baseline $p{O}_{2,0}$  = 3 mmHg shows appreciable sparing under FLASH delivery, whereas sparing is minimal when the baseline lies near either the OER floor ( $p{O}_{2,0}$  = 0.2 mmHg) or the OER saturation plateau ( $p{O}_{2,0}$  = 30 mmHg). Sensitivity analyses preserve this intermediate oxygen window while shifting the magnitude and threshold of the effect.

By explicitly resolving Precursor Lesion fixation kinetics and by treating niche-to-nucleus oxygenation as an effective target-level variable, this mechanistic LPL framework predicts that oxygen-mediated FLASH sparing is most likely when baseline oxygenation lies within an intermediate physiologic-hypoxia window. The model should therefore be viewed as a mechanistic, testable framework rather than as a universal explanation of all FLASH responses.