The influence of hypoxia on LET and RBE relationships with implications for ultra-high dose rates and FLASH modelling

Abstract

Objective. To investigate relationships between linear energy transfer (LET), fluence rates, changes in radiosensitivity and the oxygen enhancement ratio (OER) in different ion beams and extend these concepts to ultra-high dose rate (UHDR) or FLASH effects. Approach. LET values providing maximum relative biological effect (RBE), designated as LETU, are found for neon, carbon and helium beams. Proton experiments show reduced RBEs with depth in scattered (divergent) beams, but not with scanned beams, suggesting that instantaneous fluence rates (related to track separation distances) can modify RBE, all other RBE-determining factors being equal. Micro-volumetric energy transfer per μm3 (mVET) is defined by LET × fluence. High fluence rates will increase mVET rates, with proportional shifts of LETU to lower values due to more rapid energy transfer. From the relationship between LETU and OER at conventional dose rates, OER reductions in UHDR/FLASH exposures can be estimated and biological effective dose analysis of experimental lung and skin reactions becomes feasible. Main results. The Furusawa et al data show that hypoxic LETU values exceed their oxic counterparts. OER reduces from around 3–1.25 at LETU, although the relative radiosensitivities of the oxic and hypoxic α parameters (the OER(α)) exceed those of the standard OER values. Increased fluence rates are predicted to reduce LETU and OER. Large FLASH single doses will minimise RBE increments due to the β parameter reducing by a factor of 0.5–0.25 consistent with oxygen depletion, causing radioresistance. Similar results will occur for photons. Tissue α/β ratios increase by around 10 in FLASH conditions, agreeing with derived ion-beam dose rate equations. Significance. Increasing dose rates enhance local energy deposition rate per unit volume, probably causing oxygen depletion and radioresistance in pre-existing hypoxic sites during UHDR/FLASH exposures. The modelled equations provide testable hypotheses for further dose rate investigations in photon, proton and ion beams.