Modelled biological effectiveness comparisons of low, high and ultra-high (FLASH) radiation dose rates

This article considers quantitative comparisons of radiation effectiveness across a large range of dose rates, including low (LDR), medium, conventional or high (HDR) and ultra-high (or FLASH) dose rates. For comparisons of different continuous radiotherapy prescriptions, the linear quadratic model was used to derive ‘biological effective dose’ (BED) equations which included time-dependent enzymatic DNA repair in the low to high dose rate range for monophasic or biphasic repair kinetics. In a recent publication, much higher dose rates, associated with increasing overall radioresistance, was thought to be governed by a cube root (or similar) function of dose rate (which expresses the intensification of micro-volumetric linear energy transfer per unit volume and correlates with average inter-track distances) with resultant increases in the apparent α/β ratios. Explicit equations for assessments of BED* (defined as the excess BED beyond the threshold BED) are presented for dose rates ranging from around 0.1–5 × 106 Gy per hr. The method can also be adapted for tumour control comparisons. Graphical presentations are used to determine iso-effective doses of similar BED* values at different dose rates, for specified radiation doses. The threshold BEDs for radio-tolerance reduce in proportion to the change in the α radiosensitivity parameter. For dose rates above the HDR range, the intrinsic α/β ratio, which is independent of dose rate, continues to influence the magnitude of the changes in BED and dose required for a specified bio-effect, but in a modified form. For further research purposes, these tentative methods can provide isoeffective dose estimates to guide radiation use at different dose rates, but require further specific experimental validation. The methods may seem complex and contain many pitfalls. Further research is also required to identify residual enigmas, such as the exact dose rate and dose at which biological FLASH effects begin to operate and to validate these isoeffective dose predictions.