The incorporation of the concept of minimum RBE (RBEmin) into the linear-quadratic model and the potential for improved radiobiological analysis of high-LET treatments

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Abstract
Purpose: The formulation of relative biological effectiveness (RBE) for high linear energy transfer (high-LET) radiation treatments is revisited. The effects of changed production of sub-lethal damage with varying LET is now considered via the RBEmin concept, where RBEmin represents the lower limit to which RBE tends at high doses per fraction. Materials and methods: An existing linear-quadratic formulation for calculating RBE variations with fractional dose for high-LET radiations is modified to incorporate the twin concepts of RBEmax (which represents the value of RBE at an effective dose-per-fraction of 0 Gy) and RBEmin. Results: Fits of the model to data showed RBEmin values in the range of 0.1 – 2.27. In all cases the raw data was a better statistical fit to the model which included RBEmin, although this was only very highly significant in one case. In the case of the mouse oesophagus it is shown that, if change in the β-radiosensitivity coefficient with LET is considered as trivial, an underestimation >5% in RBE can be expected at X-ray doses of 2 Gy/fraction if RBEmin is not considered. To ensure that the results were not biased by the statistical method used to obtain the parameter values relevant to this analysis (i.e., using fraction-size effect or Fe-plots), an alternative method was used which provided very similar correlation with the data. Conclusions: If the production of sublethal damage is considered independent of LET, there will be a risk that non-corrected evaluation of RBE will lead to an over- or under-estimate of RBE at low doses per fractions (the clinically relevant region).

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