An empirical model of carbon-ion relative biological effectiveness based on the linear correlation between radiosensitivity to photons and carbon ions.

Objective. To develop an empirical model to predict carbon ion (C-ion) relative biological effectiveness (RBE). Approach. We used published cell survival data comprising 360 cell line/energy combinations to characterize the linear energy transfer (LET) dependence of cell radiosensitivity parameters describing the dose required to achieve a given survival level, e.g. 5% (D _5% ), which are linearly correlated between photon and C-ion radiations. Based on the LET response of the metrics D _5% and D _37% , we constructed a model containing four free parameters that predicts cells' linear quadratic model (LQM) survival curve parameters for C-ions, α _C and β _C , from the reference LQM parameters for photons, α _X and β _X , for a given C-ion LET value. We fit our model's free parameters to the training dataset and assessed its accuracy via leave-one out cross-validation. We further compared our model to the local effect model (LEM) and the microdosimetric kinetic model (MKM) by comparing its predictions against published predictions made with those models for clinically relevant LET values in the range of 23-107 keV μ m ^-1 . Main Results. Our model predicted C-ion RBE within ±7%-15% depending on cell line and dose which was comparable to LEM and MKM for the same conditions. Significance. Our model offers comparable accuracy to the LEM or MKM but requires fewer input parameters and is less computationally expensive and whose implementation is so simple we provide it coded into a spreadsheet. Thus, our model can serve as a pragmatic alternative to these mechanistic models in cases where cell-specific input parameters cannot be obtained, the models cannot be implemented, or for which their computational efficiency is paramount.
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