Modeling <i>in vivo</i> relative biological effectiveness in particle therapy for clinically relevant endpoints

<b>Background:</b> The relative biological effectiveness (RBE) of particle therapy compared to photon radiotherapy is known to be variable but the exact dependencies are still subject to debate. <i>In vitro</i> data suggested that RBE is to a large extend independent of ion type if parametrized by the beam quality Q. This study analyzed the RBE dependence of pre-clinical data on late toxicity with an emphasis on the beam quality. <b>Material and methods:</b> Published pre-clinical RBE dose-response data of the spinal cord following one and two fractions of photon and carbon ion irradiation were compiled. The beam quality for each treatment condition was obtained from Monte Carlo simulations. The <i>α_p</i> and <i>β_p</i> parameters of the linear-quadratic (LQ) model for particle irradiation were determined from the pre-clinical data and was provided as a function of <i>Q</i>. An introduced model proposed <i>α_p</i> to increase linearly with <i>Q</i> and <i>β_p</i> to remain constant. RBE values predicted by the model were compared to the published data. <b>Results:</b> The α_p parameter was highly correlated with <i>Q (R²</i> = 0.96) with a linear slope of 0.019 Gy⁻¹. No significant variation of <i>β_p</i> with <i>Q</i> was found. RBE and <i>Q</i> were also highly correlated (<i>R</i>² = 0.98) for one and two fractions. The (extrapolated) RBE at <i>Q</i> = 0 (theoretical photon limit) for one and two fractions was 1.22 and significantly larger than 1 (<i>p</i> = .004). The model reproduced the dependence of RBE on fractionation well. <b>Conclusions</b>: Fraction dose and beam quality <i>Q</i> were sufficient to describe the RBE variability for a late toxicity model within a carbon ion treatment field. Assuming the independence of the identified RBE parameters on the ion type might suggest the translation of variable (pre-) clinical RBE data from carbon ion to proton therapy.