Data-driven RBE parameterization for helium ion beams

Helium ion beams are expected to be available again in the near future for clinical use. A suitable formalism to obtain relative biological effectiveness (RBE) values for treatment planning (TP) studies is needed. In this work we developed a data-driven RBE parameterization based on published in vitro experimental values. The RBE parameterization has been developed within the framework of the linear-quadratic (LQ) model as a function of the helium linear energy transfer (LET), dose and the tissue specific parameter ${{(\alpha /\beta )}_{\text{ph}}}$ of the LQ model for the reference radiation. Analytic expressions are provided, derived from the collected database, describing the $\text{RB}{{\text{E}}_{\alpha}}={{\alpha}_{\text{He}}}/{{\alpha}_{\text{ph}}}$ and ${{\text{R}}_{\beta}}={{\beta}_{\text{He}}}/{{\beta}_{\text{ph}}}$ ratios as a function of LET. Calculated RBE values at 2 Gy photon dose and at 10% survival ($\text{RB}{{\text{E}}_{10}}$ ) are compared with the experimental ones. Pearson's correlation coefficients were, respectively, 0.85 and 0.84 confirming the soundness of the introduced approach. Moreover, due to the lack of experimental data at low LET, clonogenic experiments have been performed irradiating A549 cell line with ${{(\alpha /\beta )}_{\text{ph}}}=5.4$ Gy at the entrance of a 56.4 MeV u−1He beam at the Heidelberg Ion Beam Therapy Center. The proposed parameterization reproduces the measured cell survival within the experimental uncertainties. A RBE formula, which depends only on dose, LET and ${{(\alpha /\beta )}_{\text{ph}}}$ as input parameters is proposed, allowing a straightforward implementation in a TP system.