Derivation of a comprehensive semi-empirical proton RBE model from published experimental cell survival data collected in the PIDE database

We aimed to develop a comprehensive proton relative biological effectiveness (RBE) model based on accumulated cell survival data in the literature. Our approach includes four major components: (1) Eligible cell survival data with various linear energy transfers (LETs) in the Particle Irradiation Data Ensemble (PIDE) database (72 datasets in four cell lines); (2) a cell survival model based on Poisson equation, with α and β defined as the ability to generate and repair damage, respectively, to replace the classic linear-quadratic model for fitting the cell survival data; (3) hypothetical linear relations of α and β on LET, or $\frac{\alpha \left(LET\right)}{{\alpha }_x}={\text{α}}_{\alpha }+b_{\alpha }\ast LET$ and $\frac{\beta \left(LET\right)}{{\beta }_x}={\text{α}}_{\beta }-b_{\beta }\ast LET$ ; and (4) a multi-curve fitting (MCF) approach to fit all cell survival data into the survival model and derive the a_α , b_α , a_β , and b_β values for each cell line. Dependences of these parameters on cell type were thus determined and finally a comprehensive RBE model was derived. MCF showed that (a_α , b_α , a_β , b_β ) = (1.09, 0.0010, 0.96, 0.033), (1.10, 0.0015, 1.03, 0.023), (1.12, 0.0025, 0.99, 0.0085), and (1.17, 0.0025, 0.99, 0.013) for the four cell lines, respectively. Thus, a_α = 1.12 ± 0.04, b_α = 0.0019 ± 0.0008, a_β = 0.99 ± 0.03, and b_β = 0.013 ∗ α_x , and approximately $\alpha \sim 1.12\ast {\alpha }_x$ and $\beta =\left(0.99-0.013\ast {\alpha }_x\ast LET\right)\ast {\beta }_x$ . Consequently, a relatively reliable and comprehensive RBE model with dependence on LET, α_x , β_x , and dose per fraction was finally derived for potential clinical application.