The experimental dose ranges influence the LET_d dependency of the proton minimum RBE (RBE_min)

Cell experiments have shown the proton relative biological effectiveness (RBE) to vary with dose and linear energy transfer (LET), which has led to development of variable RBE models. The RBE is normally estimated from two independent functions, the RBE_max and RBE_min, describing the extreme RBE at low and high doses. While there is consensus that RBE_max increases with increasing LET, the RBE_min is not uniformly defined and its dependency on LET is deviating. In this work, we analysed this dependency and its sensitivity to variations of the experimental dose range. We performed a literature search to find data from existing monoenergetic proton cell survival experiments with (α/β) _x values below 5 Gy and dose averaged LET (LET_d) values below 20 keV µm^-1. From the experiments the doses and their corresponding survival data were extracted. Based on these data, multiple restricted databases were generated by sequential exclusion of low dose data in the experiments followed by a linear-quadratic (LQ) fit. The quadratic component from the LQ-fit was used to estimate RBE_min. The LET_d dependency of RBE_min was determined by fitting a linear function to the RBE_min values estimated from the restricted databases. Our analysis showed the LET_d dependency of RBE_min to be significantly influenced by the experimental dose range. By including experiments with doses below 1 Gy in the database, we found that RBE_min increased with increasing LET_d. By excluding the low dose experiments in our database, the RBE_min became constant for all LET_d values. For an LET_d value of 5 keV µm^-1, a restricted database including the data with the lowest doses gave an RBE_min of 1.4  ±  0.1, while databases with only high dose data (>2 Gy) gave an RBE_min of 1.0  ±  0.1. None of our restricted databases gave a decreasing RBE_min with increasing LET_d. Our study showed that RBE_min has a small yet significant dependency on LET_d for tissues with low (α/β) _x ratio. The LET_d dependency of RBE_min varied substantially with the experimental dose range. Including experiments with high minimum dose in RBE models may lead to underestimation of the RBE.