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

Abstract

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 RBEmax and RBEmin, describing the extreme RBE at low and high doses. While there is consensus that RBEmax increases with increasing LET, the RBEmin 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 (LETd) 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 RBEmin. The LETd dependency of RBEmin was determined by fitting a linear function to the RBEmin values estimated from the restricted databases. Our analysis showed the LETd dependency of RBEmin to be significantly influenced by the experimental dose range. By including experiments with doses below 1 Gy in the database, we found that RBEmin increased with increasing LETd. By excluding the low dose experiments in our database, the RBEmin became constant for all LETd values. For an LETd value of 5 keV µm−1, a restricted database including the data with the lowest doses gave an RBEmin of 1.4 ± 0.1, while databases with only high dose data (>2 Gy) gave an RBEmin of 1.0 ± 0.1. None of our restricted databases gave a decreasing RBEmin with increasing LETd. Our study showed that RBEmin has a small yet significant dependency on LETd for tissues with low (α/β) x ratio. The LETd dependency of RBEmin varied substantially with the experimental dose range. Including experiments with high minimum dose in RBE models may lead to underestimation of the RBE.