A simple model for calculating relative biological effectiveness of X-rays and gamma radiation in cell survival

Abstract

Objectives: The relative biological effectiveness (RBE) of X-rays and γ radiation increases substantially with decreasing beam energy. This trend affects the efficacy of medical applications of this type of radiation. This study was designed to develop a model based on a survey of experimental data that can reliably predict this trend. Methods: In our model, parameters α and β of a cell survival curve are simple functions of the frequency-average linear energy transfer (LF) of delta electrons. The choice of these functions was guided by a microdosimetry-based model. We calculated LF by using an innovative algorithm in which LF is associated with only those electrons that reach a sensitive-to-radiation volume (SV) within the cell. We determined model parameters by fitting the model to 139 measured (α,β) pairs. Results: We tested nine versions of the model. The best agreement was achieved with [Formula: see text] and β being linear functions of [Formula: see text] .The estimated SV diameter was 0.1–1 µm. We also found that α, β, and the α/β ratio increased with increasing [Formula: see text] . Conclusions: By combining an innovative method for calculating [Formula: see text] with a microdosimetric model, we developed a model that is consistent with extensive experimental data involving photon energies from 0.27 keV to 1.25 MeV. Advances in knowledge: We have developed a photon RBE model applicable to an energy range from ultra-soft X-rays to megaelectron volt γ radiation, including high-dose levels where the RBE cannot be calculated as the ratio of α values. In this model, the ionization density represented by [Formula: see text] determines the RBE for a given photon spectrum.