Effect of overdispersion of lethal lesions on cell survival curves

Abstract

The linear-quadratic (LQ) model is the most commonly used mechanism to predict radiobiological outcomes. It has been used extensively to describe dose-response in vitro and in vivo. There are, however, some questions about its applicability in terms of its capacity to represent some profound mechanistic behaviour. Specifically, empirical evidence suggests that the LQ model underestimates the survival of cells at low doses while overestimating cell death at higher doses. It is believed to be driven from the usual LQ model assumption that radiogenic lesions are Poisson distributed. In this context, we use a negative binomial (NB) distribution to study the effect of overdispersion on the shapes and the possibility of reducing dose-response curvature at higher doses. We develop an overdispersion model for cell survival using the non-homologous end-joining (NHEJ) pathway double-strand break (DSB) repair mechanism to investigate the effects of the overdispersion on probabilities of repair of DSBs. The error distribution is customised to ensure that the refined overdispersion parameter depends on the mean of the distribution. The predicted cell survival responses for V79, AG and HSG cells exposed to protons, helium and carbon ions are compared with the experimental data in low and high dose regions at various linear energy transfer (LET) values. The results indicate straightening of dose-response and approaching a log-linear behaviour at higher doses. The model predictions with the measured data show that the NB modelled survival curves agree with the data following medium and high doses. Model predictions are not validated at very tiny and very high doses; the approach presented provides an analysis of mechanisms at the microscopic level. This may help improve the understanding of radiobiological responses of survival curves and resolve discrepancies between experimental and theoretical predictions of cell survival models.