Markov chain Monte Carlo analysis for the selection of a cell-killing model under high-dose-rate irradiation

High-dose-rate irradiation with 6 MV linac x rays is a wide-spread means to treat cancer tissue in radiotherapy. The treatment planning relies on a mathematical description of surviving fraction (SF), such as the linear-quadratic model (LQM) formula. However, even in the case of high-dose-rate treatment, the repair kinetics of DNA damage during dose-delivery time plays a function in predicting the dose-SF relation. This may call the SF model selection into question when considering the dose-delivery time or dose-rate effects (DREs) in radiotherapy and in vitro cell experiments. In this study, we demonstrate the importance of dose-delivery time at high-dose-rate irradiations used in radiotherapy by means of Bayesian estimation.

To evaluate the model selection for SF, three types of models, the LQM and two microdosimetric-kinetic models with and without DREs (MKM_DR and MKM) were applied to describe in vitroSF data (our work and references). The parameters in each model were evaluated by a Markov chain Monte Carlo (MCMC) simulation.

The MCMC analysis shows that the cell survival curve by the MKM_DR fits the experimental data the best in terms of the deviance information criterion (DIC). In the fractionated regimen with 30 fractions to a total dose of 60 Gy, the final cell survival estimated by the MKM_DR was higher than that by the LQM. This suggests that additional fractions are required for attaining the total dose equivalent to yield the same effect as the conventional regimen using the LQM in fractionated radiotherapy.

Damage repair during dose-delivery time plays a key role in precisely estimating cell survival even at a high dose rate in radiotherapy. Consequently, it was suggested that the cell-killing model without repair factor during a short dose-delivery time may overestimate actual cell killing in fractionated radiotherapy.