The effect of stochastic fluctuation in radiation dose-rate on cell survival following fractionated radiation therapy

In radiobiological models, it is often assumed that the radiation dose rate remains constant during the course of radiation delivery. However, instantaneous radiation dose rate undergoes random (stochastic) temporal fluctuation. The effect of stochastic dose rate in fractionated radiation therapy is unknown and there has been no analytical formulation of stochastic dose-rate fluctuation effect in fractionated radiation therapy which we endeavor to pursue here. We have obtained the quantitative expression of cellular survival fraction considering stochastic temporal fluctuation or noise in dose rate. We have shown that the constant dose-rate approximation overestimates the survival fraction compared to that under stochastic dose rate in a fractionated radiation therapy situation and this overestimation effect increases appreciably with the increase in the fluctuation level in dose rate. However, for a given level of fluctuation in dose rate, overestimation of survival fraction also depends on the value of cellular radiation sensitivity parameter beta and the repair rate of DNA lesion. This overestimation effect is higher for the cells which have a higher value of beta parameter or have a lower repair rate. Our study draws attention to stochastic temporal fluctuation in the radiation dose rate and its potential contribution to cell survival following fractionated radiotherapy.