Biological effectiveness in hypofractionation: Modeling tumor survival probability for large doses with a stochastic cell-cycle model.

A model of irradiated cell survival probability based on cell-cycle regulation of an avascular tumor is developed. It is shown, that for high doses as used in hypofractionated regimens the conventional linear quadratic (LQ) model grossly underestimate cell survival. The surviving fraction of tumor cells in hypoxic and normoxic conditions is calculated as a function of dose for an equivalent tumor biological effective dose. The usefulness of an empirical LQ-linear model which is obtained from experimental data at high doses is investigated and the corresponding survival probabilities are compared in normoxic and hypoxic conditions. It has been found that the LQ model with hypoxia and the LQ-linear model partially coincide at high doses. Cell-cycle regulations have been found to considerably influence time-resolved response of cell populations to irradiation. In particular, if using LQ instead of LQ-linear model for high doses, a recovery of the population may be undiscovered.