Influence of time-dependent stochastic heterogeneity on the radiation response of a cell population

A solid tumor is a cell population with extensive cellular heterogeneity, which severely complicates tumor treatment by therapeutic agents such as ionizing radiation. We model the response to ionizing radiation of a multicellular population whose cells have time-dependent stochastic radiosensitivity. A reaction-diffusion equation, obtained by assuming a random process with the radiation response of a cell partly determined by competition between repair and binary misrepair of DNA double-strand breaks, is used. By a suitable transformation, the equation is reduced to that of an Ornstein-Uhlenbeck process so explicit analytic solutions are available. Three consequences of the model's assumptions are that (1) response diversity within a population increases resistance to radiation, that is, the population surviving is greater than that anticipated from considering an average cell; (2) resistant cell subpopulations preferentially spared by the first part of a prolonged radiation protocol are driven biologically into more radiosensitive states as time increases, that is, resensitization occurs; (3) an inverse dose-rate effect, that is, an increase in cell killing as overall irradiation time is increased, occurs in those situations where resensitization dominates effects due to binary misrepair of repairable damage. The results are consistent with the classic results of Elkind and coworkers on extra cell killing attributed to cell-cycle redistribution and are in agreement with some recent results on in vitro and in vivo population radiosensitivity. They also generalize the therapeutic paradigm that low dose rate or fractionated radiation can help overcome hypoxic radioresistance in tumors.