INFLUENCE OF TIME-DEPENDENT STOCHASTIC HETEROGENEITY ON THE RADIATIONRESPONSE OF A CELL-POPULATION

A solid tumor is a cell population with extensive cellular heterogenei ty, which severely complicates tumor treatment by therapeutic agents s uch as ionizing radiation. We model the response to ionizing radiation of a multicellular population whose cells have time-dependent stochas tic radiosensitivity. A reaction-diffusion equation, obtained by assum ing a random process with the radiation response of a cell partly dete rmined by competition between repair and binary misrepair of DNA doubl e-strand breaks, is used. By a suitable transformation, the equation i s reduced to that of an Omstein-Uhlenbeck process so explicit analytic solutions are available. Three consequences of the model's assumption s are that (1) response diversity within a population increases resist ance to radiation, that is, the population surviving is greater than t hat anticipated from considering an average cell; (2) resistant cell s ubpopulations preferentially spared by the first part of a prolonged r adiation protocol are driven biologically into more radiosensitive sta tes as time increases, that is, resensitization occurs; (3) an inverse dose-rate effect, that is, an increase in cell killing as overall irr adiation time is increased, occurs in those situations where resensiti zation dominates effects due to binary misrepair of repairable damage. The results are consistent with the classic results of Elkind and cow orkers on extra cell killing attributed to cell-cycle redistribution a nd are in agreement with some recent results on in vitro and in vivo p opulation radiosensitivity. They also generalize the therapeutic parad igm that low dose rate or fractionated radiation can help overcome hyp oxic radioresistance in tumors.