A generalized formulation of the 'incomplete-repair' model for cell survival and tissue response to fractionated low dose-rate irradiation

A generalized equation for cell survival or tissue effects after fractionated low dose-rate irradiations, when there is incomplete repair between fractions and significant repair during fractions, is derived in terms of the h- and g-functions of the 'incomplete-repair' (IR) model. This model was developed originally from the concept of 'dose equivalent of incomplete repair', assuming that the repair of radiation damage is an exponential function of time and that the cell survival curve can be described adequately by the linear quadratic (LQ) formalism. The generalized incomplete-repair equation is shown to be equivalent to an expression derived by Dale et al. (1988) for analysis of tissue effects of fractionated irradiations at varying dose rates. The model is critically dependent on alpha/beta, repair half-time, treatment time and interfraction interval, and should therefore be regarded primarily as a tool for the analysis of fractionation and dose-rate effects in carefully designed radiobiological experiments, although it should also be useful in exploring, in a general way, the feasibility of clinical treatment protocols using fractionated low dose-rate treatments.