Theory of radiation injury and recovery in self-renewing cell populations.

A variety of mathematical models have been proposed to account for the effects observed after irradiation of groups of animals under certain well-defined test conditions. For example, in the early work of Hagen and Simmons (1) and of Blair (2) (see also 3), it was postulated that injury decays exponentially with timethat is, according to first-order kinetics, obeying the relation dx/dt = -kx, where x is the amount of injury at time t. Here and in the following examples, we refer to radiation injury in the formal sense (cf. 4, p. 283), which is operationally defined as an equivalent residual dose, expressed in rads. In another experimental condition, that of exposure to a fixed daily dose over a predetermined number of days, the amount of experimentally measured recovery per day appears to be a constant independent of the daily dose (3, 5). A similar result has been reported for recovery after single doses (6). These facts would be consistent with a model postulating zero-order kinetics for the recovery processthat is, dx/dt = constant, where t is time and x stands for injury in its formal definition as equivalent residual dose. This is in essence the model that had been suggested earlier by Tyler and Steamer (7). Although the hypothesis of zero-order kinetics accounts for certain experimental observations, it does so only in a formal sense by means of an ad hoc assumption, and without reference to the properties of physiological recovery mechanisms or of cell population kinetics. It will be shown here that the equations derived from realistic, though still oversimplified, assumptions about cell populations have some properties which agree with the experimental results, including the finding of a constant amount of recovery per day for fractionated exposure.