Ionizing radiation damage to cells: effects of cell cycle redistribution

If a population of cycling cells is exposed to a fixed dose of ionizing radiation delivered over time T, it is sometimes observed that increasing T increases the amount of cell killing. This is essentially because at first the radiation preferentially kills cells in a sensitive portion of the cycle and the surviving, more resistant cells then have time to reach more sensitive stages. We refer to this effect as population resensitization, caused by redistribution within the cell cycle. We investigate the effect theoretically by employing the McKendrick-von Foerster equation for age-structured proliferating cell populations, generalized by introducing a radiation damage term. Within our formalism, we show that population resensitization occurs whenever: (a) prior to irradiation the cell population has the stable age-distribution approached asymptotically by an unirradiated population, and (b) T is sufficiently small. Examples and other cases are outlined. The methods of Volterra integral equations, renewal theory, and positive semigroup theory are applied. The effect of varying T is evaluated by considering the ultimate amplitude of the stable age-distribution population at times much greater than both the irradiation duration and the average cell-cycle time. The main biological limitations of the formalism are the following: considering only radiation damage which is not subject to enzymatic repair or quadratic misrepair, using an overly naive method of ensuring loss of cell cycle synchrony, neglecting nonlinear effects such as density inhibition of growth, and neglecting radiatively induced perturbations of the cell cycle. Possible methods for removing these limitations are briefly discussed.