A multi-compartment cell repopulation model allowing for inter-compartmental migration following radiation exposure, applied to leukaemia.

There is much uncertainty about cancer risks at the high radiation doses used in radiotherapy (RT). It has generally been assumed that cancer induction decreases rapidly at high doses due to cell killing. However, this is not seen in all RT groups, and a model recently developed by Sachs and Brenner [2005. Solid tumor risks after high doses of ionizing radiation. Proc. Natl Acad. Sci. USA 102, 13040-13045] proposed a mechanism for repopulation of cells after radiation exposure that explained why this might happen, at least for solid tumours. In this paper, this model is generalized to allow for heterogeneity in the dose received, and various alternate patterns of repopulation are also considered. The model is fitted to the Japanese atomic bomb survivor leukaemia incidence data, and data for various therapeutically irradiated groups. Two sets of parameters from these model fits are used to assess the sensitivity of model predictions. It is shown that in general allowing for heterogeneity in dose distribution and haematopoietic stem cell migration results in lower risks than the same average dose administered uniformly and without such migration, although this does not hold in the limiting case of complete stem cell repopulation between radiation dose fractions. We also investigate the difference made by assuming a compartmental repopulation signal, and a global repopulation signal. In general we show that in the absence of stochastic extinction, compartmental repopulation always predicts a larger number of mutated cells than global repopulation. However, in certain dose regimes stochastic extinction cannot be ignored, and in these cases the numbers of mutated cells predicted with global repopulation can exceed that for compartmental repopulation. In general, mutant cell numbers are highly overdispersed, with variance much greater than the mean.