Mathematical Model for Post-Irradiation Haemopoiesis

A model for haemopoiesis has been constructed based on the following hypothesis: (a) Haemopoietic stem cells have the capability of either reproducing as stem cells or differentiating into specialized blood cells of at least two different types; (b) The size of the stem-cell compartment is in part regulated by the rate of increase due to stem-cell reproduction and in part by the rate of loss of stem cells through differentiation; (c) In addition, the size of the stem-cell compartment is in part regulated by a competitive cell-to-cell interaction between the stem-cells themselves and between the differentiating cells and the stem-cells, such that the presence of an exceptionally large number of either cell type would have a repressive effect on the rate of increase of the stem-cell population. This model has been applied to the post-irradiation erythropoietic behaviour of the rat. In the computer studies with the model, an X-ray dose sufficient to inhibit reproduction in 50% of the erythroid stem cells was assumed. It was also assumed that reproduction and differentiation are genetically separately controlled processes and that, therefore, some part of the reproductively injured cells were still capable of differentiation. Under these conditions the model predicted an abortive rise in reticulocyte number, peaking at about 6 days. True recovery was predicted to occur at about 16 days. Both the abortive rise and the true recovery were also present in those segments of the model representing earlier erythroid cells, occurring at progressively earlier times in progressively more primitive cells. Comparison of the model's predictions with experimentally obtained data for post-irradiation erythroid recovery showed a good agreement both with respect to the time of the abortive peak and the time of true recovery. (author)