Mathematical models of marrow cell kinetics: differential effects of protracted irradiations on stromal and stem cells in mice

It is known that hematopoiesis is supported by bone-marrow stem cells, but those cells must seed and grow on a stromal microenvironment. Typically, studies have shown that a surviving fraction of about 30 hematopoietic stem cells (HSCs) (i.e., about 0.04%) correspond to the LD50, although other studies have shown that marrow can repopulate from a single viable cell under strong regiments of antibiotics and infusions of irradiated blood elements.

This paper describes comparisons between our results (from maximum-likelihood estimation techniques for cellular damage, repair, and compensatory repopulation) and published experimental data on marrow stromal cells.

After biophysical consideration of the rate constants that were derived by maximizing the likelihood function (a consideration necessary to extend the model to cell populations not indicated by the model as "critical" for recovery), the rate constants for cellular damage to stem cells are fitted to experimental data. Rate constants for repair and proliferation of stem cells are assigned based on published data on repair/proliferation half-times, and these assignments affect the evaluation of the rate constants for cellular damage. From the two models, that is one for "critical" cells (having radiosensitive and repopulation characteristics similar to stromal cells) and another for stem cells, effects on two cell populations of different radiosensitivities and repopulation rates can be demonstrated for complex schedules of protracted irradiations which could reduce either cell population below a critical need for marrow repopulation.

Our analysis of animal mortality data has indicated that recovery of an animal from potentially lethal irradiation is dominantly regulated by cells with survival and repopulation characteristics similar to those of stroma cells.

In contrast to the surviving fraction of hematopoietic stem cells, it appears that the probability of an animal's recovery is high if the "critical" population of cells is above 1% (our "best" maximum likelihood estimate, from mouse data, with the corresponding lower confidence bound at about 0.2%). Of course, a few stem cells--perhaps only one--must maintain a potential for repopulation of blood and marrow.