Dynamical Modeling of Stem Cell Regeneration

Abstract

This chapter introduces a general mathematical framework to model the dynamics of stem cell regeneration. In general, homogeneous stem cell regeneration can be described by a \\(\\mathrm {G}_{0}\\) phase model, which leads to a delay differential equation. To model heterogeneous stem cell regeneration, we generalize the \\(\\mathrm {G}_{0}\\) model to include the epigenetic states of individual cells, which results in a differential-integral equation model that can be used to describe the evolution of the distribution of the epigenetic states of cells. In the second part, we apply the stem cell regeneration model to dynamic hematological diseases, which are diseases associated with the dysregulation of hematopoiesis. We show how various oscillation patterns of blood cell numbers arise from variance in the control parameters.