Long Period Oscillations in a G0 Model of Hematopoietic Stem Cells

This paper analyzes the dynamics of a G0 cell cycle model of pluripotential stem cells to understand the origin of the long period oscillations of blood cell levels observed in periodic chronic myelogenous leukemia (PCML). The model dynamics are described by a system of two delayed differential equations. We give conditions for the local stability of the non-trivial steady state. We use this conditions to study when stability is lost and oscillations occur, and how various parameters modify the period of these oscillations. We consider a limiting case of the original model in order to compute an explicit solution and give an exact form of the period and the amplitude of oscillations. We illustrate these results numerically and show that the main parameters controlling the period are the cellular loss (the differentiation rate δ and the apoptosis rate γ) while the cell regulation parameters (proliferation rate β and cell cycle duration τ ) mainly influence the amplitude.