Bifurcation and Bistability in a Model of Hematopoietic Regulation

Stem cells and their relationship with mature tissues are of increasing interest in the biomedical sciences, but the dynamics of stem cell/tissue interactions are not well understood. We give a generic stem cell/tissue model and examine the dynamics of a specific case of this, namely, a fourcompartment model of blood cell production and regulation. We apply the findings to cyclical neutropenia and periodic chronic myelogenous leukemia, two diseases of the blood production system. We track the position of the Hopf bifurcation believed to give rise to blood cell oscillations in these diseases. Results account for the variable success of granulocyte-colony stimulating factor, a common treatment for cyclical neutropenia, in reducing oscillations. The model displays bistability of periodic solutions, presenting the opportunity to stabilize the system through a temporary perturbation that induces switching between locally stable solutions. It is found that oscillations can be suppressed by properly timed pulses of increased amplification in the platelet line. The medical interpretation of this result is that temporary administration of thrombopoietin may suppress the oscillations. Though it is neutrophil oscillations that characterize both diseases clinically, and though it is probably a destabilization in the neutrophil line that initiates the oscillations, pulses in the neutrophil amplification do not effectively suppress oscillations.