Mathematical model of cyclic kinetics of granulocytopoiesis

A model of time-course variations of granulocytopoiesis which is a system of three non-linear differential equations has been developed. The model describes the basic stages of granulocyte development and includes the chalone mechanism regulating the proliferation of granulocyte precursors in bone marrow. Theoretical investigations applying the vibration theory and computer-aided calculations have shown that the model presents aperiodic and vibrational kinetics of reduction processes in the system of granulocytopoiesis as well as steady-state vibrations of concentrations of mature granulocytes and their precursors (limiting cycles). The variations of the model parameters within which the above dynamic modes occur have been identified. The conditions under which the limiting cycles arise have been examined. The fact that the model simulates various experimentally observed situations suggests that it can be used to predict changes in granulocytopoiesis induced by adverse effects responsible for hemopoietic abnormalities.