Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model.

We consider a mathematical model describing evolution of normal and leukemic hematopoietic stem cells (HSC) and differentiated cells in bone marrow. We focus on chronic myeloid leukemia (CML), a cancer of blood cells resulting from a malignant transformation of hematopoietic stem cells. The dynamics are given by a system of ordinary differential equations for normal and leukemic cells. Homeostasis regulates the proliferation of normal HSC and leads the dynamics to an equilibrium. This mechanism is partially efficient for leukemic cells. We define homeostasis by a functional of either hematopoietic stem cells, differentiated cells or both cell lines. We determine the number of hematopoietic stem cells and differentiated cells at equilibrium. Conditions for regeneration of hematopoiesis and persistence of CML are obtained from the global asymptotic stability of equilibrium states. We prove that normal and leukemic cells can not coexist for a long time. Numerical simulations illustrate our analytical results. The study may be helpful in understanding the dynamics of normal and leukemic hematopoietic cells.