This review article presents some mathematical models of hematopoietic cell dynamics related to bone marrow transplantation. Both allogeneic and autologous stem cell transplantations are considered. The models are expressed by threedimensional systems of ordinary differential equations whose variables stand for the abundances of healthy, leukemic and infused cells. Model parameters quantify the cellular processes of growth, cell death and sensibility to microenvironment, and cellcell interactions such as anti-host, anti-cancer and anti-graft effects. Numerical simulations and stability analysis of system equilibria are performed in order to conclude about effectiveness of transplantation procedures. In the case of allogeneic transplantation, the role of initial cell concentrations is highlighted and several therapeutic scenarios for correction of bad post-transplant evolution are suggested. The exposition is mainly based on authors' papers [3,72,75,78-80].
Keywords: Dynamic system, Hematopoiesis, Hematopoietic stem cells, Mathematical model, Myeloid leukemia, Numerical simulation, Stability, Stem cell transplantation.