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.
