Computer Modeling of the Immune System Reconstruction after Peripheral Blood Stem Cell Transplantation

Attention is focused on the immune system reconstruction and the process of production of T- and B- lymphocytes and natural killer (NK) cells after autologous haematopoietic stem cells transplantation (HSCT). The mathematical model for leukopoiesis proposed in Periodic oscillations in leukopoiesis models with two delays is used as an initial point for investigations. HSCs in bone marrow are presented as two descrite groups: proliferating cell and non-proliferating (quiescent) cells. Quiescent cells have one of three possibilities: to be introduced in proliferating phase, to differentiate in a subtype of white blood cells (T-, B-, NK), or to differentiate in any of the other cell types. Four equations are generated from this scenario tree: introduction rate as a function of the number of quiescent cells (ß(Q)); differentiation rate as a function of matured white blood cells (k(W)); the rate of change of quiescent cells as a function of Q, ß(Q), and k(W); the rate of change of matured white blood cless as a function of W, Q, and k(w).