Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases

Mostafa Adimy (1, 2) , Fabien Crauste (1) , Shigui Ruan (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
3 Department of Mathematics [Miami]

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop.

Mots clés: delay differential equations; characteristic equation; delay-dependent coefficients; stability switch; Hopf bifurcation; cell population models; hematopoiesis; stem cells

Domaines: Analyse classique [math.CA]; Systèmes dynamiques [math.DS]

Mostafa Adimy, Fabien Crauste, Shigui Ruan. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bulletin of Mathematical Biology, 2006, 68 (8), pp.2321-2351. ⟨10.1007/s11538-006-9121-9⟩. ⟨hal-00376087⟩