Section:
New Results
Hematopoietic model with feedback control
Participants :
Mostafa Adimy [Contact person] , Lila Sebaa.
In collaboration with O. Angulo and C. Marquet.
We investigate a mathematical model of blood cell production in the bone marrow (hematopoiesis). The model describes both
the evolution of primitive hematopoietic stem cells and the maturation of these cells as they differentiate to form the three
types of blood cells (red blood cells, white cells and platelets). The primitive hematopoietic stem cells and the first
generations of each line (progenitors) are able to self-renew, and can be either in a proliferating or in a resting phase
(-phase). These properties are gradually lost while cells become more and more mature. The three types of progenitors
and mature cells are coupled to each other via their common origin in primitive hematopoietic stem cells compartment. Peripheral
control loops of primitive hematopoietic stem cells and progenitors as well as a local autoregulatory loop are considered in the
model. The resulting system is composed by eleven age-structured partial differential equations. To analyze this model, we don't
take into account cell age-dependence of coefficients, that prevents a usual reduction of the structured system to an unstructured
delay differential system. We investigate some fundamental properties of the solutions of this system, such as boundedness and
positivity. We study the existence of stationary solutions: trivial, axial and positive steady states. Then we give
conditions for the local asymptotic stability of the trivial steady state and by using a Lyapunov function, we obtain a sufficient
condition for its global asymptotic stability [7] . In some particular cases, we analyze the local asymptotic
stability of the positive steady state by using the characteristic equation. Finally, by numerical simulations, we illustrate our
results and we show that a change in the duration of cell cycle can cause oscillations. This can be related to observations of some
periodical hematological disease such as chronic myelogenous leukemia, cyclical neutropenia, cyclical thrombocytopenia, etc.
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