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Numerical integration of a mathematical model of hematopoietic stem cell dynamics

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
56
Issue
3
Identifiers
DOI: 10.1016/j.camwa.2008.01.003
Keywords
  • Hematopoietic Stem Cell Dynamics
  • Age-Structured Model
  • Existence Of Steady States
  • Numerical Integration
Disciplines
  • Mathematics
  • Medicine

Abstract

Abstract A mathematical model of hematopoiesis, describing the dynamics of stem cell population, is investigated. This model is represented by a system of two nonlinear age-structured partial differential equations, describing the dynamics of resting and proliferating hematopoietic stem cells. It differs from previous attempts to model the hematopoietic system dynamics by taking into account cell age-dependence of coefficients, that prevents a usual reduction of this system to an unstructured delay differential system. We prove the existence and uniqueness of a solution to our problem, and we investigate the existence of stationary solutions. A numerical scheme adapted to the problem is presented. We show the effectiveness of this numerical technique in the simulation of the dynamics of the solution. Numerical simulations show that long-period oscillations can be obtained in this model, corresponding to a destabilization of the system. These oscillations can be related to observations of some periodical hematological diseases (such as chronic myelogenous leukemia).

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