Modelling Hematopoiesis Mediated by Growth Factors With Applications to Periodic Hematological Diseases |
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Authors: | Mostafa Adimya Fabien Craustea Shigui Ruanb |
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Institution: | (1) Laboratoire de Mathématiques Appliquées UMR 5142, Université de Pau et des Pays de l’Adour, Avenue de l’université, 64000 Pau, France;(2) Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA |
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Abstract: | 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 understand
some blood diseases characterized by very long period oscillations in circulating blood cells. A system of three differential
equations with delay, corresponding to the cell cycle duration, is proposed and analyzed. The existence of a Hopf bifurcation
at 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, for reasonable cell cycle durations. These oscillations
can be related to observations on some periodic hematological diseases (such as chronic myelogenous leukemia, for example).
1Research was partially supported by the INRIA Futurs, ANUBIS Team.
2Research was partially supported by the NSF and the University of Miami. |
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Keywords: | Delay differential equations Characteristic equation Delay-dependent coefficients Stability switch Hopf bifurcation Cell population models Hematopoiesis Stem cells |
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