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| HAL : hal-00376087, version 1 |
| arXiv : 0904.2501 |
| DOI : 10.1007/s11538-006-9121-9 |
| Fiche détaillée |  Récupérer au format |
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| Bulletin of Mathematical Biology 68, 8 (2006) 2321-2351 |
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| Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases |
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| Mostafa Adimy 1, 2Fabien Crauste 1 |
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| (02/08/2006) |
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| 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. |
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| 1 : | Laboratoire de Mathématiques et de leurs Applications de Pau (LMA-PAU) |
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CNRS : UMR5142 – Université de Pau et des Pays de l'Adour [UPPA] |
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| 2 : | ANUBIS (INRIA Futurs) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3 : | Department of Mathematics [Miami] |
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University of Miami |
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| Domaine | : | Mathématiques/Analyse classique Mathématiques/Systèmes dynamiques |
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| delay differential equations – characteristic equation – delay-dependent coefficients – stability switch – Hopf bifurcation – cell population models – hematopoiesis – stem cells |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00376087, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00376087 | |
| oai:hal.archives-ouvertes.fr:hal-00376087 | |
| Contributeur : Fabien Crauste | |
| Soumis le : Jeudi 16 Avril 2009, 16:15:12 | |
| Dernière modification le : Jeudi 16 Avril 2009, 16:24:24 | |
