Skip to Main content Skip to Navigation
Theses

Etude mathématique d'équations aux dérivées partielles hyperboliques modélisant les processus de régulation des cellules sanguines - Applications aux maladies hématologiques cycliques

Abstract : The events allowing production and continuous renewal of blood cells represent a series of complex processes, called haematopoiesis, taking place in the bone marrow. Haematopoiesis is based on a pool of haematopoietic stem cells, having unique capacities of differentiation (capacity to generate all blood cells types) and self renewal (capacity to generate a daugther cell identical to the mother cell). We performed a mathematical study of haematopoiesis based on nonlinear age and maturity structured models. It allowed to highlight the influence of hematopoietic stem cells on the entire blood cell population, these cells actively acting on the population stability. Through the study of models without maturity structure, reduced by integration to a system of differential equations with distributed delay, we obtained the existence of oscillating solutions and, throughout the study of a Hopf bifurcation, of periodic solutions with very long periods compared to the cell cycle duration. These oscillations are characteristic of some blood diseases, called periodic, such as chronic myelogenous leukaemia, one of the most widespread forms of leukaemia. Our work represents a contribution to the study of this disease. Lastly, we considered a haematopoiesis model taking into account the action of some factors, external to the bone marrow, acting on stem cells differentiation. We proved the existence of oscillating solutions which may describe some periodic hematological diseases.
Document type :
Theses
Complete list of metadata

https://tel.archives-ouvertes.fr/tel-00009632
Contributor : Fabien Crauste <>
Submitted on : Friday, July 1, 2005 - 10:44:22 AM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:43:56 PM

Identifiers

  • HAL Id : tel-00009632, version 1

Collections

Citation

Fabien Crauste. Etude mathématique d'équations aux dérivées partielles hyperboliques modélisant les processus de régulation des cellules sanguines - Applications aux maladies hématologiques cycliques. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2005. Français. ⟨tel-00009632⟩

Share

Metrics

Record views

670

Files downloads

1045