Cette thèse porte sur la modélisation et l’analyse de stabilité de certains mécanismes biologiques complexes en rapport avec le cancer. Un intérêt particulier est porté au cas de l’hématopoïèse et de la leucémie aiguë myéloblastique (LAM). Les modèles utilisés et/ou introduits dans cette thèse se décrivent par des équations aux dérivées partielles structurées en âge, qui se réduisent à des systèmes à retards de plusieurs types (retards ponctuels ou distribués, à support fini ou infini). Ces modèles à retards sont parfois couplés à des équations aux différences, et possiblement avec des paramètres variant dans le temps. Un des principaux challenges dans ce travail consiste à développer des méthodes temporelles, qui se basent sur la construction de fonctionnelles de Lyapunov-Krasovskii strictes, pour les systèmes non-linéaires à retards étudiés. Les principales notions abordées dans ces travaux incluent : l’analyse de stabilité/stabilisation et de robustesse, l’emploi de techniques de modélisation des populations cellulaires saines et malades, l’étude de différentes classes de systèmes dynamiques, (possiblement à temps variant ou à commutation), et également l’introduction de quelques outils issus de l’intelligence artificielle (planification et recherche de solution) dans un contexte de modèles biologiques. Ainsi, les méthodes de modélisation et d’analyse employées dans ce travail ont permis d’une part d’étendre les résultats de stabilité de cette classe de systèmes biologiques, et d’autre part de mieux comprendre certains mécanismes biologiques liés au cancer et sa thérapie. Plus précisément, certains concepts récemment établis en biologie et en médecine sont mis en évidence dans ce travail pour la première fois dans cette classe de systèmes, telles que : la dédifférenciation des cellules (plasticité), ou encore la dormance des cellules cancéreuses dans des modèles tenant compte de la cohabitation entre cellules saines et mutées. Les résultats obtenus sont interprétés dans le cas de l’hématopoïèse et de la LAM, mais ce travail s’applique également à d’autres types de tissus où le cycle cellulaire se produit de façon similaire. / Medical research is looking for new combined targeted therapies against cancer. Our research project -which involves intensive collaboration with hematologists from Saint-Antoine Hospital in Paris- is imbued within a similar spirit and fits the expectations of a better understanding of the behavior of blood cell dynamics. In fact, hematopoiesis provides a paradigm for studying all the mammalian stem cells, as well as all the mechanisms involved in the cell cycle. We address multiple issues related to the modeling and analysis of the cell cycle, with particular insights into the hematopoietic systems. Stability features of the models are highlighted, since systems trajectories reflect the most prominent healthy or unhealthy behaviors of the biological process under study. We indeed perform stability analysis of systems describing healthy and unhealthy situations, with a particular interest in the case of acute myeloblastic leukemia (AML). Thus, we pursue the objectives of understanding the interactions between the various parameters and functions involved in the mechanisms of interest. For that purpose, an advanced stability analysis of the cell fate evolution in treated or untreated leukemia is performed in several modeling frameworks, and our study suggests new anti-leukemic combined chemotherapy. Throughout the thesis, we cover many biological evidences that are currently undergoing intensive biological research, such as: cell plasticity, mutations accumulation, cohabitation between ordinary and mutated cells, control or eradication of cancer cells, cancer dormancy, etc.Among the contributions of Part I of the thesis, we can mention the extension of both modeling and analysis aspects in order to take into account a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. We also introduce for the first time cell-plasticity features to the class of systems that we are focusing on.Next, in Part II, stability analyses of some differential-difference cell population models are performed through several time-domain techniques, including tools of Comparative and Positive Systems approaches. Then, a new age-structured model describing the coexistence between cancer and ordinary stem cells is introduced. This model is transformed into a nonlinear time-delay system that describes the dynamics of healthy cells, coupled to a nonlinear differential-difference system governing the dynamics of unhealthy cells. The main features of the coupled system are highlighted and an advanced stability analysis of several coexisting steady states is performed through a Lyapunov-like approach for descriptor-type systems. We pursue an analysis that provides a theoretical treatment framework following different medical orientations, among which: i) the case where therapy aims to eradicate cancer cells while preserving healthy ones, and ii) a less demanding, more realistic, scenario that consists in maintaining healthy and unhealthy cells in a controlled stable dormancy steady-state. Mainly, sufficient conditions for the regional exponential stability, estimate of the decay rate of the solutions, and subsets of the basins of attraction of the steady states of interest are provided. Biological interpretations and therapeutic strategies in light of emerging AML-drugs are discussed according to our findings.Finally, in Part III, an original formulation of what can be interpreted as a stabilization issue of population cell dynamics through artificial intelligence planning tools is provided. In that framework, an optimal solution is discovered via planning and scheduling algorithms. For unhealthy hematopoiesis, we address the treatment issue through multiple drug infusions. In that case, we determine the best therapeutic strategy that restores normal blood count as in an ordinary hematopoietic system.
| Identifer | oai:union.ndltd.org:theses.fr/2017SACLS470 |
| Date | 21 November 2017 |
| Creators | Djema, Walid |
| Contributors | Université Paris-Saclay (ComUE), Bonnet, Catherine |
| Source Sets | Dépôt national des thèses électroniques françaises |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation, Text |
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