Title: “Understanding Cell Dynamics in Cancer from Control and Mathematical Biology Standpoints: Particular Insights into the Modeling and Analysis Aspects in Hematopoietic Systems and Leukemia”

Keywords: Modeling, Stability, Time-delay systems, Lyapunov theory, Cancer, Cell cycle.


Abstract :The thesis deals with the modeling and analysis issues of (cancer) cell population dynamics, with particular insights on the process of blood cell formation and acute myeloid leukemia (AML). Models are described through some age-structured partial differential equations, which are suitably reduced to nonlinear time-delay systems of different types (with pointwise or finite and infinite distributed delays, possibly involving time-varying parameters, and coupled to difference equations). Thus, this work provides analysis tools for stability and control, mainly of the class of retarded functional differential equations, coupled with continuous time difference equations. The main contribution relies on the stability analysis of the different (biologically) meaningful steady states of the resulting systems. Thus, whether for healthy or unhealthy (e.g. leukemic) cases, the studied models are investigated through time-domain analysis tools. More precisely, stability properties of the steady states of interest are provided by means of sophisticated strict Lyapunov-like functionals, suitable for the studied models. At any step, insights and medical interpretations of the theoretical results, in light of cancer evolution, are provided. In addition, recent biological and medical evidences on cancer are introduced in the class of systems studied here. This is the case of cell plasticity phenomena and cancer dormancy in models taking into account cohabitation between ordinary and mutated stem cells. Thus, through suitable theoretical studies, it becomes possible to provide a better understanding of the complex mechanisms behind the triggering of some pathological disorders, such as AML. The ultimate aim behind these (stability) studies is to finally suggest some suitable optimized strategies in order to improve cancer treatment through selective combined drug infusions. 

Supervised by: Catherine Bonnet (Inria Paris-Saclay), Frédéric Mazenc (Inria Paris-Saclay) and Jean Clairambault (Sorbonne LJLL, Inria Paris)

Thesis defended November 2017 at CentraleSupélec, Gif-sur-Yvette, France.

Jury members:

  • Françoise Lamnabhi-Lagarrigue (jury president)
  • Alexandre Medvedev (examiner)
  • Raphaël Itzykson (examiner)
  • Pierdomenico Pepe (referee)
  • Mostafa Adimy (referee)
  • Catherine Bonnet (supervisor)
  • Frédéric Mazenc (co-supervisor)
  • Jean Clairambault (co-supervisor)

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