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, Stem cells.


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. 

Supervisors:

Catherine Bonnet (Inria Paris-Saclay, DISCO project-team, L2S-CNRS CentraleSupélec)

Frédéric Mazenc (Inria Paris-Saclay, DISCO project-team, L2S-CNRS CentraleSupélec)

Jean Clairambault (Sorbonne LJLL, Inria Paris, MAMBA project-team)

Thesis defended on 21st November 2017 at CentraleSupélec, Gif-sur-Yvette in France

Jury members:

  • Françoise Lamnabhi-Lagarrigue – CNRS, L2S-CentraleSupélec, Paris Saclay, France – (jury president)
  • Alexandre Medvedev – Uppsala University, Sweden – (examiner)
  • Raphaël Itzykson – AP-HP, Dr. St-Louis Hospital, Paris, France – (examiner)
  • Pierdomenico Pepe – L’Aquila University, Italy – (referee)
  • Mostafa Adimy – Inria Grenoble Rhône-Alpes – (referee)
  • Catherine Bonnet (supervisor)
  • Frédéric Mazenc (co-supervisor)
  • Jean Clairambault (co-supervisor)

Selected related papers:

[S1] W. Djema, C. Bonnet, J. Clairambault, F. Mazenc, E. Fridman, P. Hirsch, F. Delhommeau, ‘Control in Dormancy or Eradication of Tumor Stem Cells: Mathematical Modeling and Stability Issues’, Journal of Theoretical Biology (JTB), 2018. [PDF]

[S2] W. Djema, F. Mazenc, C. Bonnet, ‘Stability analysis and robustness results for a nonlinear system with distributeddelays describing hematopoiesis’, Systems & Control Letters (SCL), 2017. [PDF]

[S3] W. Djema, F. Mazenc, C. Bonnet, J. Clairambault, E. Fridman, “Stability Analysis of a Nonlinear System with Infinite Distributed Delays Describing Cell Dynamics”, American Control Conference (ACC), 2018.

[S4] W. Djema, C. Bonnet, F. Mazenc, J. Clairambault, “Introducing Cell Plasticity Mechanisms into a Class of Cell Population Dynamical Systems”, American Control Conference (ACC), 2018.

[S5] W. Djema, H. Özbay, C. Bonnet, E. Fridman, F. Mazenc, J. Clairambault, “Analysis of Blood Cell Production under Growth Factors Switching”, IFAC World Congress (IFAC WC), Toulouse, France, 2017. [PDF]

[S6] W. Djema, C. Bonnet, J. Clairambault, F. Mazenc, P. Hirsch, F. Delhommeau, “Analysis of a Model of Dormancy in Cancer as a State of Coexistence Between Tumor and Healthy Stem Cells”, IEEE American Control Conference (ACC), Seattle, USA, 2017.

[S7] W. Djema, F. Mazenc, C. Bonnet, J. Clairambault, P. Hirsch, F. Delhommeau, “Stability of a Delay System Coupled to a Delay Differential-Difference System Describing the Coexistence of Ordinary and Mutated Hematopoietic Stem Cells”, IEEE 55th Conference on Decision and Control (CDC), Las Vegas, Nevada, USA, 2016. [PDF]

[S8] E. Fridman, C. Bonnet, F. Mazenc, W. Djema“Stability of the cell dynamics in Acute Myeloid Leukemia”, Systems & Control Letters (SCL), 2016. [PDF]

[S9] W. Djema, F. Mazenc, C. Bonnet, “Analysis of a Nonlinear Delay Differential-Difference Biological Model”, IFAC Time-Delay Systems (TDS), IFAC-PapersOnLine 49.10, pp. 246-251., Istanbul, Turkey, 2016.

[S10] W. Djema, F. Mazenc, C. Bonnet, “Stability of Immature Cell Dynamics in Healthy and Unhealthy Hematopoiesis”, IEEE American Control Conference (ACC), Boston, MA, USA, pp. 6121-6126, IEEE, 2016.

[S11] W. Djema, F. Mazenc, C. Bonnet, “Lyapunov Stability Analysis of a Model Describing Hematopoiesis”, European Control Conference (ECC), Linz, Austria, pp. 2711-2716, IEEE, 2015.