Section: New Results

Mathematical Modelling of Acute Myeloid Leukemia

Participants : Catherine Bonnet, Jean Clairambault [MAMBA project-team] , François Delhommeau [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] , Walid Djema, Emilia Fridman [Tel-Aviv University] , Pierre Hirsch [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] , Frédéric Mazenc, Hitay Özbay [Bilkent University] .

The ALMA3-project is about the modeling and analysis of healthy and unhealthy cell population dynamics, with a particular focus on hematopoiesis, which is the process of blood cell production and continuous replenishment. We point out that medical research is now looking for new combined targeted therapies able to overcome the challenge of cancer cells (e.g. to stop overproliferation, to restore normal apoptosis rates and differentiation of immature cells, and to avoid the high toxicity effects that characterize heavy non-selective chemotherapy). In that quest, the ultimate goal behind mathematical studies is to provide some inputs that should help biologists to suggest and test new treatment, and to contribute within multi-disciplinary groups in the opening of new perspectives against cancer. Thus, our research project is imbued within a similar spirit and fits the expectations of a better understanding of the behavior of healthy and unhealthy blood cell dynamics. It involve intensive collaboration with hematologists from Saint Antoine hospital in Paris, and aims to analyze the cell fate evolution in treated or untreated leukemia, allowing for the suggestion of new anti-leukemic combined chemotherapy.

In 2017, we have discussed some of the issues that are related to the modeling of the cell cycle, with particular insight into hematopoietic systems. For instance, i) we introduced and studied for the first time the effect of cell plasticity (dedifferentiation and transdifferentiation mechanisms) in the class of models that we focus on, and ii) we considered the effect of cell-arrest (i.e. some cells can be arrested during their cell-cycle) in models with several maturity stages. Stability features of the resulting biological 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, particularly in the case of acute myeloblastic leukemia (AML). More precisely, these are nonlinear time-delay systems that involve finite or infinite distributed delay terms, with possibly time-varying parameters. We pursue the objectives of earlier works in order to understand the interactions between the various parameters and functions involved in the mechanisms we study. Sometimes, we extend the stability analysis and the application of some already existing models, whereas news models and variants are other times introduced to cover novel biological evidences, such as: mutations accumulation and cohabitation between ordinary and mutated cells in niches, control and eradication of cancer stem cells, cancer dormancy and cell plasticity. In fact, the challenging problem that we are facing is to steadily extend both modelling and analysis aspects to constantly better represent this complex physiological mechanism, which is not yet fully understood. So, this year, we have progressed on our project and we have extended our works in order to develop the modeling and analysis aspects in cancer dormancy by including the effects of immuno-therapies in AML [48]. Lyapunov-like techniques have been used in this work in order to derive global or local exponential stability conditions for that class of differential-difference systems. Finally, in [49], we have modeled the role played by growth factors -these are hormone-like molecules- or drugs on the regulation of various biological features that are involved in hematopoiesis.