Section: New Results
Modeling and control of Acute Myeloid Leukemia
Participants : José Luis Avila Alonso [correspondent] , Annabelle Ballesta [BANG project-team] , Frédéric Bonnans [COMMANDS project-team] , Catherine Bonnet, Jean Clairambault [BANG project-team] , Xavier Dupuis [COMMANDS project-team] , Pierre Hirsch [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] , Jean-Pierre Marie [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] , Faten Merhi [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] , Silviu Iulian Niculescu, Hitay Özbay [Bilkent University, Ankara, Turkey] , Ruoping Tang [INSERM Paris (Team18 of UMR 872) Cordeliers Research Centre and St. Antoine Hospital, Paris] .
In  we propose a new mathematical model of the cell dynamics in Acute Myeloid Leukemia (AML) which takes into account the four different phases of the proliferating compartment. The dynamics of the cell populations are governed by transport partial differential equations structured in age and by using the method of characteristics, we obtain that the dynamical system of equation can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. Local stability conditions for a particular equilibrium point, corresponding to a positive cells, are derived in terms of a set of inequalities involving the parameters of the mathematical model. A parameter estimation of our model is being performed using biological data (Annabelle Ballesta).
We have also studied a coupled model for healthy and cancer cell dynamics in Acute Myeloid Leukemia consisting of two stages of maturation for cancer cells and three stages of maturation for healthy cells. The cell dynamics are modelled by nonlinear partial differential equations. The interconnection phenomenon between the healthy and cancer cells takes place on the re-introduction functions leaving the resting compartments to the proliferating compartments of both populations of cells at the first stage. For a particular healthy equilibrium point, locally stability conditions involving the parameters of the mathematical model are obtained  ,  .