Modeling and numerical simulation of ciliated systems.
In this talk I will present work about the mathematical modeling of complex active fluids in which the activity comes from fine structures called cilia. This is the case for example of bronchial mucus, set in motion by the coordinated beating of cilia covering the walls of the bronchi. This mechanism, called mucocilar transport, is necessary for the evacuation of inhaled impurities and many pathologies – asthma, chronic bronchitis – result from its dysfunction. The study of this mechanism involves aspects of modeling, analysis and calculation, related to potential applications in medicine. Our objective is to propose an analysis and numerical simulation tool to study the impact on these biological fluids of the beating of the cilia and the dependence of certain parameters such as their density or the viscosity of the fluid. Since we wish to be able to simulate a large number of cilia, we need to consider a fluid-structure interaction model involving a low resolution cost, but sufficiently complete to allow us to reproduce the collective movements emerging in these fluids. I will present two models of different complexity, as well as different numerical strategies to solve them, and I will show the collective dynamics reproduced by our simulations.
