Sébastien Martin : "A 3d mathematical model of the mucociliary transport"

mardi 6 janv. 2026, 14:00 → 16:00 Europe/Paris

Résumé: 

We present a hierarchy of mathematical models for the numerical simulation of active thin structures in a viscous fluid,  with an application to mucociliary clearance. This requires accurate simulation of the motion of large cilia forests and analysis of their impact on the flow. In a 3D domain, individual cilia are described explicitly, and we study their collective action on the fluid, which consists of the periciliary layer (PCL) and mucus. The model is built on three key components: 

(1) a parametrization of the prescribed ciliary motion including the metachronal wave propagating through the forest, 

(2) hydrodynamic forces computed via slender body theory based  on a 1D representation of the cilia, and 

(3) the maintenance of the two-fluid structure through a surface tension mechanism between the  PCL and mucus. 

This results in a nonlocal 3D Stokes problem with singular source terms due to the 1D action of cilia on the fluid. From the 3D model, we also derive a spatially averaged 1D model describing the dynamics of the mean mucus velocity propelled by the cilia. This 
reduced model incorporates both ciliary motility and the influence of air as a transport mechanism. Together, the 3D and 1D models allow us to explore the influence of key parameters - such as ciliary motility, cilia density, and air - on transport efficiency.