The dynamics of a packed cell tissue

par Mlle Marina Amado Ferreira (Department of Mathematics, Imperial College London)

mardi 9 janv. 2018, 11:00 → 12:00 Europe/Paris

432 (4ème tage) (INRIA- antenne Lyon- La Doua, Bâtiment CEI-2 (tram: T1-IUT FEYSSINE))

In a packed tissue neighboring cells exert high pressure on each other at all times. Such mechanical interactions are believed to play an important role on the dynamics of the tissue. However, their contribution to the tissue shape is not yet fully understood. In this talk I will first present a framework to model this type of systems based on a geometric representation of individual cells. The cells interact with each other aiming at minimizing a local potential energy, subjected to non-overlapping constraints. Mathematically, the problem is formulated as a non-convex minimization problem, which will be tackled with the recently proposed damped Arrow-Hurwicz algorithm. I then apply this framework to the study of a pseudo-stratified epithelial tissue. Some preliminary numerical results will be presented to show how the tissue may be deformed when simple defects on individual cells are introduced.