Mathematical models for cell motion
 
 
Description:  Several transport-diffusion systems arise as simple models in chemotaxis (motion of bacterias or amebia interacting through a chemical signal) and in angiogenesis (development of capillary blood vessels from an exhogeneous chemoattractive signal by solid tumors). These systems describe the evolution of a density (of cells or blood vessels) coupled with the evolution equation for a chemical substance, through a nonlinear transport term depending on the gradient of the chemoattracting substance. Such systems are successful in recovering various qualitative behavior (chemotactic collapse, ring dynamics). Endothelial (i.e. cells forming blood vessels) have a tendency to form different patterns as networks, initiating the vessels shape. Then hyperbolic models seem better adapted to describe this kind of network formation.
We will present these models, their main mathematical properties (quantitative and qualitative), numerical simulations and, for bacteria E. Coli, we will give a microscopic picture based on a kinetic modelling of the inetraction (nonlinear scattering equation). We show that such models can have global solutions that converge in finite time to the Keller-Segel model, as a scaling parameter vanishes. This point of view has also the advantage of unifying all the models.

Benoit Perthame is Professor at the ??cole Normale Supérieure, Paris, on duty from University Pierre et Marie Curie (Paris 6). He received his These d'Etat from University Paris-Dauphine on Optimal stochastic control, kinetic equations and numerical methods. He has held positions at ENS and University of Orleans before joining UPMC. He was awarded the Prix Pecot of College de France, Medaille d'argent of CNRS, Premio Sacchi-Landriani from Academia Lombarda. He was Editor in Chief of the SMAI journal M2AN and member of the editorial board of several other journals. After his Thesis, he studied kinetic equations and was one of the inventors of the 'kinetic averaging lemma', he extended the notion of 'kinetic schemes' for solving numerically hyperbolic systems and built a theory on a new type of the relations between kinetic equations and hyperbolic conservation laws: the 'kinetic formulations' on which he wrote a book. His main interest concerns now Partial Differential Equations in various aspects of biology and medicine.
Area(s):
Start Date:  2006-05-30
Start Time:   14:30
Speaker:  Benoit Perthame
(??cole Normale Supérieure, Paris)
Place:  Sala 2.4 - Departamento de Matemática
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