The chemotaxis aggregation principle and application to pattern formation in the brain
by
Vincent Calvez
Ecole Normale Superieure, Paris
Coauthors: Hossein Khonsari (La Pitie-Salpetriere Hospital, Paris)

The Keller-Segel model for cell-to-cell attraction is able to reproduce the phenomenon of a critical mass. That is cells spatially organize themselves only if the total amount of cells is sufficiently high. A typical example is the cell density's blow-up occuring when the total mass is above a certain threshold in 2D.

In this talk we briefly review the Keller-Segel model and its recent extensions by the light of this phenomenon. As a consequence we suggest a 3-species model that describes pattern formation arising in a variant of Multiple Sclerosis. Instead of being homogeneous plaques, the areas of damaged myeline are in fact concentric rings in Baló's Concentric Sclerosis. We show how this simple 3-species model based on chemotaxis exhibits transition between plaques and rings, and derive several qualitative properties such as an interesting correlation between pattern formation and aggressivity of the disease.

Date received: June 19, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavg-20.