Numerical study of the stopping of aura during migraine

Guillemette Chapuisat (1) , Florence Hubert (1) , Ayman Moussa , Christina Pocci

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence of a critical radius below which the wave stops. The approximation scheme used for the simulations is first described and then a numerical study is realized, precising the dependence of the critical radius with respect to the different parameters of the model.

Domaines: Analyse numérique [math.NA]

Guillemette Chapuisat, Florence Hubert, Ayman Moussa, Christina Pocci. Numerical study of the stopping of aura during migraine. ESAIM: Proceedings, 2010, 30, pp.44-52. ⟨hal-00839301⟩