Geodesic
Numerical study of the stopping of aura during migraine
C. Pocci1 ; A. Moussa2 ; F. Hubert3 ; G. Chapuisat4
1 Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161, Rome, Italy
2 CMLA, ENS Cachan, CNRS, Pres UniverSud, 94235 Cachan, France
3 LATP, UMR 6632, Université de Provence, CMI, 39 rue Joliot-Curie 13453 Marseille Cedex 13, France
4 LATP, UMR 6632, Université Paul Cézanne Aix-Marseille 3, av Escadrille Normandie-Niemenn 13397 Marseille Cedex 20, France
ESAIM. Proceedings, Tome 30 (2010), pp. 44-52.

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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.
DOI : 10.1051/proc/2010005

C. Pocci 1 ; A. Moussa 2 ; F. Hubert 3 ; G. Chapuisat 4

1 Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161, Rome, Italy
2 CMLA, ENS Cachan, CNRS, Pres UniverSud, 94235 Cachan, France
3 LATP, UMR 6632, Université de Provence, CMI, 39 rue Joliot-Curie 13453 Marseille Cedex 13, France
4 LATP, UMR 6632, Université Paul Cézanne Aix-Marseille 3, av Escadrille Normandie-Niemenn 13397 Marseille Cedex 20, France 
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     author = {C. Pocci and A. Moussa and F. Hubert and G. Chapuisat},
     title = {Numerical study of the stopping of aura during migraine},
     journal = {ESAIM. Proceedings},
     pages = {44--52},
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     doi = {10.1051/proc/2010005},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2010005/}
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C. Pocci; A. Moussa; F. Hubert; G. Chapuisat. Numerical study of the stopping of aura during migraine. ESAIM. Proceedings, Tome 30 (2010), pp. 44-52. doi : 10.1051/proc/2010005. http://geodesic.mathdoc.fr/articles/10.1051/proc/2010005/

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