Geodesic
Numerical study of the stopping of aura during migraine
C. Pocci1 ; A. Moussa2 ; F. Hubert3 ; G. Chapuisat4
1Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161, Rome, Italy
2CMLA, ENS Cachan, CNRS, Pres UniverSud, 94235 Cachan, France
3LATP, UMR 6632, Université de Provence, CMI, 39 rue Joliot-Curie 13453 Marseille Cedex 13, France
4LATP, 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},
     year = {2010},
     volume = {30},
     doi = {10.1051/proc/2010005},
     language = {en},
     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

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