Geodesic
Modélisation des dépressions corticales envahissantes et existence de fronts progressifs
Guillemette Chapuisat1
1 CMLA, ENS Cachan, CNRS, Pres UniverSud, 94235 Cachan, France
ESAIM. Proceedings, Tome 27 (2009), pp. 90-106.

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Spreading depression is a transient depolarization of neurons that spreads slowly through a part of the brain during stroke, epilepsy or migraine with aura. They have been observed and studied in most animal species for more than 50 years, but their existence in the human brain is still discussed. Mathematical models of spreading depressions have been established; they are linked to a reaction-diffusion mechanism. After some numerical experiments, we have made the following hypothesis: The mecanisms that trigger spreading depressions are the same in the human brain as in the rodent brain for example, but the morphology of the human brain could explain the non-observation of these waves. Hence we have studied the following equation: where is the space variable. We have proved that if R is small enough, there is no travelling front solution of these equation. And if R is large enough, there exists a travelling front in the x-direction. This result is obtained by studying the energy of a solution with special initial conditions in several travelling referentials.
DOI : 10.1051/proc/2009021

Guillemette Chapuisat 1

1 CMLA, ENS Cachan, CNRS, Pres UniverSud, 94235 Cachan, France 
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     title = {Mod\'elisation des d\'epressions corticales envahissantes et existence de fronts progressifs},
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     doi = {10.1051/proc/2009021},
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Guillemette Chapuisat. Modélisation des dépressions corticales envahissantes et existence de fronts progressifs. ESAIM. Proceedings, Tome 27 (2009), pp. 90-106. doi : 10.1051/proc/2009021. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009021/

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