no. 3-4
Partial Differential Equations
A mathematical model of mast cell response to acupuncture needling
[Un modèle mathématique de la réponse des mastocytes à la manipulation dʼune aiguille dʼacupuncture]

Présenté par : the Editorial Board

Deleuze, Yannick1, 2
1 Laboratoire Jacques-Louis-Lions, université Pierre-et-Marie-Curie (Paris-6), UMR 7598, 4, place Jussieu, 75252 Paris cedex 05, France
2 Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Da-an District, Taipei 10617, Taiwan, ROC
Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 101-105.

Nous présentons un nouveau modèle de la réponse des mastocytes à la manipulation dʼune aiguille dʼacupuncture basé sur le modèle de chimiotaxie de type Keller–Segel. La manipulation de lʼaiguille induit la libération du chimioattractant par les mastocytes. Nous montrons, dans un système simplifié, que la solution devient singulière en un temps fini pour des conditions initiales suffisamment grandes et concentrées autour du point acupuncture. Dans ces conditions, lʼexplosion de la solution résulte de lʼagrégation des cellules et pourrait mesurer lʼefficacité de la manipulation de lʼaiguille sur le point dʼacupuncture.

We introduce a new model of mast cell response to acupuncture needling based on the Keller–Segel model for chemotaxis. The needle manipulation induces the release of a chemoattractant by the mast cells. We show, in a simplified case, that blow-up of the solution occurs in finite time for large initial data concentrated around the acupoint. In those conditions, blow-up is the result of aggregation of cells and could indicate the efficiency of the acupuncture manipulation of the needle at one acupoint.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.003
Deleuze, Yannick 1, 2

1 Laboratoire Jacques-Louis-Lions, université Pierre-et-Marie-Curie (Paris-6), UMR 7598, 4, place Jussieu, 75252 Paris cedex 05, France
2 Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Da-an District, Taipei 10617, Taiwan, ROC 
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Deleuze, Yannick. A mathematical model of mast cell response to acupuncture needling. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 101-105. doi : 10.1016/j.crma.2013.02.003. http://www.numdam.org/articles/10.1016/j.crma.2013.02.003/

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Cité par Sources :

☆ This work was partially supported by the ‘‘Fondation Sciences mathématiques de Paris”.

☆☆ Many thanks to Benoît Perthame for fruitful discussions about this work.