A mathematical model of mast cell response to acupuncture needling

Abstract

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. To cite this article: Y. Deleuze, C. R. Acad. Sci. Paris, Ser. I 340 (2005). RésuméUn modèle mathématique de la réponse des mastocytesà la manipulation d'une aiguille d'acupuncture. Nous présentons un nouveau modèle de la réponse des mastocytesà la manipulation d'une aiguille d'acupuncture basé sur le modèle de chimiotaxie de type Keller-Segel. La manipulation de l'aiguille 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, l'explosion de la solutions résulte de l'agrégation des cellules et pourrait mesurer l'efficacité de la manipulation de l'aiguille sur le point d'acupuncture. Pour citer cet article : Y. Deleuze, C. R. Acad. Sci. Paris, Ser. I 340 (2005).. This work was partially supported by Fondation Sciences Mathématiques de Paris. . Many thanks to Benoît Perthame for fruitful discussions about this work.

Mast Cells and Acupuncture Analgesia

“…One of the important advantages of these models is the convenience to giving deductive but reasonable quantitative results that are not possible to measure with current techniques. Yannick et al analyzed the effect of mast cells density on acupuncture by numerical simulation [ 78 ]. Shi et al established a mathematical model to simulate the intracellular calcium signal and degranulation of a mast cell [ 79 ].…”

A Biological Model of Acupuncture and its Derived Mathematical Modeling and Simulations

“…In the differential system (2.11), the total mass is conserved, that is, the total number of cells in the domain remains constant, but their localization changes: A singularity appears in a finite time and the cell density blows up at the singularity point [11], that is blow-up solution happens, if: (1) the initial density of mastocytes is high enough…”

Modeling and Simulation of the Interstitial Medium Deformation Induced by the Needle Manipulation During Acupuncture

“…A self-sustained process is created via the recruitment of regional and circulating mastocytes [10,11]. Newly recruited mastocytes at acupoints experience a degranulation triggered by the stress field.…”

“…Such a process is sustained by the recruitment of mastocytes (chemotaxis). We have developed a model of chemotactic self-sustained response of mastocytes [10,11]. The developed mathematical model constitutes a system of parabolic partial differential equations.…”