Partial Differential Equations
A mathematical model of mast cell response to acupuncture needling
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 101-105.

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.

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.

Received:
Accepted:
Published online:
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
@article{CRMATH_2013__351_3-4_101_0,
     author = {Deleuze, Yannick},
     title = {A mathematical model of mast cell response to acupuncture needling},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {101--105},
     publisher = {Elsevier},
     volume = {351},
     number = {3-4},
     year = {2013},
     doi = {10.1016/j.crma.2013.02.003},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.02.003/}
}
TY  - JOUR
AU  - Deleuze, Yannick
TI  - A mathematical model of mast cell response to acupuncture needling
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 101
EP  - 105
VL  - 351
IS  - 3-4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.02.003/
DO  - 10.1016/j.crma.2013.02.003
LA  - en
ID  - CRMATH_2013__351_3-4_101_0
ER  - 
%0 Journal Article
%A Deleuze, Yannick
%T A mathematical model of mast cell response to acupuncture needling
%J Comptes Rendus. Mathématique
%D 2013
%P 101-105
%V 351
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.02.003/
%R 10.1016/j.crma.2013.02.003
%G en
%F CRMATH_2013__351_3-4_101_0
Deleuze, Yannick. A mathematical model of mast cell response to acupuncture needling. Comptes Rendus. Mathématique, Volume 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/

[1] Blanchet, A.; Dolbeault, J.; Perthame, B. Two-dimensional Keller–Segel model: optimal critical mass and qualitative properties of the solutions, Electron. J. Differential Equations, Volume 44 (2006), pp. 1-33

[2] Calvez, V.; Corrias, L. The parabolic–parabolic Keller–Segel model in R2, Commun. Math. Sci., Volume 6 (2008), pp. 417-447

[3] Cheng, X. Chinese Acupuncture and Moxibustion, Foreign Language Press, Beijing, 1987

[4] F. Hecht, New development in FreeFem++, J. Numer. Math. (2013), in press.

[5] Hsiao, S.-H.; Tsai, L.-J. A neurovascular transmission model for acupuncture-induced nitric oxide, J. Acupuncture Meridian Stud., Volume 1 (2008), pp. 42-50

[6] Hsiu, H.; Hsu, W.-C.; Hsu, C.-L.; Huang, S.-M. Assessing the effects of acupuncture by comparing needling the Hegu acupoint and needling nearby nonacupoints by spectral analysis of microcirculatory laser Doppler signals, Evid.-Based Complement. Alternat. Med., Volume 2011 (2011), p. 435928

[7] Jager, W.; Luckhaus, S. On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., Volume 329 (1992), pp. 819-824

[8] Keller, E.F.; Segel, L.A. Model for chemotaxis, J. Theoret. Biol., Volume 30 (1971), pp. 225-234

[9] Kuo, T.C.; Chen, Y.J.; Kuo, H.Y.; Chan, C.F. Blood flow effect of acupuncture on the human meridian, Med. Acupuncture, Volume 22 (2010), pp. 33-40

[10] Langevin, H.M.; Churchill, D.L.; Cipolla, M.J. Mechanical signaling through connective tissue: a mechanism for the therapeutic effect of acupuncture, FASEB J., Volume 15 (2001), pp. 2275-2282

[11] Langevin, H.M.; Churchill, D.L.; Wu, J.; Badger, G.J.; Yandow, J.A.; Fox, J.R. et al. Evidence of connective tissue involvement in acupuncture, FASEB J., Volume 16 (2002), pp. 872-874

[12] Metcalfe, D.; Baram, D.; Mekori, Y. Mast cells, Physiol. Rev., Volume 77 (1997), pp. 1033-1079

[13] Nagai, T.; Senba, T. Global existence and blow-up of radial solutions to a parabolic–elliptic system of chemotaxis, Adv. Math. Sci. Appl., Volume 8 (1998), pp. 145-156

[14] Nilsson, G.; Johnell, M.; Hammer, C.H.; Tiffany, H.L.; Nilsson, K.; Metcalfe, D.D. et al. C3a and C5a are chemotaxins for human mast cells and act through distinct receptors via a pertussis toxin-sensitive signal transduction pathway, J. Immunol., Volume 157 (1996), pp. 1693-1698

[15] Perthame, B. Transport Equations in Biology, Birkhäuser, 2007

[16] Thiriet, M. Biology and Mechanics of Blood Flows: Part I: Biology, Springer, New York, 2008

[17] Urb, M.; Sheppard, D.C. The role of mast cells in the defence against pathogens, PLoS Pathog., Volume 8 (2012), p. e1002619

[18] Yu, X.; Ding, G.; Huang, H.; Lin, J.; Yao, W.; Zhan, R. Role of collagen fibers in acupuncture analgesia therapy on rats, Connect. Tissue Res., Volume 50 (2009), pp. 110-120

[19] Zhang, D.; Ding, G.; Shen, X.; Yao, W.; Zhang, Z.; Zhang, Y. et al. Role of mast cells in acupuncture effect: a pilot study, Explore (NY), Volume 4 (2008), pp. 170-177

Cited by Sources:

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

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