Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-19T02:58:54.884Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Flows in porous media; filtration; seepage Basic methods in fluid mechanics Physiological, cellular and medical topics Biological fluid mechanics

Published online by Cambridge University Press:  15 October 2015

Yannick Deleuze ,
Marc Thiriet  and
Tony Wen-Hann Sheu
Yannick Deleuze*
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan
Marc Thiriet
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France INRIA-Paris-Rocquencourt, EPC REO, Domaine de Voluceau, BP105, 78153 Le Chesnay Cedex
Tony Wen-Hann Sheu
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan Center for Advanced Study in Theoretical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan
*
*Corresponding author. Email addresses: yannick.deleuze@ljll.math.upmc.fr (Y. Deleuze), marc.thiriet@upmc.fr (M. Thiriet), twhsheu@ntu.edu.tw (T. W.-H. Sheu)
Get access

Abstract

In this paper, we study the effects of inserted needle on the subcutaneous interstitial flow. A goal is to describe the physical stress affecting cells during acupuncture treatment. The model consists of the convective Brinkman equations to describe the flow through a fibrous medium. Numerical studies in FreeFem++ are performed to illustrate the acute physical stress developed by the implantation of a needle that triggers the physiological reactions of acupuncture. We emphasize the importance of numerical experiments for advancing in modeling in acupuncture.

Keywords

Finite element methodFreeFem++acupunctureBrinkman modelinterstitial fluid flow

MSC classification

Secondary: 76M10: Finite element methods 76S05: Flows in porous media; filtration; seepage 76Z05: Physiological flows 92C50: Medical applications (general)
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 850 - 867
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Cheng, X., Chinese Acupuncture and Moxibustion. Beijing: Foreign Language Press, 1st ed. ed., 1987.Google Scholar
[2]Langevin, H. M., Churchill, D. L., Fox, J. R., Badger, G. J., Garra, B. S., and Krag, M. H., “Biomechanical response to acupuncture needling in humans,” Journal of Applied Physiology, vol. 91, no. 6, pp. 2471–2478, 2001.CrossRefGoogle ScholarPubMed
[3]Zhang, D., Ding, G., Shen, X., Yao, W., Zhang, Z., Zhang, Y., Lin, J., and Gu, Q., “Role of mast cells in acupuncture effect: a pilot study,” Explore (New York, N.Y.), vol. 4, no. 3, pp. 170–177, 2008.Google Scholar
[4]Ulett, G. A., Han, S., and Han, J.-s., “Electroacupuncture: mechanisms and clinical application,” Biological Psychiatry, vol. 44, pp. 129–138, July 1998.CrossRefGoogle ScholarPubMed
[5]Whittaker, P., “Laser acupuncture: past, present, and future,” Lasers in Medical Science, vol. 19, pp. 69–80, Oct. 2004.Google Scholar
[6]Huang, C. and Sheu, T. W., “Study of the effect of moxibustion on the blood flow,” International Journal of Heat and Mass Transfer, vol. 63, pp. 141–149, 2013.Google Scholar
[7]Huang, V. C. and Sheu, T. W. H., “Heat transfer involved in a warm (moxa-heated) needle treatment,” Acupuncture & Electro-Therapeutics Research, vol. 33, no. 3-4, pp. 169–178, 2008.Google Scholar
[8]Huang, V. C. and Sheu, T. W. H., “On a dynamical view on the meridian transmission,” Journal of Accord Integrative Medicine, vol. 4, no. 2, 2008.Google Scholar
[9]Huang, V. C. and Sheu, T. W. H., “Tissue fluids in microchannel subjected to an externally applied electric potential,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19, no. 1, pp. 64–77, 2009.CrossRefGoogle Scholar
[10]Deleuze, Y., “A mathematical model of mast cell response to acupuncture needling,” Comptes Rendus Mathematique, vol. 351, no. 3-4, pp. 101–105, 2013.Google Scholar
[11]Thiriet, M., Intracellular Signaling Mediators in the Circulatory and Ventilatory Systems, vol. 4 of and Biomechanical Modeling of the Circulatory and Ventilatory Systems. New York, NY: Springer New York, 2013.CrossRefGoogle Scholar
[12]Thiriet, M., Deleuze, Y., and Sheu, T. W. H., “A biological model of acupuncture and its derived mathematical modeling and simulations,” Communications in Computational Physics, 2015.Google Scholar
[13]Thiriet, M., Biology and mechanics of blood flows: Part I: Biology. CRM Series in Mathematical Physics, Springer, NY, 2008.Google Scholar
[14]Thiriet, M., “Cells and tissues,” in Cell and Tissue Organization in the Circulatory and Ventilatory Systems, no. 1 in Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems, pp. 11–67, Springer New York, Jan. 2011.Google Scholar
[15]Fung, P., “Probing the mystery of Chinese medicine meridian channels with special emphasis on the connective tissue interstitial fluid system, mechanotransduction, cells durotaxis and mast cell degranulation,” Chinese Medicine, vol. 4, no. 1, p. 10, 2009.Google Scholar
[16]Swartz, M. A. and Fleury, M. E., “Interstitial flow and its effects in soft tissues,” Annual Review of Biomedical Engineering, vol. 9, no. 1, pp. 229–256, 2007.CrossRefGoogle ScholarPubMed
[17]Pedersen, J. A., Boschetti, F., and Swartz, M. A., “Effects of extracellular fiber architecture on cell membrane shear stress in a 3D fibrous matrix,” Journal of Biomechanics, vol. 40, no. 7, pp. 1484–1492, 2007.Google Scholar
[18]Blasselle, A., Modélisation mathématique de la peau. Thèse de doctorat, Université Pierre et Marie Curie, Paris, France, 2011.Google Scholar
[19]Brinkman, H. C., “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,” Applied Scientific Research, vol. 1, pp. 27–34, Dec. 1949.Google Scholar
[20]Thiriet, M., Cell and Tissue Organization in the Circulatory and Ventilatory Systems, vol. 1 of Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems. New York, NY: Springer New York, 2011.Google Scholar
[21]Biot, M., “Theory of finite deformations of porous solids,” Indiana University Mathematics Journal, vol. 21, no. 7, pp. 597–620, 1972.Google Scholar
[22]Biot, M. A., “General theory of three–dimensional consolidation,” Journal of Applied Physics, vol. 12, no. 2, pp. 155–164, 1941.Google Scholar
[23]Biot, M. A., “Theory of elasticity and consolidation for a porous anisotropic solid,” Journal of Applied Physics, vol. 26, no. 2, pp. 182–185, 1955.Google Scholar
[24]Biot, M. A., “Mechanics of deformation and acoustic propagation in porous media,” Journal of Applied Physics, vol. 33, no. 4, pp. 1482–1498, 1962.Google Scholar
[25]Yao, W. and Ding, G. H., “Interstitial fluid flow: simulation of mechanical environment of cells in the interosseous membrane,” Acta Mechanica Sinica, vol. 27, pp. 602–610, Aug. 2011.Google Scholar
[26]Yao, W., Li, Y., and Ding, G., “Interstitial fluid flow: The mechanical environment of cells and foundation of meridians,” Evidence-Based Complementary and Alternative Medicine, vol. 2012, pp. 1–9, 2012.Google ScholarPubMed
[27]Park, J. Y., Yoo, S. J., Patel, L., Lee, S. H., and S.-Lee, H., “Cell morphological response to low shear stress in a two-dimensional culture microsystem with magnitudes comparable to interstitial shear stress,” Biorheology, vol. 47, pp. 165–178, Jan. 2010.Google Scholar
[28]Forchheimer, P., “Wasserbewegung durch boden,” Z. Ver. Deutsch. Ing, vol. 45, no. 1782, p. 1788, 1901.Google Scholar
[29]Hsu, C. T. and Cheng, P., “Thermal dispersion in a porous medium,” International Journal of Heat and Mass Transfer, vol. 33, pp. 1587–1597, Aug. 1990.CrossRefGoogle Scholar
[30]Nithiarasu, P., Seetharamu, K. N., and Sundararajan, T., “Natural convective heat transfer in a fluid saturated variable porosity medium,” International Journal of Heat and Mass Transfer, vol. 40, pp. 3955–3967, Oct. 1997.Google Scholar
[31]Vafai, K. and Tien, C. L., “Boundary and inertia effects on flow and heat transfer in porous media,” International Journal of Heat and Mass Transfer, vol. 24, pp. 195–203, Feb. 1981.Google Scholar
[32]Hecht, F., “New development in FreeFem++,” Journal of Numerical Mathematics, vol. 20, no. 3-4, p. 251, 2013.Google Scholar
[33]Decoene, A. and Maury, B., “Moving meshes with FreeFem++,” Journal of Numerical Mathematics, vol. 20, p. 195, 2013.Google Scholar
[34]Fernández, M. A., Formaggia, L., Gerbeau, J.-F., and Quarteroni, A., “The derivation of the equations for fluids and structure,” in Cardiovascular Mathematics (Formaggia, L., Quarteroni, A., and Veneziani, A., eds.), no. 1 in MS&A, pp. 77–121, Springer Milan, Jan. 2009.Google Scholar
[35]Chorin, A. J., “A numerical method for solving incompressible viscous flow problems,” Journal of Computational Physics, vol. 2, pp. 12–26, Aug. 1967.Google Scholar
[36]Témam, R., “Une méthode d’approximation de la solution des équations de Navier-Stokes,” Bulletin de la Société Mathématique de France, vol. 96, pp. 115–152, 1968.CrossRefGoogle Scholar
[37]Ladyženskaja, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach Science, 1969.Google Scholar
[38]Babuška, P. I., “Error-bounds for finite element method,” Numerische Mathematik, vol. 16, pp. 322–333, Jan. 1971.Google Scholar
[39]Brezzi, F., “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,” ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, vol. 8, no. R2, pp. 129–151, 1974.Google Scholar
[40]Levick, J. R., “Flow through interstitium and other fibrous matrices,” Experimental Physiology, vol. 72, pp. 409–437, Oct. 1987.CrossRefGoogle ScholarPubMed
[41]Happel, J., “Viscous flow relative to arrays of cylinders,” AIChE Journal, vol. 5, pp. 174–177, June 1959.CrossRefGoogle Scholar
[42]Wei, F., Shi, X., Chen, J., and Zhou, L., “Fluid shear stress-induced cytosolic calcium signaling and degranulation dynamics in mast cells,” Cell Biology International Reports, 2012.Google Scholar