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

  • Yannick Deleuze (a1) (a2), Marc Thiriet (a1) (a3) (a4) and Tony Wen-Hann Sheu (a2) (a5)
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.

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Corresponding author
*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)
References
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[1]Cheng, X., Chinese Acupuncture and Moxibustion. Beijing: Foreign Language Press, 1st ed. ed., 1987.
[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. 24712478, 2001.
[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. 170177, 2008.
[4]Ulett, G. A., Han, S., and Han, J.-s., “Electroacupuncture: mechanisms and clinical application,” Biological Psychiatry, vol. 44, pp. 129138, July 1998.
[5]Whittaker, P., “Laser acupuncture: past, present, and future,” Lasers in Medical Science, vol. 19, pp. 6980, Oct. 2004.
[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. 141149, 2013.
[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. 169178, 2008.
[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.
[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. 6477, 2009.
[10]Deleuze, Y., “A mathematical model of mast cell response to acupuncture needling,” Comptes Rendus Mathematique, vol. 351, no. 3-4, pp. 101105, 2013.
[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.
[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.
[13]Thiriet, M., Biology and mechanics of blood flows: Part I: Biology. CRM Series in Mathematical Physics, Springer, NY, 2008.
[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. 1167, Springer New York, Jan. 2011.
[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.
[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. 229256, 2007.
[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. 14841492, 2007.
[18]Blasselle, A., Modélisation mathématique de la peau. Thèse de doctorat, Université Pierre et Marie Curie, Paris, France, 2011.
[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. 2734, Dec. 1949.
[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.
[21]Biot, M., “Theory of finite deformations of porous solids,” Indiana University Mathematics Journal, vol. 21, no. 7, pp. 597620, 1972.
[22]Biot, M. A., “General theory of three–dimensional consolidation,” Journal of Applied Physics, vol. 12, no. 2, pp. 155164, 1941.
[23]Biot, M. A., “Theory of elasticity and consolidation for a porous anisotropic solid,” Journal of Applied Physics, vol. 26, no. 2, pp. 182185, 1955.
[24]Biot, M. A., “Mechanics of deformation and acoustic propagation in porous media,” Journal of Applied Physics, vol. 33, no. 4, pp. 14821498, 1962.
[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. 602610, Aug. 2011.
[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. 19, 2012.
[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. 165178, Jan. 2010.
[28]Forchheimer, P., “Wasserbewegung durch boden,” Z. Ver. Deutsch. Ing, vol. 45, no. 1782, p. 1788, 1901.
[29]Hsu, C. T. and Cheng, P., “Thermal dispersion in a porous medium,” International Journal of Heat and Mass Transfer, vol. 33, pp. 15871597, Aug. 1990.
[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. 39553967, Oct. 1997.
[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. 195203, Feb. 1981.
[32]Hecht, F., “New development in FreeFem++,” Journal of Numerical Mathematics, vol. 20, no. 3-4, p. 251, 2013.
[33]Decoene, A. and Maury, B., “Moving meshes with FreeFem++,” Journal of Numerical Mathematics, vol. 20, p. 195, 2013.
[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. 77121, Springer Milan, Jan. 2009.
[35]Chorin, A. J., “A numerical method for solving incompressible viscous flow problems,” Journal of Computational Physics, vol. 2, pp. 1226, Aug. 1967.
[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. 115152, 1968.
[37]Ladyženskaja, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach Science, 1969.
[38]Babuška, P. I., “Error-bounds for finite element method,” Numerische Mathematik, vol. 16, pp. 322333, Jan. 1971.
[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. 129151, 1974.
[40]Levick, J. R., “Flow through interstitium and other fibrous matrices,” Experimental Physiology, vol. 72, pp. 409437, Oct. 1987.
[41]Happel, J., “Viscous flow relative to arrays of cylinders,” AIChE Journal, vol. 5, pp. 174177, June 1959.
[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.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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