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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002360
pages 189-211

ENERGY-PRESERVING MUSCLE TISSUE MODEL: FORMULATION AND COMPATIBLE DISCRETIZATIONS

Dominique Chapelle
INRIA, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
P. Le Tallec
Ecole Polytechnique, 91128 Palaiseau cedex, France
P. Moireau
INRIA, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
M. Sorine
INRIA, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France

Краткое описание

In this paper, we propose a muscle tissue model-valid for striated muscles, in general, and for the myocardium, in particular-based on a multiscale physiological description. This model extends and refines an earlier-proposed formulation by allowing one to account for all major energy exchanges and balances, from the chemical activity coupled with oxygen supply to the production of actual mechanical work, namely, the biological function of the tissue. We thus perform a thorough analysis of the energy mechanisms prevailing at the various scales and proceed to propose a complete discretization strategy-in time and space-respecting the same balance laws. This will be crucial in future works to adequately model the many important physiological-normal and pathological-phenomena associated with these energy considerations.

ЛИТЕРАТУРА

  1. Balaban, R., The role of Ca<sup>2+</sup> signaling in the coordination of mitochondrial ATP production with cardiac work. DOI: 10.1016/j.bbabio.2009.05.011

  2. Balzani, D., Neff, P., Schr&ouml;der, J., and Holzapfel, G., A polyconvex framework for soft biological tissues, adjustment to experimental data. DOI: 10.1016/j.ijsolstr.2005.07.048

  3. Bestel, J., Mod&egrave;le diff&eacute;rentiel de la contraction musculaire contr&ocirc;l&eacute;e: Application au syst&egrave;me cardio-vasculaire.

  4. Bestel, J., Cl&eacute;ment, F., and Sorine, M., A Biomechanical Model of Muscle Contraction.

  5. Brezzi, F. and Fortin, M. , Mixed and Hybrid Finite Element Methods.

  6. Chabiniok, R., Chapelle, D., Lesault, P., Rahmouni, A., and Deux, J., Validation of a biomechanical heart model using animal data with acute myocardial infarction, CI2BM09-MICCAI Workshop on Cardiovascular Interventional Imaging and Biophysical Modelling.

  7. Chapelle, D., Cl&eacute;ment, F., G&eacute;not, F., Le Tallec, P., Sorine, M., and Urquiza, J., A physiologically-based model for the active cardiacmuscle.

  8. Chapelle, D., Fern&agrave;ndez, M., Gerbeau, J.-F., Moireau, P., Sainte-Marie, J., and Zemzemi, N., Numerical simulation of the electromechanical activity of the heart. DOI: 10.1007/978-3-642-01932-6_39

  9. Ciarlet, P. and Geymonat, G., Sur les lois de comportement en &eacute;lasticit&eacute; non lin&eacute;aire.

  10. Costa, K., Holmes, J., and McCulloch, A., Modeling cardiac mechanical properties in three dimensions. DOI: 10.1098/rsta.2001.0828

  11. Fung, Y., Biomechanics: Mechanical Properties of Living Tissues.

  12. G&ouml;ktepe, S., Acharya, S., Wong, J., and Kuhl, E., Computational modeling of passive myocardium. DOI: 10.1002/cnm.1402

  13. Gonzales, O., Exact energy and momentum conserving algorithm for general models in nonlinear elasticity. DOI: 10.1016/S0045-7825(00)00189-4

  14. Hauret, P. and Le Tallec, P., Energy controlling time integration methods for nonlinear elastodynamics and low velocity impact. DOI: 10.1016/j.cma.2005.11.005

  15. Hill, V., The heat of shortening and the dynamic constants of muscle. DOI: 10.1098/rspb.1938.0050

  16. Holzapfel, G. and Ogden, R., Constitutive modelling of passive myocardium: A structurally based framework for material characterization. DOI: 10.1098/rsta.2009.0091

  17. Humphrey, J., Cardiovascular Solid Mechanics&ndash;Cells Tissues and Organs.

  18. Humphrey, J., Continuum biomechanics of soft tissues. DOI: 10.1098/rspa.2002.1060

  19. Hunter, P., McCulloch, A., and ter Keurs, H., Modelling the mechanical properties of cardiac muscle. DOI: 10.1016/S0079-6107(98)00013-3

  20. Huxley, A., Muscle structure and theories of contraction.

  21. Krejci, P., Sainte-Marie, J., Sorine, M., and Urquiza, J., Solutions to muscle fiber equations and their long time behaviour. DOI: 10.1016/j.nonrwa.2005.03.021

  22. Le Tallec, P., Numerical Analysis of Viscoelastic Problems.

  23. Le Tallec, P., Numerical methods for nonlinear three-dimensional elasticity.

  24. Le Tallec, P. and Hauret, P., Energy conservation in fluid structure interactions.

  25. Mirsky, I. and Parmley, W., Assessment of passive elastics tiffness for isolated heart muscle and the intact heart. DOI: 10.1161/​01.RES.33.2.233

  26. Moireau, P., Filtering based data assimilation for second order hyperbolic PDEs: Applications in cardiac mechanics.

  27. Nash, M. and Hunter, P., Computational mechanics of the heart–from tissue structure to ventricular function. DOI: 10.1023/A:1011084330767

  28. Raoult, A., Symmetry groups in nonlinear elasticity: An exercise in vintage mathematics. DOI: 10.3934/cpaa.2009.8.435

  29. Rivlin, R. and Ericksen, J., Stress-deformation relations for isotropic materials.

  30. Sainte-Marie, J., Chapelle, D., Cimrman, R., and Sorine, M., Modeling and estimation of the cardiac electromechanical activity. DOI: 10.1016/j.compstruc.2006.05.003

  31. Saks, V., Favier, R., Guzun, R., Schlattner, U., and Wallimann, T., Molecular system bioenergetics: Regulation of substrate supply in response to heart energy demands. DOI: 10.1113/jphysiol.2006.120584

  32. Veronda, D. and Westmann, R., Mechanical characterization of skin-finite deformation. DOI: 10.1016/0021-9290(70)90055-2


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