A model of macroscale deformation and microvibration in skeletal muscle tissue
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, p. 805-823

This paper deals with modeling the passive behavior of skeletal muscle tissue including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformation and incompressibility at the macroscale with chains of coupled nonlinear oscillators. The model verifies that an externally applied vibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells. From the numerical analysis point of view, one faces here a partial differential-algebraic equation (PDAE) that after semi-discretization in space by finite elements possesses an index up to three, depending on certain physical parameters. In this context, the consequences for the time integration as well as possible remedies are discussed.

DOI : https://doi.org/10.1051/m2an/2009030
Classification:  65L05,  65M12,  65M20,  74C05
Keywords: skeletal muscle tissue, microvibrations, coherence, PDAE, index, time integration
     author = {Simeon, Bernd and Serban, Radu and Petzold, Linda R.},
     title = {A model of macroscale deformation and microvibration in skeletal muscle tissue},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {4},
     year = {2009},
     pages = {805-823},
     doi = {10.1051/m2an/2009030},
     zbl = {1168.92008},
     mrnumber = {2542878},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_4_805_0}
Simeon, Bernd; Serban, Radu; Petzold, Linda R. A model of macroscale deformation and microvibration in skeletal muscle tissue. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, pp. 805-823. doi : 10.1051/m2an/2009030. http://www.numdam.org/item/M2AN_2009__43_4_805_0/

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