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.
Mots-clés : skeletal muscle tissue, microvibrations, coherence, PDAE, index, time integration
@article{M2AN_2009__43_4_805_0,
author = {Simeon, Bernd and Serban, Radu and Petzold, Linda R.},
title = {A model of macroscale deformation and microvibration in skeletal muscle tissue},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {805--823},
publisher = {EDP-Sciences},
volume = {43},
number = {4},
year = {2009},
doi = {10.1051/m2an/2009030},
mrnumber = {2542878},
zbl = {1168.92008},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2009030/}
}
TY - JOUR AU - Simeon, Bernd AU - Serban, Radu AU - Petzold, Linda R. TI - A model of macroscale deformation and microvibration in skeletal muscle tissue JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 805 EP - 823 VL - 43 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009030/ DO - 10.1051/m2an/2009030 LA - en ID - M2AN_2009__43_4_805_0 ER -
%0 Journal Article %A Simeon, Bernd %A Serban, Radu %A Petzold, Linda R. %T A model of macroscale deformation and microvibration in skeletal muscle tissue %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 805-823 %V 43 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009030/ %R 10.1051/m2an/2009030 %G en %F 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: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 805-823. doi : 10.1051/m2an/2009030. http://archive.numdam.org/articles/10.1051/m2an/2009030/
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