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, Tome 43 (2009) no. 4 , p. 805-823
Zbl 1168.92008 | MR 2542878
doi : 10.1051/m2an/2009030
URL stable : http://www.numdam.org/item?id=M2AN_2009__43_4_805_0

Classification:  65L05,  65M12,  65M20,  74C05
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.

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