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Zbl 1168.92008
Simeon, Bernd; Serban, Radu; Petzold, Linda R.
A model of macroscale deformation and microvibration in skeletal muscle tissue. (English)
[J] ESAIM, Math. Model. Numer. Anal. 43, No. 4, 805 (2009). ISSN 0764-583X; ISSN 1290-3841/e

Summary: This paper deals with modeling the passive behavior of skeletal muscle tissues including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformations 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 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.

MSC 2000:: *92C10 Biomechanics
74A99 Generalities, etc. of continuum mechanics of solids
74C05 Small-strain, rate-independent theories
65L05 Initial value problems for ODE (numerical methods)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M20 Method of lines (IVP of PDE)

Keywords: skeletal muscle tissue; microvibrations; coherence; PDAE; index; time integration

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