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A model of macroscale deformation and microvibration in skeletal muscle tissue

Published online by Cambridge University Press:  08 July 2009

Bernd Simeon ,
Radu Serban  and
Linda R. Petzold
Bernd Simeon
Affiliation:
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85748 Garching, Germany. simeon@ma.tum.de
Radu Serban
Affiliation:
Xulu entertainment 890 Hillview Court, Milpitas, CA 95032, USA.
Linda R. Petzold
Affiliation:
Dept. of Mechanical Engineering, University of California Santa Barbara, CA 93106, USA.
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Abstract

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.

Keywords

Skeletal muscle tissuemicrovibrationscoherencePDAEindextime integration.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 4: Special issue on Numerical ODEs today , July 2009 , pp. 805 - 823
Copyright
© EDP Sciences, SMAI, 2009

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