Volume 43, Number 4, July-August 2009Special issue on Numerical ODEs today
|Page(s)||805 - 823|
|Published online||08 July 2009|
A model of macroscale deformation and microvibration in skeletal muscle tissue
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85748 Garching, Germany. firstname.lastname@example.org
2 Xulu entertainment 890 Hillview Court, Milpitas, CA 95032, USA.
3 Dept. of Mechanical Engineering, University of California Santa Barbara, CA 93106, USA.
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.
Mathematics Subject Classification: 65L05 / 65M12 / 65M20 / 74C05
Key words: Skeletal muscle tissue / microvibrations / coherence / PDAE / index / time integration.
© EDP Sciences, SMAI, 2009
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