A model of macroscale deformation and microvibration in skeletal muscle tissue

Bernd Simeon; Radu Serban; Linda R. Petzold

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 4, page 805-823
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Simeon, Bernd, Serban, Radu, and Petzold, Linda R.. "A model of macroscale deformation and microvibration in skeletal muscle tissue." ESAIM: Mathematical Modelling and Numerical Analysis 43.4 (2009): 805-823. <http://eudml.org/doc/250598>.

@article{Simeon2009,
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. },
author = {Simeon, Bernd, Serban, Radu, Petzold, Linda R.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Skeletal muscle tissue; microvibrations; coherence; PDAE; index; time integration.; skeletal muscle tissue; time integration},
language = {eng},
month = {7},
number = {4},
pages = {805-823},
publisher = {EDP Sciences},
title = {A model of macroscale deformation and microvibration in skeletal muscle tissue},
url = {http://eudml.org/doc/250598},
volume = {43},
year = {2009},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2009/7//
PB - EDP Sciences
VL - 43
IS - 4
SP - 805
EP - 823
AB - 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.
LA - eng
KW - Skeletal muscle tissue; microvibrations; coherence; PDAE; index; time integration.; skeletal muscle tissue; time integration
UR - http://eudml.org/doc/250598
ER -

References

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