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Bridging scales: An attempt to incorporate cellular responses within a three‐dimensional FEM model of active muscle contraction
Author(s) -
Röhrle O.,
Davidson J.B.,
Kim J.H.K.,
Pullan A.J.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700310
Subject(s) - finite element method , crossbridge , contraction (grammar) , elasticity (physics) , skeletal muscle , muscle contraction , discretization , transverse isotropy , mechanics , materials science , structural engineering , isotropy , mathematics , mathematical analysis , physics , anatomy , engineering , composite material , medicine , quantum mechanics
A mathematical model of the cellular responses of skeletal muscles has been integrated within a three‐dimensional biomechanical Finite Element (FEM) model. The FEM model is based on a tri‐cubic Hermite Finite Element discretisation of the governing equations of finite elasticity theory and a transversely isotropic constitutive law. To incorporate the cellular information, homogenised values of key physiological parameters, e.g. the pre‐ and post‐power stroke concentration of crossbridge attachments, are computed at the Gauss points of the FEMintegration scheme. These values are then used to modify the stress tensor in such a way that it resembles the contractile response. The advantages of such an improved three‐dimensional FEM model are far reaching. These models can be used, for example, to investigate and study local muscle contraction, muscle recruitment patterns, force generation, or fatigue response of skeletal muscles. As an illustrative example, one twitch of the tibialis anterior, in which 25% of the muscle fibres are excited by a nerve stimulus, is simulated. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)