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The Generalized Hill Model: A Kinematic Approach Towards Active Muscle Contraction.

Göktepe, Serdar; Menzel, Andreas LU and Kuhl, Ellen (2014) In Journal of the Mechanics and Physics of Solids 72. p.20-39
Abstract
Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the... (More)
Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion. (Less)
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organization
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type
Contribution to journal
publication status
published
subject
in
Journal of the Mechanics and Physics of Solids
volume
72
pages
20 - 39
publisher
Elsevier
external identifiers
  • pmid:25221354
  • wos:000343841900002
  • scopus:84906544414
ISSN
1873-4782
DOI
10.1016/j.jmps.2014.07.015
language
English
LU publication?
yes
id
0ef27e36-84ff-4587-85a3-8a9f8d080549 (old id 4691516)
date added to LUP
2014-10-08 14:20:14
date last changed
2017-11-12 03:48:44
@article{0ef27e36-84ff-4587-85a3-8a9f8d080549,
  abstract     = {Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.},
  author       = {Göktepe, Serdar and Menzel, Andreas and Kuhl, Ellen},
  issn         = {1873-4782},
  language     = {eng},
  pages        = {20--39},
  publisher    = {Elsevier},
  series       = {Journal of the Mechanics and Physics of Solids},
  title        = {The Generalized Hill Model: A Kinematic Approach Towards Active Muscle Contraction.},
  url          = {http://dx.doi.org/10.1016/j.jmps.2014.07.015},
  volume       = {72},
  year         = {2014},
}