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Smooth muscle contraction: Mechanochemical formulation for homogeneous finite strains
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
Department of Solid Mechanics, Royal Institute of Technology, Stockholm, Sweden, Institute for Biomechanics, Centre for Biomedical Engineering, Graz University of Technology, Austria.
2008 (English)In: Progress in Biophysics and Molecular Biology, ISSN 0079-6107, E-ISSN 1873-1732, Vol. 96, no 1-3, 465-481 p.Article, review/survey (Refereed) Published
Abstract [en]

Chemical kinetics of smooth muscle contraction affect mechanical properties of organs that function under finite strains. In an effort to gain further insight into organ physiology, we formulate a mechanochemical finite strain model by considering the interaction between mechanical and biochemical components of cell function during activation. We propose a new constitutive framework and use a mechanochemical device that consists of two parallel elements: (i) spring for the cell stiffness, (ii) contractile element for the sarcomere. We use a multiplicative decomposition of cell elongation into filament contraction and cross-bridge deformation, and suggest that the free energy be a function of stretches, four variables (free unphosphorylated myosin, phosphorylated cross-bridges, phosphorylated and dephosphorylated cross-bridges attached to actin), chemical state variable driven by Ca2 +-concentration, and temperature. The derived constitutive laws are thermodynamically consistent. Assuming isothermal conditions, we specialize the mechanical phase such that we recover the linear model of Yang et al. [2003a. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell. Med. Eng. Phys. 25, 691-709]. The chemical phase is also specialized so that the linearized chemical evolution law leads to the four-state model of Hai and Murphy [1988. Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am. J. Physiol. 254, C99-C106]. One numerical example shows typical mechanochemical effects and the efficiency of the proposed approach. We discuss related parameter identification, and illustrate the dependence of muscle contraction (Ca2 +-concentration) on active stress and related stretch. Mechanochemical models of this kind serve the mathematical basis for analyzing coupled processes such as the dependency of tissue properties on the chemical kinetics of smooth muscle. © 2007 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
2008. Vol. 96, no 1-3, 465-481 p.
Keyword [en]
Constitutive model, Intracellular calcium, Mechanics, Myogenic response, Smooth muscle
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-47255DOI: 10.1016/j.pbiomolbio.2007.07.025OAI: diva2:268151
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2010-12-02

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Stålhand, JonasKlarbring, Anders
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