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A calcium-driven mechanochemical model for prediction of force generation in smooth muscle

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Abstract

A new model for the mechanochemical response of smooth muscle is presented. The focus is on the res- ponse of the actin–myosin complex and on the related generation of force (or stress). The chemical (kinetic) model describes the cross-bridge interactions with the thin filament in which the calcium-dependent myosin phosphorylation is the only regulatory mechanism. The new mechanical model is based on Hill’s three-component model and it includes one internal state variable that describes the contraction/relaxation of the contractile units. It is characterized by a strain-energy function and an evolution law incorporating only a few material parameters with clear physical meaning. The proposed model satisfies the second law of thermodynamics. The results of the combined coupled model are broadly consistent with isometric and isotonic experiments on smooth muscle tissue. The simulations suggest that the matrix in which the actin–myosin complex is embedded does have a viscous property. It is straightforward for implementation into a finite element program in order to solve more complex boundary-value problems such as the control of short-term changes in lumen diameter of arteries due to mechanochemical signals.

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Authors and Affiliations

  1. Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), Osquars Backe 1, 100 44, Stockholm, Sweden

    Sae-Il Murtada, Martin Kroon & Gerhard A. Holzapfel

  2. Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, 8010, Graz, Austria

    Gerhard A. Holzapfel

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  1. Sae-Il Murtada
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  2. Martin Kroon
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  3. Gerhard A. Holzapfel
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Correspondence to Gerhard A. Holzapfel.

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Murtada, SI., Kroon, M. & Holzapfel, G.A. A calcium-driven mechanochemical model for prediction of force generation in smooth muscle. Biomech Model Mechanobiol 9, 749–762 (2010). https://doi.org/10.1007/s10237-010-0211-0

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  • DOI: https://doi.org/10.1007/s10237-010-0211-0

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