A mechanochemical 3D continuum model for smooth muscle contraction under finite strains

Stålhand, Jonas; Klarbring, Anders; Holzapfel, Gerhard

doi:10.1016/j.jtbi.2010.10.008

Cited by 72 publications

(72 citation statements)

References 24 publications

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“…Such an assumption is inspired by the fact that the activation is generated along the direction given by the sarcomeres' orientation (Tracqui et al, 2008). If we regard a compound of cells instead, we may assume that the myocytes are aligned along the direction of the collagen fibres (Stålhand et al, 2011). We specify Algorithm 1 Semi-discrete mechano-chemical coupling Table 3 that agree with the tests in Tracqui & Ohayon (2009).…”

Section: Numerical Resultsmentioning

confidence: 99%

Mathematical modelling of active contraction in isolated cardiomyocytes

Ruiz–Baier

Gizzi

Rossi

et al. 2013

Mathematical Medicine and Biology

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We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization.Keywords: cardiomyocyte modelling; active-strain contraction; nonlinear elasticity; calcium propagation; finite element formulation; coupled multiphysics.

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Section: Numerical Resultsmentioning

confidence: 99%

Mathematical modelling of active contraction in isolated cardiomyocytes

Ruiz–Baier

Gizzi

Rossi

et al. 2013

Mathematical Medicine and Biology

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“…This is done by applying fundamental principles in mechanics using a previously presented framework (see Stålhand et al 2008, andStålhand et al 2011). This framework implicitly guarantees the model to be dissipative and thermodynamically consistent.…”

Section: Introductionmentioning

confidence: 99%

A continuum model for skeletal muscle contraction at homogeneous finite deformations

Sharifimajd

Stålhand

2012

Biomech Model Mechanobiol

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In this paper we present a homogeneous continuum mechanical model for the active behavior of the skeletal muscle under finite strains. The model differs from other skeletal muscle models in the way which the contractile force is introduced. Generally, the contractile force is postulated to be the isometric force multiplied by a set of experimentally motivated functions which account for the muscles active properties. Although both flexible and simple, this approach does not automatically guarantee a thermodynamically consistent behavior but this must be checked in each case. The model proposed herein is derived from fundamental principles in mechanics using a previously presented framework (Stålhand et al., Prog Biophys Molec Biol, 96, 2008) and implicitly guarantees a dissipative and thermodynamically consistent behavior. To show the performance of the model, it is specialized to a quick-release experiment for rabbit tabialis anterior muscle. The results show that the model is able to capture important characteristics like the bell-shaped force-length curve and hyperbolic force-velocity relation.

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“…To date, there are only uniaxial active constitutive length-tension relationships in the circumferential direction of coronary arteries (1,2,24,31). Although some multi-axial active models have been proposed, those have been of theoretical forms not rooted in experimental measurements (25,36). Clearly, there is a need for multi-axial active mechanical measurements and experimentally determined multi-dimensional active strain energy functions for coronary arteries.…”

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confidence: 99%

Biaxial vasoactivity of porcine coronary artery

Huo¹,

Cheng²,

Zhao³

et al. 2012

American Journal of Physiology-Heart and Circulatory Physiology

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The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K ϩ -induced vasoconstriction, the mean Ϯ SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 Ϯ 0.17 and 3.28 Ϯ 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca 2ϩ -free-induced vasodilated state (i.e., 4.01 Ϯ 0.16 and 3.75 Ϯ 0.20 mm, respectively). The mean Ϯ SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 Ϯ 0.04 mm and 2.25 Ϯ 0.08 mm and 126 Ϯ 22°, respectively. The active stresses have a maximal value at the passive pressure of 80 -100 mmHg and at the active pressure of 140 -160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.contraction; constitutive equation; stress-strain relation; vessel mechanics VASOACTIVITY OF LARGE EPICARDIAL coronary arteries is affected by cardiovascular diseases such as diabetes (14, 15), hypertension (14, 20), atherosclerosis (11), vasospasm (10, 32), and aneurysm (26), which are major risk factors for angina pectoris or myocardial infarction in patients. The constitutive passive and active stress-strain relationships can characterize the vasoactivity and are fundamental for understanding the mechanical behaviors of vascular smooth muscle cell (SMC) in health and disease (5). The strain energy function has been widely used to characterize the passive mechanical properties of blood vessels (5,8). For large epicardial coronary arteries, extensive mechanical measurements and analysis were carried out in the passive state (18,19,23,30,33,34).The active mechanical properties of coronary arteries are much known. To date, there are only uniaxial active constitutive length-tension relationships in the circumferential direction of coronary arteries (1, 2, 24, 31). Although some multi-axial active models have been proposed, those have been of theoretical forms not rooted in experimental measurements (25, 36). Clearly, there is a need for multi-axial active mechanical measurements and experimentally determined multi-dimensional active strain energy functions for coronary arteries.The objective ...

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A mechanochemical 3D continuum model for smooth muscle contraction under finite strains

Cited by 72 publications

References 24 publications

Mathematical modelling of active contraction in isolated cardiomyocytes

Mathematical modelling of active contraction in isolated cardiomyocytes

A continuum model for skeletal muscle contraction at homogeneous finite deformations

Biaxial vasoactivity of porcine coronary artery

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