An electromechanical model of cardiac tissue: Constitutive issues and electrophysiological effects

Cherubini, Christian; Filippi, Sandra; Nardinocchi, Paola; Teresi, Luciano

doi:10.1016/j.pbiomolbio.2008.02.001

Cited by 119 publications

(109 citation statements)

References 15 publications

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“…Detailed models of stretch activated currents (SACs) can be found in the literature (see for instance [14,17,19]). However, since our approach is firstly qualitative and interested in physical mechanisms, we will instead of well accepted but rather complex models use a very simple and generic description of the SACs, inspired by [22] and also used in [7,20].…”

Section: A Governing Equationsmentioning

confidence: 99%

“…Introducing (19) in this relation provides A = σ active , where σ active is the mean value of σ active over the fiber. Eq.…”

Section: B 1-d Model and Global Couplingmentioning

confidence: 99%

“…This phenomenon has been studied for a long time, both experimentally and theoretically (see for instance [7,[11][12][13][14][15][16][17][18][19][20][21][22]) and it is now well accepted that MEF can elicit spontaneous oscillatory behavior in muscle fibers. In the present work, we propose is a theoretical and numerical analysis of such oscillations.…”

Section: Introductionmentioning

confidence: 99%

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Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Collet

Bragard

Dauby

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This article characterizes the cardiac autonomous electrical activity induced by the mechanical deformations in the cardiac tissue through the mechano-electric feedback (MEF). A simplified and qualitative model is used to describe the system and we also account for temperature effects. The analysis emphasizes a very rich dynamics for the system, with periodic solutions, alternans, chaotic behaviors, etc. The possibility of self-sustained oscillations is analyzed in detail, particularly in terms of the values of important parameters such as the dimension of the system and the importance of the stretch-activated currents. It is also shown that high temperatures notably increase the parameters ranges for which self-sustained oscillations are observed and that several attractors can appear, depending on the location of the initial excitation of the system. Finally, the instability mechanisms by which the periodic solutions are destabilized have been studied by a Floquet analysis, which has revealed period-doubling phenomena and transient intermittencies.

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Section: A Governing Equationsmentioning

confidence: 99%

“…Introducing (19) in this relation provides A = σ active , where σ active is the mean value of σ active over the fiber. Eq.…”

Section: B 1-d Model and Global Couplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Collet

Bragard

Dauby

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Here, we have chosen the active strain approach since it appears to be more robust from a mathematical point of view than the active stress one [37]. Additionally, its physiological relevance has already been shown in several biological context [28,[38][39][40][41]. In the fluid phase (i.e.…”

Section: Mechanics and Constitutive Behaviour Of The Cellmentioning

confidence: 99%

Mechanical link between durotaxis, cell polarity and anisotropy during cell migration

et al. 2015

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractCell migration, a fundamental mechanobiological process, is highly sensitive to the biochemical and mechanical properties of the environment. Efficient cell migration is ensured by the intrinsic polarity of the cell, which triggers a transition from an isotropic to an anisotropic configuration of the actomysion filaments responsible for the protrusion-contraction movement of the cell. Additionally, polarity may be highly influenced by the substrate rigidity, which results in a phenomenon called durotaxis. In the present work, we propose a two-dimensional finite element model able to capture three main features of cell migration: durotaxis, cell polarity and anisotropy. The cell is modelled as a continuum able to develop cyclic active strains regulated by the polymerization and depolymerization of the acto-myosin filaments and synchronized with the adhesion forces between the cell and the substrate underneath. A generalized Maxwell model is used to describe the viscoelastic behaviour of the cell constituted by a solid anisotropic branch with active strains (i.e. the acto-myosin filaments) and a fluid viscoelastic branch (i.e. the cytoplasm). Several types of substrate have been tested which are homogeneously soft or stiff or include both regions. The numerical results have been qualitatively compared with experimental observations showing a good agreement and have allowed us to find the mechanical link between durotaxis, cell polarity and anisotropy.

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“…However, in this preliminary study, we focus on describing quantitatively the behaviour of the principal calcium quantities inside the cardiomyocyte, noting that physiological models for [Ca 2+ ] dynamics are able to mimic the coupling of Ca 2+ with voltage (Bers, 2002). Our mathematical model is based on an active-strain formulation for the description of the cardiomyocyte active mechanical response following Cherubini et al (2008) and Ruiz-Baier et al (2013). In this approach, the mechanical activation may be represented as a virtual multiplicative splitting of the deformation gradient into a passive elastic response, and an active deformation depending directly on the nonlinear dynamics that describe chemical reactions between calcium species, CICR.…”

Section: Introductionmentioning

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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An electromechanical model of cardiac tissue: Constitutive issues and electrophysiological effects

Cited by 119 publications

References 15 publications

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Mechanical link between durotaxis, cell polarity and anisotropy during cell migration

Mathematical modelling of active contraction in isolated cardiomyocytes

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