Theoretical analysis of the adaptive contractile behaviour of a single cardiomyocyte cultured on elastic substrates with varying stiffness

Tracqui, Philippe; Ohayon, Jacques; Boudou, Thomas

doi:10.1016/j.jtbi.2008.07.036

Cited by 23 publications

(36 citation statements)

References 56 publications

(94 reference statements)

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“…It may thus serve as a basis for further theoretical analysis of modifications of intracellular calcium kinetics and cardiac cell rheological properties that may enhance the efficiency of cardiac myocyte contractility or that lead to abnormal cell contraction, with direct consequences on cardiac tissue contractility and cardiac rhythm (Stuyvers et al 2000). Even if all the complexity of the electromechanical regulatory feedbacks (Campbell et al 2008) is not considered here, the present model proposes an integrative and a rather simplified description of the cardiac myocyte contraction that may help to focus, without excessive complexity, on open questions related to the modulation of cardiac myocyte rythmic beating by the micro-environment stiffness (Engler et al 2008;Tracqui et al 2008) and more generally, to the non-homogeneous development of intracellular stress as a regulator of the mechano-transduction pathways involved in the control of the cardiac myocyte contraction.…”

Section: Discussionmentioning

confidence: 99%

“…One particular aim is to integrate comprehensive experimental data for cardiac myocyte structure and interactions between mechanical and biochemical processes within appropriate constitutive models, which may provide a relevant basis for finite-element analysis computation and prediction of cell contraction in varying conditions. Recent work has analysed the theoretical properties of isotropic continuous contracting excitable media driven by travelling nonlinear waves of excitation at a tissue level (Panfilov et al 2005(Panfilov et al , 2007, but only a small number of models of the contractile cardiac cell have been proposed in a continuum mechanics framework (Okada et al 2005;Tracqui et al 2008). Indeed, most of the developed modelling approaches usually consider mechanical couplings as a superimposition of different subsets of phenomenological relationships (Stuyvers et al 2002;Niederer et al 2006), instead of considering more fundamental constitutive laws that may be applicable to real three-dimensional cell geometries.…”

Section: Introductionmentioning

confidence: 99%

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An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

Tracqui

Ohayon

2009

Phil. Trans. R. Soc. A.

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Isolated cardiac myocytes exhibit spontaneous patterns of rhythmic contraction, driven by intracellular calcium waves. In order to study the coupling between spatio-temporal calcium dynamics and cell contraction in large deformation regimes, a new strainenergy function, describing the influence of sarcomere length on the calcium-dependent generation of active intracellular stresses, is proposed. This strain-energy function includes anisotropic passive and active contributions that were first validated separately from experimental stress-strain curves and stress-sarcomere length curves, respectively. An extended validation of this formulation was then conducted by considering this strainenergy function as the core of an integrated mechano-chemical three-dimensional model of cardiac myocyte contraction, where autocatalytic intracellular calcium dynamics were described by a representative two-variable model able to generate realistic intracellular calcium waves similar to those observed experimentally. Finite-element simulations of the three-dimensional cell model, conducted for different intracellular locations of triggering calcium sparks, explained very satisfactorily, both qualitatively and quantitatively, the contraction patterns of cardiac myocytes observed by time-lapse videomicroscopy. This integrative approach of the mechano-chemical couplings driving cardiac myocyte contraction provides a comprehensive framework for analysing active stress regulation and associated mechano-transduction processes that contribute to the efficiency of cardiac cell contractility in both physiological and pathological contexts.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

Tracqui

Ohayon

2009

Phil. Trans. R. Soc. A.

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“…Digital imaging techniques and intracellular calcium indicators provide insights concerning calcium distribution inside myocytes (Böl et al, 2012). Here, the interaction between cytosolic and sarcoplasmic calcium concentrations will be modelled following Tracqui et al (2008) and Goldbeter et al (1990). The system of partial differential equations governing the simplified nonlinear dynamics of the CICR behaviour consists of the mass balance equations…”

Section: Calcium Dynamicsmentioning

confidence: 99%

“…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. Although the adopted calcium model is a well-established simplified version of the more complex ionic dynamics of the cell physiology (Goldbeter et al, 1990;Sneyd et al, 2005;Tracqui et al, 2008), we are able to quantitatively represent, at the same time, both the anisotropic passive intracellular organization, i.e. the T-tubule system, and the anisotropic active emerging cellular structures, that may be important in the single myocyte deformation and calcium regulation.…”

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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“…1 E. Because cardiomyocytes can grow adhering to a substrate, the stiffness will have an effect on the contractile behavior of the cardiomyocyte, as described in a previous article (46). Therefore, the influence of the substrate was described by a spring with the spring constant k substrate in parallel with the cytoskeleton springs.…”

Section: Theoretical Modelmentioning

confidence: 99%

Dynamic Model for Characterizing Contractile Behaviors and Mechanical Properties of a Cardiomyocyte

Zhang

Wang

et al. 2018

Biophysical Journal

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Studies on the contractile dynamics of heart cells have attracted broad attention for the development of both heart disease therapies and cardiomyocyte-actuated micro-robotics. In this study, a linear dynamic model of a single cardiomyocyte cell was proposed at the subcellular scale to characterize the contractile behaviors of heart cells, with system parameters representing the mechanical properties of the subcellular components of living cardiomyocytes. The system parameters of the dynamic model were identified with the cellular beating pattern measured by a scanning ion conductance microscope. The experiments were implemented with cardiomyocytes in one control group and two experimental groups with the drugs cytochalasin-D or nocodazole, to identify the system parameters of the model based on scanning ion conductance microscope measurements, measurement of the cellular Young's modulus with atomic force microscopy indentation, measurement of cellular contraction forces using the micro-pillar technique, and immunofluorescence staining and imaging of the cytoskeleton. The proposed mathematical model was both indirectly and qualitatively verified by the variation in cytoskeleton, beating amplitude, and contractility of cardiomyocytes among the control and the experimental groups, as well as directly and quantitatively validated by the simulation and the significant consistency of 90.5% in the comparison between the ratios of the Young's modulus and the equivalent comprehensive cellular elasticities of cells in the experimental groups to those in the control group. Apart from mechanical properties (mass, elasticity, and viscosity) of subcellular structures, other properties of cardiomyocytes have also been studied, such as the properties of the relative action potential pattern and cellular beating frequency. This work has potential implications for research on cytobiology, drug screening, mechanisms of the heart, and cardiomyocyte-based bio-syncretic robotics.

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Theoretical analysis of the adaptive contractile behaviour of a single cardiomyocyte cultured on elastic substrates with varying stiffness

Cited by 23 publications

References 56 publications

An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

Mathematical modelling of active contraction in isolated cardiomyocytes

Dynamic Model for Characterizing Contractile Behaviors and Mechanical Properties of a Cardiomyocyte

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