Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions

Ruiz–Baier, Ricardo; Ambrosi, Davide Carlo; Pezzuto, Simone; Rossi, Simone; Quarteroni, Alfio

doi:10.1007/978-94-007-5464-5_14

Cited by 7 publications

(6 citation statements)

References 45 publications

(56 reference statements)

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“…We have presented a mathematical model of the mechano-chemical coupling in individual cardiomyocytes based on an active-strain approach (Ruiz-Baier et al, 2013). The proposed activation mechanism is consistent with a thermodynamic framework, as derived in Stålhand et al (2011), and it entails a nonlinear interaction among calcium dynamics and local stretches.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 61%

“…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%

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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: Discussion and Concluding Remarksmentioning

confidence: 61%

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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“…The upscaling strategy is incorporated in the model following an anisotropic active strain formalism [27,41], where the force balance determining the motion of the tissue depends on local distortion of the microstructure followed by a macroscopic rearrangement of the material recovering compatibility of the deformation. Mathematically, this corresponds to a decomposition of strains.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics

Rossi

Lassila

Ruiz–Baier

et al. 2014

European Journal of Mechanics - A/Solids

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175

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The complex phenomena underlying mechanical contraction of cardiac cells and their influence in the dynamics of ventricular contraction are extremely important in understanding the overall function of the heart. In this paper we generalize previous contributions on the active strain formulation and propose a new model for the excitation-contraction coupling process. We derive an evolution equation for the active fiber contraction based on configurational forces, which is thermodynamically consistent. Geometrically, we link microscopic and macroscopic deformations giving rise to an orthotropic contraction mechanism that is able to represent physiologically correct thickening of the ventricular wall. A series of numerical tests highlights the importance of considering orthotropic mechanical activation in the heart and illustrates the main features of the proposed model.

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“…Although we have recently tested numerically more complex and more realistic formulations for cardiac electromechanics, 23,33,39,42 the model simplifications applied in the present study were mainly driven by the need of addressing solvability and regularity questions often overlooked in the literature. In addition, some extensions towards physiological relevance can be readily applied without changing the core of the theoretical tools employed herein.…”

Section: Discussionmentioning

confidence: 99%

Solvability analysis and numerical approximation of linearized cardiac electromechanics

Andreïanov

Bendahmane

Quarteroni

et al. 2015

Math. Models Methods Appl. Sci.

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DRAFTThis paper is concerned with the mathematical analysis of a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction-diffusion system governing the dynamics of ionic quantities, intra and extra-cellular potentials, and the linearized elasticity equations are adopted to describe the motion of an incompressible material. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. Under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffusivities, we prove existence of weak solutions to the underlying coupled reaction-diffusion system and uniqueness of regular solutions. The proof of existence is based on a combination of parabolic regularization, the Faedo-Galerkin method, and the monotonicity-compactness method of J.L. Lions. A finite element formulation is also introduced, for which we establish existence of discrete solutions and show convergence to a weak solution of the original problem. We 1 2 Andreianov, Bendahmane, Quarteroni & Ruiz-Baier close with a numerical example illustrating the convergence of the method and some features of the model.

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Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions

Cited by 7 publications

References 45 publications

Mathematical modelling of active contraction in isolated cardiomyocytes

Mathematical modelling of active contraction in isolated cardiomyocytes

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics

Solvability analysis and numerical approximation of linearized cardiac electromechanics

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