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

Laboratory of Nonlinear Physics and Mathematical Modeling, Università Campus Bio-Medico, Roma, Italy.
Progress in Biophysics and Molecular Biology (Impact Factor: 2.27). 06/2008; 97(2-3):562-73. DOI: 10.1016/j.pbiomolbio.2008.02.001
Source: PubMed


We present an electromechanical model of myocardium tissue coupling a modified FitzHugh-Nagumo type system, describing the electrical activity of the excitable media, with finite elasticity, endowed with the capability of describing muscle contractions. The high degree of deformability of the medium makes it mandatory to set the diffusion process in a moving domain, thereby producing a direct influence of the deformation on the electrical activity. Various mechano-electric effects concerning the propagation of cylindrical waves, the rotating spiral waves, and the spiral breakups are discussed.

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    • "For instance, at the myocyte level, the binding rate of Ca 2+ to troponin-C depends on sarcomere length and some ion channels depend on the sarcomere stretch [3] [4]. At the tissue level, cardiac mechanics significantly contributes to the dynamics of complex reentrant waves [5] and also affects effective electrical tissue conductivities [6]. In [7], we presented a coupled electromechanical computer model of human left ventricle wedge preparation. "
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    ABSTRACT: Heart failure is a major and costly problem in public health, which, in certain cases, may lead to death. The failing heart undergo a series of electrical and structural changes that provide the underlying basis for disturbances like arrhythmias. Computer models of coupled electrical and mechanical activities of the heart can be used to advance our understanding of the complex feedback mechanisms involved. In this context, there is a lack of studies that consider heart failure remodeling using strongly coupled electromechanics. We present a strongly coupled electromechanical model to study the effects of deformation on a human left ventricle wedge considering normal and hypertrophic heart failure conditions. We demonstrate through a series of simulations that when a strongly coupled electromechanical model is used, deformation results in the thickening of the ventricular wall that in turn increases transmural dispersion of repolarization. These effects were analyzed in both normal and failing heart conditions. We also present transmural electrograms obtained from these simulations. Our results suggest that the waveform of electrograms, particularly the T-wave, is influenced by cardiac contraction on both normal and pathological conditions.
    Full-text · Article · Oct 2015
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    • "The solution of the field equations requires the knowledge of constitutive equations describing the Kirchhoff stress tensor ^ τ , the potential flux ^ q , and the current source ^ I ϕ . Similar to Section 2 and in contrast to the literature ( Cherubini et al . , 2008 ; Ambrosi et al . , 2011 ) , we additively decompose the free energy function into the passive part Ψ p and the active part Ψ a as similarly established in the modeling of electroactive polymers , see e . g . Ask et al . ( 2012a , b )"
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    ABSTRACT: Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.
    Full-text · Article · Nov 2014 · Journal of the Mechanics and Physics of Solids
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    • "As opposed to the concept of active stress, alternative approaches rely on the concept of active strain. An alternative formulation based on the multiplicative decomposition of the deformation gradient into active part and passive part have appeared recently in the cardiac literature [9] [10]. The formulation was based on several simplifying assumptions, which have been partially removed by other authors [3]. "
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    ABSTRACT: We present a general theoretical framework for the formulation of the nonlinear electromechanics of polymeric and biological active media. The approach developed here is based on the additive decomposition of the Helmholtz free energy in elastic and inelastic parts and on the multiplicative decomposition of the deformation gradient in passive and active parts. We describe a thermodynamically sound scenario that accounts for geometric and material nonlinearities. In view of numerical applications, we specialize the general approach to a particular material model accounting for the behavior of fiber reinforced tissues. Specifically, we use the model to solve via finite elements a uniaxial electromechanical problem dynamically activated by an electrophysiological stimulus. Implications for nonlinear solid mechanics and computational electrophysiology are finally discussed.
    Full-text · Article · Nov 2014 · Communications in Computational Physics
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