An electromechanical model of cardiac tissue: constitutive issues and electrophysiological effects.
ABSTRACT 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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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.Journal of the Mechanics and Physics of Solids 11/2014; 72:20–39. DOI:10.1016/j.jmps.2014.07.015 · 4.29 Impact Factor
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ABSTRACT: 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.European Journal of Mechanics - A/Solids 11/2014; 48:129–142. DOI:10.1016/j.euromechsol.2013.10.009 · 1.90 Impact Factor
- Computer Models in Biomechanics: From Nano to Macro, Edited by Holzapfel, Gerhard and Kuhl, Ellen, 01/2013: pages 189-201; Springer.