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.
"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 )"
[Show abstract][Hide abstract] 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(1):20–39. DOI:10.1016/j.jmps.2014.07.015 · 3.60 Impact Factor
"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  . The formulation was based on several simplifying assumptions, which have been partially removed by other authors . "
[Show abstract][Hide abstract] 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.
"The contraction, due to sliding of the myofilaments, can be interpreted as a microscopic rearrangement of the sarcomeres. Several authors have used this approach to describe deformations both at cellular and organ level (Cherubini et al., 2008; Laadhari et al., 2013; Ruiz- Baier et al., 2013b; Taber and Perucchio, 2000). From the mathematical point of view this rearrangement can be achieved through a multiplicative decomposition of the deformation gradient tensor (Lee and Liu, 1967; Menzel and Steinmann, 2007) of the form F ¼ F E F M , where F M and F E are the microstructural and elastic deformation gradient tensors, respectively. "
[Show abstract][Hide abstract] 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(1):129–142. DOI:10.1016/j.euromechsol.2013.10.009 · 1.68 Impact Factor
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