2011
DOI: 10.1002/cnm.1468
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An active strain electromechanical model for cardiac tissue

Abstract: SUMMARYWe propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that there is a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of … Show more

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Cited by 75 publications
(84 citation statements)
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“…The reaction kinetics of calcium concentrations and active shortening of the sarcomeres regarded on a single material point behave as depicted in Fig. 5, where it is possible to see a delay of activation (red dashed line) with respect to the cytosolic calcium concentration which is qualitatively comparable with the results in Rice et al (2008) (see also Iyer et al, 2004;Nobile et al (2012)). On the other hand, the present model is not yet capable of correctly describing force-velocity relationships, as we neglect the microscopical information about sarcomere dynamics.…”
Section: Calcium-induced Activation and Thermodynamic Considerationssupporting
confidence: 71%
“…The reaction kinetics of calcium concentrations and active shortening of the sarcomeres regarded on a single material point behave as depicted in Fig. 5, where it is possible to see a delay of activation (red dashed line) with respect to the cytosolic calcium concentration which is qualitatively comparable with the results in Rice et al (2008) (see also Iyer et al, 2004;Nobile et al (2012)). On the other hand, the present model is not yet capable of correctly describing force-velocity relationships, as we neglect the microscopical information about sarcomere dynamics.…”
Section: Calcium-induced Activation and Thermodynamic Considerationssupporting
confidence: 71%
“…Find F n+1 , solving the static nonlinear mechanical problem deriving from (12) and (15) by Newton iterations (see also [30])…”
mentioning
confidence: 99%
“…Our interest lies in the study of a special class of problems arising in the modeling of active deformations in soft biological tissues [14,23], which under some assumptions, can be considered as hyperelastic materials. Here we restrict ourselves to a somewhat simplified setting, where one assumes that the passive behavior of the tissue can be described by a neo-Hookean constitutive law, whereas the active contribution is encoded in some additional anisotropic terms appearing after applying a so-called active strain decomposition [19]. In turn, the stress tensor is written as…”
Section: Governing Equations Of Finite Elasticitymentioning
confidence: 99%
“…Nonlinear elasticity problems have a large number of applications in structural analysis, biomechanics and engineering design. In particular, our development is motivated by the study of anisotropic soft living materials such as the heart tissue, which presents the ability of actively deform without the need of external loads [13,14,19]. If the assumption of incompressibility of the underlying material is considered, and under a Lagrangian formulation, the momentum equation is coupled to a nonlinear volumetric constraint (the determinant of the deformation gradient must be equal to 1).…”
Section: Introductionmentioning
confidence: 99%