Mathematical modelling of active contraction in isolated cardiomyocytes

Abstract

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.

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

“…The same theoretical derivation can also be used to define an evolution law for the active stress tensor in usual active stress formulations. Similar thermodynamically consistent models to the one presented herein have been derived in [43,44,45] for smooth and skeletal muscle and in [42] for isolated cardiomyocytes. We present here a phenomenological description of the excitation-contraction coupling, but an extension to more physiologically detailed models [25,29,38,51] is conceptually straightforward.…”

“…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 [6,42,48]. From the mathematical point of view this rearrangement can be achieved through a multiplicative decomposition of the deformation gradient tensor [19,24] of the form F = F E F M , where F M and F E are the microscopic and elastic deformation gradient tensors, respectively.…”

“…Here R F L (I 4,f ) is the sarcomere force-length relationship of intact cardiac cells, fitted from [47] by the following function (see [42])…”

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

“…Interesting, but rather complex descriptions based on active strains and thermodynamics have been proposed for instance in [26][27][28][29]. Here we will instead consider the active stress approach, which amounts to simply assume that the stress tensor can be expressed as a linear superposition of an elastic contribution S M N elastic , describing the passive properties of cardiac tissue, and an active part S M N active , resulting from the contractile behavior of the muscle:…”

A 3d Electromechanical Fem-Based Model for Cardiac Tissue

“…Here, the electrophysiology is modeled on the cellular level [11][12][13][14][15] or is simplified using eikonal equations [16] or the FitzHugh-Nagumo model [17,18]. There exist a wide range of electromechanical models from the cell [10,12] over the tissue [14] to the organ level including left ventricular models [11,15], models of both ventricles [12][13][14][15]17], and whole heart models [18]. They feature a varying degree of complexity with respect to the anatomical representation, associated mesh fineness, boundary conditions, material models, underlying electrophysiological models and coupling models depending on the research objective.…”