An Integrative Model of the Self-Sustained Oscillating Contractions of Cardiac Myocytes

Abstract

Computational cell models appear as necessary tools for handling the complexity of intracellular cell dynamics, especially calcium dynamics. However, while oscillating intracellular calcium oscillations are well documented and modelled, a simple enough virtual cell taking into account the mechano-chemical coupling between calcium oscillations and cell mechanical properties is still lacking. Considering the spontaneous periodic contraction of isolated cardiac myocytes, we propose here a virtual cardiac cell model in which the cellular contraction is modelled using an hyperelastic description of the cell mechanical behaviour. According to the experimental data, the oscillating cytosolic calcium concentrations trigger the spatio-temporal variation of the anisotropic intracellular stresses. The finite element simulations of the virtual cell deformations are compared to the self-sustained contractions of isolated rat cardiomyocytes recorded by time-lapse video-microscopy.

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

“…While measurement of fiber strains in the left ventricle are in agreement with longitudinal strains measured in isolated cardiomyocytes [33,51], strain measurements along cross-fiber directions in left ventricular wall indicate that cross-fiber shortening is greater than longitudinal fiber shortening, except for the epicardial region [36,22]. We explain this macroscopic behavior through a simple geometrical model that links the microscopic deformation with the macroscopic one.…”

An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

“…Such perturbations correspond to the experimentally observed calcium sparks attributed to the local and concerted opening of a small number of ryanodine receptors (Sheehan et al 2006;Cheng & Lederer 2008). Kinetic parameter values used in the simulations (table 1) have been taken in the range of values reported by Dupont & Goldbeter (1992 and chosen in order to get cell contraction features that correspond to the measurements extracted from time-lapse videomicroscopy experiments (Pustoc'h et al 2005). Typically, contraction periodicity is approximately 10-18 s, with a contraction/relaxation phase lasting approximately 0.9-1.5 s and producing a typical cell shortening of 4-10% of cell length.…”

Theoretical analysis of the adaptive contractile behaviour of a single cardiomyocyte cultured on elastic substrates with varying stiffness

“…Let us notice that these values are significantly larger than the ones considered by Qin et al (2007), and this point will be addressed in the discussion section. Preliminary simulation results (Pustoc'h et al, 2005) have shown that PAGs may experience large deformations during cardiomyocyte contraction. Thus, we modelled PAGs as nearly incompressible neo-Hookean medium defined by a strain energy function W pag .…”

“…We previously derived from uniaxial traction experiments on isolated cardiomyocyte (Cazorla et al, 2003) a Young's modulus value E cell $6a cell $30 kPa (Pustoc'h et al, 2005), which fits quite well with the value of 35.1 kPa reported for the apparent elastic modulus of rat cardiomyocytes probed by atomic force microscopy indentation (Lieber et al, 2004). Considering again the explicit relationship between Young's modulus E cell of the cardiomyocyte and the material constant a cell for small extension ratio (Section 2), we used in our simulations the value a cell ¼ 5 kPaU…”

“…Starting from real cell morphologies, this original approach allows analysing the cell contractile behaviour under finite deformations, while providing an integrative and continuous description of the cardiomyocyte that extends previous work (Nash and Panfilov, 2004) by taking into account the impact of cell anisotropic architecture onto the contraction dynamics. We thus follow the few attempts, which have been made to provide an integrated description of the cardiomyocyte contraction within a continuum mechanics framework (Pustoc'h et al, 2005;Okada et al 2005), while avoiding the computational complexity induced when considering heterogeneous intracellular elements (Okada et al, 2005).…”