Mathematical modelling of active contraction in isolated cardiomyocytes (Q2922511)

The authors suggest a mathematical model for the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. The model is based on an active-strain formulation for the description of the cardiomyocyte response following the work of \textit{C. Cherubini} et al. [``An electromechanical model of cardiac tissue: constitutive issues and electrophysiological effects'', Prog. Biophys. Mol. Biol. 97, 562--573 (2008; \url{doi:10.1016/j.pbiomolbio.2008.02.001})] and \textit{R. Ruiz-Baier} et al. [``Activation models for the numerical simulation of cardiac electromechanical interactions'', in: G. A. Holzapfel (ed.) and E. Kuhl (ed), Computer models in biomechanics: from nano to macro. Heidelberg: Springer. 189--201 (2013; \url{doi:10.1007/978-94-007-5464-5_14})]. In this approach, the mechanical activation may be represented as a virtual multiplicative splitting of the deformation gradient into a passive elastic response and an active deformation, depending directly on the nonlinear dynamics describing chemical reactions between calcium species.NEWLINENEWLINERemarkably, the model is thermodynamically consistent in the sense that the second law of thermodynamics is satisfied. As a result, such a generalized model characterizes interactions between ionic quantities, the cellular mechanical properties and the environmental effects. Furthermore, the model explains the influence of cell shape and boundary conditions on the onset of structural anisotropies and stress concentrations.NEWLINENEWLINEThe feasibility and adequateness of employing a macroscopic description of the mechano-chemical behavior of a single cell via an active strain approach are demonstrated with the help of numerical simulations. To this end, nonlinear elasticity equations are approximated with a finite element method based on a Taylor-Hood discretization, whereas calcium concentration and mechanical activation variables are discretized using piecewise linear finite elements. Simulation results demonstrate that such a modeling strategy can be used to explore the relation between microscopic cell dynamics and macroscopic cardiac function. Model validation is performed in terms of calcium wave propagation velocity and active force versus sarcomere length relationship. A careful inspection of calcium wave propagation and stress analysis confirmed experimentally obtained values for calcium activation timing and conduction velocities, asymmetric calcium maxima and stress concentrations. Experimentally observed myocyte bending and driving contraction, due to internal calcium sparks, were confirmed too.