A two dimensional electromechanical model of a cardiomyocyte to assess intra-cellular regional mechanical heterogeneities

Abstract

Experimental studies on isolated cardiomyocytes from different animal species and human hearts have demonstrated that there are regional differences in the Ca2+ release, Ca2+ decay and sarcomere deformation. Local deformation heterogeneities can occur due to a combination of factors: regional/local differences in Ca2+ release and/or re-uptake, intra-cellular material properties, sarcomere proteins and distribution of the intracellular organelles. To investigate the possible causes of these heterogeneities, we developed a two-dimensional finite-element electromechanical model of a cardiomyocyte that takes into account the experimentally measured local deformation and cytosolic [Ca2+] to locally define the different variables of the constitutive equations describing the electro/mechanical behaviour of the cell. Then, the model was individualised to three different rat cardiac cells. The local [Ca2+] transients were used to define the [Ca2+]-dependent activation functions. The cell-specific local Young’s moduli were estimated by solving an inverse problem, minimizing the error between the measured and simulated local deformations along the longitudinal axis of the cell. We found that heterogeneities in the deformation during contraction were determined mainly by the local elasticity rather than the local amount of Ca2+, while in the relaxation phase deformation was mainly influenced by Ca2+ re-uptake. Our electromechanical model was able to successfully estimate the local elasticity along the longitudinal direction in three different cells. In conclusion, our proposed model seems to be a good approximation to assess the heterogeneous intracellular mechanical properties to help in the understanding of the underlying mechanisms of cardiomyocyte dysfunction.

Numerical Simulation of Excitation-Contraction in Isolated Cardiomyocytes

“…The results of case 3 were presented with a concentration of 0.45µM and a % of shortening from 4% to 10% , which corresponds to the results obtained both by Kamgoue et al [20] and Garcia-Canadilla et al (9%) [21].…”

A cell-based framework for modeling cardiac mechanics

“…It takes into account an explicit geometrical cell configuration that allows for refinement of cardiac tissue mechanics in a more physiologically relevant manner than one can achieve by simply using finer meshes and a homogenized tissue model. This work extends the mechanical aspect of cellbased modeling of single cells (Ruiz-Baier et al 2014;Gizzi et al 2015;Garcia-Canadilla et al 2017;Lenarda et al 2018;Tracqui et al 2008) by including the extracellular material. Our results indicate that this inclusion is important for the quantification of intracellular stresses.…”

“…The formulation used for the intracellular strain energy function i (9) is very similar to the one used in other works for isolated cardiomyocytes (Tracqui and Ohayon 2009;Ruiz-Baier et al 2014;Gizzi et al 2015), and can physiologically be motivated by the mechanical contributions of the sarcomere structure found within the cells. Other models for cardiomyocytes (Tracqui et al 2008;Okada et al 2005;Garcia-Canadilla et al 2017;Lenarda et al 2018) have assumed isotropy in the intracellular domain, not assuming that there is any difference between stress-strain values in different directions. This could, in particular, be a good assumption for cells and cell collections developed in vitro, which as immature cells have a less developed sarcomere structure.…”

“…Real geometries are much more complicated-for a single cell, the domain has a more complex shape, and for multiple cells, the cells self-organize in more complex, non-regular patterns. Images of cells can be used to construct more realistic geometries, as done in, e.g., Ruiz-Baier et al (2014); Gizzi et al (2015); Garcia-Canadilla et al (2017);Tracqui et al (2008) considering single cells, and to some degree in in Sharafi and Blemker (2011), considering a cross-section through nine cells. For the latter study, force values reported are within a comparable range to stresses observed in our study; however their setup is quite different from ours, making it hard to compare these directly.…”

“…Some mechanical continuum-based models that do take into account these explicit geometries have been developed, considering single isolated cells. These are modeled using a hyperelastic and isotropic (Tracqui et al 2008;Okada et al 2005;Garcia-Canadilla et al 2017;Lenarda et al 2018), or anisotropic material model (Tracqui and Ohayon 2009;Ruiz-Baier et al 2014;Gizzi et al 2015). The impact of the cell membrane and the extracellular matrix can be explicitly implemented using a combination of Dirichlet and Neumann boundary conditions (Ruiz-Baier et al 2014;Gizzi et al 2015;Lenarda et al 2018).…”