A modeling framework for electro-mechanical interaction between excitable deformable cells

Abstract

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.is still unchallenged due to the high computational and modeling complexities, relevant contributions regard finite element procedures for the theoretical description of single cell contractility responses under different environmental stimuli [26,27,28,29,30] or whole reconstructed heart geometries for selected pathological states [31]. In order to incorporate dominant mechanisms occurring at different scales within a constitutive framework for the cardiac tissue, microstructural properties have to be properly described, including mechano-regulated interactions occurring among tissue constituents. Though our modeling refers to the cell micro-scale, we assume a continuum approach [30]. Experimental evidences on single cell contractility showed that forces are induced where no visible stress fibers are present, thus implying that a much finer scale is responsible for the observed phenomena and therefore continuum level considerations can be adopted [27,32,33,34].Structural and physical properties of contact myocytes, in particular, will be the main object of this study. Intercellular communication between excitable contractile cells concentrates at the intercaleted discs and concerns with microscopic electrical conductance, metabolic and mechanical coupling [35]. A schematic representation of two-dimensional cardiomyocytes contact problems is provided in Fig. 1(a). The interface constitutive model concerns (i) voltage-dependent GJs ruling the electrical conductance for membrane voltage propagation, and (ii) adhesive and contact membrane interfaces dictating mechanical stress localization across adjacent cells. In addition, localized focal adhesions are described via appropriate boundary conditions. The problem at hand deserves an accurate cellular mechanical description in which structural heterogeneities, appropriate constitutive relations, and active dynamics are the three key factors to be formalized within a generalized ...

Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study

“…CV matching through σ tuning. While cell membrane capacitance C m and cell surface-to-volume ratio χ are physical quantities derived from measurements in isolated cardiac myocytes (and hence local), the conductivity σ of cardiac tissue is an average measure of how electrical activation propagates across the cell and how it is communicated in space between adjacent cardiomyocytes, thus tightly linked to the physical spatial dimension of the problem (e.g., see [16,39] and references therein). When working with a fractional excitable media model to account for the multiscale effect of microscopic heterogeneity, considering a fractional power of the diffusion operator (∇ • D∇), with diffusivity D = σ/(C m χ), is a wrong physical assumption.…”

Efficient estimation of cardiac conductivities: A proper generalized decomposition approach

“…subject to (12)- (13). Specifically, u meas denotes the experimental data measured on the observation domain, Ω obs ⊂ Ω, and u is function of σ through the (12,13,18)..…”

“…The knowledge of the differential equations for the potential propagation in the cardiac tissue is quite consolidated, as witnessed by the specific literature (see, e.g., [14,15,16]). Modeling improvements are mainly devoted to the micro-, meso-and macroscopic (i.e., cell, tissue and organ levels) description of the ions dynamics at cellular and subcellular level [17], to their behavior at the cell-cell interface [18,19], and to the spatio-temporal coupling among the different cardiac components resulting in synchronized emerging phenomena [20]. These models feature parameters that are quite hard to measure in vivo and data assimilation procedures have been recognized as a viable approach [21,22].…”

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

“…cardiomyocytes, involving different scales [57]. The study of single cell and cell-cell [45] chemomechanical and electromechanical interactions has attempted to unveil some of the underlying complex features of the cardiac function, and different multi-field nonlinear models have been gradually generalising classical approaches as the monodomain equations and Fick's law of diffusion. In particular, fractional diffusion [17], nonlinear diffusion [36], and stress-assisted diffusion formulations [11] were recently proposed to reproduce porous multiscale excitation phenomena within the framework of homogenised models for cardiac tissue.…”