Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling

Abstract

Existing models of electrical activity in myocardial tissue are unable to easily capture the effects of ephaptic coupling. Homogenized models do not account for cellular geometry, while detailed spatial models are too complicated to simulate in three dimensions. Here we propose a unique model that accurately captures the geometric effects while being computationally efficient. We use this model to provide an initial study of the effects of changes in extracellular geometry, gap junctional coupling, and sodium ion channel distribution on propagation velocity in a single 1D strand of cells. In agreement with previous studies, we find that ephaptic coupling increases propagation velocity at low gap junctional conductivity while it decreases propagation at higher conductivities. We also find that conduction velocity is relatively insensitive to gap junctional coupling when sodium ion channels are located entirely on the cell ends and cleft space is small. The numerical efficiency of this model, verified by comparison with more detailed simulations, allows a thorough study in parameter variation and shows that cellular structure and geometry has a nontrivial impact on propagation velocity. This model can be relatively easily extended to higher dimensions while maintaining numerical efficiency and incorporating ephaptic effects through modeling of complex, irregular cellular geometry.cardiac electrophysiology | extracellular conductivity | microdomain effects W hile gap junctional coupling is usually considered to be the primary mechanism for action potential propagation, there is evidence that other mechanisms are important. In particular, only a moderate reduction of cardiac propagation velocity was found in murine hearts with inactivated Connexin43 (Cx43) gene (1). In mice with heterozygous Cx43AE down-regulation, either a 23-44% decrease in propagation velocity (2-4) or no discernible decrease in propagation velocity (5-8) was found. In Cx43 − ∕− mice with no expression of the protein, propagation was still found, although discontinuous and at much slower speeds (7). These experimental findings are in conflict with the classical understanding of how gap junctions determine propagation velocity.One possible explanation for these intriguing observations is that ephaptic (i.e., field effect) coupling may be significant (1, 9-12). However, the study of ephaptic effects is made difficult by the fact that these effects are most important in microdomains such as junctional clefts.Existing homogenized models, while computationally accessible, are not able to deal with the effects of microdomains and hence do not capture the effects of ephaptic coupling (13,14). On the other hand, detailed spatial models have shown that geometry plays an important role in the conduction velocity but are too expensive to implement for a full 3D tissue (11,12,(15)(16)(17)(18)(19).Here we present a model that captures the effects of the intricate cellular geometry with simplifications that will allow the model to be extended more readily to t...

Interstitial volume modulates the conduction velocity-gap junction relationship

“…This time course may also be shorter than the time required for new G j formation (20), especially in intact tissue. Finally, cardiac conduction may involve alternative modes of intercellular coupling that are not exclusively dependent on gap junctions (25,37). Irrespective of the mechanism, V IS plays an important role in modulating conduction.…”

Three-Dimensional Impulse Propagation in Myocardium

“…The fact that transmembrane sodium channels are concentrated around the ICDs 28,32 has been seen as providing a mechanistic framework for ephaptic transmission. Computer models of 1D myocyte strands in which sodium channels were colocated with gap junctions at the interface between adjacent cells 32,33 suggest that ephaptic coupling increases CV at low gap junction conductivity and vice versa. One interpretation of these findings is that both mechanisms act in concert to stabilize impulse transmission between myocytes.…”

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

“…Alternatively, they may be able to have extracellular resolution much less than intracellular resolution. For work developing a purely-microscale version of such a generalization, see Lin and Keener (2010).…”

“…Further, in a subsequent study, they also found that gap-junctional coupling was essentially abolished in isolated cell pairs extracted for Cx43-null ventricular tissue (Yao et al 2003). These findings are surprising because gap junctions are generally accepted as the primary mechanism of normal cardiac electrical communication (Rohr 2004), and they suggest that there are important electrical coupling mechanisms in cardiac tissue besides gap-junctionally mediated coupling (Sperelakis and Mann 1977;Picone et al 1991;Ramasamy and Sperelakis 2007;Mori et al 2008;Copene and Keener 2008;Hand and Peskin 2010;Hand and Griffith 2010;Lin and Keener 2010).…”