Electrical activity in myocardial tissue

With Jim Keener
Math Biology at the University of Utah

Related papers
J. Lin and J. P. Keener, Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling, PNAS. 2010 (107) 20935-20940.

J. Lin and J. P. Keener, Ephaptic coupling in cardiac myocytes, IEEE Biomed. Eng. 2012. Accepted.

Brief description
Electrical stimulation of cardiac cells causes an action potential wave to propagate through myocardial tissue, resulting in muscular contraction and pumping blood through the body. Conduction failure in the heart has been linked to ventricular arrhythmia and cardiac death. While gap junctional proteins connecting cardiac cells are traditionally considered to be the main mode of cellular coupling, recent experimental studies have found that down-regulation of gap junctional proteins did not necessarily decrease conduction velocity, implying another mode of coupling. Additionally, our collaborators Steven Poelzing and Rengasayee Veeraraghavan at the Virginia Tech Carilion Research Institute have experimental evidence that modification of tissue structure alone is sufficient to substantially affect conduction.

A small change in transmembrane potential (the difference between the intracellular and extracellular potentials) causes sodium ion flux through voltage-gated channels, constituting the main upstroke of an action potential. The initial change may occur due to gap junctions, however, the narrow extracellular spaces have high resistances and could result in strong field coupling (or ephaptic effects) between neighboring cells. To explore ephaptic effects, microdomains of the complex geometric cardiac tissue structure must be modeled. Existing mathematical models of action potential propagation assume homogenized extracellular spaces and cannot capture these microdomain effects. More detailed numerical models show the importance of the cellular geometry, but are too computationally expensive to be used on a larger scale.

Our preliminary model uses the simplifying assumptions of isopotential intracellular spaces and collapses the extracellular space to a two-dimensional structure. Conservation of current gives rise to equations that can be numerically integrated through a careful modification of known algorithms.

In contrast to classical cable theory for cardiac conduction, we found that the distribution of transmembrane sodium ion channels and the resistance of the extracellular space has a significant impact on propagation velocity in a single strand of cylindrical cells. Cable theory (green surface in part (a) of the above figure) monotonically increases with increasing extracellular lateral conductivity (in the space between the sides of cells) and does not change with extracellular junctional conductivity (in the space between the ends of cells). With the model we developed, we found that when the sodium ion channels are located primarily on the ends of cells, (brown surface in part (a) of the figure) the propagation velocity is greatly enhanced. Even when the sodium ion channels are mostly on the sides of the cells, we see a small enhancement in the propagation velocity with small extracellular lateral conductivities. In part (b) of the figure, in which propagation velocities are plotted over a larger range of extracellular conductivities with sodium ion channels primarily in the ends of the cells, shows that these ephaptic effects occur in all areas of high extracellular resistances. The field coupling for small extracellular junctional conductivities is much stronger than that for small extracellular lateral conductivities, but field effects are evident in both. Thus, microdomains in cardiac tissue modeling cannot be ignored.