A mathematical model for electrical stimulation of a monolayer of cardiac cells

An equation governing the transmembrane potential, based on the continuity equation and Ohm's law, is solved numerically using a finite difference technique.The sheet is depolarized under the stimulating electrode and is hyperpolarized on each side of the electrode along the fiber axis.The results are similar to those obtained previously by Sepulveda et al. (Biophys J, 55: 987–999, 1989) for stimulation of a two-dimensional sheet of tissue with no perfusing bath present.Pacemakers and defibrillators work by electrical stimulation of the heart. One way to learn more about electrical stimulation is to study very simple models, such as monolayers of cardiac cells [1]. An important factor during stimulation is anisotropy, which means the tissue has different electrical properties in different directions. Cardiac tissue is anisotropic in that the individual myocardial cells are cylindrical with a length greater than their width, and the cells align with each other to form fibers. This geometry makes the electrical conductivity of the tissue greater parallel to the fibers than perpendicular to them. Cell monolayers can be grown with any fiber geometry, making them a particularly attractive model system [2,3].The goal of our study is to examine the effect of stimulating a two-dimensional sheet of cardiac tissue. We assume that the stimulating electrode is located in a bath perfusing the issue. In a previous study, Sepulveda et al. [4] simulated the electrical behavior of a two-dimensional sheet of tissue. They found that, when stimulated by a point cathode, the tissue near the cathode depolarized but adjacent regions hyperpolarized along the fiber direction. However, their model did not include a saline bath perfusing the tissue. Our study reexamines the results of Sepulveda et al., with particular emphasis on the effect of a perfusing bath.The regions of depolarization and hyperpolarization (sometimes called "virtual electrodes") are important, because they are central to