Puzzles about Excitable Media and Sudden Death. In: Levin SA, editor. Frontiers in Mathematical Biology. Berlin: Springer Berlin Heidelberg; 1994. pp. 139-58. [DOI: 10.1007/978-3-642-50124-1_8]

A spatial scale factor for electrophysiological models of myocardium

In the United States among males 20-64 years old about 1/3 of deaths are classified as 'sudden cardiac death', and 1/4 had no forewarning, nor did autopsy turn up any visible cause. The heart just switches from its normally periodic pumping to an alternative mode called 'fibrillation' more resembling electrical turbulence. In normal tissue its mechanism is a geometrically re-entrant mode of normal propagation. Everything about this spatial pattern depends upon the magnitude of 'D', the one term with dimension involving space in the pertinent biophysical equations. Explicit or implicit estimates in current literature span orders of magnitude. In this article I argue from a diversity of recent experiments for a narrower range of realistic values. It has an important role in the spatio-temporal evolution of fibrillation and in defibrillation.

On measuring curvature and electrical diffusion coefficients in anisotropic myocardium: comments on "effects of bipolar point and line simulation in anisotropic rabbit epicardium: assessment of the critical radius of curvature for longitudinal block"

Notion of "curvature" and "propagation perpendicular to the activation front" inherited from electrophysiological theory of isotropic reaction-diffusion media do not apply directly to experimental data taken in uniformly anisotropic myocardium. They apply directly only after the concept of "curvature" is normalized and propagation is made to look perpendicular to activation fronts by rescaling distances to achieve isotropy. Without rescaling, the curvature-dependence of longitudinal propagation speed turns out counter-intuitively to measure transverse intercellular electrical coupling.

Control of rotating waves in cardiac muscle: analysis of the effect of an electric field

The effect of an electric field on rotating waves in cardiac muscle is considered from a theoretical point of view. A model of excitation propagation taking into account the cellular structure of the heart is presented and studied. The application of a direct current electric field along the cardiac tissue is known to induce changes in membrane potential which decay exponentially with distance. Investigation of the model shows that the electric field induces a gradient of potential inside a cell which does not decay with distance, and results in modification of excitation propagation which extends a considerable distance from the electrodes. In two dimensions, it induces a drift of rotating waves. The effect of the electric field on propagation velocity and on rotating waves cannot be obtained in any arbitrary models of cardiac muscle. For an electric field of about 1 V cm-1 and junctional resistances of about 20 M omega, the change in velocity of propagation can be up to several percent, resulting in a drift velocity of rotating waves of the order of 1 cm s-1. To test these predictions, experiments with cardiac preparations are proposed.