Effect of an externally applied electric field on excitation propagation in the cardiac muscle

Classical theory of potential distribution in cardiac muscle (cable theory) postulates that all effects of electric field (internally or externally applied) should decay exponentially with a space constant of the order of the tissue space constant (similar to 1 mm). Classical theory does not take into account the cellular structure of the heart. Here, we formulate a mathematical model of excitation propagation taking into account cellular gap junctions. Investigation of the model has shown that the classical description is correct on the macroscopic scale only. At microscopic scale, electric field is modulated with a spatial period equal to the cell size (Plonsey and Barr), with the zero average. A very important new feature found here is that this effect of electric field does not decay at arbitrary big distances from the electrode. It opens the new way to control the excitation propagation in the cardiac muscle. In particular, we show that electric field can modify the velocity of propagation of an impulse in cardiac tissue at arbitrary big distances from electrode. In 2-dimensions, it can make rotating waves drift. To test these predictions, experiments with cardiac preparations are proposed.