Effect of a perfusing bath on the rate of rise of an action potential propagating through a slab of cardiac tissue

Abstract

Experiments show that the rate of rise of the action potential depends on the direction of propagation in cardiac tissue. Two interpretations of these experiments have been presented: (i) the data are evidence of discrete propagation in cardiac tissue, and (ii) the data are an effect of the perfusing bath. In this paper we present a mathematical model that supports the second interpretation. We use the bidomain model to simulate action potential propagation through a slab of cardiac tissue perfused by a bath. We assume an intracellular potential distribution and solve the bidomain equations analytically for the transmembrane and extracellular potentials. The key assumption in our model is that the intracellular potential is independent of depth within the tissue. This assumption ensures that all three boundary conditions at the surface of a bidomain are satisfied simultaneously. One advantage of this model over previous numerical calculations is that we obtain an analytical solution for the transmembrane potential. The model predicts that the bath reduces the rate of rise of the transmembrane action potential at the tissue surface, and that this reduction depends on the direction of propagation. The model is consistent with the hypothesis that the perfusing bath causes the observed dependence of the action-potential rate of rise on the direction of propagation, and that this dependence has nothing to do with discrete properties of cardiac tissue.