Action potential propagation in a thick strand of cardiac muscle

A theoretical model of action potential propagation in a thick strand of cardiac muscle is presented. The calculation takes into account the anisotropic and syncytial properties of the tissue, the presence of the interstitial space, the effect of the surrounding tissue bath, and the variation of the potential both along the strand length and across the strand cross section. The bidomain model is used to represent the electrical properties of the tissue, and the Ebihara-Johnson model is used to represent the properties of the active sodium channels. The calculated wave front is curved, with the action potential at the surface of the strand leading that at the center. The rate of rise of the action potential and the time constant of the action potential foot vary with depth into the tissue. The velocity of the wave front is nearly independent of strand radius for radii greater than 0.5 mm. The conduction velocity decreases as the volume fraction of the interstitial space decreases. In the limit of tightly packed cells, an action potential propagates quickly over the surface of the strand; the bulk of the tissue is then excited by a slow inward wave front initiated on the surface. This model does not predict an increase in conduction velocity when cells are tightly packed, a hypothesis that has been proposed previously to explain the fast conduction velocity in Purkinje fibers of some species.