A Quasi-One-Dimensional Theory for Anisotropic Propagation of Excitation in Cardiac Muscle

It has been shown that propagation of excitation in cardiac muscle is anisotropic. Compared to propagation at right angles to the long axes of the fibers, propagation along the long axis is faster, the extracellular action potential (AP) is larger in amplitude, and the intracellular AP has a lower maximum rate of depolarization, a larger time constant of the foot, and a lower peak amplitude. These observations are contrary to the predictions of classical one-dimensional (1-D) cable theory and, thus far, no satisfactory theory for them has been reported. As an alternative description of propagation in cardiac muscle, this study provides a quasi-1-D theory that includes a simplified description of the effects of action currents in extracellular space as well as resistive coupling between surface and deeper fibers in cardiac muscle. In terms of classical 1-D theory, this quasi-1-D theory reveals that the anisotropies in the wave form of the AP arise from modifications in the effective membrane ionic current and capacitance. The theory also shows that it is propagation in the longitudinal, not in the transverse direction that deviates from classical 1-D cable theory