DIRECTIONAL CHARACTERISTICS OF ACTION-POTENTIAL PROPAGATION IN CARDIAC-MUSCLE - A MODEL STUDY

Propagation of an elliptic excitation wave front was studied in a two-dimensional model of a thin sheet of cardiac muscle. The sheet model of 2.5 x 10 mm consisted of a set of 100 parallel cables coupled through a regular array of identical transverse resistors. The membrane dynamics was represented by a modified Beeler-Reuter model. We defined the charging factor (CF) to represent by a single number the proportion of input current used to charge the membrane locally below threshold and showed that CF is inversely correlated with the time constant of the foot of the action potential (tau-foot) during propagation on a cable. A safety factor of propagation (SF) was also defined for the upstroke of the action potential, with SF directly correlated with the maximum rate of depolarization (V(max)) and, for cablelike propagation, with propagation velocity. Propagation along the principal longitudinal axis of the elliptic wave front is cablelike but, in comparison with a flat wave front, transverse current flow provides a drag effect that somewhat reduces the propagation velocity, V(max), SF, and CF. With a longitudinal-to-transverse velocity ratio of 3:1 or more, the wave front propagating along the principal transverse axis is essentially flat and is characterized by multiple collisions between successive pairs of input junctions on a given cable; V(max), SF, and CF are larger than for longitudinal propagation, but CF is no longer correlated with tau-foot. There are transient increases in propagation velocity and V(max) with distance from the stimulation site along both principal axes until stabilized values are achieved, and a similar transient decrease in tau-foot. Away from the principal axes, the action potential characteristics change progressively along the elliptic wave front. When the isochrone curvature is relatively low, collisions take place and propagation is predominantly transverse. Beyond a certain degree of curvature, collisions are absent and propagation is predominantly longitudinal. Good correlations are found between our simulations and published experimental observations on strips of heart muscle, except for the behavior of tau-foot. Based on the indications provided by the model, it is argued that the short recording distance used in experimental measurements may have led to an overestimation of tau-foot in the longitudinal direction because of transient changes in the foot of the action potential and possible distortions caused by the stimulus.