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As yet there is no model or simulation that accounts for the anisotropic difference in the shape of the upstroke and safety factor of propagating cardiac action potentials: fast upstrokes occur with slow transverse propagation and slow upstrokes occur with fast longitudinal propagation. The purpose of this paper is to demonstrate, however, that a simplified cable model based on directional differences in the effective membrane capacitance predicts in detail the experimentally measured directionally dependent behavior of the upstroke in response to modification of the sodium conductance. Quinidine and lidocaine produced greater relative decreases in Vmax and conduction velocity with longitudinal propagation than with transverse propagation, as predicted on the basis that the shape differences should produce an anisotropic distribution in the membrane uptake of sodium channel binding drugs. The simulation predictions of the effects of positive shifts of the take-off potential due to premature action potentials were also confirmed experimentally: there was a greater relative decrease in conduction velocity, Vmax, and Vamp with a greater increase in tau foot during longitudinal propagation than with transverse propagation. The major anisotropic differences in shape occurred when the take-off potential approached the least negative value that produced a propagated response. The extensive experimental verification of the results of a simplified model based on directional differences of effective membrane capacitance, combined with directional differences in effective axial resistivity, provides an initial quantitative basis for the anisotropic behavior of propagating depolarization in response to modification of the sodium conductance in cardiac muscle.

circulation research

Propagating depolarization in anisotropic human and canine cardiac muscle: apparent directional differences in membrane capacitance. A simplified model for selective directional effects of modifying the sodium conductance on Vmax, tau foot, and the propagation safety factor.