Reconstruction of propagated electrical activity with a two-dimensional model of anisotropic heart muscle

The propagated electrical activity in normal anisotropic cardiac muscle is characterized by directionally dependent variations in the rising phase of the action potential. An important question concerns the relation between such variations and the propagation velocity and extracellular potentials. This problem was studied here in a sheet of cells, under conditions of uniform intracellular anisotropic resistivity and constant electrical membrane properties, through a numerical solution of the two-dimensional propagation equation. The numerical solution implies a lumping of the cytoplasmic and intercellular resistances into an equivalent junctional resistance to form a distributed resistive network representing the intracellular domain. The interstitial space is assumed isotropic and unbounded, with a resistivity of 100 omega X cm. The electrical properties of the cell membrane are represented by a Beeler-Reuter model. The stimulus current is applied to a small area of the sheet, and attention is focussed on the stable propagated events occurring some 5 or 6 length constants away from the stimulation site. The numerical solution is a good approximation of a continuous uniform structure when the cell size is less than 10% of the length constant along both major axes. Conditions of non-uniform propagation, with directionally dependent variations in the maximum rate of rise and time constant of the foot of the action potential were simulated by increasing the cell size to 30% of the length constant in the transverse direction of the sheet. Our results indicate that the directional changes in the maximum rate of rise correspond to small modifications of the extracellular potentials, while the directional changes in time constant of the foot are associated with the propagation velocity. The maximum effects are observed along the transverse direction as follows: a 19% increase in maximum rate of rise corresponds to a decrease of about 6% in the peak-to-peak amplitude of the extracellular potential, and a 24% increase in time constant of the foot is associated with a decrease of about 7% in the propagation velocity. Under the conditions of the present study, however, the simulated directional changes in maximum rate of rise are smaller than those experimentally observed so the corresponding changes in the extracellular potentials are probably underestimated.