ELECTRICAL-STIMULATION OF CARDIAC TISSUE - A BIDOMAIN MODEL WITH ACTIVE MEMBRANE-PROPERTIES

Numerical calculations simulated the response of cardiac muscle to stimulation by electrical current. The bidomain model with unequal anisotropy ratios represented the tissue, and parallel leak and active sodium channels represented the membrane conductance. The speed of the wavefront was faster in the direction parallel to the myocardial fibers than in the direction perpendicular to them. However, for cathodal stimulation well above threshold, the wavefront originated farther from the cathode in the direction perpendicular to the myocardial fibers than in the direction parallel to them, consistent with observations of a dog-bone-shaped virtual cathode made by Wikswo et al., Circ. Res. 68:513-530, 1991. The model showed that the virtual cathode size and shape were dependent upon both membrane and tissue conductivities. Increasing the peak sodium conductance or reducing the transverse intracellular conductivity accentuated the dog-bone shape, while the opposite change caused the virtual cathode to become more elliptical, with the major axis of the ellipse transverse to the fiber direction. A cathodal stimulus created regions of hyperpolarization that slowed conduction of the wavefront propagating parallel to the fibers. An anodal stimulus evoked a wavefront with a complex shape; activation originated from two depolarized regions 1 to 2 mm from the stimulus site along the fiber direction. The threshold current strength (0.5 ms duration pulse) for a cathodal stimulus was 0.048 mA, and for an anodal stimulus was 0.67 mA. When the model was modified to simulate the effect of electropermeabilization, which may be present when the transmembrane potential reaches very large values near the stimulating electrode, our qualitative conclusions remained unchanged. These three-dimensional calculations using an active membrane model are consistent with the results obtained previously using two-dimensional linear models and go further to provide an explanation for anodal excitation. Most importantly, by including the third dimension and a nonlinear membrane, this model provides an important physiologically realistic link between the data recorded in vivo from the canine heart and the theoretical concept that the anisotropic bidomain nature of cardiac tissue can affect cardiac activation and propagation.