Bj. Roth et Jp. Wikswo, ELECTRICAL-STIMULATION OF CARDIAC TISSUE - A BIDOMAIN MODEL WITH ACTIVE MEMBRANE-PROPERTIES, IEEE transactions on biomedical engineering, 41(3), 1994, pp. 232-240
Numerical calculations simulated the response of cardiac muscle to sti
mulation by electrical current. The bidomain model with unequal anisot
ropy ratios represented the tissue, and parallel leak and active sodiu
m channels represented the membrane conductance. The speed of the wave
front was faster in the direction parallel to the myocardial fibers th
an in the direction perpendicular to them. However, for cathodal stimu
lation 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 d
og-bone-shaped virtual cathode made by Wikswo et al., Circ. Res. 68:51
3-530, 1991. The model showed that the virtual cathode size and shape
were dependent upon both membrane and tissue conductivities. Increasin
g the peak sodium conductance or reducing the transverse intracellular
conductivity accentuated the dog-bone shape, while the opposite chang
e caused the virtual cathode to become more elliptical, with the major
axis of the ellipse transverse to the fiber direction. A cathodal sti
mulus created regions of hyperpolarization that slowed conduction of t
he wavefront propagating parallel to the fibers. An anodal stimulus ev
oked a wavefront with a complex shape; activation originated from two
depolarized regions 1 to 2 mm from the stimulus site along the fiber d
irection. 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 m
A. When the model was modified to simulate the effect of electropermea
bilization, which may be present when the transmembrane potential reac
hes very large values near the stimulating electrode, our qualitative
conclusions remained unchanged. These three-dimensional calculations u
sing an active membrane model are consistent with the results obtained
previously using two-dimensional linear models and go further to prov
ide an explanation for anodal excitation. Most importantly, by includi
ng the third dimension and a nonlinear membrane, this model provides a
n important physiologically realistic link between the data recorded i
n vivo from the canine heart and the theoretical concept that the anis
otropic bidomain nature of cardiac tissue can affect cardiac activatio
n and propagation.