Ephaptic Coupling as a Resolution to the Paradox of Action Potential Wave Speed and Discordant Alternans Spatial Scales in the Heart

Abstract

Previous computer simulations have suggested that existing models of action potential wave propagation in the heart are not consistent with observed wave propagation behavior. Specifically, computer models cannot simultaneously reproduce the rapid wave speeds and small spatial scales of discordant alternans patterns measured experimentally in the same simulation. The discrepancy is important, because discordant alternans can be a key precursor to the development of abnormal and dangerous rapid rhythms in the heart. In this Letter, we show that this paradox can be resolved by allowing so-called ephaptic coupling to play a primary role in wave front propagation in place of conventional gap-junction coupling. With this modification, physiological wave speeds and small discordant alternans spatial scales both occur with gap-junction resistance values that are more in line with those observed in experiments. Our theory thus also provides support to the hypothesis that ephaptic coupling plays an important role in normal wave propagation.

FIG. 1.

Circuit used to model a one-dimensional fiber containing gap-junction and ephaptic intercellular coupling. Black circuit elements are those typically used in standard, monodomain models of one-dimensional fibers. Red elements model ephaptic coupling. Blue dashed boxes indicate the locations of cells within this circuit description of the fiber.

FIG. 2.

APD $\left(x\right)$ vs $x$ for two consecutive waves (solid and dashed curves), showing transition(s) from long-short to short-long APDs in space for both the (a) GJ and (b) EC systems during regular pacing, with all waves being launched at the left end of the system. Data are shown approximately 120 s into the simulation, well after initial transient behavior has disappeared. Pacing interval (BCL), 207 ms.

FIG. 3.

Key discordant alternans parameters: (a) simulation domain size, (b) theoretical domain size $\lambda$, (c) $\xi$ and (d) simulation nodal width, all vs pacing cycle length.

FIG. 4.

Color plots of $V_m$ of a single action potential excited simultaneously at all points on the fiber, but with slightly different initial conditions in each half of the fiber: $h=0.55$ and $f=0.82$ for $x\le 1.6\text{ cm}$, and $h=0.50$ and $f=0.80$ for $x>1.6\text{ cm}$, for (a) the GJ system and (b) the EC system. (c),(d) Enlargement of the location of the wave back for the conditions in (a),(b).