Background: Electrical alternans, the beat-to-beat alternation of the duration of action potentials, is thought to be one of the principal causes of rapid rhythm disorders, including ventricular tachycardia and fibrillation. Discordant alternans, in which the alternation is out-of-phase in different parts of the heart, is particularly dangerous. However, the standard model of discordant alternans predicts a spacing between these out-of-phase regions that is too large to fit within the heart. The so-called ephaptic model of the gap-junction connectivity between cells can theoretically affect these characteristic spacings, and thus may provide an explanation for why discordant alternans appears in experiments, but not in realistically-sized computer simulations.
Method: We constructed a computer model that implements ephaptic connectivity between cells, which were arranged to form a one-dimensional fiber. Model parameters were chosen to maximize the ephaptic effect as measured by its effect on conduction velocity. Action potential waves were launched from one end of the fiber at regular intervals. Plots of the membrane potential versus time and space were created, and the conduction velocity and the spacings between the nodes of the out-of-phase regions were measured.
Results and Conclusions: The spacings between the nodes decreased significantly, but not dramatically (0.58 cm vs. 0.80 cm), when the ephaptic model was compared to the standard model. Examination of key electrical potentials within the ephaptic model agreed with our theory, which explains the reductions in spacings by the different gap junction conductivities “seen” by the different temporal Fourier components of the action potential wave. We speculate that the relatively small reduction in spacing we see may be due to the optimal ephaptic parameters not coinciding with those that maximize its effect on conduction velocity. This possibility will be the subject of future investigation.