Spatiotemporal Dynamics of Damped Propagation in Excitable Cardiac Tissue

Abstract

Compared to steadily propagating waves (SPW), damped waves (DW), another solution to the nonlinear wave equation, are seldom studied. In cardiac tissue after electrical stimulation in an SPW wake, we observe DW with diminished amplitude and velocity that either gradually decrease as the DW dies, or exhibit a sharp amplitude increase after a delay to become an SPW. The cardiac DW-SPW transition is a key link in understanding defibrillation and stimulation close to the refractory period, and is ideal for a general study of DW dynamics.

Examination of stimulation mechanism and strength-interval curve in cardiac tissue

“…This response can be local or can propagate (28,45), forming damped waves with diminished amplitude and velocity (43). What is the ionic mechanism of damped waves?…”

The Strength-Interval Curve in Cardiac Tissue

“…Particularly, they investigated the role of the virtual electrodes during cathodal and anodal excitation and tried to determine their strength-interval relationship. They found “complex dynamics” (i.e., a dip, plateau phase and a descent at the end of the relative refractory period) in the anodal strength-interval curve and a hyperbolic shape of the cathodal strength-interval curve and also observed a “damped wave” response in the dip of the SI curve [49]. Their optical mapping studies of rabbit hearts verified that the dip occurs only during break excitation [32].…”

“…Similarly in the anodal SI curve, they found only the anode make mechanism with proximal excitation in the interval greater than 220 ms, only the anode break mechanism with proximal excitation in intervals between 207.5 and 220 ms, and a paradoxical excitation mechanism at the transition from break to make (intervals between 207.5 and 220 ms) (Figure 10). The excitation mechanism is “paradoxical” when a nonpropagating active make response ultimately triggers excitation, in a process similar to a “damped” [49] or “graded” [51] response. The small dip in the 20 ms cathodal strength-interval curve shown in Figure 4(a) (310–320 ms) arises from a similar mechanism.…”

Virtual Electrode, Graded Responses, Reentry, Breakthrough, and Undetermined:

“…The virtual electrode polarization alone cannot explain the formation of reentry from premature stimulation. 16 Consequently, the graded responses are involved not only in strong (>10 times diastolic stimulation threshold) stimuli but also in threshold level stimulation, making the role of the graded responses more evident in ventricular vulnerability. The cellular "graded responses" link virtual electrode polarization and reentry.…”