Resetting and Annihilating Reentrant Waves in a Ring of Cardiac Tissue: Theory and Experiment

Abstract

Theory predicts that a stimulus delivered to an excitation wave circulating on a ring of excitable media will either have no effect, or it will reset or annihilate the excitation depending on the phase and magnitude of the stimulus. We summarize the basis for these theoretical predictions and demonstrate these phenomena in an experimental system consisting of a tissue culture of embryonic chick heart cells cultured in the shape of a ring.

Interactions Between Extracellular Stimuli and Excitation Waves in an Atrial Reentrant Loop

“…Previous studies have demonstrated a wide range of observed modifications to reentrant excitation waves in particular experiments or simulations; such studies include a great deal of information about termination. 7,14,[18][19][20]27,33,34 However, the range of events that occur apart from mechanisms involving geometric complexity, how frequently each one of them occurs, and how stimulus amplitude is related to stimulus timing remain unclear. By making use of the opportunity to repeatedly evaluate different combinations of stimulus amplitude and timing, this study fills in these gaps and gives a comprehensive picture of the interactions.…”

“…One‐dimensional reentry also can be modeled mathematically, and, with the aid of computers, the dynamics of a reentrant loop can be observed in detail. Although reentry in the whole heart most likely is a complex three‐dimensional phenomenon, much has been learned about reentry and its termination from previous one‐dimensional mathematical models 15–21 . The goal here is to extend these findings by mapping the interactions between the stimulus and the advancing excitation wave in a comprehensive way, by using extracellular electrodes for a more realistic stimulation protocol, and by using a more physiologically accurate membrane model while incorporating gap junctions.…”

“…Although reentry in the whole heart most likely is a complex three-dimensional phenomenon, much has been learned about reentry and its termination from previous one-dimensional mathematical models. [15][16][17][18][19][20][21] The goal here is to extend these findings by mapping the interactions between the stimulus and the advancing excitation wave in a comprehensive way, by using extracellular electrodes for a more realistic stimulation protocol, and by using a more physiologically accurate membrane model while incorporating gap junctions. The structural properties of the loop were uniform, chosen to support stable reentrant propagation with the spatial extent of the excitation wave (wavelength) less than half the circumference of the ring.…”

Termination of reentrant propagation by a single extracellular stimulus in an atrial ring model

“…The mechanism by which a properly timed depolarizing (cathodal) stimulus can result in the unidirectional block of the elicited wavefront, and the importance of this mechanism in both the initiation and termination of reentry, is well represented in the literature [2,7,8,12,13,[17][18][19][20][21][22]. However, what is less well understood is the ability of an anodal stimulus to terminate reentrant propagation.…”

“…Despite the advantage of providing for a more thorough analysis, much of the past theoretical work has used simplified models of the membrane ionic currents (i.e. Fitzhugh-Nagumo) [6][7][8], ignored the importance of intercellular coupling (gap junctions) [9,10], or relied upon unrealistic methods for stimulation (i.e. injecting current intracellularly as opposed to having electrodes positioned in a restricted extracellular space) [9][10][11][12][13].…”