Termination of figure-of-eight reentry via resonant feedback pacing

Figures

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  FIGURE 1. Schematic illustration of the stimulation protocols used to generate various spiral wave patterns and provide feedback pacing. (A) Initiation of the S1 wave (orange) via a line stimulus applied along the left edge of the simulation domain. (B) S2 stimulus (green) applied to the lower half of the domain when the waveback of the S1 wave reaches the midpoint, resulting in a clockwise-rotating spiral. (C) S2 stimulus applied to the upper half of the domain at the same waveback position produces a counterclockwise-rotating spiral. (D) S2 stimulus applied over a rectangular region away from the domain boundaries produces a stable figure-of-eight pattern. (E) Protocol for generating four spiral waves (two face-to-face figure-of-eight patterns): two S1 waves are initiated simultaneously by applying line stimuli along both the left and right edges of the domain; the S2 stimulus is applied as in (D). (F) Protocol for generating four spiral waves (two back-to-back figure-of-eight patterns): a single S1 wave is initiated by applying a vertical line stimulus along the center of the domain; the S2 stimulus is applied as in (D). (G) Protocol for generating four spiral waves (two figure-of-eight…

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  FIGURE 2. Dynamics of a single spiral wave in the absence and presence of resonant feedback antitachycardia pacing (rF-ATP). (A) Spatial distribution of transmembrane potential at the moment of S2 stimulation, producing a clockwise-rotating spiral wave. (B) Stable spiral wave observed after 5 s of simulation; the tip trajectory is overlaid in white, showing a circular path. (C) Application of rF-ATP using feedback from the geometric center of the domain results in spiral precession around the feedback site, forming an epicycloidal tip trajectory. (D–F) Corresponding results for a counterclockwise-rotating spiral: (D) S2 stimulation pattern, (E) stable spiral without feedback, and (F) spiral dynamics under rF-ATP, showing reversed epicycloidal precession. Dynamics of a single (G) clockwise-rotating spiral, and (H) counterclockwise-rotating spiral wave subjected to rF-ATP. Electrical signals were recorded from four distinct feedback sites (marked by red circles), each located in a different quadrant of the simulation domain. Regardless of feedback location, rF-ATP consistently induced spiral precession around the corresponding site, with the same sense of rotation relative to spiral chirality.

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  FIGURE 3. Application of rF-ATP to a pair of interacting spiral waves in a figure-of-eight pattern leads to termination. (A) Spatial distribution of transmembrane potential at the moment of S2 stimulation, producing a figure-of-eight pattern with two spirals of opposite chirality. (B) Stable figure-of-eight configuration, with each spiral tip tracing a circular trajectory. (C) Application of rF-ATP modifies spiral–spiral interactions, leading to termination—here via mutual collision and subsequent annihilation of the phase singularities. (D) Nine feedback points (marked by red circles) used to test the rF-ATP protocol on the same initial figure-of-eight pattern. In all cases, termination occurred via one of two mechanisms illustrated in (E) and (F). (E) Termination via mutual collision of the two phase singularities: Representative case in which rF-ATP induced mutual attraction between the spirals. (F) Termination via collision of each phase singularity with the inexcitable boundary: Representative case in which rF-ATP caused the spirals to repel each other.

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  FIGURE 4. Application of rF-ATP to two weakly interacting figure-of-eight patterns leads to termination. Spatial distribution of transmembrane potential after stabilization of two figure-of-eight patterns that (A) face each other, (B) are back-to-back, and (C) are positioned side-by-side. In each configuration, the individual spirals exhibit stable circular tip trajectories in steady state. (D) Locations of nine feedback points used in separate simulations for each 4-spiral configuration in (A)–(C) to test for positional bias of the protocol. (E) Statistics of figure-of-eight termination via the two mechanisms described in Figure 3. (F–H) Representative spatiotemporal evolutions of the patterns in (A–C) when feedback is extracted from the geometric center of the domain. In all cases, rF-ATP leads to figure-of-eight termination via annihilation of mutually colliding phase singularities.