Reentry-driven model of atrial fibrillation is maintained by paired reentries and terminated by strategic pairwise virtual ablation

Figures

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  FIGURE 1. Diagram representing the previously described interactions between propagation waves (arrows) and a boundary (in gray). Each arrow’s head marks a wavefront, and its trailing line marks a waveback. From left to right, CB1 (complete reentry), CB2 (incomplete reentry), and NCB (no reentry). Each wavefront contributes to the index by a factor of +1 or −1 depending on direction.

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  FIGURE 2. Example of the 6 starting conditions for the same mesh. Singularities in opposite directions are placed along each of the Cartesian axes (from left to right: x, y, and z axis). The top row shows the clockwise placement, and the bottom row shows the counter-clockwise placement.

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  FIGURE 3. Example of an original simulation mesh (left) and reduced mesh (right). The reduced mesh displays the geodesic Voronoi diagram connecting neighboring sampled points with white edges, and includes an additional point at the center of each anatomical hole, allowing the identification of anatomical reentries around it.

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  FIGURE 4. Example of the three types of virtual ablation line, from left to right: heuristic line (pink), straight line (blue), and random line (orange). Both the heuristic line and straight line form a loop around the same singularity detections and then connect them, but the former blocks the path of the wave, while the latter takes the shortest path. The random line connects the shortest path between two random points at a comparable distance to the other virtual ablation lines.

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  FIGURE 5. Snapshot of a successful detection, viewed from different angles. The mesh is colored according to phase values. Phase jump detections are marked with orange arrows in the direction of propagation. Detections of positive and negative singularities are marked by red and blue dots respectively. A label is placed next to each cluster of points, indicating that cluster’s contribution to the total index, and matching the color of the opposite-direction singularity associated with the same wavefront. Note that the pair marked in green is an anatomical reentry (mitral valve) paired with a functional reentry.

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  FIGURE 6. Top: Plot of the number of positive and negative singularities (solid red line and dashed blue line, respectively), and the index sum (solid black line), over time for a given simulation. Positive and negative singularities vary over time, but the index sum remains 0 for the majority of the time, with small fluctuations. Bottom: Snapshot of a moment when the index sum did not equal 0, viewed from different angles and represented with the same conventions as Figure 5. To the right, the image zooms into a section of the simulation where an incorrect detection occurred. Circles highlight which singularity detections were assigned to which clusters in the zoomed section. An unpaired −1, marked in red, results in a non-zero total index.

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  FIGURE 7. Histograms for the two performance measures. Left: f0 , the fraction of the total time where the index sum adds up to 0. Right: mind , the mean index sum over time. Both measures were consistent with the Index Theorem, f0 heavily skewing towards 1, and mind narrowly centered around 0.

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  FIGURE 8. Histograms for the three complexity measures: Left: Singularity duration. While a few singularities last for most of the simulation, by far most of them are rather short-lived. Center: Total singularity count over time. As singularities are created and destroyed through the evolution of each simulation, many singularities can be detected. Right: Maximum simultaneous singularity count. Unlike AT, where only two counter rotating reentries are typically observed, here we see up to 26 singularities co-existing in some cases.

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  FIGURE 9. Histograms for the three complexity measures: Left: Distribution of median CL values. Right: Distribution of CL interquartile range values.

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  FIGURE 10. Histograms for the two Moran’s I distributions: the self-similarity (black) and the cross-similarity (blue). The self-similarity has a higher median and higher variance.

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  FIGURE 11. Histograms for the two termination measures. Left: Distribution of early termination times. A wide variety of termination times were observed, with some lasting almost the full duration of the simulation and some terminating before even the first virtual ablation time. Right: Distribution of early termination counts–how many starting conditions terminated early per mesh. 23 meshes never terminated early, and only 3 terminated early for 5 out of 6 starting conditions. Other meshes fell somewhere between, but notably no mesh terminated early for all 6 starting conditions.