Spatial concentration and distribution of phase singularities in human atrial fibrillation: Insights for the AF mechanism

Figures

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  FIGURE 1. Getis‐Ord GI* Detects High and Low Spatial Concentrations. Examples of calculated z‐scores for three quantitatively different scenarios of spatial concentration. Statistically significant (z ≥ 1.96 or z ≤ −1.96) spatial hotspots and cold spots are identified. (A) Getis‐Ord GI* shows no evidence of hotspots or cold spots, with all calculated z‐scores being statistically insignificant (−1.96 ≤ z ≤ 1.96). (B) Getis‐Ord GI* shows evidence of hotspots, with z‐scores falling in the statistically significant range (z ≥ 1.96). (C) Getis‐Ord GI* shows evidence of cold spots, with z‐scores falling in the statistically significant range (z ≤ −1.96)

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  FIGURE 2. Moran's I detects spatial autocorrelation. Examples of spatial patterns for three quantitatively different scenarios of Moran's I. Each cell value is either 0 (blue) or 1 (yellow). (A) Moran's I demonstrates clear spatial clustering or clumping. In this scenario, I approaches 1, and P‐values are significant, reflecting the homogeneity between states of neighbouring cells. (B) Moran's I demonstrates spatial randomness. In this scenario, I values are close to 0, with P > .05, reflecting the randomness of the pattern observed. (C) Moran's I demonstrates a uniform spatial dispersion. In this scenario, neighboring cells have opposing values at all four boarders, resulting, I values near to −1, and P < .05

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  FIGURE 3. Getis‐Ord GI* analysis shows evidence of PS hotspots. Getis‐Ord Gi* analysis was performed to identify statistically significant (z ≥ 1.96 or z ≤ −1.96) spatial hotspots and cold spots of PS formation. (A) Basket catheter grid maps show evidence of localized areas of high concentration of PS formation, indicating the presence of a hotspot. (B) Basket catheter grid maps show evidence of localized areas of low concentration of PS formation, indicating the presence of a cold spot. (C) Basket catheter grid maps show evidence of localized areas of both high concentration of PS formation and low concentration of PS formation, indicating the presence of hotspots and cold spots in a single recording

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  FIGURE 4. Global clustering of phase singularity formation. Examples of basket catheter grid maps of PS formation in human persistent AF. (A) Grid maps of PS formation for positive values of Moran's I showing statistical significance, thus indicating modest spatial clustering or clumping. (B) Grid maps of PS formation for positive values approaching zero of Moran's I showing no statistical significance; thus consistent with complete spatial randomness. (C) Grid maps of PS formation for negative values of Moran's I near to zero, showing no statistical significance; thus, consistent with spatial randomness. Overall, Moran's I is consistent with the notion that PSs are randomly dispersed through the atrium in human persistent AF

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  FIGURE 5. Clustering of phase singularity formation using Moran's I. Moran's I shows evidence of spatial randomness of PS formation for a majority of cases. Overall, the Moran's I statistic showed a mean of 0.0326 (95% CI: 0.0003‐0.0649). In the LA, the mean Moran's I was found to be 0.0252 (95% CI: −0.0375 to 0.0898) and in the RA the mean Moran's I was 0.0485 (95% CI: −0.0187 to 0.1157)