Multiparametric analysis of geometric features of fibrotic textures leading to cardiac arrhythmias

Figures

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  Figure 1. Graphical representation of the graph-based automatic spiral wave core recognition algorithm. Sets containing wavefronts’ intersection points are represented as: (a) collection of 2D maps; (b) directed graphs. Green is the major (or core) group that contains points from all n sets. Blue is the minor group that contains points from only a few neighboring sets. Red is isolated points that are not attributed to any group. R is the arbitrarily chosen radius for dividing points into groups. The green dotted line (shortest path from the first set points to the last set points) corresponds to the core trajectory.

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  Figure 2. Clusters extraction example. Gray color indicates empty space; other colors show different clusters marked on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\times 8$$\end{document}8×8 grid.

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  Figure 3. Studied features of fibrosis illustrated in a local texture (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$64\times 64$$\end{document}64×64 size): Three largest clusters (a); solidity (b); zig-zag propagation (c); centroids mean distance between three clusters (d).

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  Figure 4. Arrhythmia initiation probability versus fibrosis density. Each value represents mean probability of arrhythmia for 30 calculations with unique fibrosis matrix of the same density. Calculations were performed for 30 density values (red points) in the range from 27 to 41.5%, thus in total for 900 textures.

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  Figure 5. Initiation of arrhythmia by high-frequency pacing in the non-arrhythmogenic texture (the upper row) and in arrhythmogenic texture (the lower row). The local arrhythmogenic (red) and non-arrhythmogenic (yellow) textures (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$56\times 56$$\end{document}56×56) are marked on the frames.

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  Figure 6. Distributions in arrhythmogenic and non-arrhythmogenic groups for five features for different textures’ sizes. Cohen’s d value estimates the difference between the two groups of distributions. All basic features used in the study are presented: cluster area (size), specifically for five largest clusters; solidity for one largest cluster; fibrosis density; centroids’ distance (three clusters); and zig-zag propagation path length. For this and the following figures, we use the entire dataset of 8726 textures.

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  Figure 7. Accuracy, precision, recall and f1-score for features used in the study. All values correspond to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$56\times 56$$\end{document}56×56 local textures.

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  Figure 8. Features accuracy depending on the textures size. Combination corresponds to all the features listed in the legend above, united in one feature vector.

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  Figure 9. Accuracy, precision, recall and f1-score for pairs of features. All values correspond to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$56\times 56$$\end{document}56×56 local textures.

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  Figure 10. Number of arrhythmias for 500 filtered textures. All textures were initially arrhythmogenic, but lost this feature as the texture was filtered. The x-axis shows cluster area more (a) or less (b) than the threshold.

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  Figure 11. Examples of location of arrhythmias before and after filtering the texture for small clusters. The blue points show location of arrhythmia in non-filtered texture, the red point show the location of the arrhythmia in texture filtered for clusters with the size < 20. The filtered texture is represented by the yellow color. Case (c) shows almost the same position of the spiral wave rotation before and after filtration, while cases (a) and (b) show different positions of the arrhythmias in the texture.