Vector Field Heterogeneity for the Assessment of Locally Disorganised Cardiac Electrical Propagation Wavefronts From High-Density Multielectrodes

Figures

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  Figure 1.. Representation of the bipolar loop in a recording on the epicardium of a Langendorff rabbit heart at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $37\,^{\circ }\text{C}$\end{document} and under stimulation of 4 Hz; (a) Loop traced by each bipole in its corresponding clique; (b) Closer look at the loop traced by the orthogonal bipoles in clique 2, with a vector indicating the estimated propagation direction for that clique.

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  Figure 2.. Illustration of heterogeneity depicting the heterogeneity scores of each clique \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $(\Psi)_{i,j}$\end{document} and the VFH value assigned to the map; (a) Results for a recording stimulated at 4 Hz, with the propagation vector map (left) and the heterogeneity map (right), illustrating an organised region of propagation; (b) Idem for a basal recording where the propagation map is found to be more disorganised.

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  Figure 3.. Calculation of the Spatial Inhomogeneity (SI) index, proposed by Lammers et al., for a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $6\times 6$\end{document} grid of recordings depicted in Fig. 2; (a) Results for a recording stimulated at 4 Hz, with the propagation vector map (first column), Local Activation Time relative to the earliest LAT of the map, for representation purposes (second column), the corresponding phase map (third column), and the phase differences histogram (last column); (b) Idem for a basal recording.

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  Figure 4.. (a) Box and whisker plot of the VFH values of simulated propagation maps of increasing disorganisation. For each angle range, 100 simulations were performed corresponding to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $4\times 4$\end{document} catheter grid. The trend of the VFH metric (dashed line) is calculated by running 100,000 simulations for each interval and plotting the mean VFH value; (b) Propagation maps representative of three distinct angle ranges; (c) Comparison of the VFH values from simulated propagation maps of different catheter sizes. The shaded region corresponds to the standard deviation and the line is the mean VFH value for the 100 simulations. The decrease in standard deviation from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $4\times 4$\end{document} to \documentclass[12pt]{minimal}…

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  Figure 5.. Box and whisker plots of the VFH values according to the type of stimulation. Results for different catheter sizes are shown.

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  Figure 6.. Example of heterogeneity analysis for an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $8\times 8$\end{document} catheter grid; (a) Vector map representing propagation under the catheter. The VFH values that a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $4\times 4$\end{document} grid would obtain are displayed; (b) Heterogeneity Map displaying the heterogeneity values assigned to each vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $(\Psi)_{i,j}$\end{document} and the global VFH value of the whole map.

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  Figure 7.. Box and whisker plots of the SI index values according to the type of stimulation. Results for different catheter sizes are shown.

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  Figure 8.. (a) ROC curves comparison between the VFH metric proposed in this study (solid line) and the SI index (dashed line) for the case of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $4\times 4$\end{document} electrode grid; (b) Same comparison for the PR curves.

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  Figure 9.. Box and whisker plots of the VFH values according to the type of stimulation. Results for different catheter sizes are shown; (a) Application of VFH metric to omnipolar-derived vector maps; (b) Application of the metric to LAT-derived vector maps.

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  Figure 10.. Statistical Test Results; (a) Q-Q Plots of the VFH value samples according to stimulation type (rows) and for different catheter sizes (columns). The 95\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\%$\end{document} confidence interval is indicated by the shaded region; (b) Q-Q Plots of the SI index samples according to stimulation type (rows) and for different catheter sizes (columns). The 95\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\%$\end{document} confidence interval is indicated by the shaded region; (c1) and (c2): Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves comparison between the VFH metric proposed in this study (solid line) and the SI index (dashed line).

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  Figure 11.. (a) ROC curves comparison between omnipolar-derived and LAT-derived VFH for the case of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $4\times 4$\end{document} electrode grid. SI Index results are also displayed; (b) Same comparison for the PR curves.