Atrial fibrosis identification with unipolar electrogram eigenvalue distribution analysis in multi-electrode arrays

Fig. 1. (a) Activation distribution at a particular time instant over the 2D tissue used in this work, including the fibrotic patch. Black arrows indicate propagation wavefront direction. (b) The three MEA orientations with respect to the tissue considered in this study: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi = 0^{\circ }$$\end{document}Ψ=0∘ (leftmost), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi = 30^{\circ }$$\end{document}Ψ=30∘ (middle) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi = 45^{\circ }$$\end{document}Ψ=45∘ (rightmost), where the red circle encompasses the fibrotic tissue area. It should be noted that…

Fig. 2. Arrangements of four (a) and nine (b) electrodes (2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}×2 and 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}×3 cliques, respectively) from the MEA

Fig. 3. Upper panel (a): action potentials (APs) in persistent atrial fibrillation (cAF), registered in two different nodes from the simulation mesh: in a cardiomyocyte outside the fibrotic patch (light blue line) and in a cardiomyocyte inside the fibrotic patch coupled with two fibroblasts (orange line). In order to show the effect of the applied electrical remodeling, APs were also shown in control conditions, from different simulations not including electrophysiological remodeling and not used in this work (yellow and purple lines, for uncoupled and coupled cardiomyocytes, respectively). Lower panel: Noisy unipolar EGMs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^{q}_{i,j}(n)$$\end{document}ui,jq(n) (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{v} = 46.4 \ \mu V$$\end{document}σv=46.4μV) recorded in…

Fig. 4. The PentaRay® catheter, where the 20 poles are highlighted. Two of the clique distributions considered around each catheter mapping point, with four (dashed blue line) and five (dashed orange line) electrodes, are also pointed out. This image was modified from the Biosense Webster catalog

Fig. 5. Posteroanterior (left) and anteroposterior (right) views of color-coded 3D mesh of MRI (showing dense fibrosis in red and healthy tissue in blue) generated by ADAS 3D co-registered with all EAM mapping points provided by CARTO 3 (gray). The 38 mapping points selected over fibrotic and non-fibrotic areas to compute EIGDR and bipolar indices are highlighted in green and magenta, respectively

Fig. 6. 3D reconstruction of the LA geometry (gray mesh) and corresponding co-registered MRI, showing the different regional distribution patterns of gadolinium (red areas: latest contrast enhancement, blue areas: absence of latest contrast enhancement). In the geometrical mesh, two of the mapping points acquired and considered in the analysis (point #5 at fibrosis, point #2 at non-fibrosis) are marked and color-coded according to their corresponding bipolar peak-to-peak amplitude. For each of them, the atrial activation windows extracted from the twenty filtered u-EGMs recorded with the PentaRay® catheter are also displayed. Note that not all displayed u-EGMs recorded at a particular catheter site belong to a clique, see Section 2.3, and therefore affect the EIGDR indices and bipolar amplitude computations

Fig. 7. (a) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$14 \times 14$$\end{document}14×14 and (b) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$13 \times 13$$\end{document}13×13 ground-truth masks for evaluating fibrosis detection ability of maps performed with 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}×2 and 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}×3 cliques, respectively. Green squares represent the pixels…

Fig. 8. Upper panels: maps of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}$$\end{document}R, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R}^{\mathcal{A}}$$\end{document}RA, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \mathcal{R}^{\mathcal{A}}$$\end{document}ΔRA from 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}×3 cliques and bipolar voltage maps \documentclass[12pt]{minimal} \usepackage{amsmath}…