Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials—Application to Atrial Ectopic Activity

Figures

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  Figure 1. Flowchart illustrating the outline of this study.

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  Figure 2. Meshes of the atria and torso used for forward and inverse calculations. Blue spheres on the atria indicate 200 pacing locations used to create basis vectors, while red spheres indicate 100 pacing locations used for monodomain simulations to be reconstructed. Torso electrodes are shown in blue. Red spheres on the torso mark reference nodes.

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  Figure 3. TMV templates based on the Courtemanche et al. cell model (red) and the step function (blue).

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  Figure 4. (Left) Exemplary “L-curves” for a basis length of L = 17. Black dots: original data points. Red curves: smoothing spline fits. Blue circles: Points of min. absolute slope. Red circles: Points 10% left of min. slope points. (Right) Dependency of basis dimension on basis length.

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  Figure 5. Delay-based LAT estimation. D is a difference matrix to obtain pair-wise delays from LATs.

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  Figure 6. Ectopic focus localization illustrated for exemplary reconstructions with the BSP basis (L = 33) and TikhGS. CV = 0.8m/s. SNR = 0dB. Black spheres: true focus, white spheres: reconstructed focus. Geodesic distance fields shown on the left are reversed and truncated at 3 cm (dark blue). Gray areas are not taken into account for correlation.

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  Figure 7. (Left) Examples of TMV basis vectors for L = 17. p: basis vector number. k: time step. Colors only visualize spatial morphology. (Right) Cumulative sum of singular values for different basis lengths L.

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  Figure 8. Metrics for a CV of 0.8m/s. Colors represent different SNRs. Blue: 40dB, red: 20dB, yellow: 0dB. Boxes: 25–75th percentile. Whiskers: 1.5 inter-quartile range. Filled circles and lines represent the mean. (Left) Spatial CC of TMVs. (Right) Spatial CC of LATs.

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  Figure 9. LATs for different SNRs and basis lengths L. CV = 0.8m/s.

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  Figure 10. (A) Metrics for a CV of 0.4m/s. (B) Metrics for a CV of 1.2m/s. See caption of Figure 8 for details.

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  Figure 11. LATs for different CVs and basis lengths L. SNR = 40dB.

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  Figure 12. Localization errors for all 100 ectopic foci. See caption of Figure 8 for colors and markers. Outliers are shown as empty circles. (A) CV = 0.8m/s. (B) 1.2m/s. (C) 0.4m/s. The outlier for CV = 0.4m/s and L = 33 is depicted on the bottom right. Black sphere: true focus, white sphere: reconstructed focus.