Quantitative spectral criteria for Cardiac Navigation sampling rate using Manifold Harmonics Analysis

The spatiotemporal sampling of electrograms (EGM) yielding 3-D maps of cardiac features (activation, organization, amplitude) in Cardiac Navigation System (CNS) for arrhythmia ablation, is currently driven by heuristic considerations. Manifold Harmonic Analysis (MHA) allows spectral analysis of multidimensional structures in computer graphics, however, its connection to Sampling Theory has not been fully established. Our objective was to develop a systematic and quantitative procedure to support the spatial sampling of intracardiac EGMs during electrophysiological (EPS) procedures. We used MHA for establishing quantitative spectral criteria for 3-D and 4-D maps, in connection with conventional sampling theory. After automatic segmentation in 7 Computerized Tomography images of the left atria, a 3D mesh was generated for its inner face. MHA eigendirections and spectral coefficients were calculated, showing a clear low-pass structure. Reconstruction quality was compared with the reconstruction error using mesh simplification method (Qlim) in terms of decay constant τ. Consistent τ were found when using the geometrical deviation (211.2±89 points in MHA, 173.8 ± 19.7 points in Qlim, ns), but not when using mean squared error (70.5 ± 17 vs 392.6 ± 214.1, p <; 0.001). EPS feature maps were simulated as smooth focal variations in a surrogated 4th dimension on the real atria grids, and showed a quantifiable trend to increase with the mechanism size (271-531 points for small, 135-413 for middle, 18-163 for wide size, for 85%-90% of total spectral power). MHA can be used to support the feature and spatial sampling rate in CNS-based EPS studies in connection with well-known sampling theory concepts.