Sanroman-Junquera, M.; Mora-Jimenez, I.; Garcia-Alberola, A.; Caamano, AJ.; Trenor Gomis, BA.; Rojo-Alvarez, JL. (2018). Arrhythmia Mechanism and Scaling Effect on the Spectral Properties of Electroanatomical Maps with Manifold Harmonics. IEEE Transactions on Biomedical Engineering (Online). 65(4):723-732. Abstract 13 Spatial and temporal processing of intracardiac electrograms provides relevant infor-14 mation to support the arrhythmia ablation during electrophysiological studies. Current 15

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... rdiac Navigation Systems (CNS) and Electrocardiographic Imaging (ECGI) build 16 detailed three dimensional electroanatomical maps (EAM), which represent the spatial 17 anatomical distribution of bioelectrical features, such as activation time or voltage ampli-18 tude. We present a principled methodology for spectral analysis of both EAM geometry 19 and bioelectrical feature in CNS or ECGI, including their spectral representation, cut-off 20 frequency, or spatial sampling rate (SSR). Existing manifold harmonic techniques for 21 spectral mesh analysis are adapted to account for a fourth dimension, corresponding to 22 the EAM bioelectrical feature. Scaling is required to address different magnitudes and 23 units. With our approach, simulated and real EAM showed strong SSR dependence on 24 both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high 25 frequencies increased significantly the SSR since the early-meets-late in flutter EAM, 26 compared to the sinus rhythm. Besides, higher frequencies components were obtained 27 for left atrium (more complex anatomy) than for right atrium in sinus rhythm. The 28 proposed manifold harmonics methodology opens the field towards new signal processing 29 tools for principled EAM spatio-feature analysis in CNS and ECGI, and to an improved 30 knowledge on arrhythmia mechanisms. 31 2 34 Electric potential measurements inside the heart, so-called electrograms (EGM), are used to 35 support clinicians in the treatment of cardiac arrhythmias during the electrophysiological 36 studies (EPS). The knowledge of the precise position of each EGM can help to apply the 37 therapy, usually cardiac ablation, in a more effective way. Given that there is no medical image 38 modality allowing the clinician to visualize the three-dimensional (3D) cardiac bioelectricity, 39 several technologies have been proposed for this end, namely, cardiac navigation systems 40 (CNS) or Electrocardiographic Imaging (ECGI). 4,10 In both types of systems, a mesh of the 41 cardiac chamber surface is first built to visualize its anatomical shape, and then to provide a 42 3D electroanatomical map (EAM) of a bioelectrical feature of interest (such as activation 43 time, or voltage amplitude). The anatomical mesh is composed by a set of vertices in the 3D 44 space joined by triangular faces. The bioelectrical feature is also associated to each vertex as 45 an additional dimension. 46 Until recently, CNS allowed to build the EAM by sequentially registering EGMs and their 47 corresponding anatomical positions in the cardiac endocardium, and then a basic interpolation 48 was used to help in the EAM visualization. However, the most recent CNS use multielectrode 49 catheters and fast acquisition of a much higher number of electroanatomical samples, which 50 are subsequently filtered to provide sets of quality signals 1,14 . Current ECGI systems also 51 supply with large number of virtual EGMs on the epicardium compared to traditional CNS. 10 52 As far as we are today working with several thousands of anatomically recorded EGMs, there 53 is a need for moving from heuristically based information processing procedures to advanced 54 and principled algorithms allowing to handle the redundancy and spatio-temporal correlations 55 from currently available cardiac bioelectric measurements. 56 While Fourier analysis (FA) has been often used as a well-founded technique for frequency 57 domain analysis in uniformly sampled spaces, 6 a variety of mesh Laplacian operators have 58 been proposed as an approximation of the Fourier Transform (TF) on 2-manifold surfaces. 18 59 Among these Laplacian operators, this work uses the discrete Laplacian operator based 60 on Manifold Harmonics Analysis (MHA) proposed by Vallet and Lévy. 17 We considered 61 3 triangle meshes of EAM as closed 2-manifolds. Spectral analysis has been highly informative 62 about cardiac arrhythmia mechanism from ECG and EGM time signals, however, there is no 63 principled theory suitable for handling basic concepts of spectral analysis in EAM embedded 64 in 2-manifolds. 2 65 A simple methodology for spectral processing in 2-manifolds was introduced to provide 66 useful quantitative magnitudes and qualitative comparison, such as bandwidth, spectral 67 content, or frequency bands, from EAM and anatomical meshes usually obtained in current 68 CNS and ECGI systems. 12,13 In these preceding works, a simple, yet theoretically well 69 principled method was presented for EAM spectrum representation from MHA. Nevertheless, 70 little attention has been paid to the issue of different order of magnitudes and units among 71 anatomical and physiological features (such as mV for voltage amplitude maps, or ms 72 for activation maps). As far as the matrix operations involved in MHA are related to 73 eigendecomposition operators working on mixed measurements, their different orders of 74 magnitude and units can be expected to have noticeable impact on the spectral magnitudes 75 estimated with this technique. 76 Therefore, our first objective in the present work was to analyze and provide with clear 77 guidelines when using MHA for spectral analysis of EAM in CNS and ECGI. A preliminary 78 study of the anatomical and electrical feature scaling effects was recently presented, 11 whose 79 results are here extended by evaluating two more types of scaling and also assessing the 80 impact of the scaling in the EAM spectral properties. On the other hand, and taking into 81 account that cardiac bioelectric activity is strongly linked and dependent on the underlying 82 arrhythmic mechanism, we also scrutinized the impact of different arrhythmia mechanisms 83 on EAM by using the Spatial Sampling Rate (SSR) to know its potential usefulness defining 84 the number of required anatomical samples during CNS or the resolution attainable in ECGI 85 systems. With this same purpose, we also studied the spatial smoothness on the anatomical 86 and EAM spectrum (low-pass filtered EAM), in a similar way that one-dimensional spectral 87 analysis provides operative and well-defined quantitative criteria to analyze the smoothness 88 in one-dimensional cardiac signals. For all these analyses, we used three sets of data: (1) a 89 4 simple and synthetic tear-shaped mesh example with a feature projected on it; (2) detailed 90 simulations of both temporal series of potential EAM during an atrial sinus tachycardia (AT) 91 and atrial fibrillation (AF), and activation time EAM during a sinus rhythm (SR) and a 92 flutter arrhythmia (FL) in both atria; (3) a set of real EAM registered in the left atrium 93 (LA), left ventricle (LV), and right ventricle (RV) of patients undergoing therapy supported 94 with CNS. 95 The rest of the paper is structured as follows. In the next section, we summarize the 96 theoretical framework of MHA for 2-manifolds, and its extension for spectral analysis in 97 EAM that are usually informative in the setting of EPS and cardiac arrhythmia ablation 98 support. In Section 3, spectral representation and analysis, SSR, and EAM reconstruction 99 are assessed for simulated and real EAMs. Finally, in Section 4, discussion and conclusions 100 are summarized. 101 2 Materials and Methods 102 A summary explanation of the theoretical framework for MHA and its computation is 103 first presented. Then, a new and simple methodology is proposed to estimate the spectral 104 representation of EAMs, and to establish a cut-off frequency to determine the SSR according 105 to the quality of the reconstructed EAM. Finally, the need of a scaling is pointed out when 106 different orders of magnitudes and units are mixed in the definition of the vertex coordinates. 107 2.1 Manifold Harmonics 108 Although the traditional spectral analysis is based on the FA, the FT of a signal cannot 109 be directly applied to manifold with arbitrary topology. 15 The classical FT uses a fixed 110 set of basis functions, and it can be seen as a linear combination of the Laplace Operator 111 eigenvectors. 15 However, the eigenvectors, which represent the Fourier basis for manifold 112 meshes, are dependent on the mesh topology. 113 Among the different approaches proposed to define the Laplacian in a manifold, 18 the of the rotor in the reconstructed EAMs were completely recovered. SSRs for C(w c ) ≈ 0.99 306 were from 1000 to 2000 samples, higher values than SSRs in AT, FL, and RS EAMs due to 307 more complex arrhythmia mechanism in AF. Note that the cut-off frequency, and hence, the 308 SSR are dependent on the arrhythmia dynamic or the electric substrate. 309 3.4 SSR Estimation for Real EAMs from CNS 310 Real bipolar voltage amplitude and time activation CNS EAMs of 1 LA 4 LVs, and 4 RVs were 311 analysed by following the proposed methodology. Table 1 shows the SSR for C(w c ) ≈ 0.99, 312 C(w c ) ≈ 0.95, and C(w c ) ≈ 0.90. The SSR was very dependent on the type of EAM, for 313 example, meanwhile the SSR for AI was 292 when C(w c ) ≈ 0.99, the SSR for VI-1 was 1647. 314 The explanation to this example is shown in Figures 8 (a) and (b), which represent the 315 spectra of both EAMs. The spectrum of LV-1 EAM was more spread than that of LA EAM, 316 likely due to the higher variation of the feature in the first one (see Figure 8 (c)). However, 317 the required w c and SSR could be different according to the specific EAM, for example, in 318 this case, the w c of activation time EAM of LV-1 was higher than the bipolar one (SSR = 319 1647 for activation time EAM, SSR = 352 for bipolar voltage EAM), meanwhile it was the 320 opposite for the LA (SSR = 292 for activation time EAM, SSR = 845 for bipolar voltage 321 EAM) . 322 [Figure 8 about here.] 323 15 [ Table 1 about here.] 324 4 Discussion 325 A simple methodology based on MHA has been proposed for spectral analysis of detailed 326 EAM provided by CNS and ECGI. Existing MHA formulations were only defined for 2-327 manifold, and we have extended this definition for its usefulness in EAM, which include not 328 only anatomical information but also a cardiac bioelectrical feature measured at each vertex. 329 When analyzing simulated activation time EAMs, FL in the RA apparently required a higher 330 SSR due to the early-meets-late phenomenon, which generates high variation of the feature 331 (high frequencies). On the other hand, activation time EAM in the RA required similar SSR 332 during SR and FL due to the smooth variation of the feature in the EAM. Higher complexity 333 in the propagation pattern, such as rotors in FA, required higher SSRs. For real EAMs, the 334 SSR was very dependent on the arrhythmia mechanism and the type of the EAM (bipolar or 335 activation time). 336 Several limitations can be pointed in the proposed methodology. Only some representative 337 case studies (namely, 2 simulated activation time EAMs, a temporal series of potential EAMs, 338 and 9 CNS EAM) have been used here for validation purposes. However, the actual benefit 339 for the clinical practice will be supported by extended studies for different arrhythmias in 340 simulated and real EAM in CNS. The SSR was estimated with the underlying assumption 341 of uniform spatial sampling for yielding the edge length as a summary result for a given 342 chamber (equilateral triangular faces), which is only a valid assumption for a large enough 343 number of vertices. However, both current CNS and ECGI are very densely sampled, hence 344 the assumption would be achieved in most of the cases. 345 The proposed MHA methodology opens the field towards a new set of fundamental tools 346 for principled spatio-feature spectral analysis of EAM and improved knowledge on arrhythmia 347 mechanisms.