# Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (II): Electrogram Clustering and T-Wave Alternans

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials

#### 2.1. EGM Clustering

- Assign each observation to one cluster. For each observation ${\mathbf{x}}_{i}$ ($i=1,\cdots ,m$) choose the index ${l}_{i}$ of the centroid closest to ${\mathbf{x}}_{i}$:$${l}_{i}=\underset{k}{min}d({\mathbf{x}}_{i},{\mathbf{c}}_{k}),{l}_{i}=1,\cdots ,K$$
- Recalculate the centroid ${\mathbf{c}}_{k}$ of the k-th cluster by averaging the points assigned to it.

#### 2.2. T-Wave Alternans Algorithms

## 3. Experiments and Results

#### 3.1. EGM Clustering in the Presence of Infarction

**Clustering Results for Unipolar EGMs in the Presence of Infarction.**The input space of the K-means algorithm consisted first of the pre-processed unipolar EGMs, which had been removed from the baseline and for which a time window corresponding to a heartbeat has been selected. The regions that can be qualitatively and a priori distinguished in the cardiac tissue for the example of the infarction patient are scar region, border region, valve region, and healthy region. These regions can be differentiated according to the amplitude values used in electrophysiological studies for cardiac arrhythmia ablation. In the case of unipolar EGM, the values were: scar region $\le 3$ mV, border region between 3 mV and 5 mV, valve $<3$ mV, and healthy region $\ge 5$ mV [36,37]. Several distances among beats in different locations were tested for different values of K, between $K=3$ and $K=6$, and spatial consistency was analyzed with respect to the unipolar EGMs of each node.

**Unipolar EGM Clustering in the Presence of Infarction Using the Cosine and the Correlation Distances.**We next scrutinize whether any of these two distances are more convenient to regionalize the cardiac tissue from unipolar EGM, and the effect of K is analyzed again with detail in the infarction patient example.

**Bipolar EGM Clustering in the Presence of Infarction.**We next present a regionalization analysis of the cardiac tissue with the bipolar EGM obtained with the DSPO ${\theta}_{{V}_{\alpha}}$ proposed in the companion paper [13], for the example of an infarction patient. In this case, the input vector space of the K-means algorithm is given by the bipolar EGMs obtained with the ${\theta}_{{V}_{\alpha}}$ configuration, where the continuous-time shift $\alpha $ is set to be corresponding to 40 samples. As in the study for unipolar EGM, for the bipolar EGMs obtained by applying this operator, a time window corresponding to a heartbeat is selected. For the identification of the regions, the fragmentation and amplitude clinical criteria of bipolar EGMs are used. For this case, the amplitude of the bipolar EGMs for the scar region is less than $0.5$ mV, the border region is between $0.5$ and $1.5$ mV, and the healthy region is greater than $1.5$ mV [36,37].

**Unipolar EGM Clustering in a Control Subject.**Figure 7 shows an example of clustering in a healthy control subject. We scrutinize only the case with $K=4$ classes, noting that in this case the identified regions are compact and well connected. Note that in this case the M-mode shows that region widths are long enough for not detecting any spurious region and to have the centroids as representative of those tissue zones. The smooth amplitude transitions between neighbor regions are well represented by the centroids, both when using the cosine distance (example in the figure) and when using the correlation distance (not shown). Note the positive and negative axis off the EGMs in opposite sides of the myocardium and also the progressive transitions in the repolarization waveform.

#### 3.2. Comparison of TWA Algorithms

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wang, Y.; Cuculich, P.S.; Zhang, J.; Desouza, K.A.; Vijayakumar, R.; Chen, J.; Faddis, M.N.; Lindsay, B.D.; Smith, T.W.; Rudy, Y. Noninvasive electroanatomic mapping of human ventricular arrhythmias with electrocardiographic imaging. Sci. Transl. Med.
**2011**, 3, 98ra84. [Google Scholar] [CrossRef] [Green Version] - Andrews, C.; Srinivasan, N.; Rosmini, S.; Bulluck, H.; Orini, M.; Jenkins, S.; Pantazis, A.; McKenna, W.; Moon, J.; Lambiase, P.; et al. Electrical and Structural Substrate of Arrhythmogenic Right Ventricular Cardiomyopathy Determined Using Noninvasive Electrocardiographic Imaging and Late Gadolinium Magnetic Resonance Imaging. Circ. Arrhythmia Electrophysiol.
**2017**, 10, e005105. [Google Scholar] - Cheniti, G.; Puyo, S.; Martin, C.A.; Frontera, A.; Vlachos, K.; Takigawa, M.; Bourier, F.; Kitamura, T.; Lam, A.; Dumas-Pommier, C.; et al. Noninvasive mapping and electrocardiographic imaging in atrial and ventricular arrhythmias (CardioInsight). Card. Electrophysiol. Clin.
**2019**, 11, 459–471. [Google Scholar] [CrossRef] [PubMed] - Rudy, Y. Noninvasive ECG imaging (ECGI): Mapping the arrhythmic substrate of the human heart. Int. J. Cardiol.
**2017**, 237, 13–14. [Google Scholar] [PubMed] - Rudy, Y. Role for electrocardiographic imaging in cardiac resynchronization therapy? Heart Rhythm
**2018**, 15, 1070–1071. [Google Scholar] [CrossRef] - Blom, L.; Groeneveld, S.; Wulterkens, B.; van Rees, B.; Nguyen, U.; Roudijk, R.; Cluitmans, M.; Volders, P.; Hassink, R. Novel use of repolarization parameters in electrocardiographic imaging to uncover arrhythmogenic substrate. J. Electrocardiol.
**2020**, 59, 116–121. [Google Scholar] [CrossRef] [PubMed] - Rudy, Y. Electrophysiology of heart failure: Non-invasive mapping of substrate and guidance of cardiac resynchronization therapy with Electrocardiographic imaging. In Cardiac Mapping, 5th ed.; Wiley: Oxford, UK, 2019; pp. 220–235. [Google Scholar]
- Van Oosterom, A. Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly distributed source strength. Med. Biol. Eng. Comput.
**2012**, 50, 1–9. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Aryana, A.; Bowers, M.; O’Neill, P. Outcomes Of Cryoballoon Ablation Of Atrial Fibrillation: A Comprehensive Review. J. Atr. Fibrillation
**2015**, 8, 1231. [Google Scholar] - Duchateau, J.; Sacher, F.; Pambrun, T.; Derval, N.; Chamorro-Servent, J.; Denis, A.; Ploux, S.; Hocini, M.; Jaïs, P.; Bernus, O.; et al. Performance and limitations of noninvasive cardiac activation mapping. Heart Rhythm
**2019**, 16, 435–442. [Google Scholar] [CrossRef] [Green Version] - Azpilicueta, J.; Chmelevsky, M.; Potyagaylo, D. ECGI in atrial fibrillation: A clinician’s wish list. J. Electrocardiol.
**2018**, 51, 88–91. [Google Scholar] [CrossRef] - CollFont, J.; Dhamala, J.; Potyagaylo, D.; Schulze, W.; Tate, J.; Guillem, M.; van Dam, P.; Dossel, O.; Brooks, D.; Macleod, R. The Consortium for Electrocardiographic Imaging. Comput. Cardiol.
**2016**, 43, 325–328. [Google Scholar] - Caulier-Cisterna, R.; Sanromán-Junquera, M.; Muñoz-Romero, S.; Blanco-Velasco, M.; Goya-Esteban, R.; García-Alberola, A.; Rojo-Álvarez, J. Spatial-temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials. Sensors
**2020**. [Google Scholar] [CrossRef] - Rosenbaum, D.; Albrecht, P.; Cohen, R. Predicting Sudden Cardiac Death From T Wave Alternans of the Surface Electrocardiogram. J. Cardiovasc. Electrophysiol.
**1996**, 7, 1095–1111. [Google Scholar] [CrossRef] [PubMed] - Walker, M.L.; Rosenbaum, D.S. Repolarization alternans: Implications for the mechanism and prevention of sudden cardiac death. Cardiovasc. Res.
**2003**, 57, 599–614. [Google Scholar] [CrossRef] [Green Version] - Gimeno-Blanes, F.; Blanco-Velasco, M.; Barquero-Pérez, O.; García-Alberola, A.; Rojo-Álvarez, J. Sudden Cardiac Risk Stratification with Electrocardiographic Indices—A Review on Computational Processing, Technology Transfer, and Scientific Evidence. Front. Physiol.
**2016**, 7, 82. [Google Scholar] [PubMed] [Green Version] - Andrews, C.; Cupps, B.; Pasque, M.; Rudy, Y. Electromechanics of the Normal Human Heart In Situ. Circ. Arrhythmia Electrophysiol.
**2019**, 12, e007484. [Google Scholar] - Vijayakumar, R.; Silva, J.N.; Desouza, K.A.; Abraham, R.L.; Strom, M.; Sacher, F.; Van Hare, G.F.; Haïssaguerre, M.; Roden, D.M.; Rudy, Y. Electrophysiologic substrate in congenital long QT syndrome: Noninvasive mapping with electrocardiographic imaging (ECGI). Circulation
**2014**, 130, 1936–1943. [Google Scholar] [CrossRef] [Green Version] - Zhang, J.; Hocini, M.; Strom, M.; Cuculich, P.S.; Cooper, D.H.; Sacher, F.; Haïssaguerre, M.; Rudy, Y. The Electrophysiological Substrate of Early Repolarization Syndrome: Noninvasive Mapping in Patients. JACC Clin. Electrophysiol.
**2017**, 3, 894–904. [Google Scholar] [CrossRef] - Zhu, B.; Ding, Y.; Hao, K. A novel automatic detection system for ECG arrhythmias using maximum margin clustering with immune evolutionary algorithm. Comput. Math. Methods Med.
**2013**, 2013, 453402. [Google Scholar] [CrossRef] [Green Version] - Orozco-Duque, A.; Duque, S.; Ugarte, J.; Tobon, C.; Novak, D.; Kremen, V.; Castellanos-Dominguez, G.; Saiz, J.; Bustamante, J. Fractionated electrograms and rotors detection in chronic atrial fibrillation using model-based clustering. In Proceedings of the 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Chicago, IL, USA, 26–30 August 2014; pp. 1579–1582. [Google Scholar]
- Haldar, N.; Khan, F.; Ali, A.; Abbas, H. Arrhythmia classification using Mahalanobis distance based improved Fuzzy C-Means clustering for mobile health monitoring systems. Neurocomputing
**2017**, 220, 221–235. [Google Scholar] [CrossRef] - He, H.; Tan, Y. Automatic pattern recognition of ECG signals using entropy-based adaptive dimensionality reduction and clustering. Appl. Soft Comput.
**2017**, 55, 238–252. [Google Scholar] [CrossRef] - Jiang, J.; Hao, D.; Chen, Y.; Parmar, M.; Li, K. GDPC: Gravitation-based Density Peaks Clustering algorithm. Phys. A Stat. Mech. Its Appl.
**2018**, 502, 345–355. [Google Scholar] [CrossRef] - Vesanto, J.; Alhoniemi, E. Clustering of the self-organizing map. IEEE Trans. Neural Networks
**2000**, 11, 586–600. [Google Scholar] [CrossRef] - Li, S.; Li, W.; Qiu, J. A novel divisive hierarchical clustering algorithm for geospatial analysis. ISPRS Int. J. Geo Inf.
**2017**, 6, 30. [Google Scholar] [CrossRef] [Green Version] - Rodrigues, J.; Belo, D.; Gamboa, H. Noise detection on ECG based on agglomerative clustering of morphological features. Comput. Biol. Med.
**2017**, 87, 322–334. [Google Scholar] [CrossRef] [PubMed] - Yang, M.; Nataliani, Y. Robust-learning Fuzzy C-means clustering algorithm with unknown number of clusters. Pattern Recognit.
**2017**, 71, 45–59. [Google Scholar] [CrossRef] - Ortiz-Rosario, A.; Adeli, H.; Buford, J. MUSIC-Expected maximization gaussian mixture methodology for clustering and detection of task-related neuronal firing rates. Behav. Brain Res.
**2017**, 317, 226–236. [Google Scholar] [CrossRef] [Green Version] - Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory
**1982**, 28, 129–137. [Google Scholar] [CrossRef] - Goya-Esteban, R.; Barquero-Pérez, O.; Blanco-Velasco, M.; Caamaño-Fernández, A.; García-Alberola, A.; Rojo-Álvarez, J. Nonparametric Signal Processing Validation in T-Wave Alternans Detection and Estimation. IEEE Trans. Biomed. Eng.
**2014**, 61, 1328–1338. [Google Scholar] [CrossRef] - Martínez, J.; Olmos, S. Methodological principles of T wave alternans analysis: A unified framework. IEEE Trans. Biomed. Eng.
**2005**, 52, 599–613. [Google Scholar] [CrossRef] - Blanco-Velasco, M.; Goya-Esteban, R.; Cruz-Roldán, F.; García-Alberola, A.; Rojo-Alvarez, J. Benchmarking of a T-wave alternans detection method based on empirical mode decomposition. Comput. Methods Programs Biomed.
**2017**, 145, 147–155. [Google Scholar] [CrossRef] [PubMed] - Martinez, J.P.; Olmos, S.; Laguna, P. T wave alternans detection: A simulation study and analysis of the European ST-T database. In Proceedings of the Computers in Cardiology, Cambridge, MA, USA, 24–27 September 2000; Volume 27, pp. 155–158. [Google Scholar]
- Nearing, B.; Verrier, R. Modified moving average analysis of T-wave alternans to predict ventricular fibrillation with high accuracy. J. Appl. Physiol.
**2002**, 92, 541–549. [Google Scholar] [CrossRef] [PubMed] - Marchlinski, F.; Callans, D.; Gottlieb, C.; Zado, E. Linear ablation lesions for control of unmappable ventricular tachycardia in patients with ischemic and nonischemic cardiomyopathy. Circulation
**2000**, 101, 1288–1296. [Google Scholar] [CrossRef] [Green Version] - Desjardins, B.; Crawford, T.; Good, E.; Oral, H.; Chugh, A.; Pelosi, F.; Morady, F.; Bogun, F. Infarct architecture and characteristics on delayed enhanced magnetic resonance imaging and electroanatomic mapping in patients with postinfarction ventricular arrhythmia. Heart Rhythm
**2009**, 6, 644–651. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cronin, E.M.; Bogun, F.; Maury, P.; Peichl, P.; Chen, M.; Namboodiri, N.; Aguinaga, L.; Leite, L.; Al-Khatib, S.; Anter, E.; et al. 2019 HRS/EHRA/APHRS/LAHRS expert consensus statement on catheter ablation of ventricular arrhythmias. Europace
**2019**, 21, 1143–1144. [Google Scholar] [CrossRef] [PubMed] - Sroubek, J.; Rottmann, M.; Barkagan, M.; Leshem, E.; Shapira-Daniels, A.; Brem, E.; Fuentes-Ortega, C.; Malinaric, J.; Basu, S.; Bar-Tal, M.; et al. A novel octaray multielectrode catheter for high-resolution atrial mapping: Electrogram characterization and utility for mapping ablation gaps. J. Cardiovasc. Electrophysiol.
**2019**, 30, 749–757. [Google Scholar] [CrossRef] [PubMed] - Borlich, M.; Iden, L.; Kuhnhardt, K.; Paetsch, I.; Hindricks, G.; Sommer, P. 3D mapping for PVI-geometry, image integration and incorporation of contact force into work flow. J. Atr Fibrillation
**2018**, 10, 1795. [Google Scholar] - Cluitmans, M.; Peeters, R.; Westra, R.; Volders, P. Noninvasive reconstruction of cardiac electrical activity: Update on current methods, applications and challenges. Neth. Heart J.
**2015**, 23, 301–311. [Google Scholar] [CrossRef] [Green Version] - Cluitmans, M.; Brooks, D.; MacLeod, R.; Dössel, O.; Guillem, M.; van Dam, P.M.; Svehlikova, J.; He, B.; Sapp, J.; Wang, L.; et al. Validation and Opportunities of Electrocardiographic Imaging: From Technical Achievements to Clinical Applications. Front. Physiol.
**2018**, 9, 1305. [Google Scholar] [CrossRef] - Shenasa, M.; Razavi, S.; Shenasa, H.; Al-Ahmad, A. The ideal cardiac mapping system. Card. Electrophysiol. Clin.
**2019**, 11, 739–748. [Google Scholar] [CrossRef] - Bear, L.; Dogrusoz, Y.; Svehlikova, J.; Coll-Font, J.; Good, W.; van Dam, E.; Macleod, R.; Abell, E.; Walton, R.; Coronel, R.; et al. Effects of ECG Signal Processing on the Inverse Problem of Electrocardiography. Comput Cardiol
**2018**, 45, 1–4. [Google Scholar] - Orozco-Duque, A.; Bustamante, J.; Castellanos-Dominguez, G. Semi-supervised clustering of fractionated electrograms for electroanatomical atrial mapping. Biomed. Eng. OnLine
**2016**, 15, 44. [Google Scholar] [PubMed] [Green Version] - Coll-Font, J.; Erem, B.; Brooks, D. A Potential-Based Inverse Spectral Method to Non-Invasively Localize Discordant Distributions of Alternans on the Heart from the ECG. IEEE Trans. Biomed. Eng.
**2018**, 65, 1554–1563. [Google Scholar] [PubMed] - Rudy, Y. Noninvasive Electrocardiographic Imaging ECGI of Arrhythmogenic Substrates in Humans. Circ. Res.
**2013**, 112, 863–874. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Unipolar Electrograms (EGM) in the presence of infarction. The distances used in the K-means algorithm with $K=4$ were: (

**a**) ${L}_{1}$ distance; (

**b**) Euclidean distance; (

**c**) cosine distance; (

**d**) correlation distance.

**Figure 2.**Unipolar EGM in the presence of infarction, using cosine distance with $K=3$ (

**a**) and with $k=4$ (

**b**). For each panel: (Up) centroids of each class and clustering map; (Down) M-mode of the unipolar EGM for the dotted line (left), and M-mode of their corresponding centroids (right).

**Figure 3.**Unipolar EGM in the presence of infarction, using cosine distance with $K=5$ (

**a**) and with $k=6$ (

**b**). Continued from Figure 2.

**Figure 5.**Bipolar EGMs in the presence of infarction. The distances used in the K-means algorithm with $K=5$ correspond to: (

**a**) ${L}_{1}$ distance; (

**b**) Euclidean distance; (

**c**) cosine distance; (

**d**) correlation distance.

**Figure 6.**The cosine distance method with $K=5$. The upper left panel shows the centroids of each class and the right one, the clustering map. The lower left panel shows the M-mode of the bipolar EGMs of each region where the dotted line passes, and right one, depicts the M-mode of the centroids of the same line.

**Figure 7.**Control cases. Unipolar EGM, using cosine distance with $K=4$. (

**Up**) Centroids of each class and clustering map. (

**Down**) M-mode of the unipolar EGM for the dotted line, and M-mode of their corresponding centroids.

**Figure 8.**Analysis of T-wave alternans (TWA) detection algorithms in Torso recordings, for control subject (

**left**) and Long-QT syndrome (LQTS) patient (

**right**). The first row shows the voltage maps and M-mode for EGMs on the path in white points. The second, third, and fourth rows show the maximum amplitude maps and the TWA estimation provided by the temporal estimation, by the spectral method, and by the Modified Moving Average (MMA) method, respectively. The M-modes and colorbars are adapted to give a better understanding of the results. Note that these are not EGM potentials, but instead estimation of alternans amplitudes (in the temporal method) or of its measurement though some closely related index (spectral and MMA methods). The alternans amplitudes change spatially and temporally smooth in the control subject, whereas they exhibit noticeable spatial and temporal fluctuations in the LQTS patient. The line of points for the M-mode was selected to follow significant changes in the EGM amplitudes, and hence being able to check that the alternan’s changes in amplitude were not just an echo of the EGM changes in amplitude.

**Figure 9.**Analysis of TWA detection algorithms in epicardium recordings, for control subject (

**left**) and LQTS patient (

**right**). Content of panels is similar to Figure 8 but for epicardium instead of torso.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Caulier-Cisterna, R.; Blanco-Velasco, M.; Goya-Esteban, R.; Muñoz-Romero, S.; Sanromán-Junquera, M.; García-Alberola, A.; Rojo-Álvarez, J.L.
Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (II): Electrogram Clustering and T-Wave Alternans. *Sensors* **2020**, *20*, 3070.
https://doi.org/10.3390/s20113070

**AMA Style**

Caulier-Cisterna R, Blanco-Velasco M, Goya-Esteban R, Muñoz-Romero S, Sanromán-Junquera M, García-Alberola A, Rojo-Álvarez JL.
Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (II): Electrogram Clustering and T-Wave Alternans. *Sensors*. 2020; 20(11):3070.
https://doi.org/10.3390/s20113070

**Chicago/Turabian Style**

Caulier-Cisterna, Raúl, Manuel Blanco-Velasco, Rebeca Goya-Esteban, Sergio Muñoz-Romero, Margarita Sanromán-Junquera, Arcadi García-Alberola, and José Luis Rojo-Álvarez.
2020. "Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (II): Electrogram Clustering and T-Wave Alternans" *Sensors* 20, no. 11: 3070.
https://doi.org/10.3390/s20113070