Minimizing discordances in automated classification of fractionated electrograms in human persistent atrial fibrillation

Ablation of persistent atrial fibrillation (persAF) targeting complex fractionated atrial electrograms (CFAEs) detected by automated algorithms has produced conflicting outcomes in previous electrophysiological studies. We hypothesize that the differences in these algorithms could lead to discordant CFAE classifications by the available mapping systems, giving rise to potential disparities in CFAE-guided ablation. This study reports the results of a head-to-head comparison of CFAE detection performed by NavX (St. Jude Medical) versus CARTO (Biosense Webster) on the same bipolar electrogram data (797 electrograms) from 18 persAF patients. We propose revised thresholds for both primary and complementary indices to minimize the differences in CFAE classification performed by either system. Using the default thresholds [NavX: CFEMean ≤ 120 ms; CARTO: ICL ≥ 7], NavX classified 70 % of the electrograms as CFAEs, while CARTO detected 36 % (Cohen’s kappa κ ≈ 0.3, P < 0.0001). Using revised thresholds found using receiver operating characteristic curves [NavX: CFE-Mean ≤ 84 ms, CFE-SD ≤ 47 ms; CARTO: ICL ≥ 4, ACI ≤ 82 ms, SCI ≤ 58 ms], NavX classified 45 %, while CARTO detected 42 % (κ ≈ 0.5, P < 0.0001). Our results show that CFAE target identification is dependent on the system and thresholds used by the electrophysiological study. The thresholds found in this work counterbalance the differences in automated CFAE classification performed by each system. This could facilitate comparisons of CFAE ablation outcomes guided by either NavX or CARTO in future works

Short-Time Estimation of Fractionation in Atrial Fibrillation with Coarse-Grained Correlation Dimension for Mapping the Atrial Substrate

[EN] Atrial ¿brillation (AF) is currently the most common cardiac arrhythmia, with catheter ablation (CA) of the pulmonary veins (PV) being its ¿rst line therapy. Ablation of complex fractionated atrial electrograms (CFAEs) outside the PVs has demonstrated improved long-term results, but their identi¿cation requires a reliable electrogram (EGM) fractionation estimator. This study proposes a technique aimed to assist CA procedures under real-time settings. The method has been tested on three groups of recordings: Group 1 consisted of 24 highly representative EGMs, eight of each belonging to a different AF Type. Group 2 contained the entire dataset of 119 EGMs, whereas Group 3 contained 20 pseudo-real EGMs of the special Type IV AF. Coarse-grained correlation dimension (CGCD) was computed at epochs of 1 s duration, obtaining a classi¿cation accuracy of 100% in Group 1 and 84.0¿85.7% in Group 2, using 10-fold cross-validation. The receiver operating characteristics (ROC) analysis for highly fractionated EGMs, showed 100% speci¿city and sensitivity in Group 1 and 87.5% speci¿city and 93.6% sensitivity in Group 2. In addition, 100% of the pseudo-real EGMs were correctly identi¿ed as Type IV AF. This method can consistently express the fractionation level of AF EGMs and provides better performance than previous works. Its ability to compute fractionation in short-time can agilely detect sudden changes of AF Types and could be used for mapping the atrial substrate, thus assisting CA procedures under real-time settings for atrial substrate modi¿cation.This research has been supported by grants DPI2017-83952-C3 from MINECO/AEI/FEDER EU, SBPLY/17/180501/000411 from JCCM and AICO/2019/036 from GVA.Vraka, A.; Hornero, F.; Bertomeu-Gonzalez, V.; Osca, J.; Alcaraz, R.; Rieta, JJ. (2020). Short-Time Estimation of Fractionation in Atrial Fibrillation with Coarse-Grained Correlation Dimension for Mapping the Atrial Substrate. Entropy. 22(2):1-20. https://doi.org/10.3390/e22020232S120222Go, A. S., Hylek, E. M., Phillips, K. A., Chang, Y., Henault, L. E., Selby, J. V., & Singer, D. E. (2001). Prevalence of Diagnosed Atrial Fibrillation in Adults. JAMA, 285(18), 2370. doi:10.1001/jama.285.18.2370Goette, A., Honeycutt, C., & Langberg, J. J. (1996). Electrical Remodeling in Atrial Fibrillation. Circulation, 94(11), 2968-2974. doi:10.1161/01.cir.94.11.2968Chugh, S. S., Roth, G. A., Gillum, R. F., & Mensah, G. A. (2014). Global Burden of Atrial Fibrillation in Developed and Developing Nations. Global Heart, 9(1), 113. doi:10.1016/j.gheart.2014.01.004Cappato, R., Calkins, H., Chen, S.-A., Davies, W., Iesaka, Y., Kalman, J., … Biganzoli, E. (2010). Updated Worldwide Survey on the Methods, Efficacy, and Safety of Catheter Ablation for Human Atrial Fibrillation. Circulation: Arrhythmia and Electrophysiology, 3(1), 32-38. doi:10.1161/circep.109.859116Cox, J. L., Canavan, T. E., Schuessler, R. B., Cain, M. E., Lindsay, B. D., Stone, C., … Boineau, J. P. (1991). The surgical treatment of atrial fibrillation. The Journal of Thoracic and Cardiovascular Surgery, 101(3), 406-426. doi:10.1016/s0022-5223(19)36723-6Haïssaguerre, M., Jaïs, P., Shah, D. C., Takahashi, A., Hocini, M., Quiniou, G., … Clémenty, J. (1998). Spontaneous Initiation of Atrial Fibrillation by Ectopic Beats Originating in the Pulmonary Veins. New England Journal of Medicine, 339(10), 659-666. doi:10.1056/nejm199809033391003Kornej, J., Schumacher, K., Zeynalova, S., Sommer, P., Arya, A., Weiß, M., … Hindricks, G. (2019). Time-dependent prediction of arrhythmia recurrences during long-term follow-up in patients undergoing catheter ablation of atrial fibrillation: The Leipzig Heart Center AF Ablation Registry. Scientific Reports, 9(1). doi:10.1038/s41598-019-43644-2YOSHIDA, K., ULFARSSON, M., TADA, H., CHUGH, A., GOOD, E., KUHNE, M., … ORAL, H. (2008). Complex Electrograms Within the Coronary Sinus: Time- and Frequency-Domain Characteristics, Effects of Antral Pulmonary Vein Isolation, and Relationship to Clinical Outcome in Patients with Paroxysmal and Persistent Atrial Fibrillation. Journal of Cardiovascular Electrophysiology, 19(10), 1017-1023. doi:10.1111/j.1540-8167.2008.01175.xKonings, K. T., Kirchhof, C. J., Smeets, J. R., Wellens, H. J., Penn, O. C., & Allessie, M. A. (1994). High-density mapping of electrically induced atrial fibrillation in humans. Circulation, 89(4), 1665-1680. doi:10.1161/01.cir.89.4.1665Rolf, S., Kircher, S., Arya, A., Eitel, C., Sommer, P., Richter, S., … Piorkowski, C. (2014). Tailored Atrial Substrate Modification Based on Low-Voltage Areas in Catheter Ablation of Atrial Fibrillation. Circulation: Arrhythmia and Electrophysiology, 7(5), 825-833. doi:10.1161/circep.113.001251Takahashi, Y., O’Neill, M. D., Hocini, M., Dubois, R., Matsuo, S., Knecht, S., … Haïssaguerre, M. (2008). Characterization of Electrograms Associated With Termination of Chronic Atrial Fibrillation by Catheter Ablation. Journal of the American College of Cardiology, 51(10), 1003-1010. doi:10.1016/j.jacc.2007.10.056Atienza, F., Almendral, J., Jalife, J., Zlochiver, S., Ploutz-Snyder, R., Torrecilla, E. G., … Berenfeld, O. (2009). Real-time dominant frequency mapping and ablation of dominant frequency sites in atrial fibrillation with left-to-right frequency gradients predicts long-term maintenance of sinus rhythm. Heart Rhythm, 6(1), 33-40. doi:10.1016/j.hrthm.2008.10.024Nademanee, K., McKenzie, J., Kosar, E., Schwab, M., Sunsaneewitayakul, B., Vasavakul, T., … Ngarmukos, T. (2004). A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate. Journal of the American College of Cardiology, 43(11), 2044-2053. doi:10.1016/j.jacc.2003.12.054Ciaccio, E. J., Biviano, A. B., Whang, W., Coromilas, J., & Garan, H. (2011). A new transform for the analysis of complex fractionated atrial electrograms. BioMedical Engineering OnLine, 10(1), 35. doi:10.1186/1475-925x-10-35Ciaccio, E. J., Biviano, A. B., & Garan, H. (2013). Computational method for high resolution spectral analysis of fractionated atrial electrograms. Computers in Biology and Medicine, 43(10), 1573-1582. doi:10.1016/j.compbiomed.2013.07.033TSAI, W.-C., LIN, Y.-J., TSAO, H.-M., CHANG, S.-L., LO, L.-W., HU, Y.-F., … CHEN, S.-A. (2010). The Optimal Automatic Algorithm for the Mapping of Complex Fractionated Atrial Electrograms in Patients With Atrial Fibrillation. Journal of Cardiovascular Electrophysiology, 21(1), 21-26. doi:10.1111/j.1540-8167.2009.01567.xTeh, A. W., Kistler, P. M., Lee, G., Medi, C., Heck, P. M., Spence, S. J., … Kalman, J. M. (2011). The relationship between complex fractionated electrograms and atrial low-voltage zones during atrial fibrillation and paced rhythm. Europace, 13(12), 1709-1716. doi:10.1093/europace/eur197Lin, Y.-J., Lo, M.-T., Chang, S.-L., Lo, L.-W., Hu, Y.-F., Chao, T.-F., … Chen, S.-A. (2016). Benefits of Atrial Substrate Modification Guided by Electrogram Similarity and Phase Mapping Techniques to Eliminate Rotors and Focal Sources Versus Conventional Defragmentation in Persistent Atrial Fibrillation. JACC: Clinical Electrophysiology, 2(6), 667-678. doi:10.1016/j.jacep.2016.08.005Verma, A., Jiang, C., Betts, T. R., Chen, J., Deisenhofer, I., Mantovan, R., … Sanders, P. (2015). Approaches to Catheter Ablation for Persistent Atrial Fibrillation. New England Journal of Medicine, 372(19), 1812-1822. doi:10.1056/nejmoa1408288Ammar-Busch, S., Reents, T., Knecht, S., Rostock, T., Arentz, T., Duytschaever, M., … Deisenhofer, I. (2018). Correlation between atrial fibrillation driver locations and complex fractionated atrial electrograms in patients with persistent atrial fibrillation. Pacing and Clinical Electrophysiology, 41(10), 1279-1285. doi:10.1111/pace.13483Almeida, T. P., Chu, G. S., Salinet, J. L., Vanheusden, F. J., Li, X., Tuan, J. H., … Schlindwein, F. S. (2016). Minimizing discordances in automated classification of fractionated electrograms in human persistent atrial fibrillation. Medical & Biological Engineering & Computing, 54(11), 1695-1706. doi:10.1007/s11517-016-1456-2De Bakker, J. M. T., & Wittkampf, F. H. M. (2010). The Pathophysiologic Basis of Fractionated and Complex Electrograms and the Impact of Recording Techniques on Their Detection and Interpretation. Circulation: Arrhythmia and Electrophysiology, 3(2), 204-213. doi:10.1161/circep.109.904763Luca, A., Buttu, A., Pruvot, E., Pascale, P., Bisch, L., & Vesin, J.-M. (2016). Nonlinear analysis of right atrial electrograms predicts termination of persistent atrial fibrillation within the left atrium by catheter ablation. Physiological Measurement, 37(3), 347-359. doi:10.1088/0967-3334/37/3/347Corana, A., Casaleggio, A., Rolando, C., & Ridella, S. (1991). Efficient computation of the correlation dimension from a time series on a LIW computer. Parallel Computing, 17(6-7), 809-820. doi:10.1016/s0167-8191(05)80068-7Fraser, A. M., & Swinney, H. L. (1986). Independent coordinates for strange attractors from mutual information. Physical Review A, 33(2), 1134-1140. doi:10.1103/physreva.33.1134Martínez-Iniesta, M., Ródenas, J., Alcaraz, R., & Rieta, J. J. (2017). Waveform Integrity in Atrial Fibrillation: The Forgotten Issue of Cardiac Electrophysiology. Annals of Biomedical Engineering, 45(8), 1890-1907. doi:10.1007/s10439-017-1832-6Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Doyne Farmer, J. (1992). Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena, 58(1-4), 77-94. doi:10.1016/0167-2789(92)90102-sNakamura, T., Small, M., & Hirata, Y. (2006). Testing for nonlinearity in irregular fluctuations with long-term trends. Physical Review E, 74(2). doi:10.1103/physreve.74.026205SHAPIRO, S. S., & WILK, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3-4), 591-611. doi:10.1093/biomet/52.3-4.591Mandelbrot, B. (1961). Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (Ingram Olkin, Sudhist G. Ghurye, Wassily Hoeffding, William G. Madow, and Henry B. Mann, eds.). SIAM Review, 3(1), 80-80. doi:10.1137/1003016Mann, H. B., & Whitney, D. R. (1947). On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. The Annals of Mathematical Statistics, 18(1), 50-60. doi:10.1214/aoms/1177730491Křemen, V., Lhotská, L., Macaš, M., Čihák, R., Vančura, V., Kautzner, J., & Wichterle, D. (2008). A new approach to automated assessment of fractionation of endocardial electrograms during atrial fibrillation. Physiological Measurement, 29(12), 1371-1381. doi:10.1088/0967-3334/29/12/002Haley, C. L., Gula, L. J., Miranda, R., Michael, K. A., Baranchuk, A. M., Simpson, C. S., … Redfearn, D. P. (2012). Validation of a novel algorithm for quantification of the percentage of signal fractionation in atrial fibrillation. EP Europace, 15(3), 447-452. doi:10.1093/europace/eus361Nollo, G., Marconcini, M., Faes, L., Bovolo, F., Ravelli, F., & Bruzzone, L. (2008). An Automatic System for the Analysis and Classification of Human Atrial Fibrillation Patterns from Intracardiac Electrograms. IEEE Transactions on Biomedical Engineering, 55(9), 2275-2285. doi:10.1109/tbme.2008.923155Kirchner, M., Faes, L., Olivetti, E., Riccardi, R., Scaglione, M., Gaita, F., & Antolini, R. (s. f.). Local electrical characterisation of human atrial fibrillation. Computers in Cardiology 2000. Vol.27 (Cat. 00CH37163). doi:10.1109/cic.2000.898567Cirugeda–Roldán, E., Novak, D., Kremen, V., Cuesta–Frau, D., Keller, M., Luik, A., & Srutova, M. (2015). Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study. Entropy, 17(12), 7493-7509. doi:10.3390/e17117493Corino, V. D. A., Rivolta, M. W., Sassi, R., Lombardi, F., & Mainardi, L. T. (2013). Ventricular activity cancellation in electrograms during atrial fibrillation with constraints on residuals’ power. Medical Engineering & Physics, 35(12), 1770-1777. doi:10.1016/j.medengphy.2013.07.010Rieta, J. J., Hornero, F., Alcaraz, R., & Moratal, D. (2007). Ventricular Artifacts Cancellation from Atrial Epicardial Recordings in Atrial Tachyarrhythmias. 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. doi:10.1109/iembs.2007.4353849Williams, G. (1997). Chaos Theory Tamed. doi:10.1201/9781482295412Havstad, J. W., & Ehlers, C. L. (1989). Attractor dimension of nonstationary dynamical systems from small data sets. Physical Review A, 39(2), 845-853. doi:10.1103/physreva.39.84

An interactive platform to guide catheter ablation in human persistent atrial fibrillation using dominant frequency, organization and phase mapping

Background and Objective: Optimal targets for persistent atrial fibrillation (persAF) ablation are still debated. Atrial regions hosting high dominant frequency (HDF) are believed to participate in the initiation and maintenance of persAF and hence are potential targets for ablation, while rotor ablation has shown promising initial results. Currently, no commercially available system offers the capability to automatically identify both these phenomena. This paper describes an integrated 3D software platform combining the mapping of both frequency spectrum and phase from atrial electrograms (AEGs) to help guide persAF ablation in clinical cardiac electrophysiological studies. Methods: 30 s of 2048 non-contact AEGs (EnSite Array, St. Jude Medical) were collected and analyzed per patient. After QRST removal, the AEGs were divided into 4 s windows with a 50% overlap. Fast Fourier transform was used for DF identification. HDF areas were identified as the maximum DF to 0.25 Hz below that, and their centers of gravity (CGs) were used to track their spatiotemporal movement. Spectral organization measurements were estimated. Hilbert transform was used to calculate instantaneous phase. Results: The system was successfully used to guide catheter ablation for 10 persAF patients. The mean processing time was 10.4 ± 1.5 min, which is adequate comparing to the normal electrophysiological (EP) procedure time (120∼180 min). Conclusions: A customized software platform capable of measuring different forms of spatiotemporal AEG analysis was implemented and used in clinical environment to guide persAF ablation. The modular nature of the platform will help electrophysiological studies in understanding of the underlying AF mechanisms

Are atrial fibrillation highest dominant frequency (HDF) areas the source of dominant excitation patterns? A left atrial panoramic view

Atrial fibrillation (AF) catheter ablation success depends on the possibility to accurately determine areas on the atrial endocardium at which AF activation originates. One way to determine if major AF activation pathways originate at identified source is through causality analysis. This work assessed to what extent left atrial highest dominant frequency (HDF) areas can be identified as sources of activation pathways in 10 male subjects suffering from persistent AF. Virtual electrograms were collected from 64 endocardial locations for at least 5 minutes. Frequency and causality were analyzed on 4 s signal segments Causality was assessed using the directed transfer function (DTF) algorithm, and AF activation sources were identified as endocardial locations of which the VEGM signal had high influence on other VEGM signals. Co-localization of high influence and HDF areas was evaluated for different area overlap and spectral organisation (OI) thresholds. Results show that, on average, good overlap only existed in 64.6% (± 8.8%) over all subject using the lowest threshold settings. Good overlap rates reduced with more conservative thresholds. This indicates that HDF areas might not always identify origins of main AF activation pathways

High-Density Mapping Analysis of Electrical Spatiotemporal Behaviour in Atrial Fibrillation

Tese de mestrado integrado, Engenharia Biomédica e Biofísica (Sinais e Imagens Médicas), 2022, Universidade de Lisboa, Faculdade de CiênciasDoenças cardiovasculares, tais como arritmias, são a principal causa de morte no mundo, especialmente no Sul e no Este da Ásia, e nos Estados Unidos da América [1]. As arritmas são caracterizadas pela alteração no ritmo sinusal normal do coração. Em particular, a fibrilhação auricular (FA) é a arritmia cardíaca mais comum na prática clínica, contribuindo para mais de 200 mil mortes globalmente em 2017 [2]. Caracteriza-se pela contração rápida e dessincronizada das aurículas, e está associada ao aumento da mortalidade e afecta de forma negativa a qualidade de vida dos pacientes. A FA é geralmente tratada através de medicação, porém quando esta falha, a ablação por cateter é indicada, sendo um tratamento de referência para combater esta patologia. A ablação apresenta uma taxa de sucesso de aproximadamente 50% no primeiro procedimento, sendo necessário efectuar vários procedimentos para aumentar a eficácia do tratamento [3]. A detecção desta patologia envolve, numa primeira fase, a realização de um electrocardiograma (ECG) e, posteriormente um estudo electrofisiológico para saber com precisão onde se localiza e o mecanismo subjacente à mesma. Este último implica o registo da actividade eléctrica através de electrogramas (EGM) locais em diferentes pontos das aurículas e dos ventrículos, com o auxílio de sistemas de mapeamento tridimensionais (3D) electroanatómicos, sendo um procedimento invasivo. Existem diversos métodos lineares e não lineares que permitem a análise dos EGMs nos domínios do tempo, frequência, fase, entre outros, com a finalidade de melhor compreender os mecanismos subjacentes à FA e, consequentemente aumentar a taxa de sucesso do processo de ablação e melhorar a sua eficiência. Esta área de estudo progrediu significativamente, tanto a nível de hardware, como de software. Apesar disso, os métodos desenvolvidos não têm nem acrescentado benefícios adicionais, nem melhorado significativamente a taxa de sucesso do processo de ablação. Existem várias razões para tal, e grande parte deve-se ao facto destes métodos de análise estarem incorporados nos sistemas de mapeamento e o seu software ser exclusivo. Isto leva a que não consigamos perceber como é que os algoritmos funcionam nos diferentes sistemas de mapeamento para comparar as suas diferenças e semelhanças. Devido a estes constrangimentos, os investigadores são compelidos a desenvolver os seus próprios métodos de análise e técnicas de mapeamento, o que leva à existência de uma multitude de métodos e técnicas de mapeamento que parecem ser diferentes entre si, resultando em informação ambígua e conflituosa no que diz respeito aos mecanismos da FA, e a conclusões distintas entre estudos. O sucesso do tratamento poderia aumentar se tivéssemos uma melhor compreensão dos métodos de análise e da sua aplicação no contexto da FA; perceber se os métodos apontam para o mesmo fenómeno de fibrilhação, se existe alguma correlação entre os métodos, e se a informação fornecida pelos mesmos é complementar ou redundante. Assim, o objectivo deste trabalho consistiu em implementar diferentes métodos para analisar os EGMs e a estrutura 3D da aurícula esquerda (AE) de doentes com FA, numa tentativa de responder às questões que motivaram a realização deste projecto. Em última análise, ao observar os mapas 3D da AE tendo uma melhor compreensão dos métodos, poderemos identificar com precisão as regiões na AE responsáveis por iniciar a FA, e ter mais conhecimento sobre os mecanismos responsáveis pela mesma. Desta forma, o processo de ablação poderá alcançar o seu potencial. Para este projecto, foram incluídos os mapas 3D electroanatómicos da AE de dez doentes com FA paroxística ou persistente do hospital de Santa Marta, recolhidos com o sistema de mapeamento CARTO 3. Cada ponto electroanatómico dos mapas inclui as 12 derivações do ECG, e os EGMs unipolares e bipolares registados com o cateter de mapeamento Pentaray de 20 pólos. Porém, apenas os EGMs bipolares foram incluídos na análise. Processaram-se os sinais bipolares e, devido a algumas limitações, foi possível apenas a implementação de dois métodos diferentes para os analisar: um no domínio da frequência – Frequência Dominante (FD) –, e outro no domínio da Teoria da Informação – a entropia de Shannon. De seguida, criaram-se três tipos de mapas 3D electroanatómicos da AE para cada doente: um de voltagem, cuja informação foi adquirida com o sistema de mapeamento, um de FD, e outro de entropia. A informação de cada mapa estava organizada segundo um padrão de cores. Observando os diferentes tipos de mapas da AE paralelamente, foi possível comparar os métodos, e perceber que tipo de informação cada um deles fornecia, numa tentativa de melhor compreender os mecanismos da FA. Foi possível observar em algumas regiões da AE, principalmente nos mapas de voltagem e de FD, a presença de “centros de activação” ou “centros de fibrilhação”, que poderão ser os gatilhos responsáveis por desencadear ou manter o mecanismo de fibrilhação. Para confirmar se de facto aquelas regiões eram os gatilhos de fibrilhação, seria necessário submeter os doentes ao processo de ablação e queimar essas zonas; e posteriormente acompanhar os doentes para observar os efeitos do procedimento e confirmar a hipótese. Contudo, dadas as limitações do trabalho e o facto desta área de investigação ser pouco explorada, é fulcral obter um maior número de estudo comparativos entre mais métodos de diferentes domínios e confirmar se apontam ou não para o mesmo fenómeno de fibrilhação. Apesar de terem sido implementados apenas dois métodos de análise dos EGMs, o projecto permitiu a comparação entre os mesmos, uma área de estudo por onde ainda há muito para investigar. Com mais conhecimento sobre os diferentes métodos, a sua aplicação, inter-relação e adequação no estudo dos mecanismos da FA e das propriedades electrofisiológicas desta patologia, é possível desenvolver procedimentos de ablação mais eficientes e selectivos, de forma a diminuir os riscos e aumentar a taxa de sucesso do tratamento.Atrial fibrillation (AF) is the most frequent cardiac arrhythmia in clinical practice and is described by rapid and irregular contractions of the atria. Despite catheter ablation (CA) being a well-established treatment for AF, it is sub-optimal, with a success rate of approximately 50 % after a single procedure, with some patients requiring multiple procedures to achieve long-term freedom from this pathology. This prompted the proposal and development of various quantitative electrogram (EGM)-based methods along with different mapping systems with their respective mapping techniques, to better understand the mechanisms responsible for initiating and maintaining AF, thus improving ablation outcomes. However, this diversification of methods and tools resulted in disperse and inconsistent data regarding the mechanisms of AF. This work consisted of employing two different methods to analyse the electrograms (EGM): dominant frequency (DF) and Shannon entropy (ShEn). From these EGMs, metrics were then extracted and displayed in colour-coded fashion on a 3D mesh of the left atrium (LA) from patients with paroxysmal or persistent AF. The two methods were compared to understand whether or not these indicated different phenomena/mechanisms, and if these could locate sites suspected of triggering and maintaining AF. The results, while not fully conforming to the literature, allowed the comparison between different EGM analysis methods, a field of study that requires further research. Overall, this project highlighted the limited data available within the topic, hindering our understanding of AF mechanisms and development of more effective and selective ablation procedures to avoid unnecessary complications, and ultimately improve the effects of the treatment's outcomes

Identification of atrial fibrillation drivers by means of concentric ring electrodes

The prevalence of atrial fibrillation (AF) has tripled in the last 50 years due to population aging. High-frequency (DFdriver) activated atrial regions lead the activation of the rest of the atria, disrupting the propagation wavefront. Fourier based spectral analysis of body surface potential maps have been proposed for DFdriver identification, although these approaches present serious drawbacks due to their limited spectral resolution for short AF epochs and the blurring effect of the volume conductor. Laplacian signals (BC-ECG) from bipolar concentric ring electrodes (CRE) have been shown to outperform the spatial resolution achieved with conventional unipolar recordings. Our aimed was to determine the best DFdriver estimator in endocardial electrograms and to assess the BC-ECG capacity of CRE to quantify AF activity non-invasively

Systematic differences of non-invasive dominant frequency estimation compared to invasive dominant frequency estimation in atrial fibrillation

Non-invasive analysis of atrial fibrillation (AF) using body surface mapping (BSM) has gained significant interest, with attempts at interpreting atrial spectro-temporal parameters from body surface signals. As these body surface signals could be affected by properties of the torso volume conductor, this interpretation is not always straightforward. This paper highlights the volume conductor effects and influences of the algorithm parameters for identifying the dominant frequency (DF) from cardiac signals collected simultaneously on the torso and atrial surface. Bi-atrial virtual electrograms (VEGMs) and BSMs were recorded simultaneously for 5 minutes from 10 patients undergoing ablation for persistent AF. Frequency analysis was performed on 4 s segments. DF was defined as the frequency with highest power between 4-10 Hz with and without applying organization index (OI) thresholds. The volume conductor effect was assessed by analyzing the highest DF (HDF) difference of each VEGM HDF against its BSM counterpart. Significant differences in HDF values between intra-cardiac and torso signals could be observed, independent of OI threshold. This difference increases with increasing endocardial HDF (BSM-VEGM median difference from -0.13 Hz for VEGM HDF at 6.25±0.25 Hz to -4.24 Hz at 9.75±0.25 Hz), thereby confirming the theory of the volume conductor effect in real-life situations. Applying an OI threshold strongly affected the BSM HDF area size and location and atrial HDF area location. These results suggest that volume conductor and measurement algorithm effects must be considered for appropriate clinical interpretation

Restitution Slope Affects the Outcome of Dominant Frequency Ablation in Persistent Atrial Fibrillation: CUVIA-AF2 Post-Hoc Analysis Based on Computational Modeling Study

Introduction: Although the dominant frequency (DF) localizes the reentrant drivers and the maximal slope of the action potential duration (APD) restitution curve (Smax) reflects the tendency of the wave-break, their interaction has never been studied. We hypothesized that DF ablation has different effects on atrial fibrillation (AF) depending on Smax. Methods: We studied the DF and Smax in 25 realistic human persistent AF model samples (68% male, 60 ± 10 years old). Virtual AF was induced by ramp pacing measuring Smax, followed by spatiotemporal DF evaluation for 34 s. We assessed the DF ablation effect depending on Smax in both computational modeling and a previous clinical trial, CUVIA-AF (170 patients with persistent AF, 70.6% male, 60 ± 11 years old). Results: Mean DF had an inverse relationship with Smax regardless of AF acquisition timing (p < 0.001). Virtual DF ablations increased the defragmentation rate compared to pulmonary vein isolation (PVI) alone (p = 0.015), especially at Smax <1 (61.5 vs. 7.7%, p = 0.011). In post-DF ablation defragmentation episodes, DF was significantly higher (p = 0.002), and Smax was lower (p = 0.003) than in episodes without defragmentation. In the post-hoc analysis of CUVIA-AF2, we replicated the inverse relationship between Smax and DF (r = -0.47, p < 0.001), and we observed better rhythm outcomes of clinical DF ablations in addition to a PVI than of empirical PVI at Smax <1 [hazard ratio 0.45, 95% CI (0.22-0.89), p = 0.022; log-rank p = 0.021] but not at ≥ 1 (log-rank p = 0.177). Conclusion: We found an inverse relationship between DF and Smax and the outcome of DF ablation after PVI was superior at the condition with Smax <1 in both in-silico and clinical trials.ope

Characterization of the Substrate Modification in Patients Undergoing Catheter Ablation of Atrial Fibrillation

Tesis por compendio[ES] La fibrilación auricular (FA) es la arritmia cardíaca más común. A pesar de la gran popularidad de la ablación con catéter (AC) como tratamiento principal, todavía hay margen de mejora. Aunque las venas pulmonares (VPs) son los principales focos de FA, muchos sitios pueden contribuir a su propagación, formando el sustrato de la FA (SFA). El mapeo preciso del SFA y el registro de la modificación del SFA, como marcador positivo después de AC, son fundamentales. Los electrocardiogramas (ECG) y los electrogramas (EGM) se reclutan para este propósito. Los EGM se utilizan para detectar candidatos de AC como áreas que provocan o perpetúan la FA. Por lo tanto, el análisis de EGM es una parte indispensable de AC. Con la capacidad de observar las aurículas globalmente, la principal aplicación de los ECG es evaluar la modificación del SFA analizando las ondas f o P. A pesar del extenso análisis de cualquiera de los tipos de registro, existen algunas brechas. La AC no-VP aumenta el tiempo en quirófano, provocando mayores riesgos y costos. En cuanto al análisis de la modificación del SFA, se utilizan varios umbrales para definir una onda P prolongada. El principal objetivo de la presente Tesis es contribuir al esfuerzo de análisis de SFA y de modificación de SFA. Para ello, la presente Tesis se desarrolló bajo dos hipótesis principales. Que la calidad de la información extraída durante el SFA y el análisis de modificación del SFA se puede mejorar mediante la introducción de pasos innovadores. Además, la combinación de análisis de ECG y EGM puede aumentar la resolución del mapeo y revelar nueva información sobre los mecanismos de FA. Para cumplir con el objetivo principal, el análisis se divide en 4 partes, conformando los 4 capítulos del Compendio de articulos. En primer lugar, se reclutó la dimensión de correlación de grano grueso (DCGG). DCGG localizó de manera confiable EGM complejos y la clasificación por tipos de FA arrojó una precisión del 84 %. Luego, se adoptó un análisis alternativo de la onda P, estudiando por separado su primera y su segunda parte, correspondientes a la aurícula derecha (AD) e izquierda (AI). Los resultados indicaron LA como la principal fuente de modificación del SFA y subrayaron la importancia de estudiar partes integrales de ECG. Los hallazgos de este estudio también sugieren la implementación de partes integrales de ondas P como un posible alivio de las discrepancias en los umbrales de ondas P para definir el tejido fibrótico. Posteriormente, se estudió el efecto diferente del aislamiento de la VP izquierda (AVPI) y derecha (AVPD) sobre la modificación del SFA. AVPI fue la parte crítica, siendo la fuente exclusiva de acortamiento de onda P. El análisis de los registros durante la AC también permitió una observación más cercana de las fluctuaciones de la variabilidad de la frecuencia cardíaca (VFC) a lo largo del procedimiento de CA, lo que reveló información sobre el efecto de la energía de radiofrecuencia (RF) en el tejido auricular. La última parte se centró en el seno coronario (SC), una estructura fundamental en el mapeo de FA para aumentar la resolución de la información. Se definieron los canales más y menos robustos durante el ritmo sinusal (RS) y se investigó la utilidad de SC en la evaluación de la modificación del SFA. Aunque CS no proporcionó una imagen global de la alteración del SFA, pudo registrar con mayor sensibilidad las fluctuaciones en la respuesta auricular durante la AC. Los hallazgos presentados en esta Tesis Doctoral ofrecen una perspectiva alternativa sobre la modificación del SFA y contribuyen al esfuerzo general sobre el mapeo de FA y la evaluación del sustrato posterior a la CAAC, abriendo futuras líneas de investigación hacia una resolución más alta y un mapeo más eficiente de los mecanismos desencadenantes de la FA.[CA] La fibril·lació auricular (FA) és l'arítmia cardíaca més comú. Tot i la gran popularitat de l'ablació amb catèter (AC) com a tractament principal, encara hi ha marge de millora. Tot i que les venes pulmonars (VPs) són els principals focus de FA, molts llocs poden contribuir a la seva propagació, formant el substrat de la FA (SFA). El mapatge precís de l'SFA i el registre de la modificació de l'SFA, com a marcador positiu després d'AC, són fonamentals. Els electrocardiogrames (ECG) i els electrogrames (EGM) es recluten per a aquest propòsit. Els EGM es fan servir per detectar candidats d'AC com a àrees que provoquen o perpetuen la FA. Per tant, lanàlisi dEGM és una part indispensable dAC. Amb la capacitat d'observar les aurícules globalment, la principal aplicació dels ECG és avaluar la modificació de l'SFA analitzant les ones f o P. Tot i l'extensa anàlisi de qualsevol dels tipus de registre, hi ha algunes bretxes. L'AC no-VP augmenta el temps a quiròfan, provocant majors riscos i costos. Pel que fa a l'anàlisi de la modificació de l'SFA, s'utilitzen diversos llindars per definir una ona P perllongada. L'objectiu principal d'aquesta Tesi és contribuir a l'esforç d'anàlisi de SFA i de modificació de SFA. Per això, aquesta Tesi es va desenvolupar sota dues hipòtesis principals. Que la qualitat de la informació extreta durant el SFA i lanàlisi de modificació de lSFA es pot millorar mitjançant la introducció de passos innovadors. A més, la combinació d'anàlisi d'ECG i EGM pot augmentar la resolució del mapatge i revelar informació nova sobre els mecanismes de FA. Per complir amb l'objectiu principal, l'anàlisi es divideix en 4 parts i es conforma els 4 capítols del Compendi d'articles. En primer lloc, es va reclutar la dimensió de correlació de gra gruixut (DCGG). DCGG va localitzar de manera fiable EGM complexos i la classificació per tipus de FA va donar una precisió del 84%. Després, es va adoptar una anàlisi alternativa de l'ona P, estudiant per separat la primera i la segona part corresponents a l'aurícula dreta (AD) i esquerra (AI). Els resultats van indicar LA com la font principal de modificació de l'SFA i van subratllar la importància d'estudiar parts integrals d'ECG. Les troballes d'aquest estudi també suggereixen la implementació de parts integrals d'ones P com a possible alleugeriment de les discrepàncies als llindars d'ones P per definir el teixit fibròtic. Posteriorment, es va estudiar l'efecte diferent de l'aïllament de la VP esquerra (AVPI) i la dreta (AVPD) sobre la modificació de l'SFA. AVPI va ser la part crítica, sent la font exclusiva d'escurçament d'ona P. L'anàlisi dels registres durant l'AC també va permetre una observació més propera de les fluctuacions de la variabilitat de la freqüència cardíaca (VFC) al llarg del procediment de CA , cosa que va revelar informació sobre l'efecte de l'energia de radiofreqüència (RF) en el teixit auricular. L'última part es va centrar al si coronari (SC), una estructura fonamental al mapeig de FA per augmentar la resolució de la informació. Es van definir els canals més i menys robustos durant el ritme sinusal (RS) i es va investigar la utilitat de SC a l'avaluació de la modificació de l'SFA. Tot i que CS no va proporcionar una imatge global de l'alteració de l'SFA, va poder registrar amb més sensibilitat les fluctuacions a la resposta auricular durant l'AC. Les troballes presentades en aquesta Tesi Doctoral ofereixen una perspectiva alternativa sobre la modificació de l'SFA i contribueixen a l'esforç general sobre el mapeig de FA i l'avaluació del substrat posterior a la CAAC, obrint futures línies de recerca cap a una resolució més alta i un mapeig més eficient dels mecanismes desencadenants de la FA.[EN] Atrial fibrillation (AF) is the commonest cardiac arrhythmia. Despite the high popularity of catheter ablation (CA) as the main treatment, there is still room for improvement. Time spent in AF affects the AF confrontation and evolution, with 1,15% of paroxysmal AF patients progressing to persistent annually. Therefore, from diagnosis to follow-up, every aspect that contributes to the AF confrontation is of utmost importance. Although pulmonary veins (PVs) are the main AF foci, many sites may contribute to the AF propagation, by triggering or sustaining the AF, forming the AF substrate. Precise AF substrate mapping and recording of the AF substrate modification, as a positive marker after CA sessions, are critical. Electrocardiograms (ECGs) and electrograms (EGMs) are vastly recruited for this purpose. EGMs are used to detect candidate CA targets as areas that provoke or perpetuate AF. Hence, EGMs analysis is an indispensable part of the CA procedure. With the ability to observe the atria globally, ECGs' main application is to assess the AF substrate modification by analyzing f- or P-waves from recordings before and after CA. Despite the extensive analysis on either recording types, some gaps exist. Non-PV CA increases the time in operation room, provoking higher risks and costs. Furthermore, whether non-PV CA is beneficial is under dispute. As for the AF substrate modification analysis, various thresholds are used to define a prolonged P-wave, related with poor CA prognostics. The main objective of the present Thesis is to contribute to the effort of AF substrate and AF substrate modification analysis. For this purpose, the present Thesis was developed under two main hypotheses. That the information quality extracted during AF substrate and AF substrate modification analysis can be improved by introducing innovative steps. Also, that combining ECG and EGM analysis can augment the mapping resolution and reveal new information regarding AF mechanisms. To accomplish the main objective, the analysis is split in 4 parts, forming the 4 chapters of the Compendium of publications. Firstly, coarse-grained correlation dimension (CGCD) was recruited. CGCD reliably localized highly complex EGMs and classification by AF types yielded 84% accuracy. Then, an alternative P-wave analysis was suggested, studying separately the first and second P-wave parts, corresponding to the right (RA) and left (LA) atrium. The findings indicated LA as the main AF substrate modification source and underlined the importance of studying integral ECG parts. The findings of this study additionally suggest the implementation of integral P-wave parts as a possible alleviation for the discrepancies in P-wave thresholds to define fibrotic tissue. Afterwards, the different effect of left (LPVI) and right pulmonary vein isolation (RPVI) on the AF substrate modification was studied. LPVI was the critical part, being the exclusive source of P-wave shortening. Analysis of recordings during CA also allowed a closer observation of the heart rate variability (HRV) fluctuations throughout the CA procedure, revealing information on the effect of radiofrequency (RF) energy on the atrial tissue. The last part was focused on coronary sinus (CS), a fundamental structure in AF mapping to increase the information resolution. The most and least robust channels during sinus rhythm (SR) were defined and the utility of CS in AF substrate modification evaluation was investigated. Although CS did not provide a global picture of the AF substrate alteration, it was able to record with higher sensitivity the fluctuations in the atrial response during the application of RF energy. The findings presented in this Doctoral Thesis offer an alternative perspective on the AF substrate modification and contribute to the overall effort on AF mapping and post-CA substrate evaluation, opening future lines of research towards a higher resolution and more efficient mapping of the AF drivers.Vraka, A. (2022). Characterization of the Substrate Modification in Patients Undergoing Catheter Ablation of Atrial Fibrillation [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/191410Compendi

Sample Entropy Analysis of Noisy Atrial Electrograms during Atrial Fibrillation

[EN] Most cardiac arrhythmias can be classified as atrial flutter, focal atrial tachycardia, or atrial fibrillation. They have been usually treated using drugs, but catheter ablation has proven more effective. This is an invasive method devised to destroy the heart tissue that disturbs correct heart rhythm. In order to accurately localise the focus of this disturbance, the acquisition and processing of atrial electrograms form the usual mapping technique. They can be single potentials, double potentials, or complex fractionated atrial electrogram (CFAE) potentials, and last ones are the most effective targets for ablation. The electrophysiological substrate is then localised by a suitable signal processing method. Sample Entropy is a statistic scarcely applied to electrograms but can arguably become a powerful tool to analyse these time series, supported by its results in other similar biomedical applications. However, the lack of an analysis of its dependence on the perturbations usually found in electrogram data, such as missing samples or spikes, is even more marked. This paper applied SampEn to the segmentation between non-CFAE and CFAE records and assessed its class segmentation power loss at different levels of these perturbations. The results confirmed that SampEn was able to significantly distinguish between non-CFAE and CFAE records, even under very unfavourable conditions, such as 50% of missing data or 10% of spikes.This research was supported by Research Center for Informatics (no. CZ.02.1.01/0.0/0.0/16-019/0000765).Cirugeda Roldan, EM.; Molina Picó, A.; Novák, D.; Cuesta Frau, D.; Kremen, V. (2018). Sample Entropy Analysis of Noisy Atrial Electrograms during Atrial Fibrillation. Computational and Mathematical Methods in Medicine. https://doi.org/10.1155/2018/1874651SAhmed, S., Claughton, A., & Gould, P. A. (2015). Atrial Flutter — Diagnosis, Management and Treatment. Abnormal Heart Rhythms. doi:10.5772/60700Kirchhof, P., & Calkins, H. (2016). Catheter ablation in patients with persistent atrial fibrillation. European Heart Journal, 38(1), 20-26. doi:10.1093/eurheartj/ehw260Nademanee, K., Lockwood, E., Oketani, N., & Gidney, B. (2010). Catheter ablation of atrial fibrillation guided by complex fractionated atrial electrogram mapping of atrial fibrillation substrate. Journal of Cardiology, 55(1), 1-12. doi:10.1016/j.jjcc.2009.11.002NG, J., & GOLDBERGER, J. J. (2007). Understanding and Interpreting Dominant Frequency Analysis of AF Electrograms. Journal of Cardiovascular Electrophysiology, 18(6), 680-685. doi:10.1111/j.1540-8167.2007.00832.xKottkamp, H., & Hindricks, G. (2007). Complex fractionated atrial electrograms in atrial fibrillation: A promising target for ablation, but why, when, and how? Heart Rhythm, 4(8), 1021-1023. doi:10.1016/j.hrthm.2007.05.011Křemen, V., Lhotská, L., Macaš, M., Čihák, R., Vančura, V., Kautzner, J., & Wichterle, D. (2008). A new approach to automated assessment of fractionation of endocardial electrograms during atrial fibrillation. Physiological Measurement, 29(12), 1371-1381. doi:10.1088/0967-3334/29/12/002Nademanee, K., McKenzie, J., Kosar, E., Schwab, M., Sunsaneewitayakul, B., Vasavakul, T., … Ngarmukos, T. (2004). A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate. Journal of the American College of Cardiology, 43(11), 2044-2053. doi:10.1016/j.jacc.2003.12.054Scherr, D., Dalal, D., Cheema, A., Cheng, A., Henrikson, C. A., Spragg, D., … Dong, J. (2007). Automated detection and characterization of complex fractionated atrial electrograms in human left atrium during atrial fibrillation. Heart Rhythm, 4(8), 1013-1020. doi:10.1016/j.hrthm.2007.04.021Almeida, T. P., Chu, G. S., Salinet, J. L., Vanheusden, F. J., Li, X., Tuan, J. H., … Schlindwein, F. S. (2016). Minimizing discordances in automated classification of fractionated electrograms in human persistent atrial fibrillation. Medical & Biological Engineering & Computing, 54(11), 1695-1706. doi:10.1007/s11517-016-1456-2Molina-Picó, A., Cuesta-Frau, D., Aboy, M., Crespo, C., Miró-Martínez, P., & Oltra-Crespo, S. (2011). Comparative study of approximate entropy and sample entropy robustness to spikes. Artificial Intelligence in Medicine, 53(2), 97-106. doi:10.1016/j.artmed.2011.06.007Cuesta–Frau, D., Miró–Martínez, P., Jordán Núñez, J., Oltra–Crespo, S., & Molina Picó, A. (2017). Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics. Computers in Biology and Medicine, 87, 141-151. doi:10.1016/j.compbiomed.2017.05.028Demont-Guignard, S., Benquet, P., Gerber, U., & Wendling, F. (2009). Analysis of Intracerebral EEG Recordings of Epileptic Spikes: Insights From a Neural Network Model. IEEE Transactions on Biomedical Engineering, 56(12), 2782-2795. doi:10.1109/tbme.2009.2028015Molina–Picó, A., Cuesta–Frau, D., Miró–Martínez, P., Oltra–Crespo, S., & Aboy, M. (2013). Influence of QRS complex detection errors on entropy algorithms. Application to heart rate variability discrimination. Computer Methods and Programs in Biomedicine, 110(1), 2-11. doi:10.1016/j.cmpb.2012.10.014Ganesan, P., Cherry, E. M., Pertsov, A. M., & Ghoraani, B. (2015). Characterization of Electrograms from Multipolar Diagnostic Catheters during Atrial Fibrillation. BioMed Research International, 2015, 1-9. doi:10.1155/2015/272954Lake, D. E., Richman, J. S., Griffin, M. P., & Moorman, J. R. (2002). Sample entropy analysis of neonatal heart rate variability. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 283(3), R789-R797. doi:10.1152/ajpregu.00069.2002Kim, K. K., Baek, H. J., Lim, Y. G., & Park, K. S. (2012). Effect of missing RR-interval data on nonlinear heart rate variability analysis. Computer Methods and Programs in Biomedicine, 106(3), 210-218. doi:10.1016/j.cmpb.2010.11.011Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049. doi:10.1152/ajpheart.2000.278.6.h2039Cirugeda–Roldán, E., Novak, D., Kremen, V., Cuesta–Frau, D., Keller, M., Luik, A., & Srutova, M. (2015). Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study. Entropy, 17(12), 7493-7509. doi:10.3390/e17117493PORTER, M., SPEAR, W., AKAR, J. G., HELMS, R., BRYSIEWICZ, N., SANTUCCI, P., & WILBER, D. J. (2008). Prospective Study of Atrial Fibrillation Termination During Ablation Guided by Automated Detection of Fractionated Electrograms. Journal of Cardiovascular Electrophysiology, 19(6), 613-620. doi:10.1111/j.1540-8167.2008.01189.xKonings, K. T., Kirchhof, C. J., Smeets, J. R., Wellens, H. J., Penn, O. C., & Allessie, M. A. (1994). High-density mapping of electrically induced atrial fibrillation in humans. Circulation, 89(4), 1665-1680. doi:10.1161/01.cir.89.4.1665Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics Surveys, 4(0), 1-39. doi:10.1214/09-ss051Richman, J. S. (2007). Sample Entropy Statistics and Testing for Order in Complex Physiological Signals. Communications in Statistics - Theory and Methods, 36(5), 1005-1019. doi:10.1080/03610920601036481Pincus, S. M., Gladstone, I. M., & Ehrenkranz, R. A. (1991). A regularity statistic for medical data analysis. Journal of Clinical Monitoring, 7(4), 335-345. doi:10.1007/bf01619355Alcaraz, R., & Rieta, J. J. (2009). Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation. Computer Methods and Programs in Biomedicine, 93(2), 148-154. doi:10.1016/j.cmpb.2008.09.001Alcaraz, R., Abásolo, D., Hornero, R., & Rieta, J. J. (2010). Optimal parameters study for sample entropy-based atrial fibrillation organization analysis. Computer Methods and Programs in Biomedicine, 99(1), 124-132. doi:10.1016/j.cmpb.2010.02.009Costa, M., Goldberger, A. L., & Peng, C.-K. (2002). Multiscale Entropy Analysis of Complex Physiologic Time Series. Physical Review Letters, 89(6). doi:10.1103/physrevlett.89.06810