Application of nonlinear methods to discriminate fractionated electrograms in paroxysmal versus persistent atrial fibrillation

Background and Objective: Complex fractionated atrial electrograms (CFAE) may contain information concerning the electrophysiological substrate of atrial fibrillation (AF); therefore they are of interest to guide catheter ablation treatment of AF. Electrogram signals are shaped by activation events, which are dynamical in nature. This makes it difficult to establish those signal properties that can provide insight into the ablation site location. Nonlinear measures may improve information. To test this hypothesis, we used nonlinear measures to analyze CFAE. Methods: CFAE from several atrial sites, recorded for a duration of 16 s, were acquired from 10 patients with persistent and 9 patients with paroxysmal AF. These signals were appraised using non-overlapping windows of 1-, 2- and 4-s durations. The resulting data sets were analyzed with Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA). The data was also quantified via entropy measures. Results: RQA exhibited unique plots for persistent versus paroxysmal AF. Similar patterns were observed to be repeated throughout the RPs. Trends were consistent for signal segments of 1 and 2 s as well as 4 s in duration. This was suggestive that the underlying signal generation process is also repetitive, and that repetitiveness can be detected even in 1-s sequences. The results also showed that most entropy metrics exhibited higher measurement values (closer to equilibrium) for persistent AF data. It was also found that Determinism (DET), Trapping Time (TT), and Modified Multiscale Entropy (MMSE), extracted from signals that were acquired from locations at the posterior atrial free wall, are highly discriminative of persistent versus paroxysmal AF data. Conclusions: Short data sequences are sufficient to provide information to discern persistent versus paroxysmal AF data with a significant difference, and can be useful to detect repeating patterns of atrial activation

Practical Considerations for the Application of Nonlinear Indices Characterizing the Atrial Substrate in Atrial Fibrillation

[EN] Atrial fibrillation (AF) is the most common cardiac arrhythmia, and in response to increasing clinical demand, a variety of signals and indices have been utilized for its analysis, which include complex fractionated atrial electrograms (CFAEs). New methodologies have been developed to characterize the atrial substrate, along with straightforward classification models to discriminate between paroxysmal and persistent AF (ParAF vs. PerAF). Yet, most previous works have missed the mark for the assessment of CFAE signal quality, as well as for studying their stability over time and between different recording locations. As a consequence, an atrial substrate assessment may be unreliable or inaccurate. The objectives of this work are, on the one hand, to make use of a reduced set of nonlinear indices that have been applied to CFAEs recorded from ParAF and PerAF patients to assess intra-recording and intra-patient stability and, on the other hand, to generate a simple classification model to discriminate between them. The dominant frequency (DF), AF cycle length, sample entropy (SE), and determinism (DET) of the Recurrence Quantification Analysis are the analyzed indices, along with the coefficient of variation (CV) which is utilized to indicate the corresponding alterations. The analysis of the intra-recording stability revealed that discarding noisy or artifacted CFAE segments provoked a significant variation in the CV(%) in any segment length for the DET and SE, with deeper decreases for longer segments. The intra-patient stability provided large variations in the CV(%) for the DET and even larger for the SE at any segment length. To discern ParAF versus PerAF, correlation matrix filters and Random Forests were employed, respectively, to remove redundant information and to rank the variables by relevance, while coarse tree models were built, optimally combining high-ranked indices, and tested with leave-one-out cross-validation. The best classification performance combined the SE and DF, with an accuracy (Acc) of 88.3%, to discriminate ParAF versus PerAF, while the highest single Acc was provided by the DET, reaching 82.2%. This work has demonstrated that due to the high variability of CFAEs data averaging from one recording place or among different recording places, as is traditionally made, it may lead to an unfair oversimplification of the CFAE-based atrial substrate characterization. Furthermore, a careful selection of reduced sets of features input to simple classification models is helpful to accurately discern the CFAEs of ParAF versus PerAF.This research has received partial financial support from public national grants DPI2017-83952-C3, PID2021-00X128525-IV0, and PID2021-123804OB-I00 of the Spanish Government with DOI 10.13039/501100011033 jointly with the European Regional Development Fund (EU), and regional grants SBPLY/17/180501/000411 from Junta de Comunidades de Castilla-La Mancha and AICO/2021/286 from Generalitat Valenciana.Finotti, E.; Quesada, A.; Ciaccio, EJ.; Garan, H.; Hornero, F.; Alcaraz, R.; Rieta, JJ. (2022). Practical Considerations for the Application of Nonlinear Indices Characterizing the Atrial Substrate in Atrial Fibrillation. Entropy. 24(24):1-17. https://doi.org/10.3390/e24091261117242

Discrimination Between CFAEs of Paroxysmal and Persistent Atrial Fibrillation With Simple Classification Models of Reduced Features

[EN] A significant number of variables to discriminate between paroxysmal and persistent atrial fibrillation (ParAF vs. PerAF) has been widely exploited, mostly assessed with statistical tests aimed to suggest adequate approaches for catheter ablation (CA) of AF. However, in practice, it would be desirable to utilize simple classification models readily understandable. In this work dominant frequency (DF), AF cycle length (AFCL), sample entropy (SE) and determinism (DET) of recurrent quantification analysis were applied to recordings of complex fractionated atrial electrograms (CFAEs) of AF patients, aimed to create simple models to discriminate between ParAF and PerAF. Correlation matrix filters removed redundant information and Random Forests ranked the variables by relevance. Next, coarse tree models were built, optimally combining high-ranking indexes, and tested with leave-one-out cross-validation. The best classification performance combined SE and DF with an Accuracy (Acc) of 88.2% to discriminate ParAF from PerAF, while the highest single Acc was provided by DET reaching 82.4%. Hence, careful selection of reduced sets of features feeding simple classification models is able to discriminate accurately between CFAEs of ParAF and PerAFFinotti, E.; Ciaccio, EJ.; Garan, H.; Bertomeu-Gonzalez, V.; Alcaraz, R.; Rieta, JJ. (2020). Discrimination Between CFAEs of Paroxysmal and Persistent Atrial Fibrillation With Simple Classification Models of Reduced Features. IEEE. 1-4. https://doi.org/10.22489/CinC.2020.360S1

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). 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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

Complexity of Atrial Fibrillation Electrograms Through Nonlinear Signal Analysis: In Silico Approach

Identification of atrial fibrillation (AF) mechanisms could improve the rate of ablation success. However, the incomplete understanding of those mechanisms makes difficult the decision of targeting sites for ablation. This work is focused on the importance of EGM analysis for detecting and modulating rotors to guide ablation procedures and improve its outcomes. Virtual atrial models are used to show how nonlinear measures can be used to generate electroanatomical maps to detect critical sites in AF. A description of the atrial cell mathematical models, and the procedure of coupling them within two‐dimensional and three‐dimensional virtual atrial models in order to simulate arrhythmogenic mechanisms, is given. Mathematical modeling of unipolar and bipolar electrogramas (EGM) is introduced. It follows a discussion of EGM signal processing. Nonlinear descriptors, such as approximate entropy and multifractal analysis, are used to study the dynamical behavior of EGM signals, which are not well described by a linear law. Our results evince that nonlinear analysis of EGM can provide information about the dynamics of rotors and other mechanisms of AF. Furthermore, these fibrillatory patterns can be simulated using virtual models. The combination of features using machine learning tools can be used for identifying arrhythmogenic sources of AF

Characterization of complex fractionated atrial electrograms by sample entropy: An international multi-center study

Atrial fibrillation (AF) is the most commonly clinically-encountered arrhythmia. Catheter ablation of AF is mainly based on trigger elimination and modification of the AF substrate. Substrate mapping ablation of complex fractionated atrial electrograms (CFAEs) has emerged to be a promising technique. To improve substrate mapping based on CFAE analysis, automatic detection algorithms need to be developed in order to simplify and accelerate the ablation procedures. According to the latest studies, the level of fractionation has been shown to be promisingly well estimated from CFAE measured during radio frequency (RF) ablation of AF. The nature of CFAE is generally nonlinear and nonstationary, so the use of complexity measures is considered to be the appropriate technique for the analysis of AF records. This work proposes the use of sample entropy (SampEn), not only as a way to discern between non-fractionated and fractionated atrial electrograms (A-EGM), but also as a tool for characterizing the degree of A-EGM regularity, which is linked to changes in the AF substrate and to heart tissue damage. The use of SampEn combined with a blind parameter estimation optimization process enables the classification between CFAE and non-CFAE with statistical significance (p < 0:001), 0.89 area under the ROC, 86% specificity and 77% sensitivity over a mixed database of A-EGM combined from two independent CFAE signal databases, recorded during RF ablation of AF in two EU countries (542 signals in total). On the basis of the results obtained in this study, it can be suggested that the use of SampEn is suitable for real-time support during navigation of RF ablation of AF, as only 1.5 seconds of signal segments need to be analyzed

Mapping Technologies for Catheter Ablation of Atrial Fibrillation Beyond Pulmonary Vein Isolation

Catheter ablation remains the most effective and relatively minimally invasive therapy for rhythm control in patients with AF. Ablation has consistently shown a reduction of arrhythmia-related symptoms and significant improvement in patients’ quality of life compared with medical treatment. The ablation strategy relies on a well-established anatomical approach of effective pulmonary vein isolation. Additional anatomical targets have been reported with the aim of increasing procedure success in complex substrates. However, larger ablated areas with uncertainty of targeting relevant regions for AF initiation or maintenance are not exempt from the potential risk of complications and pro-arrhythmia. Recent developments in mapping tools and computational methods for advanced signal processing during AF have reported novel strategies to identify atrial regions associated with AF maintenance. These novel tools – although mainly limited to research series – represent a significant step forward towards the understanding of complex patterns of propagation during AF and the potential achievement of patient-tailored AF ablation strategies for the near future

Characterization of complex fractionated atrial electrograms by Sample Entropy: An international multi-center study

Atrial fibrillation (AF) is the most commonly clinically-encountered arrhythmia. Catheter ablation of AF is mainly based on trigger elimination and modification of the AF substrate. Substrate mapping ablation of complex fractionated atrial electrograms (CFAEs) has emerged to be a promising technique. To improve substrate mapping based on CFAE analysis, automatic detection algorithms need to be developed in order to simplify and accelerate the ablation procedures. According to the latest studies, the level of fractionation has been shown to be promisingly well estimated from CFAE measured during radio frequency (RF) ablation of AF. The nature of CFAE is generally nonlinear and nonstationary, so the use of complexity measures is considered to be the appropriate technique for the analysis of AF records. This work proposes the use of sample entropy (SampEn), not only as a way to discern between non-fractionated and fractionated atrial electrograms (A-EGM), but also as a tool for characterizing the degree of A-EGM regularity, which is linked to changes in the AF substrate and to heart tissue damage. The use of SampEn combined with a blind parameter estimation optimization process enables the classification between CFAE and non-CFAE with statistical significance (p < 0:001), 0.89 area under the ROC, 86% specificity and 77% sensitivity over a mixed database of A-EGM combined from two independent CFAE signal databases, recorded during RF ablation of AF in two EU countries (542 signals in total). On the basis of the results obtained in this study, it can be suggested that the use of SampEn is suitable for real-time support during navigation of RF ablation of AF, as only 1.5 seconds of signal segments need to be analyzed.This work has been supported by the Spanish Ministry of Science and Innovation, Research Project TEC 2009-14222, by the Ministry of Education Youth and Sports of the Czech Republic, the Grant Agency of the Czech Technical University in Prague No. SGS13/203/OHK3/3T/13 and by the Czech Science 300 Foundation post-doctoral GACR research project GACR #P103/11/P106.Cirugeda Roldán, EM.; 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(11):7493-7509. https://doi.org/10.3390/e17117493S749375091711Haïssaguerre, M., Jaïs, P., Shah, D. C., Takahashi, A., Hocini, M., Quiniou, G., … Clémenty, J. (1998). 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The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation

This work was supported by the projects TEC2010–20633 from the Spanish Ministry of Science and Innovation and PPII11–0194–8121 and PII1C09–0036–3237 from Junta de Comunidades de Castilla-La Mancha.Alcaraz Martínez, R.; Rieta Ibañez, JJ. (2013). The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation. En Atrial Fibrillation - Mechanisms and Treatment. InTech. 181-204. https://doi.org/10.5772/53407S18120