34 research outputs found

    The Relevance of Heart Rate Fluctuation When Evaluating Atrial Substrate Electrical Features in Catheter Ablation of Paroxysmal Atrial Fibrillation

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    [EN] Coronary sinus (CS) catheterization is critical during catheter ablation (CA) of atrial fibrillation (AF). However, the association of CS electrical activity with atrial substrate modification has been barely investigated and mostly limited to analyses during AF. In sinus rhythm (SR), atrial substrate modification is principally assessed at a global level through P-wave analysis. Cross-correlating CS electrograms (EGMs) and P-waves' features could potentiate the understanding of AF mechanisms. Five-minute surface lead II and bipolar CS recordings before, during, and after CA were acquired from 40 paroxysmal AF patients. Features related to duration, amplitude, and heart-rate variability of atrial activations were evaluated. Heart-rate adjustment (HRA) was applied. Correlations between each P-wave and CS local activation wave (LAW) feature were computed with cross-quadratic sample entropy (CQSE), Pearson correlation (PC), and linear regression (LR) with 10-fold cross-validation. The effect of CA between different ablation steps was compared with PC. Linear correlations: poor to mediocre before HRA for analysis at each P-wave/LAW (PC: max. +18.36%, p = 0.0017, LR: max. +5.33%, p = 0.0002) and comparison between two ablation steps (max. +54.07%, p = 0.0205). HRA significantly enhanced these relationships, especially in duration (P-wave/LAW: +43.82% to +69.91%, p < 0.0001 for PC and +18.97% to +47.25%, p < 0.0001 for LR, CA effect: +53.90% to +85.72%, p < 0.0210). CQSE reported negligent correlations (0.6-1.2). Direct analysis of CS features is unreliable to evaluate atrial substrate modification due to CA. HRA substantially solves this problem, potentiating correlation with P-wave features. Hence, its application is highly recommended.This research received partial financial support from public grants DPI2017-83952-C3, PID2021-00X128525-IV0, PID2021-123804OB-I00. and TED2021-129996B-I00 of the Spanish Government 10.13039/501100011033 jointly with the European Regional Development Fund (EU), SB-PLY/17/180501/000411 from Junta de Comunidades de Castilla-La Mancha. and AICO/2021/286 from Generalitat Valenciana.Vraka, A.; Moreno-Arribas, J.; Gracia-Baena, JM.; Hornero, F.; Alcaraz, R.; Rieta, JJ. (2022). The Relevance of Heart Rate Fluctuation When Evaluating Atrial Substrate Electrical Features in Catheter Ablation of Paroxysmal Atrial Fibrillation. Journal of Cardiovascular Development and Disease. 9(6):1-16. https://doi.org/10.3390/jcdd90601761169

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

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    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

    High-density mapping of the average complex interval helps localizing atrial fibrillation drivers and predicts catheter ablation outcomes

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    BackgroundPersistent Atrial Fibrillation (PersAF) electrogram-based ablation is complex, and appropriate identification of atrial substrate is critical. Little is known regarding the value of the Average Complex Interval (ACI) feature for PersAF ablation.ObjectiveUsing the evolution of AF complexity by sequentially computing AF dominant frequency (DF) along the ablation procedure, we sought to evaluate the value of ACI for discriminating active drivers (AD) from bystander zones (BZ), for predicting AF termination during ablation, and for predicting AF recurrence during follow-up.MethodsWe included PersAF patients undergoing radiofrequency catheter ablation by pulmonary vein isolation and ablation of atrial substrate identified by Spatiotemporal Dispersion or Complex Fractionated Atrial Electrograms (&gt;70% of recording). Operators were blinded to ACI measurement which was sought for each documented atrial substrate area. AF DF was measured by Independent Component Analysis on 1-minute 12-lead ECGs at baseline and after ablation of each atrial zone. AD were differentiated from BZ either by a significant decrease in DF (&gt;10%), or by AF termination. Arrhythmia recurrence was monitored during follow-up.ResultsWe analyzed 159 atrial areas (129 treated by radiofrequency during AF) in 29 patients. ACI was shorter in AD than BZ (76.4 ± 13.6 vs. 86.6 ± 20.3 ms; p = 0.0055), and mean ACI of all substrate zones was shorter in patients for whom radiofrequency failed to terminate AF [71.3 (67.5–77.8) vs. 82.4 (74.4–98.5) ms; p = 0.0126]. ACI predicted AD [AUC 0.728 (0.629–0.826)]. An ACI &lt; 70 ms was specific for predicting AD (Sp 0.831, Se 0.526), whereas areas with an ACI &gt; 100 ms had almost no chances of being active in AF maintenance. AF recurrence was associated with more ACI zones with identical shortest value [3.5 (3–4) vs. 1 (0–1) zones; p = 0.021]. In multivariate analysis, ACI &lt; 70 ms predicted AD [OR = 4.02 (1.49–10.84), p = 0.006] and mean ACI &gt; 75 ms predicted AF termination [OR = 9.94 (1.14–86.7), p = 0.038].ConclusionACI helps in identifying AF drivers, and is correlated with AF termination and AF recurrence during follow-up. It can help in establishing an ablation plan, by prioritizing ablation from the shortest to the longest ACI zone

    Uncovering Atrial Fibrillation Complexity: From signals to (bio)markers

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    Confiabilidad de las Ondas de Activación Local para Evaluar el Sustrato Auricular de Pacientes con Fibrilación Auricular Paroxística

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    [ES] El análisis de electrogramas (EGMs) del seno coronario (SC) durante la ablación por catérer (AC) de fibrilación auricular (FA) es clave para la evaluación del sustrato auricular. No obstante, los canales del catéter de registro suelen verse afectados por mal contacto y por el movimiento cardíaco. Este trabajo estudia los canales más fiables para preservar las dinámicas de la FA durante el ritmo sinusal (RS). Se han empleado 44 registros bipolares multicanal del SC de 60-300 segundos de 28 pacientes con FA paroxística sometidos a AC. Cada registro contenía cinco canales: distal, medio-distal, medio, medio-proximal, proximal. En cada canal se calcularon características de las ondas de activación local (OALs): duración, área y correlación entre morfologías dominantes. Se han utilizado los tests de KruskalWallis, Mann-Whitney y Mann-Whitney con corrección de Bonferroni para la comparación multicanal, por pares y uno frente a los demás, respectivamente. El canal distal presentó resultados menos fiables, con OALs de duración larga (p = 0,047), amplitud baja (pmax < 0,003) y menos área (pmax < 0,020) y con correlación entre sus OALs y las OALs del canal proximal relativamente baja (85,57 %). Las OALs entre los canales medio y medio-próximal fueron más consistentes, con correlación entre sus OALs muy altas (95,02 %), presentando además duración más corta (p = 0,084) y amplitud (pmax < 0,050) y áreas mayores (pmax < 0,070). En consecuencia, los canales medios y medio-proximales son más robustos, preservando al máximo las dinámicas de la FA, por ello se aconseja su empleo para evaluar el sustrato auricular de pacientes con FA durante el RS.Trabajo cofinanciado por los proyectos de investigación competitiva DPI2017-83952-C3 de MINECO-AEIFEDER-UE, SBPLY/17/180501/000411 de la JCCLM y AICO/2019/036 de la GVA.Vraka, A.; Hornero Sos, F.; Bertomeu-González, V.; Osca Asensi, J.; Alcaraz Martínez, R.; Rieta, JJ. (2020). Confiabilidad de las Ondas de Activación Local para Evaluar el Sustrato Auricular de Pacientes con Fibrilación Auricular Paroxística. Sociedad Española de Ingeniería Biomédica. 430-433. http://hdl.handle.net/10251/178274S43043

    Statistical and Graph-Based Signal Processing: Fundamental Results and Application to Cardiac Electrophysiology

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    The goal of cardiac electrophysiology is to obtain information about the mechanism, function, and performance of the electrical activities of the heart, the identification of deviation from normal pattern and the design of treatments. Offering a better insight into cardiac arrhythmias comprehension and management, signal processing can help the physician to enhance the treatment strategies, in particular in case of atrial fibrillation (AF), a very common atrial arrhythmia which is associated to significant morbidities, such as increased risk of mortality, heart failure, and thromboembolic events. Catheter ablation of AF is a therapeutic technique which uses radiofrequency energy to destroy atrial tissue involved in the arrhythmia sustenance, typically aiming at the electrical disconnection of the of the pulmonary veins triggers. However, recurrence rate is still very high, showing that the very complex and heterogeneous nature of AF still represents a challenging problem. Leveraging the tools of non-stationary and statistical signal processing, the first part of our work has a twofold focus: firstly, we compare the performance of two different ablation technologies, based on contact force sensing or remote magnetic controlled, using signal-based criteria as surrogates for lesion assessment. Furthermore, we investigate the role of ablation parameters in lesion formation using the late-gadolinium enhanced magnetic resonance imaging. Secondly, we hypothesized that in human atria the frequency content of the bipolar signal is directly related to the local conduction velocity (CV), a key parameter characterizing the substrate abnormality and influencing atrial arrhythmias. Comparing the degree of spectral compression among signals recorded at different points of the endocardial surface in response to decreasing pacing rate, our experimental data demonstrate a significant correlation between CV and the corresponding spectral centroids. However, complex spatio-temporal propagation pattern characterizing AF spurred the need for new signals acquisition and processing methods. Multi-electrode catheters allow whole-chamber panoramic mapping of electrical activity but produce an amount of data which need to be preprocessed and analyzed to provide clinically relevant support to the physician. Graph signal processing has shown its potential on a variety of applications involving high-dimensional data on irregular domains and complex network. Nevertheless, though state-of-the-art graph-based methods have been successful for many tasks, so far they predominantly ignore the time-dimension of data. To address this shortcoming, in the second part of this dissertation, we put forth a Time-Vertex Signal Processing Framework, as a particular case of the multi-dimensional graph signal processing. Linking together the time-domain signal processing techniques with the tools of GSP, the Time-Vertex Signal Processing facilitates the analysis of graph structured data which also evolve in time. We motivate our framework leveraging the notion of partial differential equations on graphs. We introduce joint operators, such as time-vertex localization and we present a novel approach to significantly improve the accuracy of fast joint filtering. We also illustrate how to build time-vertex dictionaries, providing conditions for efficient invertibility and examples of constructions. The experimental results on a variety of datasets suggest that the proposed tools can bring significant benefits in various signal processing and learning tasks involving time-series on graphs. We close the gap between the two parts illustrating the application of graph and time-vertex signal processing to the challenging case of multi-channels intracardiac signals

    New Perspective in Atrial Fibrillation

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    In spite of the large volume of associated research, the pathophysiological mechanisms involved in atrial fibrillation (AF) onset and recurrence remain uncertain. This may explain why the performances of thromboembolic and bleeding prediction scores in AF patients are limited. In the past few years, the concept of atrial cardiopathy has emerged as a promising lead to connect AF to stroke, heart failure, and inflammatory processes: indeed, all of the mechanisms associated with atrial remodeling and the development of atrial cardiopathy are also likely to promote the development of AF. This recent concept of atrial cardiopathy suggests that the real trigger of stroke may be an abnormal atrial substrate rather than atrial rhythm itself. In this setting, AF could be seen as a symptom of atrial cardiopathy rather than a risk factor of stroke. In the absence of validated clinical markers of atrial cardiopathy, the search for the mechanism of AF remains the cornerstone of cardioembolic stroke prevention for now.The aim of this Special Issue is to gather basic research as well as pathophysiological and epidemiological papers focused on the relationship between atrial substrates and atrial fibrillation onset, recurrence, and outcomes

    Spatial Characterization and Estimation of Intracardiac Propagation Patterns During Atrial Fibrillation

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    This doctoral thesis is in the field of biomedical signal processing with focus on methods for the analysis of atrial fibrillation (AF). Paper I of the present thesis addresses the challenge of extracting spatial properties of AF from body surface signals. Different parameters are extracted to estimate the preferred direction of atrial activation and the complexity of the atrial activation pattern. In addition, the relation of the spatial properties to AF organization, which is quantified by AF frequency, is evaluated. While no significant correlation between the preferred direction of atrial activation and AF frequency could be observed, the complexity of the atrial activation pattern was found to increase with AF frequency. The remaining three papers deal with the analysis of the propagation of the electrical activity in the atria during AF based on intracardiac signals. In Paper II, a time-domain method to quantify propagation patterns along a linear catheter based on the detected atrial activation times is developed. Taking aspects on intra-atrial signal organization into account, the detected activation times are combined into wavefronts, and parameters related to the consistency of the wavefronts over time and the activation order along the catheter are extracted. Furthermore, the potential relationship of the extracted parameters to established measures from body surface signals is investigated. While the degree of wavefront consistency was not reflected by the applied body surface measures, AF frequency could distinguish between recordings with different degrees of intra-atrial signal organization. This supports the role of AF frequency as an organization measure of AF. In Paper III, a novel method to analyze intracardiac propagation patterns based on causality analysis in the frequency domain is introduced. In particular, the approach is based on the partial directed coherence (PDC), which evaluates directional coupling between multiple signals in the frequency domain. The potential of the method is illustrated with simulation scenarios based on a detailed ionic model of the human atrial cell as well as with real data recordings, selected to present typical propagation mechanisms and recording situations in atrial tachyarrhythmias. For simulated data, the PDC is correctly reflecting the direction of coupling and thus the propagation between all recording sites. For real data, clear propagation patterns are identified which agree with previous clinical observations. Thus, the results illustrate the ability of the novel approach to identify propagation patterns from intracardiac signals during AF which can provide important information about the underlying AF mechanisms, potentially improving the planning and outcome of ablation. However, spurious couplings over long distances can be observed when analyzing real data comprised by a large number of simultaneously recorded signals, which gives room for further improvement of the method. The derivation of the PDC is entirely based on the fit of a multivariate autoregressive (MVAR) model, commonly estimated by the least-squares (LS) method. In Paper IV, the adaptive group least absolute selection and shrinkage operator (LASSO) is introduced in order to avoid overfitting of the MVAR model and to incorporate prior information such as sparsity of the solution. The sparsity can be motivated by the observation that direct couplings over longer distances are likely to be zero during AF; an information which has been further incorporated by proposing distance-adaptive group LASSO. In simulations, adaptive and distance-adaptive group LASSO are found to be superior to LS estimation in terms of both detection and estimation accuracy. In addition, the results of both simulations and real data analysis indicate that further improvements can be achieved when the distance between the recording sites is known or can be estimated. This further promotes the PDC as a method for analysis of AF propagation patterns, which may contribute to a better understanding of AF mechanisms as well as improved AF treatment
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