data processing techniques for the characterization of ...

DATA PROCESSING TECHNIQUES FOR THE CHARACTERIZATION OF ATRIAL FIBRILLATION

THÈSE No 3982 (2007) PRÉSENTÉE À LA FACULTÉ SCIENCES ET TECHNIQUES DE L’INGÉNIEUR Institut de traitement des signaux SECTION D’ÉLECTRICITÉ

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L’OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES

PAR

Mathieu LEMAY ingénieur électricien diplômé Université Laval, Canada de nationalité canadienne

proposée au jury: Prof. Hasler Martin, président du jury Dr. Vesin Jean-Marc, directeur de thèse Prof. Kappenberger Lukas, rapporteur Prof. Aminian Kamiar, rapporteur Prof. Sergio Cerutti, rapporteur

Lausanne, EPFL 2007

Abstract Atrial fibrillation is the most common sustained cardiac rhythm disturbance, increasing in prevalence with age. During the past 20 years, there has been a 66% increase in hospital admissions related to atrial fibrillation. Neither the natural history of atrial fibrillation nor its response to therapy is sufficiently predictable from clinical and echocardiographic parameters. Treatment of atrial fibrillation is mainly based on trial and error. Thus, it seems appropriate to develop tests that quantify the state of the disease and guide its management. Standard 12-lead electrocardiogram recordings are commonly required for clinical evaluation. Therefore, possible prognostic information contained within the electrocardiogram provide a great interest. The goal of this thesis is to help clinicians treat atrial fibrillation by developing information from the standard 12-lead electrocardiogram on atrial fibrillation substrates, dynamics, and to predict the success of different treatments. Due to the much higher ventricular activity amplitude, the characterization of atrial fibrillation based on surface electrocardiogram signals requires that the ventricular activity first be cancelled. Average beat subtraction and independent component analysis algorithms are the most frequently used techniques in atrial activity extraction. To solve this problem with the best quality results, five different techniques were studied and compared in the first part of this thesis : the use of two different independent component analysis algorithms, a refined version of the average beat subtraction technique, a novel technique that treats each cardiac cycle in an independent manner, and a novel approach based on the use of atom dictionaries dedicated to atrial and ventricular activities. The performance of these five techniques was evaluated by using simulated and clinical electrocardiogram signals. The simulated signals were created by using models of the atria and the thorax. The refined version of the average beat subtraction technique and the technique that treats each cardiac cycle outperformed the other ones and produced high quality results on all leads. Their main advantage lies in the treatment of the ventricular depolarization and repolarization waves in an independent manner. The second part of this thesis aims at exploring the potential of the "clean" atrial electrocardiogram signals. So far, the complexity of the electrical atrial activity during atrial fibrillation has mainly been assessed through the analysis of the frequency spectrum or of the time-frequency analysis (spectrogram) of the electrocardiogram signal of lead V1. We propose three different approaches to characterize the atrial fibrillation that exploit the information of multiple leads in various and independent manners. Each of them considers different features that require different signal processing techniques. iii

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The first approach is based on clinician’s observations on electrocardiograms, to characterize the disorganization of fibrillatory waves. We developed the processing tools to quantify these observations. Based on these clinical features, we were able to predict self-termination of atrial fibrillation with a high accuracy. We also observed an interesting correlation between the increase in the percentage of atrial fibrillations identified as non-terminating and the increase in atrial fibrillation duration. The second approach is based on dominant frequencies observed on multiple electrocardiogram signals. Firstly, two simulated cases were analyzed to understand the correspondence between the dominant frequencies observed on the thorax and the atrial fibrillation dynamics. We observed that multiple lead signals yield more information than a single lead in terms of atrial fibrillation dynamic and that lead V1 and V5 were good candidates for the observation of the left and right atrial dynamics, respectively. In order to obtain accurate dominant frequency estimation on clinical signals that contain ventricular artifacts, a recently introduced signal processing technique was tested. We observed a positive left-to-right dominant frequency gradient preference in the overall atrial fibrillations when a negative gradient preference was to be expected based on other invasive studies. These dominant frequency features also permitted us to obtain a good prediction of the response to pharmacological cardioversion attempts. Our third approach was to extract spatial information from the dipole estimated from body surface potentials. This dipole provides a global representation of the electrical atrial activity. Then, features were used to express the complexity of the atrial fibrillation dynamics. This analysis extracted spatial information that was generally lacking in typical non-invasive atrial fibrillation studies. We observed discrimination between atrial fibrillations with both single and recurrent episodes, characterized by modal and uniform dipole distributions, respectively. This discrimination could link the different atrial fibrillation types to the electrical, contractile, and structural remodelings. This approach permitted us to identify and localize stable and single atrial activity sources in the simulations. We hypothesize that this approach, together with patient’s anatomical data, could have the power to help clinicians in ablation procedures ; by helping them to predict where ablation lines can be effective.

KEYWORDS : Atrial fibrillation, Ventricular Activity Cancellation, Electrocardiogram, Vectorcardiogram, Dominant Frequency, Classification.

Résumé La fibrillation auriculaire est l’arythmie cardiaque soutenue la plus commune. Le risque de développer une telle arythmie augmente avec l’âge. Durant les 20 dernières années, il y a eu une augmentation de 66% des admissions à l’hôpital due à la fibrillation auriculaire. Actuellement, ni l’historique de la maladie ni la réponse du patient à la thérapie ne sont suffisamment prévisibles par des paramètres cliniques et échocardiographiques. Le traitement de la fibrillation auriculaire est donc principalement basé sur l’essai et l’erreur. Ainsi, il semble approprié de développer des outils nécessaires pour déterminer l’état de la maladie et guider sa gestion. Des enregistrements d’électrocardiogramme à 12 dérivations sont généralement utilisés pour l’évaluation clinique. Par conséquent, l’information contenue dans l’électrocardiogramme présente beaucoup d’intérêt. Le but de cette thèse est d’aider les cliniciens à traiter la fibrillation auriculaire en utilisant l’information contenue dans l’électrocardiogramme pour distinguer les différents substrats, les dynamiques sousjacentes, et prédire la réponse aux différents traitements. La caractérisation de la fibrillation auriculaire basée sur l’électrocardiogramme exige que l’activité ventriculaire soit supprimée due à sa forte amplitude. Les techniques basées sur la soustraction de battements moyennés et sur les algorithmes d’analyse en composantes indépendantes sont les plus utilisées pour l’extraction de l’activité auriculaire. Afin d’obtenir les meilleurs résultats possibles, cinq techniques ont été étudiées et comparées : deux algorithmes d’analyse en composantes indépendantes, une version raffinée de la soustraction de battements moyennés, une nouvelle technique traitant chaque cycle cardiaque de façon indépendante, et une nouvelle approche basée sur l’utilisation de dictionnaires d’atome consacrés aux activités auriculaire et ventriculaire. Les performances de ces cinq techniques ont été évaluées sur des signaux simulés et cliniques. Les signaux simulés ont été créés en employant des modèles numériques d’oreillettes et de thorax. La version raffinée de la soustraction de battements moyennés et la technique traitant chaque cycle cardiaque ont surpassé les autres techniques étudiées et ont produit de bons résultats sur les différentes dérivations. L’avantage de ces deux techniques réside dans le traitement indépendant de la dépolarisation et repolarisation ventriculaire. La deuxième partie de cette thèse vise à explorer le potentiel de ces signaux "nettoyés" de toute activité ventriculaire. Jusqu’ici, la caractérisation de l’activité électrique des oreillettes pendant la fibrillation auriculaire était principalement évaluée par l’analyse du spectre fréquentiel ou par l’analyse temps-fréquence (spectrogramme) du signal de l’électrode V1. Nous proposons trois nouvelles approches pour caractériser cette fibrillation auriculaire. Ces approches exploitent l’information v

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de plusieurs électrodes de façons diverses et indépendantes. Chacune d’elles considère différentes propriétés qui nécessitent différentes techniques de traitement des signaux. La première approche est basée sur les observations des électrocardiogrammes faites par le clinicien. Elles caractérisent la désorganisation des ondes de fibrillation. Nous avons développé des outils de traitement afin de quantifier ces observations. En se basant sur ces propriétés cliniques, nous avons pu prévoir l’auto-cardioversion de la fibrillation auriculaire avec une grande exactitude. Nous avons également observé une corrélation intéressante entre l’augmentation du pourcentage de fibrillations auriculaires identifiées comme soutenues et l’augmentation de la durée de fibrillation auriculaire. La deuxième approche est basée sur l’observation des fréquences dominantes de plusieurs signaux d’électrocardiogramme. Premièrement, deux cas simulés ont été analysés pour comprendre la correspondance entre les fréquences dominantes observées sur le thorax et la dynamique de fibrillation auriculaire. Pour l’analyse de la dynamique de la fibrillation auriculaire, nous avons observé que l’utilisation de plusieurs électrodes fournit plus d’information sur la dynamique que l’utilisation d’une seule électrode. Nous avons aussi observé que les électrodes V1 et V5 sont respectivement de bonnes candidates pour l’observation de cette dynamique dans les oreillettes gauche et droite. Afin d’avoir une évaluation précise des fréquences dominantes sur les signaux cliniques contenant de l’activité ventriculaire, nous proposons une technique récemment publiée. Nous avons remarqué que dans la plupart des cas, la fréquence dominante observée sur l’électrode V1 est plus élevée que celle observée sur l’électrode V5, contrairement à ce qui était attendu. Cette prévision était basée sur les études intracardiaques montrant de plus grandes valeurs pour l’oreillette gauche. Ces estimations de fréquence dominante ont également permis d’obtenir de bonnes prévisions de la réponse aux tentatives pharmacologiques de cardioversion. Notre troisième approche consiste à extraire l’information spatiale du dipôle estimé à partir des électrocardiogrammes à 12 dérivations. Ce dipôle fournit une représentation globale de l’activité électrique des oreillettes. Ensuite, nous avons employé certaines caractéristiques pour exprimer la complexité de la dynamique de la fibrillation auriculaire. Ces caractéristiques contiennent de l’information spatiale qui manque généralement aux études extracardiaques classiques. Nous avons observé une discrimination entre les patients avec des épisodes de fibrillation auriculaire uniques ou récurrents. Ceux-ci étant respectivement caractérisés par des distributions modales ou uniformes du dipôle. Cette discrimination pourrait relier les différents types de fibrillation auriculaire aux différents remodelages électriques, contractiles, et structurels. Ces caractéristiques nous ont également permis d’identifier et de localiser la source stable et unique de la fibrillation auriculaire dans les simulations. Nous pensons que cette approche, avec les données anatomiques des patients, pourrait aider les cliniciens lors des procédures d’ablation, en les aidant principalement à prévoir où les lignes d’ablation pourraient être efficaces.

MOTS-CLÉS : Fibrillation auriculaire, Suppression de l’activité ventriculaire, Electrocardiogramme, Vectocardiogramme, Fréquence Dominante, Classification.

Remerciements Ce travail est dû à une grande collaboration. Je souhaite donc remercier sincèrement toutes les personnes qui ont participé à la réussite de ce projet : – Je tiens tout d’abord à remercier Prof. Lukas Kappenberger pour son enthousiasme pour la recherche. Il a toujours su créer une atmosphère positive au sein du Lausanne Heart Group. Pour cela et pour votre confiance envers les ingénieurs, je vous remercie. – Je tiens aussi à remercier Prof. Murat Kunt pour m’avoir accueilli dans son laboratoire qui fournit un environnement international et multiculturel propice à la recherche et à l’innovation. – Un grand merci au président de jury, Prof. Martin Hasler, et au rapporteurs, Prof. Kamian Aminian et Prof. Sergio Cerruti. Si tous les doctorants pouvaient profiter de la même ambiance que vous avez créer pour ma soutenance de thèse . . . – Je voudrais aussi souligner l’apport important du Prof. Adriaan van Oosterom à ce travail. Je n’aurais jamais cru rencontrer quelqu’un d’aussi passionné par la recherche. Pour cela, je vous dit un sincère MERCI et un gros BRAVO ! – Les connaissances et le beau modèle des oreillettes du célèbre Dr. Vincent Jacquemet m’ont également aidé au cours des dernières années. C’est encore plus apprécié venant d’un ami. Merci Vincent ! – Merci à Lam Dang et Zenichi Ihara pour l’ambiance de travail. J’espère un jour être votre "vrai" ami. – Un gros merci à Andrei Forclaz qui a su être disponible pour mes questions d’ordre médical et pour ces idées et critiques positives envers mes recherches. – Toutes les observations faites durant ces dernières années n’auraient pu exister sans données cliniques, donc sans Véronique Prudent. Merci aussi pour ta gentillesse. – Si la qualité d’anglais de cette thèse est si "remarcable", cela est dû principalement a trois personnes : Dan Jurca, Judith van Oosterom et Peter Berlin. For this, I’m really grateful. – Merci au gros cave Prudat qui a osé être mon partenaire de bureau, mon collègue de travail et surtout mon souffre douleur. Yann, il y a encore plusieurs personnes qui ne croient pas qu’on est pu écrire un papier ensemble. Dire que tu étais sympathique avant de me rencontrer. – Merci aussi à la première et peut-être seule personne qui a insisté pour être dans le même bureau que moi : j’ai nommé Dr. Dragana Viceic. Un gros bisou ! – Je voudrais remercie un ami et un gros "bosseur", Sébastien Granges. Merci pour ta détection, vii

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merci pour ta cancellation et merci pour tes fondues aux tomates :-) Merci à tous les membres de l’ITS pour l’agréable ambiance de travail et pour les activitées extra-professionelles. Saluons également la bonne humeur de notre aimable assistance logistique et administrative : Marianne Marion et Gilles Auric. Un petit clin d’oeil aux amis de Québec, spécialement à Eric Le Gallais et Philippe Guay, qui ne m’ont pas oubliés malgré la distance. Une grosse pensée à ma famille, Raymond (papa), Monique (manan), Roch et Guillaume. Je suis loin mais je vous aime ! ! ! Un merci spécial à Mattia Bertschi pour avoir été le premier à m’inviter dans les Jean-Marc Boys. Je t’en serez toujours reconnaissant. Un très très gros remerciement au dernier et non le moindre : Jean-Marc. Je ne pensais pas qu’un directeur de thèse pourrait devenir un ami aussi fidèle que toi. S’il y a une personne dont j’aimerais qu’elle soit fière de mon travail, c’est bien toi. Merci pour les idées, merci pour les soirées, merci pour les bons moments de rire, MERCI POUR TOUT ! ! !

Contents

1 Introduction 1.1 Motivation and problem statement . . . . . . . . . . . . . . . . . . . 1.1.1 Atrial fibrillation and its clinical importance . . . . . . . . . . 1.1.2 Atrial fibrillation as observed in the surface electrocardiogram 1.1.3 Factors promoting atrial fibrillation . . . . . . . . . . . . . . 1.1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Organization of the dissertation . . . . . . . . . . . . . . . . . . . . . 1.3 Original contributions . . . . . . . . . . . . . . . . . . . . . . . . . .

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I Electrocardiogram processing

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2 Cardiac arrhythmias: definition, clinical aspect and electrocardiogram signals 2.1 Bioelectricity of the heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Cardiac arrhythmias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Atrial flutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Atrial fibrillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Aetiologies and factors predisposing patients to atrial fibrillation . . . 2.2.4 Pathophysiological mechanisms of atrial fibrillation . . . . . . . . . . 2.2.5 Clinical evaluation and management . . . . . . . . . . . . . . . . . . 2.3 Clinical electrocardiogram signals . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Body surface potentials and electrocardiogram . . . . . . . . . . . . 2.3.2 Clinical 5-minute 12-lead electrocardiogram database . . . . . . . . . 2.4 Simulated electrocardiogram signals . . . . . . . . . . . . . . . . . . . . . . 2.4.1 A biophysical model of the human atria . . . . . . . . . . . . . . . . 2.4.2 Computation of body surface potentials . . . . . . . . . . . . . . . . 2.4.3 Simulated 5-minute 12-lead electrocardiogram database . . . . . . .

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3 Electrocardiogram processing 3.1 Fiducial point detection and baseline correction . . . . . . . . . . . . . . . . . . . 3.2 Suppression of ventricular activity in the electrocardiogram based on independent component analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

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3.2.1 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 3.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suppression of ventricular activity in the electrocardiogram based on average beat subtraction or single beats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Cancellation technique based on average beat subtraction . . . . . . . . . . 3.3.2 Cancellation technique applicable to single beats . . . . . . . . . . . . . . 3.3.3 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 3.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suppression of ventricular activity in the electrocardiogram based on sparse electrocardiogram signal decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Undetermined sparse source separation . . . . . . . . . . . . . . . . . . . 3.4.2 Electrocardiogram component separation . . . . . . . . . . . . . . . . . . 3.4.3 Electrocardiogram sparse decomposition by weighted orthogonal matching pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 3.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Postprocessing using empirical mode decomposition . . . . . . . . . . . . . . . . 3.5.1 Empirical mode decomposition . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 3.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

II Atrial fibrillation classification 4 Atrial fibrillation classification based on clinical features extracted from cardiogram 4.1 The Computers in Cardiology 2004 Challenge . . . . . . . . . . . . . . 4.2 Clinical feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Fibrillatory wave dissymmetry . . . . . . . . . . . . . . . . . . 4.2.2 R-R intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Fibrillatory wave intervals . . . . . . . . . . . . . . . . . . . . 4.2.4 Atrial activity amplitude . . . . . . . . . . . . . . . . . . . . . 4.2.5 Low-frequency modulation of atrial activity amplitude . . . . . 4.2.6 Similarities between atrial activities in different leads . . . . . . 4.2.7 High-frequency power in atrial activity segments . . . . . . . . 4.3 Overview of support vector machine classification . . . . . . . . . . . . 4.3.1 Classification procedure . . . . . . . . . . . . . . . . . . . . . 4.4 Statistical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Results on the Computers in Cardiology 2004 Challenge database . . .

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Atrial fibrillation classification based on clinical features 4.6.1 Modifications of the clinical feature extraction . 4.6.2 Results on simulated and clinical data . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . .

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5 Atrial fibrillation classification based on dominant frequencies extracted from the electrocardiogram 5.1 Mean firing rate of atrial fibrillation as estimated from the electrocardiogram . . . . 5.1.1 Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Results from the two selected simulated atrial fibrillations . . . . . . . . . 5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Dominant frequencies estimated trough phase-rectified signal averaging . . . . . . 5.2.1 Overview of phase-rectified signal averaging . . . . . . . . . . . . . . . . 5.2.2 Theoretical derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 5.2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Atrial fibrillation classification based on dominant frequencies . . . . . . . . . . . 5.3.1 Classification procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Results on simulated and clinical data . . . . . . . . . . . . . . . . . . . . 5.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Atrial fibrillation classification based on spatial dynamics extracted from the vectorcardiogram 97 6.1 The vectorcardiogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.1.1 Displaying vector data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1.2 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2 Results on simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.2.1 Results from the dipole distribution analysis . . . . . . . . . . . . . . . . . 103 6.2.2 Results from the dipole cluster analysis . . . . . . . . . . . . . . . . . . . 105 6.3 Atrial fibrillation classification based on the spatial vectorcardiogram features . . . 107 6.3.1 Classification procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.3.2 Results from the dipole distribution analysis . . . . . . . . . . . . . . . . . 108 6.3.3 Results from the dipole cluster analysis . . . . . . . . . . . . . . . . . . . 110 6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7 Conclusion 115 7.1 Summary of achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

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List of acronyms Acronyms

AA ABS AF AFL AV DF ECG EMD ICA IIR IMF MANOVA MSE OMP PRSA PSD PCA SVD RMS SA SR SVM VA VCG

Atrial activity Average beat subtraction Atrial fibrillation Atrial flutter Atrioventricular Dominant frequency Electrocardiogram Empirical mode decomposition Independent component analysis Infinite impulse response Intrinsic mode function Multivariate analysis of variance Mean squared error Orthogonal Matching Pursuits Phase-rectified signal averaging Power spectral density Principal component analysis Singular value decomposition Root mean square Sinoatrial Sinus rhythm Support vector machine Ventricular activity Vectorcardiogram

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List of Figures 1.1

Electrocardiogram signals during sinus rhythm and atrial fibrillation . . . . . . . .

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11

Exterior and interior structures of the heart . . . . . . . . . . . . . . . . . . . Blood flow in the heart and its electrical system . . . . . . . . . . . . . . . . Action potential propagation . . . . . . . . . . . . . . . . . . . . . . . . . . Patterns of atrial fibrillation . . . . . . . . . . . . . . . . . . . . . . . . . . . Feedback-loops of atrial remodeling on atrial fibrillation . . . . . . . . . . . Positions of electrodes used in a standard 12-lead electrocardiogram . . . . . Schematic representation of normal electrocardiogram . . . . . . . . . . . . Geometry of the atria and compartmental torso models . . . . . . . . . . . . Distribution of heterogeneities on the atrial tissue . . . . . . . . . . . . . . . Different rapid pacing locations on the atria . . . . . . . . . . . . . . . . . . Twelve examples of the atrial activity dynamics obtained from the simulations

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7 8 9 10 12 13 14 15 16 16 17

3.1 3.2 3.3

Fiducial point definition on the root mean squared signal . . . . . . . . . . . . . . Baseline correction and filtering example . . . . . . . . . . . . . . . . . . . . . . Example of ventricular cancellation on simulated electrocardiogram signal using two independent component analysis techniques . . . . . . . . . . . . . . . . . . . Example of ventricular cancellation on clinical electrocardiogram signal using two independent component analysis techniques . . . . . . . . . . . . . . . . . . . . . Flowchart of the refined average beat subtraction technique . . . . . . . . . . . . . Flowchart of the single beat technique . . . . . . . . . . . . . . . . . . . . . . . . T and U wave cancellation using a dominant wave approach . . . . . . . . . . . . Estimation of the atrial activity located in the QRS intervals . . . . . . . . . . . . . Example of ventricular activity cancellation on simulated electrocardiogram signal using refined averaged beat subtraction technique . . . . . . . . . . . . . . . . . . Example of ventricular activity cancellation on clinical electrocardiogram signal using refined average beat subtraction and single beat techniques . . . . . . . . . . Generalized Gaussian functions used to approximate the ventricular activity . . . . Gabor functions used to approximate the atrial activity . . . . . . . . . . . . . . . Example of the ventricular and atrial activity estimations through sparse signal decompositions on simulated electrocardiogram signal . . . . . . . . . . . . . . . . .

22 24

3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13

xv

. . . . . . . . . . .

. . . . . . . . . . .

2

30 31 34 36 38 39 41 42 47 47 50

xvi

L IST OF F IGURES

3.14 Example of the ventricular and atrial activity estimations through sparse signal decompositions on clinical electrocardiogram signal . . . . . . . . . . . . . . . . . . 3.15 Physical interpretation of instantaneous frequency . . . . . . . . . . . . . . . . . . 3.16 Clinical signal example with ventricular artifacts and its first intrinsic mode function 3.17 Clinical postprocessing result example obtained with the empirical mode decomposition based technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of fibrillatory wave dissymmetry . . . . . . . . . . . . Example of fibrillatory wave intervals . . . . . . . . . . . . . . Example of low-frequency modulation of atrial amplitude . . . . Example of similarities between atrial activities in different leads Optimal support vector machine separating hyperplane examples

. . . . .

63 64 65 66 67

5.1 5.2 5.3 5.4

The simulation no.3 time courses of V1 signal and its closest membrane potential . Estimated power spectral densities of simulation no.3 lead V1 and V5 signals . . . The simulation no.4 time courses of V1 signal and its closest membrane potential . Estimated power spectral densities of simulation no.4 lead V1 and V5 signals on interval #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimated power spectral densities of simulation no.4 lead V1 and V5 signals on interval #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Different simulated firing rate (atria) and dominant frequency (torso) maps . . . . . Principal of phase-rectified signal averaging . . . . . . . . . . . . . . . . . . . . . Phase-rectified signal averaging example applied to a synthetic signal composed of a sinusoid corrupted by additive impulsive noise . . . . . . . . . . . . . . . . . . . Phase-rectified signal averaging example applied to a synthetic signal composed of a sinusoid corrupted by intermittent, large sinusoids at various frequencies . . . . . Definition of the different variables for the phase-rectified signal averaging theoretical derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Histograms of clinical dominant frequency estimates on all leads . . . . . . . . . . Histograms of clinical dominant frequency estimates on lead V1 . . . . . . . . . . Histograms of clinical dominant frequency estimates on lead V5 . . . . . . . . . . Phase-rectified signal averaging results on clinical example . . . . . . . . . . . . .

77 78 78

5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

57

4.1 4.2 4.3 4.4 4.5

5.5

. . . . .

51 53 55

79 79 80 81 82 83 84 88 88 89 89

The unit sphere with the major anatomical details projected onto it . . . . . . . . . 100 Examples of the three types of vectorcardiogram displays . . . . . . . . . . . . . . 101 The three extreme distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Example of the time course of the normalized dipole during atrial fibrillation . . . . 102 Normalized vectorcardiograms for sinus rhythm, atrial flutter and atrial fibrillations 103 Time courses of the equivalent dipole and its estimate derived from the 12-lead electrocardiogram of the simulated atrial flutter . . . . . . . . . . . . . . . . . . . 104 Estimated vectorcardiogram distributions for 12 different simulated atrial fibrillations105 Vectorcardiogram spatial complexities for simulated sinus rhythm, atrial flutter and 20 atrial fibrillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

L IST OF F IGURES

6.9 6.10 6.11 6.12

xvii

Clinical results from the dipole distribution analysis on sinus rhythm and atrial flutter108 Clinical results from the dipole distribution analysis on atrial fibrillations . . . . . . 109 Fixed pulmonary vein area represented on the sphere . . . . . . . . . . . . . . . . 111 Histogram of the number of segments in which an atrial fibrillation source was considered as being present in the pulmonary vein area . . . . . . . . . . . . . . . 112

xviii

L IST OF F IGURES

List of Tables 2.1

Documentation on the simulated atrial activities. . . . . . . . . . . . . . . . . . . .

19

3.1

Batch algorithm for blind source separation via the extended maximum-likelihood estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

3.2

Estimation of the marginal densities by look-up table . . . . . . . . . . . . . . . .

28

3.3

Comparison of the QRS complex cancellation for two independent component analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

Comparison of the JQ interval cancellation for two independent component analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.5

Significant QRS residue results for two independent component analysis techniques

31

3.6

Normalized weights obtained using the extended maximum-likelihood-based technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

3.7

Normalized weights obtained using the adaptive look-up table-based technique . .

33

3.8

Spatial optimization of the QRS templates . . . . . . . . . . . . . . . . . . . . . .

35

3.9

Comparison of the QRS complex cancellation for refined average beat subtraction and single beat techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3.10 Comparison of the JQ interval cancellation for refined average beat subtraction and single beat techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3.11 Significant QRS residue results for refined average beat subtraction and single beat techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

3.12 Processing steps of the weighted orthogonal matching pursuit procedure . . . . . .

49

3.13 Performance of the ventricular and atrial activity estimations through sparse signal decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

3.14 Batch algorithm for intrinsic mode functions . . . . . . . . . . . . . . . . . . . . .

54

3.15 Batch algorithm for postprocessing based on empirical mode decomposition . . . .

54

3.4

3.16 Simulated performance of the postprocessing based on empirical mode decomposition 56 3.17 Clinical performance of postprocessing based on empirical mode decomposition . . 4.1

Statistic tests on the clinical features for non-terminating atrial fibrillations versus atrial fibrillations that terminated immediately after the recording . . . . . . . . . . xix

56

70

xx

L IST OF TABLES

4.2

4.3 4.4 4.5 4.6 4.7 4.8 5.1 5.2 5.3 5.4 5.5 5.6 5.7

Statistic tests on the clinical features for atrial fibrillations that terminated one minute after the recording versus atrial fibrillations that terminated immediately after the recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of atrial fibrillation type based on clinical features . . . . . . . . . . Classification of atrial fibrillation aetiologies based on clinical features . . . . . . . Classification of cardioversion results based on clinical features . . . . . . . . . . . Percentage of correct classification of atrial fibrillation types based on clinical features Percentage of correct classification of atrial fibrillation aetiologies based on clinical features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Percentage of correct classification of cardioversion results based on clinical features

Processing steps of the phase-rectified signal averaging based approach . . . . . . Evaluation of the different dominant frequency estimation methods on all leads . . Evaluation of the different dominant frequency estimation methods on lead V1 . . Evaluation of the different dominant frequency estimation methods on lead V5 . . Atrial fibrillation type population distribution based on the dominant frequencies . Atrial fibrillation aetiology population distribution based on the dominant frequencies Atrial fibrillation population distribution of the cardioversion attempts based on the dominant frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Percentage of correct classification of atrial fibrillation types based on dominant frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Percentage of correct classification of atrial fibrillation aetiologies based on dominant features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Percentage of correct classification of cardioversion attempts based on dominant frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

70 71 71 71 72 72 72 85 87 87 87 93 93 94 94 95 95

The three different vectorcardiogram displays . . . . . . . . . . . . . . . . . . . . 99 Dipole distribution results on the simulated atrial activities. . . . . . . . . . . . . . 107 Atrial fibrillation type distribution based on the three extreme dipole distributions . 108 Atrial fibrillation aetiology distribution based on the three extreme dipole distributions109 Distribution of the atrial fibrillation cardioversion attempts based on the three extreme dipole distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Percentage of correct classification of atrial fibrillation types based on dipole distribution features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Percentage of correct classification of atrial fibrillation aetiologies based on dipole distribution features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Percentage of correct classification of atrial fibrillation cardioversion attempts based on dipole distribution features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

1

Introduction

1.1 Motivation and problem statement 1.1.1 Atrial fibrillation and its clinical importance

A

fibrillation is an uncoordinated electrical activation of the upper heart chambers (atria), classified as supraventricular arrhythmia. The anarchic depolarization of the atria leads to an inefficient atrial contraction and thus to a compromised function of the whole heart. TRIAL

According to recent statistics collected in the United States [1], atrial fibrillation is the most common arrhythmia in clinical practice, affecting approximately 2.2 million adults. It is responsible for about one third of hospitalizations for arrhythmia problems. The prevalence of atrial fibrillation is 0.4% of the general population [2]. Atrial fibrillation is more frequent in the elderly, as its prevalence doubles with each decade of age, from 0.5% at ages between 50-59 years to almost 9% at ages between 80-89 years [3; 4]. With the increase of life expectancy, the prevalence is expected to double in the next fifty years. The yearly incidence of atrial fibrillation, also related to advancing age, is less than 0.1% among people aged under 40 years and over 1.5% among those above 80 years [5; 6]. Atrial fibrillation is an important clinical entity because of the increased risk of morbidity and mortality (1.5 to 1.9 fold in Framingham study [7]). The most frequent consequences are hemodynamic function impairment (loss of atrial synchronized contraction, irregular and inadequately rapid ventricular rate), atriogenic thromboembolic [8] events and atrial and ventricular cardiomyopathies [9]. 1

2

C HAPTER 1. I NTRODUCTION

1.1.2 Atrial fibrillation as observed in the surface electrocardiogram The diagnosis of atrial fibrillation as such has been based mainly on visual inspection of the surface electrocardiogram [10; 11]. During normal conditions, the pacemaking function of the heart originates from the sinoatrial node, located at the top of the right atrium. A single electrical activation wavefront propagates from this node over the atrial myocardium. On the electrocardiogram, this propagation is expressed by the P waves. During atrial fibrillation, instead of a single electrical activation wavefront, self-sustained multiple reentrant waves travel over the atrial myocardium in a more or less random fashion [12]. The normal P waves are replaced by continuous, apparently disorganized, fibrillatory waves. Figure 1.1 displays typical electrocardiogram signals during sinus (normal) rhythm and atrial fibrillation.

Figure 1.1: A) Recorded 5-second electrocardiogram signal during sinus (normal) rhythm (lead V3). B) Recorded 5-second electrocardiogram signal during atrial fibrillation (lead V3)

1.1.3 Factors promoting atrial fibrillation The factors promoting atrial fibrillation, such as remodeling [13] or/and focal activity [14], and the underlying mechanisms such as reentry [15] or/and multiple wavelets [16] and mother rotor [17] have been investigated in depth over the last decades. Although there are many substrate abnormalities that may cause atrial fibrillation, they are generally considered as the same arrhythmia problem. However, on closer inspection, atrial fibrillation is not a uniform phenomenon. Rather, it is a collection of more or less sustained functional and/or structural atrial disorders, whose underlying mechanisms and substrates are not clearly defined and have so far not been linked to the underlying aetiology [18].

1.2. O RGANIZATION OF THE DISSERTATION

3

1.1.4 Objectives The objectives of the present study are: • to develop methods to clear the electrocardiogram signals of any ventricular involvement and artifacts; • to propose different features to discriminate between different types of atrial fibrillation; • to validate these features by using simulated and clinical electrocardiogram signals. The ultimate goal of the project is to help clinicians treat atrial fibrillation by developing information on atrial fibrillation substrates, dynamics, and the prediction of success in different treatments.

1.2 Organization of the dissertation This dissertation is divided into two parts: 1. Electrocardiogram processing: After an introduction to cardiac arrhythmias (chapter 2), in the first part we detail the different electrocardiogram processing techniques that detect the fiducial points, correct the baseline, and remove the electrical ventricular activity (chapter 3). 2. Atrial fibrillation classification: The second part aims at exploring the potential of such "clean" atrial electrocardiogram signals. In order to discriminate between different types of atrial fibrillation, we propose different features extracted from the standard 12-lead electrocardiogram based on clinical considerations (chapter 4), dominant frequencies (chapter 5) and spatial dynamic assessed by the vectorcardiogram (chapter 6). The respective techniques used to extract these features are further detailed.

1.3 Original contributions The main contributions∗ of this work are: • Signal-processing advances in the context of non-invasive atrial fibrillation studies. – A refinement of the ventricular cancellation technique based on averaged beat subtraction; – A novel technique that cancels the ventricular involvement in each cardiac cycle in an independent manner. – A novel framework approach based on the use of atom dictionaries dedicated to atrial and ventricular activities. ∗ See

also the list of publications at the end of the text.

4

C HAPTER 1. I NTRODUCTION

• Signal-analytical advances in the context of non-invasive atrial fibrillation studies. – The use of an efficient technique to enhance the quasi-periodic signal components to improve dominant frequency estimation in electrocardiogram signals during atrial fibrillation. – The use of a novel technique based on the vectorcardiogram for the extraction of spatiotemporal information about the electrical activity of the atria, in particular during atrial fibrillation.

Part I

Electrocardiogram processing

5

Cardiac arrhythmias: definition, clinical aspect and electrocardiogram signals

T

2

human heart is a hollow mass of mainly striated muscle fibers. It is most essential to life, since its function is to pump blood through the blood vessels to the entire body by repeated, rhythmic contractions. It is situated slightly to the left of the middle of the thorax, underneath the breastbone (the sternum), at a position surrounded by the lungs [19]. It is the active center of the human cardiovascular system, circulating blood in the entire organism as a medium for transporting substances such as oxygen, nutrients, blood cells, enzymes, antibodies, as well as collecting the corresponding counterparts as wastes, toxins or external agents for disposal. HE

C 2007 Yale-New Haven HosFigure 2.1: Exterior and interior structures of the heart. Copyright ° pital

The heart consists of four chambers, namely the two upper atria and the two lower ventricles. 7

C HAPTER 2. C ARDIAC ARRHYTHMIAS : 8

DEFINITION , CLINICAL ASPECT AND ELECTROCARDIOGRAM SIGNALS

The whole heart is contained in a connective tissue layer named the pericardium. The myocardium is the middle muscular tissue layer of the heart. The endocardium is the innermost layer of tissue that lines the chambers. See Fig. 2.1 for structural details. The normal trigger for the heart to contract arises from the heart’s natural pacemaker, the sinoatria (SA) node, which is in the top right atrium close to the superior vena cava. The SA node sends out regular electrical impulses causing the atria to contract (atrial systole) and to pump blood into the ventricles. The electrical impulse then passes to the ventricles through a form of "junction box" called the atrioventricular (AV) node. This electrical impulse spreads into the ventricles, causing the muscle to contract (ventricular systole) and to pump blood to the lungs and the body. Chemicals that circulate in the blood, and which are released by the nerves that regulate the heart, alter the speed of the pacemaker and the force of the pumping action of the ventricles. For example, adrenaline increases the heart rate and the volume of blood pumped by the heart. The final complete cardiac diastole involves the relaxation of the atria and the ventricles in preparation for the refilling phase of circulatory blood. The whole cycle of blood circulation within the system is governed almost completely by the fluid mechanics regulated by the muscular contraction of the heart [20], see Fig. 2.2.

C 2002 McKesson Health Solutions, LLC) and its Figure 2.2: Blood flow in the heart (Copyright ° C 2006 Ministry Health Care). electrical system (Copyright °

2.1 Bioelectricity of the heart A difference of electrostatic potential always exists between the inside and the outside of a cardiomyocyte; the muscle cell of the heart is polarized. This membrane potential is cause by the distribution difference of ions across the cell membrane and the permeability of the membrane to

2.2. C ARDIAC ARRHYTHMIAS

9

these ions. The resting potential, in which the negative charge inside the cell is higher than the outside, is approximately at -70 mV. When the membrane becomes depolarized beyond a threshold, the cell fires, which means that the cell undergoes an action potential. This action potential is a rapid change of polarity that travels along the membrane, see Fig. 2.3.

Figure 2.3: Schematic of action potential propagation over a cell membrane.

The action potential is characterized by a sequence of seven phases: (1) the resting potential (close to the K+ equilibrium potential), (2) the stimulation (the membrane potential changes to positive inside), (3) the rising phase or depolarization phase (a positive feedback increases the inside positive charge), (4) the peak (a membrane maximal potential is reached around +40 mV), (5) the falling phase or depolarization phase (a reversal of the membrane potential to negative-inside), (6) the undershoot (a hyperpolarization phase) and (7) the refractory period (no reaction to stimulus is possible, it ensures a unidirectional propagation).

2.2 Cardiac arrhythmias 2.2.1 Atrial flutter The atrial flutter (AFL) is the most organized of atrial arrhythmia. In its typical form, instead of a single electrical activation wavefront propagating from the SA node, a right macro-reentrant circuit, bounded anteriorly by the tricuspid valve (TV) orifice, posteriorly by the specific arrangement of anatomical obstacles (orifice of the superior vena cava (SVC) and the inferior vena cava (IVC)), and functional barriers (regions of the crista terminalis located between the superior and inferior vena cava) triggers the electrical atrial activity (AA) [21], see Fig. 2.8A for the locations of these anatomical obstacles. In humans, the most common direction of activation of the AFL circuit (90%) follows a pathway between the tricuspid valve and inferior vena cava along the isthmus in the direction of the septum. This has been described as counter-clockwise reentry and clockwise reentry if the activation occurs in the opposite direction. Depending on the rate of the cycle length, two classes of AFL were initially established: AFL type I (AFL type II, respectively) characterized by an atrial rate ranging from 240 to 340 beats per minutes (from 240 to 433 beats per minutes, respectively) [22].

2.2.2 Atrial fibrillation Atrial fibrillation (AF) is characterized by uncoordinated atrial activation with consequent deterioration of the atrial mechanical function. Various systems have been suggested for clinical AF clas-



sification. The classification scheme proposed by the American College of Cardiology Foundation, the American Heart Association, Inc, and the European Society of Cardiology (ACC/AHA/ESC) Guidelines [23] is the following: when a patient has had two or more episodes, AF is considered recurrent. If the arrhythmia terminates spontaneously, AF is designated as paroxysmal; when sustained beyond seven days, AF is designated as persistent. Termination with pharmacological therapy or direct-current cardioversion does not change the designation. First-detected AF may be either paroxysmal or persistent. The category of persistent AF also includes cases of long-standing AF (e.g., more than one-year long), usually leading to permanent AF, in which cardioversion has failed or has not been attempted [11]. The term "lone AF" has been applied to young individuals (under 60 years of age) without clinical or echocardiographic evidence of cardiopulmonary disease, including hypertension [24]. F irst detected

P aroxysmal1, 4 (S elf-terminating)

P ersistent2, 4 (Not self-terminating)

P ermanent3

Figure 2.4: Patterns of AF. 1, episodes that generally last seven days or less (most less than 24 hours); 2, episodes that usually last longer than seven days; 3, cardioversion failed or not attempted; and 4, both paroxysmal and persistent AF may be recurrent.

2.2.3 Aetiologies and factors predisposing patients to atrial fibrillation AF may be related to acute, temporary causes, including alcohol intake, surgery, electrocution, myocardial infarction, pericarditis (inflammation of the pericardium), myocarditis (inflammation of the myocardium), pulmonary embolism or other pulmonary diseases, hyperthyroidism, and other metabolic disorders. In such cases, successful treatment of the underlying condition often eliminates AF. Also, AF is often an electrical manifestation of underlying cardiac disease. Although AF may occur without underlying heart disease in the elderly, the changes in cardiac structure and function that accompany aging may be associated with AF, just as heart disease in older patients may be coincidental and unrelated to AF. Obesity, which lead to left atrium dilatation, is also an important risk factor for development of AF [25]. Specific cardiovascular conditions associated with AF include valvular heart disease (especially, mitral valve disease), heart failure, coronary artery disease, and hypertension, particularly when left ventricular hypertrophy is present. Hypertrophic cardiomyopathy, dilated cardiomyopathy, or congenital heart disease, and pericarditis constitute additional potential aetiologies. A list of associated heart diseases is available in the ALFA study (Etude en Activité Libérale sur la Fibrillation Auriculaire) [26].

2.2. C ARDIAC ARRHYTHMIAS

11

2.2.4 Pathophysiological mechanisms of atrial fibrillation The onset and maintenance of a tachyarrhythmia require both an initiating event and an anatomic substrate. With respect to AF, the situation is often complex, and available data supports a "focal" mechanism [14] involving automaticity or multiple reentrant wavelets [16]. The initiating focus often lies within the region of the pulmonary veins [14]. Wavelets randomly reenter tissue previously activated by the same wavelet named mother-rotor [17] or another wavelet [15]. These mechanisms are not mutually exclusive and may at various times coexist in the same patient. Whether the source for AF is an automatic focus or a microreentrant circuit, rapid local activation in the left atrium cannot extend to the right atrium in an organized way. Invasive experiments demonstrated a dominant fibrillation frequency in the left atrium with decreasing frequency as activation progressed to the right atrium in patients with paroxysmal AF, but not in patients with persistent AF [27]. The recent findings that AF itself produces changes in the atrial function and structure have provided a possible explanation for the progressive nature of AF by three positive feedback-loops of atrial remodeling on AF [28–30]. These three feedback loops are associated to three remodelings, the electrical, the contractile, and the structural remodelings. Each of these remodelings affects the atrial function and structure in different time domain. (1) The electrical remodeling develops within the first days of AF and contributes to an increase in AF stability. This electrical change reduces the time during which atrial cells are incapable of repeating depolarization or the time it takes for atrial excitable membranes to be ready for a second stimulus once they return to their resting states. This "recovery" time is named the action potential duration. (2) The atrial contractile remodeling (loss of contractility) develops after cardioversion of AF lasting several days. This remodeling leads to a reduced atrial transport function (atrial contractile dysfunction). (3) The structural remodeling develops within weeks to months after onset of AF. The AF-induced structural changes in atrial myocytes include increase in cell size, and perinuclear accumulation of glycogen. The role in the progression of AF is still unclear [31]. In Fig. 2.5 the three positive feedback-loops of electrical, contractile and structural remodelings are depicted.

2.2.5 Clinical evaluation and management The diagnosis of AF is based on patient history and clinical examination in order to identify the aetiologies and factors mentioned in section 2.2.3. A confirmation based on the standard 12-lead electrocardiogram (ECG) recording is required to assess the high and/or variable heart rhythm, Pwave duration and morphology or presence of fibrillatory waves. Transthoracic echocardiograms are also used to reveal valvular heart disease, measure left and right atria sizes, left ventricular size and function, pericardial disease, renal and hepatic (lever) function. Additional investigation of selected patients with AF requires exercise testing, holter monitoring ( > 24 hour ECG recording), transesophageal echocardiography, etc. AF management involves three objectives; rate control, prevention of thromboembolism (formation of a clot or thrombus inside a blood vessel and its complication), and correction of the rhythm disturbance. The initial management is a decision between a rate-control or rhythm-control strategy. Under the rate-control strategy, the ventricular rate is controlled without restoration of normal or sinus rhythm (SR), that is, the patient stays in AF. The rhythm-control strategy attempts

C HAPTER 2. C ARDIAC ARRHYTHMIAS :

DEFINITION , CLINICAL ASPECT AND

12

ELECTROCARDIOGRAM SIGNALS

AP D

E lectrical ++

Ca c hannels

C ircuit S iz e

AF Anis otropy

C ontractility

Contractile

S tructural S tretch

D ilatation

F ibros is

Figure 2.5: Three proposed positive feedback-loops of atrial remodeling on AF. Down-regulation of the L-type Ca++ channels is considered to be the primary cause for electrical and contractile remodeling. Stretch of the atrial myocardium is hypothesized to act as a stimulus for structural remodeling of the atria. The resulting electro-anatomical substrate of AF consists of enlarged atria allowing intra-atrial circuits of small size due to a reduction in wavelength and increased nonuniform tissue anisotropy.

restoration of SR. Attention for the prevention of thromboembolism is always required. The decision is based on the patient’s history (type and duration of AF, severity and type of symptoms, associated cardiovascular disease, etc.). Drugs and ablation are effective for both rate and rhythm control. For rate control, drugs constitute the primary treatment in most AF patients. Ablation of the AV conduction system and permanent ventricular pacing are often the second option. For rhythm control, drugs are typically the first choice and ablation (maze of left atrium ablation techniques) constitutes the second option. The drugs mostly used for rate control modify the AV node cell membranes, contrarily to the drugs mostly used for rhythm control that modify the action potential of the atrial myocytes [32]. Surgical procedures are frequently helpful for rhythm control. The location of reentrant circuits can be disrupted either surgically or, as applied more commonly, by transcatheter ablation.

2.3 Clinical electrocardiogram signals 2.3.1 Body surface potentials and electrocardiogram The observation of the electrical activity of the heart from the body surface potential was mainly introduced by Willem Einthoven in 1901 [33]. He used a string galvanometer to record the time course of the potential differences between two points on the body surface. This was the birth of the first accurate ECG. Nowadays, the electrodes used in clinical practice are usually placed in the standard 12-lead ECG positions, see Fig. 2.6. The electrodes are placed on the left hand (VL), right hand (VR), the left foot (VF), the right foot (ground), and at six precordial positions (V1 to V6). Three leads

2.3. C LINICAL ELECTROCARDIOGRAM SIGNALS

13

(I, II and III) are derived from leads VR, VL and VF. Lead I is equal to VL minus VR, lead II is equal to VF minus VR and lead III is equal to VF minus VL. The Wilson’s central terminal (WCT) is defined as the mean value of the potentials at electrodes VR, VL, and VF. Leads V1 to V6 are defined as the potential observed in V1 to V6 positions, respectively, minus the WCT reference. Other lead systems such as the Holter one vary in the number and positions of the electrodes.

Figure 2.6: Positions of electrodes used in a standard 12-lead ECG.

As mentioned before, the action potential is the electrical discharge that travels along the membrane of a cell. In the case of the cardiac muscle, the action potential activates the contraction of the cardiomyocytes by propagating from cell to cell over the entire tissue. This propagation is affected by preferential pathways such as the bundles of His and the Bachmann’s bundles, see Fig. 2.2. In a normal patient, the instantaneous depolarization wavefront is triggered by the SA node. The Bachmann’s bundles facilitate the conduction from the right atrium to the left one. This first depolarization wavefront creates the P wave (around 80 ms) on the ECG, see Fig. 2.7. After the delay imposed by the AV node, a second depolarization wavefront propagates through the ventricles. The delay introduced by the AV node enhances the filling of the ventricles by the atria prior to their contraction. The ventricle depolarization starts first from the left side of the interventricular septum (the membrane between left and right chambers). This creates the Q wave on the ECG. Then, depolarization waves occur on both sides of the septum through the bundle of His to the Purkinje fibers and the endocardium at the apex of the heart, then finally through both ventricles, creating the R wave on the ECG. Because the left ventricular wall is thicker than the right one, activation of the left ventricular free wall continues even after depolarization of a large part of the right ventricle, creating the S wave on the ECG. A normal QRS complex is 60 to 100 ms in duration. The T wave represents the repolarization (or recovery) of the ventricles. Ventricular repolarization begins from the outer side of the ventricles and the repolarization front propagates inward. On some ECGs, a small wave follows the T wave, named U wave. This U wave is thought to represent repolarization of the papillary muscles or Purkinje fibers [34] or the late repolarization of ventricular segments [35]. On the ECG, AF is characterized by the replacement of consistent P waves by rapid oscillations of fibrillatory waves that vary in amplitude, shape, and timing, associated with irregular, frequently



QRS complex

R wave

T wave

P wave U wave PR segment

ST segment 0.25 mV

200 ms S wave PR interval

Q wave QT interval

Figure 2.7: Schematic representation of normal ECG on lead V3.

rapid ventricular response when AV conduction is intact [36], see Fig. 1.1. Atrial flutter, in the typical form, is characterized by a saw-tooth pattern of regular atrial activation named F wave. Vectorcardiogram The spatiotemporal behavior of the electrical activity during AF precludes in all likelihood the characterization of its complexity by means of an inverse procedure. This holds true in particular if the available ECG data is restricted to those of the standard 12-lead ECG. One of the methods used for the interpretation of the time course of the potentials observed on the body surface approximates the generator as one current dipole placed inside a homogeneous thorax. The resulting estimate is called the vectorcardiogram (VCG). The VCG provides a global representation of the electrical cardiac activity through the time course of the vector orientation and magnitude in 3D space using three time-varying signals as the strengths of the x, y, and z components. Each component is derived from a linear combination of potentials observed at dedicated electrode positions, of which the bestknown variant is the one proposed by Frank in 1956 [37].

2.3.2 Clinical 5-minute 12-lead electrocardiogram database A clinical database was built up in collaboration with the CHUV (Centre Hospitalier Universitaire Vaudois). The patients were selected within the currently treated people in the cardiology service of the CHUV. Their selection was based on their known clinical history. For further analysis purposes, patients with multiple pathologies leading to an unclear classification were avoided. The clinical database is composed of 120 5-minute standard ECG recordings of 120 different patients in R sustained AF. These signals were recorded and stored using a commercial system (CardioLaptop° AT-110, SCHILLER). The system used electrocardiographic filtering (0.05 to 150 Hz), a dynamic range of ± 10 mV AC (resolution of 5 µ V) and a sampling rate of 500 Hz. A file has been created for each of these patients. This file contains medical and general information including 180 different parameters such as age, sex, aetiologies (dilated cardiomyopathy, hypertrophic cardiomyopathy, valvular heart disease, pericarditis, focal, vagal, and idiopathic ones such as ectopic focii),

2.4. S IMULATED ELECTROCARDIOGRAM SIGNALS

15

AF classification as mentioned in section 2.2.2 (paroxysmal, persistent or permanent, and single or recurrent episodes), medical treatment (drugs, anterior surgical therapy), success of pharmacological and/or electrical cardioversion (if available).

2.4 Simulated electrocardiogram signals 2.4.1 A biophysical model of the human atria In order to facilitate the development of innovative therapeutic strategies, there is a need to better integrate knowledge and progresses from both clinical research and basic science. In this context, a three-dimensional, thick-walled, biophysical model of the atria that simulates the propagation of the electrical impulse was developed based on magnetic resonance images [38; 39]. The resulting atrial geometry is shown in 2.8A. The major anatomical details indicated are those of the valves and connections to the major vessels, where no propagation takes place: the tricuspid valve (TV), the mitral valve (MV), the inferior vena cava (IVC), the superior vena cava (SVC), and the pulmonary veins (PV). The SA node (SAN), the AV node (AVN) and the left atrium appendage (LAA) are also indicated. The electrical propagation of the cardiac impulse was simulated using a reactiondiffusion system (monodomain formulation) comprising a total of 800,000 units based on a detailed ionic model of the cell membrane kinetics, formulated by Courtemanche et al. [40].

Figure 2.8: (A) Geometry of the model representing the atria from a left anterior 45o view (on the left) and from a right posterior 45o view (on the right). (B) Geometry of the compartmental torso model (nearly frontal view) including the atria, the ventricles, and the lungs.

Besides a normal SR, an episode of typical AFL and 20 episodes of AF were simulated. To create a substrate for AF, heterogeneities in action potential duration were introduced by modifying the local membrane properties [41; 42]. An example of the distribution of these intrinsic action potential duration values is shown in Fig. 2.9. The white regions (respectively black regions) correspond to an effective refractory period of 125 ms (respectively 250 ms). This example corresponds to the AF substrate with two regions (see inhomogeneous substrate with two specific regions in Table 2.1). Simulated AF was induced by cross-shock or rapid pacing protocol in either one of the eight different locations, as shown in Fig. 2.10. Specifications of the various conditions setting up



Figure 2.9: Distribution of heterogeneities using isotropic diffusion.

the 22 different types of AA are listed in Table I. In the sequel, these types are labeled as no.1, no.2, . . . etc. The electrical activity of the entire ensemble of 800,000 units was represented by the equivalent double layer specified at the closed surface bounding the myocardium [39; 41]. This double layer expresses the electric activity within the atrial myocardium by a sheet of electric current dipoles located on the surface bounding the atria (endocardium and epicardium: 1297 nodes), whose local strength is proportional to the time course of the local transmembrane potential, Vm (t). Modifications of the substrates and of the AF initiating procedures created different dynamics such as rapid pacing [14], micro-reentries [15] and mother-rotor [17]. The documentation of the simulated dynamics is presented in Table 2.1 and Fig. 2.11. Table 2.1 relates each simulated AA

Figure 2.10: Eight different rapid pacing locations used to induce AA. The figure shows the atrial model from a left anterior 45o view, from a right posterior 45o view, from below, and from an isthmus view.


17

with its specific dynamics and displays the available duration of the different simulations (the fifth and sixth columns, respectively). Figure 2.11 displays the transmembrane potential distribution map of 12 different simulated AAs and their various dynamics denoted by white spots and arrows. These 12 simulated AAs represent the different types of dynamics observed among all 22 simulations.

2.4.2 Computation of body surface potentials The expression of the electrical potential field generated by the atrial sources demands the specification of a volume into which the electric currents flow, thus setting observable potential differences. The effect of the heterogeneity in the electric conductivity of the tissues surrounding the atrial myocardium was computed by means of the boundary element method. This was applied to a compartmental torso model derived from MR images, which includes atria, ventricles and lungs [41]. Body surface potential maps of AA were computed over the entire torso. The potentials at the locations of the nine electrodes of the standard 12-lead ECG system were selected to simulate ECG signals. Figure 2.8B displays the torso geometry (left anterior 20o view), also derived from MR images, as well as the positions of the nine electrodes contributing to the information content of the standard 12-lead ECG (Fig. 2.6).

Figure 2.11: 12 different examples of the AA dynamics obtained from the 22 simulated AAs, including SR (no.1), typical AFL (no.2) and 10 different AF sources. White circled arrows represent the stable dynamics (macro-reentry circuit (AFL) and mother-rotors (AF)), see no.2 to 7 and 9. White spots represent the burst pacing that mediates focal AA (including SR), see no.1, 13, 14 and 22. See Table 2.1 for the complete documentation.



2.4.3 Simulated 5-minute 12-lead electrocardiogram database Each of the 22 ECG episodes of simulated AA were duplicated to cover five minutes. In some of our studies, realistic R-R intervals were necessary. For these studies, the different electrical ventricular activities (VA) were incorporated as sequences of ventricular complexes extracted from four different clinical ECGs (5-minute long) recorded during sinus rhythm in four patients with paroxysmal AF, sampled at 500 Hz. The assigned timing of the complexes was based on the atrial activation times close to the AV node, using the model of human AV node function proposed by Jørgensen et al [43]. This mode predicts the output sequence of ventricular activations on a beat-to-beat basis as a response to an input sequence of atrial activations. The AV node has a refractory period θ following the conduction of a cardiac impulse through the AV node to the ventricles. Any activation arriving at the AV node during this refractory period is blocked and prolongs the refractory period by ∆. The conduction time through the AV node (AV delay) is assumed to be a function of the recovery time from the end of the preceding refractory period. In total, 5 parameters are involved in the model. The values used were taken from [43]: θ = 114ms, ∆ = 81ms, AV∞ = 70ms, α = 280ms, τ = 60ms. For each of the four patients, the clinical ventricular complexes were sorted according to the preceding R-R interval, creating four databases of clinical complexes. The timing of the ventricular activation onset was predicted using the Jørgensen model. A complex was selected in each database of clinical ventricular complexes according to the preceding predicted R-R interval. The Q wave starting point of each selected complex was aligned with the predicted onset of the ventricular activation. Exhaustive combination of the 22 series with the 12-lead ECG VA signals of the four databases produced 88 realistic simulated 5-minute AF signals. In other studies that did not require the simulation of the AV node, the 22 5-minute ECG signals of simulated AA were directly combined with the same four clinical 5-minute standard 12-lead ECGs mentioned above with the P waves removed. In this manner, 88 simulated 5-minute AF signals at 500 Hz were created in the standard 12-lead ECG.


19

Table 2.1: Documentation on the simulated atrial activities. no. 1

AA SR

Substrate Homogeneous Homogeneous (except crista terminalis)

2

AFL

3

AF

Homogeneous

AF

Inhomogeneous ERP*: 50 to 100ms

4

AF

Inhomogeneous ERP: 125 to 140ms ERP: 160 to 230ms

Initiation

Dynamics

s

SA node pacing (1 beat)

1

Site no 2

counter-clockwise

6

Cross-shock

mother-rotor TV

6

Cross-shock

mother-rotor left appendage +mother-rotor lower right PV

4

Rapid Pacing Site no 3

-

-

Site

5

"

5% fibrosis

"

6 7 8

" " "

10% fibrosis 15% fibrosis 20% fibrosis

" " "

AF


no

1

mother-rotor lower right PV + mother-rotor IVC mother-rotor lower right PV mother-rotor upper right PV complex dynamic

Rapid Pacing Site no 3

-

9

"

"

During 11 s

10 11 12

" " "

" " "

During 13 s During 14 s During 16 s

mother-rotor lower right PV + mother-rotor between PVs " " "

Focal source

-

AF


13

"

"

Site no 3

14

"

"

Site no 4

15 16 17 18 19 20

21

22

" " " " " "

" " " " " "

no

Site Site no Site no Site no Site no Site no

6 5 2 7 8 9

burst pacing mediated + focal lower left PV burst pacing mediated + focal lower left PV complex dynamic " " " " "

8 10 6 11 10 8 8 6 8 5 9 6 9 8 8 8

AF

Left atrium ERP: 125 to 140ms ERP: 205 to 250ms Right atrium ERP: 200 ms

Rapid pacing Site no 3

complex dynamic

10

AF

Right atrium ERP: 125 to 140ms ERP: 205 to 250ms Left atrium ERP: 130 ms

Rapid pacing Site no 3

burst pacing mediated + focal lower right PV

4

* Effective refractory period (ERP).



3

Electrocardiogram processing

T

He

major problem in most of the non-invasive studies that try to characterize the AF with surface ECG signals is the presence of electrical VA. Due to its much higher amplitude, cancellation of the ventricular involvement is crucial. A straightforward approach consists in performing the analysis on the ECG segments free of ventricular complexes. However, the information contained in the rejected parts (i.e with VA) is lost, which is not suitable when the analysis requires continuous AA signals or when the ventricular rate is too high to produce ECG segments without VA involvement. Because of the spectral overlapping of the AA and VA, classical, linear-filter based does not permit to extract the AA ECG signals during AF. Three approaches are generally used to perform this task: adaptive recurrent filtering, source separation algorithms and average beat subtraction (ABS). The adaptive filtering essentially minimizes the error between a primary input, which is the original ECG signal, and a reference input, which is an impulse train coincident with the QRS complexes [44]. The filter output and the filter error represent respectively the VA and AA. It has, however, been shown that the filter output of one complete cardiac cycle is equivalent to a weighted average of the preceding cardiac cycles, which is equivalent to an ABS based approach [45]. Another approaches to extract the AA exploit the property that the AA and the VA arise from different bioelectrical sources and that these two sources exhibit different statistical properties. One may assume that the ECG signals can be viewed as a weighted sum of atrial and ventricular electrical sources, noise and artifacts. Principal component analysis (PCA) and independent component analysis (ICA) are the two main representatives of these separation approaches. PCA exploits second-order statistic and the ICA methods exploit high-order statistics. Both approaches have found their way into the AF analysis [46–48]. ABS is the most used technique for the AA ECG signal extraction during AF. The technique relies on the fact that AA is uncoupled with the VA during AF. It also assumes that, in the same patient, ventricular complexes generally exhibit a limited number of forms. Hence, subtraction of 21

22

C HAPTER 3. E LECTROCARDIOGRAM PROCESSING

the average VA complex or "template" should produce a residual signal cleared of any VA involvement. This technique was initially developed to study the fetal electrocardiogram [49], but has later been used in non-invasive AF studies [50–52]. The purpose of this chapter is to evaluate novel and existing techniques for the AA extraction by using standard 12-lead ECG signals. First, we propose the use of two existing ICA techniques to separate the AA from the VA. These two techniques are presented in Sec. 3.2. We assess the performance of these algorithms in terms of VA suppression and AA extraction directly on our simulated and clinical data. In the following section, a novel version of the ABS approach is proposed, see Sec. 3.3. Another new technique named the single beat one, which treats each cardiac cycle in an independent manner, is also proposed. In the following section, a new VA cancelation framework based on dedicated multi-component dictionaries is briefly explored. Details concerning the technique and its performance on simulated and clinical data are presented in Sec. 3.4. Finally, we studied the effectiveness of a proposed postprocessing technique based on an existing algorithm, namely empirical mode decomposition, after the VA cancelation. All of these studies were validated by using the simulated and clinical databases presented in Sec. 2.4.3 and 2.3.2. For most of these techniques, preprocessing of the ECG signals and fiducial point detection were required. It is a crucial part to obtain accurate AA extraction, mainly for ABS based approaches. The following section presents the techniques used for the preprocessing of the ECG signals and the fiducial point detection.

r i−1 timing of R wave (r i )

timing of J point (j i )

timing of the onset of Q wave (qi )

Ai

r i+1

timing of T wave peak (ki+1 )

Bi

0.1 mV

Ci 0.5 sec

Figure 3.1: Fiducial points defined on a two second RMS signal. The timing of the onset of the ventricular depolarization , the R wave timing, the J point and T wave peak timings are denoted as qi , ri , ji and ki , respectively. Locations of QRS complex (Ai ), JQ interval (Bi ) and cardiac cycle (Ci ) are also indicated.

3.1. F IDUCIAL POINT DETECTION AND BASELINE CORRECTION

23

3.1 Fiducial point detection and baseline correction In the standard 12-lead ECG, only two of the first six leads (I, II, III, VR, VL and VF) are linearly independent. This justifies the expression of the pertinent information contained in the 12-lead ECG by an T -by-8 matrix X that comprises T samples from eight leads: two limb leads (VR and VL) and six precordial leads (V1 to V6). Leads I, II, III and VF were recaptured by the appropriate linear combination of leads VR and VL. The intervals showing major artifacts (patient motion, muscular activity, and cable and electrode malfunction) were identified by visual inspection. These segments were set to zero. The fiducial points, that is, the timing of the onset of the ventricular depolarization, the timing of R waves, the timing of J points and T wave peaks, were derived from the root mean squared (RMS) signal of the ECG signals. This RMS signal is defined as: s RMS(t) =

1 8 ∑ xl (t)2 , t = 1 · · · T, 8 l=1

(3.1)

where xl (t) is sample t of the l th lead signal. A derivative-based technique was applied to the RMS signal to detect ventricular complexes [53; 54]. In the ith cardiac cycle, the timing of the onset of the ventricular depolarization was denoted as qi . The timing of the R wave, denoted as ri , was defined as the middle point between the two samples below 50% of the maximum value on either side of the R wave peak on the RMS signal. The J point timing, denoted as ji , was defined as the local minimum of the RMS signal between ri and the timing of the subsequent T wave peak. The T wave peak timing on the RMS signal was denoted as ki (see Fig. 3.1). Concerning the baseline correction, some non-invasive AF studies used a linear phase filtering [55] that modified the original signal mainly by introducing a widening of the QRS complex. In the present case, a baseline correction was applied to each of the eight lead signals by means of a cubic spline interpolation anchored on the onset points qi [55]. The fiducial point detection and the baseline correction were iteratively applied until no further changes in the timings were observed. The eight resulting ECG signals were smoothed by applying a zero-phase fifth-order lowpass Butterworth filter with a cutoff frequency of 50 Hz. Figure 3.2 shows the results of the entire preprocessing applied to a recorded signal (lead V2).

3.2 Suppression of ventricular activity in the electrocardiogram based on independent component analysis ICA and blind source separation techniques are emerging techniques that aim to recover the unobserved sources from several observed mixture signals. These observed signals are typically acquired from a set of sensors, where each sensor receives a different mixture of the source signals. The adjective "blind" is related to the fact that the source signals and the mixture properties are unknown, however, the assumption that the sources are independent, that the number of observed signals is equal or higher than the number of source signals, and that the observed signals are mixture source signals are made [56]. ICA techniques were first popular in the speech processing field [57; 58]

24


A)

B)

2 mV

2 sec

Figure 3.2: (A) Recorded 10-second ECG signal during AF (lead V2). (B) Cleaned up version after preprocessing.

and promising applications can already be found in processing of communication signals [59], in biomedical electroencephalogram signals [60], in monitoring [61], or as an alternative to PCA [62]. The standard framework of ICA for linear instantaneous mixtures as presented here uses the following notations. If s(t) = [s1 (t), s2 (t), ..., sM (t)]T denotes the source vector at time t, one assumes that the observation x(t) = [x1 (t), x2 (t), ..., xN (t)]T is given by: x(t) = Ms(t),

(3.2)

where M is the mixing matrix, the symbol T denotes transposition, and N ≥ M. Under the assumption of mutual independence of the sources, the goal is to estimate a demixing matrix W such that the output vector: u(t) = Wx(t) (3.3) recovers the sources s(t) up to permutation and scaling. Millet et al. were the first to propose the use of ICA techniques for the separation of AA and VA from ECG signals during AF [63]. The observed signals xl (t) are the ECG signals, while sources sl (t) being the AA source, the VA source, artifacts, or noise. Other studies have proposed different ICA techniques for the separation of AA and VA [64–66]. As noted in [64; 66; 67], there are three assumptions that make the use of ICA techniques possible for the separation of AA and VA from ECG signals during AF. First, the bioelectrical atrial and ventricular activities are assumed to be independent. Second, the AA and VA sources are assumed to be approximated by point sources. Third, the AA and VA sources are assumed to exhibit different statistical properties. It has been shown that the amplitude distributions of AA and VA ECG signals are non Gaussian and respectively characterized by subgaussian (uniform) and supergaussian (peak) distributions [68]. These two distributions have respectively negative and positive kurtosis values. If these three assumptions are respected, the ECG signals can be viewed as a weighted sum of atrial and ventricular electrical

3.2. S UPPRESSION OF VENTRICULAR ACTIVITY IN THE ELECTROCARDIOGRAM BASED ON 25

INDEPENDENT COMPONENT ANALYSIS

sources, noise and artifacts. One or more of the independent components obtained from the surface ECG lead signals should correspond to AA only. In the following section, two different ICA algorithms are proposed to perform the separation of AA and VA sources from standard 12-lead ECG signals. The first algorithm [69] is a version of an algorithm based on the extended maximum-likelihood [65]. The second one [70] is based on an adaptive estimation of the marginal probability density functions of the sources. ICA techniques were preferred to PCA due to the facts (1) that the ICA is a source separation alternative to PCA (second-order statistic) based on high-order statistics, and (2) that the performance of ICA algorithms has been demonstrated to be better in the context of the AA and VA separation from 12-lead ECG signals during AF [71]. We assessed the performance of the two proposed ICA algorithms in terms of VA suppression and AA extraction on simulated and clinical data described in sections 2.4.3 and 2.3.2. Several criteria were defined to judge the success of AA extraction. The physiological relevance of the demixing coefficients was also studied.

3.2.1 Algorithms Whitening procedure In most of the ICA techniques, it is necessary to first perform a decorrelation and normalization of observations, commonly referred to as standardization or whitening [72]. The source estimations recover the sources up to a permutation and scaling. Therefore, the sources are assumed to be uncorrelated unit-power signals. The source estimation covariance matrix becomes: 4

Rs = E[SST ] = I,

(3.4)

where S is an T -by-M matrix that comprises T samples from M estimated sources, and I is the identity matrix. Consider the singular value decomposition (SVD) [73] of the mixing matrix M = UΣQT . The covariance matrix Rx of the observations may then be expressed as a function of M and its SVD, or in terms of its own eigenvalue decomposition: ( MRs MT = UΣ2 UT 4 T Rx = E[XX ] = , (3.5) V∆VT where ∆ and V respectively denote the diagonal matrix of eigenvalues and eigenvector matrix of Rx . The pseudo-inverse [73] of UΣ is referred to as the whitening matrix B since when it is applied to the observations x(t), it supplies a set of uncorrelated unit-variance components: z(t) = (UΣ)† x(t) = Qs(t), 4

Rz = E[ZZT ] = QRs QT = I,

(3.6) (3.7)

where Z is an T -by-N matrix that comprises T samples from N uncorrelated unit-variance components, and (·)† denotes the pseudo-inverse matrix. It assumes that the number of sources equals the number of observations (M = N). During the whitening procedure, it is possible to reduce the size of the matrix Z by selecting the uncorrelated unit-variance components associated with the highest singular values of Σ. Observe that the second-order analysis leaves a unitary transformation undisclosed: the matrix Q in Eq. 3.6 that relates the whitened signals z(t) to the true sources s(t).

26


Extended maximum-likelihood In the case of two sources, s(t) = [s1 (t), s2 (t)]T , and two mixture signals x(t) = [x1 (t), x2 (t)]T , only a Givens rotation matrix Q defined by: " # cos θ −sin θ Q= (3.8) sin θ cos θ has to be estimated after applying the whitening procedure to perform the demixing of the two sources. The angle θ can be estimated through a maximum-likelihood procedure (see [65; 74] for details). By definition, the maximum-likelihood estimator of θ is the value of the rotation angle that maximizes the log-likelihood of the given z(t) that can be expressed as: T

θˆ ML = arg max ∑ log pz (z(t)|θ) θ

(3.9)

t=1

for T independent observations z(t), t = 1, 2, · · · , T , where pz (·) denotes the probability density function of z(t). If the sources are assumed to be characterized by kurtosis values between 0 to 4 and to have the same symmetric distribution (at least up to the fourth-order), the maximum-likelihood estimator of θ is found to be [74]: 1 ∑ ρ4 sin 4φt , θˆ ML = arctan t 4t 4 ∑t ρt cos 4φt

(3.10)

where ρt and φt are the amplitude and angle of the polar representation of z1 (t) + jz2 (t) = ρt e jφt respectively, and j is the square root of -1. These two assumptions are necessary to truncate the estimator of θ at the fourth-order term. The extended maximum-likelihood estimator that dropped the time index t uses the estimates: 1 T 4 ξˆ = E[(z1 (t) + jz2 (t))4 ] ≈ ∑ (z1 (t) + jz2 (t))4 and T t=1

(3.11)

1 T 2 ∑ (z1 (t) + z22 (t))2 − 8 T t=1

(3.12)

4

γˆ = E[(z21 (t) + z22 (t))2 ] − 8 ≈ to express θ as:

1 (3.13) θˆ EML = arg(ξ · sign(γ)), 4 where the angle (or argument) function arg (·) provides the phase in [-π,π] of its complex argument. To separate more than two sources, an algorithm based on the iterative application of the former procedure to pairwise combinations of observations has been proposed [69]. It is described in Table 3.1. We refer to this algorithm as EML in the sequel. Hybrid independent component analysis by adaptive look-up table activation functions For separating the independent sources from the mixtures, a neural network can be used where the observations x or the whitening signals z are the network inputs, the demixing matrix W denotes



Table 3.1: Batch algorithm for blind source separation of more than two signals via the EML estimator (symbol ’:=’ means variable assignment). Step 1.

Step 2.

Step 3.

Obtain whitened signals from given observations. Consider the whiteningmatrix pseudo-inverse and the whitened signals as a first estimate of the mixing ˆ z → u. matrix and the sources, respectively: B → M, T For all signals pairs Ui j = [ui , u j ] : ˆ i j from EML estimator in 2.1 Estimate (2 × 2)-unitary transformation Q T T Eq. 3.13 (with [z1 , z2 ] = [u1 , u2 ] ). ˆ T Ui j , 2.2 Counter-rotate: update Ui j := Q ij ˆ i j , where [·]i, j denotes the matrix composed of only the ith ˆ i, j := [W] ˆ i, j Q [W] and the jth columns. Repeat step 2 until convergence.

the connection-matrix, and the source estimations u are the outputs. In order to achieve separation, the network connection-matrix may be trained so that the network outputs become as independent as possible, that is, they satisfy the complete factorization principle: pu (u) = p1 (u1 )p2 (u2 ) · · · pn (un ),

(3.14)

where pu (u) denotes the joint probability density function of the outputs, and the functions: 4

pi (ui ) =

Z Rn−1

pu (u)du1 · · · dui−1 dui+1 dun ,

(3.15)

denote the marginal probability densities of the network output signals. A way to achieve separation is thus, to define a measure of the disagreement between the two sides of Eq. 3.14 and then to use a learning algorithm to learn the connection-matrix in order to minimize such disagreement. A widely used technique for the separation is the natural-gradient one proposed by Amari [75; 76]. It is based on the natural-gradient version of the stochastic minimal mutual information learning rule [77]. This learning rule expresses the update 4 W of the demixing matrix W by: £ ¤ 4W = η I − Φ(u)uT W,

(3.16)

where η is a positive learning step size and the vector Φ is defined by: µ 0 ¶ r (u1 ) r20 (u2 ) r0 (un ) T 4 Φ(u) = − 1 ,− ,...,− n , r1 (u1 ) r2 (u2 ) rn (un )

(3.17)

In this equation, the functions ri (ui ) stand for the unknown marginal probabilities of the vector output components ui (t), while ri0 (ui ) are their derivatives. Fiori proposed to iteratively estimate the marginal probabilities ri (ui ) and their derivatives ri0 (ui ) via histograms [70]. The "time-varying" histograms of the amplitude distribution source estimates

28


u(t + 1) and the demixing matrix W are successively updated by the new inputs x(t + 1) and the update 4W. This iterative procedure is displayed in Table 3.2. We refer to this algorithm as LUT (for histogram look-up table). In the LUT, as in the EML, a whitening procedure was applied first to the surface ECG signals, and 64-bin histograms were used (NuP = 64). The LUT algorithm was run once on all signals to ensure convergence, and the extracted results were obtained during the second run.

3.2.2 Results on simulated and clinical data The AA signals derived by ICA do not represent the AA signals of specific ECG leads but rather the single or multiple global AA signals derived from all leads. A further processing step was proposed by Langley et al. to facilitate the evaluation of ICA algorithm results in the context of the AA and VA separation from ECG signals [71]. The inverse transform of the demixing matrix W allows the estimated sources ui (t) to be projected back into each original lead. The inverse transform is described by: kn

sˆ j (t) =

∑ W−1 i, j ui (t)

(k ∈ [1, 8]),

(3.18)

i=k1

where sˆ j (t) is the estimated AA in the jth significant ECG lead, and i represent the indices of the estimated sources that represent AA. To minimize the risk of adding estimated sources containing Table 3.2: Estimation of the marginal densities by LUT. Step 1.

Initialization of umin and umax , NuP , r := 0, and φ := 0, where umin and umax are respectively the minimum and maximum values of the components of output u, and NuP is the number of columns on the histogram. We suppose that p(u) 4

Step 2. Step 3. Step 4. Step 5.

Step 6. Step 7. Step 8.

differs significantly from zero only in a finite interval P = [umin , umax ], outside of which p(u) ≈ 0; max | Compute ∆u = |uminN−u ; P u Input ui ; ¥ min ¦ + 1, where symbol b·c stands for floor operator and nu Compute nu = u−u ∆u is the index vector; If nu ≥ 1 AND nu ≤ NuP then rnu := rnu + 1; 5.1 If nu > 1 AND nu < NuP then r j := r j / (∑k rk ), j = nu − 1, nu , nu + 1; rnu +1 −rnu −1 φ(ui ) := − 2(r ; nu +ε)∆u 5.1 End if End if Repeat 3 to 5 for n input ui ; Output n -vector φ(u). Update ∆W in Eq. 3.16 and compute u(t) in Eq. 3.3; Repeat 3 to 7 at each time interval t.



Table 3.3: The normalized MSE on the QRS complexes for each significant lead of the 88 simulated ECGs for the EML and LUT techniques. normalized MSE

EML

LUT

VR VL V1 V2 V3 V4 V5 V6

302.49 ± 479.57 307.24 ± 501.28 1.50 ± 1.35 48.98 ± 63.02 199.46 ± 295.76 201.48 ± 256.70 181.97 ± 157.06 363.71 ± 537.31

30.81 ± 51.64 57.34 ±103.51 2.03 ± 1.78 47.69 ± 62.11 3.07 ± 2.28 7.70 ± 11.22 29.59 ± 49.58 30.88 ± 64.06

Average

200.85 ± 286.51

26.14 ± 20.52

VA involvement, only one estimated source ui (t) was selected. Considering that the estimated sources are unit-power signals, the estimated AA source was selected by taking the signal ui (t) with the highest variance after a projection on lead V1. This estimated source ui (t) was then projected on each lead to obtain the complete standard 12-lead ECG signals of AA for further analysis. Evaluation procedure Both the EML and the LUT performance were evaluated using the simulated and clinical data described in sections 2.4.3 and 2.3.2. The normalized MSE was evaluated for the QRS complex locations Ai and for the locations of all JQ intervals Bi separately. Tables 3.3 and 3.4 summarize the performance of the various techniques for the 88 simulated ECGs created without the AV node model. On the 9th row, the average of all normalized MSE values for each technique is indicated. Figure 3.3 shows the results obtained by the two proposed techniques for a simulated 10-second segment. The performance of the two proposed ICA techniques was also tested on clinical data. In these signals, the real AA on the ECG was unknown. The only evidence of the success of the VA cancellation was the absence of clear QRS residues. The testing of the performance on the 120 clinical signals for each lead carried out as follows: Table 3.4: The normalized MSE on the JQ intervals for each significant lead of the 88 simulated ECGs for the EML and LUT techniques. normalized MSE

EML

LUT


194.66 ± 327.87 126.67 ± 180.86 0.66 ± 0.34 36.14 ± 34.85 117.22 ± 169.65 151.69 ± 187.93 124.85 ± 90.65 762.85 ± 1225.20

11.38 ± 16.52 19.72 ± 24.88 0.87 ± 0.55 28.95 ± 46.14 2.33 ± 1.49 5.79 ± 9.23 22.03 ± 41.33 21.50 ± 40.88

Average

189.34 ± 239.86

14.07 ± 10.42

30


1. The quartile (qr) and the median (m) values of the amplitude distribution of the estimated AA signals were captured for all techniques. 2. The standard deviation (σ) was estimated from qr as: σ = qr/0.6745; the denominator corresponding to the value pertaining to the normal distribution. This estimation approach for σ was used to eliminate the impact of outliers. 3. The QRS complex intervals that contained absolute values above the threshold ς were identified with ς = m + 2σ. The QRS complex residues in these intervals were defined as being "significant". (A) (B) (C) (D) (E) (F)

1 mV 1 sec

(G)

(H)

(I)

0.25 mV 1 sec

Figure 3.3: (A) Original simulated 10-second AA ECG on lead V1. (B) Real VA from a 76 year old patient in sinus rhythm. (C) ECG signal obtained by the addition of AA and VA ECG signals. (D) Estimated AA amplified by 0.2 with EML after applying a high pass filter with a cutoff frequency of 1 Hz. (E) Estimated AA with LUT after applying the same high pass filter. (F) Original simulated 10-second AA ECG. (G) Estimated AA of (D) amplified 4 times; QRS normalized MSE of 26.89 & JQ normalized MSE of 25.98. (H) Estimated AA of (E) amplified 4 times; QRS normalized MSE of 2.57 & JQ normalized MSE of 2.60. (I) Original AA of (A) amplified 4 times.

Table 3.5 shows the percentage of QRS complexes in our database of 120 clinical 5-minute ECG results that were imperfectly cancelled. The 9th row represents the average percentage for each technique. Figure 3.4 shows, for a clinical 10-second segment, the results obtained by the two proposed techniques. Tables 3.6 and 3.7 show the normalized weights (appropriate row of the W · B) for the first five trials (first five rows) and the averaged values for all clinical patients (sixth row) obtained with the EML and LUT techniques respectively.

3.2.3 Discussion First, it is worth mentioning that the projection of the estimated AA sources on the original leads proposed by Langley et al. produces interesting results on lead V1 as is demonstrated by the evaluation of the ICA algorithm performance on simulated and clinical data. However, the projection



Table 3.5: Percentage of significant QRS residues detected on 120 clinical 5-minute ECG results. This percentage is calculated for each significant leads for the EML and LUT techniques. % of significant QRS residue

EML (%)

LUT (%)


91.8 91.2 49.0 87.3 82.7 87.8 92.3 88.1

71.9 83.7 28.1 82.0 74.7 68.1 69.2 64.6

Average

83.8

67.8

on the other leads is not accurate. The coefficients of the demixing matrix corresponding to the other leads are lower than the coefficients related to V1, see Tables 3.6 and 3.7. The inverse coefficients produce estimated AA projected on original leads with overestimated amplitudes. This is well illustrated by the simulated and clinical example shown in Figs 3.3 and 3.4. This observation explains the huge difference of performance on simulated data between the lead V1 and the other leads in terms of normalized MSEs and percentage of significant QRS residues. Note also that, in the example with simulated data, the estimated AA obtained from the EML algorithm on lead V1 needs an amplification of 0.2 to conserve the same range of values with respect to the real simulated AA ECG signal.

(A) (B) (C)

5 mV

(D) 1 sec

(E)

(F)

1 mV 1 sec

Figure 3.4: (A) Clinical 10-second ECG signal on lead V1. (B) Clinical 10-second ECG signal after preprocessing. (C) Estimated AA with EML after applying the high pass filter with a cutoff frequency of 1 Hz. (D) Estimated AA with LUT after applying the same high pass filter. (E) Estimated AA of (C) amplified 5 times; the 10th QRS complex residue was considered significant in this 10-second segment. (F) Estimated AA of (D) amplified 5 times; the 10th QRS complex residue was considered significant in this 10-second segment.

32


However, our results indicate that adaptive LUT performs better than EML, with respect to the specific data set we used. This difference may be due to the fact that we did not implement the adaptive version of EML [66]. It may be that the specificities of the source mixture in ECG, i.e. that VA is not always present, makes adaptive algorithms more suitable than batch ones. Tables 3.6 and 3.7 show that the weights for the lead V1 are much larger; this seems intuitively appealing, since this lead is located on the upper right part of the thorax, close to the atria and far from the ventricles. The weights across the recordings are also quite similar, which indicates that the extraction dynamic is stable. The suppression of VA worked well with four different leads or more when one of them was the lead V1. Note that, when directly applied to the simulated 12-lead AA ECG signals, the average number (± standard deviation) of estimated sources was equal to 4.79 ± 0.72 for both ICA techniques. The ICA algorithms have been selected arbitrarily and may not be the ones with the best performance in the context of AA and VA source separation from standard 12-lead ECG signals. However, our results clearly indicate that adaptive ICA algorithms combined with an adaptive whitening procedure should be preferred to batch ones.

3.3 Suppression of ventricular activity in the electrocardiogram based on average beat subtraction or single beats As mentioned before, the ABS is the most used technique for the AA extraction that relies on the assumption that AA is uncoupled with the VA. It uses average (template) of these distinct complexes to subtract the VA. To facilitate the reading, this standard ABS technique is labeled as ABS1 . Studies of diagnosis of AF [52], non-invasive assessment of the atrial cycle length [50], frequency analysis of AF [78], drug effects and classification of paroxysmal and persistent AF [51], are some of the numerous studies in which ABS1 was used to cancel ventricular involvement. A refined ABS based technique was described by Stridh, Sörnmo et al. [79–82], labeled ABS2 . In their technique, two major features are added to the standard ABS technique (ABS1 ): F wave reduction and spatiotemporal alignment. Before computing the ventricular templates, the fibrillatory waves on each lead are estimated and subtracted to facilitate further processing. The estimates are based on replications of ECG segments free of VA. Note that the estimation technique is not accurate when fibrillatory waves are complex and disorganized. After this fibrillatory wave estimation and subtraction, ventricular templates are created. Spatiotemporal alignment (translation, Table 3.6: Normalized weights obtained using the extended maximum-likelihood-based technique Patient

EML normalized weights V2 V3 V4

VR

VL

V1

V5

V6

1 2 3 4 5

0.0357 0.0155 0.3673 0.0306 0.1436

0.1092 0.1169 0.0738 0.0217 0.0338

0.4028 0.3067 0.0373 0.4538 0.1980

0.1125 0.1349 0.0147 0.0665 0.0808

0.1111 0.2128 0.0701 0.1522 0.1469

0.0591 0.0020 0.2433 0.0897 0.1124

0.1215 0.0970 0.0038 0.1210 0.0695

0.0481 0.1141 0.1897 0.0645 0.2151

120 patients

0.1091

0.1325

0.2575

0.0990

0.1184

0.0869

0.0864

0.1103


AVERAGE BEAT SUBTRACTION OR SINGLE BEATS

Table 3.7: Normalized weights obtained using the adaptive look-up table-based technique Patient

LUT normalized weights V2 V3 V4

VR

VL

V1

V5

V6

1 2 3 4 5

0.2686 0.1116 0.4298 0.0688 0.2856

0.0947 0.3238 0.2726 0.0596 0.0244

0.2874 0.2860 0.0325 0.3726 0.1098

0.0691 0.0516 0.0084 0.0231 0.0174

0.0667 0.1031 0.0114 0.0251 0.1168

0.1232 0.0730 0.0641 0.0682 0.1679

0.0756 0.0293 0.0029 0.0642 0.0388

0.0147 0.0217 0.1783 0.3184 0.2394

120 patients

0.1658

0.1352

0.2178

0.0581

0.0788

0.0974

0.1071

0.1398

amplitude scaling and rotation) is applied to the ventricular templates to correct the variation in the electrical axis of the heart. The major limitation of these techniques is that several beats for each morphology are needed to create the templates. In clinical practice, the standard ECG consists of a 10-second recording, and a good template could be difficult to create in this case. In this section, we propose two techniques for ventricular wave suppression. The first one is a further refinement of ABS1 , labeled ABS3 , and as such, can be applied only if a sufficiently long episode of AF is available in the ECG signal. The second is a technique that permits cancellation of the ventricular involvement on short episodes of AF in the ECG signal, with a minimum length of one complete cardiac cycle. This technique is named single beat and labeled as SB. Both techniques treat the ventricular depolarization (QRS complexes) and repolarization (T and U waves) separately. The three main steps of ABS3 are explained in detail in Sec. 3.3.1: QRS templates, QRS complex cancellation, and T and U wave cancellation. The two main steps of the single beat technique are presented in detail in Sec. 3.3.2: cancellation of the repolarization waves using dominant T and U wave, and estimation of AA located in the QRS complexes using a weighted sum of sinusoids. The performance of the two techniques was studied in their application to ECG signals generated by a biophysical model of the atria, as well as to clinical recordings, as presented in Sec. 2.4.3 and 2.3.2. By using the model, realistic separate contributions of the atria and the ventricles became available for testing the techniques. The performance of the two techniques was compared to that of the standard ABS technique (ABS1 ) and the refined version (ABS2 ) as proposed in [80].

3.3.1 Cancellation technique based on average beat subtraction As suggested first by Waktare et al. [83], our technique treats the QRS complexes and JQ intervals (extended ST-T intervals) separately. The ith QRS complex was represented by an Li -by-8 matrix Ai containing the samples between qi and ji as defined in Sec. 3.1. The ith JQ interval was represented by an Mi -by-8 matrix Bi containing the samples between ji and qi+1 . The whole cardiac cycle was represented by an Ni -by-8 matrix Ci containing the samples between qi and qi+1 , see Fig. 3.1. Averages of similar QRS complexes Ai or JQ intervals Bi were used as templates. A flowchart of the technique is shown in Fig. 3.5.

34


Figure 3.5: Flowchart of the proposed technique based on average beat subtraction (ABS3 ).

QRS complex templates The QRS complexes were clustered based on the morphology of each of their eight lead signals. In order to compare the morphology of the QRS complex Ai and A j , the normalized zero-delay cross-correlation between the corresponding columns (leads) of the two matrices aligned with ri and r j was computed. The matrices were considered "similar" if all eight correlation values were above a given threshold (θ). The clustering procedure was applied to each QRS complex consecutively as follows: any QRS complex Ai was compared to other QRS complex A j assigned to the cluster set {Ωk }. If Ai was considered "similar" to one of these QRS complex A j , then Ai was assigned to it. If not, Ai was placed into a new cluster. The procedure was initiated by placing A1 into the cluster Ω1 . The QRS complexes within cluster Ωk were aligned using their R wave timings (ri ). The individual QRS complexes within any cluster Ωk were permitted to be of different lengths. The template Tk was defined as the sample-wise average of the QRS complexes composing Ωk : the averaging at



each time index was carried out only if more than one sample was available at that time index. If not, the values of the raw of template Tk at that time index were set to zero. Ventricular activity cancellation in the QRS complexes Each template Tk was temporally aligned with R wave timings for all QRS complexes assigned to cluster Ωk . A spatial optimization was applied to the QRS templates to compensate possible variations in the electrical axis, in tissue conductivity and heart position [73]. This was performed by applying the transform defined by the product of rotation matrix Qi and a diagonal matrix Di to the template Tk , where index i refers to the complex Ai : e i = Tk Qi Di . T

(3.19)

The matrices Qi (Di , respectively) represents a rotation in 8 dimensions applied to Tk (a specific amplitude scaling on each lead of Tk , respectively). The evaluation of Qi and Di was performed as displayed in Table 3.8 [79]: Table 3.8: Spatial optimization of the QRS templates. Step 1. Step 2.

Qi was initially set to the identity matrix. The diagonal values Di (l) of Di were updated by Di (l) :=

Step 3.

[Tk ]Tl [Ai QTi ]l , [Tk ]Tl [Tk ]l

(3.20)

where [·]l is the l th column of the matrix. Qi was updated as: Qi := UVT ,

(3.21)

where U and V are the two orthonormal matrices of the singular value decomposition of DTi TTk Ai .

New Di and Qi values were iteratively obtained by repeating steps 2 and 3. After each step, e i was evaluated. This procedure the squared Frobenius norm ∆i of the difference between Ai and T stopped when ∆i had only a marginal decrease. The final estimate of AA inside the complex Ai was e i . In contrast to ABS2 , which applies temporal alignment, taken to be the residual difference Ai − T the proposed QRS complex cancellation uses the same timings as in the template creation to realign the templates before the spatial optimization. Ventricular activity cancellation in the JQ intervals There were three differences between the algorithms used for treating either the QRS complex or the JQ interval. The first relates to the fact that the normalized zero-delay cross-correlation values

36


used for the comparison were measured on the RMS signals related to different beats Bi and B j . The second was the timing used for the JQ interval and template alignment. These timings were defined at a fixed distance following the R wave timings ri . This distance was the average distance between all T wave timings ki and their preceding R wave timings ri . In the same way as described for the QRS complexes, a template Tz was built for each JQ cluster Ωz using the same samplewise average approach. The third was that no spatial optimization was applied to the JQ interval templates Tz . The estimate of the AA inside Bi was taken to be the difference Bi − Tz , with Tz the JQ interval template corresponding to Bi . A zero-phase fifth-order lowpass Butterworth filter with a cutoff frequency of 50 Hz was applied after the cancellation to smooth any remaining discontinuity between each QRS complex and the subsequent JQ interval.

3.3.2 Cancellation technique applicable to single beats In contrast with the ABS techniques, the single beat technique treats each cardiac cycle independently. First, the JQ intervals were processed with a dominant wave approach. Then, the AA located in the QRS intervals was estimated with a finite sum of sinusoids by using the estimated AA located in the neighbor JQ intervals. A flowchart of the technique is shown in Fig. 3.6.

Figure 3.6: Flowchart of the proposed single beat technique.



T and U wave cancellation using a dominant wave approach The shapes of the T waves as observed in different leads placed on the thorax are very similar. The dominant T wave, Tdom (t), has been introduced as a means to characterize this general signal shape [84]. It is estimated by the first principal component over the ST-T interval: Tdom = eT ΦT ,

(3.22)

where the V -by-8 matrix Φ represents the ECG lead signals during the ST-T interval, the 8-vector e represents the first eigenvector (associated with the highest eigenvalue) of the estimated covariance matrix of Φ, and Tdom represents Tdom (t) over the ST-T interval. Since this technique uses information within the individual beat only, here the index i corresponding to cardiac beats is dropped. Based on a biophysical model of the genesis of the T wave, it was shown that an individual T wave could be represented by a linear combination of the function Tdom (t) and its time derivatives [85]. In the AF context, we observed that taking third-order, or higher-order derivatives generally resulted in components that could hardly be distinguished from noise. In the current application, derivatives up to the second-order only were included. Before taking its derivatives, Tdom (t) over the JQ interval was fitted with a smooth analytical function, from which the derivatives could be taken without introducing noise. The function used was the multiplication of two logistic functions [86]: ¶ µ 1 1 · , (3.23) f (t) = p1 p2 + 1 + e p3 (t−p5 ) 1 + e p4 (t−p5 ) where p1 is an overall scaling factor, p2 sets the initial value, p3 and p4 are parameters for the positive and negative slopes, and p5 sets the timing of the apex of the dominant T wave. The JQ interval ends at the onset of depolarization of the subsequent beat. In longer JQ intervals, this increases the likelihood of U waves being present [35]. Indeed, in the ECGs of most AF patients U waves were observed. The shape of the observed U waves was similar to that of a Gaussian function. Correspondingly, the general dominant shape of the U wave was expressed as: 2

g(t) = p6 e−[(t−p8 )/p7 ] ,

(3.24)

where p6 is an overall scaling factor of U wave amplitude, p7 represents its width, and p8 is the timing of its apex. The cancellation of the VA in the JQ interval was based on the two dominant functions f (t) and g(t). The eight parameters involved were found by fitting the function f (t) + g(t) to the function Tdom (t) as computed from the JQ interval of the cardiac cycle considered. Since f (t) + g(t) depends nonlinearly on some of the parameters involved, a nonlinear parameter estimation technique needed to be used. We selected here the Levenberg-Marquart algorithm [87]. In the final step, a linear combination of the functions f (t), f 0 (t), f 00 (t) and g(t) was fitted to the observed data matrix B. This constitutes a linear parameter estimation problem and hence, the 4-by-8 matrix W representing the linear weights for the individual leads was computed as: W = (UT U)−1 UT B,

(3.25)

where the columns of matrix U are the functions f (t), f 0 (t), f 00 (t) and g(t) over the JQ interval. The estimate of AA inside the JQ interval was taken to be the difference B − UW. Figure 3.7 illustrates the results of the various steps taken, as well as the final result for a single lead.

38


Figure 3.7: (A) One recorded cardiac cycle on lead V2. (B) The estimated Tdom over the JQ interval represented by a solid line and its dominant function f (t) in dashed line. (C) First and second derivatives of f (t) ( f 0 (t) and f 00 (t), respectively). f 0 (t) and f 00 (t) are represented by a solid line, and a dashed line, respectively. (D) Dominant function g(t) that represents the U wave in Tdom . (E) Final estimate of the ventricular repolarization represented by a solid line; original signal in dashed line. (F) Result signal after T & U wave cancellation.

Estimation of the atrial activity located in the QRS intervals The cancellation of the ventricular involvement in the JQ intervals Bi−1 and Bi produces a time interval of length (Mi−1 + Li + Mi ) in which the ventricular involvement in the QRS interval Ai remains to be treated. Techniques like standard filtering in the frequency domain, wavelet based, or dominant QRS wave approach as described for the T and U waves, did not yield satisfactory results. The technique finally adopted is the one described below. In contrast to a cancellation technique, it estimates directly the atrial components in segments Ai , based on the AA observed in the cleaned up segments Bi−1 and Bi . The approach assumes that the AA signals are stationary over one cardiac cycle. Frequency analysis of AF signals free of ventricular involvement has demonstrated a narrow band aspect in the frequency domain. This led us to express the AA signal over the QRS intervals Ai of a single lead as a finite sum of sinusoids: P

s(t) =

∑ sk (t) =

k=1

P

∑ αk cos(2π fkt) + βk sin(2π fkt).

(3.26)

k=1

Applied to the complete set of leads, this expression reads: Ai = Si Ei ,

(3.27)

where the columns of the Li -by-2P matrix Si are the P cosine and P sinus functions during the interval Ai , and the columns of the 2P-by-8 coefficient matrix Ei are the P parameters αk and βk of

3.3. S UPPRESSION OF VENTRICULAR ACTIVITY IN THE ELECTROCARDIOGRAM BASED ON AVERAGE BEAT SUBTRACTION OR SINGLE BEATS

39

each lead. The frequencies fk of the P cosine and P sinus functions were uniformly distributed at P values between 0 and 10 Hz. The matrix Ei was computed as: Ei = S†i BCi ,

(3.28)

where S†i is the pseudoinverse of SCi , which contains the P cosine and P sinus functions during the intervals Bi−1 and Bi , and BCi is the concatenation of the JQ matrices Bi−1 and Bi . As in the ABS3 technique, a zero-phase fifth-order lowpass Butterworth filter with a cutoff frequency of 50 Hz was applied at the end of this process to smooth the difference of levels between estimated AAs located before, during, and after the interval Ai . Leads I, II, III and VF were recaptured by the appropriate combination of leads VR and VL. Figure 3.8 shows an example of the AA estimation during the QRS interval.

Figure 3.8: (A) One recorded cardiac cycle on lead V2, from the timing of the J point ji−1 preceding the ith QRS complex, to the timing of the following onset of the Q wave qi+1 . Estimated AA located in the i − 1th and ith JQ intervals after T and U wave cancellation in solid line and the QRS complex Ai in dashed line. (B) Solid line: magnified segments of the estimated AA after T and U wave cancellation located in the i − 1th and ith JQ intervals. Dashed line: representation of the segments of estimated AA by sum of sinusoids (P = 50), normalized MSE of 0.17. (C) Magnified estimated AA of the whole signal after the filtering at 50 Hz.

3.3.3 Results on simulated and clinical data The normalized MSE between the original and the estimated AA was used to evaluate the simulated performance of the proposed refined ABS (ABS3 ) and the single beat (SB) techniques on all significant leads. The performance of the two techniques on these simulated signals was compared to the standard ABS technique (ABS1 ) and its refined version (ABS2 ), as proposed in [79]. The standard algorithms were based on the details mentioned in the respective literature. For ABS1 and ABS2 , the clustering procedure presented in Sec. 3.3.1 was applied to every cardiac cycle Ci , in order to

40


obtain complete ventricular complex clusters instead of treating the complexes in two separate parts as in the ABS3 technique. The thresholds θ (see Sec. 3.3.1) were selected by analyzing the evolution of class numbers. The thresholds were selected as the θ values that correspond to the point just before the class numbers rapidly increased. For the ABS3 technique, the value of threshold θ for the QRS complexes (JQ intervals) was 0.93 (0.76, respectively). The one for ABS1 and ABS2 was fixed to 0.69. In the single beat technique, the parameter P was fixed at 50. This value resulted in a good balance between estimation error and over-fitting of the matrix Bi−1 and Bi . A zero-phase fifth-order highpass Butterworth filter with a cutoff frequency at 1 Hz was applied to the resulting signals for all techniques, in order to remove any remaining frequency components below the physiological range. The normalized MSE was evaluated for the QRS complex locations Ai and for the locations of all JQ intervals Bi separately. Tables 3.9 and 3.10 summarize the performance of the various techniques for the 88 simulated ECGs. On the 9th row, the average of all normalized MSE values for each technique is indicated. Figure 3.9 shows the results obtained by the two proposed techniques for a simulated 10-second segment. Note that the ventricular complexes from patients in sinus rhythm used for the simulated AF ECGs exhibit a more limited number of forms compared to the clinical ventricular complexes of AF patients. Table 3.9: The normalized MSE of the QRS complexes for each significant leads of the 88 simulated ECGs. Both proposed techniques (ABS3 and SB) are compared to the standard ABS (ABS1 ) and its refined version (ABS2 ). normalized MSE

ABS1

ABS2

ABS3

SB


1.58 ± 1.45 1.90 ± 1.19 1.06 ± 0.36 1.96 ± 0.82 4.16 ± 3.58 6.08 ± 7.79 4.33 ± 3.90 2.82 ± 1.67

1.36 ± 0.22 1.63 ± 0.40 1.01 ± 0.09 1.06 ± 0.25 1.22 ± 0.45 1.33 ± 0.73 1.26 ± 0.41 1.43 ± 0.24

1.31 ± 0.19 1.43 ± 0.22 1.09 ± 0.19 1.17 ± 0.22 1.46 ± 0.54 1.41 ± 0.60 1.30 ± 0.36 1.32 ± 0.23

1.12 ± 0.09 1.28 ± 0.17 1.13 ± 0.12 1.17 ± 0.09 1.14 ± 0.11 1.16 ± 0.17 1.18 ± 0.14 1.13 ± 0.12

Average

2.99 ± 2.60

1.29 ± 0.35

1.31 ± 0.32

1.16 ± 0.12

Table 3.10: The normalized MSE of the JQ intervals for each significant lead of the 88 simulated ECGs. Both proposed techniques (ABS3 and SB) are compared to the standard ABS (ABS1 ) and its refined version (ABS2 ). normalized MSE

ABS1

ABS2

ABS3

SB


0.30 ± 0.21 0.35 ± 0.21 0.27 ± 0.23 0.31 ± 0.22 0.35 ± 0.24 0.32 ± 0.24 0.31 ± 0.21 0.35 ± 0.21

0.44 ± 0.20 0.52 ± 0.24 0.32 ± 0.21 0.33 ± 0.22 0.32 ± 0.21 0.33 ± 0.19 0.38 ± 0.21 0.50 ± 0.22

0.16 ± 0.04 0.27 ± 0.12 0.12 ± 0.04 0.16 ± 0.04 0.22 ± 0.13 0.20 ± 0.15 0.16 ± 0.07 0.18 ± 0.06

0.60 ± 0.28 1.08 ± 0.91 0.45 ± 0.10 0.80 ± 0.22 0.62 ± 0.21 0.61 ± 0.35 0.48 ± 0.15 0.55 ± 0.11

Average

0.32 ± 0.22

0.39 ± 0.21

0.18 ± 0.08

0.65 ± 0.29


41

Figure 3.9: (A) Original 10-second ECG simulated AA on lead VR. (B) Real VA from a 76 year old patient in sinus rhythm. (C) ECG signal obtained by the addition of AA and VA ECG signal. (V) Estimated AA with ABS3 after applying a highpass filter with a cutoff frequency of 1 Hz. (E) Estimated AA with SB after applying the same highpass filter. (F) Original 10-second ECG simulated AA. (G) Estimated AA of (D) amplified 4 times; QRS normalized MSE of 0.25 & JQ normalized MSE of 0.08. (H) Estimated AA of (E) amplified 4 times; QRS normalized MSE of 0.53 & JQ normalized MSE of 0.47. (I) Original AA of (A) amplified 4 times.

We also used clinical data to validate the performance of our two techniques. In these signals, the real AA on the ECG was obviously unknown. The only evidence of the success of the ventricular complex cancellation was the absence of clear QRS residues. The testing of the performance on the 120 clinical signals carried out for each lead is the same as described in Sec. 3.2.2. Table 3.11 shows the percentage of QRS complexes that were imperfectly cancelled in our database. The 9th row represents the average percentage for each technique. Figure 3.10 shows the results obtained by the two proposed techniques for a clinical 10-second segment. When tested on the simulated signals, it was observed that this validation threshold ς detected less than 1 % of all QRS intervals as significant QRS residues for each of the four techniques.

3.3.4 Discussion For any VA cancellation study, the major problem was the validation and the optimization of the different parameters. In this study, a biophysical model of the atria provided realistic ECG signals in AF together with their atrial and ventricular components. The latter were used to validate the approach based on separate ventricular depolarization and repolarization templates, and to analyze the effect of the spatial optimization on the QRS complexes and on the T and U waves, which had

42


Table 3.11: Percentage of significant QRS residues detected on 120 clinical 5-minute ECG results. This percentage is calculated for each significant lead. Both proposed techniques (ABS3 and SB) are compared to the standard ABS (ABS1 ) and its refined version (ABS2 ). % of QRS

ABS1

ABS2

ABS3

SB


33.4 % 43.0 % 31.0 % 58.1 % 57.7 % 57.6 % 54.4 % 49.6 %

13.7 % 14.1 % 8.0 % 21.6 % 20.6 % 22.4 % 20.2 % 16.4 %

4.9 % 5.8 % 3.2 % 10.7 % 10.8 % 12.9 % 11.7 % 8.0 %

2.4 % 4.4 % 2.3 % 3.4 % 1.7 % 3.4 % 2.7 % 3.2 %

Average

48.1 %

17.1 %

8.5 %

2.9 %

Figure 3.10: (A) Clinical 10-second ECG signal on lead V2. (B) Clinical 10-second ECG signal after preprocessing. (C) Estimated AA with ABS3 after applying the highpass filter with a cutoff frequency of 1 Hz. (D) Estimated AA with SB after applying the same highpass filter. (E) Estimated AA of (C) amplified 10 times; the 3rd and 11th QRS complexes residue were considered significant in this 10-second segment. (F) Estimated AA of (D) amplified 10 times; no QRS complex residue was considered significant in this 10-second segment.

led to the proposed refined version of the standard ABS technique. The simulated ECG signals were also used to optimize the dominant wave approach (number of derivatives, and T and U wave functions) and the estimation of the AA located in the QRS complexes (observations on the AA signal properties, and number of sinusoids), which led to the single beat technique. It was important to justify the details of both techniques.


43

One of the hardest task in AF ECG signal processing is the detection of fiducial points. Both techniques were based on the R wave timings, which was the easiest fiducial point to detect. In the proposed ABS technique, the use of JQ intervals instead of T and U wave intervals eliminated the problem of detecting the end of the VA in AF ECG signals. The sample-wise average approach was also used to minimize the influence of the unprecise detection of the Q wave starting point timings or VA ending point timings. The templates were well adapted by depending only on the R wave timing for the alignment of the QRS complex templates and cancellation algorithms, as for the JQ interval templates and cancellation algorithms. In the single beat technique, the T and U wave estimation algorithm only used the fiducial points in the initial process of the parameter estimation to decrease the processing time (less than 0.1 sec to estimate the eight parameters per T and U wave estimation), see Sec. 3.3.1. Another major step in the proposed refined ABS technique was the clustering one. By using the zero-delay cross-correlation values of all leads instead of only one, the accuracy of the clusters was optimal for the QRS complexes. As for the T and U wave clusters, the use of the same values of all leads was useless. The AA and VA energy levels were too close to obtain good morphological clustering. The use of the zero-delay cross-correlation values on the RMS signal related to JQ intervals combined the information of all leads and decreased the AA influence. The major limitation of the proposed refined ABS technique is the need for long ECG signals with regular VA complexes of the same type, including extra-systoles. The major limitation of the single beat technique is the use of the first principal component to obtain the T and U wave estimates. In some cases, the correlation between AA and VA is too high and the first principal component contains some AA. Some of it is removed by the analytical fitting step, but in a limited number of patients, some AA components are included in the analytical function f(t) of the Eq. 3.23. It was also important to analyze the effects of the separate approach for ventricular depolarization and repolarization cancellation, and the effect of the spatial optimization on the templates. Simulated results show the performance improvement by this separate approach used in the proposed ABS3 technique, as compared to the ABS based techniques that treat QRS complexes and T and U waves together (ABS1 and ABS2 ), see Tables 3.9 and 3.10. We attributed this amelioration to three factors. The first factor was related to the physiological origin of ventricular waves. It may happen that repolarization waves are of different kinds even if their respective depolarization waves are not. The second factor was that the morphologies of repolarization and depolarization waves were different. The VA templates were more accurate if they came from separate depolarization and repolarization wave clusters. These two factors may explain why the proposed ABS3 technique obtains better cancellation results in the JQ intervals than the standard ABS technique (ABS1 ), see first and third columns of Table 3.10. The only difference between the performance on the JQ intervals of these two techniques were their clusters. The third factor was related to the criteria used for template modification. Modification by rotation and scaling of the ventricular templates is beneficial for the QRS complexes but not for the JQ intervals. The minimization of the Frobenius norm between the ventricular templates and the original complexes produced efficient results on the QRS complexes because, in the QRS intervals, the energy related to VA was much higher than the one related to AA. This explains the excellent results for both ABS based techniques that apply these modifications to the QRS complex templates (ABS2 and ABS3 ), see second and third columns of

44


Table 3.9. In the JQ intervals, the VA and AA energies were too close to use an optimized criteria as used for the QRS complexes. The second column of Table 3.10 also shows that the modification applied on the complete ventricular templates decreased the cancellation quality in the JQ segments. The processing of the complete JQ intervals instead of the T wave intervals minimized the influenced of the low heart rate of the ventricular complex signals used in the performance evaluation with simulated data. The simulated results shown in Fig. 3.9 demonstrate the high quality of the proposed refined ABS technique with a separate approach for the QRS complexes and the T and U waves. The single beat technique produced good results. In the validations on simulated signals, the normalized MSE values were used to evaluate the cancellation performance. Usually, the QRS residues were more important than T and U wave residues (average of all normalized MSE of 1.68 for QRS and 0.39 for T and U). These QRS residues were typically wide bands of frequencies, and therefore, had a stronger impact, for instance, on the estimated PSD of the AA, for example. They were regularly present in clinical cancellation results obtained by ABS based techniques, where the ventricular complexes are not as regular as in sinus rhythm. This is also why the single beat technique is still interesting, even if its performance on simulated signals was less accurate than the other ones for the T and U waves. Table 3.11 shows that the single beat technique contained fewer detected QRS complex residues than the other ABS based techniques. We can also see that the modification of the ventricular templates and the separate approach for QRS complexes and T and U waves reduced the number of episodes showing significant residues (ABS3 technique versus ABS1 and ABS2 techniques). For the estimated AA obtained with the proposed ABS3 technique showed in Fig. 3.10E , the QRS residues in the third and eleventh QRS complex intervals were considered significant, but typical ABS based technique residues were also visible within the others QRS complex and T wave intervals. These residues did not show up in the typical single beat result showed in Fig. 3.10F. The clinical results demonstrated that the local estimation of the AA produced smaller significant QRS complex residues than the cancellation techniques based on subtraction. The AA estimation technique was efficient because it involved the estimation of relatively short segments (QRS intervals), while using the local information on longer AA segments (JQ intervals) that became available by means of the cancellation of ventricular repolarization waves by the dominant wave approach.

3.4 Suppression of ventricular activity in the electrocardiogram based on sparse electrocardiogram signal decompositions During the past decade, many important advances have been achieved in nonlinear signal approximation techniques to represent signals by using non orthogonal bases. In many applications, thanks to their good capacity for efficient signal modeling, these techniques offer better performance than those based on orthonormal transforms or direct time domain processing. These new methodologies decompose the signal into a weighted sum of waveforms, called atoms. These atoms are selected from a large redundant family of functions called dictionary [88]. One of the methods used for the atom selection is the matching pursuit (MP) approach [88]. The general goal of this technique is to

3.4. S UPPRESSION OF VENTRICULAR ACTIVITY IN THE ELECTROCARDIOGRAM BASED ON SPARSE ELECTROCARDIOGRAM SIGNAL DECOMPOSITIONS

45

obtain a sparse signal representation by choosing, at each iteration, the atom that has the best fit on a segment of the original signal. A later refinement has been termed orthogonal matching pursuit (OMP) [89]. It iteratively selects the atoms through the MP criterion. The improvement is that the whole set of coefficients is updated to minimize the distance to the original signal instead of only optimizing the coefficient of the newly selected atom. However, since it selects the atoms according to the MP prescription, the selection criterion is sub-optimal in the sense of minimizing the residual of the new approximation. The use of sparse signal representations in source separation problems was proposed in [90] to exploit some prior knowledge about the structural characteristics of each source. In this section, we present a novel approach for VA and AA estimation based on such technique. Such an approach allows for the consideration of priors on the structural nature of the AA and VA. The multi-component dictionary was composed by functions specially designed to match the main structural characteristics of VA and AA signals. We also present a refined OMP algorithm, named weighted OMP [91], as a tool for generating ECG sparse approximations for source separation.

3.4.1 Undetermined sparse source separation Let x j (t) be the jth signal mixture of a set of N signal mixtures generated by the weighted superposition of M source signals si (t), such that: M−1

x j (t) =

∑ a j,i · si (t) + n j (t),

(3.29)

i=0

where n j (t) represents some additive noise associated to the jth signal mixture, and a j,i represent the specific mixing coefficients. Such signals can be sparsely represented by the superposition of a limited number of atoms from an adapted dictionary of functions (D ): x j (t) =

|Λ|

∑ bl · gl (t) + Rx (t) ,

l∈Λ

j

(3.30)

where gl is the l th selected atom, bl is the corresponding atom coefficient, Λ is the selected set of atoms gl , and RxΛj (t) is an eventual residual that depends on Λ. As mentioned before, the mixing coefficients a j,i must be estimated in order to recover the sources si (t) up to permutation and scaling. Furthermore, to obtain accurate sparse decompositions, the set of coefficients bl must be recovered while the n j (t) are kept as small as possible. Indeed, accurate sparse models can efficiently capture the structural nature of signals, leading to better source separation results, as exposed in [90]. A challenging form of sparse source separation problem is when there are fewer mixtures than sources. An underdetermined source separation problem consists, for example, in trying to separate the different components from a single ECG channel trace. This is studied in this section through the use of a novel sparse source separation approach. In order to do this, we adapt the two stage separation process proposed in [90] to the particular case of ECG component estimations. First, we a priori design an overcomplete dictionary where sources are assumed to be sparsely representable. Second, the sources are unmixed by exploiting their sparse representability.

46


3.4.2 Electrocardiogram component separation We formulate the ECG activity estimation according to the signal models and sparse source separation strategy described in Sec. 3.4.1. The ECG signal (xECG ) is modeled as a noisy mixture of the AA and VA of interest (respectively, sAA and sVA ): xECG = sAA + sVA + n,

(3.31)

where n stands for the noise. The generation of good sparse models for sAA and sVA requires the use of basis functions fitting their particular structures. As shown in the following, sAA and sVA have quite different characteristics, and this is what enables us to separate them. The proposed approach was based on the decomposition of xECG on a redundant dictionary (D ) composed by the union of two sub-dictionaries, DVA and DAA suited for VA and AA, respectively. In what follows, D, DVA and DAA stand for the synthesis matrices of D , DVA , and DAA respectively, in which each column represents an atom of the dictionary. Hence, xECG ' D · b = DAA · bAA + DVA · bVA , (3.32) where b, bAA , and bVA stand for the synthesis vectors of the atom coefficients of dictionaries D , DVA , and DAA respectively. Given the noisy nature of xECG and the high complexity of each of its components, sparse approximations were exclusively considered. According to Eq. 3.32, b is composed of two parts (bAA and bVA ). The approach was simple: we generated a sparse approximation of xECG on D by recovering the atom coefficients b. Then, estimates for sAA and sVA were reconstructed by using the appropriate part of b, bAA for the AA or bVA for the VA, and their appropriate dictionary: sAA ' DAA · bAA

and sVA ' DVA · bVA .

(3.33)

Modeling electrocardiogram ventricular activity The sub-dictionary DVA was generated by all possible translations of the generalized Gaussian function: Ã µ ¶ ! |t − p| β gVA (t) = C1 exp − , (3.34) α where C1 is a normalizing constant, α determines the scale and β the peakiness. This waveform allowed us to approximate well the structure of a ventricular complex using only few atoms. Figure 3.11A shows a QRST complex and its approximation by three atoms only. With respect to the simpler Gaussian function, an appropriate choice of β allowed us to approximate wave peaks with more accuracy (see Fig. 3.11B). The range of values for α and β had been chosen experimentally after an extensive series of tests: α ∈ {3, 4, ..., 7} ∪ {49, 50, ..., 54}. The first set was adapted for Q, R, and S waves and the second one was adapted for the T wave approximation, while β ∈ {1.5, 1.6, ..., 2.2}. Together with p, this made DVA highly coherent, but also very flexible for VA approximation. However, such a dictionary is far from being optimal, and several improvements are still possible, mainly concerning the approximation of T waves.


47

Figure 3.11: (A) Ventricular complex and its approximation using three atoms only. (B) Influence of β on the generalized Gaussian function (see Eq. 3.34). Modeling electrocardiogram atrial activity The sub-dictionary DAA was generated by all possible translations of a real Gabor function: Ã µ µ ¶ ! ¶ 2πk(t − p) t−p 2 √ cos gAA (t) = C2 exp − −ψ , (3.35) N α 2 where C2 is a normalizing constant, N is the signal length, α tunes the scale, the integer k represents the frequency, and ψ represents the phase. This waveform was especially adapted for AA approximation. Indeed, as can be observed in Fig. 3.12A, a fibrillating AA is of oscillatory nature, which yields a good fit due to the optimal spatiotemporal frequency localization of Gabor functions (see Fig. 3.12B).

Figure 3.12: (A) Example of a simulated AA wave during fibrillation. (B) Gabor atom. The values of the Gabor function parameters were determined through an extensive analysis on several ECG signals (see [92]). During the design of DAA , special care in limiting the maximum correlation between DAA and DVA atoms was required. Indeed, excessive coherence between this two sub-dictionaries turns into a complete failure of the algorithm. Finally D turned out to be highly redundant and able to represent well the ECG signals. However, some problems are still present especially for the T waves. The dictionary proposed in this

48


section was the result of empirical and theoretical studies on the simulated and clinical traces described in Sec. 2.4.3 and 2.3.2. The dictionary D design has been deeply studied in [93], where a particular care has been exercised in bounding the coherence between DAA and DVA .

3.4.3 Electrocardiogram sparse decomposition by weighted orthogonal matching pursuit To Eq. 3.31 corresponds an underdetermined problem that has no unique solution. The search for the sparsest approximation of xECG requires an exhaustive test of all coefficient subsets, i.e. it is a combinatorial problem. Different approaches have been proposed in order to make the retrieval of a solution for the dictionary coefficients b computationally affordable (see [94] for a review of some of them). These approaches in general do not guarantee the recovery of the sparsest solution. Nevertheless, recent results show that under certain conditions on the dictionary and the signal, even these fast sub-optimal techniques find the sparsest approximation [95]. Weighted orthogonal matching pursuit As described before, the OMP algorithm selects the atoms by updating the whole set of coefficients b to minimize the distance to the original signal instead of only optimizing the coefficient of the newly selected atom gl (t). In this study, a weighted OMP [91] is propose to decompose the ECG signals into AA and VA sources. Weighted OMP iteratively builds h-term approximants f of the original signal x. These approximants represent the function that iteratively fits best the original signal x after the orthogonal projection of the selected atoms. These atoms glh are selected according to the same rule as MP. Each iteration h can be seen as a two step procedure displays in Table 3.12. The signal representation generated by weighted OMP is thus of the form described by Eq. 3.30. Weighted OMP was recently proved in [91] to outperform OMP when using coherent dictionaries and reliable prior information. Weighted OMP can consider, in the decomposition algorithm, a priori models about the behavior of the dictionary in use with the class of signals to decompose. Weight generation: relation between electrocardiogram a priori knowledge and the dictionary The ECG signal xECG during AF can be divided in cardiac cycles. Each cardiac cycle can be divided into a set of intervals corresponding to the different VA waves (Q, R, S, T and U waves) and an interval with AA only. VA intervals can be estimated and identified, in practice, through the use of fiducial point detection, see Sec. 3.1. This prior information can thus be used to define the weights wl in step 1 of Table 3.12. The a priori knowledge obtained from the fiducial point detection needs to be related with the redundant dictionary D in the following way. D was divided in DAA and DVA . During AF, the AA was found through the entire ECG signal xECG . Hence, atoms contained in DAA can not be penalized in terms of this information. This is the reason why the weights wl associated to the dictionary DAA were forced to 1. To the contrary, the selection of the atoms gl in the dictionary DVA can be successfully influenced by the use of the available a priori information. Sub-dictionary DVA , as seen in Sec. 3.34, was composed of a sub-dictionary optimized for QRS waves and a sub-dictionary designed for T waves. Depending on


49

Table 3.12: Processing steps of the weighted orthogonal matching pursuit procedure. Initial step Step 1.

Initialization of the first residual to the original signal x(t) (rh = x, where h denotes the hth iteration.). Selection step where an atom glh ∈ D is chosen according to: glh = arg max |hrh , gl i| · wl , gl ∈D

Step 2.

where rh is the residual that depends on gl , l = 0, 1, · · · , h − 1, and wl ∈ [0, 1] is a pre-estimated weight that reflects, according to a predefined model, the a priori likelihood that atom gl may belong to the good set of atoms best approximating the signal. An orthogonal projection step where an approximant fh+1 ∈ span(gi p , p = 0, 1, · · · , h), and a residual rh+1 = x − fh+1 are generated (notice that rh+1 ⊥ fh+1 ∀h). This step is the one in charge to update, at every iteration, the set of scalar expansion coefficients.

the VA interval, the weights wl can be set to 1 for every atom gl in the dictionary DVA belonging to the appropriate kind for that interval. In case an atom gl is unsuitable for a given interval, the corresponding weight wl can be set to a penalizing factor 0 ≤ wl < 1. Thanks to the reliability of the estimators, it turned out that the best value for the coefficients wl associated to the dictionary DVA in our experiments was 0. This means that the atoms gl associated to the dictionary DVA were forced to be located only in appropriate intervals (QRS complex or T wave intervals).

3.4.4 Results on simulated and clinical data Validation Two 4-second ECG signals (one simulated and one clinical ECG signals) described in Sec. 2.4.3 and 2.3.2 were used to validate the proposed source separation approach. The normalized MSE between the original and the estimated AA and VA was used to evaluate the simulated performance of the proposed source separation method on three significant leads (VR, V1 and V4). In order to study the influence of the AA amplitude on the method, three different simulated AA signals were created: 50%, 100% and 150% of the original simulated AA amplitude. The number and length of the ECG signals used in this validation were limited due to the high computation load of the algorithm, that is, almost 24 hours for a 4-second ECG signal. Results First of all, we underline that we validated our choice of weighted OMP over OMP with these simulated measured 4-second ECG signals. By using weighted OMP, we decreased the normalized MSE in the recovery of VA (respectively, AA) by -0.83 (respectively, -0.86). All the following

50


Figure 3.13: (A) Simulated measured 4-second ECG signal on lead V1. (B) Original VA on lead V1. (C) Estimated VA on lead V1 (normalized MSE = 0.14). (D) Simulated AA on lead V1. (E) Estimated AA on lead V1 (normalized MSE = 0.21). results were obtained by approximating ECG signals with 50 atoms. Figure 3.13 shows the resulting separation of VA and AA of the simulated measured 4-second ECG signal on lead V1. We observed that our method approximates each one of the VA periods, and at the same time, separates the AA with a great fidelity. Table 3.13 displays the normalized MSE values on leads VR, V1, and V4 for the different AA amplitudes. Table 3.13: Normalized MSE on leads VR, V1 and V4. The performance of the method is tested on three different AA amplitudes (50, 100 and 150 % of the original simulated signal). normalized MSE

AA amplitude

VA

AA

VR VR VR

50% 100% 150%

0.08 0.08 0.08

4.95 1.27 0.55

V1 V1 V1

50% 100% 150%

0.08 0.14 0.57

0.44 0.21 0.37

V4 V4 V4

50% 100% 150%

0.06 0.06 0.07

4.50 1.20 0.58

Figure 3.14 shows the resulting separation of the VA and AA for a clinical 4-second ECG signal on lead V2. Apart from the visually satisfying component separation, these resulting signals were validated using estimated PSD and their respective DFs. Further results can be found in [92].

3.5. P OSTPROCESSING USING EMPIRICAL MODE DECOMPOSITION

51

Figure 3.14: (A) Clinical 4-second ECG signal on lead V2 with a DF of 1.56 Hz (see its estimated PSD (E)). (B) Estimated VA on lead V2 with a DF of 1.56 Hz (estimated PSD in (F)). (C) Estimated AA on lead V2 with a DF of 7.55 Hz (estimated PSD in (G)). (D) Estimated AA on lead V2 magnified five times.

3.4.5 Discussion In the ICA based approaches, a major disadvantage is that only statistical priors are considered without taking into account the structural nature of signals. A possible enhancement could thus be the use of sparse source separation approaches based on signal adapted redundant dictionaries, as presented in this section. We observe that the quality of the AA estimation depends on the lead and its original amplitude. The AA normalized MSE values are much lower with the amplified amplitude (150%) and the overall performance on lead V1 is better than that of the other two leads. Of course, the normalized MSE values are directly related to the signal amplitude, and, in lead V1, the AA amplitude is higher compared to the other leads. In the same time, we observe a decrease of VA estimation performance in lead V1. The DF of VA (AA, respectively) is between 1 and 2.5 Hz (between 4 and 10 Hz, respectively). The fact that there is no presence of DFs associated with the VA in the AA estimated PSD demonstrates the quality of the results on clinical data.

3.5 Postprocessing using empirical mode decomposition In a general context, the frequency of a vibratory motion is defined as the number of oscillations per unit time, where a vibratory motion is any back and forth motion, and an oscillation is a complete

52


back and forth motion. An oscillation is defined as a complete cycle of the vibrating reference that moves from the equilibrium position to one extremity, then to the other extremity, and finally back to the equilibrium position. A simple harmonic motion is a vibratory motion in which the acceleration is proportional to the emplacement and always directed toward the equilibrium position. In signal processing, the concept of frequency is commonly related to the Fourier representation ¯ is defined as the average frequency derived from the of a signal, where the global frequency ω Fourier coefficients F(ω) as follows: Z

¯= ω

ω|F(ω)|2 dω.

(3.36)

This definition is meaningful only for stationary signals. In 1946, Van der Pol [96] defined the instantaneous frequency by analysing the expression for a simple harmonic motion s(t) = a cos(2π f t + θ), where a is the amplitude, f is the frequency of the oscillation, and θ is a phase constant. The entire argument of the cosine function, 2π f t + θ, is the phase φ(t). It leads to the definition of the instantaneous frequency as: ˆ = ω(t)

1 dφ(t) . 2π dt

(3.37)

In the same year, Gabor [97] proposed a method to generate unique complex signals from real ones, computing the analytic representation of a signal x(t) = a(t) cos(φ(t)) defined as: z(t) = x(t) + jy(t) = a(t)e jφ(t) ,

(3.38)

where z(t) is Gabor complex signal, x(t) is the real signal and y(t) is its Hilbert transform. Conceptually, the instantaneous frequency can be interpreted as the frequency of a sine wave which locally fits the signal of interest. It has a meaning only for monocomponent signals characterized by a narrow range of frequencies varying as a function of time [98]. In order to have a welldefined instantaneous frequency, the signal has to be symmetric, and without riding waves [99]. These conditions are related to the general concept of frequency described before. They insure that the analytic form of the signal has fixed distance from a reference point, and therefore, a meaningful instantaneous frequency. Figure 3.15 displays the physical interpretation of a well-defined instantaneous frequency (case a) for the signal x(t) = α + sin( f t), where z(t) = a + sin( f t) + j cos( f t), as defined in Eq, 3.38. It also displays the instantaneous phase in Fig. 3.15B and its instantaneous frequency in Fig. 3.15C, defined as the derivative of θ1 (t). The stationary frequency f of signal x(t) equals 0.1 and α equals zero. It also displays the negative effects of asymmetries where α ≤ 0 (case b) and riding waves where α ≥ 0 (case c) on the instantaneous phase and frequency.

3.5.1 Empirical mode decomposition Fourier techniques, wavelet analysis and PCA are some of the major approaches used for decomposing time series into components. All of these satisfy two criteria: (1) completeness of the basis and (2) orthogonality of the basis. The limitation of stationarity, of time resolution (wavelet) or the lack of characteristic time of frequency components (PCA) are some of the motivations for exploring new analysis techniques.


53

Figure 3.15: Physical interpretation of instantaneous frequency. (A) The phase plane for the functions of x(t) = α + 0.1 sin(t). (a) α = 0; (b) α < 1; (c) α > 1. (B) The unwrapped instantaneous phase of these three functions. (C) The instantaneous frequency of the three functions computed according to Eq. 3.37.

EMD was first introduced by Huang et al. in 1998 [100]. This technique was proposed to analyze non-stationary and nonlinear time series and to determine characteristic time/frequency scales. The EMD technique decomposes time series into complete, almost orthogonal, local and adaptive basis functions, named IMFs. These IMFs should have a well-behaved Hilbert transform (and thus a well-defined instantaneous frequency). In order to have a well-behaved Hilbert transform, the IMFs are required to satisfy two criteria: (1) the number of extrema and the number of zero crossings must differ by one at most, and (2) the mean value of the envelopes, one defined by the local maxima (upper envelope) and the other by the local minima (lower envelope), must be zero. Any signal that satisfies these two criteria is considered to be an IMF. This definition of IMFs is empirical and there is no explicit equation for estimating them. Rilling et al. proposed an effective implementation of EMD [101], see Table 3.14. Recently, Andrade et al. proposed the use of filtering technique based on EMD to denoise electromyographic signals [102]. In this section, we study the effectiveness of an EMD based technique for postprocessing the ECG signals after VA cancellation. The technique selects the IMFs that represent AA through their DFs and the energy ratios with respect to the TQ and QRS segments. An IIR highpass filter is applied to remove the baseline drift in the last stage. The performance of this technique was studied on ECG signals generated by a biophysical model of the atria, as well as on the clinical recordings described in Sec. 2.4.3 and 2.3.2. The performance of the technique was compared to that of an IIR bandpass filtering alone. Electrocardiogram postprocessing Let x(t) be the ECG signal obtained after the application of VA cancellation. In some cases, baseline drift and VA residues are still present. The proposed postprocessing procedure is the one showed in Table 3.15. Welch’s technique was used to obtain the PSD estimate. Due to the properties of IMFs, the DFs slowly decrease from the first to the last IMF. We defined all the values of the ith IMF in the TQ segments (respectively QRS segments) by an N-by-1 vector ai (respectively M-by-1 vector bi ). The energy ratio ri of the ith IMF was computed as follows: ri = (∑ a2i /N)/(∑ b2i /M). The IMFs taken

54


Table 3.14: Batch algorithm for decomposing a signal into IMFs. Given a signal x(t) to be decomposed, the initial step is defining xi, j (t) to be equal to x(t), where the first index i refers to the ith IMF and the second index j refers to the jth iteration to find the ith IMF. The subsequent steps are: Step 1. Step 2. Step 3. Step 4. Step 5.

Step 6.

Identification of all extrema of xi, j (t); up Extrapolation of the lower envelope elo i, j (t) (respectively upper envelope ei, j (t)) by an interpolation between minima (respectively maxima); up lo Computation of the mean of both envelopes eme i, j (t) = (ei, j (t) + ei, j (t))/2; Extraction of the ith IMF candidate ci, j (t) = xi, j (t) − eme i, j (t); If candidate ci, j (t) fulfills the criteria defining an IMF, it is assigned as the ith IMFi (t), the new xi+1,1 (t) = x(t) − ∑ik=1 IMFk (t) and steps (1) to (5) are repeated; If candidate ci, j (t) does not fulfill the criteria defining an IMF, it is assigned to the variable xi, j+1 (t) and the steps (1) to (5) are repeated.

When xi, j (t) is equal to eme i, j (t), the whole procedure stops and xi, j (t) is assigned as the th last i IMF. The criteria defining an IMF were the ones proposed by Rilling et al.,[101]. A candidate ci, j (t) is considered as an IMF if its evaluation function σi, j (t) is lower than θ2 for all values, and lower than θ1 for (1 − α)% of the values. The evaluation function up lo is defined as σi, j (t) = |eme i, j (t)/mi, j (t)|, where mi, j (t) = (ei, j − ei, j )/2.

Table 3.15: Batch algorithm for postprocessing based on empirical mode decomposition. Step 1. Step 2. Step 3. Step 4. Step 5. Step 6.

Decomposition of x(t) into IMFs; Identification of the dominant frequencies for each IMF by using a power spectral density (PSD) estimate; Computation of the energy ratio between TQ and QRS segments for each IMF; Selection of the IMFs that represent AA using their dominant frequencies and energy ratios; Reconstruction of the estimated AA with the summation of the selected IMFs; Application of a final highpass filter to the estimated AA signal.

to represent AA were those with DFs below 10 Hz and ri above 0.5. The highpass IIR filter used to remove the baseline drift was a zero-phase fifth-order Butterworth filter with a cutoff frequency of 2 Hz.


55

3.5.2 Evaluation The performance of the proposed postprocessing was evaluated on simulated and clinical data describes in sections 2.4.3 and 2.3.2. The simulated ECG signals during AF were the ones with the addition of the AV node model. The energy ratio between the TQ and QRS segments, the kurtosis and the DF values were used to evaluate the performance of the postprocessing on lead V1. This lead was preferred to the other leads due to its typical clear ventricular residues after applying VA cancellation. The normalized MSE between the estimated AA signals and the original simulated AA signals was computed. The energy ratio (respectively the kurtosis value) is generally close to 1 (respectively lower than 0) for an AA signal. The results were compared to those of a bidirectional IIR bandpass filter (zero-phase fifth-order Butterworth). The cutoff frequencies for the bandpass filter were 2 and 15 Hz.

3.5.3 Results on simulated and clinical data Figure 3.16 shows the first iteration on an ECG signal during AF after VA cancellation. It demonstrates that the typical VA residues after applying VA cancellation have the tendency to be include in the first IMFs.

Figure 3.16: (A) Clinical 2-second ECG signal on V1 (saturated R waves). (B) Signal (A) after VA cancellation. Blue (respectively black) dashed ellipses represent possible QRS residues (respectively T-wave residues). Red dashed ellipses represent step like residuals after template subtraction. up lo (C) Mean envelope eme 1,1 (t) of (B) with its upper (e1,1 (t)) and lower (e1,1 (t)) envelopes. (D) The first candidate c1,1 (t).

Tables 3.16 and 3.17 summarize the performance of both techniques applied, respectively to the 88 simulated ECGs and to the 120 clinical ECGs. Figure 3.17 shows the results obtained by the proposed technique and with the other bandpass IIR filter applied to a clinical 2-second segment. For all results, the three parameters θ1 , θ2 , and α of the EMD algorithm were fixed at 0.5, 0.05, and 0.05, and the maximum number of iterations was fixed at 300, default values in [101].

56


Energy ratio

Kurtosis

normalized MSE

DF (Hz)

Real VA simulated AA after cancellation

0.0 ± 0.0 1.0 ± 0.1 1.3 ± 0.2

18.1 ± 2.3 -0.5 ± 0.5 0.4 ± 0.4

1.2 ± 0.1

2.0 ± 1.0 6.2 ± 1.2 1.5 ± 2.6

EMD IIR bandpass

1.1 ± 0.2 1.2 ± 0.2

0.0 ± 0.4 -0.1 ± 0.4

0.6 ± 0.1 0.5 ± 0.1

5.9 ± 1.3 6.2 ± 1.2

Table 3.16: The performance of the EMD-based technique compared to that of IIR bandpass filtering. Documented are: the energy ratio between the TQ and the QRS segments, the kurtosis, the normalized MSE, and the DF values (mean ± standard deviation) on the 88 simulated signals. Energy ratio

Kurtosis

DF (Hz)

ECG (V1) after cancellation

0.03 ± 0.04 1.16 ± 0.32

10.00 ± 4.85 1.30 ± 2.24

3.08 ± 1.95 0.87 ± 1.47

EMD IIR bandpass

1.02 ± 0.24 1.05 ± 0.28

0.62 ± 0.99 0.64 ± 1.05

5.83 ± 1.36 5.70 ± 1.41

Table 3.17: The performance of the EMD based technique is compared to that of applying a IIR bandpass filter. Documented are: the energy ratio between the TQ and the QRS segments, the kurtosis and the DF values (mean ± standard deviation) on the 120 clinical signals.

3.5.4 Discussion With regard to the simulated ECG signals, Table 3.16 shows that no significant statistical difference exists between the performances of the EMD based technique and those of the IIR bandpass filtering over the 88 simulated signals in terms of energy ratio and kurtosis values. In terms of normalized MSE, the IIR bandpass filtering (0.5 ± 0.1%) outperformed the EMD based technique (0.6 ± 0.1%). In terms of DF accuracy, the IIR bandpass filter also outperformed the EMD based technique; the average of DFs of the simulated AAs is 6.2 ± 1.2 Hz in comparison to the bandpass filtered signals (6.2 ± 1.2 Hz) and the EMD postprocessed signals (5.9 ± 1.3 Hz). Table 3.17 shows no significant statistical difference between the performance of the EMD based technique and the IIR bandpass filtering over the 120 clinical signals in terms of energy ratio, kurtosis, and DF values. The average of DFs estimated from these signals with the EMD based technique (5.83 ± 1.36 Hz) and the average of the ones estimated with the IIR bandpass filter (5.70 ± 1.41 Hz) also show that no significant statistical difference was present between the performances of both techniques. Interestingly, in some of the clinical cases, the performance of the EMD based technique was better than the performance of the IIR bandpass filter in terms of DF accuracy. These few results are masked in Table 3.17 by the averaging on a large number of signals. The clinical example showed in Fig. 3.17 is one of these cases. The frequency components of the VA residues (around 10 and 15 Hz) are still present after applying the IIR bandpass filter which is not the case with the EMD technique. The normalized MSE and the estimated DFs in the simulated and in most of the clinical cases demonstrate that the IIR bandpass filtering performs well when the VA residues do not dominate. Filtering may obviously be inefficient in cases where the artifacts have significant power inside the

3.6. C ONCLUSION

57

Figure 3.17: (A) Clinical 2-second ECG signal on V1 (R-waves saturated) and its PSD estimate (G) with a DF of 7.48 Hz. (B) Signal (A) after VA cancellation and its PSD estimate (F) with a DF of 0.50 Hz. (C) and (d) are the IMFs obtained from (B) and their corresponding PSD estimates ((I) and (J)). The black IMFs (group (D))were the ones that represent AA. (E) Post-processed estimated AA (sum of black IMFs, group (D)) with the EMD-based technique and its PSD estimate (K) with a DF of 4.97 Hz. (F) Post-processed estimated AA with a bandpass IIR filter (cutoff frequency of 2 and 15 Hz) and its PSD estimate (L) with a DF of 9.98 Hz.)

band of interest (see Fig. 3.17L). In these specific cases, the EMD based technique performs well in terms of DF accuracy. This may be explained by the properties of the IMFs. The IMFs are forced to be symmetric and without riding waves. When VA residues, pacemaker pulses, and other artifacts are dominant, they are mainly contained in the first IMFs. The VA residues present in the other IMFs are less concentrated and their impact on the estimate DF is attenuated, see Fig. 3.17C.

3.6 Conclusion In the ICA algorithms, a major disadvantage remains even if the components obtained do not seem to contain any VA involvement. The selected components represent synthesized AA signals characterized by their uncorrelation (second-order statistic) with synthesized VA (PCA), or by high-order statistical properties of AA, such as kurtosis values (ICA). When ICA algorithms are used, each

58


source is assumed to be a single point source. In the ECG, the ventricular and atrial electrical sources are too extended spatially to be considered point sources. The signals obtained with source separation algorithms, which are apparently free of ventricular involvement, cannot represent the complete spatial information contained in a 12-lead surface ECG even if they are re-projected using the demixing matrices. Concerning the weighted OMP based technique, the high computation load and the T wave representation remains the principal limitation. The dedicated preprocessing step that includes fiducial point detection and baseline correction is crucial. It insures that each ventricular complex starts with a potential of zero on each lead without any VA complex enlargement or delay, and that the fiducial points are well located. The refined ABS and the single beat techniques proposed outperformed the others techniques. They canceled the ventricular involvement in ECG signals with high quality results. In the situations where the ventricular complexes are highly regular, and where the ECG record contains a sufficient number of ventricular complexes, the refined ABS technique is appropriate. In the situation where the ventricular complex morphology is variable, which is the case in most AF patients, or when the ECG record contains only a few ventricular complexes, the use of the single beat technique is preferred.

Part II

Atrial fibrillation classification

59

Atrial fibrillation classification based on clinical features extracted from the electrocardiogram

T

4

development of accurate predictors of the acute or abrupt onset of paroxysmal AF is clinically important because of the increasing possibility of electrically stabilizing and preventing atrial arrhythmias with different pacing techniques [103]. The advances in anti-tachycardia pacing, drug management, and defibrillation may be successfully used to prevent the acute onset of paroxysmal AF prior to loss of normal SR. In 2001, the board of the Computers in Cardiology conference and PhysioNet, a public service of the Research Resource for Complex Physiologic Signals, have proposed a challenge. This challenge consisted in determining if segments of surface ECG that do not include paroxysmal AF contain sufficient information in order to distinguish subjects at risk of paroxysmal AF from others not at risk, and to predict imminent paroxysmal in at-risk subjects. The best challenge performances indicate that roughly 80% of the subjects can be correctly classified as at-risk or not, and that imminent paroxysmal AF can be predicted in roughly 80% of subjects at risk. The most successful approaches were based on analysis of the incidence of premature atrial complexes and P wave variability [104; 105]. HE

In 2004, the Computers in Cardiology conference and PhysioNet have continued in the AF area with a new challenge, which consisted in predicting if and when an episode of AF will selfterminate. The risks of sustained AF are serious and include strokes and myocardial infarctions caused by the formation of blood clots. Although spontaneous terminating episodes of AF are often very short, it is interesting to note that longer episodes lasting several minutes also occur. These appear to be very similar to permanent AF. Subtle changes in rhythm during the final minutes or seconds of such episodes may lead to (or announce) termination of AF. Improved understanding of the mechanisms of spontaneous termination of AF may lead to improvements in treatment of sustained AF. If it was possible to recognize the conditions under which episode of paroxysmal AF is likely to self-terminate, it might also be possible to intervene on affected individuals to increase the likelihood of self-termination of what would otherwise became sustained AF. 61

C HAPTER 4. ATRIAL FIBRILLATION CLASSIFICATION BASED ON CLINICAL FEATURES 62

EXTRACTED FROM THE ELECTROCARDIOGRAM

Over twenty teams have participated at the 2004 Computers in Cardiology 2004 Challenge and most of them were able to classify sustained and spontaneously terminating AF with high accuracy with six teams classifying 90% or more of the non-terminating AFs, and AFs that terminate immediately after the end of the record. Only three teams achieved high accuracy by classifying 90% or more of the AFs that terminate one minute after the end of the record, and AFs that terminate immediately after the end of the record. Most of the approaches began by subtraction of the QRS complexes from the ECG signals, followed by a frequency-domain analysis. We decided to approach the challenge from a clinician’s point of view. Prof. Kappenberger of the Centre Hospitalier Universitaire Vaudois (CHUV) identified various observations that characterize the disorganization of fibrillatory waves. Next, we developed the processing tools to quantify these observations. These features are presented in Sec. 4.2. A support vector machine (SVM) approach was used to solve the classification problem, see Sec. 4.3. Classification results on the challenge database are presented in Sec. 4.5. This classification based on clinical features was also applied on our own simulated and clinical database. A similar classification approach was used to separate AFs with complex dynamics from those with stable dynamics (simulated database) and to separate different AF types (paroxysmal, persistent, permanent, single and recurrent AF episode), different AF aetiologies or AF pharmacological and electrical cardioversion results (clinical database) see Sec. 2.4.3 and 2.3.2, respectively. To evaluate the real potential of these 12 features, a statistical test (Student’s t-test) and a multivariate analysis of variance (MANOVA) were used. A brief discussion concludes this first AF classification approach in Sec. 4.7.

4.1 The Computers in Cardiology 2004 Challenge The challenge required a collection of AF recordings of known types. In order to locate episodes of sustained and paroxysmal AF, the organizers reviewed the R-R interval scattergrams and instantaneous heart rate tachograms from a large set of long-term (20-24 hours) ECG recordings. The sustained AF episodes were defined as episodes of duration exceeding one hour that did not terminate before the end of the recording. Paroxysmal AF episodes were episodes that lasted one minute (in many cases, at least two minutes). Then, they examined the ECG signals at high resolution in areas of interest and selected sustained and paroxysmal AF excerpts to be used. All in all, 80 one-minute recordings of AF from 60 different subjects were collected. Each record contains two unspecified-lead ECG signals simultaneously recorded. Three different types of AF had to be classified: non-terminating AF (Group N) defined as sustained AF at least an hour following the one-minute record, AF terminating one minute after the end of the one-minute record (Group S) and AF terminating immediately after the end of the oneminute record (Group T). Note that the records in Group S and T come from the same long-term ECG recordings. The database was divided into a learning set of 30 one-minute records (10 labeled records from each group) and two test sets. The test set A contained 30 records of groups N and T. The test set B contained 20 records of groups S and T. These test sets had to be classified correctly using an automated technique. Each one-minute record was labeled as follows: first, the name of the group, than, the record number (ex.: t09 is the 9th record in Group T).

4.2. C LINICAL FEATURE EXTRACTION

63

4.2 Clinical feature extraction We applied systematically a baseline removal step consisting of a zero-phase fifth-order highpass Butterworth filter with a cutoff frequency of 0.5 Hz on each ECG signal. An accurate segmentation was crucial in our approach because most of our observations were based on time segments where only AA is present. These segments included fibrillatory waves or organized P waves. The fiducial point detection was the same as the one described in Sec. 3.1. The only difference was that the RMS signal was computed from two leads only, instead of eight. The timings of the onset of the AA segments were defined as the local minimum of the RMS signal after each T wave. The timings of the AA segment endings were equal to the timing of the onset of the following ventricular depolarization, see Fig 3.1. When AF converts to SR, the completely unstructured fibrillatory waves tend to be more organized and structured. This behavior was detected by different clinical observations, which lead to the features used in this study. These are presented in the next seven subsections.

4.2.1 Fibrillatory wave dissymmetry The first observation is on the symmetry or the dissymmetry of the fibrillatory waves in the AA. When AF is to terminate soon, P waves tend to reappear and fibrillatory waves are more organized. This translates into a stable (positive or negative) fibrillatory wave polarity that brings dissymmetry that is absent in a non-terminating AF. As such, the clinician tries to identify fibrillatory wave asymmetry. Figure 4.1 shows a typical example (record t09 of the challenge database), in which a clear dissymmetry can be observed.

Figure 4.1: Example of fibrillatory wave dissymmetry

Mathematically, features #1 and #2 (one for each lead) were expressed by the skewness of the AA segments: ¡ ¢3 ∑Ni=1 x(i) − µx skewness = , (N − 1) σ3

(4.1)

where the x(i) are the samples over all AA segments, µx and σ are the estimated mean and standard deviation of these samples, and N is the total number of samples x(i) in all segments. The skewness



value is close to zero for a signal with symmetric amplitude distribution and positive or negative when the distribution is asymmetric. A zero-mean signal with positive values larger in amplitude than the negative ones will be characterized by a negative skewness value. In the example displayed in Fig. 4.1, the skewness value was equal to -0.60.

4.2.2 R-R intervals When the ventricular rate is high, AF is more likely to terminate soon because the heart is thought to be unable to sustain a high ventricular rate in AF for a long period of time. We quantified this observation using the average R-R interval value, which gave feature #3. The R wave peaks are first detected. Then the R-R interval values were regularly resampled using spline interpolation [106]. There is often a marked change (positive or negative) in ventricular rhythm prior to AF termination. This was quantified using a simple R-R interval analysis: the difference between the R-R interval averages during the first and the last ten seconds of the record, which gave feature #4. Such extended R-R analysis has previously been reported in [107; 108].

4.2.3 Fibrillatory wave intervals When AF reverts to SR, the fibrillatory wave intervals decrease and multiple fibrillatory waves reduce to a P wave. To quantify this clinical observation, first, a zero-phase fifth-order lowpass Butterworth filter with a cutoff frequency of 8 Hz was applied. This cutoff frequency is appropriate for the identification of fibrillatory waves: it is high enough not to disturb the shape of fibrillatory waves and low enough to produce a single peak for each wave. Next, a derivative-based method was applied to the AA segments to detect the fibrillatory wave peaks. Figure 4.2 shows a typical example (record t03 with fibrillatory wave intervals around 142.9 ms). The bold dashed lines represent the filtered AA segments and the black dots corresponds to the identified fibrillatory wave peaks. For each AA interval, the number of positive peaks per time unit was computed on both leads. The feature #5 was defined as the highest value of all AA intervals.

0.5 mV

1s

Figure 4.2: Example of fibrillatory wave intervals

4.2. C LINICAL FEATURE EXTRACTION

65

4.2.4 Atrial activity amplitude When the AF is more organized in the atrial tissue, the resulting fibrillatory waves in the ECG are larger. To have a correct estimate of the AA amplitude, we used the detected fibrillatory wave peaks identified for the previous feature. The identified peaks and the minima between these peaks were used to compute an average AA amplitude on both leads, which gave features #6 and #7.

4.2.5 Low-frequency modulation of atrial activity amplitude The next observation relates to the possible low-frequency modulation in the amplitude of AA. It has been observed empirically that, prior to AF termination, fibrillatory wave amplitude oscillates slowly. A good example is the record t07 displays in Fig. 4.3 where this amplitude modulation is clearly visible.

0.5 mV

1s

Figure 4.3: Example of low-frequency modulation of atrial amplitude

To quantify this observation, we applied first a zero-phase fifth-order bandpass Butterworth filter to the signal with cutoff frequencies at 1 and 8 Hz. The filtering below 1 Hz is used to eliminate any residual baseline drift. After the filtering, the same peak detector described for the two preceding features was applied to identify the maximum values of the AA. To minimize the power of VA, a saturation operation was applied to each ECG signal. This operation is a hyperbolic tangent one: x(t) ˆ = amax · tanh(

2 · x(t) ), amax

(4.2)

where amax is the maximum value of the AA segments, x(t) is the ECG signal after applying the bandpass filter, x(t) ˆ is the saturated version of x(t), and tanh denotes the hyperbolic tangent. A morphological envelope detector was used to extract the upper and lower envelopes of the resulting signal x(t). ˆ The final amplitude estimate a(t) was obtained by subtraction of the upper envelope from the lower one and the estimated PSD was computed without the DC component. Features #8 and #9 represent the total power of this amplitude signal a(t) below 0.6 Hz on each of the two leads.



4.2.6 Similarities between atrial activities in different leads Another observation is the similarity between AAs in the two leads. During non-terminating AF, the fibrillatory waves in the two leads are quite dissimilar, possibly due to the large number of wavefronts propagating in the atrial tissue. Before AF returns to SR, fibrillatory wave shapes become similar, reflecting the structuration of AF. The two leads of record s02 display this similarity (Fig. 4.4). In the first 3.5-second interval, the fibrillatory waves are correlated, and in the second 1.5-second interval, the fibrillatory waves are anti-correlated.

Figure 4.4: Example of similarities between atrial activities in different leads. In the first 3.5 interval, the fibrillatory waves are correlated, and in the second 1.5-second interval, the fibrillatory waves are anti-correlated.

Mathematically, this observation can be expressed as the normalized cross-covariance: Nj

q

∑i=1 (xi j − µx j )(yi j − µy j ) Nj

Nj

,

(4.3)

∑i=1 (xi j − µx j )2 ∗ ∑i=1 (yi j − µy j )2 where xi j and yi j are the ith samples on leads #1 and #2 in the jth segments. µx j and µy j are the estimated means of the jth segment for each of the two leads, and N j is the total number of samples in the jth segment (the same for both leads). The average of the absolute cross-covariance values for all AA segments was computed, which gave feature #10.

4.2.7 High-frequency power in atrial activity segments The final observation is the power of the AA segments in the high-frequency range. It is assumed that the fibrillatory waves close to conversion into a P wave have more high-frequency components than the fibrillatory waves in non-terminating AF. The quantification used was the average of the estimated spectral power above 20 Hz across the AA segments on both leads (features #11 and #12).

4.3. OVERVIEW OF SUPPORT VECTOR MACHINE CLASSIFICATION

67

4.3 Overview of support vector machine classification In this chapter and the next two ones, various AF classifications are performed based on different features. We chose to use a support vector machine (SVM) approach to perform these AF classifications. In this section the basic SVM concepts will be briefly described. Details related to the SVM can be found in Müller et al. [109]. For two linearly separable classes, which means that all the examples including the training ones can be separable by a hyperplane, one considers the problem of separating the feature vector xi with a hyperplane defined as wT xi − b = 0, where the index i stands for the ith class, the vector w defines the perpendicular to the separating hyperplane, and b is its y − intercept of the line. In this case, the SVM chooses a hyperplane that maximizes the minimal Euclidean distance between the hyperplane and the training examples, the so-called margin. It can be shown that it is equivalent to minimizing the following expression: 1 min kwk2 w,b 2

(4.4)

subject to ci (wT xi + b) ≥ 1, where i = 1 · · · N, ci ∈ −1, 1 denotes the class labels, and N is the number of training examples. The margin may be proved to correspond to the quantity 1/||w||, thus a maximization of the margin is achieved by minimizing ||w||2 . Figure 4.5A displays a geometrical interpretation of this optimization problem, where dmin = 1/||w||.

Figure 4.5: (A) Optimal separating hyperplane example in a separable class context. (B) and (C) Generalized optimal separating hyperplane examples in unseparable class contexts where C = +∞ and 0 respectively.

In the case where the training set is not linearly separable, no solution that respects all constraints exists. In 1995, Cortes and Vapnik introduced the following cost function associated with misclassification [110]: 1 min kwk2 +C ∑ ξi 2 i

w,b,ξi

(4.5)

T

subject to ci (w xi + b) ≥ 1 − ξi and ξi ≥ 0, where the ξi are slack variables, and C is a penalty function. If C is infinite, this problem is equivalent to the problem in Eq.4.4. Figure 4.5B illustrates this situation. However, if C is small enough,



some training examples are allowed to lie inside the margin or on the wrong side of the hyperplane, see Fig. 4.5C. In 1992, Boser et al. proposed to implement nonlinear classifiers by applying the kernel trick to maxium-margin hyperplanes [111]. The kernel trick replaces the scalar products by different kernel functions to link higher-dimensional spaces to the original space. For example, with the kernel function defined as k(xi , x j ) = xTi x j , we obtain a linear SVM, and with a kernel function defined as exp(−γkxi − x j k2 ), we obtain a nonlinear SVM with a radial basis function.

4.3.1 Classification procedure For the different AF classifications of the next three chapters, the procedure was the following. A SVM algorithm was used to perform the separation between different AF groups based on various features. The Matlab SVM Toolbox produced by Gunn et al. was used to implement this SVM algorithm [112]. Two different kernel functions were used, the linear and the radial basis ones, see Sec. 4.3. For each kernel, the best training result between penalty coefficient values fixed at one and infinity was used for the AF classifications. If both linear and radial basis kernel functions produced accurate or similar training errors, the linear one was preferred in order to avoid overfitting when applied to the test sets. Concerning the Computers in Cardiology 2004 Challenge, the classification procedure used the 12 features to separate the non-terminating AFs (group N) from the AFs that terminate immediately after the records (group T), and to separate the AF that terminate one minute after the record (group S) from the AFs that terminate immediately after the records (group T). The classifier was first trained on the two training sets N-T and S-T that contain ten records of group N (respectively S) and ten records of group T. Then, the resulting hyperplanes were used to classify the two test sets A and B. The resulting hyperplane obtained from the training set N-T was also applied to our simulated and clinical databases described in Sec. 2.4.3 and 2.3.2. As for the other AF classifications present in this chapter and the two following ones, a leaveone-out procedure was applied due to the limited number of records [113]. In brief, the SVM was trained on all recordings except one. This one recording was used for testing. This procedure was applied to all recordings to provide an accurate estimation of the percentage of good classification.

4.4 Statistical tests In 1908, William Sealy Gosset introduced the t statistic to cheaply monitor the quality of beer brews using the pen name "Student" [114]. The most frequently used t test is a test of the null hypothesis that the means of two normally distributed populations are equal. Given two data sets, the t test determine if the means are distinct, provided that the distributions can be assumed to be normal. The test is named Student’s t test when the variances of the two populations are assumed to be equal and named Welch’s t test when this assumption is dropped. The p value of the Student’s t test defines the probability of observing a value in the corresponding population if the null hypothesis is rejected. If this p value is below a fixed threshold chosen for significance (usually 0.05 level), then the null hypothesis is rejected. In the Student’s t test, the means of the two groups are then

4.5. R ESULTS ON THE C OMPUTERS IN C ARDIOLOGY 2004 C HALLENGE DATABASE

69

considered different. In statistics, analysis of variance (ANOVA) is a collection of statistical models in which the variance is partitioned into components due to different explanatory variables [115]. This technique was developed by R. A. Fischer in the 1920s and 1930s, and is also known as Fischer’s ANOVA, or Fischer’s analysis of variance, due to the use of Fisher’s F-distribution in the statistical significance test. Different conceptual classes of models exist. The most common one is the fixed-effect model which assumes that the data comes from normal populations that differ only in their means and that they have homogeneity of variances. These are the same assumptions as for the Student’s t test. The multivariate analysis of variance (MANOVA) is an extension of ANOVA to treat more than one dependent variable [116]. It tests the null hypothesis that the multivariate means of each group are the same n-dimensional multivariate vector, and that any difference observed in the sample is due to random chance, where n is the number of features. If all n features produce statistical differences between the group means, then the multivariate means will lie in a n-dimensional space. The MANOVA p value defines the probability that the group means lie in this n-dimensional space. It is common to declare a result significant, if the MANOVA p value is less than 0.05. Note that a high MANOVA p value denotes that multivariate means probably lie in a lower dimensional space, which only means that one or more features do not produce statistical differences between the groups. To evaluate the accuracy of the 12 clinical features, Student’s t-test and MANOVA were applied to the group pairs N-T and S-T with respect to the 12 features. A Kolmogorov-Smirnov test and a F test were also applied to the group pairs N-T and S-T to verify that the two assumptions required for the Student’s t-test were respected (normal distributions and equal variances of the populations compared, respectively). The p values of all statistical tests are displayed in Sec. 4.5. MANOVA was also applied to the other simulated and clinical AF groups with respect to the 12 clinical features. For the other AF classifications included in the two following chapters, MANOVA was also used to evaluate the accuracy of various features. MANOVA was applied to different AF groups (ex.: different AF aetiologies) with respect to different features (ex.: DFs observed in leads V1 and V5).

4.5 Results on the Computers in Cardiology 2004 Challenge database Two different AF classifications are presented in this section, a first classification of non-terminating AFs versus AFs terminating immediately after the end of the record and a second one of AFs terminating one minute after the end of the record versus AFs terminating immediately after the end of the record. These two classifications are respectively named NT and ST. For the NT and ST classifications, the SVM with a linear kernel and a penalty coefficient fixed at 1 was trained on all records of the learning sets N-T and S-T, respectively. The best result for the NT classifier was obtained with ECG signals restricted to time intervals between 40 to 60 seconds. This classifier resulted in a score of 20 out of 20 for the learning sets N-T and 27 out of 30 for the test set A, which represents 94% of classification accuracy on the learning set and test set put together. The best result for the ST classifier was obtained with ECG signals restricted to time intervals between 0 to 60 seconds. For this ST classification, we obtained a score of 20 out of 20



for the learning sets S-T and 12 out of 20 for the test set B, which represents 80% classification accuracy on the learning set and test set put together. Tables 4.1 and 4.2 display the p values of the three different statistical tests (Kolmogorov-Smirnov, F and Student’s t tests) on the population formed by the groups N and T, and S and T respectively, with respect to the 12 features. The MANOVA p values of the population formed by the groups N and T, and S and T were equal to 0.22 and 0.82, respectively. Note that, by using the five features with the lowest Student’s t test p values (features #2, #3, #6, #8 and #9), the new NT classifier produced only three training errors. Table 4.1: Statistic tests on the clinical features for non-terminating AFs versus AFs that terminated immediately after the recording. Features #

1

2

3

4

5

6

7

8

9

10

11

12

Kolmogorov-Smirnov test F test

0.95 0.20

0.20 0.00

0.06 0.04

0.76 0.02

0.17 0.06

0.40 0.08

0.61 0.11

0.05 0.00

0.57 0.08

0.28 0.29

0.97 0.25

0.41 0.01

Student’s t test

0.55

0.18

0.04

0.94

0.75

0.16

0.67

0.19

0.17

0.22

0.98

0.41

Table 4.2: Statistics tests on the clinical features for AFs that terminated one minute after the recording versus AFs that terminated immediately after the recording. Features # KolmogorovSmirnov test F test Student’s t test

1

2

3

4

5

6

7

8

9

10

11

12

0.92

0.43

0.99

0.34

0.98

0.58

0.99

0.92

0.47

0.96

0.86

0.51

0.91

0.01

0.81

0.56

0.93

0.83

0.54

0.01

0.05

0.74

0.88

0.00

0.95

0.17

0.81

0.55

0.74

0.35

0.78

0.43

0.21

0.80

0.68

0.23

4.6 Atrial fibrillation classification based on clinical features 4.6.1 Modifications of the clinical feature extraction Minor modifications were required for the clinical feature approach when applied to our simulated and clinical 12-ECG signal databases. First, the baseline was corrected and the fiducial points were detected by using the techniques mentioned in Sec. 3.1. We identified that, for most of the Computers in Cardiology 2004 Challenge records, the two unspecified leads were leads VR and V1. These two leads were selected for classification purposes on our simulated and clinical databases. VA was removed from the ECG signals by applying the refined ABS cancellation and the single beat techniques described in Sec. 3.3. For each AF 5-minute record, the best VA cancellation result, identified by visual inspection, was selected for further processing. Most of the clinical features were extracted from one-minute ECG segments without strong artifacts. As for the similarities between AAs in different leads (features #10), the normalized cross-covariance was estimated on 30 consecutive 2-second segments and the absolute cross-covariance values of all 2-second segments were averaged. This average value constitutes the feature #10. The saturation operation used in the procedures for features #8 and #9 (low-frequency modulation of AA amplitude) was not necessary after VA cancellation.

4.6. ATRIAL FIBRILLATION CLASSIFICATION BASED ON CLINICAL FEATURES

71

4.6.2 Results on simulated and clinical data We applied the NT classifier obtained in Sec. 4.5 on the 22 simulated AA and on the 120 clinical ECG signals, respectively described in sec. 2.4.3 and 2.3.2. For the clinical ECG signals, the NT classifier was applied with respect to the AF types (paroxysmal, persistent, permanent, single and recurrent episodes), the AF aetiologies (dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) or valvular heart disease (VHD), pericarditis, focal or vagal and ectopic focii), and the pharmacological and electrical cardioversion results. The ST classifier was dropped due to is limited accuracy (60% of good classification on the test set B). Concerning the NT classifier results on the simulated AAs, all of the simulated AAs were identified as non-terminating AFs (group N), except for the simulated SR (simulation no.1), AFL (simulation no.2) and four AFs (simulations no.3, 19, 21 and 22) that were identified as AFs terminating immediately (group T). The clinical database (Tables 4.3, 4.4, and 4.5) display the percentage of classification in the groups N and T for the five different AF types, the five different AF aetiologies, and the four different AF cardioversion verdict, respectively. The MANOVA p value of the 22 simulated AA groups with simple (n=14) or complex (n=8) dynamic with respect to the 12 features was equal to 0.02, which means that these two populations were significantly different. The MANOVA p values of the paroxysmal, persistent and permanent AF groups, or AF groups with single and recurrent AF episodes, or of all six AF aetiology groups, or of the pharmacological or electrical cardioversion result groups was equal to 0.09, 0.02, 0.99, 0.87, 0.54, and 0.25, respectively. It denotes that the single AF episode population was significantly different than the recurrent AF episode one with respect to the 12 features. Table 4.3: N-T classification of AF type based on clinical features. Group

Paroxysmal (n=47)

Persistent (n=26)

Permanent (n=41)

Single (n=29)

Recurrent (n=29)

N T

21.3% 78.7%

26.9% 73.1%

36.6% 63.4%

41.4% 58.6%

20.7% 79.3%

Table 4.4: N-T classification of AF aetiologies based on clinical features. Group

DCM (n=9)

HCM (n=16)

VHD (n=12)

Pericarditis (n=2)

Focal (n=4)

Vagal (n=3)

Ectopic focii (n=60)

N T

22.2% 78.8%

6.3% 93.7%

25% 75%

50.0% 50.0%

0.0% 100.0%

0.0% 100.0%

18.3% 81.7%

Table 4.5: Classification of cardioversion results based on clinical features. Group N T

Pharmacological cardioversion No success Success (n=47) (n=21) 38.3% 61.7%

33.3% 66.7%

Electrical cardioversion No success Success (n=7) (n=7) 57.1% 42.9%

14.3% 85.7%



New SVM trainings were applied on the simulated and clinical databases to separate the simulated AAs with simple dynamic from the ones with complex dynamic, and to separate clinical AF types, AF aetiologies, and AF cardioversion verdicts grouped in pairs with respect to the 12 clinical features. A linear kernel with penalty coefficient C fixed at one has produced the best training results for the classifications of simulated AAs, and responses of electrical cardioversion attempts. A radial basis function kernel with a penalty fixed at infinity was used for the classifications of the other clinical AFs groups. These training setups produced a perfect classification (zero training error) for the simulated AAs and the different pairs of clinical AF aetiologies (dilated cardiomyopathy, hypertrophic cardiomyopathy and valvular heart disease), three training errors for the different pairs of paroxysmal, persistent and permanent AF (AF types), four training errors for the single and recurrent AF episodes (AF types), and one training error for the pharmacological and electrical cardioversion verdicts. Tables 4.6, 4.7, and 4.8 display the percentage of correct classification with respect to paroxysmal dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and valvular heart disease (VHD) pairs based on the mean DF values of leads V1 and V5 and on the 12 clinical features. Concerning the AF eatiologies, the other three groups (pericarditis, focal and vagal AFs) were not large enough to permit a meaningful classification. The ectopic focii group, composed of all AFs having no clear aetiology, is so variable in population that its classification with respect to the other aetiologies is meaningless. Table 4.6: Percentage of correct classification of AF types based on clinical features. Pair

Paroxysmal (n=47)

Persistent (n=26)

Permanent (n=41)

Single (n=29)

Recurrent (n=29)

Total

Paroxysmal vs persistent Paroxysmal vs permanent Persistent vs permanent

70.2% 57.4% -

38.5% 38.5%

56.1% 56.1%

-

-

58.9% 56.8% 49.3%

Single vs recurrent

-

-

-

48.3%

65.5%

56.9%

Table 4.7: Percentage of correct classification of AF aetiologies based on clinical features. Pair

DCM (n=9)

HCM (n=16)

VHD (n=12)

Total

DCM vs HCM DCM vs VHD HCM vs VHD

33.3% 55.6% -

81.3% 75.0%

66.7% 58.3%

64.0% 61.9% 67.9%

Table 4.8: Percentage of correct classification of cardioversion results based on clinical features. Group Pharmacological Electrical

Pharmacological cardioversion No success Success (n=47) (n=21) 57.4% -

71.4% -

Electrical cardioversion No success Success (n=7) (n=7) 28.6%

71.4%

Total 48.5% 50.0%

4.7. D ISCUSSION

73

4.7 Discussion Our objective was to determine whether an approach based on clinician’s expertise was able to predict the termination of AF. At the beginning, the clinician examined the learning set and identified seven observations that characterized the disorganization of fibrillatory waves. These observations were subjectively classified into three categories. These categories were associated to the three different groups (N, S and T). The observations were quantified into 12 features. Our "clinical" features worked well on the training set of the Computers in Cardiology 2004 Challenge. Our classification was also able to separate non-terminating AFs from AFs terminating immediately after the records, and AFs terminating one minute after the end of the record from AFs terminating immediately after the end of the record without any error on the learning sets N-T and S-T, respectively. The 90% of accuracy for the test set A was good (non-terminating AFs versus AFs terminating immediately), but the result on test set B (60%) was below our expectation (AFs terminating immediately or after one minute). There are some explanations for this. The main reason is probably that there were not enough records in the training sets to represent all the characteristics of each of our quantified clinical observations; the five features with the lowest Student’s t test p values produced almost the same results as using the 12 features. Note that the lowest p value for the classification of groups N and T was feature #3, which is the R-R interval feature. The lowest p value for the classification of groups S and T was feature #2, which is the fibrillatory wave polarity in lead V1. Another explanation maybe that, without the possibility to build a validation set due to the small size of the learning set, some overfitting took place. The clinician’s visual classifications of test sets N-T and S-T produced the same percentage of correct classification as our automatic classifier. Most of our simulated AFs were classified as non-terminating AFs. It means that, despite of unnatural AF initiations (cross-shock protocol or rapid pacing), our simulated AF ECG signals have the same characteristics as the sustained clinical AF ECG signals. It is also interesting to observe a correlation between an increase in the percentage of clinical AFs identified as non-terminating AF and the increase in AF duration (from paroxysmal to permanent AF). However, this increase is not significant enough to consider the 12 clinical features as good indicators of AF type. Note that the clinical features were not proposed by the clinician to separate complex or stable AF dynamics, AF types, or AF aetiologies. Note also that the three group definitions N, S and T are not the same as the paroxysmal, persistent and permanent AF types. The S and T records were coming from the same patient. This could explain why the clinical features performed well for the classification of extreme AF types (group N vs T or paroxysmal vs persistent AFs or paroxysmal vs permanent AFs), but not in the other cases. For the latter, the distributions of the different AF groups in terms of the proposed clinical features are probably overlapping.

4.8 Conclusion The main objective of this study was to build an automated method based on a clinician’s electrocardiogram observations that was able to predict self-termination during AF from sustained AF. An overall 90% of classification accuracy was reached when the automated method was applied to the



Computers in Cardiology Challenge 2004 database. This automated method also classified our 20 simulated sustained atrial fibrillations into non-terminating ones. As for our clinical database, an interesting correlation between the increase in the percentage of AFs identified as non-terminating and the increase in AF duration was also observed.

Atrial fibrillation classification based on dominant frequencies extracted from the electrocardiogram

N

5

EITHER the natural history of AF nor its response to therapy is sufficiently predictable by clini-

cal and echocardiographic parameters. AF treatment is mainly based on trial and error. Thus, it seems appropriate to develop tests that quantify AF disease states and guide the AF management [117]. As mentioned before, standard 12-lead ECG recordings are commonly required for the clinical evaluation of AF. Possible prognostic information contained within the ECG may present a lot of interest. The underlying mechanisms of the wavefront dynamics of AF relate to their substrates, which manifest themselves on different time scales. As an example, shortening of atrial refractoriness is a hallmark of atrial remodelling [28]. Invasive electrophysiological as well as non-invasive studies based on the surface ECG have frequently used two types of analysis to characterize these time scales. (1) In the Fourier-based spectral analysis, the DF observed from electrogram or the ECG lead is believed to determine respectively the mean firing rate [118] or the most common fibrillatory rate of nearby endocardial sites [50]. In this analysis, the DF is defined as the modal frequency in the Fourier spectrum of the AA signal. In the non-invasive analysis situation, the DF is usually estimated on the signal of lead V1 after first suppressing the ECG components related to the VA. Lead V1 is the lead having its sensing electrode closest to the atria, the other lead signals are generally not considered. (2) Time-frequency analysis additionally quantifies the changes in fibrillatory rate. As for the Fourier-based analysis, the time-frequency analysis is usually applied to the signal of lead V1 after VA cancellation. Both analyses have found their way into clinical AF studies [119– 125]. Recently, Cervigón et al. proposed an interesting continuous and discrete wavelet transform based analysis to predict the effectiveness of electrical cardioversion [126]. Their methodology discriminates patients with effectiveness of electrical cardioversion from those that return in AF with 75

C HAPTER 5. ATRIAL FIBRILLATION CLASSIFICATION BASED ON DOMINANT FREQUENCIES 76


a diagnostic capability of 82%. These studies are some of the numerous ones devoted to AF, but much remains to be done in this vast domain. References [127; 128] constitute good reviews of the various approaches based on Fourier-based and time-frequency analysis tested. In 2006, Jason Ng et al. published an interesting invasive study [129]. The purpose of this study was to compare the firing rates of the atrial myocytes and the DFs observed from atrial electrocardiograms. Their conclusion was that the greater the complexity of the atria electrogram in terms of fractionation and the greater the variation in amplitude and frequency, the less likely that the DF analysis provides accurate information regarding activation rate. In the first part of this chapter, we propose to analyze the correspondence between firing rate of atrial myocytes and the DFs observed from ECG lead signals during AF, on the basis of signals numerically simulated by using atrial and torso biophysical models. We also investigated the application of a newly introduced method, named phase-rectified signal averaging (PRSA), for the study of quasi-periodic oscillations in non-stationary signals to estimate the DFs in noisy 12-lead ECG signals (Sec. 5.2). The method performance was evaluated by using our simulated and clinical databases described in Sec. 2.4.3 and 2.3.2. In the last part, various SVM based classifications that used DF features were applied to our simulated and clinical databases. The classification procedure, DF features and classification results are presented in Sec. 5.3.

5.1 Mean firing rate of atrial fibrillation as estimated from the electrocardiogram The correspondence between the firing rates of atrial myocytes during AF and the DFs observed from the ECG lead signals is assumed in most of the non-invasive AF studies based on Fourier-based spectral analysis. We propose to evaluate this correspondence by using a biophysical model of the human atria embedded in a realistic inhomogeneous model of the volume conduction aspects within the thorax, as described in Sec. 2.4. Of the 20 different realizations of sustained AF with various substrates described in Sec. 2.4.3, simulations no.3 and 4 were selected from the two ends of the range of AF complexity, respectively. For simulation no.3, the membrane properties were changed uniformly, and resulted in a slow propagation. For simulation no.4, patched inhomogeneities were created. In both cases, AF was induced by a cross-shock protocol applied in the pulmonary vein area, see Table 2.1. The time courses of the membrane potential of 1297 elements specified at 1 ms intervals [41] was computed for each simulation as described in Sec. 2.4 The effect of volume conduction inhomogeneities on the atrial contribution to body surface potentials was computed as described in Sec. 2.4.2. Body surface potentials were computed at 590 points distributed over a refined torso surface; the electrode locations of the 12-lead ECG formed a subset.

5.1.1 Signal processing The general comments on the global dynamics of the AF variants presented below are based on the visual inspection of animations of the time course membrane potential distribution on the atrial surface.

5.1. M EAN FIRING RATE OF ATRIAL FIBRILLATION AS ESTIMATED FROM THE ELECTROCARDIOGRAM

77

The timing of the upstrokes of the time course of the membrane potential assigned to the equivalent double layer source elements was taken as the marker of the timing of local depolarization. For each source element, the number of upstrokes observed within a given time interval is referred to as the local firing rate. The resulting values were mapped on the atrial surface. For each of the 590 field points on torso surface, the time course of the simulated potentials was documented. The estimated PSD of all 590 lead signals were computed. In each of the estimated PSD, the DF was taken to be the frequency displaying the highest peak.

5.1.2 Results from the two selected simulated atrial fibrillations The two selected simulations differ by the complexity of their dynamics and their atrial firing rate patterns. The dynamics of simulation no.3 was characterized by 1-to-3 wavelets having wavelengths of 6.2 ± 2.7 cm (mean ± standard deviation values). Two stable rotors were present, both having a frequency of about 4 Hz, one of them rotating clockwise (as viewed from outside the heart) around the tricuspid valve, the other, around the superior vena cava. The distribution of the firing rates over the atrial surface was stable and almost uniform: 3.85 ± 0.11 Hz estimated from an 8-second period. Similarly, the distribution of the DFs over the thorax surface was stable and almost uniform: 4.08 ± 0.24 Hz estimated from the same 8-second period. An example of the corresponding wave forms is presented in Fig. 5.1. Figure 5.1A shows the time course of the membrane potential at the source element closest to the sensing electrode of lead V1, and Figure 5.1B represents the corresponding, simulated ECG on lead V1. The estimated PSD of the V1 signal estimated from the same 8-second period is shown in Fig. 5.2.

Figure 5.1: A) The time course of the membrane potential of the simulation no.3 acting as the strength of the source element closest to electrode V1, shown over a time interval period of 8 s. B) Corresponding V1 signal.

In contrast to simulation no.1, the dynamics observed in the non-uniform substrate of simulation no.4 was far less stable. Up to six wavelets were found. Moreover, different transitions in the dynamics were observed, occurring at irregular intervals. Here we describe one such transition.



Figure 5.2: A) Estimated PSD of the signal of lead V1 shown in Fig. 5.1B and B) the corresponding estimated PSD of lead V5.

Figure 5.3: A) The time course of the membrane potential of the simulation no.4 acting as the strength of the source element closest to electrode V1, shown over a time interval period of 8 s. B) Corresponding V1 signal.

As in Fig. 5.1A, Fig. 5.3A depicts the time course of the membrane potential at the source element closest to the sensing electrode of lead V1 and the corresponding, simulated ECG of lead V1, in the case of simulation no.4. Between the 19th and the 20th second, a visual inspection of lead V1 signal reveals a clear transition. The dynamics preceding the transition included a stable rotor at a frequency of 14 Hz, rotating clockwise around the left atrial appendage. A second one was found, rotating at a frequency of about 11 Hz around the lower right pulmonary vein. The latter triggered a wide wave front on the right atrial surface, propagating from left to right. During the period following the transition, a stable rotor was present, rotating clockwise around the left atrial appendix at 14 Hz, a stable rotor rotating the lower right pulmonary vein at about 11 Hz, accompanied by unstable reentries set up over the frontal part of the right atrium. The estimated PSDs of leads V1 and V5 during 8-second intervals preceding and following the transition are

5.1. M EAN FIRING RATE OF ATRIAL FIBRILLATION AS ESTIMATED FROM THE ELECTROCARDIOGRAM

79

shown in Fig. 5.4 and Fig. 5.5, respectively .

Figure 5.4: A) Estimated PSD of the signal of lead V1 computed over the interval preceding the transition. B) The corresponding estimated PSD of lead V5. The observed DFs and some of their higher harmonics are marked.

Figure 5.5: A) Estimated PSD of the signal of lead V1 computed over the interval following the transition. B) The corresponding estimated PSD of lead V5. The observed DFs and some of their higher harmonics are marked.

Although only slight shifts following the transition were observed in the distribution of firing rates over the atrial surface, the transition was clearly noticeable in the distributions of the DF on the torso surface. This is illustrated in Fig. 5.6.

5.1.3 Discussion Simulation studies such as the one discussed here permit the study of AF related signals under fully controlled conditions and in complete absence of interference of signal components generated by VA. The two simulations selected here span a wide range of possible mechanisms of AF, and permit the study of their expression on body surface potentials.



Figure 5.6: A) Simulation no.4 distribution of the firing rate preceding the transition mapped on the atrial surface. B) Distribution of the DF computed from the period preceding the transition mapped on the torso surface. C) Distribution of the DF computed from the period following the transition. All geometries shown in the natural, frontal view.

The global description of the dynamics of simulation no.3 suggests a flutter-like phenomenon. The accompanying distribution of the firing rates is almost uniform. The stability of the firing rates as well as that of the DFs seems to confirm this. However, the spurious wavelets set up around the regions of the colliding wave fronts of the two rotors complicate matters. In the estimated PSD, their effect is represented by the wide elevation of the spectrum to the left of the peak of the DF. The simulation no.4 is clearly the most interesting one. The two rotors have different frequencies, both higher than in the simulation no.3. Prior to the transition, two distinct DFs were observed (Fig. 5.4), each corresponding to those of the two major rotors. Classifying this spectrum by its DF (only) would clearly obscure the view on the complexity of the underlying phenomena. The identification of both spectral peaks is facilitated by considering the presence of their harmonics. This holds true even more so if the dynamics is more complex, as was the case after the transition (compare Fig. 5.4 and Fig. 5.5). A correct interpretation is also hampered if the time interval on which the spectrum is based is too small. The results indicate that the full spectrum yields more information about the complexity of a particular variant of AF than the analysis of merely its DF. The same holds true for analyzing the spectra of multiple lead signals rather than using observations from a single lead.

5.2 Dominant frequencies estimated trough phase-rectified signal averaging In clinical practice, only the body surface potentials related to the nine electrodes of the standard 12-lead ECG are available, which is the case for our clinical database. As mentioned before, most of the non-invasive studies based on Fourier-based spectral analysis are limited to lead V1 information. The main reason is related to the facility of performing a more accurate VA cancellation in lead V1

5.2. D OMINANT FREQUENCIES ESTIMATED TROUGH PHASE - RECTIFIED SIGNAL AVERAGING81

than in other leads, due to its low AA and VA amplitude ratio. This is well illustrated by the various VA cancellation method results studied in chapter 3. Therefore, it could be interesting to propose an approach that accurately extracts the spectral information in leads contaminated by noise and VA cancellation artifacts. In 2006, Bauer et al. have introduced a new method named PRSA [130]. This technique was proposed for the study of quasi-periodic oscillations in noisy, non-stationary signals, which makes the assessment of system dynamics possible despite phase resetting and noise. It is based on a very simple, intuitively appealing principle; phase-rectification of the oscillatory fluctuations is possible by aligning and averaging signal segments based on specific anchor points. The method has been shown to be advantageous over classical PSD estimation when the perturbation to the quasi-periodic component of interest is 1/ f noise. In the following section, we present briefly the principle of PRSA. We also present the results of extensive experiments on simulated and clinical data described in Sec. 2.4.3 and 2.3.2 and discuss them.

5.2.1 Overview of phase-rectified signal averaging The basic principle of PRSA is the averaging of segments of a signal x(n). These segments are symmetric with respect to the so-called anchor points. The anchor points are selected as samples at which the signal instantaneous phase is close to a specific value (typically zero). In this way, the averaging process enhances the quasi-periodic component of the signal and eventually cancels correlated, non-periodic components (non-stationarity, noise, and artifacts).

Figure 5.7: Principle of PRSA. (A) Signal (generated using an auto-regressive model). (B) Anchor points. (C)-(F) Segments of length 2L + 1 around anchor points. (G) PRSA average.

In the simplest version of PRSA, the anchor points correspond to increases of the signal, i.e. all indices n for which x(n) > x(n − 1).

(5.1)



Segments of length 2L + 1 centered on the anchor points, x(nν − L), x(nν − L + 1), . . . , x(nν + L − 2), x(nν + L − 1)

(5.2)

are considered, with nν , ν = 1, . . . , M the indices of the anchor points. Then, all these segments are averaged to obtain the PRSA average x˜k , x(k) ˜ =

1 M ∑ x(nν + n), n = −L, −L + 1, . . . , L − 2, L − 1. M ν=1

(5.3)

Anchor points located in the first and last L-sample segments are disregarded. Finally, a classical PSD estimation technique is applied to x(k). ˜ The different steps of PRSA are illustrated in Fig. 5.7 for a signal generated using an autoregressive model of order two. The theoretical justification of the PRSA is not trivial. To prove that the PRSA average represents the quasi-periodic component of a given signal, at least in simple cases, we studied the PRSA for a pure sinusoid with a rational or irrational normalized frequency in Sec. 5.2.2. This analysis shows that the PRSA average of a single sinusoid with rational normalized frequency is the sum of four sinusoids at the same frequency with a relative phase and amplitude. It was also demonstrated that the PRSA average of a single sinusoid with an irrational normalized frequency can be approximated by a cosine at the same frequency with a different amplitude. In both cases, the DFs observed on the estimated PSDs are equals to the real signal frequencies. Extension of this calculation to more complex situations, for instance when noise is added or multiple sinusoids are present, becomes very complex, due particulary to the determination of the anchor points.

Figure 5.8: Comparison of (A) the original signal x(n) (a sum of 100 impulses and a stable lowamplitude 5000-sample sinusoid at 0.24 fn ), (B) the corresponding PSD of the original data, (C) the PRSA average x(k) ˜ calculated with T = 1 and L = 512, (D) the PSD of the PRSA average. One frequency peak corresponding to periodicity is indicated by arrows; it can be recognized much more clearly in the PRSA spectrum.

Figure 5.8 shows an example of PRSA applied to a signal composed of a sinusoid (present all along the signal, but barely visible in Fig. 5.8A, corrupted by additive impulsive noise. This impulsive noise is characterized by positive and negative impulses randomly distributed over the entire


signal. The estimated PSD of the signal is displayed in Fig. 5.8B, with the peak of interest hidden among the peaks corresponding to the additive impulsive noise. Spectral analysis of Fig. 5.8D of the PRSA averaged segment clearly illustrates the enhancement of this peak.

Figure 5.9: Comparison of (A) the original signal x(n) (a sum of sixty 100-sample sinusoids at different frequencies and a stable low-amplitude 5000-sample sinusoid at a normalized frequency of 0.24, (B) the corresponding PSD of the original data, (C) PRSA averaged segment x(k) ˜ calculated with L = 512, (D) the PSD of the PRSA averaged segment. The frequency peak corresponding to the stable sinusoidal component is indicated by arrows; it can be recognized much more clearly in the PRSA spectrum.

Another example is shown in Fig. 5.9. It shows an example of PRSA applied to a signal composed of a sinusoid (present all along the signal, but barely visible in Fig. 5.9A corrupted by intermittent, large amplitude sinusoids at various frequencies. The estimated PSD of the signal is displayed in Fig. 5.9B, with the peak of interest hidden among the peaks corresponding to the intermittent terms. The spectral analysis shown in Fig. 5.9D of the PRSA averaged segment illustrates clearly the enhancement of this peak.

5.2.2 Theoretical derivation In this section, theoretical derivation of the average segment resulting from the application of PRSA to two very simple signals is presented. This illustrates the contrast between the simplicity of the concept PRSA relies on and the difficulty in extracting exact calculations on this approach. Sinusoid with a rational normalized frequency Let x(n) be a sinusoid with rational normalized frequency ab : a x(n) = sin(2πn + δ), n = 1, . . . , N b

(5.4)



Figure 5.10: Definition of the different variables : the signal phase δ and the phase δ0 .

where a and b are integers and δ an arbitrary phase. Since x(n) = x(n + b), the sections centered on these two samples are identical and we focus only on the first b successive samples of the signal. Anchor points are selected using (5.1). These points correspond to the increasing part of the sinusoid. So we have: h i π πa π πa a − + < mod2π 2 pinν + δ < + (5.5) 2 b b 2 b for every anchor point x(nν ), with mod2π [·] being the 2π-modulo function. The PRSA signal x(k) ˜ is the mean of all the windows (5.3) taken around the anchor points x(nν ): µ ³ µ ¶ ´ a a 2π 1 sin 2π (k + k0 ) + δ + sin 2π (k + k0 ) + +δ x(k) ˜ = M b b b µ ¶¶ a 2π + · · · + sin 2π (k + k0 ) + (M − 1) +δ (5.6) b b ´ 1 M−1 ³ m a = ∑ sin 2π (k + k0 ) + 2π + δ , M m=0 b b where M is the number of anchor points and k0 is the anchor point for which the phase is the closest to − π2 , and k = −L, −L + 1, . . . , L − 1, L. The number of anchor points M depends on b and on the phase δ, and is equal to the integer part of b2 plus or minus 1. To calculate the sum of the sinusoids, we can express it as the imaginary part of a complex sum. This sum is a geometric series: ¡ ¡ ¢¢ ¡ ¡ ¢¢ 1 − exp j2π Mb 1 − exp − j2π b1 m´ ¡ ¡ ¢¢ . ∑ exp j2π b = 2 1 − cos 2π m=0 b

M−1

³

(5.7)

Developing the product and taking the imaginary part, we finally obtain the PRSA signal : µ ³ µ µ ¶ ¶ ´ a (k + k0 ) a M x(k) ˜ = K sin 2π (k + k0 ) + δ − sin 2π + +δ b b b µ µ ¶ ¶ µ µ ¶ ¶¶ (k + k0 ) a 1 (k + k0 ) a M − 1 − sin 2π − + δ + sin 2π + +δ , b b b b

(5.8)


where K =

1 . 2M (1−cos( 2π b ))

Then, the PRSA signal for the case of a single sinusoid of frequency ba without noise is the sum of four sinusoids at the same frequency with a relative phase depending of the frequency. Spectral analysis of the PRSA signal provides then the correct estimate of the frequency content of the signal under study. Sinusoid with an irrational normalized frequency If the frequency f of the sinusoid x(n) is irrational, there is no repetition in the anchor points and £ ¤ they fill the phase interval − π2 , π2 . If the number of samples is large enough, the sum (5.6) can be approximated by an integral and the PRSA signal is: Z

x(k) ˜ =

π 2

− π2

sin(2πk f + φ)

dφ π

2 = cos(2π f k) π

(5.9)

5.2.3 Procedure For all the simulated and clinical ECG signals described in Sec 2.4.3 and 2.3.2, 5-second nonoverlapping intervals from ECG leads VR, VL, and V1 to V6 were considered. Leads V1 and V5 were also considered in an independent manner. The processing steps are displayed in Table 5.1. Table 5.1: Processing steps of the phase-rectified signal averaging based approach. Step 1. Step 2. Step 3. Step 4. Step 5. Step 6. Step 7.

Baseline correction as described in Sec. 3.1. PSD estimation on the resulting signal from step 1. PRSA on the resulting signal from step 1. VA cancellation using the method described in Sec. 3.3. PSD estimation on the resulting signal from step 4. PRSA on the resulting signal from step 4. Identification of the DF estimates as the frequency corresponding to the largest spectral power in the various estimates (results of steps 2, 3, 5 and 6).

In all experiments, the parameter L in Eq. 5.3 was set to 512, so that the length of the averaged PRSA segments was 2 × L + 1 = 1025. The PSD estimates of these averaged segments were smoothed periodograms (Hamming window). All classical PSD estimates were modified periodograms (Hamming window, window length 1025, overlap 50%), so that the frequency resolution was the same (0.24 Hz) in all cases, as required for a fair comparison of the performance of the methods.



5.2.4 Evaluation Simulated atrial activity The DF may be sometimes ill-defined, be it for real or simulated AF. In some of the episodes of simulated AF, a single dominant peak was clearly observed in the estimated PSD. In other cases, no dominant peak or more than one single dominant peak were visible. In order to identify the 5-second simulated AA intervals characterized by a single DF, the sparseness criterion proposed in [131]: ³ ´ q √ N − ∑Nj=1 |y( j)| / ∑Nj=1 y( j)2 √ Sparseness(y(n)) = , (5.10) N −1 where N is the number of samples, was used on the PSD estimates obtained from the 5-second simulated AA intervals prior to the addition of ventricular complexes, in the interval from 3 to 15 Hz. The sparseness measure quantifies how much energy of a vector is packed into only a few components. Its value is equal to 1 if and only if the vector contains only a single non-zero component, and equals 0 if and only if all components are equal. The 5-second simulated intervals with sparseness values above 0.6 were considered as presenting only one significant spectral peak, and were retained for the evaluation procedure. A visual inspection was also applied to PSD estimates from the simulated AA ECG signals to identify the few undesirable ones, that is, simulations with sparseness values above 0.6 without clear single dominant peak. The results presented below were obtained from the analysis of 520 such intervals. The frequencies of the unique spectral peaks in the interval from 3 to 15 Hz of the simulated AA ECG signals were taken as the reference values. Clinical atrial activity We extracted the first 30 seconds of all 120 recordings in the database, and split them into 5-second intervals for the eight leads considered. Visual inspection led us to remove 83 of these intervals, due to problems such as recording artifacts. As a consequence, the results presented below are restricted to the analysis of 7117 intervals. Since for the clinical signals the true DFs were not available, we focused on the plausibility of the estimates. We defined a plausible DF estimate as one in the range between 4 Hz and 10 Hz. The upper bound is based on studies that have shown that the atrial cycle length during human AF is only rarely below 100 ms [129].

5.2.5 Results on simulated and clinical data For all the estimation methods tested, the frequency with the highest power between 3 and 15 Hz was identified as the estimated DF. Table 5.2 summarizes the results obtained for the 520 simulated ECGs of the eight leads considered. The second column contains the mean and standard deviation of the differences between the estimated DF and the reference values. The third column contains the percentages of errors larger than twice the frequency resolution. The entry PRSAAA corresponds to the results obtained with PRSA on the ECG signals free of ventricular involvement (simulated AAs only). All the other entries correspond to results obtained on the ECG signals with the ventricular complexes added: PSDECG and PRSAECG , classical PSD estimation and PRSA after baseline


correction; PSDVAC and PRSAVAC , classical PSD estimation and PRSA after VA cancellation. Table 5.3 summarizes the results obtained for the 90 simulated 5-second ECG intervals of lead V1. Table 5.4 summarizes the results obtained for the 45 simulated 5-second ECG intervals of lead V5. Figure 5.11 displays the histograms of the DF estimates obtained on all leads. The bins inside the plausibility range as defined in subsection 5.2.4 are in black, those outside in white. Also, the numbers of DF estimates in the various regions are displayed, with those outside the plausibility range shown within a box. Fig. 5.12 displays the histograms of the DF estimates obtained on the signals of lead V1. Fig. 5.13 displays DF estimates obtained on lead V5. Table 5.2: Evaluation of the different dominant frequency estimation methods on eight leads: the mean and standard deviation (Hz), and the percentage of the errors over 0.5 Hz on 520 5-second intervals Methods PRSAAA PSDECG PRSAECG PSDVAC PRSAVAC

Error(mean ± std)

% of false detections (> 0.5Hz)

0.02 ± 0.02 1.5 ± 1.5 1.0 ± 1.5 0.2 ± 0.5 0.2 ± 0.4

0.0 58.5 39.0 9.4 5.2

Table 5.3: Evaluation of the different DF estimation methods on lead V1: the mean and standard deviation (Hz), and the percentage of the errors over 0.5 Hz on 90 5-second intervals Methods PRSAAA PSDECG PRSAECG PSDVAC PRSAVAC

Error(mean ± std)


0.01 ± 0.01 1.5 ± 1.7 0.6 ± 1.2 0.1 ± 0.4 0.1 ± 0.3

0.0 53.3 22.2 5.6 2.2

Table 5.4: Evaluation of the different DF estimation methods on lead V5: the mean and standard deviation (Hz), and the percentage of the errors over 0.5 Hz on 45 5-second intervals Methods PRSAAA PSDECG PRSAECG PSDVAC PRSAVAC

Error(mean ± std)


0.02 ± 0.02 1.2 ± 1.4 1.0 ± 1.4 0.1 ± 0.2 0.1 ± 0.2

0.0 57.8 40.0 4.4 2.2

5.2.6 Discussion The results on the synthetic signals (Tables 5.2, 5.3 and 5.4) show that the DF estimates obtained by applying the PRSA to signals free of ventricular involvement are consistent with those obtained with a classical PSD estimation in the three sets of experiments performed. PRSA was also found to improve significantly the direct DF estimation applied to ECG signals in which only a baseline



Figure 5.11: (A) Histogram of DF estimates on the 7117 baseline-corrected ECG 5-second intervals on eight leads. (B) Histogram of DF estimates after VA cancellation. (C) Histogram of DF estimates with PRSA applied to the baseline-corrected ECG 5-second intervals. (D) Histogram of DF estimates with PRSA applied after VA cancellation. The dotted lines represent the mean values (± one standard deviation) of each distribution. The boxed numbers (unboxed numbers) represent the number of dubious results (respectively plausible results) for each method.

Figure 5.12: (A) Histogram of DF estimates on the 911 baseline-corrected ECG 5-second intervals on lead V1. (B) Histogram of DF estimates after VA cancellation. (C) Histogram of DF estimates with PRSA applied to the baseline-corrected ECG 5-second interval. (D) Histogram of DF estimates with PRSA applied after VA cancellation. The dotted lines represent the mean values (± one standard deviation) of each distribution. The boxed numbers (unboxed numbers) represent the number of dubious results (respectively plausible results) for each method.

correction was performed. These observations indicate that PRSA does not induce any loss in performance in optimal conditions with respect to standard spectral analysis, and that the averaging process underlying PRSA may be quite efficient in cancelling VA, despite the large amplitude of this perturbation. Poor spectral estimation, obtained by applying the PRSA to the ECG signals after the baseline correction only, occurred in the simulated ECG signals that had a very regular ventricular rate. A


Figure 5.13: (A) Histogram of DF estimates on the 882 baseline-corrected ECG 5-second intervals on lead V5. (B) Histogram of DF estimates after VA cancellation. (C) Histogram of DF estimates with PRSA applied to the baseline-corrected ECG 5-second intervals. (D) Histogram of DF estimates with PRSA applied after VA cancellation. The dotted lines represent the mean values (± one standard deviation) of each distribution. The boxed numbers (unboxed numbers) represent the number of dubious results (respectively plausible results) for each method.

Figure 5.14: (A) Clinical 5-second ECG signal on lead V5 and its estimate PSD (B) with a DF of 8.1 Hz (in doted lines) and the 5-second ECG signal after the ventricular activity cancellation and its estimate PSD with a DF of 3.9 Hz (in black lines). (B) The PRSA transform of the original ECG signal calculated with T = 1 and L = 512 and its estimate PSD (D) with a DF of 8.3 Hz. (E) The PRSA transform of the ECG signal after the VA cancellation and its estimate PSD (F) with a DF of 8.1 Hz.

possible reason for this is that some anchor points are selected in the ventricular complexes. In such cases, the averaging process of the PRSA does not lead to a reduction of their influence in the averaged segment, i.e. they appear as a quasi-periodic component. Results from the application to simulated ECG signals also demonstrate that the percentage of false detections obtained with the PRSA procedure combined with VA cancellation is lower than the percentage obtained with VA cancellation only.



Classical PSD estimation on the clinical ECG signals (Figs. 5.11A, 5.12A and 5.13A) results in a large number of DF estimates outside the plausibility range. This is especially true in the low-frequency region, VA being responsible for a large spectral peak at the heart rate frequency, typically 1-2 Hz. Application of VA cancellation (Figs. 5.11B, 5.12B, and 5.13B) followed by classical PSD estimation decreases substantially the number of DF underestimates at the expense of a larger number of DF overestimates. These overestimates are caused by the artifacts induced by VA cancellation. The application of PRSA to the clinical ECG signals results in a large decrease of DF underestimates, indicating that PRSA deals efficiently with the ventricular involvement (Figs. 5.11C, 5.12C, and 5.13C). One can also observe that DF overestimates are suppressed. Finally, the combination of VA cancellation and PRSA also leads to a complete suppression of DF overestimates, and thus compensates for the negative effect of VA cancellation in that respect (Figs. 5.11D, 5.12D, and 5.13D). Also, it leads to a more than twofold decrease of the number of DF underestimates in the three experiments (eight leads, lead V1, and lead V5). Not surprisingly, the best results are those obtained on lead V1. When combined with VA cancellation, less than 4 percent of the estimates are outside the plausibility range. The good performance of PRSA after baseline correction only is worth mentioning. It indicates that in many cases a reliable DF estimate can be obtained without having to rely on complex preprocessing steps such as VA cancellation. The performance on lead V5 is not as impressive as the performance on lead V1, but quite acceptable when PRSA is combined with VA cancellation in the light of the low signal-to-interference ratio of AA on that lead. Global clinical results on the eight leads are somewhat in between those on lead V1 and those on lead V5. It is interesting to note that for lead V5, application of PRSA after baseline correction only may in some cases work better than application of PRSA on the signal after VA cancellation. Figs. 5.14A and 5.14B show respectively the baseline-corrected signal (dotted line), the result of VA cancellation (solid line), and their PSD estimates. No significant peak is visible in the PSD estimate of the baseline-corrected signal, and the PSD estimate of the result of VA cancellation would lead us to select a DF value of 3.9 Hz outside the plausibility range, due to cancellation artefacts. Figs. 5.14C and 5.14E show the PRSA averages obtained on the two signals of Fig. 5.14A, Figs. 5.14D, and 5.14F the spectra of these two PRSA averages. Both spectra give plausible DF estimates, respectively 8.1 and 8.3 Hz, equivalent with regard to the frequency resolution (0.24 Hz) of PSD estimation. The results above indeed highlight the potential of PRSA to improve DF estimation, especially when VA (or the artifacts resulting from its cancellation) are not located too regularly on the time axis. Since PRSA tends to enhance periodical structures, an interference appearing regularly will not be cancelled in the averaging process of PRSA. The limitation of the PRSA is that all information about the power of AA frequency components is lost. As showed in the theoretical derivation, it is possible in the most simple case (a simple sinusoid) to obtain an analytical relationship between the amplitude of this sinusoid and the PRSA average. However, it is impossible when several periodical components are present; for instance, in the case of a weighted sum of two sinusoids. The location of the anchor points, which is of course influential on the averaging process of PRSA, is highly dependent, in a complex way, upon the frequencies, phases, and relative amplitudes of the two sinusoids. This causes PRSA to be

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91

nonlinear, since the PRSA average for the sum of two signals is different from the sum of the two averages obtained separately on the two signals. A possible approach, not yet explored, to obtain at least an approximate correspondence between the power information in the PRSA average and the power characteristics of the original AA, is to perform a regression [132] between those two quantities on the synthetic signals. Using this regression, it would be possible to infer the power in the original AA starting from the PRSA average for the clinical signals.

5.3 Atrial fibrillation classification based on dominant frequencies Differences in the DFs have been observed between electrograms recorded in the left and right atria during AF [27; 133]. Intracavitary recordings have shown the presence of higher DFs close to the pulmonary veins (negative left-to-right gradients), and it has been suggested that they are a marker of the presence of an AF "driver", which is a single or multiple sources that insure the AF maintenance. Our findings presented in Sec. 5.1 suggest that these differences are also observable on the body surface potentials and that more information on the complexity of AF is provided by an analysis based on multiple leads. It was also observed that leads V1 and V5 are good candidates to extract the AA information with respect to the right and the left atria. Based on these observations, the purpose of the following AF classifications was to use DF values observed on leads V1 and V5, with the aim to distinguish between the activities in the right and left atria. AF simulations were used to identify the conditions that produce DF differences between leads V1 and V5. First, the VA was removed from the ECG signals by applying the refined ABS cancellation and the single beat techniques described in Sec 3.3. For each AF patient, the best VA cancellation result, identified by visual inspection, was selected. The DF estimates were obtained by applying the PRSA approach described in Sec. 5.2 to 10-second ECG segments on lead V1 and V2 with L fixed at 640. The first two features represent the mean value of the DF estimate over the 29 10-second ECG signal segments for each AF patient record, the first and last 5-second segments not being used. Principal component analysis (PCA) is an orthogonal linear transformation that projects vector data into a new coordinate system defined by the eigenvectors of its covariance matrix such that the greatest variance resides in the first components of the new system. These first components correspond to the dimensions that have the strongest correlation in the data set. In our case, PCA was used to extract the two components with the largest variances, which are assumed to best represent the overall AA. The DF estimates of these 1st and 2nd principal components were obtained by applying the PRSA approach described in Sec.5.2 to 10-second segments of these two first components. The third and fourth features represent the mean value of the DF estimate over the 29 10-second 1st and 2nd principal component segments, the first and last 5-second segments not being used.



5.3.1 Classification procedure From the two clinical ECG signals (leads V1 and V5) and the two synthetic signals (1st and 2nd principal components), we obtained 4 features. A SVM approach, described in Sec. 4.3.1, was used to perform the AF classifications based on DF features. The SVM classification procedure was applied to the clinical database to separate AFs with different AF types (paroxysmal, persistent, and permanent or single, and recurrent AF episodes), AF aetiologies (dilated cardiomyopathy, hypertrophic cardiomyopathy or valvular heart disease), or responses to cardioversion attempts (positive and negative responses to pharmacological or electrical cardioversion attempts). These different AF types, AF aetiologies, or responses to cardioversion were grouped in pairs. The SVM classification based on the four DF features was applied to each pair. Due to the limited number of records, a leave-one-out procedure, described in Sec. 4.3.1, was applied. As for the AF classification based on clinical features, MANOVA was applied to the different AF groups to evaluate the relevance of the four features based on DF.

5.3.2 Results on simulated and clinical data The only simulated AAs that produced a negative left-to-right gradient were the ones with a simulated focal source located in the right atrium (simulations no.19 and 20), the one with shorter effective refractory periods in the left atrium and rapid pacing in the left appendage, and the one with stable rotors located in the left appendage and in the lower right pulmonary vein (simulation no.4, see Sec. 5.1.2)). The only simulated AAs that produced a positive left-to-right gradient were the ones with a simulated focal source located in the left atrium close to the coronary sinus (simulation no.9) and in the isthmus region (simulation no.17). The other simulated AAs produced equal DFs in V1 and V5. No differences were observed between the DFs on the 1st and 2nd principal components. Tables 5.5, 5.6, and 5.7 display the distribution of the populations of AF types, AF aetiologies, and responses to cardioversion attempts, with respect to positive, null, and negative left-to-right gradients observed on ECG signals (lead V5 vs lead V1). They also display the population distributions with respect to the various DF differences observed on 1st and 2nd principal components. In order to determine if a specific preference was observable for each AF type, AF aetiology, or response to cardioversion attempts, a Student’s t test was applied to the lead V1 and V5 groups with respect to each AF type, AF aetiology, or pharmacologic or electrical cardioversion response. The p values of these Student t test are displayed in the fourth and ninth rows. It denotes left-to-right gradient preferences for paroxysmal and persistent AFs, or AF with valvular heart disease and AF with ectopic focii, or AF patients with negative response to pharmacological cardioversion attempts. The SVM training, described in Sec 5.3.1, was applied to the clinical database to separate AF types, AF aetiologies, and AF cardioversion verdicts grouped in pairs with respect to the four DF features. A radial basis function kernel with a penalty fixed at infinity produced the best training results for all pairs. This training setup produced a perfect classification (zero training error) for the different pairs of AF types, AF aetiologies, and pharmacological and electrical cardioversion verdicts. Tables 5.8, 5.9, and 5.10 displays the percentage of correct classification with respect to AF types pairs, to paroxysmal dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM)

5.3. ATRIAL FIBRILLATION CLASSIFICATION BASED ON DOMINANT FREQUENCIES

93

Table 5.5: AF type population distribution based on the dominant frequencies. V1 vs V5 V1 > V5 V1 = V5 V1 < V5 Students’s t-test 1st vs 2nd 1st

2nd

> 1st = 2nd 1st < 2nd Students’s t-test

Paroxysmal (n=41)

Persistent (n=25)

Permanent (n=39)

Single (n=24)

Recurrent (n=22)

61.0% 26.8% 12.2% 0.03

56.0% 32.0% 12.0% 0.01

51.2% 38.5% 10.3% 0.09

58.3% 25.0% 16.7% 0.09

50.0% 36.4% 13.6% 0.30

Paroxysmal

Persistent

Permanent

Single

Recurrent

14.6% 12.2% 73.2% 0.00

28.0% 16.0% 56.0% 0.15

20.5% 12.8% 66.7% 0.02

25.0% 8.0% 67.0% 0.02

13.6% 27.3% 59.1% 0.15

Table 5.6: AF aetiology population distribution based on the dominant frequencies. V1 vs V5

DCM (n=9)

HCM (n=16)

VHD (n=12)

Pericarditis (n=2)

Focal (n=3)

Vagal (n=3)

Ectopic Focii (n=54)

V1 > V5 V1 = V5 V1 < V5 Students’s t-test

44.4% 44.4% 25.0% 0.67

50.0% 25.0% 75% 0.59

41.7% 50.0% 8.3% 0.05

0.0% 100.0% 0.0% 0.94

100.0% 0.0% 0.0% 0.27

66.7% 33.3% 0.0% 0.28

61.1% 27.8% 11.1% 0.01

1st vs 2nd

DCM

HCM

VHD

Pericarditis

Focal

Vagal

Ectopic Focii

1st > 2nd 1st = 2nd 1st < 2nd Students’s t-test

33.3% 11.1% 55.6% 0.15

12.5% 12.5% 75.0% 0.05

16.7% 16.7% 66.6% 0.09

50.0% 0.0% 50.0% 0.88

33.3% 0.0% 66.7% 0.12

0.0% 0.0% 100.0% 0.10

24.1% 13.0% 72.9% 0.00

and valvular heart disease (VHD) pairs, and to positive and negative responses to cardioversion attempts based on the mean DF values of leads V1 and V5 and on the mean DF values of the 1st and 2nd principal components. Concerning the AF eatiologies, the other three groups (pericarditis, focal and vagal AFs) were not large enough to permit a meaningful classification. The ectopic focii group, composed of all AFs having no clear aetiology, is so variable in population that its classification with respect to the other aetiologies is meaningless. The MANOVA p values of the paroxysmal, persistent and permanent AF groups, or AF groups with single and recurrent AF episodes, or of all six AF aetiology groups, or of the pharmacological or electrical cardioversion result groups was equal to 0.29, 0.18, 0.12, 0.38, and 0.61 respectively, with respect to DF values observed on the ECG signals. The MANOVA p values of the same groups was equal to 0.42, 0.38, 0.47, 0.19, and 0.06 respectively, with respect to DF values observed on the 1st and 2nd principal components.

5.3.3 Discussion It is first interesting to observe that the simulated results with respect to the left-to-right DF gradients corroborate the hypothesis that DF gradients may be related to the presence of non-global specific focal source, stable rotor or heterogeneity regions. It is also interesting to observe the preferential positive left-to-right DF gradient on our clinical data. Almost 65% of the entire AF population



Table 5.7: AF population distribution of the cardioversion attempt based on the dominant frequencies. V1 vs V5 V1 > V5 V1 = V5 V1 < V5 Students’s t-test 1st vs 2nd 1st > 2nd 1st = 2nd 1st < 2nd Students’s t-test

Pharmacological cardioversion No success Success (n=40) (n=17) 50.0% 40.0% 10.0% 0.03

Electrical cardioversion No success Success (n=5) (n=7)

41.2% 35.3% 23.5% 0.80

60.0% 20.0% 20.0% 0.49

Pharmacological cardioversion No success Success 20.0% 20.0% 60.0% 0.00

42.9% 42.9% 14.2% 0.98

Electrical cardioversion No success Success

17.6% 11.8% 70.6% 0.02

20.0% 0.0% 80.0% 0.06

42.9% 42.9% 14.2% 0.89

Table 5.8: Percentage of correct classification of AF types based on dominant frequencies. V1 vs V5 Paroxysmal vs persistent Paroxysmal vs permanent Persistent vs permanent Single vs recurrent

Paroxysmal (n=41)

Persistent (n=25)

Permanent (n=39)

Single (n=24)

Recurrent (n=22)

Total

48.8% 53.7% -

28.0% 16.0%

56.4% 46.2%

-

-

40.9% 55.0% 34.4%

-

-

-

33.3%

45.5%

39.1%

was characterized by this positive DF gradient. The PCA results confirm this observation. Almost 75% of the entire AF population was characterized by higher DFs in the 2nd principal components in comparison to the 1st ones. Due to the high correlation between lead V3-V6 ECG signals, the 1st principal component has the tendency to represent the left AA. Note that the correspondence between the mean firing rates and the ECG DFs is complex in terms of locations as discussed in Sec. 5.1. Paroxysmal and Persistent AF populations demonstrate this same preferential positive left-toright DF gradient on our clinical data with 61.0% and 56.0%, respectively. Permanent AF is characterized by a higher percentage of null gradient cases. This could be explained as follows: most of the AFs are initiated by specific trigger and, after a relatively long period, the entire myocardium is modified by electrical, contractile and structural remodelings leading to uniform conduction characteristics. Unfortunately, these four DF features (two with leads V1 and V5 and two with the 1st and 2nd principal components) were not sufficient to permit correct classification of AF types grouped in pairs (less than 56%). The same observations can be made on the results on AF aetiologies. The only AF aetiologies that demonstrated this preferential positive left-to-right DF gradient are the ventricular heart disease, mainly associated to the mitral valve, and the ectopic focii, assumed to be mainly located in the pulmonary vein area. These results corroborate with the hypothesis that DF gradients may be related to the presence of focal or heterogeneity regions non-globally distributed. Unfortunately, as for the AF types, the four DF features did not permit correct classification of pairs of AF aetiologies (less than 51%).

5.4. C ONCLUSION

95

Table 5.9: Percentage of correct classification of AF aetiologies based on dominant frequencies. AF types

DCM (n=9)

HCM (n=16)

VHD (n=12)

Total


44.4% 44.4% -

50.0% 56.3%

50.0% 41.7%

48.0% 52.4% 50.0%

Table 5.10: Percentage of correct classification of cardioversion attempts based on dominant frequencies. Cardioversion type Pharmacological Electrical


57.1% -


57.1%

Total 70.6% 66.7%

However, the DF features permitted to obtain a good prediction on the pharmacological cardioversion attempts with an overall accuracy of 70.6%. This good performance may be explained by the relation between the drug effect and the AF DFs. The effect of cardioversion drugs is to modify the effective refractory period that is directly related to the atrial firing cycle length. Patients with shorter atrial firing cycle length (higher DFs) are believed to have less chance of pharmacological cardioversion then the ones with lower atrial firing cycle length (lower DFs); sustained AFs need a minimum number of reentries and a minimum atrial firing cycle length to stay sustained. In our database, the mean DF values on lead V1 was 5.96 ± 1.58Hz for the positive pharmacological cardioversion attempts in comparison to 6.32 ± 1.09Hz for the negative attempts.

5.4 Conclusion Our understanding of the correspondence between the dominant frequencies observed on the thorax and the atrial fibrillation dynamic was improved by the two AF cases studied. It was observed that simultaneous AF triggers with different frequencies produce different dominant frequencies on the thorax. It was also observed that the relation between the torso dominant frequency and the atrial firing rate maps is complex. These considerations raise more questions than answers. Phase-rectified signal averaging has been introduced as a simple, robust tool to enhance quasiperiodic signal components. We show how this technique can be used to improve the estimation of dominant frequency of the atrial activity electrocardiogram during atrial fibrillation. The results on realistic synthetic signals generated using a computer model of atrial fibrillation show that the phase-rectified signal average, when combined with some ventricular activity cancellation scheme, yields accurate dominant frequency estimates. When this combination is used on clinical electrocardiogram recordings, one observes a clear shift of dominant frequency estimates towards plausible values. The price paid in applying the process is the loss of information about the power of the frequency components. The phase-rectified signal average can be useful to improve the dominant frequency estimates for any ventricular activity cancellation scheme.



Based on the case study observations, the phase-rectified signal average technique was used to classify atrial fibrillation by using dominant frequencies characterizing the left and the right atria. Positive left-to-right dominant frequency gradient preference in the overall AFs was observed when a negative gradient preference was expected based on invasive studies. These dominant frequency features also permitted us to obtain a good prediction performance on the pharmacological cardioversion attempts with an overall accuracy of 70.6%.

Atrial fibrillation classification based on spatial dynamics extracted from the vectorcardiogram

T

6

HE 12-lead ECG is currently the standard non-invasive tool used in the diagnosing of AF. So far,

the complexity of the electrical AA during AF has mainly been assessed through the analysis of its frequency spectrum, or through the time-frequency analysis (spectrogram) of the ECG signals [127; 134]. An improved diagnosis of atrial ECG signals, in particular during AF, could result from the extraction of information derived from the spatial dynamics of the signals. Some studies have proposed to exploit the spatial information by looking at the correlation between multiple electrograms [135], or by looking at the transient nature of the links between atrial signals [136]. Recently, nonlinear patterns have been documented in multiple electrogram recordings [137; 138]. In 2006, Mainardi et al. proposed three different methods to quantify the atrial state space through linear parameter, nonlinear association estimator, and synchronization index [139]. These parameters were used to observe changes in the AF determinisms and dynamics. The spatiotemporal behavior of the electrical activity during AF precludes in all likelihood the characterization of its complexity by means of an inverse procedure. This holds true in particular if the available ECG data are restricted to those of the standard 12-lead ECG, the data that are usually the only ones available in the clinical setting. One of the methods used for the interpretation of the time course of the potentials observed on the body surface is the vectorcardiogram (VCG). The VCG provides a global representation of the electrical cardiac activity; the time course of the vector orientation and magnitude in 3D space. The atrial VCG is an estimate of the so-called equivalent dipole current source that summarizes all of the instantaneously ongoing electric activity of the atria. In model studies involving realistic source descriptions, the equivalent dipole can be computed with great accuracy, and may be taken as the gold standard for testing the potential of the VCG [140]. In the first part of this study, the expression of the spatial complexity of the different AA dy97

C HAPTER 6. ATRIAL FIBRILLATION CLASSIFICATION BASED ON SPATIAL DYNAMICS 98

EXTRACTED FROM THE VECTORCARDIOGRAM

namics as observable in the VCG was analyzed. A biophysical model of the dynamics of AA was used to generate electrophysiologically realistic source descriptions during SR, AFL and episodes of AF resulting from different substrates. The equivalent dipoles, as well as the VCGs resulting from these sources were computed [140]. This allowed us to compare the quality of the VCG for characterizing AA dynamics with that of the gold standard, the equivalent dipole. In addition to documenting the basic differences in the VCG signals corresponding to different types of AA, we introduced some methods for extracting a sparse set of features from the VCG. In the second part, an analysis based on these features, named dipole distribution analysis, was used to express the spatial complexity of the AA dynamics. The biophysical model of the atria [38] was employed to validate the proposed analysis, using the same simulations of SR, AFL and AF. The clinical database was also used after VA cancellation. The dipole distribution analysis was used on the simulated AA database to discriminate different simulated AF substrates that produce specific electrical propagations such as micro-reentries, broad and multiple wavelets. The dipole distribution analysis was applied to the clinical AA database to classify clockwise and counterclockwise AFL and to discriminate between different AF subgroups (paroxysmal, persistent, and permanent or single, and recurrent AF episodes). A refinement of that analysis, named dipole cluster analysis, was also explored. It was used on the simulated AA database to localize the SA node in SR, the macro-reentrant circuit of AFL [141] and different AF substrates: focal AF, rotor mother, complex dynamic, etc. The dipole cluster analysis was also used on the clinical AA database to estimate the localization of the AF substrates in the pulmonary vein area.

6.1 The vectorcardiogram → − The equivalent dipole D E (t) represents, to a first order approximation, the spatial distribution throughout the myocardium of the time course of the currents generated at the membranes of all cardiac myocytes. Based on equivalent double layer, the time courses of its three components in → − → − → − 3D space, D Ex (t), D Ey (t) and D Ez (t), are equal to the integral (summation) over the atrial surface → − → − → − Sa of Vm (t)d S , the local equivalent double layer strengths at the elements d S of Sa . Note that d S has the nature of a vector in 3D space, directed along the local surface normal of Sa . The integration reads: I → − → − D E (t) ∝ Vm (t)d S . (6.1) Sa

The proportionality symbol ∝ is used since σ, the electric conductivity of the medium scaling the result, is not shown. The integral in Eq. 6.1 was computed numerically, the elementary surface elements being the elements of a triangular mesh describing Sa . In any clinical application, neither the atrial surface Sa , nor the equivalent double layer source → − → − strength is available. An accurate estimate of D E (t), denoted here as D B (t), can be computed from the full potential field on the Φ(t) on the body surface as: → − D B (t) ∝

I SB

→ − Φ(t)d S .

(6.2)

This expression is known as the Gabor-Nelson equation [142]. Its evaluation requires a full specification of the potential field on the body surface, as well as of the geometry of the body surface,

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99

data that is not readily available.

→ − When relying on clinical ECG data, the VCG, denoted here as V (t), is an even cruder estimate → − of D E (t). Classically, it is derived from the linear combination of the potentials at seven locations → − on the thorax as proposed by Frank [37]. Alternative schemes for the estimation of D E (t) from the potentials observed on a limited number of electrodes have been described in the literature. In essence, all these estimates are of the type: → − V (t) = TΦECG (l,t),

(6.3)

with T being a matrix of size 3 × L that produces the estimated three vector components from the potentials ΦECG (l,t) observed at l = l,. . . L electrodes on the thorax. A version of matrix T that uses the potentials observed at the nine electrodes of the standard 12-lead ECG system, dedicated to the analysis of atrial signals, has recently been proposed [140]. This is the one used in the results shown in this chapter.

6.1.1 Displaying vector data The evolution in space and time of vector data can be displayed in different ways. In this chapter the three different displays showed in Table 6.1 were used. Table 6.1: The three different vectorcardiogram displays. Display #1. Display #2. Display #3.

The display of the trajectory of the projection of the vector on three (2D) planes (horizontal, frontal and left sagittal). The display of the vector magnitude (m(t)) and its three components (x(t), y(t) and z(t)). The display of the trajectory of the normalized vector (the vector magnitude) on a unit sphere, similar to the method proposed by Dower [143].

For display #3, the origin of a unit sphere was placed at the center of gravity of the atrial tissue. To facilitate the interpretation of the orientation of the sphere and the link between vector direction and atrial geometry, the contours of the major atrial details (valves and vessel connections) were also projected on the unit sphere, see Fig. 6.1. Examples of the three different types of displays of the VCG during SR (one complete cardiac cycle; duration 512 ms) are presented in Fig. 6.2. When followed over some longer periods, most AF trajectories could not be interpreted easily. In such situations, an alternative display was used. The projections of the subsequent samples in time were left unconnected, resulting in a scatter plot of the vector directions on the sphere (Fig. 6.3 and 6.4).



Figure 6.1: Geometry of the model representing the atria from a left anterior 45o view (on the left) and from a right posterior 45o view (on the right). The unit sphere is used to represent the normalized dipole points. The contours of some major details of the atrial geometry (valves and vessel orifices) are projected onto the unit sphere.

6.1.2 Feature extraction Dipole distribution analysis The analysis and ultimate quantification of the spatiotemporal information on AF as derived from the vector data, ultimately requires the identification of relevant features. A first attempt at the identification of useful features was carried out in this study. These were tested in their application in order to distinguish the 22 different types of AA for which both the true dipole (Eq. 6.1) and its crude estimate (Eq. 6.3) became available by means of the model-based simulations. The spatial distribution of the dipole orientations observed in the VCG was estimated by using an un-normalized kernel approach [144]. This approach estimates the distribution from the sum of Gaussian functions (kernels) centered on the sample locations of the dipole on the unit sphere. The following features were used to characterize the complexity of the spatial distribution, extracted from the normalized VCGs. For each of the signal segments studied, the second-order raw moment matrix C of the three components of a dipole d(t) was computed as: 1 C= t2 − t1

Z t2 d(t) · d0 (t) t1

kd(t)k2

dt

(6.4)

over the time interval [t1,t2], with d0 (t) denoting the transpose of the vector in 3D space expressed as a vector of linear algebra. The eigenvalues λ1 ≥ λ2 ≥ λ3 ≥ 0, of this matrix C of size 3 × 3, were used as features. Because the trace of the integrand in Eq. 6.4 is 1, we have λ1 + λ2 + λ3 = 1. This approach is related to the analysis of bidirectional data by parametric statistical modeling [145]. As an illustration, Fig. 6.3 shows three different (extreme) types of scatter plots and their λ values. The robustness of the λ values with respect to the perturbing elements (nine electrode limitations, ventricular artefacts, etc.) has been studied previously [146]. The results indicated that the first two eigenvalues λ1 and λ2 yield a robust measure of spatial complexity of the VCG during AF. For each of the simulated and clinical ECG signals, the three-components of the dipole d(t) were estimated on the entire ECG signals. Each of the clinical estimated dipole d(t) was segmented into 74 4-second intervals, the first and the last 2-second intervals being removed. The three spatial complexity features (λs) were computed on the entire simulated dipoles and on each clinical dipole

6.1. T HE VECTORCARDIOGRAM

101

Figure 6.2: Example of the VCG during the PQ interval (duration 512ms) in simulated SR. The trajectory of the VCG displayed in three planes: a) horizontal, b) frontal, and c) left sagittal. The dashed line is used during the duration of the P wave, whereas the dashed line represents the PQ segment. The corresponding amplitude scales are expressed in µV . D) The dipole magnitude m(t) and its components x(t), y(t) and z(t). E) The projection of the VCG on the unit sphere.

segments. In order to diminish the impact of the segments containing artifacts, noise, etc., the median values of the three features over the 74 clinical dipole intervals were kept as descriptors of the spatial complexity for each patient. The ternary (triangle) plot was used to display the λ values in 2D, where each corner represents one of the three extreme distributions displayed in Fig. 6.3. In a ternary plot, the proportions of the three variables must add up to a constant, in our case λ1 + λ2 + λ3 = 1. Thus there are only two degrees of freedom involved in plotting a sample point (λ1 , λ2 and λ3 ). To this end, the variables λ1 , λ2 and λ3 were converted into α1 , α2 and α3 , where α1 = λ1 − λ2 , α2 = 2 · (λ2 − λ3 ) and α3 = 3 · λ3 , see example in Fig. 6.8. Dipole cluster analysis Additional insight into the AA dynamic can be obtained based on the assumption that locations of clusters in the estimated equivalent dipole distributions may reveal the location of AA sources (SA node (SR), macro-reentry circuit (AFL) and rotor-mother and focal (AF)) projected on the



Figure 6.3: The three extreme distribution cases: the modal distribution (uni- or bi-modal), the distribution along a great circle and the uniform distribution.

unit sphere, see 6.1. To this end, the spatial distribution of the dipole was estimated using an unnormalized kernel approach [144], as mentioned in Sec. 6.1.2.

6.2 Results on simulated data In order to illustrate the potential of spatiotemporal information on AA provided by the VCG, Fig. 6.5 displays the loop derived from the normalized 12-lead VCG for the simulated SR (simulation no.1 of Table 2.1)[146]. In addition, it displays the time course of the vector for selected episodes of typical AFL (no.2) and AFs (no.7 and 15, respectively). Note that the trajectory of the VCG of typical AFL is correlated with its counter-clockwise macro-reentry direction and it is opposite to the trajectory during SR. As mentioned previously, the VCG derived from the 12-lead ECG is an estimate of the dipole derived from the complete body surface potential field which is, itself, an estimate of the equivalent dipole. Fig. 6.6 displays an example of the time course differences between the true dipole and the one derived from the 12-lead ECG for simulation no.2 (typical AFL). The three different types of displays are used.

1 2 3

A)

= 0.48 = 0.37 = 0.16

B)

Figure 6.4: Example (simulation no.19) of the time course of the normalized dipole (A) converted into a scatter plot of the vector directions (B).

6.2. R ESULTS ON SIMULATED DATA

103

Figure 6.5: Normalized VCGs for four different types of AA: right posterior 45o view (left panel) and left anterior 45o view (right panel). A) SR and B) typical AFL simulations are displayed. C) AF simulation no.5 features the stable mother-rotors located in the left appendage and the lower right pulmonary vein characterized by stable micro-reentries. D) AF simulation no.19 features the complex dynamics characterized by multiple wavelet reentries.

6.2.1 Results from the dipole distribution analysis The spatial information contained in the normalized 12-lead VCG is displayed in Fig. 6.7. It shows the VCG spatial distributions of the same simulated AAs as shown in Fig. 2.11. The observations based on the presence of VCG distribution clusters has suggested a separation of the simulated data into three groups. Group one (n=14) includes the simulated AAs in which the dipole distributions were coherent with the AA dynamics, i.e., a distribution cluster was located close to the AA source location for the AAs with stable dynamics (simulations no.1, 2, 3, 7, 13, and 22), or the dipole distribution was uniform (α1 < 0.17) for the AFs with complex dynamics (simulations no.8, 15, 16, 17, 18, 19, 20, and 21). For instance, the VCG distribution in Fig. 6.7 that represents the simulation no.1 is characterized by a dipole cluster at the sinoatrial (SA) node location, which corresponds to the SA node pacing in SR. The VCG distribution that represents the simulation no.13 is characterized by a dipole cluster at the left appendage location, which corresponds to a focal AF induced by burst pacing in the left appendage. Group two (n=3) includes the AFs with multiple AF sources with a dipole cluster close to one of the multiple AF source locations (simulations no.9, 10 and 11). In Fig. 6.7, the simulation no.9 that corresponds to AF with two mother-rotors (one around the lower right pulmonary vein and one between the pulmonary veins) displays a dipole cluster near the lower right pulmonary vein but no cluster is present between the pulmonary veins. Group three (n=5) includes the AFs with no dipole cluster close to the AA source location (simulations no.4, 5, 6, 10, and 14). These observations were also tested on the equivalent dipole. The use of the gold standard dipole had a small impact on the dipole cluster locations and produced the same groups as for the 12-lead VCGs. Figure. 6.8 shows the results on the ternary plot for the simulation of SR (star), the simulation of typical AFL (cross) and the 20 simulations of AF (circles). Simulated AFs with specific electrical propagation such as micro-reentries, broad and multiple wavelets (no.5, 13 and 19, respectively)



Figure 6.6: Time courses of the equivalent dipole and its estimate derived from the 12-lead ECG of the simulation no.2 (typical AFL) during three F waves (duration 542 ms), projected on the unit sphere. The trajectory of the ED (estimate, resp.) is displayed by dotted lines (black lines, reps.) in: A) horizontal, B) frontal, and C) left sagittal displays. The corresponding amplitude scales are expressed in µV . The equivalent dipole (D) and the estimate (E) magnitudes m(t) and their components x(t), y(t) and z(t). F) The projection of the equivalent dipole on the unit sphere. G) The projection of the estimate on the unit sphere.

are indicated. The white noise simulation is also indicated by a black dot. Note its position halfway between the uniform distribution and the distribution along a great circle.

6.2. R ESULTS ON SIMULATED DATA

105

Figure 6.7: The estimated VCG distributions of the same simulated episodes of AA showed in Fig. 6.4. See Table I for the documentation of the simulated types of AAs.

6.2.2 Results from the dipole cluster analysis Table 6.2 summarizes the results on all simulated AAs documented in Table 2.1. The first column of Table 6.2 describes the type of AA (SR, AFL or AF). It also indicates the number of AA with the same dynamic (counter-clockwise macro-reentrant circuit for AFL, mother-rotor, burst pacing, and complex dynamic for AFs). The second column displays the simulated AA reference number. The third, fourth and fifth columns display the α values (α1 , α2 , and α3 , respectively) mentioned in section 6.1.2. These α values were preferred to the λ values due to their intuitive interpretation with respect to the three extreme cases; high α1 values represent modal distributions, high α2 values represent distributions along a great circle, and α3 values represent uniform distributions. A first observation is that the AFs with complex dynamic were characterized by uniform distributions (α1 < 0.17). Table 6.2 was roughly partitioned with respect to three simulated AA groups. Group one includes the simulated AAs in which the dipole distributions were coherent with the AA dynamic, i.e. a distribution cluster was located close to the AA source location for the AAs with stable dynamic or the distribution was uniform for the AFs with complex dynamic. For instance, the estimated VCG distribution of the simulation no.1 in Fig. 6.7, whose dynamic corresponds to SA node pacing in SR, is characterized by a dipole cluster at the SA node location. The estimated VCG



Figure 6.8: Results of the VCG spatial complexities for the simulated SR (star marker), AFL (cross marker) and 20 AFs (circle markers). Three AF specific electrical propagations (micro-reentries (no.5), broad and multiple wavelets (no.13 and 19, respectively)) are included. Simulated white noise is marked by a black dot.

distribution of the simulation no.13 in Fig. 6.7, whose dynamic corresponds to a focal AF induced by burst pacing on the left appendage, is characterized by a dipole cluster at the left appendage location. Group two includes the AFs with multiple AF sources with a dipole cluster close to one of the multiple AF source locations. The estimated VCG distribution of the simulation no.9 in Fig. 6.7, whose dynamic corresponds to AF with two mother-rotors (one around the lower right pulmonary vein and one between pulmonary veins), features a dipole cluster near the lower right pulmonary vein but no dipole cluster between the pulmonary veins. Group three includes the AFs with no dipole cluster close to the AA source location (see simulation no.6 in Fig. 6.7). This was tested on the equivalent dipole derived from the complete body surface potential. The use of the equivalent dipole (300 ECG signals) had a small impact on the dipole cluster locations and produced the same groups as for the estimated equivalent dipole (9 ECG signals).

6.3. ATRIAL FIBRILLATION CLASSIFICATION BASED ON THE SPATIAL VECTORCARDIOGRAM FEATURES 107 Table 6.2: Dipole distribution results on the simulated atrial activities. Group 1 SR 1

no. 1

0.68

α values 0.30 0.02

AFL 1 counter-clockwise

no. 2

0.42

α values 0.51 0.07

AF 4 simulated AFs with stable dynamic (4 AFs with one source)

no. 3 7 13 22 8 15 16 17 18 19 20 21

0.32 0.18 0.40 0.30 0.17 0.02 0.09 0.07 0.12 0.11 0.17 0.02

α values 0.33 0.47 0.42 0.32 0.52 0.68 0.51 0.38 0.48 0.43 0.39 0.64

0.11 0.08 0.18

α values 0.55 0.34 0.60 0.32 0.49 0.33

0.18 0.35 0.31 0.10 0.05

α values 0.33 0.25 0.33 0.55 0.62

8 simulated AFs with complex dynamic

0.35 0.35 0.18 0.38 0.31 0.30 0.40 0.55 0.40 0.47 0.44 0.34

Group 2 AF 3 simulated AFs with stable dynamic

no. 8 9 11 Group 3

AF 5 simulated AFs with stable dynamic (2 AFs with one source & 3 AFs with two sources)

no. 4 5 6 12 14

0.49 0.40 0.36 0.35 0.33

6.3 Atrial fibrillation classification based on the spatial vectorcardiogram features 6.3.1 Classification procedure The λ values were computed for each 2-second intervals. To avoid the impact of outliers due to the presence of artifacts, the λ median values of each patient were used in the classification procedure. A SVM approach, described in Sec. 4.3.1, was used to perform the AF classifications based on spatial vectorcardiogram features. The SVM classification procedure was applied to the clinical database to separate into different AF types (paroxysmal, persistent, and permanent or single, and recurrent AF episodes), AF aetiologies (dilated cardiomyopathy, hypertrophic cardiomyopathy or valvular heart disease), or responses to cardioversion attempts (positive and negative responses to pharmacological or electrical cardioversion attempts). These different AF types, AF aetiologies, or responses to cardioversion were grouped in pairs. The SVM classification based on the three spatial vectorcardiogram features was applied to each pair. Because of the limited number of available records, a leave-one-out procedure (Sec. 4.3.1) was applied. In the AF classification based on



clinical features, MANOVA was applied to the different AF groups to evaluate the relevance of the four features based on DF.

Figure 6.9: A) Results of the spatial complexity on the estimated equivalent dipole for the 7 patients in SR. B) Results of the spatial complexity of the estimated equivalent dipole for the 8 patients in typical counter-clockwise AFL and 7 patients in clockwise AFL.

6.3.2 Results from the dipole distribution analysis Figure 6.9A shows the results on the ternary plot for the 7 patients in SR. Figure 6.9B shows the clinical results for the 8 typical counter-clockwise and the 7 clockwise AFLs. The α values permit the separation of the two AFL types with a threshold on α1 fixed at 0.8 (1 outlier, p < 0.000002). Figure 6.10A shows the SVM training results for the discrimination of the 25 patients in paroxysmal AF (black dots) and the 39 patients in permanent AF (white dots). The discriminant function is shown by a dashed line. The training percentage of correct classification for paroxysmal AF patients and permanent AF patients was 62.0% and 74.0%, respectively (see Table 6.6). Figure 6.10B shows the training results for the discrimination of the 24 patients with single AF episode (black dots) and the 22 patients with recurrent AF episodes (white dots). The discriminant function is presented by a dashed line. The training percentage of correct discrimination for single AF episode and recurrent AF episodes was 59.0% and 84.0%, respectively, (see Table 6.6). Tables 6.3, 6.4, and 6.5 display the distribution of the populations of AF types, AF aetiologies, and responses to cardioversion attempts with respect to the three extreme dipole distribution (modal, along great circle, and uniform). Table 6.3: AF type distribution based on the three extreme dipole distributions. 3 extreme distributions Modal Great circle Uniform

Paroxysmal (n=42)

Persistent (n=25)

Permanent (n=39)

Single (n=25)

Recurrent (n=22)

52.4% 28.6% 19.0%

52.0% 8.0% 40.0%

64.1% 10.3% 25.6%

48.0% 24.0% 28.0%

59.1% 13.6% 27.3%

6.3. ATRIAL FIBRILLATION CLASSIFICATION BASED ON THE SPATIAL VECTORCARDIOGRAM FEATURES 109

Figure 6.10: A) Classification results on the 42 patients in paroxysmal AF (black dots) and 39 patients in permanent AF (white dots) obtained with a SVM approach. B) Classification results on the 25 patients with single AF episode (black dots) and 22 patients with recurrent AF episodes (white dots) obtained with a SVM approach.

Table 6.4: AF aetiology distribution based on the extreme dipole distributions. 3 extreme distributions

DCM (n=9)

HCM (n=16)

VHD (n=12)

Pericarditis (n=2)

Focal (n=3)

Vagal (n=3)

Ectopic Focii (n=55)

Modal Great circle Uniform

77.8% 11.1% 11.1%

37.5% 18.8% 43.7%

66.7% 0.0% 33.3%

50.0% 50.0% 0.0%

66.7% 0.0% 33.3%

66.7% 33.3% 0.0%

38.2% 27.3% 34.5%

The SVM trainings (Sec 5.3.1) were applied to the clinical database to separate AF types, AF aetiologies, and AF cardioversion verdicts grouped in pairs with respect to the spatial vectorcardiogram features. A linear kernel with penalty coefficient C fixed at one produced the best training results for the classification of AF types grouped in pairs. A radial basis function kernels with a penalty fixed at infinity produced the best training results for the other AF pairs. These training setups produced 25, 26, 11, and 13 training errors for the paroxysmal-persistent, paroxysmalpermanent, persistent-permanent, and AF with single and recurrent AF episodes pairs, respectively. For the AF aetiology pairs, the training setups produced 6, 9, and 9 training errors for the dilated cardiomyopathy-hypertrophic cardiomyopathy, dilated cardiomyopathy-valvular heart disease, and hypertrophic cardiomyopathy-valvular heart disease pairs, respectively. Tables 6.6, 6.7, and 6.8 displays the percentage of correct classification with respect to paroxysmal dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and valvular heart disease (VHD) pairs, based on the spatial vectorcardiogram features. Concerning the AF eatiologies, the other three groups (pericarditis, focal and vagal AFs) were not large enough to permit a meaningful classification. The ectopic focii group, composed of all AFs having no clear aetiology, is so variable in population that its classification with respect to the other aetiologies is meaningless. The MANOVA p values of the paroxysmal, persistent and permanent AF groups, or AF groups with single and recurrent AF episodes, or of all six AF aetiology groups, or of the pharmacological or electrical cardioversion result groups were equal to 0.02, 0.02, 0.18, 0.84, and 0.63 respectively,



Table 6.5: Distribution of the AF cardioversion attempts based on the three extreme dipole distributions. Pharmacological cardioversion No success Success (n=40) (n=18)

3 extreme distributions Modal Great circle Uniform

57.5% 15.0% 27.5%

Electrical cardioversion No success Success (n=5) (n=7)

44.4% 27.8% 27.8%

60.0% 20.0% 20.0%

71.4% 0.0% 28.6%

with respect to spatial vectorcardiogram features. It denotes that the AF type populations were significantly different with respect to the dipole distribution features. Table 6.6: Percentage of correct classification of cardioversion results based on dipole distribution features. AF types Paroxysmal vs persistent Paroxysmal vs permanent Persistent vs permanent

Paroxysmal (n=42)

Persistent (n=25)

Permanent (n=39)

Single (n=25)

Recurrent (n=22)

Total

100.0% 54.8% -

0.0% 52.0%

74.4% 61.5%

-

-

62.7% 64.2% 57.8%

-

-

-

76.0%

54.5%

66.0%

Single vs recurrent

Table 6.7: Percentage of correct classification of AF aetiologies based on dipole distribution features. AF types

DCM (n=9)

HCM (n=16)

VHD (n=12)

Total


22.2% 0.0% -

87.5% 56.3%

100.0% 33.3%

64.0% 57.1% 46.4%

Table 6.8: Percentage of correct classification of AF cardioversion attempts based on dipole distribution features. Cardioversion types Pharmacological Electrical


33.3% -


71.4%

Total 66.2% 66.7%

6.3.3 Results from the dipole cluster analysis Our clinical AA database does not include any information on the 3D space location and geometry of the atria and the AA source during AF. So, we focused on the absence or presence of dipole clusters over time in an approximately determined pulmonary vein area. The borders of that pulmonary vein area are displayed in Fig. 6.11 by a dashed line. Each estimated 5-minute equivalent

6.4. D ISCUSSION

111

dipole time evolution d(t) was segmented into 74 4-second segments, the first and the last 2-second segments being removed. An AF source was considered as being present in the pulmonary vein area if the dipole d(t) spent more than 70% of the time in the pulmonary vein area defined. For each patient, the number of 4-second segments in which an AF source was considered as being present in the pulmonary vein area was computed. Figure 6.12 shows the histogram of these numbers of 4-second segments for all patients. Three different groups can be identified on that histogram. The first group contains AF patients for whom AF source was considered as rarely being present in the pulmonary vein area (less than 20 times out of 74). This group is displayed in black on the left side of the histogram. In that group, for 23 patients no AF source was considered as being present in the pulmonary vein area over the 74 segments (first bin on the left). The second group contains AF patients for whom the AF source was considered as being present occasionally in the pulmonary vein area (more than 20 times and less than 45 times out of 74). This group is displayed in white in the middle of the histogram. The third group contains AF patients for whom the AF source was considered as being often present in the pulmonary vein area (more than 45 times out of 74). In that group, for 31 patients an AF source was considered as being present in the pulmonary vein area for each segment (last bin on the right). The mean (± the standard deviation) values of the three groups are represented by dotted lines. The boxed numbers represent the corresponding number of patients.

6.4 Discussion Several studies have already been dedicated to the investigation of different types of AF derived from electrograms [147] or surface ECG recordings [126–128]. These works have focused mainly on the prediction of AF termination (paroxysmal vs persistent), the efficacy of drugs and the discrimination of AF type I, II and III (Wells’ criteria). Time-frequency and information theory tools were mostly used. We have investigated how accurately the global representation of the electrical AA can be obtained from an atrial VCG derived from the 12-lead ECG signals. This global representation of the electrical AA is well reflected in the results observed during SR and the typical AFL, as observed

PV area Figure 6.11: Fixed pulmonary vein area represented on the sphere: lateral views from the left (left panel) and from the right (right panel). The projection of the four pulmonary veins as well as the MV, the TV, the IVC and SVC and the coronary sinus (CS) are shown. Note that both atria are represented on the same sphere.



32.5 ±5.6

20

n=69

3.4 ±5.1 n=40

3.4 ±5.1 n=10

10

5 patients 0 10 segments

Figure 6.12: Histogram that displays for each AF patient the number of segments in which an AF source was considered as being present in the pulmonary vein area. Three different groups with their respective mean and standard values are shown. The boxed numbers represent their number of patients.

by either of the display methods described in Table 6.1. During SR, the VCG during depolarization points in the frontal-downward direction, away from the SA node. During repolarization, the vector predominantly points in the opposite direction. The typical AFL VCG displays complete loops that correspond to the counter-clockwise orientation of the AFL macro-reentry; its trajectory passes between the coronary sinus and the MV areas projected on the unit sphere. The well-documented SR VCG trajectory is more complex than the AFL VCG trajectory. This is due to the regularity and completeness of the AFL macro-reentry cycle in opposition to the activity that follows the pacing of the SA node in SR. During AF, the VCG trajectory is more complex and the presence of a preferential circuit is hardly observable. The difference between the time course of the true dipole and the VCG derived from the nine electrodes of the 12-lead ECG on the unit sphere for the simulation no.2 (typical AFL) demonstrates the effect of a limited set of electrodes. As observed in [146], this discrepancy is mainly due to the difficulty in estimating the z component (front-back axis). However when we compare the different AFL dipole results, even if the 12-lead VCG is not identical to the true dipole, the general trajectory is similar. The direction of the VCG still corresponds to the counter-clockwise orientation. The observation of the atrial VCG spatial distributions was our first attempt to identify relevant differences between the 22 simulated AAs. The identification of the distribution peaks, i.e. regions of the unit sphere most frequently visited by the dipole over time, has revealed the location of a stable and unique AA source such as micro-reentry, mother-rotor or focal (AF) in most of the simulated AAs. The simulated SR and AFL constitute typical example of this situation. Their dipole distributions revealed peaks at the location of the SA node (SR) or between the MV and the coronary sinus (typical AFL macro-reentry circuit). Cases where those peaks were absent probably corresponded to complex AF dynamics.

6.4. D ISCUSSION

113

As illustrated, the VCG spatial complexity can be visualized in a very natural and synthetic way by the spatial vectorcardiogram features. Any AA dynamics can be represented as a point inside a triangle, the corners of which correspond to archetypal dynamics (focal AA, AA that evolves around a fixed circuit and complex disorganized AA). The simulated SR has enabled us to validate one of the three extreme distributions, the modal one (bottom left of the triangle). The simulated typical AFL is closer to the bottom right corner. The parameters λ for the simulated SR (AFL, respectively) were λ1 = 0.86, λ2 = 0.13, and λ3 = 0.01 (λ1 = 0.72, λ2 = 0.26, and λ3 = 0.02, respectively). This is consistent with the fact that AFL has a stable dynamic, slightly more complex than that of SR and characterized by a fixed circuit. The two VCGs for simulations no.5 (stable micro-reentries) and no.19 (multiple wavelet reentries) differ by the complexity of their dynamics, as visible in Fig. 6.5, and on the triangle in Fig. 6.7. The AF episodes were characterized by λ1 = 0.65, λ2 = 0.23 and λ3 = 0.12 for AF simulation no.5, and λ1 = 0.42, λ2 = 0.31 and λ3 = 0.27 for AF simulation no.19. This reflects the fact that the average wavelength of the depolarization waves is shorter in AF simulation no.19 (7.3 cm) than that of AF simulation no.5 (9.4 cm), leaving enough space for more wavelets and reentries. The results based on the clinical AA database correlate well with those results obtained by the biophysical atrial model. The dipole distributions of the 7 patients in SR, displayed on the triangle (Fig. 6.9A), are close to the bottom left corner. Anatomical differences may explain the variation in the clinical results, especially the SA node structure and the possible fibrosis in the right atrial tissue due to the age of the patients in SR (74.2 ± 9.2 years old). The dipole distributions of the 8 patients in counter-clockwise AFL are coherent with the results obtained with the biophysical atrial model. They exhibit dipole distributions concentrated along a preferential circuit (modal distribution or distribution along a great circle). The dipole distributions of the 7 patients in clockwise AFL form a different cluster. Their dipole distributions are still related to a stable circuit (bottom left corner) albeit more complex (upper region). This may be explained by the different electrical atrial propagations resulting from the anatomy and the direction of the macro-reentrant circuit. The most promising results are those illustrated in Fig. 6.10A and B. Although not perfect, a clear discrimination between single and recurrent AF episodes and to a lesser extent, between persistent and permanent AF is observed in the triangle. Also, the locations of the various clusters are consistent with what is known about the evolution of remodeling [148]. In persistent and non recurrent AFs, mostly electrical remodeling is engaged. This translates into shorter wavelengths and thus distributions closer to the region occupied by the simulated AFs in Fig. 6.8. Permanent and recurrent AFs are most probably linked both to an electrical and structural remodeling. The addition of the latter leads to preferential electrical circuits and thus to simpler dynamics. We have also investigated how supplementary information can be extracted from the distribution of the estimated equivalent dipole. Identification of the distribution peaks i.e. regions of the unit sphere most frequently visited by the dipole over time may reveal the location of the stable AA source, such as SA node (SR), macro-reentrant circuit (AFL) and mother-rotor or focus (AF). We have illustrated this on simulated AA. This correspondence between distribution peaks and AA sources cannot be established on the clinical data used in this study. However, we observed an intriguing partitioning of the AF patients with respect to the value of the estimated equivalent dipole distribution in an approximately determined pulmonary vein area on the unit sphere.



As mentioned in [146], the major problem of the 12-lead VCG is related to the difficulty in estimating the z component (front-back axis) of the equivalent dipole from the signals observed on just nine electrodes. This limitation for characterizing the AA dynamic is visible on the ternary plot. White noise simulation should be close to the uniform distribution; and indeed, we observed this with the equivalent dipole based results. The results of the characterization using the λ values applied to the 20 AF variants form a cluster located between the uniform distribution and the distribution along a great circle. The variation in the spatial complexity analysis results obtained from the equivalent dipole was higher and closer to the uniform distribution. The use of an optimized lead system dedicated to the extraction of an atrial VCG [140] significantly improved the estimation of the equivalent dipole. The examples we show in this chapter indicate that the relationship between the VCG spatial distribution cluster and the AA source location is not always feasible, in particular when multiple AA sources are present. Figure 6.9 demonstrates that, if the estimated equivalent dipole parameters (α values) are good indicators of AA dynamic complexity, they cannot be used to discriminate between different types of atrial arrhythmias such as clockwise flutter and permanent AF. To this end, other approaches such as frequency based ones [149] can be added. The examples we provide in this study on the location of the AA source indicate that the relationship between the distribution and the AA source is not perfect. Problems arise when multiple AA sources are present.

6.5 Conclusion Based on the simulations, the atrial vectorcardiogram seems to be a promising, useful tool for summarizing the spatiotemporal complexity of electrical atrial activity. Even in a limited electrode set context such as the standard 12-lead electrocardiogram, the equivalent dipole was still well estimated by the vectorcardiogram in terms of trajectory and global distribution. Analysis of the dipole distribution yielded spatial information that was generally lacking in typical non-invasive atrial fibrillation studies. This analyzes the spatial complexity of the atrial activity dynamics, such as the average wavelength, and the atrial fibrillation complexity. This analysis permitted us to discriminate between AFs with single and recurrent episodes, characterized by modal and uniform distributions, respectively. It also allowed us to predict the result of pharmacological and electrical cardioversion with a 66.2% and a 66.7% of success, respectively. The dipole cluster analysis facilitates the estimation and localization of a stable and unique AA source. Based on the simulated and clinical results, we hypothesize that the dipole cluster analysis, together with the patient anatomical data, may help clinicians in ablation procedures, mainly by predicting where the ablation lines could be most effective.

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work presented in this thesis is part of a larger project to establish a general research framework for atrial fibrillation. It is the continuation of the four previous theses accomplished by Olivier Blanc [150], Vincent Jacquemet [151], Lam Dang [152], and Zenichi Ihara [153]. The works accomplished by Olivier Blanc and Vincent Jacquemet focused mainly on the development of a biophysical model of the human atria: development of an atrial geometry, implementation of membrane kinetics models, study of electrogram signal morphology, and recently, particular pathology effects on the electrical and structural properties of the atrial myocardium [154]. The work completed by Lam Dang used the biophysical model to investigate, validate, and proposed new strategies in terms of ablation procedure and therapeutic pacing. The part of the work achieved by Zenichi Ihara that was linked to the present thesis, focused on the design of optimized electrocardiogram systems and optimized vectorcardiographic leads dedicated to the analysis of atrial fibrillation. HE

The next step was to use this knowledge to propose and develop new tools for the characterization of atrial fibrillation. This thesis includes details concerning the pertinent tools, and the related pertinent observations with the aim developing classifications based on scientific arguments and validated by the biophysical computer model and clinical data. The final objective is to permit the development of information from the 12-lead standard electrocardiogram on atrial fibrillation substrates, dynamics, and prediction of success for different treatments. Investigation of atrial fibrillation by means of surface electrocardiogram signals has three principal advantages when compared to invasive investigation: the procedure to acquire patient data does not entail complex clinical manipulation, it constitutes the standard tool for interpreting cardiac abnormalities, and it provides an important macro description of the cardiac activity. On the other hand, the atrial activity is hidden by the dominant ventricular activity in the surface electrocardiogram signals. Hence, it is important to eliminate the ventricular activity from the electrocardiogram signals. 115

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The purpose of the current work was first the development and the evaluation of methods to extract the atrial activity from the standard 12-lead electrocardiogram during atrial fibrillation. Simulated electrocardiograms created by using the biophysical model of the atria and of the volume conduction effects of the thorax as well as clinical electrocardiograms were used for the evaluation of the various methods proposed. Using a biophysical model of the atria provided realistic electrocardiogram atrial fibrillation signals with their separate atrial and ventricular components. Secondly, a study that aimed at exploring the potential of such "clean" atrial electrocardiograms was performed. Atrial fibrillation classifications based on various features were investigated. The extraction of these various features requires specific techniques that were also validated by using simulated and clinical electrocardiograms.

7.1 Summary of achievements In this thesis, the major achievements can be summarized as follows:

Ventricular activity cancellation techniques Two different techniques were developed to cancel the ventricular involvement in the standard 12lead electrocardiogram signals. • The first technique is a refinement of the average beat subtraction technique. It treats the ventricular depolarization and repolarization waves with independent templates; • The second technique cancels the ventricular involvement in each cardiac cycle in an independent manner. Both methods have their advantages. They both treat the ventricular depolarization and repolarization waves in independent manner. The refinement of the average beat subtraction technique lies in the optimized procedure based on template subtraction to obtain high quality results on long electrocardiogram recordings. On the other side, the single beat technique needs only one complete cardiac cycle to perform a ventricular activity cancellation with high quality results, which is appropriate for standard 10-second electrocardiogram recordings.

Prediction of self-terminating arial fibrillation We proposed an automated method based on clinician’s suggestion to predict self-termination of atrial fibrillation. A link between the fibrillatory wave disorganization and the sustained atrial fibrillation was made. We reached a percentage of correct classification of 90%. This prediction might increase the possibility to intervene in affected individuals to increase the likelihood of selftermination of what would otherwise be sustained atrial fibrillation.

Two cases studied: from the firing rate to the torso dominant frequencies The study of simulated atrial fibrillation related signals under fully controlled conditions permitted us to gain some understanding about the correspondence between the dominant frequencies observed on the body surface potentials and the atrial fibrillation dynamics. Two simultaneous stable

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rotors and their effects on the firing rates of the atrial myocytes and on the torso dominant frequency map were analyzed. We observed that atrial fibrillation dynamics, simple or complex, create different body surface potential patterns, but these differences may be hidden by dominant frequency analysis applied to a single lead. Therefore, dominant frequency analysis on multiple leads is to be preferred. We also observed in simulations that left and right atria may be controlled by different atrial fibrillation triggers and that lead V1 and V5 are good candidates for observing the trigger rhythms. This result may facilitate the clinical identification of atrial fibrillation triggers and their importance in intra-cardiac approaches, and thereby, improve the electrical cardioversion chance of success.

Left-to-right dominant frequency gradient Most of the non-invasive studies limit the atrial information to lead V1; the other lead signals may in some case contain too much ventricular residue after cancellation. In order to extract more information, we propose the use of phase-rectified signal average technique to estimate the dominant frequency on all leads. This technique extracts quasi-periodic oscillations in noisy, non-stationary signals. It permitted us to observe the general atrial fibrillation preference for a positive left-to-right dominant frequency gradient on the torso, when a preference for negative left-to-right dominant gradient on the atrial tissue was observed by other groups. This observation confirms our hypothesis that the relationship between the torso dominant frequency and the atrial firing rate maps is complex.

Discrimination between patients with positive and negative pharmacological cardioversion responses The estimated dominant frequencies obtained by phase-rectified signal average technique also permitted us to observe a discrimination between the atrial fibrillation patients with positive pharmacological cardioversion responses associated with low dominant frequencies and the ones with negative responses associated with high dominant frequencies. This result may help in the prediction of pharmacological cardioversion, and therefore help the clinicians in the atrial fibrillation management.

Atrial fibrillation discriminations based on vectorcardiograms The vectorcardiogram was proposed as a tool to globally represent electrical atrial activity. Two proposed analyses based on the time course of the dipole (vectorcardiogram) were applied to simulated and clinical data. These two analyses allowed us to: • Relate the complexity of the atrial fibrillation dynamic to the the dipole distribution; • Discriminate different atrial fibrillation types, mainly the single from the recurrent atrial fibrillation episodes. • Identify the presence and the location the single atrial fibrillation "trigger" or source.

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As for the other achievements, the ultimate goal was to help clinicians treat the atrial fibrillation by developing information concerning atrial fibrillation substrates, dynamics, and prediction of success for different treatments. The discrimination between atrial fibrillation types with the dipole distribution analysis may confirm or invalidate a clinician’s classification that results from patient history and not from fibrillatory wave characterisitics. As for the identification and localization of atrial fibrillation sources, it may help clinicians in the ablation procedures, mainly by helping them to predict where the ablation lines could be effective.

7.2 Perspectives The information contained in the ECG signals has just recently begun to be explored. Therefore, a lot of promising findings are to be expected in the future. This work presented our main tools to characterize ECG signals during atrial fibrillation, and our major observations. This work can be extended in various ways.

Ventricular activity cancellation In order to promote the study of atrial fibrillation via non-invasive records, the implementation of ventricular activity cancellation in commercial monitoring systems is necessary. It requires real time processing, high average performance, and arrhythmia detectors. A new project in collaboration with a commercial company has been started.

Vectorcardiogram features We have investigated the spatial information of the dipole time course to characterize the atrial activity dynamic. However, other features that include vectorcardiogram temporal information (trajectory) may extract information that was previously hidden in the classical analysis.

Clinical study: ablation line procedure Based on the simulated and clinical results, we hypothesize that the dipole cluster analysis, with the patient anatomical data, may help clinicians in ablation procedures. Clinical validation of this hypothesis is necessary. A database of patients that have required ablation lines in the pulmonary vein area or in the right atrium is being set up in collaboration with Dr. Lam Dang at the Herz Gefäss Zentrum (Zurich, Switzerland) in order to evaluate the clinical potential of such analysis.

Other clinical studies The various techniques and features proposed in this thesis are applicable to any non-invasive study that concerned the characterization of atrial fibrillation. It could be interesting to investigate more specific databases (ex.: specific treatment responses), patient follow-up after cardioversion and studies that combine invasive and non-invasive data to increase the chance of identifying determinant atrial fibrillation characterization.

Bibliography [1] C. Ayala, W. A. Wattigney, J. B. Croft, A. Hyduk, and G. A. Mensah, “Public health and aging: Atrial fibrillation as a contributing cause of death and medicare hospitalization - united states, 1999,” MMWR, vol. 52, pp. 128–131, Feb. 2003. [2] S. Stewart, C. L. Hart, D. L. Hole, and J. J. McMurray, “Population prevalence, incidence, and predictors od atrial fibrillation in the renfrew/paisley study,” Heart, vol. 86, pp. 516–521, 2001. [3] W. B. Kannel, P. A. Wolfs, E. J. Benjamin, and D. Levy, “Prevalence,incidence, prognosis, and predisposing conditions for atrial fibrillation: population-based estimates,” Am. J. Cardiol., vol. 82, pp. 2N–9N, 1998. [4] C. D. Furberg and al., “Prevalence of atrial fibrillation in elderly subjects (the cardiovascular health study),” Am. J. Cardiol., vol. 74, pp. 236–241, 1994. [5] B. M. Psaty and al., “Incidence of and risk factors for atrial fibrillation in older adults,” Circulation, vol. 96, pp. 2455–2461, 1997. [6] P. A. Wolf, R. D. Abbott, and W. B. Kannel, “Atrial fibrillation: a major contributor to stroke in the elderly: the framingham study,” Arch. Intern. Med., vol. 147, pp. 1561–1564, 1978. [7] E. J. Benjamin, “Impact of atrial fibrillation on the risk of death: the framingham heart study,” Circulation, vol. 98, pp. 946–952, 1991. [8] P. A. Wolf, R. D. Abbott, and W. B. Kannel, “Atrial fibrillation as an independent risk factor for stroke: the framingham study,” Stroke, vol. 22, pp. 983–988, 1991. [9] J. S. Shinbane and al., “Tachycardia-induced cardiomyopathy: a review of animal models and clinical studies,” J. Am. Coll. Cardio., vol. 29, pp. 709–715, 1997. [10] M. S. Stanton, W. M. Miles, and D. P. Zipes, Atrial Fibrillation and Flutter. W.B. Saunders Compagny, 1990. [11] V. Fuster, L. Ryden, and al., “ACC/AHA/ESC guidelines for the management of patients with atrial fibrillation : Executive summary: A report of the american college of cardiology/american heart association task force on practice guidelines and the european society of 119

120

B IBLIOGRAPHY

cardiology committee for practice guidelines and policy conferences,” J. Am. Coll. Cardiol., vol. 38, no. 4, pp. 1231–1265, 2001. [12] M. A. Allessie, P. L. Rensma, J. Brugada, and J. Smeets, Pathophysiology of Atrial Fibrillation. W.B. Saunders Compagny, 1990. [13] M. Courtemanche, R. J. Ramirez, and S. Nattel, “Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: Insights from a mathematical model,” Card. Res., vol. 42, pp. 477–489, 1999. [14] M. Haisaguerre, P. Jais, D. C. Shah, A. Takahashi, M. Hocini, G. Quiniou, S. Garrigue, A. Le Mouroux, P. Le Metayer, and J. Clementy, “Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins,” N. Eng. J. Med., vol. 339, pp. 659–666, 1998. [15] F. Xie, A. Garfinkel, and J. N. Weiss, “Electrical refractory period restitution and spiral wave reentry in simulated cardiac tissue,” Am. J. Physiol.(Heart Circ. Physiol.), vol. 283, pp. H448–H460, 2003. [16] M. A. Allessie, K. Konings, C. Kirchhof, and M. Wijffels, “Electrophysiologic mechanisms of perpetuation of atrial fibrillation,” Am. J. Cardiol., vol. 77, no. 3, pp. 10A–23A, 1996. [17] J. Jalife, “Rotors and spiral waves in atrial fibrillation,” J. Cardiovasc. Electrophysiol., vol. 14, pp. 776–780, 2003. [18] J. Brugada, “Relevance of atrial fibrillation classification in clinical practice,” J. Cardiovascular Electrophysiol., vol. 13(1 Suppl), pp. S27–S30, 2002. [19] H. Gray and W. H. Lewis, Anatomy of the human body. Lea and Febiger, 20th ed., 1918. [20] E. R. a. Behr, “When a young person dies suddenly.” Cardiac Risk in the Young - CRY, Unit 7 - Epsom Downs Metro Centre Waterfield, Tadworth (Surrey, UK), 2003. [21] W. A. Jolly and T. W. Ritchie, “Auricular flutter and fibrillation,” Heart, vol. 3, pp. 177–221, 1911. [22] A. L. Waldo, Atrial Flutter: From Mechanism to Treatment, vol. 14 of Clinical approaches to tachyarrhythmias. Futura Publishing Compagny, Inc., 2001. [23] V. Fuster, L. E. Ryden, and et al., “ACC/AHA/ESC guidelines for the management of patients with atrial fibrillation: full text. a report of the american college of cardiology/american heart association task force on practice guidelines and the european society of cardiology committee for practice guidelines (writing committee to revise the 2001 guidelines for the management of patients with atrial fibrillation),” Europace, vol. 8, 2006. [24] S. L. Kopecky, B. J. Gersch, M. D. McGoon, and et al., “The natural history of lone atrial fibrillation. a population-based study over three decades,” N Engl J Med, vol. 317, pp. 669– 674, 1987.

B IBLIOGRAPHY

121

[25] L. Frost, L. J. Hune, and P. Vestergaard, “Overweight and obesity as risks factors for atrial fibrillation or flutter: the danish diet, cancer, and health study,” Am J Med, vol. 118, pp. 489– 95, 2005. [26] S. Levy, M. Maarek, P. Coumel, and et al., “Characterization of different subsets of atrial fibrillation in general practice in france: the ALFA study. the college of french cardiologists.,” Circulation, vol. 99, pp. 3028–3035, 1999. [27] S. Lazar, S. Dixit, F. E. Marchlinski, D. J. Callans, and E. P. Gerstenfeld, “Presence of left-toright atrial frequency gradient in paroxysmal but not persistent atrial fibrillation in humans,” Circulation, vol. 110, pp. 3181–3186, 2004. [28] M. C. Wijffels, C. J. Kirchhof, R. Dorland, and M. A. Allessie, “Atrial fibrillation begets atrial fibrillation. a study in awake chronically instrumented goats,” Circulation, vol. 92, pp. 1954–1968, 1995. [29] C. A. Morillo, G. J. Klein, D. L. Jones, and C. M. Guiraudon, “Chronic rapid atrial pacing. structural, functional, and electrophysical characteristics of a new model of sustained atrial fibrillation,” Circulation, vol. 91, pp. 1588–1595, 1995. [30] W. Logan, D. Rowlands, G. Howitt, and A. Holmes, “Left atrial activity following cardioversion,” Lancet, vol. 286 (7410), pp. 471–473, 1965. [31] M. Allessie, J. Ausma, and U. Schotten, “Electrical, contractile and structural remodelling during atrial fibrillation,” Cardiovasc Res, vol. 54, pp. 230–246, 2002. [32] R. Fogoros, Electrophysiologic Testing. Blackwell Publishers, 4th ed., 2006. [33] W. Einthoven, “Die galvanometrische registrierung des menschlichen elektrokardiogramms, zugleich eine beurtheilung der anwendung des capillarelektrometers in der physiologie,” Pfügers Archiv für die Gesamte Physiologie des Menschen und der Tiere, vol. 99, pp. 472– 480, 1903. [34] C. Conrath and T. Opthof, “The patient U wave,” Cardiovasc Res, vol. 67(2), pp. 184–186, 2005. [35] H. J. Ritsema van Eck, J. A. Kors, and G. van Herpen, “The U wave in the electrocardiogram: A solution for a 100-year-old riddle,” Cardiovascular Research, vol. 67, pp. 256–262, 2005. [36] S. Bellet, Clinical. Lea and Febiger, 3rd ed., 1971. [37] E. Frank, “An accurate, clinically practical system for spatial vectorcardiography,” Circulation, vol. 13, pp. 737–749, 1956. [38] V. Jacquemet, N. Virag, Z. Ihara, L. Dang, O. Blanc, S. Zozor, J. M. Vesin, L. Kappenberger, and C. S. Henriquez, “Study of unipolar electrogram morphology in a computer model of atrial fibrillation,” J. Cardiovasc. Electrophysiol., vol. 14, no. 10(Suppl.), pp. S172–S179, 2003.

122

B IBLIOGRAPHY

[39] V. Jacquemet, A. van Oosterom, J. M. Vesin, and L. Kappenberger, “Analysis of electrocardiograms during atrial fibrillation: A biophysical model approach,” IEEE Eng. Med Biol. Mag., vol. 25(6), pp. 79–88, 2006. [40] M. Courtemanche, R. J. Ramirez, and S. Nattel, “Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model,” Am. J. Physiol., vol. 275, pp. H301–H321, 1998. [41] A. van Oosterom and V. Jacquemet, “Genesis of the P wave: atrial signals as generated by the equivalent double layer source model,” Europace, vol. 7 (suppl. 2), pp. S21–S29, 2005. [42] N. Virag, V. Jacquemet, C. Henriquez, S. Zozor, O. Blanc, J. M. Vesin, E. Pruvot, and L. Kappenberger, “Study of atrial arrhythmias in a computer model based on MR images of human atria,” Chaos, vol. 12, no. 3, pp. 754–763, 2002. [43] P. Jørgensen, C. Schäfer, P. Guerra, M. Talajic, S. Nattel, and L. Glass, “A mathematical model of human atrioventricular nodal function incorporating concealed conduction,” Bull Math Biol, vol. 64, pp. 1083–1099, 2002. [44] N. V. Thakor and Y. S. Zhu, “Applications of adaptive filtering to ecg analysis: Noise cancellation and arrhythmia detection,” IEEE Trans Biomed Eng, vol. 38 (8), pp. 785–793, 1991. [45] P. Laguna, R. Jane, E. Masgrau, and P. Caminal, “The adaptive linear combiner with a perioidic-impulse reference input as a linear comb filter,” Signal Proc, vol. 48 (3), pp. 193– 203, 1996. [46] D. Raine, P. Langley, A. Murrray, A. Dunuwille, and J. P. Bourke, “Surface atrial frequency analysis in patients with atrial fibrillation,” J. Cardiovascular Electrophysiol., vol. 15, pp. 1021–1026, 2004. [47] D. Raine, P. Langley, A. Murrray, S. S. Furniss, and J. P. Bourke, “Surface atrial frequency analysis in patients with atrial fibrillation: assessing the effects of linear left atrial abalation,” J. Cardiovascular Electrophysiol., vol. 16, pp. 838–844, 2005. [48] J. J. Rieta, F. Castells, C. Sánchez, V. Zarzoso, and J. Millet, “Atrial activity extraction for atrial fibrillation analysis using blind source separation,” IEEE Trans. Biomed. Eng., vol. 51, pp. 1176–1186, 2004. [49] G. Pardi, E. Tucci, A. Uderzo, and D. Zanini, “Fetal electrocardiogram changes in relation to fetal heart rate patterns during labour,” Am J Obstet Gynecol, vol. 118 (2), pp. 243–250, 1974. [50] M. Holm, S. Pehrson, M. Ingemansson, L. Sörnmo, R. Johansson, L. Sandhall, M. Sunemark, B. Smideberg, C. Olsson, and S. B. Olsson, “Non-invasive assesment of the atrial cycle length during atrial fibrillation in man: introducing, validation and illustrating a new ECG method,” Cardiovasc. Res., vol. 38, pp. 69–81, 1998.

B IBLIOGRAPHY

123

[51] A. Bollmann, K. Sonne, E. H. D, I. Toepffer, J. J. Langberg, and H. U. Klein, “Non-invasive assesment of fibrillatory activity in patients with paroxysmal and persistent atrial fibrillation using the holter ECG,” Cardiovasc. Res., vol. 44, pp. 60–66, 1999. [52] J. Slocum, A. Sahakian, and S. Swiryn, “Diagnosis of atrial fibrillation from the surface electrocardiograms based on computer-detected atrial activity,” J. Electrocardiol., vol. 25, pp. 1–8, 1992. [53] R. M. Rangayyan, Biomedical Signal Analysis : A Case-Study Approach. John Wiley & Sons, inc., 2002. [54] B. U. Köhler, C. Hennig, and R. Orglmeister, “The principles of software QRS detection,” IEEE Eng Med Biol Mag, vol. 21(1), pp. 42–57, 2002. [55] L. Sörnmo and P. Laguna, Bioelectrical Signal Processing in Cardiac and Neurological Applications. Elsevier Academic Press, 2005. [56] S. Amari, A. Cichocki, and H. H. Yang, “A new learning algorithm for blind signal separation.,” in Advances in Neural Information Processing Systems 8, pp. 757–763, MIT Press, 1996. [57] K. Torkkola, “Blind separation for audio signals - are we there yet?,” in Proc. 1st Int. Workshop Indep. Compon. Anal. Signal Sep., pp. 239–244, 1999. [58] H. Saruwatari, T. Kawamura, and K. Shikano, “A training algorithm for optimal margin classifiers,” in Fifth Annual Workshop on Computational Learning Theory (D. Haussler, ed.), vol. 5, pp. 144–152, ACM Press, 1992. [59] K. Anand, G. Mathew, and V. Reddy, “Blind source of multiple co-channel bpsk signals arriving at an antenna array,” IEEE Signal Processing Lett, vol. 2, pp. 176–178, 1995. [60] S. Makeig, A. Bell, T. P. Jung, and T. J. Sejnowski, “Independent component analysis of electroencephalographic data,” in Advances in Neural Information Processing Systems, vol. 8, MIT Press, 1995. [61] G. d’Urso, P. Prieur, and C. Vincent, “Blind identification methods applied to EDF civil works and power plants monitoring,” in Proc. HOS’97, 1997. [62] A. Back and A. Weigend, “A first application of independent component analysis to extracting structure from stuck returns,” Int J Neural Syst, vol. 8 (4), 1997. [63] J. Millet-Roig, J. J. Rieta, V. Zarzoso, A. Cebrián, F. Castells, C. Sánchez, and R. GarcíaCivera, “Surface-ECG atrial activity extraction via blind source separation: Spectral validation,” in Computers in Cardiology 2002, pp. 605–608, 2002. [64] J. J. Rieta, V. Zarzoso, J. Millet-Roig, R. García-Civera, and R. Ruiz-Granell, “Atrial activity extraction based on blind source separation as an alternative to QRST cancellation for atrial fibrillation analysis,” in Computers in Cardiology 2000, vol. 27, pp. 69–72, 2000.

124

B IBLIOGRAPHY

[65] V. Zarzoso and A. K. Nandi, “Blind separation of independent sources for virtually any source probability density function,” IEEE Trans Signal Process, vol. 47, no. 9, pp. 2419– 2432, 1999. [66] F. Castells, J. Igual, J. J. Rieta, C. Sanchez, and J. Millet, “Atrial fibrillation analysis based on ICA including statistical and temporal source information,” in ICASSP 2003, pp. 59–64, 2003. [67] M. Lemay, J. M. Vesin, Z. Ihara, and L. Kappenberger, “Suppression of ventricular activity in the surface electrocardiogram of atrial fibrillation,” in ICA 2004, pp. 1095–1102, 2004. [68] F. Castells, J. J. Rieta, J. Millet, and V. Zarzoso, “Spatiotemporal blind source separation approach to atrial activity estimation in atrial tachyarrhytmias,” IEEE Trans. Biomed. Eng., vol. 52, pp. 258–267, 2005. [69] V. Zarzoso and A. K. Nandi, “Adaptive blind source separation for virtually any source probability density function,” IEEE Trans Signal Process, vol. 48, no. 2, pp. 477–488, 2000. [70] S. Fiori, “Hybrid independent component analysis by adaptive LUT activation function neurons,” Neural Networks, vol. 15, pp. 85–94, 2002. [71] P. Langley, J. J. Rieta, M. Stridh, J. Millet, L. Sörnmo, and A. Murray, “Comparison of atrial signal extraction algorithms in 12-lead ecgs with atrial fibrillation,” IEEE Trans Biomed Eng, vol. 53(2), pp. 343–346, 2006. [72] P. Comon, “Indepdendent component analysis, a new concept?,” Signal Process, vol. 36(3), pp. 287–314, 1994. [73] G. Golub and C. van Loan, Matrix Computations. The Johns Hopkins University Press, 2nd ed., 1989. [74] F. Harroy and J. L. Lacoume, “Maximum likelihood estimators and Cramer-Rao bounds in source separation,” Signal Process, vol. 55, pp. 167–177, 1996. [75] S. I. Amari, “Natural gradient works efficiently in learning,” Neural Computation, vol. 10, pp. 251–276, 1998. [76] H. H. Yang and S. I. Amari, “Adaptive online learning algorithms for blind source separation: maximum entropy and minimum mutual information,” Neural Computation, vol. 9, pp. 1457–1482, 1997. [77] S. Haykin, Unsupervised adaptive filtering, vol. 1. J. Wiley & Sons, 2000. [78] A. Bollmann, N. K. Kanuru, K. K. McTeague, P. F. Walter, D. B. DeLurgio, and J. J. Langberg, “Frequency analysis of human atrial fibrillation using the surface electrocardiogram and its response to ibutilide,” Am. J. Cardiol., vol. 81, pp. 1439–1445, 1998.

B IBLIOGRAPHY

125

[79] M. Stridh and L. Sörnmo, “Spatiotemporal QRST cancellation techniques for analysis of atrial fibrillation,” IEEE Trans. Biomed. Eng., vol. 48, pp. 105–111, Jan 2001. [80] M. Stridh and L. Sörnmo, “Spatiotemporal QRST cancellation techniques for atrial fibrillation analysis in the surface ECG,” tech. rep., Lund University, Sweden, 1998. [Online]. Available:http://www.tde.lth.se/research/sig/Sigreport.html. [81] M. Stridh and L. Sörnmo, “Spatiotemporal QRST cancellation techniques for analysis of atrial fibrillation: Methods and performance,” in Proc. Computers in Cardiology, pp. 633– 636, 1998. [82] M. Stridh and L. Sörnmo, “Spatiotemporal QRST cancellation techniques for improved characterization of atrial fibrillation in the surface ecg,” in Proc. Engineering in Medicine and Biology Society, vol. 1, pp. 48–49, Oct-Nov 1997. [83] J. Waktare, K. Hnatkova, C. J. Meurling, H. Nagayoshi, T. Janota, A. J. Camm, and M. Malik, “Optimal lead configuration in the detection and subtraction of QRS and T wave templates in atrial fibrillation,” in Proc. Computers in Cardiology, vol. 25, pp. 629–632, 1998. [84] A. van Oosterom, “The dominant T wave and its significance,” J. Cardiovasc. Electrophysiol., vol. 14, no. 10, pp. S180–S187, 2003. [85] A. van Oosterom, “Singular value decomposition of the T wave: Its link with a biophysical model of repolarization,” Int. J. Bioelectromagnetism, vol. 4, p. 59, 2003. [86] A. van Oosterom and V. Jacquemet, “A parametrized description of transmembrane potential used in forward and inverse procedures,” in Folia Cardiologica, vol. 12 (suppl. D), p. 111, 2005. [87] D. W. Marquart, “An algorithm for least-squares estimation of non-linear parameters,” J. Soc. Indust. Appl. Math, vol. 2, pp. 431–441, 1963. [88] S. Mallat and Z. Zhang, “Matching pursuit in time-frequency dictionary,” IEEE Trans. Signal Processing, vol. 41, pp. 3397–3415, 1993. [89] Orthogonal matching pursuits: Recursive function approximation with applications to wavelet decomposition, IEEE Press, 1993. [90] M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation, vol. 13, no. 4, pp. 863–882, 2001. [91] O. Divorra Escoda, L. Granai, and P. Vandergheynst, “On the use of a priori information for sparse signal approximations,” IEEE Trans. Signal Processing, vol. 54, no. 9, pp. 3468–3482, 2006. [92] J. Molinero Hernandez, “Sparse decompositions for ventricular and atrial activity separation,” Master’s thesis, Signal Processing Institute, École Polytechnique Fédérale de Lausanne, Switzerland, August 2005.

126

B IBLIOGRAPHY

[93] J. Molinero Hernandez, “Sparse decompositions for ventricular and atrial activity separation,” Master’s thesis, Signal Processing Institute, École Polytechnique Fédérale de Lausanne, Switzerland, August 2005. [94] S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comp., vol. 20, no. 1, pp. 33–61, 1999. [95] D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inform. Theory, vol. 52, no. 1, pp. 6–18, 2006. [96] B. Van der Pol, “The fundamental principles of frequency modulation,” in Proc. IEE, vol. 93 (III), pp. 153–158, 1946. [97] D. Gabor, “Theory of communication,” in Proc. IEE, vol. 93 (III), pp. 429–457, 1946. [98] B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal - part 1: Fundamentals,” in Proc. IEEE, vol. 80 (4), pp. 520–538, IEEE Press, 1992. [99] L. Cohen, Time-frequency Analysis. Prentice Hall Signal Processing Series, Prentice Hall, 1995. [100] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shin, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A, vol. 454, pp. 903–995, 1998. [101] G. Rilling, P. Flandrin, and P. Gonçalvès, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, 2003. [Online]. Available:http://perso.ens-lyon.fr/patrick.flandrin/emd.html. [102] A. O. Andrade, S. Nasuto, P. Kyberd, C. M. Sweeney-Reed, and F. R. Van Kanij, “EMG signal fitering based on empirical mode decomposition,” Biomedical Signal Processing and Control, vol. 1, pp. 44–55, 2006. [103] A. Prakash, S. Saksena, M. Hill, R. B. Krol, A. N. Munsif, I. Giorgberidze, P. Mathew, and R. Mehra, “Acute effects of dual-site right atrial pacing in patients with spontaneous and inducible atrial flutter and fibrillation,” J Am Coll Cardiol, vol. 29, pp. 1007–1014, 1997. [104] G. Schreier, P. Kastner, and W. Marko, “An automatic ecg processing algorithm to identify patients prone to paroxysmal atrial fibrillation,” [105] W. Zong, R. Mukkamala, and M. R. G, “A methodology for predicting paroxysmal atrial fibrillation based on ecg arrhytmia feature analysis,” in Computers in Cardiology 2001, vol. 28, pp. 125–128, 2001. [106] C. de Boor, A Practical Guide to Splines. Springer-Verlag, 1978.

B IBLIOGRAPHY

127

[107] A. C. C. Yang and H. W. Yin, “Prediction of paroxysmal atrial fibrillation by footprint analysis,” in Computers in Cardiology 2001, vol. 28, pp. 401–404, 2001. [108] T. Thong, J. McNames, M. Aboy, and B. Goldstein, “Prediction of paroxysmal atrial fibrillation by analysis of atrial premature complexes,” IEEE Trans. Biomed. Eng., vol. 51, no. 4, pp. 561–569, 2004. [109] K. R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, “An introduction to kernelbased learning algorithms,” IEEE Trans. Neural Networks, vol. 12(2), pp. 181–201, 2001. [110] C. Cortes and V. Vapnik, “Support vector networks,” Machine Learning, vol. 20, pp. 1–25, 1995. [111] B. E. Boser, I. M. Guyon, and V. N. Vapnik, “A training algorithm for optimal margin classifiers,” in Fifth Annual Workshop on Computational Learning Theory (D. Haussler, ed.), vol. 5, pp. 144–152, ACM Press, 1992. [112] S. R. Gunn, “Support vector machines for classification and regression,” tech. rep., University of Southampton, 1998. [113] K. Fukunaga and D. M. Hummels, “Leave-one-out procedures for nonparametric error estimates,” IEEE Trans. Pattern Anal. and Machine Intell., vol. 11, no. 4, pp. 421–423, 1989. [114] Student, “The probable error of a mean,” Biometrika, vol. 6(1), pp. 1–25, 1908. [115] R. V. Hoog and J. Ledolter, Engineering Statistics. MacMillan, 1987. [116] W. J. Krzanowski, Principles of Multivariate Analysis. Oxford University Press, 1988. [117] A. Bollmann, “First comes diagnosis then comes treatment: an underappreciated paradigm in atrial fibrillation management,” Eur Heart J, vol. 26, pp. 2487–2489, 2005. [118] K. Ropella, J. Baerman, and S. Swiryn, “Effects of procainamide on intra-atrial electrograms during atrial fibrillation: implications for detection algorithms,” Circulation, vol. 77, pp. 1047–1054, 1988. [119] E. N. Prystowsky, G. V. Naccarelli, W. M. Jackman, R. L. Rinkenberger, J. J. Heger, and D. P. Zipes, “Enhanced parasympathetic tone shortens atrial refractoriness in man,” Am J Cardiol, vol. 51, pp. 96–100, 1983. [120] W. Shimizu, Y. Tsuchioka, S. Karakawa, and et al., “Differential effect of pharmacological autonomic blockade on some electrophysiological properties of the human ventricle and atrium,” Br Heart J, vol. 71, pp. 34–7, 1994. [121] M. C. Wijffels, R. Dorland, F. Mast, and M. A. Allessie, “Widening of the excitable gap during pharmacological cardioversion of atrial fibrillation in the goat: effects of cibenzoline, hydroquinidine, flecainide, and d-sotalol,” Circulation, vol. 102, pp. 260–267, 2000.

128

B IBLIOGRAPHY

[122] A. Bollmann, K. Sonne, H. D. Esperer, I. Toepffer, and H. U. Klein, “Circadian variations in atrial fibrillatory frequency in persistent human atrial fibrillation,” Pacing Clin Electrophysiol, vol. 23, pp. 1867–1871, 2000. [123] C. J. Meurling, J. E. Waktare, F. Holmqvist, and et al., “Diurnal variations of the dominant cycle length of chronic atrial fibrillation,” Am J Physiol Heart, vol. 280, pp. H401–406, 2001. [124] A. Fujiki, M. Sakabe, K. Nishida, K. Mizumaki, and H. Inoue, “Role of fibrillation cycle length in spontaneous and drug-induced termination of human atrial fibrillation- spectral analysis of fibrillation waves from surface electrocardiogram,” Circ J, vol. 67, pp. 391–395, 2003. [125] F. Nilsson, M. Stridh, A. Bollmann, and L. Sörnmo, “Predicting spontaneous termination of atrial fibrillation using the surface ecg,” Med Eng Phys, vol. 28, pp. 802–808, 2006. [126] R. Cervigón, C. Sánchez, F. Castells, J. M. Blas, and J. Millet, “Wavelet analysis of electrocardiograms to characterize recurrent atrial fibrillation,” J Franklin Inst, vol. 344, pp. 196– 211, 2007. [127] A. Bollmann, D. Husser, L. Mainardi, F. Lombardi, P. Langley, A. Murray, J. J. Rieta, J. Millet, S. B. Olsson, M. Stridth, and L. Sörnmo, “Analysis of surface electrocardiograms in atrial fibrillation: techniques, research, and clinical applications,” Europace, vol. 8, no. 11, pp. 911–926, 2006. [128] V. D. A. Corino, R. Sassi, L. T. Mainardi, and S. Cerutti, “Signal processing methods for the information enhancement in atrial fibrillation: Spectral analysis and non-linear parameters,” Biomedical Signal Processing and Control, vol. 1(4), pp. 271–281, 2006. [129] J. Ng, A. Kadish, and J. Goldberger, “Effect of electrogram characteristics on the relationship of dominant frequency to atrial activation rate in atrial fibrillation,” Heart Rhythm, vol. 3, no. 11, pp. 1295–1305, 2006. [130] A. Bauer, J. W. Kantelhardt, A. Bunde, P. Barthel, R. Schneider, M. Malik, and G. Schmidt, “Phase-rectified signal averaging detects quasi-periodicities in non-stationary data,” Physica A, vol. 364, pp. 423–434, 2006. [131] P. O. Hoyer, “Nonnegative matrix factorization with sparseness constraints,” J. Machine Learning Research, vol. 5, pp. 1457–1469, 2004. [132] N. R. Draper and H. Smith, Applied Regression Analysis. Wiley-Interscience, 1998. [133] M. Mansour, R. Mandapati, O. Berenfeld, J. Chen, F. H. Samie, and J. Jalife, “Left-toright gradient of atrial frequencies during acute atrial fibrillation in the isolate sheep heart,” Circulation, vol. 103, pp. 2631–2636, 2001. [134] M. Stridh, L. Sörnmo, C. J. Meurling, and S. B. Olsson, “Sequential characterization of atrial tachyarrhtyhmias based on ECG time-frequency analysis,” IEEE Trans. Biomed. Eng., vol. 51, no. 1, pp. 100–114, 2004.

B IBLIOGRAPHY

129

[135] G. W. Botteron and J. M. Smith, “A technique formeasurement of the extent of spatial organization of atrial activation during atrial fibrillation in the intact human heart,” IEEE Trans. Biomed. Eng., vol. 42, pp. 579–586, 1995. [136] H. J. Sih, K. M. Ropella, S. Swiryn, E. P. Gerstenfeld, and A. V. Sahakian, “Observations from intraatrial recordings on the termination of electrically induced atrial fibrillation in humans,” Pacing Clin. Electrophysiol., vol. 17, pp. 1231–1242, 1994. [137] F. Censi, V. Barbaro, P. Bartolini, G. Calcagnini, and G. G. F. C. S. Michelucci, A, “Recurrent patterns of atrial depolarization during atrial fibrillation assessed by recurrent plot quantification,” Ann. Biomed. Eng., vol. 28, pp. 61–70, 2000. [138] L. T. Mainardi, A. Porta, G. Calcagnini, P. Bartolini, A. Michelucci, G. F. Genuini, and S. Cerutti, “Linear and non-linear analysis of atrial signals and local activation period series during atrial fibrillation episodes,” Med. Biol. Eng. Comput., vol. 39, pp. 249–254, 2001. [139] L. T. Mainardi, V. Corino, L. Lombardi, C. Tondo, M. Mantica, F. Lombardi, and S. Cerutti, “Linear and nonlinear coupling between atrial signals,” IEEE Eng. Med. Biol. Mag., vol. 25(6), pp. 63–70, 2006. [140] A. van Oosterom, Z. Ihara, V. Jacquement, and R. Hoekema, “Vectorcardiographic lead systems for the characterization of atrial fibrillation,” J. Electrocardiol., vol. 40(4), 2007. [141] J. E. Olgin, J. M. Kalman, A. P. Fitzpatrick, and M. D. Lesh, “Circus movement in the canine atrium around the tricuspid ring during experimental atrial flutter and during reentry in vitro,” Circulation, vol. 92(7), pp. 1839–1848, 1995. [142] D. Gabor and C. V. Nelson, “Determination of the resultant dipole of the heart from measurements on the body surface,” Journal of Applied Physics, vol. 25, no. 4, pp. 413–416, 1954. [143] G. E. Dower, “An arrhythmia clarified by polarcardiography,” J. Electrocardiol., vol. 3, no. 34, pp. 231–238, 1970. [144] T. Poggio and F. Griosi, Networks for approximation and learning, vol. 78-79. IEEE, 1990. [145] K. V. Mardia, Statistical of Directional Data. New York: Academic Press, 1972. [146] V. Jacquemet, M. Lemay, A. van Oosterom, and L. Kappenberger, “The equivalent dipole used to characterize atrial fibrillation,” in Computers in Cardiology 2006, vol. 33, pp. 149– 152, 2006. [147] F. Censi, V. Barbaro, P. Bartolini, G. Calcagnini, A. Michelucci, and S. Cerutti, “Non-linear coupling of atrial activation processes during atrial fibrillation in humans,” Biol. Cybern., vol. 85, pp. 195–201, 2001. [148] M. Allessie, J. Ausma, and U. Schotten, “Electrical, contractile and structural remodeling during atrial fibrillation,” Cardiovasc Res, vol. 54, pp. 230–246, 2002.

130

B IBLIOGRAPHY

[149] A. Bollmann, D. Husser, M. Stridh, L. Sörnmo, M. Majic, H. Klein, and S. B. Olsson, “Frequency measures obtained from the surface electrocardiogram in atrial fibrillation research and clinical decision-making,” J. Cardiovasc. Electrophysiol., vol. 14, no. 10, pp. S154– S161, 2003. [150] O. Blanc, A computer model of human atrial arrhytmia. PhD thesis, Swiss Federal Institute of Technology, 2001. [151] V. Jacquemet, A biophysical model of atrial fibrillation and electrograms: Formulation, validation and applications. PhD thesis, Swiss Federal Institute of Technology, 2004. [152] L. Dang, An investigation into therapies for atrial arrhytmias using a biophysical model of the human atria. PhD thesis, Swiss Federal Institute of Technology, 2005. [153] Z. Ihara, Design and performance of lead systems for the analysis of atrial signal components in the ECG. PhD thesis, Swiss Federal Institute of Technology, 2006. [154] V. Jacquemet, N. Virag, and L. Kappenberger, “Wavelength and vulnerability to atrial fibrillation: insights from a computer model of human atria,” Europace, vol. 7, pp. S83–S92, 2005.

Curriculum Vitæ Mathieu LEMAY Electrical Engineer, PhD Student Chemin de Chandieu 22 1006 Lausanne / VD SWITZERLAND Phone: +41 21 601 34 77 Mobile: +41 78 760 33 87 [email protected]

Canadian March 30th 1978 Single

Education • 2003 - : PH. D. Thesis in Biomedical Signal Processing Signal Processing Institute (ITS), Swiss Federal Institute of Technology (EPFL), Lausanne / VD, Switzerland Research Areas: My main interest lies in the study of atrial arrythmias, mainly the atrial fibrillation, therapies, and related signal processing techniques. Adviser: Jean-Marc Vesin, PhD, Email: [email protected] • 2003: Bachelor’s degree in Electrical Engineering, Université Laval, Québec, Canada

Academic Experience • 2003 - : Teaching Assistant at EPFL Areas: Signal Processing, Biomedical Signal Processing. Duties: Assistantship for problem or computer lab sessions, preparation of problem sessions, overseeing of semester and master thesis projects, oral presentations for lab visitors and conference and journal paper reviews. • 2000 - 2001: Student Project at Université Laval Areas: Member of the Université Laval delegation of the Machine Challenge of Engineering Games 2001. Duties: Modeling and design of an automated robot. 131

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Post-graduate Education • 2004: - Nonlinear signal modeling and prediction, J.-M. Vesin, PhD, Doctoral School, EPFL. • 2005: - Advanced Digital Image Processing and Analysis, Prof. M. Kunt, Doctoral School, EPFL.

Work Experience • 2000: Trainee at EXFO (Québec) Areas: Optic Network Testing. Duties: Calibration and research on the optical time domain reflectometer’s platform. • 2001: Trainee at EXFO (Québec) Areas: Optic Network Testing. Duties: Complete simulation of the optical time domain reflectometer including optical fiber modelisation, numerical and analogical processing (acquisition, filtering, and detection).

Languages French: English:

Native Advanced

Computer Skills Operating Systems User: Programming languages: Tools:

UNIX, Linux, Windows 95/98/NT/XP. C/C++, VHDL, PHP, HTML. Matlab, Simulink, PSpice, Latex, MS Office

Hobbies • Rock climbing, Wakeboard, Tennis, Skiing.

Publications Journal papers • M. Lemay, J.-M. Vesin, A. van Oosterom, V. Jacquemet and L. Kappenberger. Cancellation of Ventricular Activity in the ECG: Evaluation of novel and existing methods, IEEE Transaction on Biomedical Engineering, 54 (3), 542-546, 2007. • M. Lemay, J.-M. Vesin, V. Jacquemet, A. Forclaz, L. Kappenberger and A. van Oosterom. Spatial dynamics of atrial activity assessed by the vectorcardiogram: from sinus rhythm to atrial fibrillation, Europace, 9, vi109-vi118, 2007. • M. Lemay, Y. Prudat, V. Jacquemet, J.-M. Vesin. Phased-Rectified Signal Averaging Used to Estimate the Dominant Frequencies in ECG Signals During Atrial Fibrillation, IEEE Transaction on Biomedical Engineering, accepted. • Z. Ihara, M. Lemay, A, van Oosterom, L. Kappenberger. Performance of lead systems dedicated to atrial fibrillation: application to clinical data, J Electrocardiol, to be submitted.

Conference papers and abstracts • M. Lemay, J. Vesin, Z. Ihara and L. Kappenberger. Suppression of ventricular activity in the surface electrocardiogram of atrial fibrillation, in Proc ICA 2004, 1995-1102, ICA 2004, Granada, Spain, September 2004. • M. Lemay, Z. Ihara, J. Vesin and L. Kappenberger. Computers in cardiology/physioNet challenge 2004: AF classification based on clinical features, in Proc Comput Cardiol 2004, 31, 669-672, CinC 2004, Chicago, USA, September 2004. • V. Jacquemet, M. Lemay, J.-M. Vesin, L. Kappenberger and A. van Oosterom. Dominant Frequency of Atrial Fibrillation Estimated from the surface ECG, in Proc Heart Rhythm 2005, 2, 302-303, Heart Rhythm 2005, New Orleans, USA, May 2005. • M. Lemay, A. Forclaz, S. Granges, J.-M. Vesin, L. Kappenberger. The Hidden Organization of Atrial Fibrillation, Médecine Cardiovasculaire, 8(S8), SSC 2005, Lausanne, Switzerland, June 2005. 133

134

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• V. Jacquemet, M. Lemay, J.-M. Vesin, A. van Oosterom and L. Kappenberger. Electrocardiograms during atrial fibrillation: a biophysical model, In Proc SSBE, F11, SSBE 2005, Lausanne, Switzerland, September 2005. • M. Lemay, A. Forclaz, J.-M. Vesin, L. Kappenberger. Discrimination of atrial fibrillation using a frequency analysis based on aetiology, European Heart Journal, Abstr. Suppl., ESC 2005, Stockholm, Sweden, September 2005. • V. Jacquemet, M. Lemay, J.-M. Vesin, A. van Oosterom, L. Kappenberger. A Biophysical Model of ECG Signals during Atrial Fibrillation to Evaluate the Performance of QRST Cancellation Algorithms, In Proc Comput Cardiol 2005, 343-346, CinC 2005, Lyon, France, September 2005. • M. Lemay, V. Jacquemet, A. Forclaz, J.-M. Vesin and L. Kappenberger. Spatiotemporal QRST Cancellation Method Using Separate QRS and T-waves templates, In Proc Comput Cardiol 2005, 611-614, CinC 2005, Lyon, France, September 2005. • O. Divorra Escoda, L. Granai, M. Lemay, P. Vandergheynst and J.-M. Vesin. Ventricular and Atrial Activities Estimation through Sparse ECG Signal Decompositions, In Proc ICASSP 2006, BIO-P1.7, ICASSP 2006, Toulouse, France, April 2006. • A. Forclaz, M. Lemay, S. Granges, J.-M. Vesin and L. Kappenberger. The Hidden Organization of Atrial Fibrillation, Cardiostim 2006, Nice, France, June 2006. • V. Jacquemet, M. Lemay, A. van Oosterom and L. Kappenberger. Spatiotemporal Complexity of Atrial Arrhythmias Assessed through the Dynamics of the Equivalent Dipole, In Proc 33rd International Congress on Electrocardiology, 41-42, ICE 2006, Köln, Germany, June-July 2006. • V. Jacquemet, M. Lemay, A. van Oosterom and L. Kappenberger. The Equivalent Dipole Used to Characterize Atrial Fibrillation, In Proc Comput Cardiol 2006, CinC 2006, Valencia, Spain, September 2006. • M. Lemay and J.-M. Vesin. Improved QRST Cancellation based on the Empirical Mode Decomposition, In Proc Comput Cardiol 2005, 561-564, CinC 2006, Valencia, September 2006. • M. Lemay, J.-M. Vesin, A. von Oosterom, V. Jacquemet, A. Forclaz, L. Kappenberger. Evaluation of novel and existing QRST cancelation methods, Médecine Cardiovasculaire, SSC 2007, Geneva, Switzerland, June 2007. • M. Lemay, Y. Prudat, V. Jacquemet, J.-M. Vesin. Phase-rectified Signal Averaging: A Useful tool for the Estimation of the Dominant Frequency in ECG Signals during Atrial Fibrillation, In Proc EMBS 2007, 35-38, EMBS 2007, Lyon, France, August 2007. • M. Lemay, V. Jacquemet, F. Jousset, J.-M. Vesin, A. van Oosterom. The Mean Firing Rate of Atrial Fibrillation as Estimated from the ECG Evaluation Using a Biophysical Model, In Proc Comput Cardiol 2007, CinC 2007, Durham, USA, October 2007.

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