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Tensor Modeling of the ECG for Persistent Atrial Fibrillation Analysis

Abstract : Atrial Fibrillation (AF) is the most common sustained arrhythmia diagnosed in clinical practice, responsible for high hospitalization and death rates. Furthermore, the electrophysiological mechanisms underlying this cardiac rhythm disorder are not completely understood. A non-invasive and efficient strategy to study this challenging cardiac condition is analyzing the atrial activity (AA) from the Electrocardiogram (ECG). However, the AA during AF is masked by the ventricular activity (VA) in each heartbeat and often presents a very low amplitude, hampering its analysis. Throughout the years, signal processing methods have helped cardiologists in the study of AF by extracting the AA from the ECG. In particular, matrix-based blind source separation (BSS) methods have proven to be ecient AA extraction tools. However, some constraints need to be imposed to guarantee the uniqueness of such matrix factorization techniques that, although mathematically coherent, may lack physiological grounds and hinder results interpretation. In contrast, tensor decompositions can ensure uniqueness under more relaxed constraints. Particularly, the block term decomposition (BTD), recently proposed as a BSS technique, can be unique under some constraints over its matrix factors, easily satisfying in the mathematical and physiological sense. In addition, cardiac sources can be well modeled by specific mathematical functions that, when mapped into the structured matrix factors of BTD, present a link with their rank. Another advantage over matrix-based methods is that the tensor approach is able to extract AA from very short ECG recordings. The present doctoral thesis has its first focus on the investigation of the Hankel-BTD as an AA extraction tool in persistent AF episodes, with validation based on statistical experiments over a population of AF patients and several types of ECG segments. ECG recordings with a short interval between heartbeats and an AA with significantly low amplitude are challenging cases common in this stage of the arrhythmia. Such cases motivate the use of other tensor-based approach to estimate an AA signal with better quality, the Löwner-BTD. Such an approach is presented along a novel optimal strategy to ensure the Löwner structure that is implemented as a variant of a recently proposed robust algorithm for BTD computation. Another contribution is the model of persistent AF ECGs by a coupled Hankel-BTD, which shows some advantages in terms of improved AA extraction and reduced computational cost over its non-coupled counterpart. Further contributions focus on challenges that arise from the problem of AA extraction from AF ECGs, such as detecting the AA source among the other separated sources in real experiments, where the ground truth it's unknown. For this task, several approaches that use machine learning algorithms and neural networks are assessed, providing satisfactory accuracy. Another challenge that is dealt with is the difficulty in measuring the quality of AA estimation. Here, new indices for AA estimation quality from ECG recordings during AF are proposed and assessed. In summary, this PhD thesis provides the first thorough investigation of the application of tensor-based signal processing techniques to the analysis of atrial fibrillation, showing the interest of the tensor approach and its potential in the management and understanding of this challenging cardiac condition.
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Submitted on : Tuesday, March 23, 2021 - 2:57:08 PM
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Pedro Marinho Ramos de Oliveira. Tensor Modeling of the ECG for Persistent Atrial Fibrillation Analysis. Signal and Image processing. Université Côte d'Azur, 2020. English. ⟨NNT : 2020COAZ4057⟩. ⟨tel-03177971⟩

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