Tensor decomposition of ECG records for persistent atrial fibrillation analysis

Description

Considered as the last great frontier of cardiac electrophysiology, atrial fibrillation (AF) is the most common sustained arrhythmia encountered in clinical practice, responsible for high hospitalization rates and a significant proportion of brain strokes in the Western world. Analyzing AF electrophysiological complexity noninvasively requires the extraction of the atrial activity (AA) signal from the electrocardiogram (ECG). To perform this task, most approaches including classical average beat subtraction need sufficiently long ECG records, thus limiting real-time analysis. Linear algebra techniques based on matrix factorizations can also be used for AA signal estimation by exploiting the spatial diversity of the multilead ECG, but require some constraints to guarantee uniqueness that may lack physiological grounds and hinder results interpretation.This talk will review our recent results on multilinear algebra techniques such as tensor decompositions for noninvasive AA signal extraction in AF ECGs, which guarantee uniqueness under milder constraints on their factors. Specifically, the block term decomposition (BTD) has been shown to be particularly suitable to address this biomedical problem, as atrial and ventricular cardiac activity sources can be modeled by matrices with special structure. The structure of these matrices ensures model uniqueness while their rank is linked to signal complexity. In this framework, we have put forward the Hankel and Löwner BTD as AA extraction tools in AF ECG episodes, with validation in a population of persistent AF patients and several challenging types of ECG segments, including short beat-to-beat intervals and low-amplitude fibrillatory waves. Accurate AA extraction can be achieved from ECG segments as short as a single heartbeat. We have also developed a robust computational algorithm - the so-called alternating group lasso BTD (BTD-AGL) - to simultaneously recover the model structure (number of block terms and multilinear rank of each term) and the model factors. In addition, tensor modeling allows us to derive a novel index to quantify AF complexity nonivasively, useful to characterize stepwise catheter ablation, a first-line therapeutic option for the treatment of persistent forms of the arrhythmia. The index correlates with the expected decrease in AF complexity over ablation steps and is predictive of AF recurrence, which presents clear clinical interest.

Abstract

International audience

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