Persistent homology as a new method of the assessment of heart rate variability.

Grzegorz Graff,Dariusz Gąsecki,Paweł Pilarczyk,Krzysztof Narkiewicz,Grzegorz Jabłoński,Beata Graff

doi:10.1371/journal.pone.0253851

Abstract

Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.

Highlights

Computational Topology [1] is a modern branch of science that combines the century-long experience in Algebraic Topology with the new capabilities of contemporary computers
In the first section we provide precise definition of the persistent homology method and introduce the parameters based on persistence diagram in details
The results for models based on standard hrv parameters are shown in Figs 4 and 5: the area under the receiver operating characteristic (ROC) curve (AUC) was 0.75 ± 0.08 for the frequency-domain parameters, and 0.79 ± 0.11 for the time-domain parameters

Summary

Introduction

Computational Topology [1] is a modern branch of science that combines the century-long experience in Algebraic Topology with the new capabilities of contemporary computers. [2]) is the main concept that allows for multiscale data analysis, and a fundamental mathematical tool of Topological Data Analysis (TDA) This powerful tool encompasses the concept of topological persistence for sublevel sets of real-valued functions, developed already in the 1990s [3,4,5] and considered a fundamental idea that was further generalized into Persistent Homology.

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