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

Graff, Grzegorz; Graff, Beata; Pilarczyk, Paweł; Jabłoński, Grzegorz; Gąsecki, Dariusz

doi:10.1371/journal.pone.0253851

Cited by 12 publications

(9 citation statements)

References 39 publications

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“…A difficulty in this is that it may be difficult to know what a “correct” subset of a signal is in order for it to be considered a P,Q,S, or T-wave. Additionally, information about optimal 1-cycles identified as P,Q,S, and T-waves could be combined with other existing approaches such as analyzing other persistent homology statistics, wavelet decompositions, and machine learning for automated arrhythmia detection in future work [12] [13] [17] [19] [21].…”

Section: Resultsmentioning

confidence: 99%

“…Thus the analysis of ECGs is important for accurate diagnosis and proper treatment of cardiovascular diseases. Several approaches to automated ECG analysis have been performed, including machine learning [4] [5] [6] [7] [8] [9] [10] [11], wavelet transforms [12] [13] [14] [15] [16], and persistent homology [17] [18] [19] [20] [21] [22] [23]. Due to the high accuracy required of ECG-analysis software and the fact that the bulk of ECG analysis is carried out by healthcare providers, the development of algorithms that identifies P,Q,R,S, and T-waves, measures intervals of interest, and/or detects arrhythmias is an active area of research.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, from this perspective, there are two distinct types of topological features associated with ECG data: 0-dimensional homology features represent equivalence classes of connected components, while 1-dimensional homology features represent equivalence classes of non-contractible loops. The 0-dimensional homology features are useful in analyzing clustering phenomena and have recently shown utility as a metric of heart rate variability when applied to ECG signals [21] [22].…”

Section: Introductionmentioning

confidence: 99%

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Electrocardiogram feature extraction and interval measurements using optimal representative cycles from persistent homology

Dlugas

2022

Preprint

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Cardiovascular diseases are among the leading causes of death, and their early detection and treatment is important for lowering their prevalence and mortality rate. Electrocardiograms (ECGs) record electrical activity of the heart to provide information used to diagnose and treat various cardiovascular diseases. Many approaches to computer-aided ECG analysis have been performed, including Fourier analysis, principal component analysis, analyzing morphological changes, and machine learning. Due to the high accuracy required of ECG-analysis software, there is no universally-agreed upon algorithm to identify P,Q,R,S, and T-waves and measure intervals of interest. Topological data analysis uses tools from algebraic topology to quantify hole-like shapes within data, and methods using persistence statistics and fractal dimension with machine learning have been applied to ECG signals in the context of detecting arrhythmias within recent years. To our knowledge, there does not exist a method of identifying P,Q,S, and T-waves and measuring intervals of interest which relies on topological features of the data, and we propose a novel topological method for performing these aspects of ECG analysis. Specifically, we establish criteria to identify cardinality-minimal and area-minimal 1-cycles with certain properties as P,Q,S, and T-waves. This yields a procedure for measuring the PR-interval, QT-interval, ST-segment, QRS-duration, P-wave duration, and T-wave duration in Lead II ECG data. We apply our procedure to 400 sets of simulated Lead II ECG signals and compare with the interval values set by the model. Additionally, the algorithm is used to identify cardinality-minimal and area-minimal 1-cycles as P,Q,S, and T-waves in two sets of 200 randomly sampled Lead II ECG signals of real patients with 11 common rhythms. Analysis of optimal 1-cycles identified as P,Q,S, and T-waves and comparison of interval measurements shows that 1-cycle reconstructions can provide useful information about the ECG signal and could hold utility in characterizing arrhythmias.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electrocardiogram feature extraction and interval measurements using optimal representative cycles from persistent homology

Dlugas

2022

Preprint

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“…Reference ( Ignacio et al, 2019 ) demonstrated how to map ECGs onto high-dimensional point clouds through delayed embedding to extract topological features and finally apply random forests for classification. Study ( Graff et al, 2021 ) examined when persistence diagram was obtained by SLS filtering, and a set of indicators was extracted to distinguish the RR interval of healthy subjects and stroke patients. In addition ( Yan et al, 2019 ) applied TDA to reconstruct a signal point cloud to extract persistent landscape features to classify heart rate variability.…”

Section: Introductionmentioning

confidence: 99%

Dynamic ECG signal quality evaluation based on persistent homology and GoogLeNet method

et al. 2023

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Cardiovascular disease is a serious health problem. Continuous Electrocardiograph (ECG) monitoring plays a vital role in the early detection of cardiovascular disease. As the Internet of Things technology continues to mature, wearable ECG signal monitors have been widely used. However, dynamic ECG signals are extremely susceptible to contamination. Therefore, it is necessary to evaluate the quality of wearable dynamic ECG signals. The topological data analysis method (TDA) with persistent homology, which can effectively capture the topological information of high-dimensional data space, has been widely studied. In this study, a brand-new quality assessment method of wearable dynamic ECG signals was proposed based on the TDA with persistent homology method. The point cloud of an ECG signal was constructed, and then the complex sequence was generated and displayed as a persistent barcode. Finally, GoogLeNet based on the transfer learning model with a 10-fold cross-validation method was used to train the classification model. A total of 12-leads ECGs Dataset and single-lead ECGs Dataset, established based on the 2011 PhysioNet/CinC challenge dataset, were both used to verify the performance of this method. In the study, 773 “acceptable” and 225 “unacceptable” signals were used as 12-leads ECGs Dataset. We relabeled 12,000 ECG signals in the challenge dataset, and treated them as single-lead ECGs Dataset after empty lead detection and balance datasets. Compared with the traditional ECG signal quality assessment method mainly based on waveform characteristics and time-frequency characteristics, the performance of the quality assessment method proposed. In this study, the classification performance of the proposed method are fairly great, mAcc = 98.04%, F1 = 98.40%, Se = 97.15%, Sp = 98.93% for 12-leads ECGs Dataset and mAcc = 98.55%, F1 = 98.62%, Se = 98.37%, Sp = 98.85% for single-lead ECGs Dataset.

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“…Dynamical system analysis is used to model cardiac dynamical system through phase space reconstruction [ 16 , 17 , 18 , 19 , 20 ]. Topological data analysis transforms ECG signals into point clouds by time-delay embedding or Fourier transform and then extracts topological features from point clouds [ 21 , 22 , 23 , 24 , 25 , 26 ]. Above mentioned methods are adaptive with different applied conditions.…”

Section: Introductionmentioning

confidence: 99%

ECG Classification Based on Wasserstein Scalar Curvature

Sun

Luo

et al. 2022

Entropy

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Electrocardiograms (ECG) analysis is one of the most important ways to diagnose heart disease. This paper proposes an efficient ECG classification method based on Wasserstein scalar curvature to comprehend the connection between heart disease and the mathematical characteristics of ECG. The newly proposed method converts an ECG into a point cloud on the family of Gaussian distribution, where the pathological characteristics of ECG will be extracted by the Wasserstein geometric structure of the statistical manifold. Technically, this paper defines the histogram dispersion of Wasserstein scalar curvature, which can accurately describe the divergence between different heart diseases. By combining medical experience with mathematical ideas from geometry and data science, this paper provides a feasible algorithm for the new method, and the theoretical analysis of the algorithm is carried out. Digital experiments on the classical database with large samples show the new algorithm’s accuracy and efficiency when dealing with the classification of heart disease.

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

Cited by 12 publications

References 39 publications

Electrocardiogram feature extraction and interval measurements using optimal representative cycles from persistent homology

Electrocardiogram feature extraction and interval measurements using optimal representative cycles from persistent homology

Dynamic ECG signal quality evaluation based on persistent homology and GoogLeNet method

ECG Classification Based on Wasserstein Scalar Curvature

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