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Chaos Theory and ARTFA: Emerging Tools for Interpreting ECG Signals to Diagnose Cardiac Arrhythmias

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Abstract

Timely detection of cardiac abnormalities from an Electrocardiogram (ECG) signal is very essential. This requires its appropriate and efficient processing. In the literature, most of the researchers focussed on linear techniques that were applied on filtered ECG datasets leaving an ample scope for exploring the use of non-linear techniques in the presence and absence of natural noise-processes. Therefore, there is a need of supplementing the existing research on ECG signal interpretation by using non-linear techniques on noisy ECG data. Non-linear techniques are expected to yield supplementary clues about the non-linearities in the underlying cardiovascular system. One such promising non-linear technique, known as chaos theory (analysis), has been considered here to estimate reliable and robust thresholds for R-peak detection using fractal dimension, Approximate Entropy, Sample Entropy, correlation dimension, and Lyapunov exponent based on time-delay dimension (embedding). Also, time–frequency analysis techniques have shown their effectiveness for analyzing such types of non-linear and non-stationary signals due to simultaneous interpretation of the signal in both time and frequency domain. Among existing TFA techniques such as wavelet transform, short time Fourier transform, Hilbert transform, Auto-regressive Time Frequency Analysis (ARTFA) offers good time–frequency resolution. Therefore, Chaos theory and ARTFA have been considered in this paper. First, raw ECG signal was filtered using Savitzky Golay Digital Filtering (SGDF) because it retains all important signal features after filtering. Second, a novel optimal trajectory detection step was proposed on the basis of phase space reconstruction (attractors) in chaos theory. Third, ARTFA has been used to find the spectral components of the extracted features using chaos theory. Here, ARTFA has been used for finding the autoregressive coefficients in the first step and time–frequency description in the second step. Burg method has been considered for Auto-regressive modeling to fit an ARTFA model for analyzing ECG signal by minimizing (least squares) the forward and backward prediction errors. MIT-BIH arrhythmia database has been considered for validating the present research effort. Some real time signals were also tested to explore direct usage of the proposed technique in practical applications. The obtained results show that the proposed technique enhances sensitivity, positive predictive value and accuracy thereby improving the detection of arrhythmias. Computational cost of the proposed technique is reduced to a great extent by using the chaos theory (analysis) yielding efficient detection performance. All results have been obtained in MATLAB environment R2011a. Improved values viz. 99.96% SE, 99.97% PPV, and 99.93% ACC are obtained.

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Data Availability

Available on physionet website (https://physionet.org).

Code Availability

Software application which is developed by present authors.

Abbreviations

BLW:

Base Line Wandering

ECG:

Electrocardiogram

SGDF:

Savitzky-Golay Digital Filtering

HRV:

Heart Rate Variability

ARTFA:

Auto-regressive Time Frequency Analysis

FD:

Fractal dimension

AE-χ:

Approximate Entropy

SE-χ′:

Sample Entropy

PCs:

Principal Components

PSD:

Power Spectral Density

MATLAB:

Matrix Laboratory

MIT-BIH:

Massachusetts Institute of Technology-Beth Israel Hospital

Arr:

Arrhythmia

Hz:

Hertz

FN:

False Negative

FP:

False Positive

TP:

True Postive

KNN:

K-Nearest Neighbor

DT:

Decision Tree

YW:

Yule-Walker

IFs:

Instantaneous frequencies

CWT:

Continuous wavelet transform

EMD:

Empirical mode decomposition

CD:

Correlation dimension

LE:

Lyapunov exponent

TF:

Time–Frequency

AR:

Auto-Regressive

TFA:

Time–Frequency analysis

BM:

Burg method

AIC:

Akaike’s information criterion

PCA:

Principal Component Analysis

DSE :

Sensitivity

DPPV :

Positive Predictive Value

DACC :

Accuracy

FFT:

Fast Fourier Transform

dB:

Decibel

LBBB:

Left Bundle Branch Block

PVC:

Premature ventricular contraction

AF:

Atrial fibrillation

VF:

Ventricular fibrillation

SSS:

Sick sinus syndrome

STFT:

Short-time Fourier transform

ST:

Synchrosqueezed transform

IMFs:

Intrinsic mode functions

SWT:

Synchrosqueezed wavelet transforms

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  1. KIET Group of Institutions, Delhi-NCR, Ghaziabad, Uttar Pradesh, 201206, India

    Varun Gupta

  2. National Institute of Technology, Kurukshetra, Haryana, 136119, India

    Monika Mittal & Vikas Mittal

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  1. Varun Gupta
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Gupta, V., Mittal, M. & Mittal, V. Chaos Theory and ARTFA: Emerging Tools for Interpreting ECG Signals to Diagnose Cardiac Arrhythmias. Wireless Pers Commun 118, 3615–3646 (2021). https://doi.org/10.1007/s11277-021-08411-5

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