Tensor Cardiography: A Novel ECG Analysis of Deviations in Collective Myocardial Action Potential Transitions Based on Point Processes and Cumulative Distribution Functions
Shingo Tsukada , Yu-ki Iwasaki, Yayoi Tetsuo Tsukada
Abstract
To improve clinical diagnoses, assessments of potential cardiac disease risk, and predictions of lethal arrhythmias, the analysis of electrocardiograms (ECGs) requires a more accurate method of weighting waveforms to efficiently detect abnormalities that appear as minute strains in the waveforms. In addition, the inverse problem of estimating the myocardial action potential from the ECG has been a longstanding challenge. To analyze the variance of the ECG waveforms and to estimate collective myocardial action potentials (APs) from the ECG, we designed a model equation incorporating the probability densities of Gaussian functions of time-series point processes in the cardiac cycle and dipoles of the collective APs in the myocardium. The equation, which involves taking the difference between the cumulative distribution functions (CDFs) that represent positive endocardial and negative epicardial potentials, fits both R and T waves.
Introduction
Developed by Willem Einthoven in 1901, the electrocardiogram (ECG) has been widely used in clinical practice to this day as a simple, inexpensive, non-invasive tool for evaluating the heart’s electrical phenomena [1,2]. ECG analysis is conducted in accordance with strict guidelines on voltage, width, potential and interval of the P-QRS-T wave, electrical axis, and ST segment deviation [3,4]. In clinical ECG diagnosis, classifications rely on the amplitude, interval, and morphology of the ECG’s main vertex (PQRST), as represented by the Minnesota code [5]. However, ECG diagnosis is quite difficult even for cardiologists because of the broad range of normal variance.
Methods
On the Relation between ECG and Myocardial Aps
Previous studies have shown that the relationship between ventricular cardiomyocyte APs and ECGs is mainly formed by the asymmetric structure of the ventricular muscle and the non-uniform distribution of myocardial potentials caused by the propagation patterns of APs originating from the ventricular endocardium and reaching the epicardium, the basal to the apex [11] (Fig 1A). APs on the endocardial side of the ventricle (including middle layer, M-cell[12,13]) have a longer duration and give positive potentials to the ECG II leads, while those on the epicardial side have a shorter duration and give negative potentials to the ECG.
Results
RT Separate Method
In the RT separate method, the two CDF difference equations were fitted independently to the QRS interval of the R wave and to the interval from the start to end of the T wave. (Fig 3, blue dotted line).
Specifically, the differences, fRp—fRn and fTp–fTn, were calculated on the QRS interval of the R wave and the T-wave interval (from the start to the peak and end point of the T wave) by using the least squares method. The anodic CDF fRp and inverse CDF fTp obtained from the fitting are represented by the orange lines in Fig 3, and the cathodic CDF fRn and inverse CDF fTn obtained from the fitting are represented by the green lines. The results of the approximation equation are shown by the red line. Smooth waveforms without noise signals were obtained from the original waveforms.
Discussion
The van der Pol oscillator and Nagumo models serve as mathematical formulations of the electrocardiogram (ECG), and they have been used in the development of ECG wave generators [28,29,30]. The application of Fourier and wavelet transforms to ECG frequency analysis reveals the spectral characteristics of ECG signals. Notably, recent advances have involved using machine learning for generation and classification of ECG [8,31]. However, mathematical models specifically designed to analyze myocardial population action potentials, their duration (APD), and cardiac electromagnetic field (EMF) dipoles have not been developed.
Citation: Tsukada S, Iwasaki Y-k, Tsukada YT (2024) Tensor cardiography: A novel ECG analysis of deviations in collective myocardial action potential transitions based on point processes and cumulative distribution functions. PLOS Digit Health 3(8): e0000273. https://doi.org/10.1371/journal.pdig.0000273
Editor: Ryan S. McGinnis, Wake Forest University School of Medicine, UNITED STATES OF AMERICA
Received: May 11, 2023; Accepted: June 17, 2024; Published: August 8, 2024
Copyright: © 2024 Tsukada et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The ECG, TCG data from the case reports (case 1, case 2), and the sample code for TCG analysis, written in Python and capable of processing specific ECG data in Physionet, is available at Zenodo. DOI 10.5281/zenodo.10437619 https://zenodo.org/records/10437619.
Funding: This study was supported by the KAKENHI grant from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Japan (https://www.mext.go.jp/) for all authors (ST, YI, YT) (22K08217). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: ST is an employee of NTT corporation. The patent for this method is pending in Japan (ST is the inventor of the patent).
