Extracting the atrial signal from an electrocardiogram (ECG) Semester 2 MPhys Project Sarah Medley Jerry Orme

The ECG signal atria Voltage (mV) ventricles Time (s) ECG = a recording of the electrical activity of the heart 10 electrodes = 12 leads Images from Wikimedia Commons and University of Maryland Medical Centre

Atrial Fibrillation (AF) Normal Sinus Rhythm Atrial Fibrillation Difficult to accurately diagnose AF GPs: 79.8% of cases correctly diagnosed [Mant et. al] Interpretative software: 83.3% Long-term goal: accurate automated diagnostic systems Mant et. al, Accuracy of diagnosing AF on ECG by primary care practitioners and interpretative diagnostic software, BMJ (2007). Images from Wikimedia Commons and New Zealand Guidelines Group

Extraction of the atrial signal Aims & Implementation Extraction of the atrial signal Develop quantitative methods to distinguish between ECGs of NSR/AF patients Implementation: PCA, Fourier analysis and wavelet transform methods – all in C++ 5s of real ECG data from 6 patients (PhysioNET) Assume the body is a homogeneous isotropic sphere and the heart is a dipole Image from A. Reisner et. al, The Physiological Basis of the Electrocardiogram

Principal Component Analysis Express a dataset in terms of a set of uncorrelated and orthogonal variables: principal components 5 seconds of a 12-lead ECG = 5001 x 12 matrix Covariance matrix of mean-centred data Eigenvectors of covariance matrix ordered by eigenvalue = principal components Express original data in terms of PCs Select atrial activity components Reconstruct original leads using atrial components

PCA results – healthy patients

PCA results – patients with AF

PCA – Grouping by Eigenvalue Previous research shows inconsistent methods of selecting atrial components Developed the eigenvalue grouping method Advantages: Based on a clear mathematical rule Suits the fact that PCs differ between patients Our results: group containing PC3 provides the best atrial reconstruction Disadvantages: Can result in loss of distinction between atrial and ventricular activity Inconsistent for comparison of “subtracted” and reconstructed leads

Fourier Transform Discrete-Time Fourier Transform (DTFT) Periodicity: assumption about the behaviour of the signal outside the known range Signal truncation Zero-padding Limiting sampling frequency: Aliasing  upper limit: Nyquist frequency = 2×(highest frequency in signal) In practice, (highest frequency in sample) = 1/(sampling rate) = 1 kHz 24 spectra to analyse per patient... http://www.control.isy.liu.se/student/tsrt78/zeropadding.pdf https://en.wikipedia.org/wiki/File:AliasingSines.svg

Spectral Spread  

Noise Sources of noise: respiratory, muscular, powerline hum, shot noise Choice of threshold frequencies? Baseline wander poses a problem Average respiratory rate is 12-18 breaths per minute Bradypnoea at < 12 or 13 breaths per minute → five seconds of data may not show a full breathing cycle   http://www.cs.umd.edu/~djacobs/CMSC828seg/SmoothingConvolution.pdf

Heart Rate Variability Index Goal: single, quantitative index to distinguish NSR from AF Combination of WT and PCA [Sree et. al] DWT used to preprocess leads PCA performed on convoluted leads Largest three eigenvalues Sree’s results (using a Morlet wavelet): NSR: 32.429 ± 15.9 AF: 17.340 ± 12.9 Sree et al.; Cardiac arrhythmia diagnosis by HRV signal processing using PCA; Mechanics in Medicine and Biology (2012)

Heart Rate Variability Index Our results using Lorentzian wavelet Haar wavelet Scope for optimisation commons.wikimedia.org mathworld.wolfram.com

Vectorcardiography Erratum: mV Vectorcardiographic plots for Patient 113. The amplitude of the cardiac vector is visualised in the V3-V4 plane (left) and in the aVF-V1 plane (right). All units are in millivolts.

Summary PCA: Developed eigenvalue grouping method Identified that the group containing PC3 provides optimal representation of atrial activity Fourier analysis and wavelet transform: Defined a measure of spectral spread and demonstrated expected increase across PCs 1-12 Showed how wavelet transform can be used to suppress/magnify ECG features

Summary Combined wavelet transform & PCA: Tested the HRVI proposed by Sree et. al Demonstrated that the Lorentzian wavelet marginally outperformed the Haar wavelet, due to a smaller standard deviation on the HRVI Potential further developments: Use of a reference atrial signal for comparison Spectral spread & HRVI – potential indices to quantify AF Lead normalisation using vectorcardiography

Thank you for listening Any questions?