Wavelet entropy as a measure of ventricular beat suppression from the electrocardiogram in atrial fibrillation

A novel method of quantifying the effectiveness of the suppression of ventricular activity from electrocardiograms (ECGs) in atrial fibrillation is proposed. The temporal distribution of the energy of wavelet coefficients is quantified by wavelet entropy at each ventricular beat. More effective ventricular activity suppression yields increased entropies at scales dominated by the ventricular and atrial components of the ECG. Two studies are undertaken to demonstrate the efficacy of the method: first, using synthesised ECGs with controlled levels of residual ventricular activity, and second, using patient recordings with ventricular activity suppressed by an average beat template subtraction algorithm. In both cases wavelet entropy is shown to be a good measure of the effectiveness of ventricular beat suppression

The atrial T wave: The elusive electrocardiographic wave exposed by a case of shifting atrial pacemaker

The atrial T wave (Ta wave) is the body surface manifestation of atrial repolarisation and, unlike the P wave (atrial depolarisation), is little recognised. We report the case of a patient with shifting pacemaker which clearly demonstrates the effect of the Ta wave on ST segment and T wave. A simple conceptual model is used to explain the observed phenomenon. The case serves as a reminder of this often forgotten ECG wave and its potential effects on other ECG features

The U wave in atrial fibrillation

The U wave in ECGs of patients is difficult to observe because it is hidden under the atrial fibrillatory wave. Measurement and characteristics of the U wave in atrial fibrillation have not previously been described. Beat averaging was used to reveal the U waves in 12-lead ECGs of 8 patients with atrial fibrillation taking account of heart rate dependency of U wave characteristics. U wave polarity and amplitude in 12-lead ECG and the amplitude ratio of U wave to atrial fibrillatory wave in lead VI were measured. U waves were measureable in all patients. U waves were predominantly positive in leads 1. 11. aVF. V2. V3, V4, V5 and V6, negative in leads aVR. Amplitudes were largest in the precordial leads measuring up to 55 fJ V. In lead VI the U wave amplitude was on average 0.17 (range 0.1 to 0.4) times the amplitude of the atrial fibrillatory wave. U waves can be measured by ventricular beat averaging in AF patients. U waves were normal in this small group of patients

Numerical modelling of the deformation of elastic material by the TLM method

The transmission line matrix (TLM) method is a numerical tool for the solution of wave and diffusion type equations. The application of TLM to physical phenomena such as heat flow and electromagnetic wave propagation is well established. A previous attempt to apply TLM models to the area of elastic wave propagation and elastic deformation had limited success. The work of this thesis extends the application base of TLM to the area of elastic deformation modelling and validates the model for several two-dimensional situations. In doing this it has been necessary to develop new nodal structures which facilitate the scaling of differential coefficients and incorporation of cross derivatives. Nodal structures which allow the modelling of two and three-dimensional, and anisotropic, elastic deformation are described.The technique is demonstrated by applying the elastic deformation model to several elastic problems. These include two-dimensional isotropic models and models of anisotropic elastic deformation. Provision is also made for the application of various boundary conditions which include displacement, force and frictional boundaries

Abnormal heart sounds detected from short duration unsegmented phonocardiograms by wavelet entropy

© 2016 CCAL. Segmentation of the characteristic heart sounds is thought to be an essential requirement for the automatic classification of phonocardiograms. The aim of this work was to test the feasibility of classification using short duration, unsegmented recordings. Recordings from the 2016 PhysioNet/Computing in Cardiology Challenge were analysed. Wavelet entropy of unsegmented 5 s duration recordings was calculated and the optimum wavelet scale and wavelet entropy threshold determined from the training set. The algorithm was validated on the test set. At a wavelet scale of 1.7 wavelet entropy was significantly reduced in abnormal recordings (median (IQR), 6.3 (1.8) vs 8.0 (1.8)

Heart sound classification from unsegmented phonocardiograms

Objective Most algorithms for automated analysis of phonocardiograms (PCG) require segmentation of the signal into the characteristic heart sounds. The aim was to assess the feasibility for accurate classification of heart sounds on short, unsegmented recordings. Approach PCG segments of 5 second duration from the PhysioNet/Computing in Cardiology Challenge database were analysed. Initially the 5 second segment at the start of each recording (seg 1) was analysed. Segments were zero-mean but otherwise had no pre-processing or segmentation. Normalised spectral amplitude was determined by fast Fourier transform and wavelet entropy by wavelet analysis. For each of these a simple single feature threshold based classifier was implemented and the frequency/scale and thresholds for optimum classification accuracy determined. The analysis was then repeated using relatively noise free 5 s segments (seg 2) of each recording. Spectral amplitude and wavelet entropy features were then combined in a classification tree. Main results There were significant differences between normal and abnormal recordings for both wavelet entropy and spectral amplitude across scales and frequency. In the wavelet domain the differences between groups were greatest at highest frequencies (wavelet scale 1, pseudo frequency 1 kHz) whereas in the frequency domain the differences were greatest at low frequencies (12 Hz). Abnormal recordings had significantly reduced high frequency wavelet entropy: (Median (interquartile range)) 6.63 (2.42) vs 8.36 (1.91), p < 0.0001, suggesting the presence of discrete high frequency components in these recordings. Abnormal recordings exhibited significantly greater low frequency (12 Hz) spectral amplitude: 0.24 (0.22) vs 0.09 (0.15), p< 0.0001. Classification accuracy (mean of specificity and sensitivity) was greatest for wavelet entropy: 76% (specificity 54%, sensitivity 98%) vs 70% (specificity 65%, sensitivity 75%) and was further improved by selecting the lowest noise segment (seg 2): 80% (specificity 65%, sensitivity 94%) vs 71% (specificity 63%, sensitivity 79%). Classification tree with combined features gave accuracy 79% (specificity 80%, sensitivity 77%). Significance The feasibility of accurate classification without segmentation of the characteristic heart sounds has been demonstrated. Classification accuracy is comparable to other algorithms but achieved without the complexity of segmentation

Extracting fetal heart beats from maternal abdominal recordings: Selection of the optimal principal components

This study presents a systematic comparison of different approaches to the automated selection of the principal components (PC) which optimise the detection of maternal and fetal heart beats from non-invasive maternal abdominal recordings. A public database of 75 4-channel non-invasive maternal abdominal recordings was used for training the algorithm. Four methods were developed and assessed to determine the optimal PC: (1) power spectral distribution, (2) root mean square, (3) sample entropy, and (4) QRS template. The sensitivity of the performance of the algorithm to large-amplitude noise removal (by wavelet de-noising) and maternal beat cancellation methods were also assessed. The accuracy of maternal and fetal beat detection was assessed against reference annotations and quantified using the detection accuracy score F1 [2*PPV*Se / (PPV + Se)], sensitivity (Se), and positive predictive value (PPV). The best performing implementation was assessed on a test dataset of 100 recordings and the agreement between the computed and the reference fetal heart rate (fHR) and fetal RR (fRR) time series quantified. The best performance for detecting maternal beats (F1 99.3%, Se 99.0%, PPV 99.7%) was obtained when using the QRS template method to select the optimal maternal PC and applying wavelet de-noising. The best performance for detecting fetal beats (F1 89.8%, Se 89.3%, PPV 90.5%) was obtained when the optimal fetal PC was selected using the sample entropy method and utilising a fixed-length time window for the cancellation of the maternal beats. The performance on the test dataset was 142.7 beats2/min2 for fHR and 19.9 ms for fRR, ranking respectively 14 and 17 (out of 29) when compared to the other algorithms presented at the Physionet Challenge 2013

Recurring patterns of atrial fibrillation in surface ECG predict restoration of sinus rhythm by catheter ablation

Background Non-invasive tools to help identify patients likely to benefit from catheter ablation (CA) of atrial fibrillation (AF) would facilitate personalised treatment planning. Aim To investigate atrial waveform organisation through recurrence plot indices (RPI) and their ability to predict CA outcome. Methods One minute 12-lead ECG was recorded before CA from 62 patients with AF (32 paroxysmal AF; 45 men; age 57±10 years). Organisation of atrial waveforms from i) TQ intervals in V1 and ii) QRST suppressed continuous AF waveforms (CAFW), were quantified using RPI: percentage recurrence (PR), percentage determinism (PD), entropy of recurrence (ER). Ability to predict acute (terminating vs. non-terminating AF), 3-month and 6-month postoperative outcome (AF vs. AF free) were assessed. Results RPI either by TQ or CAFW analysis did not change significantly with acute outcome. Patients arrhythmia-free at 6-month follow-up had higher organisation in TQ intervals by PD (