Convolutive blind source separation algorithms applied to the electrocardiogram of atrial fibrillation: study of performance

The analysis of the surface electrocardiogram (ECG) is the most extended noninvasive technique in medical diagnosis of atrial fibrillation (AF). In order to use the ECG as a tool for the analysis of AF, we need to separate the atrial activity (AA) from other cardioelectric signals. In this matter, statistical signal processing techniques, like blind source separation (BSS), are able to perform a multilead statistical analysis with the aim to obtain the AA. Linear BSS techniques can be divided in two groups depending on the mixing model: algorithms where instantaneous mixing of sources is assumed, and convolutive BSS (CBSS) algorithms. In this work, a comparison of performance between one relevant CBSS algorithm, namely Infomax, and one of the most effective independent component analysis (ICA) algorithms, namely FastICA, is developed. To carry out the study, pseudoreal AF ECGs have been synthesized by adding fibrillation activity to normal sinus rhythm. The algorithm performances are expressed by two indexes: the signal to interference ratio (SIRAA) and the cross-correlation (RAA) between the original and the estimated AA. Results empirically prove that the instantaneous mixing model is the one that obtains the best results in the AA extraction, given that the mean SIRAA obtained by the FastICA algorithm (37.6 +/- 17.0 dB) is higher than the main SIRAA obtained by Infomax (28.5 +/- 14.2 dB). Also the RAA obtained by FastICA (0.92 +/- 0.13) is higher than the one obtained by Infomax (0.78 +/- 0.16).     

Atrial activity extraction for atrial fibrillation analysis using blind source separation

This contribution addresses the extraction of atrial activity (AA) from real electrocardiogram (ECG) recordings of atrial fibrillation (AF). We show the appropriateness of independent component analysis (ICA) to tackle this biomedical challenge when regarded as a blind source separation (BSS) problem. ICA is a statistical tool able to reconstruct the unobservable independent sources of bioelectric activity which generate, through instantaneous linear mixing, a measurable set of signals. The three key hypothesis that make ICA applicable in the present scenario are discussed and validated: 1) AA and ventricular activity (VA) are generated by sources of independent bioelectric activity; 2) AA and VA present non-Gaussian distributions; and 3) the generation of the surface ECG potentials from the cardioelectric sources can be regarded as a narrow-band linear propagation process. To empirically endorse these claims, an ICA algorithm is applied to recordings from seven patients with persistent AF. We demonstrate that the AA source can be identified using a kurtosis-based reordering of the separated signals followed by spectral analysis of the sub-Gaussian sources. In contrast to traditional methods, the proposed BSS-based approach is able to obtain a unified AA signal by exploiting the atrial information present in every ECG lead, which results in an increased robustness with respect to electrode selection and placement.     

Spatiotemporal QRST cancellation techniques for analysis of atrial fibrillation

A new method for QRST cancellation is presented for the analysis of atrial fibrillation in the surface electrocardiogram (ECG). The method is based on a spatiotemporal signal model which accounts for dynamic changes in QRS morphology caused, e.g., by variations in the electrical axis of the heart. Using simulated atrial fibrillation signals added to normal ECGs, the results show that the spatiotemporal method performs considerably better than does straightforward average beat subtraction (ABS). In comparison to the ABS method, the average QRST-related error was reduced to 58 percent. The results obtained from ECGs with atrial fibrillation agreed very well with those from simulated fibrillation signals.     

Noninvasive ECG as a tool for predicting termination of paroxysmal atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia and entails an increased risk of thromboembolic events. Prediction of the termination of an AF episode, based on noninvasive techniques, can benefit patients, doctors and health systems. The method described in this paper is based on two-lead surface electrocardiograms (ECGs): 1-min ECG recordings of AF episodes including N-type (not terminating within an hour after the end of the record), S-type (terminating 1 min after the end of the record) and T-type (terminating immediately after the end of the record). These records are organised into three learning sets (N, S and T) and two test sets (A and B). Starting from these ECGs, the atrial and ventricular activities were separated using beat classification and class averaged beat subtraction, followed by the evaluation of seven parameters representing atrial or ventricular activity. Stepwise discriminant analysis selected the set including dominant atrial frequency (DAF, index of atrial activity) and average HR (HRmean, index of ventricular activity) as optimal for discrimination between N/T-type episodes. The linear classifier, estimated on the 20 cases of the N and T learning sets, provided a performance of 90% on the 30 cases of a test set for the N/T-type discrimination. The same classifier led to correct classification in 89% of the 46 cases for N/S-type discrimination. The method has shown good results and seems to be suitable for clinical application, although a larger dataset would be very useful for improvement and validation of the algorithms and the development of an earlier predictor of paroxysmal AF spontaneous termination time.     

Temporal and spatial phase analyses of the electrocardiogram stratify intra-atrial and intra-ventricular organization

We hypothesized that electrocardiogram (ECG) spatial phase analysis would define a spectrum of intracardiac organization from atrial fibrillation (AF), nonisthmus-dependent and isthmus-dependent atrial flutter (AFL) to supraventricular tachycardias (SVT), and similarly for ventricular arrhythmias. We analyzed arrhythmia ECGs of 33 patients with isthmus (n = 9) and nonisthmus (n = 5) dependent AFL and SVT: atrial (n = 3), atrioventricular nodal (n = 3), and orthodromic reciprocating (n = 3) tachycardias, as well as AF (n = 5), ventricular tachycardia (monomorphic, VT-MM; n = 7), and fibrillation (VF; n = 3). ECG spatial phase was considered coherent when the correlation coefficient of an atrial (or ventricular) template to its ECG over time maintained a constant relationship in XY, XZ, and YZ planes. Regularity was quantified spectrally from ECG and correlation series. Spatial coherence occurred in 9/9 cases of isthmus--but only 1/5 of cases of nonisthmus-dependent AFL (p < 0.01; chi2). All showed one dominant spectral peak (temporal coherence). In AF, spatial phase was inconsistent in all planes and spectra were broad band. Temporal and spatial coherence occurred in other SVT. VT-MM maintained spatial phase and a single spectral peak, while VF displayed neither. Our conclusions are that temporal and spatial phase analysis from the ECG stratifies intra-atrial and intra-ventricular organization and reveals subtle variability lost on visual inspection.     

Comparison of atrial signal extraction algorithms in 12-lead ECGs with atrial fibrillation

Analysis of atrial rhythm is important in the treatment and management of patients with atrial fibrillation. Several algorithms exist for extracting the atrial signal from the electrocardiogram (ECG) in atrial fibrillation, but there are few reports on how well these techniques are able to recover the atrial signal. We assessed and compared three algorithms for extracting the atrial signal from the 12-lead ECG. The 12-lead ECGs of 30 patients in atrial fibrillation were analyzed. Atrial activity was extracted by three algorithms, Spatiotemporal QRST cancellation (STC), principal component analysis (PCA), and independent component analysis (ICA). The amplitude and frequency characteristics of the extracted atrial signals were compared between algorithms and against reference data. Mean (standard deviation) amplitude of QRST segments of V1 was 0.99 (0.54) mV, compared to 0.18 (0.11) mV (STC), 0.19 (0.13) mV (PCA), and 0.29 (0.22) mV (ICA). Hence, for all algorithms there were significant reductions in the amplitude of the ventricular activity compared with that in V1. Reference atrial signal amplitude in V1 was 0.18 (0.11) mV, compared to 0.17 (0.10) mV (STC), 0.12 (0.09) mV (PCA), and 0.18 (0.13) mV (ICA) in the extracted atrial signals. PCA tended to attenuate the atrial signal in these segments. There were no significant differences for any of the algorithms when comparing the amplitude of the reference atrial signal with that of the extracted atrial signals in segments in which ventricular activity had been removed. There were no significant differences between algorithms in the frequency characteristics of the extracted atrial signals. There were discrepancies in amplitude and frequency characteristics of the atrial signal in only a few cases resulting from notable residual ventricular activity for PCA and ICA algorithms. In conclusion, the extracted atrial signals from these algorithms exhibit very similar amplitude and frequency characteristics. Users of these algorithms should be observant of residual ventricular activities which can affect the analysis of the fibrillatory waveform in clinical practice.     

A high-temporal resolution algorithm for quantifying organization during atrial fibrillation

Atrial fibrillation (AF) has been described as a "random" or "chaotic" rhythm. Evidence suggests that AF may have transient episodes of temporal and spatial organization. We introduce a new algorithm that quantifies AF organization by the mean-squared error (MSE) in the linear prediction between two cardiac electrograms. This algorithm calculates organization at a finer temporal resolution. (approximately 300 ms) than previously published algorithms. Using canine atrial epicardial mapping data, we verified that the MSE algorithm showed nonfibrillatory rhythms to be significantly more organized than fibrillatory rhythms (p < .00001). Further, we compared the sensitivity of MSE to that of two previously published algorithms by analyzing AF with simulated noise and AF manipulated with vagal stimulation or by adenosine administration to alter the character of the AF. MSE performed favorably in the presence of noise. While all three algorithms distinguished between low and high vagal AF, MSE was the most sensitive in its discrimination. Only MSE could distinguish baseline AF from AF with adenosine. We conclude that our algorithm can distinguish different levels of organization during AF with a greater temporal resolution and sensitivity than previously described algorithms. This algorithm could lead to new ways of analyzing and understanding AF as well as improved techniques in AF therapy.     

Frequency tracking of atrial fibrillation using hidden Markov models.

A hidden Markov model (HMM) is employed to improve noise robustness when tracking the dominant frequency of atrial fibrillation (AF) in the electrocardiogram (ECG). Following QRST cancellation, a sequence of observed frequency states is obtained from the residual ECG, using the short-time Fourier transform. Based on the observed state sequence, the Viterbi algorithm retrieves the optimal state sequence by exploiting the state transition matrix, incorporating knowledge on AF characteristics, and the observation matrix, incorporating knowledge of the frequency estimation method and signal-to-noise ratio (SNR). The tracking method is evaluated with simulated AF signals to which noise, obtained from ECG recordings, has been added at different SNRs. The results show that the use of HMM improves performance considerably by reducing the rms error associated with frequency tracking: at 4-dB SNR, the rms error drops from 0.2 to 0.04 Hz.     

Extraction and analysis of T waves in electrocardiograms during atrial flutter

Analysis of T waves in the ECG is an essential clinical tool for diagnosis, monitoring, and follow-up of patients with heart dysfunction. During atrial flutter, this analysis has been so far limited by the perturbation of flutter waves superimposed over the T wave. This paper presents a method based on missing data interpolation for eliminating flutter waves from the ECG during atrial flutter. To cope with the correlation between atrial and ventricular electrical activations, the CLEAN deconvolution algorithm was applied to reconstruct the spectrum of the atrial component of the ECG from signal segments corresponding to TQ intervals. The locations of these TQ intervals, where the atrial contribution is presumably dominant, were identified iteratively. The algorithm yields the extracted atrial and ventricular contributions to the ECG. Standard T-wave morphology parameters (T-wave amplitude, T peak-T end duration, QT interval) were measured. This technique was validated using synthetic signals, compared to average beat subtraction in a patient with a pacemaker, and tested on pseudo-orthogonal ECGs from patients in atrial flutter. Results demonstrated improvements in accuracy and robustness of T-wave analysis as compared to current clinical practice.     

Temporal BYY learning for state space approach, hidden Markovmodel, and blind source separation

The temporal Bayesian Yang-Yang (TBYY) learning has been presented for signal modeling in a general state space approach, which provides not only a unified point of view on the Kalman filter, hidden Markov model (HMM), independent component analysis (ICA), and blind source separation (BSS) with extensions, but also further advances on these studies, including a higher order HMM, independent HMM for binary BSS, temporal ICA (TICA), and temporal factor analysis for real BSS without and with noise. Adaptive algorithms are developed for implementation and criteria are provided for selecting an appropriate number of states or sources. Moreover, theorems are given on the conditions for source separation by linear and nonlinear TICA. Particularly, it has been shown that not only non-Gaussian but also Gaussian sources can also be separated by TICA via exploring temporal dependence. Experiments are also demonstrated     

Detection of Fetal Heart Rate Through 3-D Phase Space Analysis From Multivariate Abdominal Recordings

A novel three-stage methodology for the detection of fetal heart rate (fHR) from multivariate abdominal ECG recordings is introduced. In the first stage, the maternal R-peaks and fiducial points (maternal QRS onset and offset) are detected, using band-pass filtering and phase space analysis. The maternal fiducial points are used to eliminate the maternal QRS complexes from the abdominal ECG recordings. In the second stage, two denoising procedures are applied to enhance the fetal QRS complexes. The phase space characteristics are employed to identify fetal heart beats not overlapping with the maternal QRSs, which are eliminated in the first stage. The extraction of the fHR is accomplished in the third stage, using a histogram-based technique in order to identify the location of the fetal heart beats that overlap with the maternal QRSs. The methodology is evaluated on simulated multichannel ECG signals, generated by a recently proposed model with various SNRs, and on real signals, recorded from pregnant women in various weeks during gestation. In both cases, the obtained results indicate high performance; in the simulated ECGs, the accuracy ranges from 72.78% to 98.61%, depending on the employed SNR, while in the real recordings, the average accuracy is 95.45%. The proposed methodology is advantageous since it copes with the existence of noise from various sources while it is applicable in multichannel abdominal recordings.      

非线性盲源分离的原理及算法综述

本文主要阐述了非线性盲源分离(BSS)/独立成分分析(ICA)模型的基本数学原理、分离算法、算法性能及其应用。首先对线性和非线性BSS/ICA的数学模型作了介绍,重点介绍了非线性BSS/ICA解的不确定性,然后在此基础上对近十年来出现的各种非线性BSS/ICA算法进行简单综述,着重分析了一类可解且应用比较广泛的非线性BSS/ICA模型-后非线性BSS/ICA模型及其分离算法。最后对非线性BSS/ICA存在的问题和发展趋势进行了总结。     

Frequency domain algorithm for quantifying atrial fibrillation organization to increase defibrillation efficacy

We hypothesized that frequency domain analysis of an interatrial atrial fibrillation (AF) electrogram would show a correlation of the variance of the signal and the amplitude of harmonic peaks with the periodicity and morphology (organization) of the AF signal and defibrillation efficacy. We sought to develop an algorithm that would provide a high-resolution measurement of the changes in the spatiotemporal organization of AF. AF was initiated with burst atrial pacing in ten dogs. The atrial defibrillation threshold (ADFT50) was determined, and defibrillation was repeated at the ADFT50. Bipolar electrograms from the shocking electrodes were acquired immediately preshock, digitally filtered, and a FFT was performed. The organization index (OI) was calculated as the ratio of the area under the first four harmonic peaks to the total area of the spectrum. For a 4-s window, the mean OI was 0.505 +/- 0.087 for successful shocks, versus 0.352 +/- 0.068 for unsuccessful shocks (p < 0.001). Receiver operator characteristic (ROC) curve analysis was used to determine the optimal sampling window for predicting successful shocks. The area of the ROC curve was 0.8 for a 1-s window, and improved to 0.9 for a 4-s window. We conclude that the spectrum of an AF signal contains information relating to its organization, and can be used in predicting a successful defibrillation.     

A technique for measurement of the extent of spatial organizationof atrial activation during atrial fibrillation in the intact humanheart

Atrial fibrillation (AF) is a common clinical problem, associated with considerable morbidity and motility, for which effective management strategies have yet to be devised. The absence of objective measures to guide selection of antiarrhythmic drug therapy for maintenance of sinus rhythm leaves only clinical endpoints (either beneficial or detrimental) for assessment of drug action, with occasional catastrophic consequences. As part of an attempt to provide an objective framework for the assessment of antiarrhythmic drug action on the electrophysiologic determinants of atrial fibrillation, the authors have developed a measure of the spatial organization of atrial activation processes during atrial fibrillation. By recording activation sequences at multiple equally spaced locations on the endocardial surface of the atrial during atrial fibrillation in humans and determining the degree of correlation between these activation sequences as a function of distance, the authors have been able to construct spatial correlation functions for atrial activation. They have found that atrial activation remains well-correlated, independent of distance during normal sinus rhythm and atrial flutter. During atrial fibrillation, correlation decays monotonically with distance and the space-constant for this decay may be used to describe the relative spatial organization of atrial fibrillation. The authors provide examples of the impact of antiarrhythmic agents on the space-constant and suggest that assessment of the relative spatial organization of atrial activation using this methodology may potentially provide an objective framework to guide therapy in patients with AF     

P-wave morphology assessment by a gaussian functions-based model in atrial fibrillation patients

Aim of this study was to present a P-wave model, based on a linear combination of Gaussian functions, to quantify morphological aspects of P-wave in patients prone to atrial fibrillation (AF). Five-minute ECG recordings were performed in 25 patients with permanent dual chamber pacemakers. Patients were divided into high-risk and low-risk groups, including patients with and without AF episodes in the last 6 mo preceding the study, respectively. ECG signals were acquired using a 32-lead mapping system for high-resolution biopotential measurement (ActiveTwo, Biosemi, The Netherlands, sample frequency 2 kHz, 24-bit resolution). Up to 8 Gaussian models have been computed for each averaged P-wave extracted from every lead. The P-wave morphology was evaluated by extracting seven parameters. Classical time-domain parameters, based on P-wave duration estimation, have been also estimated. We found that the P-wave morphology can be effectively modeled by a linear combination of Gaussian functions. In addition, the combination of time-domain and morphological parameters extracted from the Gaussian function-based model of the P-wave improves the identification of patients having different risks of developing AF.     

Phase-rectified signal averaging used to estimate the dominant frequencies in ECG signals during atrial fibrillation

Phase-rectified signal averaging (PRSA) is a technique recently introduced to enhance quasi-periodic signal components. An important parameter that can be extracted from surface ECG is the dominant frequency (DF) of atrial fibrillation (AF). AF signal components are always highly contaminated by the ventricular complexes, and the cancellation of these components is never perfect. The remaining artifacts tend to induce erroneous DF estimates. In this paper, we report on the use of PRSA in the context of noninvasive AF classification procedures for improving DF estimation. The potential of PRSA is demonstrated by experiments both on synthetic and clinical ECG signals.     

An atrioventricular node model for analysis of the ventricular response during atrial fibrillation

This paper introduces a model of the atrioventricular node function during atrial fibrillation (AF), and describes the related ECG-based estimation method. The proposed model is defined by parameters that characterize the arrival rate of atrial impulses, the probability of an impulse choosing either one of the two atrioventricular nodal pathways, the refractory periods of these pathways, and the prolongation of the refractory periods. These parameters are estimated from the RR intervals using maximum likelihood estimation, except for the shorter refractory period which is estimated from the RR interval Poincaré plot, and the mean arrival rate of atrial impulses by the AF frequency. Simulations indicated that 200-300 RR intervals are generally needed for the estimates to be accurate. The model was evaluated on 30-min ECG segments from 36 AF patients. The results showed that 88% of the segments can be accurately modeled when the estimated probability density function (PDF) and an empirical PDF were at least 80% in agreement. The model parameters were estimated during head-up tilt test to assess differences caused by sympathetic stimulation. Both refractory periods decreased as a result of stimulation, and the likelihood of an impulse choosing the pathway with the shorter refractory period increased.     

Waveform Characterization of Atrial Fibrillation Using Phase Information

A novel method for characterization of f-wave morphology in atrial fibrillation (AF) is presented. The method decomposes atrial activity into fundamental and harmonic components, dividing each component into short blocks for which the amplitudes, frequencies, and phases are estimated. The phase delays between the fundamental and each of the harmonics, here referred to as harmonic phase relationships, are used as features of f-wave morphology. The estimated waves are clustered into typical morphologic patterns. The performance of the method is illustrated by simulated signals, ECG signals recorded from 36 patients with organized AF, and an ECG signal recorded during drug loading with flecainide. The results show that the method can distinguish a wide variety of f-wave morphologies, and that typical morphologies can be established for further analysis of AF.      

A novel method for detection of the transition between atrial fibrillation and sinus rhythm

Automatic detection of atrial fibrillation (AF) for AF diagnosis, especially for AF monitoring, is necessarily desirable for clinical therapy. In this study, we proposed a novel method for detection of the transition between AF and sinus rhythm based on RR intervals. First, we obtained the delta RR interval distribution difference curve from the density histogram of delta RR intervals, and then detected its peaks, which represented the AF events. Once an AF event was detected, four successive steps were used to classify its type, and thus, determine the boundary of AF: 1) histogram analysis; 2) standard deviation analysis; 3) numbering aberrant rhythms recognition; and 4) Kolmogorov-Smirnov (K-S) test. A dataset of 24-h Holter ECG recordings (n = 433) and two MIT-BIH databases (MIT-BIH AF database and MIT-BIH normal sinus rhythm (NSR) database) were used for development and evaluation. Using the receiver operating characteristic curves for determining the threshold of the K-S test, we have achieved the highest performance of sensitivity and specificity (SP) (96.1% and 98.1%, respectively) for the MIT-BIH AF database, compared with other previously published algorithms. The SP was 97.9% for the MIT-BIH NSR database.     

盲信号分离

阵列处理和数据分析的一个典型问题是从混合的观测数据向量中恢复不可观测的各个源信号.盲信号分离是解决这一问题的一门新技术,近几年吸引了信号处理学界和神经网络学界众多学者的研究兴趣.本文将以独立分量分析和非线性主分量分析为主要对象,综述盲信号分离技术的理论、方法及应用等方面的发展,并作有关展望.