Spatiotemporal blind source separation approach to atrial activity estimation in atrial tachyarrhythmias

The analysis and characterization of atrial tachyarrhythmias requires, in a previous step, the extraction of the atrial activity (AA) free from ventricular activity and other artefacts. This contribution adopts the blind source separation (BSS) approach to AA estimation from multilead electrocardiograms (ECGs). Previously proposed BSS methods for AA extraction-e.g., independent component analysis (ICA)-exploit only the spatial diversity introduced by the multiple spatially-separated electrodes. However, AA typically shows certain degree of temporal correlation, with a narrowband spectrum featuring a main frequency peak around 3.5-9 Hz. Taking advantage of this observation, we put forward a novel two-step BSS-based technique which exploits both spatial and temporal information contained in the recorded ECG signals. The spatiotemporal BSS algorithm is validated on simulated and real ECGs from a significant number of atrial fibrillation (AF) and atrial flutter (AFL) episodes, and proves consistently superior to a spatial-only ICA method. In simulated ECGs, a new methodology for the synthetic generation of realistic AF episodes is proposed, which includes a judicious comparison between the known AA content and the estimated AA sources. Using this methodology, the ICA technique obtains correlation indexes of 0.751, whereas the proposed approach obtains a correlation of 0.830 and an error in the estimated signal reduced by a factor of 40%. In real ECG recordings, we propose to measure performance by the spectral concentration (SC) around the main frequency peak. The spatiotemporal algorithm outperforms the ICA method, obtaining a SC of 58.8% and 44.7%, respectively.     

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.     

Optimized wavelets for blind separation of nonstationary surface myoelectric signals

Surface electromyography (EMG) signals detected over the skin surface may be mixtures of signals generated by many active muscles due to poor spatial selectivity of the recording. In this paper, we propose a new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures. The method is based on whitening of the observations and rotation of the whitened observations. The rotation is performed by joint diagonalization of a set of spatial wavelet distributions (SWDs). The SWDs depend on the selection of the mother wavelet which can be defined by unconstrained parameters via the lattice parameterization within the multiresolution analysis framework. As the sources are classically supposed to be mutually uncorrelated, the design parameters of the mother wavelet can be blindly optimized by minimizing the average (over time lags) cross correlation between the estimated sources. The method was tested on simulated and experimental surface EMG signals and results were compared with those obtained with spatial time-frequency distributions and with second-order statistics (only spectral information). On a set of simulated signals, for 10-dB signal-to-noise ratio (SNR), the cross-correlation coefficient between original and estimated sources was 0.92 +/- 0.07 with wavelet optimization, 0.74 +/- 0.09 with the wavelet leading to the poorest performance, 0.85 +/- 0.07 with Wigner-Ville distribution, 0.86 +/- 0.07 with Choi-Williams distribution, and 0.73 +/- 0.05 with second-order statistics. In experimental conditions, when the flexor carpi radialis and pronator teres were concomitantly active for 50% of the time, crosstalk was 55.2 +/- 10.0% before BSS and was reduced to 15.2 +/- 6.3% with wavelet optimization, 30.1 +/- 15.0% with the worst wavelet, 28.3 +/- 12.3% with Wigner-Ville distribution, 26.2 +/- 12.0% with Choi-Williams distribution, and 35.1 +/- 15.5% with second-order statistics. In conclusion, the proposed approach resulted in better performance than previous methods for the separation of nonstationary myoelectric signals.     

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.     

Multiple window correlation analysis of HRV power and respiratory frequency

In this paper, we evaluate the correlation estimate, based on multiple window spectrum analysis, between the respiratory center frequency and the high-frequency band of the heartrate variability (HRV) power. One aim is to examine whether a more restricted frequency range would better capture respiratory related HR variation, especially when the HR variation is changing rapidly. The respiratory peak is detected and a narrow-banded measure of the high-frequency (HF) band of the HRV is defined as the respiratory frequency +/-0.05 Hz. We compare the mean square error of the correlation estimate between the frequency of the respiratory peak and the power of the HRV with the power in the usual 0.12-0.4 Hz frequency band. Different multiple window spectrum techniques are used for the estimation of the respiratory frequency as well as for the power of the HRV. We compare the peak-matched multiple windows with the Welch method while evaluating the two different HF-power estimates mentioned above. The results show that using a more narrow band for the power estimation gives stronger correlation which indicates that the estimate of the power is more robust.     

Estimation of the ventricular fibrillation duration byautoregressive modeling

An accurate estimation of ventricular fibrillation (VF) duration could be critical in selecting the most effective therapeutic intervention. The authors test the hypothesis that changes in frequency content of VF signals can be quantified by using autoregressive (AR) modeling, and the duration since the onset of VF can be estimated by using this method. VF signals were recorded for up to 300 s in five isolated rabbit hearts. Fourth-order AR parameters of successive segments were estimated, and frequencies of the first poles (the pole with lower frequency) were pooled together and a curve was fitted: F(t)=Aexp(-α_t)+B, where F(t) is the estimated frequency of the first pole at t'th time instant, α is the decay constant, B is the offset frequency, and A is the frequency at time zero minus the offset frequency. The utility of this curve in estimating the VF duration was tested in four new experiments, and the difference between the actual and the estimated VF duration (estimation error) was calculated. F(t), the frequency of the first pole, decreased from 12 to 6 Hz with duration of VF, while the frequency of the other pole decreased from 25 to 20 Hz. Parameters of the fitted curve were calculated as A=7.8, α=0.0041 and B was selected as four. Testing on a new set of VF signals produced very little estimation error for the first 100 s of VF, although this error increased with VF duration, For these new signals, the mean value of the absolute estimation error was 26 s. Results of this study show that changes in the frequency content of electrocardiogram (ECG) during VF can be quantified by AR modeling and that the frequency changes associated with a pole of this model can be used to estimate the VF duration     

Heart instantaneous frequency (HIF): an alternative approach to extract heart rate variability

Our study focuses on a new method of estimating the heart rate variability (HRV) which does not require the use of electrocardiogram (ECG) R-wave detection. Contrary to the R-wave detection method which requires a sampling frequency higher than 100 Hz, the one proposed here can be used to calculate the HRV from an ECG signal sampled at a frequency of approximately 5 Hz with a relative mean error of 0.03. This new method is based on extracting the instantaneous fundamental frequency from the ECG. The method could be efficiently used to extract the HRV from an ECG measured for healthy subjects performing an exercise in which the HRV increases linearly with time, and for subjects with respiratory and cardiac problems. The overall error decreased as we low-pass filtered the HRV with lower cut-off frequencies. Moreover, it was shown that the method could be efficiently used to calculate the HRV from blood pressure measurements and to be robust to noise.     

Nonstationarity broadening reduction in pulsed Doppler spectrummeasurements using time-frequency estimators

The spectral width of Doppler signals is used as measure of lesion-induced flow disturbance. Its estimation accuracy is compromised using the conventional short-term Fourier transform (STFT) since this method implicitly assumes signal stationarity during the signal window while the Doppler signals from arteries are markedly nonstationary. The Wigner-Ville (WVD), Choi-Williams (CWD) and Bessel distributions (BD), specifically designed for nonstationary signals, have been optimized for spectral width estimation accuracy and compared to the STFT under different signal to noise ratios using simulated Doppler signals of known time-frequency characteristics. The optimum parameter values for each method were determined as a Hanning window duration of 10 ms for the STFT, 40 ms for the WVD and CWD and 20 ms for the BD and dimensionless time-frequency smoothing constant values of five in the CWD and two in the BD. Thresholding was used to reduce the effect of cross terms and side lobes in the WVD and BD. With no added noise the WVD gave the lowest estimation error followed by the CWD. At signal-to-noise ratios (SNRs) of 10 dB and 20 dB the CWD and BD had similar errors and were markedly better than the other estimators. Overall the CWD gave the best performance     

Comparison of the non linear energy operator and the Hilbert transform in the estimation of the instantaneous amplitude and frequency

The instantaneous amplitude (ai) and frequency (fi) parameters of a biomedical signal can be useful for identification of signal physiological states or state changes. In this article the features ai and fi of simulated and experimental (real EEG and ECG) signals, are estimated using three methods: one based on the Hilbert Transform (HT), a modified version of this that improves the fi estimation in experimental signals (HTM), and the energy separation algorithm (DESA1), based on Teager’s energy operator (TEO). The algorithm comparison is made using the average relative error obtained in the signals’ demodulation process, their noise sensitivity, and computational efficiency. The obtained results showed that the HTM method produces the least fi estimation errors in noisy signals, and depending on the kind of signal considered, DESA1 and HTM methods produce the least ai estimation errors.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels     

Error analysis of tissue resistivity measurement

We identified the error sources in a system for measuring tissue resistivity at eight frequencies from 1 Hz to 1 MHz using the four-terminal method. We expressed the measured resistivity with an analytical formula containing all error terms. We conducted practical error measurements with in-vivo and bench-top experiments. We averaged errors at all frequencies for all measurements. The standard deviations of error of the quantization error of the 8-bit digital oscilloscope with voltage averaging, the nonideality of the circuit, the in-vivo motion artifact and electrical interference combined to yield an error of +/- 1.19%. The dimension error in measuring the syringe tube for measuring the reference saline resistivity added +/- 1.32% error. The estimation of the working probe constant by interpolating a set of probe constants measured in reference saline solutions added +/- 0.48% error. The difference in the current magnitudes used during the probe calibration and that during the tissue resistivity measurement caused +/- 0.14% error. Variation of the electrode spacing, alignment, and electrode surface property due to the insertion of electrodes into the tissue caused +/- 0.61% error. We combined the above errors to yield an overall standard deviation error of the measured tissue resistivity of +/- 1.96%.     

石英微机械陀螺敏感器件减振设计

石英微机械陀螺敏感器件在多轴陀螺应用中,各敏感器件之间存在振动干扰,导致陀螺噪声过大,输出信号中存在低频信号,无法满足使用要求。应用减振技术设计了一款集成式的减振器,该减振器具有体积小、质量轻等特点。利用有限元法模拟计算减振器减振效率及固有频率,该减振器在敏感器件激励频率范围内减振效率大于96%;减振器转动振动模态固有频率大于陀螺带宽(150Hz)的两倍以上;减振器低阶线性振动模态固有频率大于敏感器件检测频率与激励频率之差(340Hz)的两倍以上。     

一种基于短时傅里叶变换的机载SAR自聚焦算法

短时傅里叶变换(Short-Time Fourier Transform, STFT)是研究非平稳信号最为广泛使用的重要方法。该文在讨论了利用STFT对线性调频信号(LFM)进行滤波以及调频率估计后,提出一种基于STFT的机载SAR自聚焦算法。该算法首先利用STFT对影响SAR图像质量的主要相位误差二次相位误差(QPE)进行估计和补偿,然后在残余相位误差估计时利用STFT对时变信号进行滤波以提高信杂比(SCR)。仿真和实测数据的处理结果验证了该文算法的有效性。     

A comparative study of simultaneous vibromyography andelectromyography with active human quadriceps

Vibromyographic (VMG) signals, which are low-frequency vibration signals generated during muscle contraction, were studied in comparison with electromyographic (EMG) signals recorded simultaneously during isometric contraction of the human quadriceps muscles. The comparison was accomplished by evaluating the averaged root mean squared (rms) value, mean frequency (MF), and peak frequency (PF) of the VMG and EMG signals for four muscle contraction levels at joint angles of 30 degrees, 60 degrees, and 90 degrees. The four contraction levels, namely 20, 40, 60, and 80% of maximum voluntary contraction (MVC), were estimated and controlled by the torque readings of a Cybex II dynamometer. It was found that the VMG and EMG under the same conditions on the same muscle group are in general equally sensitive to the levels of muscle contraction. Results show that the rms value of the VMG signal increases linearly, in a manner similar to the EMG rms/%MVC relationship, with increasing muscle contraction levels. Furthermore, the study indicates that the averaged MF (6-24 Hz) and PF (9-19 Hz) of the VMG signals are much lower than the MF (75-109 Hz) and PF (40-80 Hz) of the EMG signals. The slopes of MF/%MVC curves for the VMG and EMG are approximately the same for 60 degrees and 90 degrees joint angles (approximately 3.1 Hz per 20% MVC for VMG and approximately 2.6 Hz per 20% MVC for EMG).(ABSTRACT TRUNCATED AT 250 WORDS)     

A device to apply user-specified strains to biomaterials in culture

An apparatus was developed to apply user-specified displacements to biomaterial samples in culture. The device allowed cyclic waveforms of bandwidth 0 Hz to 20 Hz to be applied under physiologic thermal (37.5 degrees C) and [CO2] (5%) conditions. For a 0 Hz to 20 Hz bandwidth signal similar in shape to a ventricular pressure waveform, the mean displacement error was 0.26% of the full-scale output. The maximum overshoot was 0.700%. Environmental system evaluation tests demonstrated a specimen cartridge temperature of 37.20 +/- 0.15 degrees C during cyclic loading and 37.23 +/- 0.21 degrees C during static conditions. [CO2] was 5.29 +/- 0.54% during cyclic loading and 5.25 +/- 0.61% during static conditions. Laminar flow applied at the loading rod entrances to the specimen cartridge ensured the sample remained sterile during testing. As a preliminary evaluation, polyurethane samples were seeded with fetal foreskin fibroblasts and subject to intermittent cyclic displacements. Results demonstrated enhanced cell proliferation and increased [PGE2] for samples subjected to 10% strain compared with unstrained controls. A next step will be to evaluate cell response sensitivity to strain magnitude, duration, direction, and frequency. The long-term intent is to establish mechanical loading configurations that induce acceptable or adaptation-inducing responses for use in implant design and tissue engineering applications.     

The integral pulse frequency modulation model with time-varying threshold: application to heart rate variability analysis during exercise stress testing

In this paper, an approach for heart rate variability analysis during exercise stress testing is proposed based on the integral pulse frequency modulation (IPFM) model, where a time-varying threshold is included to account for the nonstationary mean heart rate. The proposed technique allows the estimation of the autonomic nervous system (ANS) modulating signal using the methods derived for the IPFM model with constant threshold plus a correction, which is shown to be needed to take into account the time-varying mean heart rate. On simulations, this technique allows the estimation of the ANS modulation on the heart from the beat occurrence time series with lower errors than the IPFM model with constant threshold (1.1% ± 1.3% versus 15.0% ± 14.9%). On an exercise stress testing database, the ANS modulation estimated by the proposed technique is closer to physiology than that obtained from the IPFM model with constant threshold, which tends to overestimate the ANS modulation during the recovery and underestimate it during the initial rest.     

Selective discrete Fourier transform algorithm for time-frequencyanalysis: method and application on simulated and cardiovascular signals

The Selective Discrete Fourier transform (DFT) Algorithm [SDA] method for the calculation and display of time-frequency distribution has been developed and validated. For each time and frequency, the algorithm selects the shortest required trace length and calculates the corresponding spectral component by means of DFT. This approach can be extended to any cardiovascular related signal and provides time-dependent power spectra which are intuitively easy to consider, due to their close relation to the classical spectral analysis approach. The optimal parameters of the SDA for cardiovascular-like signals were chosen. The SDA perform standard spectral analysis on stationary simulated signals as well as reliably detect abrupt changes in the frequency content of nonstationary signals. The SDA applied during a stimulated respiration experiment, accurately; detected the changes in the frequency location and amplitude of the respiratory peak in the heart rate (HR) spectrum. It also detected and quantified the expected increase in vagal tone during vagal stimuli. Furthermore, the HR time-dependent power spectrum displayed the increase in sympathetic activity and the vagal withdrawal on standing. Such transient changes in HR control would have been smeared out by standard heart rate variability (HRV), which requires consideration of long trace lengths. The SDA provides a reliable tool for the evaluation and quantification of the control exerted by the Central Nervous System, during clinical and experimental procedures resulting in nonstationary signals     

Blind separation of linear instantaneous mixtures of nonstationary surface myoelectric signals

Electromyographic (EMG) recordings detected over the skin may be mixtures of signals generated by different active muscles due to the phenomena related to volume conduction. Separation of the sources is necessary when single muscle activity has to be detected. Signals generated by different muscles may be considered uncorrelated but in general overlap in time and frequency. Under certain assumptions, mixtures of surface EMG signals can be considered as linear instantaneous but no a priori information about the mixing matrix is available when different muscles are active. In this study, we applied blind source separation (BSS) methods to separate the signals generated by two active muscles during a force-varying task. As the signals are non stationary, an algorithm based on spatial time-frequency distributions was applied on simulated and experimental EMG signals. The experimental signals were collected from the flexor carpi radialis and the pronator teres muscles which could be activated selectively for wrist flexion and rotation, respectively. From the simulations, correlation coefficients between the reference and reconstructed sources were higher than 0.85 for signals largely overlapping both in time and frequency and for signal-to-noise ratios as low as 5 dB. The Choi-Williams and Bessel kernels, in this case, performed better than the Wigner-Ville one. Moreover, the selection of time-frequency points for the procedure of joint diagonalization used in the BSS algorithm significantly influenced the results. For the experimental signals, the interference of the other source in each reconstructed source was significantly attenuated by the application of the BSS method. The ratio between root-mean-square values of the signals from the two sources detected over one of the muscles increased from (mean +/- standard deviation) 2.33 +/- 1.04 to 4.51 +/- 1.37 and from 1.55 +/- 0.46 to 2.72 +/- 0.65 for wrist flexion and rotation, respectively. This increment was statistically significant. It was concluded that the BSS approach applied is promising for the separation of surface EMG signals, with applications ranging from muscle assessment to detection of muscle activation intervals, and to the control of myoelectric prostheses.     

A nonlinear Bayesian filtering framework for ECG denoising

In this paper, a nonlinear Bayesian filtering framework is proposed for the filtering of single channel noisy electrocardiogram (ECG) recordings. The necessary dynamic models of the ECG are based on a modified nonlinear dynamic model, previously suggested for the generation of a highly realistic synthetic ECG. A modified version of this model is used in several Bayesian filters, including the Extended Kalman Filter, Extended Kalman Smoother, and Unscented Kalman Filter. An automatic parameter selection method is also introduced, to facilitate the adaptation of the model parameters to a vast variety of ECGs. This approach is evaluated on several normal ECGs, by artificially adding white and colored Gaussian noises to visually inspected clean ECG recordings, and studying the SNR and morphology of the filter outputs. The results of the study demonstrate superior results compared with conventional ECG denoising approaches such as bandpass filtering, adaptive filtering, and wavelet denoising, over a wide range of ECG SNRs. The method is also successfully evaluated on real nonstationary muscle artifact. This method may therefore serve as an effective framework for the model-based filtering of noisy ECG recordings.     

Development and evaluation of the piecewise Prony method for evoked potential analysis

A new method is presented to decompose nonstationary signals into a summation of oscillatory components with time varying frequency, amplitude, and phase characteristics. This method, referred to as piecewise Prony method (PPM), is an improvement over the classical Prony method, which can only deal with signals containing components with fixed frequency, amplitude and phase, and monotonically increasing or decreasing rate of change. PPM allows the study of the temporal profile of post-stimulus signal changes in single-trial evoked potentials (EPs), which can lead to new insights in EP generation. We have evaluated this method on simulated data to test its limitations and capabilities, and also on single-trial EPs. The simulation experiments showed that the PPM can detect amplitude changes as small as 10%, rate changes as small as 10%, and 0.15 Hz of frequency changes. The capabilities of the PPM were demonstrated using single electroencephalogram/EP trials of flash visual EPs recorded from one normal subject. The trial-by-trial results confirmed that the stimulation drastically attenuates the alpha activity shortly after stimulus presentation, with the alpha activity returning about 0.5 s later. The PPM results also provided evidence that delta activity undergoes phase alignment following stimulus presentation.