Multiple site electromyograph amplitude estimation

Temporal whitening of individual surface electromyograph (EMG) waveforms and spatial combination of multiple recording sites have separately been demonstrated to improve the performance of EMG amplitude estimation. This investigation combined these two techniques by first whitening, then combining the data from multiple EMG recording sites to form an EMG amplitude estimate. A phenomenological mathematical model of multiple sites of the surface EMG waveform, with analytic solution for an optimal amplitude estimate, is presented. Experimental surface EMG waveforms were then sampled from multiple sites during nonfatiguing, constant-force, isometric contractions of the biceps or triceps muscles, over the range of 10-75% maximum voluntary contraction. A signal-to-noise ratio (SNR) was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Results showed that SNR performance: 1) increased with the number of EMG sites, 2) was a function of the sampling frequency, 3) was predominantly invariant to various methods of determining spatial uncorrelation filters, 4) was not sensitive to the intersite correlations of the electrode configuration investigated, and 5) was best at lower levels of contraction. A moving average root mean square estimator (245-ms window) provided an average ± standard deviation (A±SD) SNR of 10.7±3.3 for single site unwhitened recordings. Temporal whitening and four combined sites improved the A±SD SNR to 24.6±10.4. On one subject, eight whitened combined sites were achieved, providing an A±SD SNR of 35.0±13.4     

Influence of joint angle on the calibration and performance of EMGamplitude estimators

Multiple-channel electromyogram (EMG) amplitude estimators incorporating temporal whitening filters and/or spatial uncorrelation filters contain a characterization of the EMG waveform (specifically, auto- and cross-correlation information) which may vary with joint angle. This paper reports on an experimental study which investigated the influence of joint angle on these EMG amplitude estimators. It was found that little or no relative improvement in estimator performance resulted from altering either temporal whitening or spatial uncorrelation filters as a function of joint angle. Also, the absolute performance level of these estimators did not vary with joint angle     

Influence of smoothing window length on electromyogram amplitudeestimates

A systematic, experimental study of the influence of smoothing window length on the signal-to-noise ratio (SNR) of electromyogram (EMG) amplitude estimates is described. Surface EMG waveforms were sampled during nonfatiguing, constant-force, constant-angle contractions of the biceps or triceps muscles, over the range of 10%-75% maximum voluntary contraction. EMG amplitude estimates were computed with eight different EMG processor schemes using smoothing length durations spanning 2.45-500 ms. An SNR was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Over these window lengths, average ± standard deviation SNR's ranged from 1.4±0.28 to 16.2±5.4 for unwhitened single-channel EMG processing and from 3.2±0.7 to 37.3±14.2 for whitened, multiple-channel EMG processing (results pooled across contraction level). It was found that SNR increased with window length in a square root fashion. The shape of this relationship was consistent with classic theoretical predictions, however none of the processors achieved the absolute performance level predicted by the theory. These results are useful in selecting the length of the smoothing window in traditional surface EMG studies. In addition, this study should contribute to the development of EMG processors which dynamically tune the smoothing window length when the EMG amplitude is time varying     

Nonlinear Spatial Filtering of Multichannel Surface Electromyogram Signals During Low Force Contractions

This study introduces the application of nonlinear spatial filters to help identify single motor unit discharge from multiple channel surface electromyogram (EMG) signals during low force contractions. The nonlinear spatial filters simultaneously take into account the instantaneous amplitude and frequency information of a signal. This property was used to enhance motor unit action potentials (MUAPs) in the surface EMG record. The advantages of nonlinear spatial filtering for surface MUAP enhancement were investigated using both simulation and experimental approaches. The simulation results indicate that when compared with various linear spatial filters, nonlinear spatial filtering achieved higher SNR and higher kurtosis of the surface EMG distribution. Over a broad range of SNR and kurtosis levels for the input signal, nonlinear spatial filters achieved at least 32 times greater SNR and 11% higher kurtosis for correlated noise, and at least 15 times greater SNR and 1.7 times higher kurtosis for independent noise, across electrode array channels. The improvements offered by nonlinear spatial filters were further documented by applying them to experimental surface EMG array recordings. Compared with linear spatial filters, nonlinear spatial filters achieved at least nine times greater SNR and 25% higher kurtosis. It follows that nonlinear spatial filters represent a potentially useful supplement to linear spatial filters for detection of motor unit activity in surface EMG at low force contractions.     

Estimation of muscle fiber conduction velocity with a spectral multidip approach

We propose a novel method for estimation of muscle fiber conduction velocity from surface electromyographic (EMG) signals. The method is based on the regression analysis between spatial and temporal frequencies of multiple dips introduced in the EMG power spectrum through the application of a set of spatial filters. This approach leads to a closed analytical expression of conduction velocity as a function of the auto- and cross-spectra of monopolar signals detected along the direction of muscle fibers. The performance of the algorithm was compared with respect to that of the classic single dip approach on simulated and experimental EMG signals. The standard deviation of conduction velocity estimates from simulated single motor unit action potentials was reduced from 1.51 m/s [10 dB signal-to-noise ratio (SNR)] and 1.06 m/s (20 dB SNR) with the single dip approach to 0.51 m/s (10 dB) and 0.23 m/s (20 dB) with the proposed method using 65 dips. When 200 active motor units were simulated in an interference EMG signal, standard deviation of conduction velocity decreased from 0.95 m/s (10 dB SNR) and 0.60 m/s (20 dB SNR) with a single dip to 0.21 m/s (10 dB) and 0.11 m/s (20 dB) with 65 dips. In experimental signals detected from the abductor pollicis brevis muscle, standard deviation of estimation decreased from (mean +/- SD over 5 subjects) 1.25 +/- 0.62 m/s with one dip to 0.10 +/- 0.03 m/s with 100 dips. The proposed method does not imply limitation in resolution of the estimated conduction velocity and does not require any iterative procedure for the estimate since it is based on a closed analytical formulation.     

Adaptive whitening of the electromyogram to improve amplitude estimation

Previous research showed that whitening the surface electromyogram (EMG) can improve EMG amplitude estimation (where EMG amplitude is defined as the time-varying standard deviation of the EMG). However, conventional whitening via a linear filter seems to fail at low EMG amplitude levels, perhaps due to additive background noise in the measured EMG. This paper describes an adaptive whitening technique that overcomes this problem by cascading a nonadaptive whitening filter, an adaptive Wiener filter, and an adaptive gain correction. These stages can be calibrated from two, five second duration, constant-angle, constant-force contractions, one at a reference level [e.g., 50% maximum voluntary contraction (MVC)] and one at 0% MVC. In experimental studies, subjects used real-time EMG amplitude estimates to track a uniform-density, band-limited random target. With a 0.25-Hz bandwidth target, either adaptive whitening or multiple-channel processing reduced the tracking error roughly half-way to the error achieved using the dynamometer signal as the feedback. At the 1.00-Hz bandwidth, all of the EMG processors had errors equivalent to that of the dynamometer signal, reflecting that errors in this task were dominated by subjects' inability to track targets at this bandwidth. Increases in the additive noise level, smoothing window length, and tracking bandwidth diminish the advantages of whitening.     

Probability density of the surface electromyogram and its relationto amplitude detectors

When the surface electromyogram (EMG) generated from constant-force, constant-angle, nonfatiguing contractions is modeled as a random process, its density is typically assumed to be Gaussian. This assumption leads to root-mean-square (RMS) processing as the maximum likelihood estimator of the EMG amplitude (where EMG amplitude is defined as the standard deviation of the random process). Contrary to this theoretical formulation, experimental work has found the signal-to-noise-ratio [(SNR), defined as the mean of the amplitude estimate divided by its standard deviation] using mean-absolute-value (MAV) processing to be superior to RMS. This paper reviews RMS processing with the Gaussian model and then derives the expected (inferior) SNR performance of MAV processing with the Gaussian model. Next, a new model for the surface EMG signal, using a Laplacian density, is presented. It is shown that the MAV processor is the maximum likelihood estimator of the EMG amplitude for the Laplacian model. SNR performance based on a Laplacian model is predicted to be inferior to that of the Gaussian model by approximately 32%. Thus, minor variations in the probability distribution of the EMG may result in large decrements in SNR performance. Lastly, experimental data from constant-force, constant-angle, nonfatiguing contractions were examined. The experimentally observed densities fell in between the theoretic Gaussian and Laplacian densities. On average, the Gaussian density best fit the experimental data, although results varied with subject. For amplitude estimation, MAV processing had a slightly higher SNR than RMS processing.     

Frequency spectra of ventricular tachycardia and sinus rhythm inhuman intracardiac electrograms-application to tachycardia detection forcardiac pacemakers

Presently available antitachycardia pacemakers detect ventricular tachycardia (VT) by measurement of the period of the intracardiac electrogram (EGM). The resulting inability to differentiate between VT and rapid normal sinus rhythm (NSR) can cause inappropriate pacemaker output, possibly initiating an arrhythmia where none existed previously. It is reported that FFT analysis of matched-pair NSR-VT EGM recordings from 33 patients revealed a mean (±SD) NSR-VT difference in the peak amplitude point of 8 (±7) Hz and a difference of 18 (±18) Hz in the -3 dB point. NSR-VT amplitude differences could be significantly increased by filtering over the range of greatest spectral differences. Variable-passband programmable filters could enhance VT detection in antitachycardia pacemakers     

Optimal detection, classification, and superposition resolution inneural waveform recordings

The effects of noise autocorrelation on neural waveform recognition (detection, classification, and superposition resolution) are investigated, using microelectrode recordings from the cortex of a monkey. Optimal waveform recognition is accomplished by passing the data through a whitening filter before matched filtering for detection or template matching for classification and superposition resolution. Template matching without whitening requires about 40% higher signal-to-noise ratio (SNR) than template matching with whitening for comparable classification and superposition resolution. The comparable difference for detection is 15%     

Entropy-based optimization of wavelet spatial filters

A new class of spatial filters for surface electromyographic (EMG) signal detection is proposed. These filters are based on the 2-D spatial wavelet decomposition of the surface EMG recorded with a grid of electrodes and inverse transformation after zeroing a subset of the transformation coefficients. The filter transfer function depends on the selected mother wavelet in the two spatial directions. Wavelet parameterization is proposed with the aim of signal-based optimization of the transfer function of the spatial filter. The optimization criterion was the minimization of the entropy of the time samples of the output signal. The optimized spatial filter is linear and space invariant. In simulated and experimental recordings, the optimized wavelet filter showed increased selectivity with respect to previously proposed filters. For example, in simulation, the ratio between the peak-to-peak amplitude of action potentials generated by motor units 20 degrees apart in the transversal direction was 8.58% (with monopolar recording), 2.47% (double differential), 2.59% (normal double differential), and 0.47% (optimized wavelet filter). In experimental recordings, the duration of the detected action potentials decreased from (mean +/- SD) 6.9 +/- 0.3 ms (monopolar recording), to 4.5 +/- 0.2 ms (normal double differential), 3.7 +/- 0.2 (double differential), and 3.0 +/- 0.1 ms (optimized wavelet filter). In conclusion, the new class of spatial filters with the proposed signal-based optimization of the transfer function allows better discrimination of individual motor unit activities in surface EMG recordings than it was previously possible.     

Adaptive whitening in electromyogram amplitude estimation for epoch-based applications

Epoch-based electromyogram (EMG) amplitude estimates have not incorporated signal whitening, even though whitening has demonstrated significant improvements for stream-based estimates. This paper presents new epoch-based algorithms, for both single- and multiple-channel EMG, which include a whitening stage. The best multiple-channel whitening processor provided a 21.4%-22.5% improvement over single-channel unwhitened estimation in an EMG-to-torque application.     

A Spatiotemporal Framework for Estimating Trial-to-Trial Amplitude Variation in Event-Related MEG/EEG

A spatiotemporal framework for estimating trial-to-trial variability in evoked response (ER) data is presented. Spatial and temporal bases capture the aspects of the response that are consistent across trials, while the basis expansion coefficients represent the variable components of the response. We focus on the simplest case of constant spatiotemporal response shape and varying amplitude across trials. Two different constraints on the amplitude evolution are employed to effectively integrate the individual responses and improve robustness at low SNR. The linear dynamical system response constraint estimates the current trial amplitude as an unknown constant scaling of the estimate in the previous trial plus zero-mean Gaussian noise with unknown variance. The independent response constraint estimates response amplitudes across trials as independent Gaussian random variables having unknown mean and variance. We develop a generalized expectation-maximization algorithm to obtain the maximum-likelihood (ML) estimates of the signal waveform, noise covariance matrix, and unknown constraint parameters. ML source localization is achieved by scanning the likelihood over different sets of spatial bases. We demonstrate the variability estimation and source localization effectiveness of the proposed algorithms using both real and simulated ER data.     

Estimation of motor unit conduction velocity from surface EMG recordings by signal-based selection of the spatial filters

Muscle fiber conduction velocity (CV) can be estimated by the application of a pair of spatial filters to surface electromagnetic (EMG) signals and compensation of the spatial filter transfer function with equivalent temporal filters. This method integrates the selection of the spatial filters for signal detection to the estimation of CV. Using this approach, in this paper, we propose a novel technique for signal-based selection of the spatial filter pair that minimizes the effect of nonpropagating signal components (end-of-fiber effects) on CV estimates (optimal filters). The technique is applicable to signals with one propagating and one nonpropagating component, such as single motor unit action potentials. It is shown that the determination of the optimal filters also allows the identification of the propagating and nonpropagating signal components. The new method was applied to simulated and experimental EMG signals. Simulated signals were generated by a cylindrical, layered volume conductor model. Experimental signals were recorded from the abductor pollicis brevis with a linear array of 16 electrodes. In the simulations, the proposed approach provided CV estimates with lower bias due to nonpropagating signal components than previously proposed methods based on the entire signal waveform. In the experimental signals, the technique separated propagating and nonpropagating signal components with an average reconstruction error of 2.9 +/- 0.9% of the signal energy. The technique may find application in single motor unit studies for decreasing the variability and bias of CV estimates due to the presence and different weights of the nonpropagating components.     

Maximum-likelihood estimation of low-rank signals for multiepoch MEG/EEG analysis

A maximum-likelihood-based algorithm is presented for reducing the effects of spatially colored noise in evoked response magneto- and electro-encephalography data. The repeated component of the data, or signal of interest, is modeled as the mean, while the noise is modeled as the Kronecker product of a spatial and a temporal covariance matrix. The temporal covariance matrix is assumed known or estimated prior to the application of the algorithm. The spatial covariance structure is estimated as part of the maximum-likelihood procedure. The mean matrix representing the signal of interest is assumed to be low-rank due to the temporal and spatial structure of the data. The maximum-likelihood estimates of the components of the low-rank signal structure are derived in order to estimate the signal component. The relationship between this approach and principal component analysis (PCA) is explored. In contrast to prestimulus-based whitening followed by PCA, the maximum-likelihood approach does not require signal-free data for noise whitening. Consequently, the maximum-likelihood approach is much more effective with nonstationary noise and produces better quality whitening for a given data record length. The efficacy of this approach is demonstrated using simulated and real MEG data.     

A novel approach for estimating muscle fiber conduction velocity by spatial and temporal filtering of surface EMG signals

We describe a new method for the estimation of muscle fiber conduction velocity (CV) from surface electromyography (EMG) signals. The method is based on the detection of two surface EMG signals with different spatial filters and on the compensation of the spatial filtering operations by two temporal filters (with CV as unknown parameter) applied to the signals. The transfer functions of the two spatial filters may have different magnitudes and phases, thus the detected signals have not necessarily the same shape. The two signals are first spatially and then temporally filtered and are ideally equal when the CV value selected as a parameter in the temporal filters corresponds to the velocity of propagation of the detected action potentials. This approach is the generalization of the classic spectral matching technique. A theoretical derivation of the method is provided together with its fast implementation by an iterative method based on the Newton's method. Moreover, the lowest CV estimate among those obtained by a number of filter pairs is selected to reduce the CV bias due to nonpropagating signal components. Simulation results indicate that the method described is less sensitive than the classic spectral matching approach to the presence of nonpropagating signals and that the two methods have similar standard deviation of estimation in the presence of additive, white, Gaussian noise. Finally, experimental signals have been collected from the biceps brachii muscle of ten healthy male subjects with an adhesive linear array of eight electrodes. The CV estimates depended on the electrode location with positive bias for the estimates from electrodes close to the innervation or tendon regions, as expected. The proposed method led to significantly lower bias than the spectral matching method in the experimental conditions, confirming the simulation results.     

GF-7星载激光测高仪全波形自适应高斯滤波

全波形星载激光测高仪通过向地表发射激光,获得目标表面的后向散射完整波形,可用于地表剖面高程信息及目标表面几何物理参数的反演。GF-7星载激光测高仪部分原始波形存在噪声显著、波峰左偏/右偏和非饱和平峰等情况,对提取有效信息造成干扰。针对GF-7星载激光测高仪全波形数据,首先提出了一种波形背景噪声迭代去除方法,然后对波形噪声特点及几何结构进行分析,并进行定量化描述,最终设计了一种顾及波形噪声与结构异构的自适应高斯滤波器。在实验中,将文中方法与已有经典波形滤波算法进行比较,最终验证了文中方法在噪声去除、有效信号保留及非饱和平峰波形处理上的有效性。使用文中方法进行波形滤波后,波形信噪比更高,同时波形幅值下降量均在3倍的噪声标准差以内,非饱和平峰波形滤波后波形高斯分解参数振幅、均值和标准差的分解精度分别为(0.69 ± 2.34) mV, (0.007 ± 0.024) ns和(0.026 ± 0.069) ns。     

Simulation Techniques in Electromyography

A motor unit action potential (MUAP) recorded in clinical electromyography (EMG) is the spatial and temporal summation of the action potentials (AP's) from all muscle fibers in a motor unit (MU). An important determinant of MUAP waveform characteristics is the size of the recording electrode. In this paper, we have described the use of a modified line source model of single muscle fiber action potentials to simulate MUAP's as recorded by single fiber (SF) EMG, concentric needle (CN) EMG, and macro-EMG electrodes. Results indicate that SFEMG recordings from a normal MU contain mainly the AP's of the closest one to three muscle fibers of the MU. The amplitude, area, and duration of the simulated CNEMG MUAP's are determined mainly by the number and size of muscle fibers within a semicircular territory of 0.5, 1.5, and 2.5 mm, respectively, around the tip of the electrode. The amplitude and area of simulated macro-EMG MUAP's increase with the number of muscle fibers in the MU.     

Selectivity of spatial filters for surface EMG detection from the tibialis anterior muscle

Many spatial filters have been proposed for surface electromyographic (EMG) signal detection. Although theoretical and modeling predictions on spatial selectivity are available, there are no extensive experimental validations of these techniques based on single motor unit (MU) activity detection. The aim of this study was to compare spatial selectivity of one- and two-dimensional (1-D and 2-D) spatial filters for EMG signal detection. Intramuscular and surface EMG signals were recorded from the tibialis anterior muscle of ten subjects. The simultaneous use of intramuscular wire and surface recordings (with the spike triggered averaging technique) allowed investigation of the activity of single MUs at the skin surface. The surface EMG signals were recorded with a grid of point electrodes (3 x 3 electrodes) and a ring electrode system at 15 locations over the muscle, with the wires detecting signals from the same intramuscular location. For most subjects, it was possible to classify, from the intramuscular recordings, the activity of the same MUs for all the contractions. The surface EMG signals were averaged with the intramuscularly detected MU action potentials as triggers. In this way, eight spatial filters--longitudinal and transversal, single and double differential (LSD, TSD, LDD, TDD), Laplacian (NDD), inverse binomial filter of the second order (IB2), inverse rectangle filter (IR), and differential ring system (C1)--could be compared on the basis of their spatial selectivity. The distance from the source (transversal with respect to the muscle fiber orientation) after which the surface detected potential did not exceed +/- 5% of the maximal peak-to-peak amplitude (detection distance) was statistically smaller for the 2-D systems and TDD than for the other filters. The MU action potential duration was significantly shorter with LDD and with the 2-D systems than with the other filters. The 2-D filters investigated (including C1) showed very similar performance and were, thus, considered equivalent from the point of view of spatial selectivity.     

Analysis and comparison of reflex times and electromyograms of cervical muscles under impact loading using surface and fine-wire electroces

Myoelectric signals [electromyograms (EMGs)] can be collected using either surface or fine-wire electrodes. Application of the latter results in higher-frequency contents of EMG. In the field of impact biomechanics, surface electrodes are more often utilized than fine-wire ones. However, the removal of motion artefacts from EMG recorded under transient loads requires application of high-pass filters with relatively high cutoff frequencies, which may eliminate a significant part of the surface EMG power spectra. Therefore, in the current study, both surface and fine-wire electrodes were utilized to record the EMG of cervical muscles under conditions simulating a rear-end car collision at low speed. The results indicated that application of high-pass filtering at 50 Hz can be necessary to remove motion artefacts from the EMG collected under such conditions. Such filtering resulted in a higher decrease in amplitude of the surface EMG than that of the fine-wire one. However, the reflex times obtained here were not significantly affected by the type of the electrodes utilized to collect EMG.     

Volume conduction in an anatomically based surface EMG model

A finite-element model to simulate surface electromyography (EMG) in a realistic human upper arm is presented. The model is used to explore the effect of limb geometry on surface-detected muscle fiber action potentials. The model was based on magnetic resonance images of the subject's upper arm and includes both resistive and capacitive material properties. To validate the model geometry, experimental and simulated potentials were compared at different electrode sites during the application of a subthreshold sinusoidal current source to the skin surface. Of the material properties examined, the closest approximation to the experimental data yielded a mean root-mean-square (rms) error of the normalized surface potential of 18% or 27%, depending on the site of the applied source. Surface-detected action potentials simulated using the realistic volume conductor model and an idealized cylindrical model based on the same limb geometry were then compared. Variation in the simulated limb geometry had a considerable effect on action potential shape. However, the rate of decay of the action potential amplitude with increasing distance from the fiber was similar in both models. Inclusion of capacitive material properties resulted in temporal low-pass filtering of the surface action potentials. This effect was most pronounced in the end-effect components of action potentials detected at locations far from the active fiber. It is concluded that accurate modeling of the limb geometry, asymmetry, tissue capacitance and fiber curvature is important when the specific action potential shapes are of interest. However, if the objective is to examine more qualitative features of the surface EMG signal, then an idealized volume conductor model with appropriate tissue thicknesses provides a close approximation.