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.     

Spatial Filtering of Noninvasive Multielectrode EMG: Part II?Filter Performance in Theory and Modeling

Spatial filtering, particularly common in the field of engineering, is adapted in theory and practice to the filtering of propagating spatial EMG signals. This technique offers a new flexibility in the design of selective EMG measurement configurations. Longitudinal as well as two-dimensional spatial filters can be used. The conditions for the design of suitable spatial filters are deduced by signal theory. The performances of different selected configurations are compared by means of a given simple model of an excited motor unit. The modeling results compare well to the previously described experimental signals.     

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.     

Improvement of spatial resolution in surface-EMG: a theoretical andexperimental comparison of different spatial filters

In the present study, different isotropic and anisotropic filters have been compared by means of theoretical field simulations and experiments in volunteers. A tripole model for an excited motor unit (MU) was used as the basis for simulating the spatial extension of the filter response for each of the investigated filters. The spatial extension is an indicative of the spatial resolution. For the experimental validation, the total number of single motor units was not directly investigated, but the signal-to-noise ratio (SNR) has been determined. Therefore, the potential distribution generated on the skin surface during maximum voluntary contraction has been simultaneous spatially filtered with each of the investigated filters. The simulations show that an isotropic spatial filtering procedure reduces the spatial extension of the filter response and improves the spatial resolution of the electromyography (EMG)-recording arrangement in comparison to anisotropic spatial filters up to 30%. In other words, the spatial selectivity of the arrangement is increased. This improvement in the filter performance is more pronounced for MU's located close to the skin surface than for MU's more distantly located. Additionally, this theoretical improvement in selectivity depends on the direction of the excitation spread relative to the filter alignment. However, the investigations also show that isotropic filters offer an advantage, compared to anisotropic filters, only when the investigated MU is located extremely close to the filter input. The results of the simulations can be confirmed by the experimental investigations. An improvement of 11% in the SNR, relative to anisotropic spatial filters, can be established when using an isotropic spatial filter. This experimental improvement in selectivity is less than the theoretical improvement because the experimentally investigated MU's have less portion in the anisotropic range of the filters than the simulated one at best     

The relationship between the surface EMG and force transients in muscle: Simulation and experimental studies

The surface electromyogrmn (EMG) is an easily measured signal which when quantified by present techniques is a reliable measure of whether a muscle is active, a fairly reliable measure of steady state force and a rather unreliable measure of force transients in muscle. There is a real need for a reliable indicator of dynamic changes in muscle activity for the control of prosthetics, in diagnosis of neuromuscular diseases, in studies of the motor control system and in fundamental studies of muscle mechanics. This paper outlines the principles underlying the development of force and the EMG in muscle. The EMG is a poor estimate of muscle force since it is the result of the linear superposition of biphasic action potentials which result in an interference pattern. This in turn is dependent on the details of the firing intervals for each motor unit, whereas the force is quite insensitive to these details. Experimental results for the human biceps brachii are described in which it was not possible to obtain a consistent estimate of muscle active state from the EMG. An extensive computer simulation was used to explore the relationship between EMG and force under a variety of assumptions. The conclusion is that it is technically impossible to obtain consistent estimates of muscle force (or active state) unless a filter with a time constant of 300 ms is applied to the rectified EMG. This is inconsistent with the estimation of active state for voluntary contractions with observed rise time constants of 30-70 ms. It is susgested that the only solution is to repeat an experiment many times and average the rectified EMG. Unfortunately, in practice it is difficult to repeat certain aspects of voluntary muscular contractions.     

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     

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.     

Spatial Filtering of Noninvasive Multielectrode EMG: Part I?Introduction to Measuring Technique and Applications

Complementary to its conventional applications, surface EMG is also suited to gain more detailed information on the functional state of a muscle, when measurement configurations with smaller pickup areas are used. A new category of suitable measurement configurations is obtained by application of the spatial filtering principle to electromyography. In a spatial filter unit, the signals of several recording electrodes are combined to form one output signal channel. The filter characteristic is determined by the weighting factors used and by the geometrical arrangement of the electrodes. Extended multielectrode arrays and multichannel recording make possible the detection of correlated excitations at different sites of the muscle. Even in high levels of muscle contraction, single motor unit impulses that are suitably shaped by filtering can be repeatedly recognized in the surface EMG signal. In clinical studies, pathologically shaped impulses have been identified indicating multiple innervation zones. The initiation and the propagation of excitation within single motor units can be detected with improved accuracy even from very small muscles.     

Modeling of surface myoelectric signals. II. Model-based signalinterpretation

Experimental electromyogram (EMG) data from the human biceps brachii were simulated using the model described in [10] of this work. A multichannel linear electrode array, spanning the length of the biceps, was used to detect monopolar and bipolar signals, from which double differential signals were computed, during either voluntary or electrically elicited isometric contractions. For relatively low-level voluntary contractions (10%-30% of maximum force) individual firings of three to four-different motor units were identified and their waveforms were closely approximated by the model. Motor unit parameters such as depth, size, fiber orientation and length, location of innervation and tendonous zones, propagation velocity, and source width were estimated using the model. Two applications of the model are described. The first analyzes the effects of electrode rotation with respect to the muscle fiber direction and shows the possibility of conduction velocity (CV) over- and under-estimation. The second focuses on the myoelectric manifestations of fatigue during a sustained electrically elicited contraction and the interrelationship between muscle fiber CV, spectral and amplitude variables, and the length of the depolarization zone. It is concluded that a) surface EMG detection using an electrode array, when combined with a model of signal propagation, provides a useful method for understanding the physiological and anatomical determinants of EMG waveform characteristics and b) the model provides a way for the interpretation of fatigue plots.     

Linear optimization in synthesis of nonlinear spatial filters

Generally, the synthesis of coherent spatial filters is restricted to the linear region of the transfer characteristic of a photographic film. However, a technique of synthesizing a nonlinear spatial filter such that the signal detection may be optimum will be described. In this paper, a generalized linear optimization technique is formulated. The application of this optimization technique toward a simple nonlinear spatial filter is demonstrated, and the extension of this optimization technique for a more complicated nonlinear spatial filter is also given. The signal detection by nonlinear optimum spatial filtering is analyzed. Finally, it is concluded that, instead of restricting the spatial-filter recording to the linear region of the transfer characteristic of the photographic film, an optimum nonlinear spatial filter may be achieved.     

Analysis and simulation of changes in EMG amplitude during high-level fatiguing contractions

Changes in surface electromyographic (EMG) amplitude during sustained, fatiguing contractions are commonly attributed to variations in muscle fiber conduction velocity (MFCV), motor unit firing rates, transmembrane action potentials and the synchronization or recruitment of motor units. However, the relative contribution of each factor remains unclear. Analytical relationships relating changes in MFCV and mean motor unit firing rates to the root mean square (RMS) and average rectified (AR) value of the surface EMG signal are derived. The relationships are then confirmed using model simulation. The simulations and analysis illustrate the different behaviors of the surface EMG RMS and AR value with changing MFCV and firing rate, as the level of motor unit superposition varies. Levels of firing rate modulation and short-term synchronization that, combined with variations in MFCV, could cause changes in EMG amplitude similar to those observed during sustained isometric contraction of the brachioradialis at 80% of maximum voluntary contraction were estimated. While it is not possible to draw conclusions about changes in neural control without further information about the underlying motor unit activation patterns, the examples presented illustrate how a combined analytical and simulation approach may provide insight into the manner in which different factors affect EMG amplitude during sustained isometric contractions.     

Application of higher order statistics techniques to EMG signals to characterize the motor unit action potential

The electromyographic (EMG) signal provides information about the performance of muscles and nerves. At any instant, the shape of the muscle signal, motor unit action potential (MUAP), is constant unless there is movement of the position of the electrode or biochemical changes in the muscle due to changes in contraction level. The rate of neuron pulses, whose exact times of occurrence are random in nature, is related to the time duration and force of a muscle contraction. The EMG signal can be modeled as the output signal of a filtered impulse process where the neuron firing pulses are assumed to be the input of a system whose transfer function is the motor unit action potential. Representing the neuron pulses as a point process with random times of occurrence, the higher order statistics based system reconstruction algorithm can be applied to the EMG signal to characterize the motor unit action potential. In this paper, we report results from applying a cepstrum of bispectrum based system reconstruction algorithm to real wired-EMG (wEMG) and surface-EMG (sEMG) signals to estimate the appearance of MUAPs in the Rectus Femoris and Vastus Lateralis muscles while the muscles are at rest and in six other contraction positions. It is observed that the appearance of MUAPs estimated from any EMG (wEMG or sEMG) signal clearly shows evidence of motor unit recruitment and crosstalk, if any, due to activity in neighboring muscles. It is also found that the shape of MUAPs remains the same on loading.     

Single site electromyograph amplitude estimation

Previous investigators have experimentally demonstrated and/or analytically predicted that temporal whitening of the surface electromyograph (EMG) waveform prior to demodulation improves the EMG amplitude estimate. However, no systematic study of the influence of various whitening filters upon amplitude estimate performance has been reported. The authors describe a phenomenological mathematical model of a single site of the surface EMG waveform and reports on experimental studies which examined the performance of several temporal whitening filters. Surface EMG waveforms were sampled 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). A moving average root mean square estimator (245 ms window) provided an average±standard deviation (A±SD) SNR of 10.7±3.3 for the individual recordings. Temporal whitening with one fourth-order whitening filter designed per site improved the A±SD SNR to 17.6±6.0     

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.     

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.     

Adaptive template filtering for signal-to-noise ratio enhancementin magnetic resonance imaging

In this paper, a local shape-adaptive template filtering is proposed for the enhancement of the signal-to-noise ratio (SNR) without the loss of resolution in magnetic resonance (MR) imaging. Unlike conventional filtering, where the template shape and coefficients are fixed, multiple templates are defined in the proposed algorithm. An optimal template is selected and optimal filtering, based on the template, is applied on a pixel-by-pixel basis. Using the proposed process, edge blurring is minimized and SNR enhancement is maximized by selecting the optimally matched template. Compared to existing two-dimensional (2-D) adaptive linear least square error (LLSE) filters or direction-adaptive recursive filters, the proposed adaptive template filter provides higher SNR and sharper edges for both MR and artificial resolution phantom images.     

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.     

Design of perturbation signals for the estimation of proprioceptive reflexes

This study aimed to identify the functional contribution of reflexes to human motor control during posture maintenance. Continuous random force disturbances were applied at the hand while the subjects were instructed to minimize the deviation resulting from the force disturbances. The results were analyzed in the frequency domain with frequency response functions (FRFs). Two FRFs were evaluated: 1) the mechanical admittance and 2) the reflexive impedance, expressing the dynamic relation between position and muscle activation (assessed via electromyography, EMG). The reflexive impedance is a direct measure of the proprioceptive reflexes. To record all relevant dynamical characteristics of the arm, wide bandwidth signals were used as force disturbance. Distributing the power of the signal over fewer frequencies within the bandwidth improved the signal-to-noise-ratio SNR of the EMG recordings, facilitating reliable estimation of the reflexive impedance. The coherence indicated that the relation between force disturbance and EMG is linear under the given conditions and improved with the SNR. The method of designing disturbance signals and the estimation of the reflexive impedance are useful for studies aiming to quantify proprioceptive reflexes and to investigate its functionality.     

Conjugate linear filtering

Aspects of optimum filtering for complex valued random processes are presented. Ordinary linear filters are complemented with conjugate linear filters. It is found that the incorporation of conjugate linear filtering improves signal-to-noise ratio by a factor of two in matched filter receivers. For optimum least squares filtering the inclusion of conjugate processing reduces mean-square error by a factor as great as two; the improvement depends primarily on the degree of correlation between the real and imaginary parts of the signal process. The analysis utilizes special correlation properties of receiver noise. Also, in the absence of phase lock, conjugate linear processing offers no improvement. Finally, it is observed that in the Gaussian case the least squares nonlinear receiver for modulations consists of the derived linear-conjugate linear receiver followed by demodulators comparable to those used in practice.     

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.