Frequency Parameters of the Myoelectric Signal as a Measure of Muscle Conduction Velocity

Dunrng a sustained muscle contraction, the spectrum of the myoelectric signal is known to undergo compression as a function of time. Previous investigators have shown that the frequency compression is related to the decreasing conduction velocity of the muscle fibers. It is proposed that the frequency compression may be tracked by obtaining a continuous estimate of a characteristic frequency of the spectrum, such as the mean and median, or the ratio of low-frequency components to high-frequency components of the spectrum. A theoretical analysis was performed to investigate the restrictions in estimating the three parameters, as well as their sensitivity to the conduction velocity. The ratio parameter was found to be most sensitive to conduction velocity, but was the least reliable of the three. The median frequency was the least sensitive to noise. Therefore, from a theoretical point of view, the median frequency is the preferred parameter. A technique is described which determines an unbiased consistent estimate of the median frequency. The technique may be readily implemented in analog hardware.     

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.     

Errors in frequency parameters of EMG power spectra

Frequency shifts in random signals, e.g., EMG or Doppler ultrasound, can be followed by monitoring one or more parameters of the power spectrum. When such a frequency parameter is determined over a finite length of the signal, a random error and sometimes a systematic error or bias are introduced. Approximate expressions, in terms of moments of the power spectrum, have been derived for bias and standard deviation of the estimates for mean frequency, zero-crossing frequency, and fractile frequency (of which the median frequency is a special case). Experimental results from surface EMG recordings of three human muscles in constant force isometric contractions were in agreement with the theoretical predictions. In this case the mean frequency had the smallest random error. It turned out that the measured values of the zero-crossing frequency can deviate considerably from the predictions by the Rice formula when the amplitude distribution is not exactly Gaussian. In the presence of noise, all frequency parameters show a systematic deviation, depending on the signal-to-noise ratio. In addition to known results on this deviation for mean and zero-crossing frequency, an exact and an approximate expression for the fractile frequency are given. In the case of EMG plus wide-band white noise, the median frequency has the best immunity to noise.     

基于二维幅值谱的正弦信号频率估计

信号中含有噪声或非整周期截断时发生的频谱泄漏是导致正弦信号频率估计精度不高的主要原因。针对这一问题,从扩展信号频谱表征方式出发,将经典幅值谱扩展至不受频谱泄漏制约、表现力更强、可读性更好的二维幅值谱。与经典幅值谱相比,二维幅值谱除包含信号的频率个数、幅值信息外还包含了易于获取的周期信息,且具有一定的抗噪性,在信噪比低至-10dB时仍有较好表现力。提出一种估计方法,先从二维幅值谱中估计出信号的周期T,然后根据信号采样频率、信号频率、以及信号周期T之间的定量关系完成信号的频率估计。实验结果证明了该方法的有效性。基于二雏幅值谱的正弦信号频率估计方法为正弦信号的频谱估计提供了一种新思路。     

Assessment of average muscle fiber conduction velocity from surface EMG signals during fatiguing dynamic contractions

In this paper, we propose techniques of surface electromyographic (EMG) signal detection and processing for the assessment of muscle fiber conduction velocity (CV) during dynamic contractions involving fast movements. The main objectives of the study are: 1) to present multielectrode EMG detection systems specifically designed for dynamic conditions (in particular, for CV estimation); 2) to propose a novel multichannel CV estimation method for application to short EMG signal bursts; and 3) to validate on experimental signals different choices of the processing parameters. Linear adhesive arrays of electrodes are presented for multichannel surface EMG detection during movement. A new multichannel CV estimation algorithm is proposed. The algorithm provides maximum likelihood estimation of CV from a set of surface EMG signals with a window limiting the time interval in which the mean square error (mse) between aligned signals is minimized. The minimization of the windowed mse function is performed in the frequency domain, without limitation in time resolution and with an iterative computationally efficient procedure. The method proposed is applied to signals detected from the vastus laterialis and vastus medialis muscles during cycling at 60 cycles/min. Ten subjects were investigated during a 4-min cycling task. The method provided reliable assessment of muscle fatigue for these subjects during dynamic contractions.     

An Application of Signal Processing Techniques to the Study of Myoelectric Signals

This paper describes the use of power spectral density and cumulative power functions in the examination of the electromyogram (EMG). The EMG signals were obtained with surface electrodes from two muscles, the flexor pollicis brevis and the extensor digitorum, in four subjects. Each muscle was studied at two levels of contraction, both before and during fatigue. The power spectral density functions are compared, using a cumulative power difference function and the mean frequency of the spectrum, to determine differences between loading conditions in an individual muscle, before and during fatigue, between different muscles, between individuals (same muscle), and combinations of these conditions.     

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.     

Muscle Fatigue Monitor (MFM): Second Generation

As a muscular contraction is sustained, the spectrum of the myoelectric signal is shifted toward the lower frequencies. This spectral shift is associated with localized muscular fatigue. This communication describes a computer-assisted device, the Muscle Fatigue Monitor, that performs a quantitative assessment of localized muscular fatigue by tracking changes in the median frequency parameter of the myoelectric signal's spectrum.     

Muscle Fatigue Monitor: A Noninvasive Device for Observing Localized Muscular Fatigue

As a muscular contraction is sustained, the spectrum of the myoelectric signal is compressed into lower frequencies. This spectral compression has been associated with localized muscular fatigue by several investigators. A device is presented that implements a technique to track the spectral compression by calculating the median frequency and two other parameters of the spectrum. The device is referred to as the muscle fatigue monitor (MFM) and is built with analog circuitry so that parameters are calculated and displayed in real-time and on-line. The technique is based on modulated filters which are implemented by using periodically-controlled switches to effectively vary the cutoff frequencies of the filters. The median frequency of a myoelectric signal obtained during a sustained, constant-force, isometric contraction was calculated by the MFM and digital computation. The results obtained by the two techniques were essentially the same, verifying the operation of the MFM.     

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)     

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.     

Standardized evaluation of techniques for measuring the spectralcompression of the myoelectric signal

A digital algorithm was designed to produce band-limited noise with adjustable median frequency and amplitude. This algorithm produces test signals with spectral characteristics typical of those of the surface myoelectric signals encountered in muscle fatigue studies. These synthesized signals provide the basis for standardized evaluation of the performance of various techniques which monitor the spectral compression of the myoelectric signal during muscle fatigue.     

Modeling of surface myoelectric signals. I. Model implementation

The relationships between the parameters of active motor units (MU's) and the features of surface electromyography (EMG) signals have been investigated using a mathematical model that represents the surface EMG as a summation of contributions from the single muscle fibers. Each MU has parallel fibers uniformly scattered within a cylindrical volume of specified radius embedded in an anisotropic medium. Two action potentials, each modeled as a current tripole, are generated at the neuromuscular junction, propagate in opposite directions and extinguish at the fiber-tendon endings. The neuromuscular junctions and fiber-tendon endings are uniformly scattered within regions of specified width. Muscle fiber conduction velocity and average fiber length to the right and left of the center of the innervation zone are also specified. The signal produced by MU's with different geometries and conduction velocities are superimposed. Monopolar, single differential and double differential signals are computed from electrodes placed in equally spaced locations on the surface of the muscle and are displayed as functions of any of the model's parameters. Spectral and amplitude variables and conduction velocity are estimated from the surface signals and displayed as functions of any of the model's parameters. The influence of fiber-end effects, electrode misalignment, tissue anisotropy, MU's location and geometry are discussed. Part II of this paper will focus on the simulation and interpretation of experimental signals.     

Circuit for Monitoring the Median Frequency of the Spectrum of the Surface EMG Signal

The power spectrum of the surface EMG signal is known to undergo a compression towards the lower frequencies during sustained muscle contractions. The median frequency appears to be the preferred parameter to monitor this compression. This paper describes a simple circuit which can provide an estimate of the median frequency.     

Motor Unit Firing Rate During Static Contraction Indicated by the Surface EMG Power Spectrum

In this study, power spectral density functions (PSDF's) were computed of interference EMG of various facial and jaw-elevator muscles during nonfatiguing submaximal static contractions, recorded with surface electrodes. A distinct peak was found in the PSDF's in the frequency region below 40 Hz. It was shown that the peak was due to genuine EMG activity and that it could not be considered as an artifact, which was caused by electrode displacements during contraction. An increase of contraction strength resulted in a shift of the peak to higher frequencies and a decrease of peak amplitude relative to the power spectral estimates above 40 Hz, which were shown to be determined by the shape of the motor unit (MU) action potentials. In accordance with mathematical models of the EMG PSDF, it was demonstrated that the peak indicates the dominant firing rate of the sampled MU's. Our results suggest that this can be defined as the firing rate of the first recruited low-threshold MU's, which may be expected to dominate the interference EMG signal because of their preponderance in number. The data further suggest that the peak can be more readily observed in PSDF's of facial and jaw-elevator muscles than in PSDF's of limb muscles. This might be related to differences in MU firing statistics.     

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.     

Time-frequency parameters of the surface myoelectric signal forassessing muscle fatigue during cyclic dynamic contractions

The time-dependent shift in the spectral content of the surface myoelectric signal to lower frequencies has proven to be a useful tool for assessing localized muscle fatigue. Unfortunately, the technique has been restricted to constant-force, isometric contractions because of limitations in the processing methods used to obtain spectral estimates. A novel approach is proposed for calculating spectral parameters from the surface myoelectric signal during cyclic dynamic contractions. The procedure was developed using Cohen class time-frequency transforms to define the instantaneous median and mean frequency during cyclic dynamic contractions. Changes in muscle length, force, and electrode position contribute to the nonstationarity of the surface myoelectric signal. These factors, unrelated to localized fatigue, can be constrained and isolated for cyclic dynamic contractions, where they are assumed to be constant for identical phases of each cycle. Estimation errors for the instantaneous median and mean frequency are calculated from synthesized signals. It is shown that the instantaneous median frequency is affected by an error slightly lower than that related to the instantaneous mean frequency. In addition, we present a sample application to surface myoelectric signals recorded from the first dorsal interosseous muscle during repetitive abduction/adduction of the index finger against resistance. Results indicate that the variability of the instantaneous median frequency is related to the repeatability of the biomechanics of the exercise.     

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.     

两路微振动信号的光纤F-P腔干涉测量

法布里-珀罗(F-P)腔传感器结构简单,复用能力强,对导致其腔长发生变化的物理量灵敏度高,在超精密测量领域日益受到重视。为了使用一套光纤F-P腔测量两个目标,设计了两路反馈信号光纤F-P腔干涉系统,同时开展两路微振动信号测量。对两路微振动反馈F-P腔干涉信号,经多次取包络分解,得到了高、低频信号频谱,进而计算出待测目标振幅。实验结果表明,通过低频信号恢复待测目标振幅的误差为1.32%,通过高频信号恢复待测目标振幅的误差为6.63%。该方法有效实现了两路反馈光纤F-P腔干涉信号的分离,拓展了测量通道,提高了抗干扰能力。     

基于信道化谱增强的混合DS/FH扩频信号跳速估计

该方法首先利用非线性变换获得携带跳速信息的参考信号,并利用循环谱预估计该信号的频率集;在此基础上,提出一种新的信道化谱增强系统。该系统所具有的外在线性内在非线性(ELIN)特性能够在防止信号失真的前提下有效克服噪声及干扰对后续时频分析的影响;最后,通过SPWVD(平滑伪Wigner-Ville分布)实现精确的跳速估计。该算法无需信号的先验知识,并易于通信侦测接收机实现。仿真实验证明了该算法在低信噪比下对跳速估计的有效性。