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.     

Estimation of motor unit twitches

This study deals with estimation of the mechanical twitch of a single motor unit in human muscle during voluntary contraction. The existing estimation method is based on averaging of the force produced by the whole muscle, using the motor unit action potential for triggering. This method leads to underestimation of twitch amplitude and rise time due to partial fusion of the twitches, even at the lowest firing rates which can be maintained during voluntary contraction. To obtain unbiased twitch estimates, even when the twitches partially fuse, three versions of a nonparametric system identification method are explored: averaging plus least squares estimation; least squares estimation; and Markov estimation. Averaging plus least squares estimation give poorer noise reduction than least squares estimation. The noise reduction obtained by least squares estimation is about the same as the noise reduction obtained by averaging alone. The noise is mainly due to the contraction of all active motor units, except the unit being studied. This noise has dominating low-frequency components. Markov estimation takes the spectrum of the noise into account, and thus in most cases provides a better estimate than least squares estimation.     

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.     

Investigation on parametric analysis of dynamic EMG signals by amuscle-structured simulation model

In the analysis of electromyographic (EMG) signals during dynamic movement, we have proposed an estimation algorithm for the time-varying parameters of an autoregressive model. The parameters correspond to less biased time-varying reflection coefficients. We determined the less biased estimation using a locally quasi-stationary model and named these parameters "k parameters." We estimated k parameters up to the fifth order for the surface EMG signals of a masseter muscle during rapid open-close movement of the lower jaw, a ballistic contraction, and fatigue. According to the results, the time courses of the k parameters displayed remarkable properties. In order to study the behavior of k parameters physiologically, we produced a muscle-structured simulation model based on anatomical and physiological data. The simulation results suggested that the behavior of the third parameter is related to the number of active motor units (MU's) at the shallow layer of a muscle. The detailed recruitment mechanism in terms of the MU's types has not yet been solved. Although further study is required, the parametric analysis using k parameters offers a new perspective for evaluation of muscle dynamics during several movements.     

Automatic decomposition of selective needle-detected myoelectricsignals

A procedure for the storage and documentation of myoelectric signals has been developed that consists of a selective needle signal detection protocol, a data collection-compression routine, an adaptive signal decomposition algorithm, and an error filter. The collection-compression routine stores only fixed-length signal epochs that contain motor unit action potentials (MUAPs) detected during individual motor unit firings. The decomposition algorithm assigns the collected MUAPs to candidate motor units, based on template matching using power-spectrum domain features and firing-time criteria calculated from the motor units' firing statistics. Power spectrum features allow the use of Nyquist sampling rates and remove the need for template alignment. The algorithm is adaptive and attempts to minimize dependent errors. The error filter, using firing statistics, accounts for unresolved superpositions and other decomposition errors. Using a standard TECA single-fiber needle electrode, signal recorded during isometric, constant, or slow force-varying contractions of up to 50% of the maximal voluntary contraction level, have been successfully analyzed     

Decomposition of multiunit electromyographic signals

We have developed a comprehensive technique to identify single motor unit (SMU) potentials and to decompose overlapped electromyographic (EMG) signals into their constituent SMU potentials. This technique is based on one-channel EMG recordings and is easily implemented for many clinical EMG tests. There are several distinct features of our technique: 1) it measures waveform similarity of SMU potentials in the wavelet domain, which gives this technique significant advantages over other techniques; 2) it classifies spikes based on the nearest neighboring algorithm, which is less sensitive to waveform variation; 3) it can effectively separate compound potentials based on a maximum signal energy deduction algorithm, which is fast and relatively reliable; and 4) it also utilizes the information on discharge regularities of SMU's to help correct possible decomposition errors. The performance of this technique has been evaluated by using simulated EMG signals composed of up to eight different discharging SMU's corrupted with white noise, and also by using real EMG signals recorded at levels up to 50% maximum voluntary contraction. We believe that it is a very useful technique to study SMU discharge patterns and recruitment of motor units in patients with neuromuscular disorders in clinical EMG laboratories.     

Evaluation of the Effectiveness of EMG Parameters in the Study of Neurogenic Diseases-A Statistical Approach Using Clinical and Simulated Data

Of interest here is the problem of determining to what extent combinations of parameters derived from the EMG signal allow 1) discriminating two subclasses of neurogenic myopathies, and 2) recognizing different morphologies of the motor unit action potential underlying a measured EMG signal. EMG signals measured on clinical subjects and computer-simulated EMG signals were collected in a database and used cooperatively in this study. Suitable statistical models were developed which allow testing hypotheses on the role of accepted EMG parameters for the two purposes named above, and deriving new suitable combinations of EMG parameters. Results support the hypothesis that frequency-domain parameters are very clearly related to the morphology of the motor unit action potential. However, the attempt to use them in order to discriminate the two pathologic subclasses considered appears to be jeopardized by the fact that the signal may be measured in territories which do not reflect the morphology of the motor unit action potential dominant in such subclasses. On the basis of time-domain parameters, a significant discrimination was obtained between the two subclasses, and such discrimination is related mainly to a time-domain parameter which has already proved successful in the discrimination between myopathic and normal subjects. Data corroborate the hypothesis that the diagnostic yield improves when time-domain EMG parameters are measured at recruitment.     

A model for the generation of synthetic intramuscular EMG signals to test decomposition algorithms

As more and more intramuscular electromyogram (EMG) decomposition programs are being developed, there is a growing need for evaluating and comparing their performances. One way to achieve this goal is to generate synthetic EMG signals having known features. Features of interest are: the number of channels acquired (number of detection surfaces), the number of detected motor unit action potential (MUAP) trains, their time-varying firing rates, the degree of shape similarity among MUAPs belonging to the same motor unit (MU) or to different MUs, the degree of MUAP superposition, the MU activation intervals, the amount and type of additive noise. A model is proposed to generate one or more channels of intramuscular EMG starting from a library of real MUAPs represented in a 16-dimensional space using their Associated Hermite expansion. The MUAP shapes, regularity of repetition rate, degree of superposition, activation intervals, etc. may be time variable and are described quantitatively by a number of parameters which define a stochastic process (the model) with known statistical features. The desired amount of noise may be added to the synthetic signal which may then be processed by the decomposition algorithm under test to evaluate its capability of recovering the signal features.     

船舶航行辐射噪声信号仿真方法研究

船舶航行辐射噪声是被动声纳探测、声纳目标识别、听音判型等工作的重要信息源,其信号仿真是解决上述研究工作中噪声样本类型少或数量不足的有效方法,前提是所仿真信号必须满足逼真度要求。提出了一种基于实测信号重构的船舶航行辐射噪声信号仿真方法。通过谱估计提取信号的连续谱、线谱、调制谱特征,根据谱估计数据合成满足信号谱特征要求的船舶航行辐射噪声,并通过听觉感受调整调制谱参数。仿真结果显示所合成船舶航行辐射噪声信号能够从谱估计和听觉感受两方面逼近实测辐射噪声信号。      

A Reliable Myoelectric Signal Detector Based on the Propagation Characteristics of Motor Unit Action Potentials

A method was proposed for detecting and rejecting motion artifacts superimposed on myoelectric (ME) signals which are used in the estimation of muscular activity, in the control of powered prostheses, and in other applications. The method is based on the propagation characteristics of motor unit action potentials derived with multiple surface electrodes placed along the muscle fibers. The contamination of artifacts was detected by the decrease of the normalized correlation coefficient calculated at the time shift corresponding to the potential propagation. The product of two correlated signals was found to be less affected by the artifacts and was a better estimate of muscular activity than the root mean square of the ME signal which is conventionally used in the applications of ME signals.     

Characterization of signals and noise rejection with bipolarlongitudinal intrafascicular electrodes

Longitudinal intrafascicular electrodes (LIFEs) are fine electrodes threaded into the extracellular space between axons in peripheral nerves or spinal roots. The authors are developing these electrodes for application in functional electrical stimulation and in basic physiology. An area of concern in chronic recording application of LIFEs is the possibility of electromyogram and other external noise sources masking the recorded neural signals. The authors characterized neural signals recorded by LIFEs and confirmed by three independent methods that increasing interelectrode spacing for bipolar LIFEs increases signal amplitude. The spectrum of neural signal from bipolar and monopolar LIFE lies between 300 Hz and 10 kHz. The amplitude of the spectrum increases with increasing interelectrode spacing, although the distribution is not affected. Single unit analysis of LIFE recordings show that they record selectively from units closest to the electrode active site. Units with conduction velocities ranging from 50-120 m/s were identified. Extraneural noise, as stimulus artifact or electromyogram, is much reduced with bipolar LIFE recording, as compared to monopolar recordings. Relative improvement in neural signal to extraneural noise increases with interelectrode spacing up to about 2 mm. Since there is no further improvement beyond 2 mm, the authors conclude that the preferred interelectrode spacing for bipolar LIFEs is 2 mm     

Manipulation of Muscle Force with Various Firing Rate and Recruitment Control Strategies

A computer-controlled, dual-channel neuromuscular stimulation system capable of manipulating skeletal muscle force with a wide range of action potential firing rates and motor-unit recruitment control strategies was designed and evaluated on the m. gastrocnemius muscle of the cat. The muscle force could be controlled with control strategies in which motor unit recruitment accounted for from 50 percent and up to 100 percent of the initial muscle force while firing rate induced the remaining force segment. The force response to linearly increasing recruitment was linear, whereas a saturation nonlinearity was evident in response to the firing rate input. Initial and terminal nonlinear force segments during 100 percent recruitment range were shown to be due to the viscoelastic components of the muscle fibers and their tendons. Recruitment of the muscle's motor units at rates that generated from 36 percent/s and up to 360 percent/s of the maximal force range was shown to correlate linearly to the input stimulus (R 0.9889). Reduction of the maximal firing rate from 55 to 40 pps showed that although minimization of fatigue at a cost of 10 percent reduction in the maximal force is possible, the correlation of the force response to the input signal remains high (R 0.9929) and linear. Some preliminary conclusions about rehabilitative applications were drawn based on the data presented in conjunction with previous studies.     

Time-frequency analysis of myoelectric signals during dynamic contractions: a comparative study

In this paper, we introduce the nonstationary signal analysis methods to analyze the myoelectric (ME) signals during dynamic contractions by estimating the time-dependent spectral moments. The time-frequency analysis methods including the short-time Fourier transform, the Wigner-Ville distribution, the Choi-Williams distribution, and the continuous wavelet transform were compared for estimation accuracy and precision on synthesized and real ME signals. It is found that the estimates provided by the continuous wavelet transform have better accuracy and precision than those obtained with the other time-frequency analysis methods on simulated data sets. In addition, ME signals from four subjects during three different tests (maximum static voluntary contraction, ramp contraction, and repeated isokinetic contractions) were also examined.     

一种新的含噪混沌信号降噪算法

该文针对低信噪比、非高斯加性噪声和混沌动力学系统参数未知的含噪混沌信号降噪问题,提出了一种基于粒子滤波(Particle Filtering, PF)的降噪新算法。该算法将混沌信号和动力学系统中的未知参数作为一个多维状态矢量,利用PF方法递推计算多维状态矢量的联合后验概率分布,进而实现了对混沌信号的最优估计。对于混沌信号轨道分离过快所导致的退化问题,提出了有效的解决方法,并利用核平滑和自回归(Auto-Regression, AR)模型建模的方法分别实现了非时变以及时变参数的递推估计。仿真实验的结果表明,与现有的降噪方法相比,该文提出的新算法能够更加有效地抑制含噪混沌信号中的加性噪声。     

Two dimensional autoregressive estimation from noisy observations as a quadratic eigenvalue problem

We consider the problem of two dimensional (2-D) autoregressive (AR) parameter estimation in the presence of observation noise. The proposed method is based on Yule-Walker Equations. We express the Yule Walker equations as a quadratic eigenvalue problem then by solving these equations, the parameters of the signal and noise are estimated. We also apply the proposed method to (2-D) spectrum estimation of the sinusoidal signals in noise. The performance of the proposed method is evaluated by computer simulation examples.     

基于空间演化谱的Chirp信号极化和DOA的联合估计

本文研究了时变幅度Chirp信号的演化谱,提出了分别在时间轴和频率轴上聚集能量的方法,改善了演化周期谱的能量聚集性。同时,基于时变幅度Chirp信号的空间演化谱,提出了一种新的空间极化时频分布,用此空间极化时频矩阵代替自相关矩阵估计信号子空间和噪声子空间。采用L型正交短偶极子阵列,用ESPRIT算法实现了多Chirp信号DOA和极化参量的联合估计,并提出一种新的多信号参量配对的方法。通过仿真将本文的算法其他一些算法进行了比较。     

Stabilization of smoothness priors time-varying autoregressive models

The stability of time-varying autoregressive (AR) models is an important issue in such applications as time-varying spectrum estimation and electroencephalography simulation and estimation. In some cases, such as time-varying spectrum estimation, the models that exhibit roots near unit moduli are difficult to use. Thus a tighter stability condition such as stability with a positive margin is needed. A time-varying AR model is stable with a positive margin if the moduli of the roots of the time-varying characteristic polynomial are somewhat less than unity for every time instant. Recently, a new method for the estimation of the time-varying AR models was introduced. This method is based on the interpretation of the underdetermined time-varying prediction equations as an ill-posed inverse problem that is solved by Tikhonov regularization. The method is referred to as the deterministic regression smoothness priors (DRSP) scheme. In this paper, a stabilization method in which the DRSP scheme is augmented with nonlinear stability constrainst is proposed. The problem is formulated so that stability with a positive margin can also be achieved. The problem is solved iteratively with an exterior point algorithm. The performance of the algorithm is studied with a simulation. It is shown that the proposed approach is well suited to stable modeling of signals containing narrowband transitions.     

A Nonstationary Model for the Electromyogram

A theoretical model of the electromyographic (EMG) signal has been developed. In the model, the neural pulse train inputs were considered to be point processes which passed through linear, time-invariant systems that represented the respective motor unit action potential. The outputs were then summed to produce the EMG. It was assumed, that in the production of muscle force, the controlled parameter was the number of active motor units, n(t). The model then showed that the EMG can be represented as an amplitude modulation process of the form EMG = [Kn(t)1/2 w(t) with the stochastic process, w(t), having the spectral and probability characteristics of the EMG during a constant contraction. Various assumptions made in the model development have been verified by experiments.     

High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection

Chaotic signals with a flat power spectrum over 20 GHz have been generated using two commercially available semiconductor lasers coupled in a unidirectional master-slave scheme. The master laser has an external optical feedback that induces optical chaos in the laser output. A part of the chaotic light output from the master laser is injected into the slave laser. We experimentally demonstrated the generation of broad-band signals up to 22 GHz using lasers whose relaxation oscillation frequency in the free-running state is only around 6.4 GHz. We also show that the experimental results can be well reproduced by numerical simulations using two coupled rate equations. The numerical investigation shows that the high-frequency broad-band signal generation is owing to two key effects: high-frequency oscillations as a result of beating between the master and slave laser lights, and spectrum flattening due to the injection of the chaotic signal. The flatness, stability, and tunability of the power spectra demonstrated in our experiments suggests that the proposed system can be potentially useful for generation of high-frequency broad-band random signals.     

Automated decomposition of intramuscular electromyographic signals

We present a novel method for extracting and classifying motor unit action potentials (MUAPs) from one-channel electromyographic recordings. The extraction of MUAP templates is carried out using a symbolic representation of waveforms, a common technique in signature verification applications. The assignment of MUAPs to their specific trains is achieved by means of repeated template matching passes using pseudocorrelation, a new matched-filter-based similarity measure. Identified MUAPs are peeled off and the residual signal is analyzed using shortened templates to facilitate the resolution of superimpositions. The program was tested with simulated data and with experimental signals obtained using fine-wire electrodes in the biceps brachii during isometric contractions ranging from 5% to 30% of the maximum voluntary contraction. Analyzed signals were made of up to 14 MUAP trains. Most templates were extracted automatically, but complex signals sometimes required the adjustment of 2 parameters to account for all the MUAP trains present. Classification accuracy rates for simulations ranged from an average of 96.3% +/- 0.9% (4 trains) to 75.6% +/- 11.0% (12 trains). The classification portion of the program never required user intervention. Decomposition of most 10-s-long signals required less than 10 s using a conventional desktop computer, thus showing capabilities for real-time applications.