A Procedure for Decomposing the Myoelectric Signal Into Its Constituent Action Potentials?Part I: Technique, Theory, and Implementation

A technique has been developed which enables the decomposition (separation) of a myoelectric signal into its constituent motor unit action potential trains. It consists of a multichannel (via one electrode) myoelectric signal recording procedure, a data compression algorithm, a digital filtering algorithm, and a hybrid visual-computer decomposition scheme. The algorithms have been implemented on a PDP 11/34 computer. Of the four major segments of the technique, the decomposition scheme is by far the most involved. The decomposition algorithm uses a-sophisticated template matching routine and details of the firing statistics of the motor units to identify motor unit action potentials in the myoelectric signal, even when they are super-imposed with other motor unit action potentials. In general, the algorithms of the decomposition scheme do not run automatically. They require input from the human operator to maintain reliability and accuracy during a decomposition.     

AR modeling of myoelectric interference signals during a rampcontraction

The authors investigated the time-varying behavior of the autoregressive (AR) parameters in a myoelectric (ME) signal detected during a linear force increasing contraction. The AR parameters of interest mere the reflection coefficients, the AR model spectrum, and the prediction errors. The authors used well-conditioned ME signals for which the complete time record of the motor units firings was available. In addition, the influence of the recruitment of a new motor unit, the conduction velocity of action potentials, and additive broad-band noise were investigated using simulated ME signals. The simulated ME signals were constructed from a selected group of the available motor unit action potential trains. The results revealed that, as the contraction progressed, the AR parameters displayed a time-varying behavior which coincided with the recruitment of newly recruited motor units whose spectrum of the waveform differed from that of the rest of the ME signal. This property of the AR parameters was obscured by the presence of broad-band noise and low-amplitude motor unit action potentials, both of which are more pronounced during low-level force contractions     

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     

Modeling of muscle motor unit innervation process correlation and common drive

Concurrently active motor units (MUs) of a given muscle can exhibit a certain degree of synchronous firings, and a certain degree of common variation in their firing rates. The former property is referred to as motor unit synchrony in the literature, which is termed motor unit innervation process (MUIP) correlation in this study. The latter is referred to as motor unit common drive and can be quantified by the common drive coefficient, which is the correlation coefficient between the smoothed firing rates of the two MUs. Both properties have important roles and implications in the generation and resulting characteristics of the myoelectric signal and for the development of signal processing algorithms in myoelectric signal (MES) applications. In order to study these implications and characteristics, in this paper estimation procedures are developed to quantify the degree of MUIP correlation and common drive as functions of physiological parameters. Also, the interaction between MUIP correlation and motor unit common drive is studied in a physiologically realistic simulation model. Neurons modeled by Hodgkin-Huxley systems form the framework of the simulation model in which excitation and synaptic characteristics can be modified. MUIP correlation and common drive degree and interaction are studied through a number of simulations. To support the simulation results, experimental in vivo motor unit trains were collected at low levels of contraction from 11 subjects, and decomposed into the constituent unit trains giving 50 concurrently active motor unit pairs. The simulation demonstrated that the innervation process correlation coefficient is controlled primarily by the postsynaptic conductance, gsyn, and was less than 0.05 mS/cm2 for realistic values of gsyn. The common drive was found to be controlled by the exciting neuron input with no statistically significant interaction between it and the MUIP correlation. The experimental data gave results in close agreement with those of the simulation.     

The contribution of motor unit pairs to the correlation functions computed from surface myoelectric signals

The contribution of motor unit action potential trains (MUAPT) of distinct motor units (MU) to the crosscorrelation function between myoelectric signals (MES) recorded at the skin surface is studied. In specific, the significance of the correlation between the firing activity of concurrently active MUs (which results in cross-terms in the overall correlation function) is compared to the representation obtained using the contributions of single MUs at each recording site (auto-terms). A model for the generation of surface MUAPs is combined with the generation of MU firing statistics in order to obtain surface MUAPTs. MU firing statistics are simulated to incorporate MU synchronization levels reported in the literature. Alternatively, experimental firing statistics are fed to the model generating the MUAPTs. The contribution of individual MU pairs to the global myoelectric signal correlation function is assessed. Results indicate that the cross-terms from different MUs decrease steadily contributing very little to the overall correlation for record lengths as short as 30 s. Thus, the error expected when computing the crosscorrelation function between two channels of MES as the superposition of the auto-terms contributed by single MUs (i.e., ignoring the cross-terms from different MUs) is shown to be very small.     

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.     

The Myoelectric Signal of Electrically Stimulated Muscle During Recruitment: An Inherent Feedback Pareter for a Closed-Loop Control Scheme

The myoelectric profile of an electrically stimulated muscle with separate and simultaneous control of firing rate and recruitment was determined. The signal consists of low amplitude, desynchronous discharge at low recruitment levels and exhibits monotonic, distinct compound action potentials at moderate to full recruitment. The myoelectric signal-force model is described by sigmoidal function when the signal is represented by its median frequency (MF), rms, or mean absolute value (MAV) at firing rates inducing just above fused force response (~28 pps). At firing rates corresponding to the maximal tetanic force of the muscle (~51 pps) the MES-force model is represented by a second-order polynomial for MF, rms, and MAV. Dynamic tracking of force induced by a sinusoidal recruitment/derecruitment of the muscle's motor unit pool at frequencies in the range of 0-1 Hz show that the MAV is independent, whereas the rms and MF are dependent on tracking frequency. The linearized MAV-force model was found superior for use as a sensorless force feedback measurement in a closed-loop control scheme aimed at restoration of regulated movement to a paralyzed limb joint.     

A wavelet-based continuous classification scheme for multifunction myoelectric control

This work represents an ongoing investigation of dexterous and natural control of powered upper limbs using the myoelectric signal. When approached as a pattern recognition problem, the success of a myoelectric control scheme depends largely on the classification accuracy. A novel approach is described that demonstrates greater accuracy than in previous work. Fundamental to the success of this method is the use of a wavelet-based feature set, reduced in dimension by principal components analysis. Further, it is shown that four channels of myoelectric data greatly improve the classification accuracy, as compared to one or two channels. It is demonstrated that exceptionally accurate performance is possible using the steady-state myoelectric signal. Exploiting these successes, a robust online classifier is constructed, which produces class decisions on a continuous stream of data. Although in its preliminary stages of development, this scheme promises a more natural and efficient means of myoelectric control than one based on discrete, transient bursts of activity.     

Unsupervised pattern recognition for the classification of EMGsignals

The shapes and firing rates of motor unit action potentials (MUAPs) in an electromyographic (EMG) signal provide an important source of information for the diagnosis of neuromuscular disorders. In order to extract this information from EMG signals recorded at low to moderate force levels, it is required: i) to identify the MUAPs composing the EMG signal, ii) to classify MUAPs with similar shape, and iii) to decompose the superimposed MUAP waveforms into their constituent MUAPs. For the classification of MUAPs two different pattern recognition techniques are presented: i) an artificial neural network (ANN) technique based on unsupervised learning, using a modified version of the self-organizing feature maps (SOFM) algorithm and learning vector quantization (LVQ) and ii) a statistical pattern recognition technique based on the Euclidean distance. A total of 1213 MUAPs obtained from 12 normal subjects, 13 subjects suffering from myopathy, and 15 subjects suffering from motor neuron disease were analyzed. The success rate for the ANN technique was 97.6% and for the statistical technique 95.3%. For the decomposition of the superimposed waveforms, a technique using crosscorrelation for MUAP's alignment, and a combination of Euclidean distance and area measures in order to classify the decomposed waveforms is presented. The success rate for the decomposition procedure was 90%     

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.     

Noninvasive estimation of motor unit conduction velocity distribution using linear electrode arrays

Determining the conduction velocity of motor unit action potentials is one of the most important problems in surface electromyography. The estimate of one average conduction velocity value depends on a variety of uncontrollable factors. More meaningful information is obtained from the estimation of the distribution of the different delays in the myoelectric signals. A solution to the problem is the separation and characterization of the individual components propagating at different velocities. A technique, based on surface electrode array recording, is proposed to estimate motor unit conduction velocity distribution. The method consists in the identification of the single action potentials in the time scale domain (with the continuous wavelet transform) and in the estimation of their conduction velocities based on the beamforming algorithm. The performances of the technique have been evaluated using simulated and real myoelectric signals. The results demonstrate that the technique is accurate and reliable. The method may be useful for the diagnosis of neuromuscular disorders, for the monitoring of muscle fatigue and for noninvasive investigation of individual motor units.     

The Effect of Electromyographic Jitter on Single Motor Unit EMG Potentials

Variability between successive discharges of the single motor unit potential in the biceps brachii muscle, due to electromyographic (EMG) jitter, has been investigated. This jitter results from random arrival times of single fiber potentials at the electrode. A computer model has been used to generate single motor unit potentials incorporating the effects of EMG jitter. A computed variance peak was found in the fast rising edge of the motor unit potential for electrode sites outside of the motor unit territory. This peak was also observed in experimental data recorded from human subjects. The peak variance outside of the motor unit territoxy has also been mathematically related to the number of fibers in the motor unit, jitter, and the slope of the mean action potential at the center of the fast rising edge.     

Decomposition of intramuscular EMG signals using a heuristic fuzzy expert system

Although increasingly sophisticated algorithms have been proposed to decompose intramuscular electromyography signals into the concurrent activities of individual motor units (MUs), the human operator is still able to improve decomposition results by visual inspection. The rationale for this paper was to combine components from previous decomposition procedures in an expert systems approach utilizing fuzzy logic and attempting to replicate the thought process of an accomplished decomposer in order to minimize the user interaction subsequently needed to enhance decomposition results. The decomposition procedure is discussed and examples are given of the type of information it can yield. The method has been used to identify the discharge activities of up to 15 MUs with up to 95$%$ accuracy.      

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.     

Concentric-ring electrode systems for noninvasive detection ofsingle motor unit activity

New recording techniques for detecting surface electromyographic (EMG) signals based on concentric-ring electrodes are proposed in this paper. A theoretical study of the two-dimensional (2-D) spatial transfer function of these recording systems is developed both in case of rings with a physical dimension and in case of line rings. Design criteria for the proposed systems are presented in relation to spatial selectivity. It is shown that, given the radii of the rings, the weights of the spatial filter can be selected in order to improve the rejection of low spatial frequencies, thus increasing spatial selectivity. The theoretical transfer functions of concentric systems are obtained and compared with those of other detection systems. Signals detected with the ring electrodes and with traditional one-dimensional and 2-D systems are compared. The concentric-ring systems show higher spatial selectivity with respect to the traditional detection systems and reduce the problem of electrode location since they are invariant to rotations. The results shown are very promising for the noninvasive detection of single motor unit (MU) activities and decomposition of the surface EMG signal into the constituent MU action potential trains.     

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.     

基于GPU的SAR方位向信号分解的高效实现方法

提出了一种基于图形处理器(GPU)的SAR方位向信号分解的高效实现方法。SAR方位向信号可以通过四参数Chirplet分解方法来分解。此方法的关键难题是计算量过大,计算量主要由2部分组成:构建Chirp原子库,以及SAR方位向信号在过完备库上分解的计算量。与传统的CPU相比,GPU更加适用于密集型和大量数据并行化的计算。提出将算法的核心部分移植到GPU上进行并行计算,充分挖掘其运算潜能。结果表明:该方法与传统的基于CPU的算法相比有两位数以上的效率提升。     

A centrosymmetric kernel decomposition for time-frequency distribution computation

Time-frequency distributions (TFDs) are bilinear transforms of the signal and, as such, suffer from a high computational complexity. Previous work has shown that one can decompose any TFD in Cohen's class into a weighted sum of spectrograms. This is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of windows. In this paper, we introduce a mathematical framework for kernel decomposition such that the windows in the decomposition algorithm are not arbitrary and that the resulting decomposition provides a fast algorithm to compute TFDs. Using the centrosymmetric structure of the time-frequency kernels, we introduce a decomposition algorithm such that any TFD associated with a bounded kernel can be written as a weighted sum of cross-spectrograms. The decomposition for several different discrete-time kernels are given, and the performance of the approximation algorithm is illustrated for different types of signals.     

Operator error in a level coded myoelectric control channel

Two forms of error exist in the level coded myoelectric control channel: system error and operator error. Currently, in level coded (three-state) myoelectric prostheses, target and switching level settings are optimized for the presence of system error only. In this study, system error was minimized in order to examine operator error. The magnitude of the operator error was found to exceed the magnitude of the experimental system error as well as the system error associated with a typical prosthesis control unit. These findings suggest that operator error should be considered when optimizing target levels and decision boundaries for level coded myoelectric prosthesis controllers. Since the operator response was estimated to be normally distributed, it is described by its mean and standard deviation. This information can be used to determine the desired optimal settings     

A hybrid classifier fusion approach for motor unit potential classification during EMG signal decomposition

In this paper, we propose a hybrid classifier fusion scheme for motor unit potential classification during electromyographic (EMG) signal decomposition. The scheme uses an aggregator module consisting of two stages of classifier fusion: the first at the abstract level using class labels and the second at the measurement level using confidence values. Performance of the developed system was evaluated using one set of real signals and two sets of simulated signals and was compared with the performance of the constituent base classifiers and the performance of a one-stage classifier fusion approach. Across the EMG signal data sets used and relative to the performance of base classifiers, the hybrid approach had better average classification performance overall. For the set of simulated signals of varying intensity, the hybrid classifier fusion system had on average an improved correct classification rate (CCr) (6.1%) and reduced error rate (Er) (0.4%). For the set of simulated signals of varying amounts of shape and/or firing pattern variability, the hybrid classifier fusion system had on average an improved CCr (6.2%) and reduced Er (0.9%). For real signals, the hybrid classifier fusion system had on average an improved CCr (7.5%) and reduced Er (1.7%).