Simulation Techniques in Electromyography

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

Spectral Analysis of Surface Motor Unit Action Potentials and Surface Interference Electromyogram

Surface interference electromyograms (EMG's) were recorded from the tibial muscle of a healthy subject during 50 percent maximal contraction and single motor unit action potentials (MUAP's) were isolated by averaging from the interference pattern. The formation of the EMG was simulated by summing isolated MUAP's according to the statistical properties of the corresponding motor unit discharges. Power spectral density functions (PSDF's) were finally computed for single MUAP's as well as for simulated and experimental EMG's and compared with each other.     

Probabilistic inference-based classification applied to myoelectricsignal decomposition

A new probabilistic inference based technique (IBC) for the classification of motor unit action potentials (MUAP's) is presented. This new technique discovers statistically significant relationships in the data and uses these relationships to generate classification rules. The technique was applied to the classification of MUAP's extracted from simulated myoelectric signals. Its performance was compared to that of classical template matching algorithms (TBC) applied to the same data. Using 32 time samples as features to represent the MUAP's it was found that the IBC based technique performed significantly better (p less than 0.005) than the TBC algorithms (83.0 +/- 2.6% versus 78.1 +/- 2.8% peak correct classification performance). As the size of the training set was reduced or as increasing numbers of random classification errors were introduced into the training data, the performance of the IBC and TBC techniques declined similarly. IBC performance remained superior until very small training sets (less than 30 MUAP's per motor unit) or training sets with large numbers of errors (greater than 50%) were used. Because the probabilistic inference technique can utilize nominal data it has the potential to use declarative problem domain knowledge which conceivably could improve its performance.     

The Most General Time-Varying Filter Bank and Time-Varying Lapped Transforms

In this paper, a model-based method is used to analyze the most general time-varying filter bank, where all parameters in the filter bank change with time, including filter length, decimator factor, and the number of channel. Through modeling the time-varying filter bank at a fixed time point as a time-invariant filter bank, we change the study of the most general time-varying filter bank to study of the established model. Based on the model, the most general time-varying filter bank is analyzed in both polyphase domain and modulation domain. The general perfect reconstruction (PR) conditions of the most general time-varying filter bank are given using time-varying polyphase matrices in the polyphase domain. In the modulation domain, the time-varying distortion-matrix is presented, and the distortion-free condition of the most general time-varying filter bank is given. Based on the established theory for the most general time-varying filter bank, in the second part of this paper, the time-varying cosine-modulated lapped transform (TV-MLT) as an example is analyzed in detail. An interesting design approach called the window-switching technique, used to design the time-varying prototype windows for a perfectly reconstructed TV-MLT, is introduced. The window-switching technique provides us with the possibility to design a perfectly reconstructed TV-MLT without complex mathematical optimization computation, and simply by graphically building the prototype windows in the transition period based on the given diagrams of the prototype windows before and after the transform changing.     

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%     

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.     

Time-varying discrete-time signal expansions as time-varying filter banks

The time-varying discrete-time signal expansion was analysed based on the theory of time-varying filter banks in detail. A general definition of time-varying discrete-time wavelet transforms is provided. Usually, a time-varying discrete-time signal expansion can be implemented using a time-varying filter bank. Using the time-varying filter bank theory, the authors developed a useful algorithm to calculate the dual basis function in a biorthogonal time-varying discrete-time signal expansion. Example is given to show the usage of the algorithm. In the last part, the authors provide a detailed analysis of the general time-varying discrete-time wavelet transform. Some useful properties of the time-varying discrete-time wavelet transform including their proofs are given. The relationship between the tree-structured implementation and the non-uniform filter bank implementation is discussed.     

Time-varying analysis-synthesis systems based on filter banks andpost filtering

Perfect reconstruction (PR) time-varying analysis-synthesis filter banks are those in which the filters are allowed to change from one set of PR filter banks to another as the input signal is being processed. Such systems have the property that, in the absence of coding, they faithfully reconstruct every sample of the input. Various methods have been reported for the time-varying filter bank design; all of them, however, utilize structures for conventional PR filter banks. These conventional structures that have been applied in the past result in different limitations in each method. This paper introduces a new structure for exactly reconstructing time-varying analysis-synthesis filter banks. This structure consists of the conventional filter bank followed by a time-varying post filter. The new method requires neither the redesign of the analysis sections nor the use of any intermediate analysis filters during transition periods. It provides a simple and elegant procedure for designing time-varying filter banks without the disadvantages of the previous methods     

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.     

An Analysis of the Electromyogram by Fourier, Simulation and Experimental Techniques

The electromyogram of a single motor unit is studied by considering it as a time function defined by a convolution integral where a point process input passes through a filter whose impulse response is the shape of a single motor unit action potential. The interspike intervals are assumed to be normally distributed, independent random variables. Simulation is performed on a digital computer. The theoretical analysis shows that the absolute value of the ensemble average of the Fourier transform of the simulated EMG approaches the absolute value of the Fourier transform of the motor unit potential. This has been confirmed by simulation except at the very low end of the spectrum. These results are compared with the Fourier transforms of the recorded surface EMG data from human muscles.     

基于REKF的异类传感器异步数据融合算法研究

提出了一种基于异类传感器(R和IR)的数据融合目标跟踪算法,两种传感器具有不同的测量维数,量测数据异步采样并以不同的速率传输到融合中心站点.通过时间匹配技术,完成两种异步数据的融合,然后实现滤波器的状态更新.同时文中讨论了一种REKF(旋转推广卡尔曼滤波:Rotation Extended Kalman Filter)算法,可以有效地解决量测非线性和降低计算量的问题.     

Identification of Hammerstein models with cubic spline nonlinearities

This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses a separable least squares Levenberg-Marquardt optimization to identify Hammerstein cascades whose nonlinearities are modeled by either cubic splines or polynomials. These algorithms are compared in simulation, where the effects of variations in the input spectrum and distribution, and those of the measurement noise are examined. The two algorithms are used to fit Hammerstein models to stretch reflex electromyogram (EMG) data recorded from a spinal cord injured patient. The model with the cubic spline nonlinearity provides more accurate predictions of the reflex EMG than the polynomial based model, even in novel data.     

Factorization approach to unitary time-varying filter bank treesand wavelets

A complete factorization of all optimal (in terms of quick transition) time-varying FIR unitary filter bank tree topologies is obtained. This has applications in adaptive subband coding, tiling of the time-frequency plane and the construction of orthonormal wavelet and wavelet packet bases for the half-line and interval. For an M-channel filter bank the factorization allows one to construct entry/exit filters that allow the filter bank to be used on finite signals without distortion at the boundaries. One of the advantages of the approach is that an efficient implementation algorithm comes with the factorization. The factorization can be used to generate filter bank tree-structures where the tree topology changes over time. Explicit formulas for the transition filters are obtained for arbitrary tree transitions. The results hold for tree structures where filter banks with any number of channels or filters of any length are used. Time-varying wavelet and wavelet packet bases are also constructed using these filter bank structures. the present construction of wavelets is unique in several ways: 1) the number of entry/exit functions is equal to the number of entry/exit filters of the corresponding filter bank; 2) these functions are defined as linear combinations of the scaling functions-other methods involve infinite product constructions; 3) the functions are trivially as regular as the wavelet bases from which they are constructed     

Optimal time-frequency deconvolution filter design fornonstationary signal transmission through a fading channel: AF filterbank approach

The purpose of this paper is to develop a new approach-time-frequency deconvolution filter-to optimally reconstruct the nonstationary (or time-varying) signals that are transmitted through a multipath fading and noisy channel. A deconvolution filter based on an ambiguity function (AF) filter bank is proposed to solve this problem via a three-stage filter bank. First, the signal is transformed via an AF analysis filter bank so that the nonstationary (or time-varying) component is removed from each subband of the signal. Then, a Wiener filter bank is developed to remove the effect of channel fading and noise to obtain the optimal estimation of the ambiguity function of the transmitted signal in the time-frequency domain. Finally, the estimated ambiguity function of the transmitted signal in each subband is sent through an AF synthesis filter bank to reconstruct the transmitted signal. In this study, the channel noise may be time-varying or nonstationary. Therefore, the optimal separation problem of multicomponent nonstationary signals is also solved by neglecting the transmission channel     

A fast and reliable technique for muscle activity detection from surface EMG signals

The estimation of on-off timing of human skeletal muscles during movement is an important issue in surface electromyography (EMG) signal processing with relevant clinical applications. In this paper, a novel approach to address this issue is proposed. The method is based on the identification of single motor unit action potentials from the surface EMG signal with the use of the continuous wavelet transform. A manifestation variable is computed as the maximum of the outputs of a bank of matched filters at different scales. A threshold is applied to the manifestation variable to detect EMG activity. A model, based on the physical structure of the muscle, is used to test the proposed technique on synthetic signals with known features. The resultant bias of the onset estimate is lower than 40 ms and the standard deviation lower than 30 ms in case of additive colored Gaussian noise with signal-to-noise ratio as low as 2 dB. Comparison with previously developed methods was performed, and representative applications to experimental signals are presented. The method is designed for a complete real-time implementation and, thus, may be applied in clinical routine activity.     

Recursive time-varying filter banks for subband image coding

Filter banks, subband/wavelets, and multiresolution decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. The new filter bank framework is presented and discussed in the context of subband image coding. In the absence of quantization errors, exact reconstruction can be achieved. By the proper choice of an adaptation scheme, it is shown that recursive linear time-varying (LTV) filter banks can yield improvement over conventional ones.     

Blind decorrelating RAKE receivers for long-code WCDMA

The problem of blind and semiblind channel estimation and symbol detection is considered for long-code wideband code division multiple access (CDMA) systems, including systems with multirate and multicode transmissions. A decorrelating matched filter, implemented efficiently in state-space, eliminates multiaccess interference and produces a bank of vector processes. Each vector process spans a one-dimensional (1-D) subspace from which channel parameters and data symbols of one user are estimated jointly by least squares. A new identifiability condition is established, which suggests that channels unidentifiable, in short-code CDMA systems are almost surely identifiable when aperiodic spreading codes are used. The decorrelating matched filter is implemented efficiently based on time-varying state-space realizations that exploit the structure of sparsity of the code matrix. The mean square error of the estimated channel is compared to the Cramer-Rao bound, and a bit error rate (BER) expression for the proposed algorithm is presented.     

A passivity-based method for induction motor control

The control of an induction motor is a difficult problem, since the dynamics of the induction motor are nonlinear, the rotor electrical state variables (i.e., rotor fluxes or currents) are usually unavailable for measurement, and the motor parameters can vary significantly from their nominal values. The main purpose of this paper is to develop a control algorithm that forces the induction motor to track time-varying speed, position, and flux trajectories without knowledge of the rotor electrical state variables. To achieve this, a passivity-based method is developed. The key point with this method is the identification of terms, known as workless forces, which appear in the dynamic equations of the induction motor but do not have any effect on the energy balance equation of the induction motor. These terms do not influence the stability properties of the induction motor and, hence, there is no need to cancel them with feedback control. This leads to a simpler control structure and enhances the robustness of the control system. Experimental results show that the passivity-based method provides close tracking of time-varying speed, position, and flux trajectories without knowledge of the rotor electrical state variables     

Gesture-based control and EMG decomposition

This paper presents two probabilistic developments for the use with electromyograms (EMGs). First described is a neuroelectric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMGs into individual motor unit action potentials (MUAPs). This Bayesian decomposition method allows for distinguishing individual muscle groups with the goal of enhancing gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture-based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models, which are used to recognize the gestures as they are being performed in real time from moving averages of EMGs. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMGs do not provide an easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups, we present a Bayesian algorithm to separate surface EMGs into representative MUAPs. The algorithm is based on differential variable component analysis, which was originally developed for electroencephalograms. The algorithm uses a simple forward model representing a mixture of MUAPs as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data were obtained using a custom linear electrode array designed for this study.     

Filter-based coded-excitation system for high-speed ultrasonic imaging

We have recently presented a new algorithm for high-speed parallel processing of ultrasound pulse-echo data for real-time three-dimensional (3-D) imaging. The approach utilizes a discretized linear model of the echo data received from the region of interest (ROI) using a conventional beam former. The transmitter array elements are fed with binary codes designed to produce distinct impulse responses from different directions in ROI. Image reconstruction in ROI is achieved with a regularized pseudoinverse operator derived from the linear receive signal model. The reconstruction operator can be implemented using a transversal filter bank with every filter in the bank designed to extract echoes from a specific direction in the ROI. The number of filters in the bank determines the number of image lines acquired simultaneously. In this paper, we present images of a cyst phantom reconstructed based on our formulation. A number of issues of practical significance in image reconstruction are addressed. Specifically, an augmented model is introduced to account for imperfect blocking of echoes from outside the ROI. We have also introduced a column-weighting algorithm for minimizing the number of filter coefficients. In addition, a detailed illustration of a full image reconstruction using subimage acquisition and compounding is given. Experimental results have shown that the new approach is valid for phased-array pulse-echo imaging of speckle-generating phantoms typically used in characterizing medical imaging systems. Such coded-excitation-based image reconstruction from speckle-generating phantoms, to the best of our knowledge, have not been reported previously.