Selectivity of spatial filters for surface EMG detection from the tibialis anterior muscle

Many spatial filters have been proposed for surface electromyographic (EMG) signal detection. Although theoretical and modeling predictions on spatial selectivity are available, there are no extensive experimental validations of these techniques based on single motor unit (MU) activity detection. The aim of this study was to compare spatial selectivity of one- and two-dimensional (1-D and 2-D) spatial filters for EMG signal detection. Intramuscular and surface EMG signals were recorded from the tibialis anterior muscle of ten subjects. The simultaneous use of intramuscular wire and surface recordings (with the spike triggered averaging technique) allowed investigation of the activity of single MUs at the skin surface. The surface EMG signals were recorded with a grid of point electrodes (3 x 3 electrodes) and a ring electrode system at 15 locations over the muscle, with the wires detecting signals from the same intramuscular location. For most subjects, it was possible to classify, from the intramuscular recordings, the activity of the same MUs for all the contractions. The surface EMG signals were averaged with the intramuscularly detected MU action potentials as triggers. In this way, eight spatial filters--longitudinal and transversal, single and double differential (LSD, TSD, LDD, TDD), Laplacian (NDD), inverse binomial filter of the second order (IB2), inverse rectangle filter (IR), and differential ring system (C1)--could be compared on the basis of their spatial selectivity. The distance from the source (transversal with respect to the muscle fiber orientation) after which the surface detected potential did not exceed +/- 5% of the maximal peak-to-peak amplitude (detection distance) was statistically smaller for the 2-D systems and TDD than for the other filters. The MU action potential duration was significantly shorter with LDD and with the 2-D systems than with the other filters. The 2-D filters investigated (including C1) showed very similar performance and were, thus, considered equivalent from the point of view of spatial selectivity.     

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.     

A novel approach for estimating muscle fiber conduction velocity by spatial and temporal filtering of surface EMG signals

We describe a new method for the estimation of muscle fiber conduction velocity (CV) from surface electromyography (EMG) signals. The method is based on the detection of two surface EMG signals with different spatial filters and on the compensation of the spatial filtering operations by two temporal filters (with CV as unknown parameter) applied to the signals. The transfer functions of the two spatial filters may have different magnitudes and phases, thus the detected signals have not necessarily the same shape. The two signals are first spatially and then temporally filtered and are ideally equal when the CV value selected as a parameter in the temporal filters corresponds to the velocity of propagation of the detected action potentials. This approach is the generalization of the classic spectral matching technique. A theoretical derivation of the method is provided together with its fast implementation by an iterative method based on the Newton's method. Moreover, the lowest CV estimate among those obtained by a number of filter pairs is selected to reduce the CV bias due to nonpropagating signal components. Simulation results indicate that the method described is less sensitive than the classic spectral matching approach to the presence of nonpropagating signals and that the two methods have similar standard deviation of estimation in the presence of additive, white, Gaussian noise. Finally, experimental signals have been collected from the biceps brachii muscle of ten healthy male subjects with an adhesive linear array of eight electrodes. The CV estimates depended on the electrode location with positive bias for the estimates from electrodes close to the innervation or tendon regions, as expected. The proposed method led to significantly lower bias than the spectral matching method in the experimental conditions, confirming the simulation results.     

A simplified technique for measuring fast surface states

A technique is presented which measures the number of fast states (/cm²) between (flat band) φ_s = 0 and φ_s = 2φ_B using a high frequency C ? V and d.c. ramp I ? V tracing of any MIS capacitor. For cases where fast state densities near flat band are insignificant, the true flat band point V(φ_s = 0) is obtained from the high frequency C ? V curve. Then from the (I ? V) curve the V(φ_s = 2φ_B) point is obtained by graphically measuring off an area = I_max (2kT/q) ln (N_B/ni) between V = V_FB, V = V₁, I = Imax, and I ? V curve. Then the fast state density (N_FS(/cm²)), is obtained from the expression: $\text{Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 2φ}{}_{\mathrm{B}}\text{? Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 0 = 2φ}{}_{\mathrm{B}}\text{+}\text{q}\text{C}{}_{\mathrm{<mtext>ins</mtext>}}\text{[N}{}_{\mathrm{si}}\text{+ N}{}_{\mathrm{FS}}\text{]}$ where all values are known. For cases where significant fast states exist near flat band, the true flat band point can be obtained graphically from the I ? V tracing using any value of surface potential near mid gap calculated from the high frequency capacitance.     

Nonstationary harmonic modeling for ECG removal in surface EMG signals

We present a compact approach for mitigating the presence of electrocardiograms (ECG) in surface electromyographic (EMG) signals by means of time-variant harmonic modeling of the cardiac artifact. Heart rate and QRS complex variability, which often account for amplitude and frequency time variations of the ECG, are simultaneously captured by a set of third-order constant-coefficient polynomials modulating a stationary harmonic basis in the analysis window. Such a characterization allows us to significantly suppress ECG from the mixture by preserving most of the EMG signal content at low frequencies (less than 20?Hz). Moreover, the resulting model is linear in parameters and the least-squares solution to the corresponding linear system of equations efficiently provides model parameter estimates. The comparative results suggest that the proposed method outperforms two reference methods in terms of the EMG preservation at low frequencies.     

A method for fast amplitude detection of variable period sinusoidal signals

In this work a method for fast detection of sinusoidal signal amplitude of variable period is proposed. Information for the signal amplitude is taken with several sample pulses in each half period with the aid of a multiplier and a differentiator. The sampled signal values are held and equalized with the signal amplitude by a weighting amplifier.     

Simulation of surface EMG signals for a multilayer volume conductor with triangular model of the muscle tissue

This study analytically describes surface electromyogram (sEMG) signals generated by a model of a triangular muscle, i.e., a muscle with fibers arranged in a fan shape. Examples of triangular muscles in the human body are the deltoid, the pectoralis major, the trapezius, the adductor pollicis. A model of triangular muscle is proposed. It is a sector of a cylindrical volume conductor (with the fibers directed along the radial coordinate) bounded at the muscle/fat interface. The muscle conductivity tensor reflects the fan anisotropy. Edge effects have been neglected. A solution of the nonspace invariant problem for a triangular muscle is provided in the Fourier domain. An approximate analytical solution for a two plane layer volume conductor model is obtained by introducing a homogeneous layer (modeling the fat) over the triangular muscle. The results are implemented in a complete sEMG generation model (including the finite length of the fibers), simulating single fiber action potentials. The model is not space invariant due to the changes of the volume conductor along the direction of action potential propagation. Thus the detected potentials at the skin surface change shape as they propagate. This determines problems in the extraction and interpretation of parameters. As a representative example of application of the simulation model, the influence of the inhomogeneity of the volume conductor in conduction velocity (CV) estimation is addressed (for two channels; maximum likelihood and reference point methods). Different fiber depths, electrode placements and small misalignments of the detection system with respect to the fiber have been simulated. The error in CV estimation is large when the depth of the fiber increases, when the detection system is not aligned with the fiber and close to the innervation point and to the tendons.     

Simulation of surface EMG signals generated by muscle tissues with inhomogeneity due to fiber pinnation

Surface electromyographic (EMG) signal modeling has important applications in the interpretation of experimental EMG data. Most models of surface EMG generation considered volume conductors homogeneous in the direction of propagation of the action potentials. However, this may not be the case in practice due to local tissue inhomogeneities or to the fact that there may be groups of muscle fibers with different orientations. This study addresses the issue of analytically describing surface EMG signals generated by bi-pinnate muscles, i.e., muscles which have two groups of fibers with two orientations. The approach will also be adapted to the case of a muscle with fibers inclined in the depth direction. Such muscle anatomies are inhomogeneous in the direction of propagation of the action potentials with the consequence that the system can not be described as space invariant in the direction of source propagation. In these conditions, the potentials detected at the skin surface do not travel without shape changes. This determines numerical issues in the implementation of the model which are addressed in this work. The study provides the solution of the nonhomogenous, anisotropic problem, proposes an implementation of the results in complete surface EMG generation models (including finite-length fibers), and shows representative results of the application of the models proposed.     

Estimation of elbow-induced wrist force with EMG signals using fast orthogonal search

In many studies and applications that include direct human involvement-such as human-robot interaction, control of prosthetic arms, and human factor studies-hand force is needed for monitoring or control purposes. The use of inexpensive and easily portable active electromyogram (EMG) electrodes and position sensors would be advantageous in these applications compared to the use of force sensors, which are often very expensive and require bulky frames. Multilayer perceptron artificial neural networks (MLPANN) have been used commonly in the literature to model the relationship between surface EMG signals and muscle or limb forces for different anatomies. This paper investigates the use of fast orthogonal search (FOS), a time-domain method for rapid nonlinear system identification, for elbow-induced wrist force estimation. It further compares the forces estimated using FOS with the forces estimated by MLPANN for the same human anatomy under an ensemble of operational conditions. In this paper, the EMG signal readings from upper arm muscles involved in elbow joint movement and sensed elbow angular position and velocity are utilized as inputs. A single degree-of-freedom robotic experimental testbed has been constructed and used for data collection, training and validation.     

A finite element model for describing the effect of muscle shortening on surface EMG

A finite-element model for the generation of single fiber action potentials in a muscle undergoing various degrees of fiber shortening is developed. The muscle is assumed fusiform with muscle fibers following a curvilinear path described by a Gaussian function. Different degrees of fiber shortening are simulated by changing the parameters of the fiber path and maintaining the volume of the muscle constant. The conductivity tensor is adapted to the muscle fiber orientation. In each point of the volume conductor, the conductivity of the muscle tissue in the direction of the fiber is larger than that in the transversal direction. Thus, the conductivity tensor changes point-by-point with fiber shortening, adapting to the fiber paths. An analytical derivation of the conductivity tensor is provided. The volume conductor is then studied with a finite-element approach using the analytically derived conductivity tensor. Representative simulations of single fiber action potentials with the muscle at different degrees of shortening are presented. It is shown that the geometrical changes in the muscle, which imply changes in the conductivity tensor, determine important variations in action potential shape, thus affecting its amplitude and frequency content. The model provides a new tool for interpreting surface EMG signal features with changes in muscle geometry, as it happens during dynamic contractions.     

A new technique for transmission of signals from implantabletransducers

To reduce space requirements for implant electronics in in vivo telemetry applications, the purpose of this project was to develop and test a new data transmission method that utilizes the ionic properties of bodily fluids as the transmission medium. Motivated by an interest in using the new method to transmit information from a sensor which measures tension in anterior cruciate ligament (ACL) grafts, a sine wave was injected into a cadaver leg using platinum electrodes implanted into the lateral femoral epicondyle. The signal was detected by electromyogram (EMG) surface electrodes. The effect of transmission frequency, the current injected, interelectrode separation, distance of the electrodes from the joint line, and the surface of electrode placement on the signal attenuation was studied. The logarithmic relation between attenuation and frequency was constant from 2 kHz until 10 kHz. For frequencies above 10 kHz, the attenuation increased linearly at the rate of 1 dB/octave. Attenuation was inversely sensitive to both current and interelectrode separation with larger separations and currents giving less attenuation. Attenuation was significantly less for the lateral thigh surface than for the anterior surface and increased with increasing distance from the joint line for both surfaces. For the application of interest here, suitable values of transmission variables to avoid the possible negative consequences of injecting current into living tissue are a current of 3 mA injected at a frequency of 37 kHz. The values of reception variables for minimum attenuation are wide interelectrode separation (5 cm) with the electrodes placed 5 cm proximal of the joint line on the lateral surface of the thigh. With the exception of the surface which is application dependent, these values of the reception variables should also be appropriate for other applications     

A series technique for the optimum detection of stochastic signals in noise

A procedure for the optimum detection of stochastic signals in noise is discussed. The optimum test function is expanded in a point-wise convergent series for which a bound on the convergence properties can be obtained. Knowledge of this bound permits the substitution of a truncated version of the series for the optimum test function. This leads to a test procedure that uses a variable number of terms of the series for each decision and also gives the same decision as the optimum detector. For detection of stochastic signals in Gaussian noise, an expansion is obtained in terms of the eigenfunctions associated with the Gaussian probability density function, which leads to optimum decisions with a moderate number of terms of the series. It is also well suited for adaptive detection in which the distribution function of the stochastic signal is unknown--the coefficients of the expansion factor into two terms, one dependent only on the noise distribution and the other dependent on the distribution of the stochastic signal. Computer results for Gaussian noise are given. For this case, the test procedure can be viewed as a sequence of linear, quadratic, etc., detectors that, when a basic inequality is met, terminates with an optimum decision.     

A reliable blind convergence technique for phase-splittingequalizers

This article proposes a technique for providing reliable blind convergence of the phase-splitting equalizer. It is shown that the phase-splitting equalizer is difficult to train blindly with the conventional blind algorithm. The proposed technique modifies the cost function of the blind algorithm so that the two filters of the phase-splitting equalizer constitute a Hilbert pair. We also investigate the steady-state performance of the proposed blind algorithm for high-speed digital transmission application     

An EMG integrator for muscle activity studies in ambulatory subjects

A portable digital integrator is described for the measurement of electromyographic activity in the natural environment. integrated muscle activity exceeding an adjustable threshold is accumulated and displayed on a seven digit LED readout in ?V·s. Technical specifications, schematic diagram, and application examples are provided.     

线性调频信号快速检测与参数估计算法研究

讨论一种基于RAT的LFM信号快速检测算法。根据信号模糊函数的能量分布特性,首先采用二分法快速逼近信号能量中心分布区域,然后进行小范围高精度搜索,以精确估计其调频斜率。仿真结果表明,该算法在保持有效检测性能的条件下可大大降低运算量,显著提高对LFM信号的实时检测处理速度。     

A fast and unilateral monolithic switch for analog signals

This correspondence deals with a monolithic switch circuit for voltage-type analog signals. The circuit constitutes a unilateral, impedance buffering changeover switch, which is capable of fast signal switching (10 ns changeover time) and can handle wide-spectrum signals (dc-100 MHz). The switch introduces only a small offset (<1 mV) and causes only small (<50 mV), short lasting (<50 ns) switching spikes.     

Independence of myoelectric control signals examined using a surface EMG model

The detection volume of the surface electromyographic (EMG) signal was explored using a finite-element model, to examine the feasibility of obtaining independent myoelectric control signals from regions of reinnervated muscle. The selectivity of the surface EMG signal was observed to decrease with increasing subcutaneous fat thickness. The results confirm that reducing the interelectrode distance or using double-differential electrodes can increase surface EMG selectivity in an inhomogeneous volume conductor. More focal control signals can be obtained, at the expense of increased variability, by using the mean square value, rather than the root mean square or average rectified value.     

多分量信号快速时频分析方法

针对目前多分量时频分析方法计算复杂度高,难以实现持续信号实时处理的问题,提出一种多分量信号快速时频分析方法。该方法通过信号流逐窗时频变换,实现信号的快速时频分析,其主要计算过程为短时傅立叶变换,时间和空间复杂度低,易于工程实现。性能分析结果表明:该方法时频分辨率高,避免了交叉项干扰,能有效分析低信噪比信号。     

一种快速实现超宽带信号捕获的算法

信号的同步是超宽带技术实现和发展的关键环节，本文介绍一种能快速实现超宽带脉冲信号同步的串行捕获算法，即自适应门限块搜索算法。该算法将相位搜索范围进行分块处理，通过对信噪比进行实时估计不断调整其判决门限，达到最佳判决，用较少的硬件代价实现脉冲信号的快速捕获。     

A fast reliable iteration method for dc analysis of nonlinear networks

A new iteration method for nonlinear dc analysis, based on Broyden's modification of the Newton-Raphson method, is described. Broyden introduces a variable correction factor which is chosen so as to minimize, or at least reduce, the size of the error vector at each iteration. This completely precludes divergence of the algorithm. Broyden also develops a means for updating the inverse Jacobian matrix without ever having to compute or invert it explicitly. Two algorithms are described, one for solving a single nonlinear problem and the other for solving a large number of neighboring problems such as are encountered in statistical (Monte Carlo) analysis. Timing measurements on these two algorithms are reported. Application of these algorithms to statistical ac analysis and to frequency response calculations is proposed and a possible method of improving the basic algorithm by means of a sparse matrix technique is described.