Deconvolution estimation of motor unit conduction velocity distribution

A conduction velocity distribution (CVD) estimator that incorporates volume conductor modeling of the muscle voluntary response is introduced in this paper. The CVD estimates are obtained from two correlation functions, an autocorrelation and a cross, computed from myoelectric signal recorded at the skin surface. The performance of the proposed estimator is evaluated for simulated and experimental data. The study includes assessment of the estimator bias and standard deviation, as well as its sensitivity to errors in the model parameters. Simulations show its good performance in terms of estimator bias. A filtering technique also helps reduce its variance. However, the inaccuracy introduced in the estimation of model parameters considerably deteriorates the estimator performance.     

Motor unit conduction velocity distribution estimation from evoked motor responses

Action potentials travel along the muscle fibers with a specific conduction velocity that depends on their structural and functional properties. Only the estimation of muscle conduction velocity distribution (MCVD) may be able to depict this propagation heterogeneity. Based on the method proposed by Cummins et al. (Electroenceph Clin Neurophysiol, 46:647-658, 1979) to estimate nerve conduction velocity distribution (NCVD), the present paper proposes a method that modifies the Cummins' approach to make it suitable for MCVD estimation from electrically evoked motor responses. The MCVD estimation algorithm was first assessed by means of simulated signals in order to control all signal features during the optimization process. Simulations showed that estimated distributions were very close to the true ones when taking into account the specificities of the muscle action potential, due to its generation and extinction (MSE divided by 5 on distribution standard deviation). This method was then applied to real signals. Elicited motor responses were recorded on the biceps brachii of healthy subjects either during repeated maximal stimulations at 20 Hz or during increasing intensity stimulations at 1 Hz. MCVD estimates were used to analyze fatigue and motor unit recruitment processes, respectively.     

Deconvolution estimation of nerve conduction velocity distribution

A conduction velocity distribution (CVD) estimator that incorporates volume conductor modeling of the nerve-evoked response is introduced in this paper. The CVD estimates are obtained from two compound nerve action potentials (CNAP) recorded at the skin surface. A third channel is introduced in order to assess the estimator performance in the experimental case. The relevance of using an accurate signal model is shown by comparing the performance of the proposed estimator with a previous approach based on a different CNAP model. The performance of the proposed estimator is evaluated for simulated and experimental data. The study assesses signal-to-noise ratio immunity and sensitivity to errors in the model parameters.     

Pattern characteristics of linear arrays using the constrained least squares distribution

The constrained least squares (CLS) distribution is a method for obtaining distribution functions that yield low sidelobe patterns with specified constraints on the aperture efficiency, and are especially useful for the transmit patterns of active array antennas. The widely used Taylor distribution optimizes only pattern performance while the CLS distribution optimizes pattern performance while taking into account the constraints on both the peak element amplitude and the total effective radiated voltage (ERV) of the aperture distribution. The paper compares the pattern characteristics of linear arrays with CLS and Taylor distributions. The results help to establish guidelines on when a CLS distribution would be preferable over a Taylor distribution when a specified aperture efficiency is important.     

Estimation of conduction velocity distribution byregularized-least-squares method

A novel technique for estimating the distribution of the conduction velocity of peripheral nerve fibers is described in this paper. In order to overcome the sensitivity of present methods to noisy data, a regularized-least-squares (RLS) method with a smoothing constraint and a self-adaption of regularization parameter was adopted. The simulation results demonstrated that the improved technique maybe applied in clinical diagnosis because it yielded reliable and almost undistorted results even when the simulated data are severely contaminated by noise     

Estimation of motor unit conduction velocity from surface EMG recordings by signal-based selection of the spatial filters

Muscle fiber conduction velocity (CV) can be estimated by the application of a pair of spatial filters to surface electromagnetic (EMG) signals and compensation of the spatial filter transfer function with equivalent temporal filters. This method integrates the selection of the spatial filters for signal detection to the estimation of CV. Using this approach, in this paper, we propose a novel technique for signal-based selection of the spatial filter pair that minimizes the effect of nonpropagating signal components (end-of-fiber effects) on CV estimates (optimal filters). The technique is applicable to signals with one propagating and one nonpropagating component, such as single motor unit action potentials. It is shown that the determination of the optimal filters also allows the identification of the propagating and nonpropagating signal components. The new method was applied to simulated and experimental EMG signals. Simulated signals were generated by a cylindrical, layered volume conductor model. Experimental signals were recorded from the abductor pollicis brevis with a linear array of 16 electrodes. In the simulations, the proposed approach provided CV estimates with lower bias due to nonpropagating signal components than previously proposed methods based on the entire signal waveform. In the experimental signals, the technique separated propagating and nonpropagating signal components with an average reconstruction error of 2.9 +/- 0.9% of the signal energy. The technique may find application in single motor unit studies for decreasing the variability and bias of CV estimates due to the presence and different weights of the nonpropagating components.     

Modeling and estimation of ambiguities in linear arrays

The problem of ambiguities inherent in the manifold of any linear array structure is investigated. Ambiguities, which can be classified into trivial and nontrivial, depending on the ease of their identification, arise when an array cannot distinguish between two different sets of directional sources. Initially, the new concept of an ambiguous generator set is introduced; it represents/generates an infinite number of ambiguous sets of directions. Then, by uniformly/nonuniformly partitioning the array manifold curve of a linear array, different ambiguous generator sets ran be calculated, and as a direct result, a sufficient condition for the presence of ambiguities is obtained. The theoretical aspects of the investigation are followed by the proposal of an innovative approach that calculates not only all such ambiguities existing in a linear array of arbitrary geometry but the rank of ambiguity in each case as well. The main results presented in the paper are supported by a number of representative examples     

Improved coherent DOA estimation algorithm for uniform linear arrays

An improved algorithm on coherent direction-of-arrival (DOA) estimation is presented in this article, with the objective to overcome the unsatisfactory performances of estimation of signal parameter via rotational invariance techniques (ESPRIT)-like algorithms (Han and Zhang, IEEE Antennas and Wireless Propagation Letters 2005;4:443–446). On the basis of trilinear model by reconstructing a series of Toeplitz matrix from the co-variance matrix of array output, our proposed algorithm is to resolve the DOAs of coherent signals, which not only has much better DOA estimation performance than algorithms of ESPRIT-like and multi-invariance ESPRIT but also identifies more DOAs than ESPRIT-like algorithm. Simulation results demonstrate its validity.     

Nerve-bundle conduction velocity distribution measurement and transfer function analysis

Human peripheral nerves are composed of thousands of individual nerve fibers whose signal conduction velocities vary from 0.2 to 100 m/s. Though good correlation exist between fiber velocity and the physiological function subserved by these fibers, considerable variation is found for specific end organs (20 to 40 m/s for a single muscle). Though clinical neurophysiologists have routinely measured the maximum conduction velocity of peripheral motor nerves for 30 years, it has not been possible to determine the velocity distributions. This report details a model and noninvasive methodology for motor axon conduction latency distribution mesurement. This distribution, proportional to velocity dispersion, possesses a low-pass filter characteristic which agrees with theoretical predictions and may be significant in some sensory and motor functions.     

Beam reconfiguration of linear arrays using parasitic elements

An innovative method for linear arrays beam reconfiguration is presented. This pattern reconfigurability is achieved by a mechanical displacement of a parasitic array located in front of an active one. Two worked examples that use parallel dipoles are presented.     

Synthesis of linear antenna arrays using Z transforms

It is well known that a linear antenna array with equally spaced elements can be represented by a polynomial whose roots correspond to the nulls of its antenna pattern. Since the linear array has equally spaced elements, its polynomial has only integral powers of the variable, so that the array can be represented by aZtransform. Therefore, the effect of moving roots of the polynomial can be represented as a linear sampled-data system problem, which is solved by using a table ofZtransforms or by discrete numerical convolution. In this paper, the quantitative effects on the array and its antenna pattern caused by moving roots of the polynomial are determined, and these effects are utilized for array synthesis to produce desired antenna patterns. Examples illustrating the use of this new synthesis technique include modification of a uniform array to obtain low sidelobes in the antenna pattern and synthesis of an array to produce nulls in its antenna pattern in the directions of discrete and spatially distributed interference sources.     

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.     

Control of loudspeakers using disturbance-observer-type velocity estimation

A new approach to obtain sensorless velocity feedback for loudspeakers is developed. The back electromotive force (back-EMF) of the moving coil is estimated by using a disturbance-observer-type estimator based on the coil current measurement. The cone velocity of a loudspeaker can be obtained based on its proportionality to the back-EMF. Instead of relying on the coupled mechanical dynamics as reported in previous work, the proposed velocity estimation is based on the precise knowledge of electrical impedance, which makes it more robust to changes in acoustic loading. The proposed approach enables the development of a robust velocity controller for a subwoofer without an expensive velocity measuring device. Experimental results demonstrated that closed-loop velocity control using the proposed scheme of velocity estimation achieved a performance comparable to that obtained by using measured velocity feedback. The proposed approach can be easily adapted to other moving-coil-type linear actuators.     

Determination of nerve conduction velocity distribution fromsampled compound action potential signals

The sampled compound action potential (CAP) data sequence was expressed as the circular convolution of the delay sequence and the sampled single fiber action potential (SFAP) data sequence. An algorithm, based on Hirose's method (1986) was then developed to separate the delay sequence from the sampled CAP data sequence, and the nerve conduction velocity distribution (NCVD) was consequently calculated from the delay sequence. The NCVD was found to be the product of the amplitude of the SFAP and the number of fibers. Simulations show that the estimated results were in good agreement with the calculated results. Experiments were performed on ten sciatic nerves from five bullfrogs (Rana pipens) using two independent variables: interelectrode distance and stimulus current strength. The results estimated from CAP's recorded under each condition reflect the corresponding feature of NCVD of the condition. The advantage of the technique is to provide detailed information about both slow and fast conducting fibers. This technique also offers the possibility to directly calculate the nerve fiber diameter distribution from the sampled CAP data sequences     

Two-dimensional direction-of-arrival estimation and pairing using L-shaped arrays

This paper proposes a computationally efficient azimuth and elevation estimation and pairing method using L-shaped uniform arrays. The azimuths and elevations of the incident signals are estimated independently at first using the outputs of the two array arms via equation rooting, which well avoids the computationally demanding spatial scanning procedure contained in most of the previous direction-of-arrival estimation methods. The order of the equations equals the number of the incident signals; thus, this procedure is computationally very cheap and can be implemented using various numeric algorithms. Then two optional methods are proposed for azimuth–elevation pairing. One method exploits the cross-correlation of the two subarray outputs of the L-shaped array, and the other method is realized by estimating the signal powers based on the direction estimates. Both of the two direction-pairing methods are implemented using numerical computations; thus, this procedure is also computationally very cheap. In-depth analyses are provided on the selection of the two optional azimuth–elevation pairing methods in different environments. Numerical examples are carried out to demonstrate the performance of the proposed method.     

Positive-definite Toeplitz completion in DOA estimation fornonuniform linear antenna arrays. II. Partially augmentable arrays

For pt. I see ibid., vol.46, p.2458-71 (1998). This paper considers the problem of direction-of-arrival (DOA) estimation for multiple uncorrelated plane waves incident on “partially augmentable” antenna arrays, whose difference set of interelement spacings is not complete. The DOA estimation problem for the case when the number of sources exceeds the number of contiguous covariance lags gives rise to the covariance matrix completion problem. Maximum-entropy (ME) positive-definite (p.d.) completion for partially specified Toeplitz covariance matrices is developed using convex programming techniques. By this approach, the classical Burg (1975) ME extension problem for the given set of covariance lags is generalized for the situation when some lags are missing. For DOA estimation purposes, we find the p.d. Toeplitz matrix with fixed eigensubspace dimension that is the closest approximation of the ME-completed matrix. Computer simulation results are presented to demonstrate the high DOA estimation accuracy of the proposed technique compared with the corresponding Cramer-Rao bound     

Positive-definite Toeplitz completion in DOA estimation fornonuniform linear antenna arrays. I. Fully augmentable arrays

This paper considers the problem of direction-of arrival (DOA) estimation for multiple uncorrelated plane waves incident on so-called “fully augmentable” sparse linear arrays. In situations where a decision is made on the number of existing signal sources (m) prior to the estimation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case where m is less than the number of antenna sensors (M), a new approach called “MUSIC-maximum-entropy equalization” is proposed to improve DOA estimation performance in the “preasymptotic region” of finite sample size (N) and signal-to-noise ratio. A full-sized positive definite (p.d.) Toeplitz matrix is constructed from the M×M direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace (“signal subspace truncations”). When m⩾M, Cramer-Rao bound analysis suggests that the minimal useful sample size N is rather large, even for arbitrarily strong signals. It is demonstrated that the well-known direct augmentation approach (DAA) cannot approach the accuracy of the corresponding Cramer-Rao bound, even asymptotically (as N→∞) and, therefore, needs to be improved. We present a new estimation method whereby signal subspace truncation of the DAA augmented matrix is used for initialization and is followed by a local maximum-likelihood optimization routine. The accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios (m⩾M) presented     

Design of surface electrode array for measuring conduction velocity in the human genioglossus muscle

A new appliance, incorporating linear arrays of pin electrodes for genioglossus (GG) surface electromyography measurement, is presented. This design enables the estimation of GG muscle fiber conduction velocity, which decreases with fatigue. The performance of the device was evaluated for ten healthy human subjects during fatiguing and force varying contractions.