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.     

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.     

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.     

A model for surface EMG generation in volume conductors with spherical inhomogeneities

Most models for surface electromyography (EMG) signal generation are based on the assumption of space-invariance of the system in the direction of source propagation. This assumption implies the same shape of the potential distribution generated by a source in any location along the propagation direction. In practice, the surface EMG generation system is not space invariant and, therefore, the surface signal detected along the direction of the muscle fibers may significantly change shape along the propagation path. An important class of nonspace invariant systems is that of volume conductors inhomogeneous in the direction of source propagation. In this paper, we focused on inhomogeneities introduced by the presence of spheres of different conductivities with respect to the tissue where they are located. This effect may prove helpful to model the presence of glands, vessels, or local changes in the conductivity of a tissue. We present an approximate analytical solution that accounts for an arbitrary number of spheres in an arbitrary complex volume conductor. As a representative example, we propose the solution for a planar layered volume conductor, comprised of fat and muscle layers with spherical inhomogeneities inside the fat layer. The limitations of the approximations introduced are discussed. The model is computationally fast and constitutes an advanced means for the analysis and interpretation of surface EMG signal features.     

An analytical model for surface EMG generation in volume conductors with smooth conductivity variations

A nonspace invariant model of volume conductor for surface electromyography (EMG) signal generation is analytically investigated. The volume conductor comprises planar layers representing the muscle and subcutaneous tissues. The muscle tissue is homogeneous and anisotropic while the subcutaneous layer is inhomogeneous and isotropic. The inhomogeneity is modeled as a smooth variation in conductivity along the muscle fiber direction. This may reflect a practical situation of tissues with different conductivity properties in different locations or of transitions between tissues with different properties. The problem is studied with the regular perturbation theory, through a series expansion of the electric potential. This leads to a set of Poisson's problems, for which the source term in an equation and the boundary conditions are determined by the solution of the previous equations. This set of problems can be solved iteratively. The solution is obtained in the two-dimensional Fourier domain, with spatial angular frequencies corresponding to the longitudinal and perpendicular direction with respect to the muscle fibers, in planes parallel to the detection surface. The series expansion is truncated for the practical implementation. Representative simulations are presented. The proposed model constitutes a new approach for surface EMG signal simulation with applications related to the validation of methods for information extraction from this signal.     

Exact surface impedance for a spherical conductor

A spherically concentric model of the earth is employed to obtain expressions for the surface impedance matrix at the surface. It is shown the surface impedance is a function of both the earth's electrical parameter and the source field configuration. In some cases the latter dependence is of minor consequence.     

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.     

The surface Laplacian operator of the potentials on a bounded volume conductor has a unique inverse

In the discussion on the use of the surface Laplacian (SL) of the distribution of bioelectric potentials on the body surface, the question remained open whether a complete specification of the SL of the potential over the surface bounding a volume conductor would uniquely specify the potential on that surface up to a constant. This paper reports that this is indeed the case. In addition, it is shown that the integral of the SL over a closed surface is zero, a property that may serve as a check on the accuracy of any numerical approximation of the SL.     

On the algorithm for computing body surface Laplacians in aninhomogeneous volume conductor of arbitrary shape

In this short communication, a corrected version of algorithm for calculating the body surface Laplacian (BSL) in an inhomogeneous volume conductor of arbitrary shape is described. The present computer simulation results show that the corrected algorithm can give an accurate numerical solution. This algorithm was then applied to examine the effect of the lung inhomogeneity on the BSLs in a realistically shaped torso model. The simulation results show that the low-conductivity lungs have little effect on both topology and magnitudes of body surface Laplacian maps (BSLMs) for a single dipole source     

Simulation of intramuscular EMG signals detected using implantable myoelectric sensors (IMES)

The purpose of this study was to test the feasibility of recording independent electromyographic (EMG) signals from the forearm using implantable myoelectric sensors (IMES), for myoelectric prosthetic control. Action potentials were simulated using two different volume conductor models: a finite-element (FE) model that was used to explore the influence of the electrical properties of the surrounding inhomogeneous tissues and an analytical infinite volume conductor model that was used to estimate the approximate detection volume of the implanted sensors. Action potential amplitude increased progressively as conducting electrodes, the ceramic electrode casing and high resistivity encapsulation tissue were added to the model. For the muscle fiber locations examined, the mean increase in EMG root mean square amplitude when the full range of material properties was included in the model was 18.2% (+/-8.1%). Changing the orientation of the electrode with respect to the fiber direction altered the shape of the electrode detection volume and reduced the electrode selectivity. The estimated detection radius of the IMES electrode, assuming a cylindrical muscle cross section, was 4.8, 6.2, and 7.5 mm for electrode orientations of 0 degree, 22.5 degrees, and 45 degrees with respect to the muscle fiber direction.     

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.     

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.     

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.      

Phenomenological loss equivalence method for planar quasi-TEMtransmission lines with a thin normal conductor or superconductor

The incremental inductance rule for conductor loss calculations is not valid if conductor thickness decreases and becomes comparable to the penetration depth. A simple approach, referred to as the phenomenological loss equivalence method is proposed for characterizing a planar quasi-TEM transmission line with a thin normal conductor or superconductor over a wide range of field penetrations. For microstrip lines with a thin copper or high-T_c superconductor, the conductor losses calculated by this method agree very well with the published data calculated by the finite-element method and the Monte Carlo method, respectively. Because of the simplicity of the calculation, the method should be very useful for the computer-aided design of monolithic microwave circuits     

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.     

Computation of the potential distribution in a four-layeranisotropic concentric spherical volume conductor

A method for solving the potential distribution in a multilayer anisotropic concentric spherical volume conductor, which has recently been described in the literature, has been tested and found to be numerically unstable. In this paper it is demonstrated how these numerical difficulties can be avoided. Moreover, the method is extended by lifting the previously imposed restriction on the innermost region to be isotropic. A convergence criterion for determining the required number of terms in the final series expansion is proposed. The influences of radial and tangential conductivity values of the skull and brain tissue on the dipole-induced potential are investigated.     

A volume conductor model of the thorax for the study of defibrillation fields

The authors develop a physiologically realistic volume conductor model for calculating epicardial potentials during transthoracic stimulation. The objective of the study is to measure cardiac potentials during a transthoracic stimulus and compare the measurements to calculated epicardial potentials obtained from the model. The results for all four stimulus configurations (anterior-posterior, neck-waist, precordial, and right-left) on the torso consistently yield correlation coefficients of about 0.90 and RMS errors of 47% between calculated and measured epicardial potentials for a homogeneous torso. Incorporating the effects of the skeletal muscle layer improves the agreement, i.e., correlation coefficients increase to about 0.914 and RMS errors decrease to about 42%. At the same time, the lungs and heart have little influence on the agreement between measured and calculated epicardial potentials. The results of the study demonstrate the importance of the skeletal muscle layer in physiologically realistic volume conductor models.<>     

A ray representation of surface diffraction by a multilayer cylinder

The exact expressions for the field produced by a point source radiating in the presence of an infinitely long cylindrical structure comprising layers of different materials is evaluated asymptotically for source and observation points that are widely removed from the cylinder surface and related so that the cylinder shadows the source from the observer. The diffracted field is interpreted in a ray-optic format. It is observed that surface-propagating waves along the layers can be slowed significantly as compared with those on an impenetrable cylinder of the same radius. This wave slowing requires that rays attaching to the cylinder refract into a layer-guided mode and refract a second time as the curved structure sheds energy into the scattered field. Consequently, rays attaching to and shedding from the cylinder are not tangent to it when the layer profile slows the surface-propagating waves. The analysis applies for both metallically backed and open-shell layers. Computed diffraction coefficient results are given for a coated metallic cylinder as a function of coating thickness.