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.     

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.     

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.     

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.     

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.     

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 multiple-layer finite-element model of the surface EMG signal

The effect of skin, muscle, fat, and bone tissue on simulated surface electromyographic (EMG) signals was examined using a finite-element model. The amplitude and frequency content of the surface potential were observed to increase when the outer layer of a homogeneous muscle model was replaced with highly resistive skin or fat tissue. The rate at which the surface potential decreased as the fiber was moved deeper within the muscle also increased. Similarly, the rate at which the surface potential decayed around the surface of the model, for a constant fiber depth, increased. When layers of subcutaneous fat of increasing thickness were then added to the model, EMG amplitude, frequency content, and the rate of decay of the surface EMG signal around the limb decreased, due to the increased distance between the electrodes and the active fiber. The influence of bone on the surface potential was observed to vary considerably, depending on its location. When located close to the surface of the volume conductor, the surface EMG signal between the bone and the source and directly over the bone increased, accompanied by a slight decrease on the side of the bone distal to the active fiber. The results emphasize the importance of distinguishing between the effects of material properties and the distance between source and electrode when considering the influence of subcutaneous tissue, and suggest possible distortions in the surface EMG signal in regions where a bone is located close to the skin surface.     

Estimation of muscle fiber conduction velocity with a spectral multidip approach

We propose a novel method for estimation of muscle fiber conduction velocity from surface electromyographic (EMG) signals. The method is based on the regression analysis between spatial and temporal frequencies of multiple dips introduced in the EMG power spectrum through the application of a set of spatial filters. This approach leads to a closed analytical expression of conduction velocity as a function of the auto- and cross-spectra of monopolar signals detected along the direction of muscle fibers. The performance of the algorithm was compared with respect to that of the classic single dip approach on simulated and experimental EMG signals. The standard deviation of conduction velocity estimates from simulated single motor unit action potentials was reduced from 1.51 m/s [10 dB signal-to-noise ratio (SNR)] and 1.06 m/s (20 dB SNR) with the single dip approach to 0.51 m/s (10 dB) and 0.23 m/s (20 dB) with the proposed method using 65 dips. When 200 active motor units were simulated in an interference EMG signal, standard deviation of conduction velocity decreased from 0.95 m/s (10 dB SNR) and 0.60 m/s (20 dB SNR) with a single dip to 0.21 m/s (10 dB) and 0.11 m/s (20 dB) with 65 dips. In experimental signals detected from the abductor pollicis brevis muscle, standard deviation of estimation decreased from (mean +/- SD over 5 subjects) 1.25 +/- 0.62 m/s with one dip to 0.10 +/- 0.03 m/s with 100 dips. The proposed method does not imply limitation in resolution of the estimated conduction velocity and does not require any iterative procedure for the estimate since it is based on a closed analytical formulation.     

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.     

Signal strength versus cuff length in nerve cuff electrode recordings

When a nerve cuff electrode is used for the recording of signals from peripheral nerves, cuff dimensions have to be chosen. Traditionally, the peak-to-peak amplitude of the single-fiber action potential (SFAP) is optimized through the choice of cuff diameter and cuff length. In this paper, the dependency of the root-mean-square (RMS) value of the nerve signal on the cuff dimensions was studied and compared with the peak-to-peak value of the SFAP. A simple approximation for signal optimization by cuff dimensioning is suggested. The results were obtained from modeled SFAPs and from the electroneurogram (ENG) created by superimposed SFAPs, obtained from an inhomogeneous volume conductor model. The results show that the RMS value of the nerve signal is considerably more sensitive to the cuff length than the SFAP peak-to-peak amplitude, and that the RMS of the ENG is a linear function of the fiber diameter.     

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.     

Volume conduction in an anatomically based surface EMG model

A finite-element model to simulate surface electromyography (EMG) in a realistic human upper arm is presented. The model is used to explore the effect of limb geometry on surface-detected muscle fiber action potentials. The model was based on magnetic resonance images of the subject's upper arm and includes both resistive and capacitive material properties. To validate the model geometry, experimental and simulated potentials were compared at different electrode sites during the application of a subthreshold sinusoidal current source to the skin surface. Of the material properties examined, the closest approximation to the experimental data yielded a mean root-mean-square (rms) error of the normalized surface potential of 18% or 27%, depending on the site of the applied source. Surface-detected action potentials simulated using the realistic volume conductor model and an idealized cylindrical model based on the same limb geometry were then compared. Variation in the simulated limb geometry had a considerable effect on action potential shape. However, the rate of decay of the action potential amplitude with increasing distance from the fiber was similar in both models. Inclusion of capacitive material properties resulted in temporal low-pass filtering of the surface action potentials. This effect was most pronounced in the end-effect components of action potentials detected at locations far from the active fiber. It is concluded that accurate modeling of the limb geometry, asymmetry, tissue capacitance and fiber curvature is important when the specific action potential shapes are of interest. However, if the objective is to examine more qualitative features of the surface EMG signal, then an idealized volume conductor model with appropriate tissue thicknesses provides a close approximation.     

Modeling of surface myoelectric signals. I. Model implementation

The relationships between the parameters of active motor units (MU's) and the features of surface electromyography (EMG) signals have been investigated using a mathematical model that represents the surface EMG as a summation of contributions from the single muscle fibers. Each MU has parallel fibers uniformly scattered within a cylindrical volume of specified radius embedded in an anisotropic medium. Two action potentials, each modeled as a current tripole, are generated at the neuromuscular junction, propagate in opposite directions and extinguish at the fiber-tendon endings. The neuromuscular junctions and fiber-tendon endings are uniformly scattered within regions of specified width. Muscle fiber conduction velocity and average fiber length to the right and left of the center of the innervation zone are also specified. The signal produced by MU's with different geometries and conduction velocities are superimposed. Monopolar, single differential and double differential signals are computed from electrodes placed in equally spaced locations on the surface of the muscle and are displayed as functions of any of the model's parameters. Spectral and amplitude variables and conduction velocity are estimated from the surface signals and displayed as functions of any of the model's parameters. The influence of fiber-end effects, electrode misalignment, tissue anisotropy, MU's location and geometry are discussed. Part II of this paper will focus on the simulation and interpretation of experimental signals.     

A novel approach for precise simulation of the EMG signal detected by surface electrodes

We propose a new electromyogram generation and detection model. The volume conductor is described as a nonhomogeneous (layered) and anisotropic medium constituted by muscle, fat and skin tissues. The surface potential detected in space domain is obtained from the application of a two-dimensional spatial filter to the input current density source. The effects of electrode configuration, electrode size and inclination of the fibers with respect to the detection system are included in the transfer function of the filter. Computation of the signal in space domain is performed by applying the Radon transform; this permits to draw considerations about spectral dips and clear misunderstandings in previous theoretical derivations. The effects of generation and extinction of the action potentials at the fiber end plate and at the tendons are included by modeling the source current, without any approximation of its shape, as a function of space and time and by using again the Radon transform. The approach, based on the separation of the temporal and spatial properties of the muscle fiber action potential and of the volume conductor, includes the capacitive tissue properties.     

Investigation of optimum electrode locations by using an automatized surface electromyography analysis technique.

Identification of the innervation zone is widely used to optimize the accuracy and precision of noninvasive surface electromyography (EMG) signals because the EMG signal is strongly influenced by innervation zones. However, simply structured fusiform muscle, such as biceps brachii muscle, has been employed mainly due to the simplicity with which the propagation from raw EMG signals can be observed. In this study, the optimum electrode location (OEL), free from innervational influence, was investigated by the propagation pattern of action potentials for brachii muscles and more complicated deltoid muscle structures using an automatized signal analysis technique. The technique employed newly developed computer software with additional clinical uses and minimized subjective differences. EMG signals were recorded using surface array electrodes during voluntary isometric contractions obtained from 12 healthy male subjects. Peaks in EMG signals were detected and averaged for each muscle. The propagation patterns and OEL were examined from biceps brachii muscles for all subjects and from deltoid muscles for seven subjects. The estimated locations were partially confirmed by comparing the root mean squares of the EMG signals. These results show that propagation patterns and OEL could be estimated simply and automatically even from the surface EMG signals of deltoid muscles.     

A dynamic neural network identification of electromyography and armtrajectory relationship during complex movements

The authors propose a new approach based on dynamic recurrent neural networks (DRNN) to identify, in human, the relationship between the muscle electromyographic (EMG) activity and the arm kinematics during the drawing of the figure eight using an extended arm. After learning, the DRNN simulations showed the efficiency of the model. The authors demonstrated its generalization ability to draw unlearned movements. They developed a test of its physiological plausibility by computing the error velocity vectors when small artificial lesions in the EMG signals were created. These lesion experiments demonstrated that the DRNN has identified the preferential direction of the physiological action of the studied muscles. The network also identified neural constraints such as the covariation between geometrical and kinematics parameters of the movement. This suggests that the information of raw EMG signals is largely representative of the kinematics stored in the central motor pattern. Moreover, the DRNN approach will allow one to dissociate the feedforward command (central motor pattern) and the feedback effects from muscles, skin and joints     

Recording from a Single Motor Unit During Strong Effort

During strong voluntary effort it is rarely possible to identify the action potentials from single motor units. In large muscles the most selective recordings are obtained with bipolar wire electrodes. To elucidate this experimental finding we have calculated the extracellular field around a single muscle fiber from an intracellular muscle action potential. This model showed that the selectivity of a bipolar electrode is high provided: i) the diameter of the recording surfaces is less than half the diameter of the muscle fibers; ii) the center distance between the recording surfaces is of the same order or smaller than the diameter of the muscle fibers, and when iii) the center-line between the recording surfaces is oriented perpendicular to the direction of the muscle fibers.     

Physiologically based simulation of clinical EMG signals

An algorithm that generates electromyographic (EMG) signals consistent with those acquired in a clinical setting is described. Signals are generated using a model constructed to closely resemble the physiology and morphology of skeletal muscle, combined with line source models of commonly used needle electrodes positioned in a way consistent with clinical studies. The validity of the simulation routines is demonstrated by comparing values of statistics calculated from simulated signals with those from clinical EMG studies of normal subjects. The simulated EMG signals may be used to explore the relationships between muscle structure and activation and clinically acquired EMG signals. The effects of motor unit (MU) morphology, activation, and neuromuscular junction activity on acquired signals can be analyzed at the fiber, MU and muscle level. Relationships between quantitative features of EMG signals and muscle structure and activation are discussed.     

Entropy-based optimization of wavelet spatial filters

A new class of spatial filters for surface electromyographic (EMG) signal detection is proposed. These filters are based on the 2-D spatial wavelet decomposition of the surface EMG recorded with a grid of electrodes and inverse transformation after zeroing a subset of the transformation coefficients. The filter transfer function depends on the selected mother wavelet in the two spatial directions. Wavelet parameterization is proposed with the aim of signal-based optimization of the transfer function of the spatial filter. The optimization criterion was the minimization of the entropy of the time samples of the output signal. The optimized spatial filter is linear and space invariant. In simulated and experimental recordings, the optimized wavelet filter showed increased selectivity with respect to previously proposed filters. For example, in simulation, the ratio between the peak-to-peak amplitude of action potentials generated by motor units 20 degrees apart in the transversal direction was 8.58% (with monopolar recording), 2.47% (double differential), 2.59% (normal double differential), and 0.47% (optimized wavelet filter). In experimental recordings, the duration of the detected action potentials decreased from (mean +/- SD) 6.9 +/- 0.3 ms (monopolar recording), to 4.5 +/- 0.2 ms (normal double differential), 3.7 +/- 0.2 (double differential), and 3.0 +/- 0.1 ms (optimized wavelet filter). In conclusion, the new class of spatial filters with the proposed signal-based optimization of the transfer function allows better discrimination of individual motor unit activities in surface EMG recordings than it was previously possible.