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 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.     

Simulation of surface EMG signals for a multilayer volume conductor with a superficial bone or blood vessel

This study analytically describes surface electromyogram (EMG) signals generated by a planar multilayer volume conductor constituted by different subdomains modeling muscle, bone (or blood vessel), fat, and skin tissues. The bone is cylindrical in shape, with a semicircular section. The flat portion of the boundary of the bone subdomain is interfaced with the fat layer tissue, the remaining part of the boundary is in contact with the muscle layer. The volume conductor is a model of physiological tissues in which the bone is superficial, as in the case of the tibia bone, backbone, and bones of the forearm. The muscle fibers are considered parallel to the axes of the bone, so that the model is space invariant in the direction of propagation of the action potential. The proposed model, being analytical, allows faster simulations of surface EMG with respect to previously developed models including bone or blood vessels based on the finite-element method. Surface EMG signals are studied by simulating a library of single-fiber action potentials (SFAP) of fibers in different locations within the muscle domain, simulating the generation, propagation, and extinction of the action potential. The decay of the amplitude of the SFAPs in the direction transversal to the fibers is assessed. The decay in the direction of the bone has a lower rate with respect to the opposite direction. Similar results are obtained by simulating motor unit action potentials (MUAPs) constituted by 100 fibers with territory 5 mm2. M waves and interference EMG signals are also simulated based on the library of SFAPs. Again, the decay of the amplitude of the simulated interference EMG signals is lower approaching the bone with respect to going farther from it. The findings of this study indicate the effect of a superficial bone in enhancing the EMG signals in the transversal direction with respect to the fibers of the considered muscle. This increases the effect of crosstalk. The same mathematical method used to simulate a superficial bone can be applied to simulate other physiological tissues. For example, superficial blood vessels (e.g., basilic vein, brachial artery) can influence the recorded EMG signals. As the electrical conductivity of blood is high (it is of the same order as the longitudinal conductivity in the muscle), the effect on EMG signals is opposite compared to the effect of a superficial bone.     

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.     

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.     

The Forward Problem in Electroneurography I: A Generalized Volume Conductor Model

We describe a generalized volume conductor model for the compound action potential (CAP) of a peripheral nerve in situ. The extracellular single fiber action potentials (SFAP's), the constituting elements of the CAP, are expressed in terms of the intracellular action potentials and of the effect of volume conduction using a convolution formulation. The model incorporates variations in the intracellular action potential duration over the fiber population. Volume conduction is described in a generalized formalism for a class of cylinder symmetrical configurations. The CAP is finally formulated as a linear sumation of the SFAP's, with incorporation of the distribution of propagaytion velocities over the fiber population. We show that the final expressions for SFAP's and CAP can be given in a mathematically transparent form, which gives a clear insight into the mechanisms involved in the genesis of different potential waveshapes.     

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.     

A model of the magnetic fields created by single motor unitcompound action potentials in skeletal muscle

We have developed a computationally simple model for calculating the magnetic-field strength at a point due to a single motor unit compound action potential (SMUCAP). The motor unit is defined only in terms of its anatomical features, and the SMUCAP is approximated using the tripole model. The distributed current density J is calculated within the volume defined by the motor unit. The law of Biot and Savart can then be cast in a form necessitating that J be integrated only over the region containing current sources or conductivity boundaries. The magnetic-field strength is defined as the summation of the contributions to the field made by every muscle fiber in the motor unit. Applying this model to SMUCAP measurements obtained using a high-resolution SUper Conducting Quantum Interference Device (SQUID) magnetometer may yield information regarding the distribution of action currents (AC's) and the anatomical properties of single motor units within a muscle bundle     

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.     

A new method to derive white matter conductivity from diffusion tensor MRI

We propose a new algorithm to derive the anisotropic conductivity of the cerebral white matter (WM) from the diffusion tensor MRI (DT-MRI) data. The transportation processes for both water molecules and electrical charges are described through a common multicompartment model that consists of axons, glia, or the cerebrospinal fluid (CSF). The volume fraction (VF) of each compartment varies from voxel to voxel and is estimated from the measured diffusion tensor. The conductivity tensor at each voxel is then computed from the estimated VF values and the decomposed eigenvectors of the diffusion tensor. The proposed VF algorithm was applied to the DT-MRI data acquired from two healthy human subjects. The extracted anisotropic conductivity distribution was compared with those obtained by using two existing algorithms, which were based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. The present results suggest that the VF algorithm is capable of incorporating the partial volume effects of the CSF and the intravoxel fiber crossing structure, both of which are not addressed altogether by existing algorithms. Therefore, it holds potential to provide a more accurate estimate of the WM anisotropic conductivity, and may have important applications to neuroscience research or clinical applications in neurology and neurophysiology.      

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.     

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.     

Simulation of propagation along a cylindrical bundle of cardiactissue. II. Results of simulation

Previous evaluations of the cylindrical bidomain model of a bundle of cardiac tissue, have been obtained by using an analytic function for the transmembrane potential and assuming the activating wavefront through the bundle cross section is planar. In this paper, nonlinear membrane kinetics are introduced into the bidomain membrane and equal anisotropy ratios are assumed, permitting the transmembrane potential to be computed and its behavior examined at different depths in the bundle and for different values of conductivity and bundle diameters. In contrast with single fiber models, the bundle model reveals that the shape of the action potential is influenced by tissue resistivities. In addition, the steady-state activation wavefront through the cross-section perpendicular to the long axis of the bundle is not planar and propagates with a velocity that lies between that of a single fiber in an unbounded volume and a single fiber in a restricted extracellular space. In general, the bundle model is shown to be significantly better than the classical single fiber model in describing the behavior of real cardiac tissue.     

Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing

The simulation of the propagation of electrical activity in a membrane-based realistic-geometry computer model of the ventricles of the human heart, using the governing monodomain reaction-diffusion equation, is described. Each model point is represented by the phase 1 Luo-Rudy membrane model, modified to represent human action potentials. A separate longer duration action potential was used for the M cells found in the ventricular midwall. Cardiac fiber rotation across the ventricular wall was implemented via an analytic equation, resulting in a spatially varying anisotropic conductivity tensor and, consequently, anisotropic propagation. Since the model comprises approximately 12.5 million points, parallel processing on a multiprocessor computer was used to cut down on simulation time. The simulation of normal activation as well as that of ectopic beats is described. The hypothesis that in situ electrotonic coupling in the myocardium can diminish the gradients of action-potential duration across the ventricular wall was also verified in the model simulations. Finally, the sensitivity of QRST integral maps to local alterations in action-potential duration was investigated.     

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 model of the muscle action potential for describing the leadingedge, terminal wave, and slow afterwave

The leading edge, terminal wave, and slow afterwave of the motor-unit action potential (MUAP) are produced by changes in the strength of electrical sources in the muscle fibers rather than by movement of sources. The latencies and shapes of these features are, therefore, determined primarily by the motor-unit (MU) architecture and the intracellular action potential (IAP), rather than by the volume-conduction characteristics of the limb. We present a simple model to explain these relationships. The MUAP is modeled as the convolution of a source function related to the IAP and a weighting function related to the MU architecture. The IAP waveform is modeled as the sum of a spike and a slow repolarization phase. The MU architecture is modeled by assuming that the individual fibers lie along a single equivalent axis but that their action potentials have dispersed initiation and termination times. The model is illustrated by simulating experimentally recorded MUAPs and compound muscle action potentials.     

On Modeling the Single Motor Unit Action Potential

A model has been proposed for the generation of single motor unit potentials routinely observed in the clinical EMG examination of the normal biceps brachii muscle. A dipole representation was chosen for the single fiber activity. The motor unit was constructed from a uniform random array of single fibers. Motor unit potentials generated by this array have been observed at various distances both inside and outside the array. The effects of single fiber dipole axial dispersions on the potentials observed at increasing distances from the array have also been investigated. Motor unit potentials generated by the model have been compared with existing data from multielectrode studies in the biceps brachii.