Advances in surface electromyographic signal simulation with analytical and numerical descriptions of the volume conductor

A myoelectric digital twin for fast and realistic modelling in deep learning

Muscle electrophysiology has emerged as a powerful tool to drive human machine interfaces, with many new recent applications outside the traditional clinical domains, such as robotics and virtual reality. However, more sophisticated, functional, and robust decoding algorithms are required to meet the fine control requirements of these applications. Deep learning has shown high potential in meeting these demands, but requires a large amount of high-quality annotated data, which is expensive and time-consuming to acquire. Data augmentation using simulations, a strategy applied in other deep learning applications, has never been attempted in electromyography due to the absence of computationally efficient models. We introduce a concept of Myoelectric Digital Twin - highly realistic and fast computational model tailored for the training of deep learning algorithms. It enables simulation of arbitrary large and perfectly annotated datasets of realistic electromyography signals, allowing new approaches to muscular signal decoding, accelerating the development of human-machine interfaces.

Investigating the spatial resolution of EMG and MMG based on a systemic multi-scale model

While electromyography (EMG) and magnetomyography (MMG) are both methods to measure the electrical activity of skeletal muscles, no systematic comparison between both signals exists. Within this work, we propose a novel in silico model for EMG and MMG and test the hypothesis that MMG surpasses EMG in terms of spatial selectivity, i.e. the ability to distinguish spatially shifted sources. The results show that MMG provides a slightly better spatial selectivity than EMG when recorded directly on the muscle surface. However, there is a remarkable difference in spatial selectivity for non-invasive surface measurements. The spatial selectivity of the MMG components aligned with the muscle fibres and normal to the body surface outperforms the spatial selectivity of surface EMG. Particularly, for the MMG’s normal-to-the-surface component the influence of subcutaneous fat is minimal. Further, for the first time, we analyse the contribution of different structural components, i.e. muscle fibres from different motor units and the extracellular space, to the measurable biomagnetic field. Notably, the simulations show that for the normal-to-the-surface MMG component, the contribution from volume currents in the extracellular space and in surrounding inactive tissues, is negligible. Further, our model predicts a surprisingly high contribution of the passive muscle fibres to the observable magnetic field.

Analytical Modelling of Surface EMG Signals Generated by Curvilinear Fibers with Approximate Conductivity Tensor

OBJECTIVE

Mathematical modelling of surface electromyographic (EMG) signals has been proven a valuable tool to interpret experimental data and to validate signal processing techniques. Most analytical EMG models only consider muscle fibers with specific and fixed arrangements. However, the fiber orientation and curvature may change along the fiber paths and may differ from fiber to fiber. Here we propose a subject-specific EMG model that simulates the fiber trajectories in muscles of the upper arm and analytically derives the action potentials assuming an approximate conductivity tensor.

METHODS

Magnetic Resonance (MR) images were acquired to identify and generate muscle fiber paths and to determine the muscle locations in a cylindrical volume conductor. While the propagation of the action potentials followed the identified curvilinear fiber paths, the conductivity tensor was not adapted to the fiber direction but approximated along the longitudinal axis of the cylindrical volume conductor. Single fiber action potentials (SFAPs) were computed by simulating the generation, propagation, and extinction of membrane current sources. To validate the assumption of the approximate conductivity tensor, two numerical models were implemented for comparison with the analytical solution. The first numerical model reproduced the analytical model and therefore included an approximation for the conductivity tensor. The second numerical model included the exact conductivity tensor derived from the fiber curvatures.

RESULTS

The motor unit action potentials generated by the proposed analytical model and the two numerical models were highly similar (cross-correlation >0.98, normalized root mean square error, nRMSE 0.04, relative error in the median frequency of the simulated waveforms of approximately 3%). The proposed analytical model was also evaluated by comparing simulated and experimentally recorded compound muscle action potentials (CMAPs). The CMAPs simulated with the proposed model better matched the experimental data (cross-correlation >0.90 and nRMSE <0.25 for the majority of the channels) than a model with straight fibers. Finally, the proposed model was representatively used to test the accuracy of an EMG decomposition algorithm, providing a realistic benchmark.

CONCLUSIONS AND SIGNIFICANCE

The proposed analytical model generates action potentials that reflect the spatial distributions of muscle fibers with curvilinear paths. The simulated signals are more realistic than signals generated by analytical models with straight fibers and can therefore be applied for testing EMG processing algorithms with a trade-off between simulation accuracy and computational speed.

Implementation and experimental validation of surface electromyogram and force model of Tibialis Anterior muscle for examining muscular factors

This study reports a surface electromyogram and force of contraction model. The objective was to investigate the effect of changes in the size, type and number of motor units in the Tibialis Anterior muscle to surface electromyogram and force of dorsiflexion. A computational model to simulate surface electromyogram and associated force of contraction by the Tibialis Anterior muscle was developed. This model was simulated for isometric dorsiflexion, and comparative experiments were conducted for validation. Repeated simulations were performed to investigate the different parameters and evaluate inter-experimental variability. An equivalence statistical test and the Bland–Altman method were used to observe the significance between the simulated and experimental data. Simulated and experimentally recorded data had high similarity for the three measures: maximal power of power spectral density ( p < 0.0001), root mean square of surface electromyogram ( p < 0.0001) and force recorded at the footplate ( p < 0.03). Inter-subject variability in the experimental results was in-line with the variability in the repeated simulation results. This experimentally validated computational model for the surface electromyogram and force of the Tibialis Anterior muscle is significant as it allows the examination of three important muscular factors associated with ageing and disease: size, fibre type and number of motor units.

Modelling the electrical activity of skeletal muscle tissue using a multi-domain approach

Electromyography (EMG) can be used to study the behaviour of the motor neurons and thus provides insights into the physiology of the central nervous system. However, due to the high complexity of neuromuscular control, EMG signals are challenging to interpret. While the exact knowledge of the excitation patterns of a specific muscle within an in vivo experimental setting remains elusive, simulations allow to systematically investigate EMG signals in a controlled environment. Within this context, simulations can provide virtual EMG data, which, for example, can be used to validate and optimise signal analysis methods that aim to estimate the relationship between EMG signals and the output of motor neuron pools. However, since existing methods, which are employed to compute EMG signals, exhibit deficiencies with respect to the physical model itself as well as with respect to numerical aspects, we propose a novel homogenised continuum model that closely resolves the electro-physiological behaviour of skeletal muscle tissue. The proposed model is based on an extension of the well-established bidomain model and includes a biophysically detailed description of the electrical activity within the tissue, which is due to the depolarisation of the muscle fibre membranes. In contrast to all other published EMG models, which assume that the electrical potential field for each muscle fibre can be calculated independently, the proposed model assumes that the electrical potential in the muscle fibres is coupled to the electrical potential in the extracellular space. We show that the newly proposed model is able to simulate realistic EMG signals and demonstrate the potential to employ the predicted virtual EMG signal in order to evaluate the goodness of automated decomposition algorithms.

Anatomically accurate model of EMG during index finger flexion and abduction derived from diffusion tensor imaging

This study presents a modelling framework in which information on muscle fiber direction and orientation during contraction is derived from diffusion tensor imaging (DTI) and incorporated in a computational model of the surface electromyographic (EMG) signal. The proposed model makes use of the principle of reciprocity to simultaneously calculate the electric potentials produced at the recording electrode by charges distributed along an arbitrary number of muscle fibers within the muscle, allowing for a computationally efficient evaluation of extracellular motor unit action potentials. The approach is applied to the complex architecture of the first dorsal interosseous (FDI) muscle of the hand to simulate EMG during index finger flexion and abduction. Using diffusion tensor imaging methods, the results show how muscle fiber orientation and curvature in this intrinsic hand muscle change during flexion and abduction. Incorporation of anatomically accurate muscle architecture and other hand tissue morphologies enables the model to capture variations in extracellular action potential waveform shape across the motor unit population and to predict experimentally observed differences in EMG signal features when switching from index finger abduction to flexion. The simulation results illustrate how structural and electrical properties of the tissues comprising the volume conductor, in combination with fiber direction and curvature, shape the detected action potentials. Using the model, the relative contribution of motor units of different sizes located throughout the muscle under both conditions is examined, yielding a prediction of the detection profile of the surface EMG electrode array over the muscle cross-section.

Advances in diffusion tensor imaging are providing new information on muscle architecture and the orientation of muscle fibers in vivo. The arrangement of muscle fibers, in combination with geometrical and electrical properties of the surrounding biological tissues, shapes the electrical signal recorded at the skin surface during muscle contraction. As new recording and analysis methods enable muscle and motor unit activity to be examined during complex dynamic contractions, changes in muscle fiber orientation and surrounding tissue properties pose challenges for the interpretation of these data. Here we incorporate details of tissue geometry and muscle fiber architecture obtained using anatomical and diffusion MRI into an anatomically accurate model of electromyography (EMG) signal generation in the first dorsal interosseous muscle of the hand. The new modeling approach presented integrates interdependent electrical and geometrical properties in an anatomically accurate manner, leading to a realistic EMG model where tissue electrical properties are inherently related to bioelectric aspects of muscle activation. The results show how muscle fiber orientation and curvature change according to the direction of force generation, influencing the EMG signal, and provide new insights on how constitutive, anatomical and physiological properties contribute to shape motor unit action potentials detected at the skin surface.

Motor Unit Action Potential Clustering-Theoretical Consideration for Muscle Activation during a Motor Task

During dynamic or sustained isometric contractions, bursts of muscle activity appear in the electromyography (EMG) signal. Theoretically, these bursts of activity likely occur because motor units are constrained to fire temporally close to one another and thus the impulses are "clustered" with short delays to elicit bursts of muscle activity. The purpose of this study was to investigate whether a sequence comprised of "clustered" motor unit action potentials (MUAP) can explain spectral and amplitude changes of the EMG during a simulated motor task. This question would be difficult to answer experimentally and thus, required a model to study this type of muscle activation pattern. To this end, we modeled two EMG signals, whereby a single MUAP was either convolved with a randomly distributed impulse train (EMG-rand) or a "clustered" sequence of impulses (EMG-clust). The clustering occurred in windows lasting 5-100 ms. A final mixed signal of EMG-clust and EMG-rand, with ratios (1:1-1:10), was also modeled. A ratio of 1:1 would indicate that 50% of MUAP were randomly distributed, while 50% of "clustered" MUAP occurred in a given time window (5-100 ms). The results of the model showed that clustering MUAP caused a downshift in the mean power frequency (i.e., ~30 Hz) with the largest shift occurring with a cluster window of 10 ms. The mean frequency shift was largest when the ratio of EMG-clust to EMG-rand was high. Further, the clustering of MUAP also caused a substantial increase in the amplitude of the EMG signal. This model potentially explains an activation pattern that changes the EMG spectra during a motor task and thus, a potential activation pattern of muscles observed experimentally. Changes in EMG measurements during fatiguing conditions are typically attributed to slowing of conduction velocity but could, per this model, also result from changes of the clustering of MUAP. From a clinical standpoint, this type of muscle activation pattern might help describe the pathological movement issues in people with Parkinson's disease or essential tremor. Based on our model, researchers moving forward should consider how MUAP clustering influences EMG spectral and amplitude measurements and how these changes influence movements.

A computational model to investigate the effect of pennation angle on surface electromyogram of Tibialis Anterior

This study has described and experimentally validated the differential electrodes surface electromyography (sEMG) model for tibialis anterior muscles during isometric contraction. This model has investigated the effect of pennation angle on the simulated sEMG signal. The results show that there is no significant effect of pennation angle in the range 0° to 20° to the single fibre action potential shape recorded on the skin surface. However, the changes with respect to pennation angle are observed in sEMG amplitude, frequency and fractal dimension. It is also observed that at different levels of muscle contractions there is similarity in the relationships with Root Mean Square, Median Frequency, and Fractal Dimension of the recorded and simulated sEMG signals.

Predicting electromyographic signals under realistic conditions using a multiscale chemo-electro-mechanical finite element model

This paper presents a novel multiscale finite element-based framework for modelling electromyographic (EMG) signals. The framework combines (i) a biophysical description of the excitation-contraction coupling at the half-sarcomere level, (ii) a model of the action potential (AP) propagation along muscle fibres, (iii) a continuum-mechanical formulation of force generation and deformation of the muscle, and (iv) a model for predicting the intramuscular and surface EMG. Owing to the biophysical description of the half-sarcomere, the model inherently accounts for physiological properties of skeletal muscle. To demonstrate this, the influence of membrane fatigue on the EMG signal during sustained contractions is investigated. During a stimulation period of 500 ms at 100 Hz, the predicted EMG amplitude decreases by 40% and the AP propagation velocity decreases by 15%. Further, the model can take into account contraction-induced deformations of the muscle. This is demonstrated by simulating fixed-length contractions of an idealized geometry and a model of the human tibialis anterior muscle (TA). The model of the TA furthermore demonstrates that the proposed finite element model is capable of simulating realistic geometries, complex fibre architectures, and can include different types of heterogeneities. In addition, the TA model accounts for a distributed innervation zone, different fibre types and appeals to motor unit discharge times that are based on a biophysical description of the α motor neurons.

Volume conductor models in surface electromyography: computational techniques

Models of surface electromyogram (EMG) are useful to assess the effect of geometrical or conductivity properties of the tissue on the recorded signal. This paper provides a review of structure based models describing specific volume conductors. The technique for the development of advanced analytical and numerical simulators is described. A new model is also introduced, simulating a layered volume conductor including a subcutaneous tissue with variable thicknesses, providing an approximate analytical solution in the Fourier transform domain. Note that volume conductors are described using Poisson equation, fundamental model of Mathematical Physics, which applies also to mechanics, diffusion, electrostatics problems.

Insights gained into the interpretation of surface electromyograms from the gastrocnemius muscles: A simulation study

Interpretation of surface electromyograms (EMG) is usually based on the assumption that the surface representation of action potentials does not change during their propagation. This assumption does not hold for muscles whose fibers are oblique to the skin. Consequently, the interpretation of surface EMGs recorded from pinnate muscles unlikely prompts from current knowledge. Here we present a complete analytical model that supports the interpretation of experimental EMGs detected from muscles with oblique architecture. EMGs were recorded from the medial gastrocnemius muscle during voluntary and electrically elicited contractions. Preliminary indications obtained from simulated and experimental signals concern the spatial localization of surface potentials and the myoelectric fatigue. Specifically, the spatial distribution of surface EMGs was localized about the fibers superficial extremity. Strikingly, this localization increased with the pinnation angle, both for the simulated EMGs and the recorded M-waves. Moreover, the average rectified value (ARV) and the mean frequency (MNF) of interference EMGs increased and decreased with simulated fatigue, respectively. The degree of variation in ARV and MNF did not depend on the pinnation angle simulated. Similar variations were observed for the experimental EMGs, although being less evident for a higher fiber inclination. These results are discussed on a physiological context, highlighting the relevance of the model proposed here for the interpretation of gastrocnemius EMGs and for conceiving future experiments on muscles with pinnate geometry.

Geometry assessment of anal sphincter muscle based on monopolar multichannel surface EMG signals

Anatomical studies on the external anal sphincter (EAS) indicate that superficial muscle fibres are circular at low depth within the anal canal. A more complex geometry of the fibres is documented for increasing depth within the muscle and along the anal canal. Monopolar intra-anal EMG signals recorded using an array of electrodes placed in circular direction have no common mode components if the muscle fibres are circular, with constant depth within the muscle and parallel to the detection array. Thus, the presence of common mode signals may provide indications about the geometry of muscle fibres of EAS. Intra-anal EMG signals were recorded from EAS of 12 subjects using an anal probe carrying three circumferential arrays of 16 electrodes at three depths within the anal canal. Contribution of common mode components in single MUAPs was lower for MUs located superficially in the muscle (Pearson correlation coefficient: R=-0.75, p≪0.001) and at a lower depth within the anal canal (non-parametric one way Kruskal-Wallis ANOVA, Χ=17.3, p<0.001), in line with EAS anatomy. A large contribution of common mode components was found in the interference signal, suggesting that the signal receives contributions from far, large muscles (e.g. puborectalis, glutei).

Detection of individual motor units of the puborectalis muscle by non-invasive EMG electrode arrays

PURPOSE

The purpose of the study was to demonstrate that anatomical features of individual motor units of the puborectalis muscle can be detected with non-invasive electromyography (EMG) and to evaluate differences in electrophysiological properties of the puborectalis muscles in a small group of healthy and pathologic subjects.

METHODS

Multichannel EMG was recorded by means of a flexible probe applied on the gloved index finger and carrying an array of eight equally spaced (1.15 mm) electrodes. A multichannel EMG amplifier provided seven outputs corresponding to the pairs of adjacent electrodes. Tests were performed in three different positions (dorsal, left and right) over the puborectalis muscle on 20 subjects (nine healthy, seven constipated and four incontinent patients). Motor unit action potentials (MUAPs) generated at the innervation zone of a MU and propagating along the muscle fibers generated repetitive characteristic patterns on the seven output channels allowing identification of anatomical features of the motor units.

RESULTS

MUAPs were observed travelling in either one or both directions with the array in dorsal position, and mainly in ventral-to-dorsal direction in either lateral position. MUAP amplitude was lower in constipated and incontinent patients with respect to healthy subjects. The conduction velocity estimated on the identified MUAPs was lower for constipated patients with respect to healthy subjects suggesting different mechanical properties of the active motor units.

CONCLUSIONS

This technique allows the extraction of relevant information about the anatomical features (innervation zone position and overlapping of motor unit branches) of the puborectalis muscle and its electrophysiological properties and maybe can be applied as an novel methodology for assessing the anorectal function in patients.

Distribution of electrical stimulation current in a planar multilayer anisotropic tissue

This study analytically addresses the problem of neuromuscular electrical stimulation for a planar, multilayer, anisotropic model of a physiological tissue (referred to as volume conductor). Both conductivity and permittivity of the volume conductor are considered, including dispersive properties. The analytical solution is obtained in the 2-D Fourier transform domain, transforming in the planes parallel to the volume conductor surface. The model is efficient in terms of computational cost, as the solution is analytical (only numerical Fourier inversion is needed). It provides the current distribution in a physiological tissue induced by an electrical current delivered at the skin surface. Three representative examples of application of the model are considered. 1) The simulation of stimulation artefact during transcutaneous electrical stimulation and EMG detection. Only the effect of the volume conductor is considered, neglecting the other sources of artefact (such as the capacitive coupling between the stimulating and recording electrodes). 2) The simulation of the electrical current distribution within the muscle and the low-pass filter effect of the volume conductor on sinusoidal stimulation currents with different stimulation frequencies. 3) The estimation of the amplitude modulated current distribution within the muscle for interferential stimulation. The model is devoted to the simulation of neuromuscular stimulation, but the same method could be applied in other fields in which the estimation of the electrical current distribution in a medium induced by the injection of a current from the boundary of the medium is of interest.

Estimation of average muscle fiber conduction velocity from simulated surface EMG in pinnate muscles

The aim of this simulation study was to assess the bias in estimating muscle fiber conduction velocity (CV) from surface electromyographic (EMG) signals in muscles with one and two pinnation angles. The volume conductor was a layered medium simulating anisotropic muscle tissue and isotropic homogeneous subcutaneous tissue. The muscle tissue was homogeneous for one pinnation angle and inhomogeneous for bipinnate muscles (two fiber directions). Interference EMG signals were obtained by simulating recruitment thresholds and discharge patterns of a set of 100 and 200 motor units for the pinnate and bipinnate muscle, respectively (15 degrees pinnation angel in both cases). Without subcutaneous layer and muscle fibers with CV 4m/s, average CV estimates from the pinnate (bipinnate) muscle were 4.81+/-0.18 m/s (4.80+/-0.18 m/s) for bipolar, 4.71+/-0.19 m/s (4.71+/-0.12 m/s) for double differential, and 4.78+/-0.16 m/s (4.79+/-0.15m/s) for Laplacian recordings. When subcutaneous layer was added (thickness 1mm) in the same conditions, estimated CV values were 4.93+/-0.25 m/s (5.16+/-0.41 m/s), 4.70+/-0.21 m/s (4.83+/-0.33 m/s), and 4.89+/-0.21 m/s (4.99+/-0.39 m/s), for the three recording systems, respectively. The main factor biasing CV estimates was the propagation of action potentials in the two directions which influenced the recording due to the scatter of the projection of end-plate and tendon locations along the fiber direction, as a consequence of pinnation. The same problem arises in muscles with the line of innervation zone locations not perpendicular to fiber direction. These results indicate an important limitation in reliability of CV estimates from the interference EMG when the innervation zone and tendon locations are not distributed perpendicular to fiber direction.

Clinical applications of high-density surface EMG: A systematic review

High density-surface EMG (HD-sEMG) is a non-invasive technique to measure electrical muscle activity with multiple (more than two) closely spaced electrodes overlying a restricted area of the skin. Besides temporal activity HD-sEMG also allows spatial EMG activity to be recorded, thus expanding the possibilities to detect new muscle characteristics. Especially muscle fiber conduction velocity (MFCV) measurements and the evaluation of single motor unit (MU) characteristics come into view. This systematic review of the literature evaluates the clinical applications of HD-sEMG. Although beyond the scope of the present review, the search yielded a large number of "non-clinical" papers demonstrating that a considerable amount of work has been done and that significant technical progress has been made concerning the feasibility and optimization of HD-sEMG techniques. Twenty-nine clinical studies and four reviews of clinical applications of HD-sEMG were considered. The clinical studies concerned muscle fatigue, motor neuron diseases (MND), neuropathies, myopathies (mainly in patients with channelopathies), spontaneous muscle activity and MU firing rates. In principle, HD-sEMG allows pathological changes at the MU level to be detected, especially changes in neurogenic disorders and channelopathies. We additionally discuss several bioengineering aspects and future clinical applications of the technique and provide recommendations for further development and implementation of HD-sEMG as a clinical diagnostic tool.

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.

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 Finite Element Model for Describing the Effect of Muscle Shortening on Surface EMG

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

A 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.

Sensitivity of surface EMG-based conduction velocity estimates to local tissue in-homogeneities – influence of the number of channels and inter-channel distance

The aim of this simulation study was to investigate the influence of local tissue in-homogeneities on the estimates of muscle fiber conduction velocity (CV) from surface EMG signals. A recently developed analytical surface EMG model was used to generate simulated surface EMG signals from a planar layered volume conductor, comprised of the muscle tissue and fat layer, with spheres (1 mm radius) in the fat layer of conductivity different from the surrounding tissue. CV was estimated with a maximum likelihood multi-channel approach, varying the number of channels and the inter-channel distance used for the estimate. The action potentials detected along the muscle fiber direction changed shape due to the presence of the in-homogeneities, thus affecting CV estimates. CV estimates were influenced by the location of the in-homogeneities with respect to the fiber and detection electrodes. The maximum percent variation of CV estimates due to the presence of in-homogeneities decreased with increasing number of channels and inter-channel distance: 19.6% (2 channels), 12.1% (3 channels), 6.4% (4 channels), for 5 mm inter-channel distance, and 12.0% (2 channels), 5.2% (3 channels), 2.4% (4 channels), for 10 mm inter-channel distance (for double differential detection). The results were in agreement and explained previous experimental findings. It was concluded that multi-channel methods for CV estimation significantly reduce the sensitivity of CV estimates to tissue in-homogeneities.

Methods for estimating muscle fibre conduction velocity from surface electromyographic signals

The review focuses on the methods currently available for estimating muscle fibre conduction velocity (CV) from surface electromyographic (EMG) signals. The basic concepts behind the issue of estimating CV from EMG signals are discussed. As the action potentials detected at the skin surface along the muscle fibres are, in practice, not equal in shape, the estimation of the delay of propagation (and thus of CV) is not a trivial task. Indeed, a strictly unique definition of delay does not apply in these cases. Methods for estimating CV can thus be seen as corresponding to specific definitions of the delay of propagation between signals of unequal shape. The most commonly used methods for CV estimation are then reviewed. Together with classic methods, recent approaches are presented. The techniques are described with common notations to underline their relationships and to highlight when an approach is a generalisation of a previous one or when it is based on new concepts. The review identifies the difficulties of CV estimation and underlines the issues that should be considered by the investigator when selecting a particular method and detection system for assessing muscle fibre CV. The many open issues in CV estimation are also presented.