Analytical generation model of surface electromyogram for multi-layer volume conductors (original) (raw)
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IEEE Transactions on Biomedical Engineering, 2006
This study analytically describes surface electromyogram (sEMG) signals generated by a model of a triangular muscle, i.e., a muscle with fibres 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 fibres 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 non space 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 (modelling the fat) over the triangular muscle. The results are implemented in a complete sEMG generation model (including the finite length of the fibres), simulating single fibre 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 CV estimation is addressed (for two channels; maximum likelihood and reference point methods). Different fibre depths, electrode placements and small misalignments of the detection system with respect to the fibre have been simulated. The error in CV estimation is large when the depth of the fibre increases, when the detection system is not aligned with the fibre and close to the innervation point and to the tendons.
Medical & Biological Engineering & Computing, 2004
Surface electromyographic (EMG) signal modelling is important for signal interpretation, testing of processing algorithms, detection system design and didactic purposes. Various surface EMG signal models have been proposed in the literature. This study focuses on the proposal of a method for modelling surface EMG signals, using either analytical or numerical descriptions of the volume conductor for space-conductor by numerical approaches, accurately describing the volume conductor geometry and the conductivity, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function has been derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fibre orientation. In some cases (e.g. multi-pinnate muscles), accurate description of the conductivity tensor can be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibres is presented and applied to investigate representatively a bi-pinnate muscle with rectilinear and curvilinear fibres. The study thus proposes an approach for surface EMG signal simulation in space invariant systems, as well as new models of the volume conductor using numerical methods.
A surface EMG generation model with multilayer cylindrical description of the volume conductor
IEEE Transactions on Biomedical Engineering, 2004
We propose a model for surface EMG signal generation with cylindrical description of the volume conductor. The model is more general and complete with respect to previous approaches. The volume conductor is described as a multi-layered cylinder in which the source can be located either along the longitudinal or the angular direction, in any of the layers. The source is represented as a spatio-temporal function which describes the generation, propagation, and extinction of the intracellular action potential at the end-plate, along the fiber, and at the tendons, respectively. The layers are anisotropic. The volume conductor effect is described as a two dimensional spatial filtering. Electrodes of any shape or dimension are simulated, forming structures which are described as spatial filters. The analytical derivation which leads to the signal in the temporal domain is performed in the spatial and temporal frequency domains. Numerical issues related to the frequency-based approach are discussed. The descriptions of the volume conductor and of the source are applied to the cases of signal generation from a limb and a sphincter muscle. Representative simulations of both cases are provided. The resultant model is based on analytical derivations and constitutes a step forward in surface EMG signal modeling, including features not described in any other analytical approach.
IEEE Transactions on Biomedical Engineering, 2006
A non-space invariant model of volume conductor for surface 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.
Volume conductor models in surface electromyography: Computational techniques
Computers in Biology and Medicine, 2013
Simulation of surface electromyogram (EMG) provided support for the development and test of algorithms and for the interpretation of experimental results. This is the second part of a pair of papers: the first explains the methods for the development of structure based models of surface EMG; this one provides a summary of interesting applications for the interpretation of signals and test of algorithms. Simulations from some models already introduced in the literature are compared. Moreover, estimation of indexes from an innovative layered volume conductor including a subcutaneous tissue with variable thickness in space is studied.
A novel approach for precise simulation of the EMG signal detected by surface electrodes
IEEE Transactions on Biomedical Engineering, 2001
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.
IEEE Transactions on Biomedical Engineering, 2004
Surface 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 in-homogeneities 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 in-homogeneous 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 non-homogenous, 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.
A model for surface EMG generation in volume conductors with spherical inhomogeneities
IEEE Transactions on Biomedical Engineering, 2005
Most models for surface 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, thus the surface signal detected along the direction of the muscle fibers may significantly change shape along the propagation path. An important class of non-space invariant systems is that of volume conductors in-homogeneous in the direction of source propagation. In this study we focused on inhomogeneities introduced by the presence of spheres of different conductivities with respect to the tissue where they are located. This may 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 analytically discussed. The model is computationally fast and constitutes an advanced mean for the analysis and interpretation of surface EMG signal features.
Three-Layer Volume Conductor Model and Software Package for Applications in Surface Electromyography
Annals of Biomedical Engineering, 2002
On comparing multichannel surface electromyographic measurements of the m. biceps brachii with simulations performed with a previously developed two-layer volume conduction model, we found substantial discrepancies. To incorporate an apparent distorting effect of the skin tissue, the model was extended to three layers. This new model describes the potential resulting from an eccentric bioelectric source in a finite, cylindrical, and anisotropic volume conductor consisting of three layers, representing muscle, subcutaneous fat, and skin tissue. This contribution presents the governing mathematical equations of the three-layer volume conductor model as well as our approach to their solution. A comparison of various models shows that the three-layer model best describes measured potential distributions. Furthermore, we present the ''ANVOLCON'' Í‘analytical volume conductorÍ’ software package. This package has been developed to facilitate the use of the model for scientific and educational purposes and is freely available from
IEEE Transactions on Biomedical Engineering, 2008
This study analytically describes surface electromyogram (sEMG) signals generated by a model of a triangular muscle, i.e., a muscle with fibres 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 fibres 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 non space 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 (modelling the fat) over the triangular muscle. The results are implemented in a complete sEMG generation model (including the finite length of the fibres), simulating single fibre 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 CV estimation is addressed (for two channels; maximum likelihood and reference point methods). Different fibre depths, electrode placements and small misalignments of the detection system with respect to the fibre have been simulated. The error in CV estimation is large when the depth of the fibre increases, when the detection system is not aligned with the fibre and close to the innervation point and to the tendons.