Point Electrode Model Research Articles

Flexible-Center Hat Complete Electrode Model for EEG Forward Problem.

This study aims to develop a more realistic electrode model by incorporating the non-uniform distribution of electrode contact conductance (ECC) and the shunting effects, to accurately solve EEG forward problem (FP). Firstly, a hat function is introduced to construct a more realistic hat-shaped distribution (HD) for ECC. Secondly, this hat function is modified by applying two parameters - offset ratio and offset direction - to account for the variability in ECC's center and to develop the flexible-center HD (FCHD). Finally, by integrating this FCHD into the complete electrode model (CEM) with the shunting effects, a novel flexible-center hat complete electrode model (FCH-CEM) is proposed and used to solve FP. Simulation experiments using a realistic head model demonstrate the necessity of FCH-CEM and its potential to improve the accuracy of the FP solution compared to current models, i.e., the point electrode model (PEM) and CEM. And compared to PEM, it has better performance under coarse mesh conditions (2 mm). Further experiments indicate the significance of considering shunting effects, as ignoring them results in larger errors than coarse mesh when the average contact conductance is large (101S/m2). The proposed FCH-CEM has better accuracy and performance than PEM and complements CEM in finer meshes, making it necessary for coarse meshes. This study proposes a novel model that enhances electrode modeling and FP accuracy, and provides new ideas and methods for future research.

Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography

This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes. The results are first proven for the unit disk via trigonometric interpolation and quadrature rules, and they are subsequently extended to more general domains with the help of conformal mappings.

On the effect of electrode finiteness in small-scale electrical resistivity imaging

Electrical resistivity tomography (ERT) profiles including finite steel-rod electrodes have been widely used in assuming a surface-node current injection for inversion. This hypothesis was shown by others to be safe for ratios of electrode embedment to electrode spacing smaller than 20%. Relying on the conductive cell model (CCM), we took into account the complete electrodes in the DC forward problem. We found that an electrode effect is included in resistivity sections inverted with a surface point electrode model. Several synthetic examples indicated that this unwanted effect is particularly developed when the electrode spacing does not meet a double constraint from the characteristic size of a shallow heterogeneity and from the electrode embedment. This effect deserved correction. A point approximation for a finite electrode referred to as the equivalent electrode point (EEP) was sought by placing a point-source current in the ground along the electrode length. The appropriate EEP depth was the one for which the CCM and a buried point source minimized a systematic geometric error; i.e., the relative change of the geometric factors obtained with the CCM and with an EEP. An EEP placed at 73% of the electrode length was declared as a suitable point approximation for an electrode. Use of this point assumption for inversion remedied efficiently the electrode effect subject to conditions. More precisely, the electrode spacing should stay within a lower bound equal to twice the electrode embedment and an upper bound equal to the shallow heterogeneity characteristic size divided by 0.75. The interest of such a metrological appraisal of the suitable acquisition layout to be used on the field was illustrated by a small-scale ERT field survey. This case study permitted us to understand more reliably the impact from fires upon a centimetric shallow layer in a calcareous wall.

Advanced Boundary Electrode Modeling for tES and Parallel tES/EEG.

This paper explores advanced electrode modeling in the context of separate and parallel transcranial electrical stimulation (tES) and electroencephalography (EEG) measurements. We focus on boundary condition-based approaches that do not necessitate adding auxiliary elements, e.g., sponges, to the computational domain. In particular, we investigate the complete electrode model (CEM) which incorporates a detailed description of the skin-electrode interface including its contact surface, impedance, and normal current distribution. The CEM can be applied for both tES and EEG electrodes which are advantageous when a parallel system is used. In comparison to the CEM, we test two important reduced approaches: the gap model (GAP) and the point electrode model (PEM). We aim to find out the differences of these approaches for a realistic numerical setting based on the stimulation of the auditory cortex. The results obtained suggest, among other things, that GAP and GAP/PEM are sufficiently accurate for the practical application of tES and parallel tES/EEG, respectively. Differences between CEM and GAP were observed mainly in the skin compartment, where only CEM explains the heating effects characteristic to tES.

Forward and inverse effects of the complete electrode model in neonatal EEG.

This paper investigates finite element method-based modeling in the context of neonatal electroencephalography (EEG). In particular, the focus lies on electrode boundary conditions. We compare the complete electrode model (CEM) with the point electrode model (PEM), which is the current standard in EEG. In the CEM, the voltage experienced by an electrode is modeled more realistically as the integral average of the potential distribution over its contact surface, whereas the PEM relies on a point value. Consequently, the CEM takes into account the subelectrode shunting currents, which are absent in the PEM. In this study, we aim to find out how the electrode voltage predicted by these two models differ, if standard size electrodes are attached to a head of a neonate. Additionally, we study voltages and voltage variation on electrode surfaces with two source locations: 1) next to the C6 electrode and 2) directly under the Fz electrode and the frontal fontanel. A realistic model of a neonatal head, including a skull with fontanels and sutures, is used. Based on the results, the forward simulation differences between CEM and PEM are in general small, but significant outliers can occur in the vicinity of the electrodes. The CEM can be considered as an integral part of the outer head model. The outcome of this study helps understanding volume conduction of neonatal EEG, since it enlightens the role of advanced skull and electrode modeling in forward and inverse computations.NEW & NOTEWORTHY The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.

Analysis of partial discharge Ultrasonic wave characteristic on typical Defects in GIS

For analyzing partial discharge ultrasonic wave characteristic on typical defects in SF6 gas insulation switchgear (GIS), a 110 kV GIS was taken as an object to design and simulate the typical partial discharge models in GIS� There are point electrode model on bus and cavity of GIS, floating electrode model, air interstice model in insulator, metal particle and iron core electromagnetic shock models. PD signals on different defects were thus detected with the ultrasonic method� The experimental results indicated that the ultrasonic signals of different defects showed different characteristics in waveform, amplitude and phase resolved partial discharge chart, which is helpful in PD pattern recognition for GIS�

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Construction of Indistinguishable Conductivity Perturbations for the Point Electrode Model in Electrical Impedance Tomography

We explain how to build indistinguishable isotropic conductivity perturbations of the unit conductivity in the framework of the point electrode model for two-dimensional electrical impedance tomography. The theoretical approach, based on solving a fixed point problem, is constructive and allows the implementation of an algorithm for approximating the invisible perturbations. The functionality of the method is demonstrated via numerical examples.

The Research of Electric Fields Calculation Based on Ring Current Source Model

This paper establishes a point electrode model, and obtain the analytic equation of electric fields produced by this model using vector superposition. Then do some further research to the analytic equation using ring current source model, and obtain the analytic equation of electric fields produced by ring current source. At last do some simulation about the analytic equation of electric fields, that can obtain the value of electric fields in the air - sea - the sea-bed three-media model.

The Simulation Research of Circle-Electrode's Electric Field of Steady Current Model

This paper is based on Point-electrode model of electric field of steady current in sea, and regards the seawater as lining,uniformity and apiece-direction congenialitily half-infinity conductor space. Founding on the comparability of steady current field and static current field,the paper calculates the distribution of circle-electrode's electric potential of the steady current in the three-layers medium(air-sea water-seabed) by image method and gets the expession. Thus the paper takes the model of the circle-electrode's electric field of steady current of in the sea .

Complete electrode model in EEG: relationship and differences to the point electrode model

In electroencephalography (EEG) source analysis, a primary current density generated by the neural activity of the brain is reconstructed from external electrode voltage measurements. This paper focuses on accurate and effective simulations of EEG through the complete electrode model (CEM). The CEM allows for the incorporation of the electrode size, shape and effective contact impedance into the forward simulation. Both neural currents in the brain and shunting currents between the electrodes and the skin can affect the measured voltages in the CEM. The goal of this study was to investigate the CEM by comparing it with the point electrode model (PEM), which is the current standard electrode model for EEG. We used a three-dimensional, realistic and high-resolution finite element head model as the reference computational domain in the comparison. The PEM could be formulated as a limit of the CEM, in which the effective impedance of each electrode goes to infinity and the size tends to zero. Numerical results concerning the forward and inverse errors and electrode voltage strengths with different impedances and electrode sizes are presented. Based on the results obtained, limits for extremely high and low impedance values of the shunting currents are suggested.

JUSTIFICATION OF POINT ELECTRODE MODELS IN ELECTRICAL IMPEDANCE TOMOGRAPHY

The most accurate model for real-life electrical impedance tomography is the complete electrode model, which takes into account electrode shapes and (usually unknown) contact impedances at electrode-object interfaces. When the electrodes are small, however, it is tempting to formally replace them by point sources. This simplifies the model considerably and completely eliminates the effect of contact impedance. In this work we rigorously justify such a point electrode model for the important case of having difference measurements ("relative data") as data for the reconstruction problem. We do this by deriving the asymptotic limit of the complete model for vanishing electrode size. This is supplemented by an analogous result for the case that the distance between two adjacent electrodes also tends to zero, thus providing a physical interpretation and justification of the so-called backscattering data introduced by two of the authors.

Effects of electrode properties on EEG measurements and a related inverse problem

A trend in EEG measurements is to increase the number of measurement electrodes in order to improve the spatial resolution of the recorded voltage distribution at the scalp. It is assumed that this would implicate better accuracy in the EEG inverse estimates. However, this does not necessarily hold. The reason for this is that the electrodes create a well conducting shunting “layer” on the scalp which affects the voltage distribution. This may decrease the information obtained and may therefore worsen the inverse estimates. Electrodes in EEG inverse problems are commonly modeled as point electrodes. This model cannot take into account the possible shunting effect of the electrodes. In this study the measurement electrodes are modeled using the so-called complete electrode model which takes into account the actual size of the electrode, the contact impedance between the skin and the electrode and also the shunting effect of the electrodes. In this paper the effects of the electrode size and the contact impedance on the voltage distribution are studied by simulations. It is shown that, depending on the size and the contact impedance of the electrodes, increasing the number of electrodes does not necessarily improve the accuracy of the inverse estimates. We also conclude that the use of the point electrode model is quite adequate in normal EEG studies. The use of a complete electrode model is nececssary if electrodes cover more than 50% of the surface area.