Forward EEG Research Articles

Accuracy of dipole source reconstruction in the 3-layer BEM model against the 5-layer BEM-FMM model.

To compare cortical dipole fitting spatial accuracy between the widely used yet highly simplified 3-layer and modern more realistic 5-layer BEM-FMM models with and without adaptive mesh refinement (AMR) methods. We generate simulated noiseless 256-channel EEG data from 5-layer (7-compartment) meshes of 15 subjects from the Connectome Young Adult dataset. For each subject, we test four dipole positions, three sets of conductivity values, and two types of head segmentation. We use the boundary element method (BEM) with fast multipole method (FMM) acceleration, with or without (AMR), for forward modeling. Dipole fitting is carried out with the FieldTrip MATLAB toolbox. The average position error (across all tested dipoles, subjects, and models) is ~4 mm, with a standard deviation of ~2 mm. The orientation error is ~20° on average, with a standard deviation of ~15°. Without AMR, the numerical inaccuracies produce a larger disagreement between the 3- and 5-layer models, with an average position error of ~8 mm (6 mm standard deviation), and an orientation error of 28° (28° standard deviation). The low-resolution 3-layer models provide excellent accuracy in dipole localization. On the other hand, dipole orientation is retrieved less accurately. Therefore, certain applications may require more realistic models for practical source reconstruction. AMR is a critical component for improving the accuracy of forward EEG computations using a high-resolution 5-layer volume conduction model. Improving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

On the geometrical perturbation of a three‐shell spherical model in electroencephalography

The forward electroencephalography (EEG) problem is studied in the framework of a multilayered structure, which models the scalp, skull, cerebrospinal fluid, and brain. Both the exterior and all inner boundaries are perturbed spheres so that special localized defects in head‐brain imaging are considered in analytic fashion. Linear perturbation analysis is implemented, providing exact expression for the first significant term of the forward EEG solution of the perturbed problem. Comparison with the solution of the corresponding unperturbed spherical problem is included, together with numerical demonstration of the produced errors in special deformation cases. The results suggest that significant errors are caused when large inaccuracies in the head‐brain structure in the vicinity of EEG source are not taken into account. Moreover, the suggested procedure provides a mathematical tool for evaluating quantitatively the impact of special deformations in the head representation on the EEG forward analytic solution.

Power Dissipation and Surface Charge in EEG: Application to Eigenvalue Structure of Integral Operators.

To demonstrate the role of surface charge and power dissipation in the analysis of EEG measurements. The forward EEG problem is formulated in terms of surface charge density. Using bounds based on power dissipation, the integral equations for forward solutions are shown to satisfy bounds on their eigenvalue structure. We show that two physical variables, dissipated power and the accumulated charge at interfaces, can be used in formulating the forward problem. We derive the boundary integral equations satisfied by the charge and show their connection to the integral equations for the potential that are known from other approaches. We show how the dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in EEG boundary element methods. Using the eigenvalue structure, we propose a new method for the solution of the forward problem, where the integral kernels are regularized by the exclusion of eigenvectors associated to a finite range of eigenvalues. We demonstrate the method on a head model with realistic shape. The eigenvalue analysis of the EEG forward problem is given a clear interpretation in terms of power dissipation and surface charge density. The use of these variables enhances our understanding of the structure of EEG, makes connection with other techniques and contributes to the development of new analysis algorithms.

Error analysis for nonconfocal ellipsoidal systems in the forward problem of electroencephalography

Electroencephalography (EEG) remains the utmost important technique recording brain activity. The present investigation examines the sensitivity of analytic algorithms employed in order to evaluate EEG data with respect to different brain template models. These algorithms are based on mathematical models built upon certain geometrical and/or physical assumptions regarding the head‐brain shape or the neuronal source. While the ellipsoidal head model provides a realistic approach regarding the interpretation of EEG signals in view of diverse geometries, its eccentricities influence strongly the results. The present study quantifies the deviation of the computed electric potentials when nonconfocal ellipsoids are used to model a homogeneous head conductor. To this end, a correspondence is proposed between points of the different ellipsoids, in view of the Gauss map. The investigation demonstrates that the introduction of nonconfocality imports a highly elevated error rate when EEG recordings are misinterpreted by arriving from different head‐brain models, including ellipsoidal vs spherical ones. Moreover, evidence is presented concerning the location of extrema regarding the errors in the upper brain hemisphere, which could lead to a more precise and accurate protocol regarding the placement of sensors. Although the present work refers to the forward EEG problem, its results may be used under other approaches as well. In particular, it provides the error in the solution of an elliptic boundary value problem with transmission conditions under small perturbations of the eccentricities of its ellipsoidal domain.

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation.

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivities of different head tissues. The conductivity of tissues is subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing a lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of support points in the conductivity space. Our approach accelerates the computation time, while controlling the approximation error. Our method is tested on simulated and measured EEG data for brain and skull conductivity estimation. This test demonstrates that the approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.

A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach

In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject's head into account. In this context, the finite element (FE) method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article, we introduce and analyze the application of a discontinuous Galerkin (DG) method, an FEM that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applicat...

The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem.

The purpose of this study is to introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the electroencephalography (EEG) forward problem. This new approach for source analysis does not use a geometry conforming volume triangulation, but instead uses a structured mesh that does not resolve the geometry. The geometry is described using level set functions and is incorporated implicitly in its mathematical formulation. As no triangulation is necessary, the complexity of a simulation pipeline and the need for manual interaction for patient-specific simulations can be reduced and is comparable with that of the FEM for hexahedral meshes. In addition, it maintains conservation laws on a discrete level. Here, we present the theory for UDG-FEM forward modeling, its verification using quasi-analytical solutions in multilayer sphere models and an evaluation in a comparison with a discontinuous Galerkin (DG-FEM) method on hexahedral and on conforming tetrahedral meshes. We furthermore apply the UDG-FEM forward approach in a realistic head model simulation study. The results show convergence to the quasi-analytical solution and indicate a good accuracy of UDG-FEM. UDG-FEM performs comparable or even better than DG-FEM on a conforming tetrahedral mesh while providing a less complex simulation pipeline. When compared to DG-FEM on hexahedral meshes, an overall better accuracy is achieved. The UDG-FEM approach is an accurate, flexible, and promising method to solve the EEG forward problem. This study shows the first application of the UDG-FEM approach to the EEG forward problem.

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

Effects of head models and dipole source parameters on EEG fields.

Head model and an efficient method for computing the forward EEG (electroencephalography)problem are essential to dipole source localization(DSL). In this paper, we use less expensive ovoid geometry to approximate human head, aiming at investigating the effects of head shape and dipole source parameters on EEG fields. The application of point least squares (PLS) based on meshless method was introduced for solving EEG forward problem and numerical simulation is implemented in three kinds of ovoid head models. We present the performances of the surface potential in the face of varying dipole source parameters in detail. The results show that the potential patterns are similar for different dipole position in different head shapes, but the peak value of potential is significantly influenced by the head shape. Dipole position induces a great effect on the peak value of potential and shift of peak potential. The degree of variation between sphere head model and non-sphere head models is seen at the same time. We also show that PLS method with the trigonometric basis is superior to the constant basis, linear basis, and quadratic basis functions in accuracy and efficiency.

Sensitivity Analysis of the Forward Electroencephalographic Problem Depending on Head Shape Variations

A crucial aspect in clinical practice is the knowledge of whether Electroencephalographic (EEG) measurements can be assigned to the functioning of the brain or to geometrical deviations of the human cranium. The present work is focused on continuing to advance understanding on how sensitive the solution of the forward EEG problem is in regard to the geometry of the head. This has been achieved by developing a novel analytic algorithm by performing a perturbation analysis in the linear regime using a homogenous spherical model. Notably, the suggested procedure provides a criterion which recognizes whether surface deformations will have an impact on EEG recordings. The presented deformations represent two major cases: (1) acquired alterations of the surface inflicted by external forces and (2) deformations of the upper part of the human head where EEG signals are recorded. Our results illustrate that neglecting geometric variations present on the heads surface leads to errors in the recorded EEG measurements less than 2%. However, for severe instances of deformations combined with cortical brain activity in the vicinity of the distortion site, the errors rise to almost 25%. Therefore, the accurate description of the head shape plays an important role in understanding the forward EEG problem only in these cases.

Effects of sutures and fontanels on MEG and EEG source analysis in a realistic infant head model.

In infants, the fontanels and sutures as well as conductivity of the skull influence the volume currents accompanying primary currents generated by active neurons and thus the associated electroencephalography (EEG) and magnetoencephalography (MEG) signals. We used a finite element method (FEM) to construct a realistic model of the head of an infant based on MRI images. Using this model, we investigated the effects of the fontanels, sutures and skull conductivity on forward and inverse EEG and MEG source analysis. Simulation results show that MEG is better suited than EEG to study early brain development because it is much less sensitive than EEG to distortions of the volume current caused by the fontanels and sutures and to inaccurate estimates of skull conductivity. Best results will be achieved when MEG and EEG are used in combination.

Comparison of Boundary Element and Finite Element Approaches to the EEG Forward Problem

Article Comparison of Boundary Element and Finite Element Approaches to the EEG Forward Problem was published on September 6, 2012 in the journal Biomedical Engineering / Biomedizinische Technik (volume 57, issue SI-1-Track-O).

Coupling of Point Collocation Meshfree Method and FEM for EEG Forward Solver

For solving electroencephalographic forward problem, coupled method of finite element method (FEM) and fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed using meshfree method. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM adopts point collocation scheme. Suggested method is tested using simple equation using 1‐, 2‐, and 3‐dimensional models, and error tendency according to node distance is studied. In addition, electroencephalographic forward problem is solved using spherical head model. Proposed hybrid method can produce well‐approximated solution.

Spatiotemporal dynamic analysis of phase synchronized sources based on factor analysis

Correlations in time courses of scalp electroencephalogram(EEG) may be represented by the phase synchronization in cerebral cortex sources to a certain some degree. Therefore, it is very important to localize the sources of phase synchronization and find corresponding time courses in the brain imaging study. Based on coupled Rössler oscillators with different coupling strengths, we propose a new method of simulating phase synchronized dipole sources and use a concentric 4-sphere head model to obtain simulation forward scalp EEG data. In addition, we propose the spatiotemporal dynamic analysis of phase synchronized sources based on the maximum likelihood factor analysis, verify the simulated and real scalp EEG data, and further compare the results with those of principal component analysis. Simulation results demonstrate that time courses estimated by maximum likelihood factor analysis have higher correlation with simulated sources, and less locational error between estimated sources and simulated sources. Factor analysis shows a better robust to the spatial resolution and the noise than principal component analysis. Furthermore, real data from spatial attention experiments show that factor analysis is capable of obtaining time courses and spatial distribution under the physiological base.

Effect of model resolution and tissue surfaces on forward EEG and MEG simulations

Event Abstract Back to Event Effect of model resolution and tissue surfaces on forward EEG and MEG simulations Ceon Ramon1*, Elham Rejvanian2, Mark Holmes2, Paul Schimpf3, Walter J. Freeman4 and Jens Haueisen5 1 University of Washington and Reykjavik University, United States 2 University of Washington, United States 3 Eastern Washington University, United States 4 University of California, United States 5 Technical University Ilmenau, Germany Finite element method (FEM) models of human heads are routinely being used in forward and inverse modeling of the EEG and MEG data. The models are developed from the segmented MR images with a resolution of 1-3 mm. This pixel resolution and the slice thickness influences the forward EEG and MEG computations. Similarly, FEM models of the head could have 5 to 19 different tissue-types identified in them. How the complexity of the model and different tissues influence the forward and inverse EEG and MEG computations? These topics we examined with different FEM head models varying in model resolutions (1-3 mm) and the tissue-types. All major tissue-types were identified, such as, scalp, hard and soft skull bone, gray and white matter, CSF, cerebellum, corpus callosum, dura etc. Models also included anisotropic conductivities of gray and white matter and detailed structures of the eyes, nose and occipital holes. We used single and distributed dipolar sources to simulate forward EEG and MEG patterns. The dipoles were oriented normal to the local cortical surface. The dipole moments were random with a uniform distribution in the range of 0.0 to 0.1 mA-meter. All computations were performed with a uniform-mesh FE solver with the mesh density identical to the MR image resolution. We found that skull bone, CSF and gray and white matter tissue boundaries and also their anisotropies severely influence the forward EEG and MEG modeling. A more complex model with 1.0 mm resolution performed better than the coarser (2-3 mm) model with fewer tissue-types. This was particularly true for modeling the sulcal and gyral structures in the brain which severely influenced the scalp EEGs and MEGs. The average source localization errors were 2-3 mm for complex models as compared to 5-10 mm for coarser models. We also found that an electrode spacing of about 3 mm is needed for extraction of cortical patterns from scalp EEGs in humans. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Oral Presentation Topic: MEG Modeling Citation: Ramon C, Rejvanian E, Holmes M, Schimpf P, Freeman WJ and Haueisen J (2010). Effect of model resolution and tissue surfaces on forward EEG and MEG simulations. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00035 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 19 Mar 2010; Published Online: 19 Mar 2010. * Correspondence: Ceon Ramon, University of Washington and Reykjavik University, Seattle, United States, ceon@uw.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Ceon Ramon Elham Rejvanian Mark Holmes Paul Schimpf Walter J Freeman Jens Haueisen Google Ceon Ramon Elham Rejvanian Mark Holmes Paul Schimpf Walter J Freeman Jens Haueisen Google Scholar Ceon Ramon Elham Rejvanian Mark Holmes Paul Schimpf Walter J Freeman Jens Haueisen PubMed Ceon Ramon Elham Rejvanian Mark Holmes Paul Schimpf Walter J Freeman Jens Haueisen Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Inverse sensitivity to approximate dipolar source models

Abstract The current dipole is a widely used source model in forward and inverse EEG and MEG applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite element method have become popular because they allow the use of anatomically detailed head models. Although numeric methods can represent more realistic domains, the sources in such models are often an approximation of the ideal dipole. We previously compared the electromagnetic fields produced by alternative models of dipolar sources in finite element models of the head to the fields produced by infinitesimal dipolar sources in analytic models of the head. That study found that the practice of projecting current sources to the nearest nodes of a finite element mesh was inaccurate. The “subtraction approach” was found to be very accurate, but can be difficult to apply, especially with commercial solver codes. That work also presented an approximate formulation that provided reasonably good results, based on the Laplace equivalence between voltage and current sources. In this article we verify the applicability of the Laplace dipole approximation to inverse problems using a realistic finite element model of the head.

Effects of Geometric Head Model Perturbations on the EEG Forward and Inverse Problems

We study the effect of geometric head model perturbations on the electroencephalography (EEG) forward and inverse problems. Small magnitude perturbations of the shape of the head could represent uncertainties in the head model due to errors on images or techniques used to construct the model. They could also represent small scale details of the shape of the surfaces not described in a deterministic model, such as the sulci and fissures of the cortical layer. We perform a first-order perturbation analysis, using a meshless method for computing the sensitivity of the solution of the forward problem to the geometry of the head model. The effect on the forward problem solution is treated as noise in the EEG measurements and the Cramér-Rao bound is computed to quantify the effect on the inverse problem performance. Our results show that, for a dipolar source, the effect of the perturbations on the inverse problem performance is under the level of the uncertainties due to the spontaneous brain activity. Thus, the results suggest that an extremely detailed model of the head may be unnecessary when solving the EEG inverse problem.

A common formalism for the Integral formulations of the forward EEG problem

The forward electroencephalography (EEG) problem involves finding a potential V from the Poisson equation inverted Delta x (sigma inverted Delta V) f, in which f represents electrical sources in the brain, and sigma the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the boundary element method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this paper we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single- and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.

The forward EEG solutions can be computed using artificial neural networks.

Study of electroencenphalography (EEG) is the one of the most utilized methods in both basic brain research and clinical diagnosis of neurological disorders. Recent technological advances in computer and electronic systems have allowed the EEG to be recorded from large electrode arrays. Modeling the brain waves using a head volume conductor model provides an effective method to localize functional generators within the brain. However, the forward solutions to this model, which represent theoretical potentials in response to current sources within the volume conductor, are difficult to compute because of time-consuming numerical procedures utilized in either the boundary element method (BEM) or the finite element method (FEM). This paper presents a novel computational approach using an artificial neural network (ANN) to map two vectors of forward solutions. These two vectors correspond to different head models but with respect to the same current source. The input vector to the ANN is based on the spherical head model, which can be computed efficiently but involves large errors. The output vector from the ANN is based on the spheroidal model, which is more precise, but difficult to compute directly using the traditional means. Our experiments indicate that this ANN approach provides a remarkable improvement over the BEM and FEM methods: 1) the mean-square error of computation was only approximately 0.3% compared to the exact solution; 2) the online computation was extremely efficient, requiring only 168 floating point operations per channel to compute the forward solution, and 10.2 K-bytes of storage to represent the entire ANN. Using this approach it is possible to perform real-time EEG modeling accurately on personal computers.