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2002
The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography 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 and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.
A mathematical dipole is widely used as a model for the primary current source in electroencephalography (EEG) source analysis. In the governing Poisson-type differential equation, the dipole leads to a singularity on the right-hand side, which has to be treated specifically. In this paper, we will present a full subtraction approach where the total potential is divided into a singularity and a correction potential. The singularity potential is due to a dipole in an infinite region of homogeneous conductivity. The correction potential is computed using the finite element (FE) method. Special care is taken to appropriately evaluate the right-hand side integral with the objective of achieving highest possible convergence order for linear basis functions. Our new approach allows the construction of transfer matrices for fast computation of the inverse problem for volume conductors with arbitrary local and remote conductivity anisotropy. A constrained Delaunay tetrahedralisation (CDT) approach is used for the generation of high-quality FE meshes. We validate the new approach in a four-layer sphere model with anisotropic skull compartment. For radial and tangential sources with eccentricities up to 1mm below the cerebrospinal fluid compartment, we achieve a maximal relative error of 0.71% in a tetrahedra model with 360K nodes which is not locally refined around the source singularity. The combination of the full subtraction approach with the high quality CDT meshes leads to accuracies that, to the best of the authors knowledge, have not yet been presented before.
Electroencephalography and Clinical Neurophysiology, 1997
The paper describes finite element related procedures for inverse localization of multiple sources in realistically shaped head models. Dipole sources are modeled by placing proper monopole sources on neighboring nodes. Lead field operators are established for dipole sources. Two different strategies for the solution of inverse problems, namely combinatorial optimization techniques and regularization methods are discussed and applied to visually evoked potentials, for which exemplary results are shown. Most of the procedures described are fully automatic and require only proper input preparation. The overall work for the example presented (from EEG recording to visual inspection of lhe results) can be performed in roughly a week, most of which is waiting time for the computation of the lead field matrix or inverse calculations on a standard and affordable engineering workstation. © 1997 Elsevier Science Ireland Ltd.
Biomedizinische Technik/Biomedical Engineering, 2001
2000
We derive Cramer-Rao bounds (CRB's) on the errors of estimating the parameters (location and moment) of a current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities, obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are computed using the boundary or the finite element method (BEM or FEM), with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images. The results include contours of equal precision in the estimation and surfaces showing the size of the 90% confidence volume for a dipole on a sphere inside the brain.
2006
This Thesis concerns the application of two numerical methods, Boundary Element Method (BEM) and Finite Element Method (FEM) to forward problem solution of bioelectromagnetic source localization in the brain. The aim is to improve the accuracy of the forward problem solution in estimating the electrical activity of the human brain from electric and magnetic field measurements outside the head. Electro-and magnetoencephalography (EEG, MEG) are the most important tools enabling us to gather knowledge about the human brain non-invasively. This task is alternatively named brain mapping. An important step in brain mapping is determining from where the brain signals originate. Using appropriate mathematical models, a localization of the sources of measured signals can be performed. A general motivation of this work was the fact that source localization accuracy can be improved by solving the forward problem with higher accuracy. In BEM studies, accurate representation of model geometry using higher order elements improves the solution of the forward problem. In FEM, complex conductivity information can be incorporated into numerical model. Using Whitneytype finite elements instead of using singular sources such as point dipoles, primary and volume currents are represented as continuous sources. With comparison to analytical solutions available in simple geometries such as sphere, the studied numerical methods show improvements in the forward problem solution of bioelectromagnetic source imaging.
IEEE Transactions on Biomedical Engineering, 2004
The influence of head tissue conductivity on magnetoencephalography (MEG) was investigated by comparing the normal component of the magnetic field calculated at 61 detectors and the localization accuracy of realistic head finite element method (FEM) models using dipolar sources and containing altered scalp, skull, cerebrospinal fluid, gray, and white matter conductivities to the results obtained using a FEM realistic head model with the same dipolar sources but containing published baseline conductivity values. In the models containing altered conductivity values, the tissue conductivity values were varied, one at a time, between 10% and 200% of their baseline values, and then varied simultaneously. Although changes in conductivity values for a single tissue layer often altered the calculated magnetic field and source localization accuracy only slightly, varying multiple conductivity layers simultaneously caused significant discrepancies in calculated results. The conductivity of scalp, and to a lesser extent that of white and gray matter, appears especially influential in determining the magnetic field. Comparing the results obtained from models containing the baseline conductivity values to the results obtained using other published conductivity values suggests that inaccuracies can occur depending upon which tissue conductivity values are employed. We show the importance of accurate head tissue conductivities for MEG source localization in human brain, especially for deep dipole sources or when an accuracy greater than 1.4 cm is needed.
Journal of Physics: Conference Series, 2010
Realistic computer modelling of biological objects requires building of very accurate and realistic computer models based on geometric and material data, type, and accuracy of numerical analyses. This paper presents some of the automatic tools and algorithms that were used to build accurate and realistic 3D finite element (FE) model of whole-brain. These models were used to solve the forward problem in magnetic field tomography (MFT) based on Magnetoencephalography (MEG). The forward problem involves modelling and computation of magnetic fields produced by human brain during cognitive processing. The geometric parameters of the model were obtained from accurate Magnetic Resonance Imaging (MRI) data and the material propertiesfrom those obtained from Diffusion Tensor MRI (DTMRI). The 3D FE models of the brain built using this approach has been shown to be very accurate in terms of both geometric and material properties. The model is stored on the computer in Computer-Aided Parametrical Design (CAD) format. This allows the model to be used in a wide a range of methods of analysis, such as finite element method (FEM), Boundary Element Method (BEM), Monte-Carlo Simulations, etc. The generic model building approach presented here could be used for accurate and realistic modelling of human brain and many other biological objects.
Electroencephalography and Clinical Neurophysiology, 1975
Annals of Biomedical Engineering, 2003
Volume currents are important for the accurate calculation of magnetoencephalographic ͑MEG͒ forward or inverse simulations in realistic head models. We verify the accuracy of our finite element method implementation for MEG simulations by comparing its results for spheres containing dipoles to those obtained from the analytic solution. We then use this finite element method to show that, in an inhomogeneous, nonspherical realistic head model, the magnetic field normal to the MEG detector due to volume currents often has a magnitude on the same order or greater than the magnitude of the normal component of the primary magnetic field from the dipole. We also demonstrate the disparity in forward solutions between a model that employs spheres, one that uses the realistic head and primary currents alone, and a realistic head model that incorporates both primary and volume currents. In forward and inverse MEG simulations using the inhomogeneous realistic model, the results obtained from calculations containing volume currents are more accurate than those derived without considering volume currents.
Inverse Problems, 2011
Electroencephalography (EEG) is a non-invasive imaging modality in which a primary current density generated by the neural activity in the brain is to be reconstructed based on external electric potential measurements. This paper focuses on the finite element method (FEM) from both forward and inverse aspects. The goal is to establish a clear correspondence between the lowest order Raviart-Thomas basis functions and dipole sources as well as to show that the adopted FEM approach is computationally effective. Each basis function is associated with a dipole moment and a location. Four candidate locations are tested. Numerical experiments cover two different spherical multilayer head models, four mesh resolutions and two different forward simulation approaches, one based on FEM and one based on the boundary element method (BEM) with standard dipoles as sources. The forward simulation accuracy is examined through column-and matrix-wise relative errors as well as through performance in inverse dipole localization. A closed-form approximation of dipole potential was used as the reference forward simulation. The results suggest that the present approach is comparable or superior to BEM and to the recent FEM based subtraction approach regarding both accuracy, computation time and accessibility of implementation.
Siam Journal on Scientific Computing, 2007
In electroencephalography (EEG) source analysis, a dipole is widely used as the model of the current source. The dipole introduces a singularity on the right-hand side of the gov- erning Poisson-type differential equation that has to be treated specifically when solving the equation towards the electric potential. In this paper, we give a proof for existence and uniqueness of the
2000
We derive Cramér-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a static current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are formulated for solving them by the boundary or the finite element method (BEM or FEM) with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images. I. INTRODUCTION N EURAL activity in a brain tissue produces an electromagnetic field distribution that can be detected by measuring the induced electric potential or magnetic field. Electroencephalography (EEG) and magneto-encephalography (MEG) are noninvasive methods for studying the brain activity based on records of electric potentials and magnetic fields. They are used for estimating an instantaneous current distribution representing electrically active tissues with a time resolution on the order of milliseconds. The source of activity is typically described with a model whose parameters are to be estimated. EEG instruments measure the electric potential at multiple points on the scalp by means of a sensor cap, often with more than hundred electrodes. Available MEG instruments measure the magnetic field, and possibly some of its gradient components, from an array of superconducting quantum interference
Human Brain Mapping, 2011
We used computer simulations to investigate finite element models of the layered structure of the human skull in EEG source analysis. Local models, where each skull location was modelled differently, and global models, where the skull was assumed to be homogeneous, were compared to a reference model, in which spongy and compact bone were explicitly accounted for. In both cases, isotropic and anisotropic conductivity assumptions were considered. We considered sources in the entire brain and determined errors both in the forward calculation and the reconstructed dipole position.
IEEE Transactions on Signal Processing, 2001
We derive Cramér-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a static current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are formulated for solving them by the boundary or the finite element method (BEM or FEM) with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images.
Keyword: MATLAB Software Head modeling EEG Boundary Element Method BEM Realistic 4-layer head model MNI Inverse problem Source localization a b s t r a c t This paper introduces a Neuroelectromagnetic Forward Head Modeling Toolbox (NFT) running under MATLAB (The Mathworks, Inc.
Brain Topography, 2001
The performance of the finite difference reciprocity method (FDRM) to solve the inverse problem in EEG dipole source analysis is investigated in the analytically solvable three-shell spherical head model for a large set of test dipoles. The location error for a grid with 2 mm and 3 mm node spacing is in general, not larger than twice the internode distance,
2010
Keyword: MATLAB Software Head modeling EEG Boundary Element Method BEM Realistic 4-layer head model MNI Inverse problem Source localization a b s t r a c t This paper introduces a Neuroelectromagnetic Forward Head Modeling Toolbox (NFT) running under MATLAB (The Mathworks, Inc.
Computational Intelligence and Neuroscience, 2010
The accuracy of forward models for electroencephalography (EEG) partly depends on head tissues geometry and strongly affects the reliability of the source reconstruction process, but it is not yet clear which brain regions are more sensitive to the choice of different model geometry. In this paper we compare different spherical and realistic head modeling techniques in estimating EEG forward solutions from current dipole sources distributed on a standard cortical space reconstructed from Montreal Neurological Institute (MNI) MRI data. Computer simulations are presented for three different four-shell head models, two with realistic geometry, either surface-based (BEM) or volume-based (FDM), and the corresponding sensor-fitted spherical-shaped model. Point Spread Function (PSF) and Lead Field (LF) cross-correlation analyses were performed for 26 symmetric dipole sources to quantitatively assess models' accuracy in EEG source reconstruction. Realistic geometry turns out to be a rel...
IEEE Transactions on Biomedical Engineering, 1990
Methods for localizing electrical dipolar sources in the brain differ from one another by the models they use to represent the head, the specific formulas used in the calculation of the scalp potentials, the way that the reference electrode is treated, and by the algorithm employed to find the least-squares fit between the measured and calculated EEG potentials. The model presented here is based on some of the most advanced features found in other models, and on some improvements. The head is represented by a three-layer spherical model. The potential on any point on the scalp due to any source is found by a closed formula, which is not based on matrix rotations. The formulas will accept any surface electrode as the reference electrode. The least-squares procedure is based on optimal dipoles, reducing the number of unknowns in the iterations from six to three.
2007
In EEG/MEG source analysis, a mathematical dipole is widely used as the “atomic” structure of the primary current distribution. When using realistic finite element models for the forward problem, the current dipole introduces a singularity on the right-hand side of the governing differential equation that has to be treated specifically. We evaluated and compared three different numerical approaches, a subtraction method, a direct approach using partial integration and a direct approach using the principle of Saint Venant.
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