Numerical Mathematics of the Subtraction Method for the Modeling of a Current Dipole in EEG Source Reconstruction Using Finite Element Head Models

Wolters, Carsten H.; Köstler, Harald; Möller, C.; Härdtlein, Jochen; Grasedyck, Lars; Hackbusch, Wolfgang

doi:10.1137/060659053

Cited by 85 publications

(127 citation statements)

References 25 publications

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“…However, our FE model, with simple structure geometries and a reasonable mesh density, might already provide reasonable results for the quantities under study. Even if first examinations with regard to numerical convergence for a similar potential problem in FE head volume conductor models has been carried out (Wolters et al, 2007), a completely satisfying qualitative convergence proof for a problem with discontinuous tissue conductivities is difficult and has not yet been achieved. We have however checked that doubling the node number changes only the potential values by amounts always smaller than 1.75%.…”

Section: Model Geometrymentioning

confidence: 99%

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation

Walckiers

Fuchs

Thiran

et al. 2010

Journal of Neuroscience Methods

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a b s t r a c tElectrical deep brain stimulation (DBS) is an efficient method to treat movement disorders. Many models of DBS, based mostly on finite elements, have recently been proposed to better understand the interaction between the electrical stimulation and the brain tissues. In monopolar DBS, clinically widely used, the implanted pulse generator (IPG) is used as reference electrode (RE).In this paper, the influence of the RE model of monopolar DBS is investigated. For that purpose, a finite element model of the full electric loop including the head, the neck and the superior chest is used. Head, neck and superior chest are made of simple structures such as parallelepipeds and cylinders. The tissues surrounding the electrode are accurately modelled from data provided by the diffusion tensor magnetic resonance imaging (DT-MRI). Three different configurations of RE are compared with a commonly used model of reduced size.The electrical impedance seen by the DBS system and the potential distribution are computed for each model. Moreover, axons are modelled to compute the area of tissue activated by stimulation.Results show that these indicators are influenced by the surface and position of the RE. The use of a RE model corresponding to the implanted device rather than the usually simplified model leads to an increase of the system impedance (+48%) and a reduction of the area of activated tissue (−15%).

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Section: Model Geometrymentioning

confidence: 99%

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation

Walckiers

Fuchs

Thiran

et al. 2010

Journal of Neuroscience Methods

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“…Due to the high mesh complexity, the typical direct method for computing the leadfield matrix becomes unreasonably slow for finite element models. To overcome this, alternative methods for calculating the leadfield matrix, such as the adjoint [18], subtraction [19,20], and reciprocity [21,22] approaches have been devised. The approach taken here was derived from Helmholtz's principle of reciprocity and first applied to EEG by Rush and Driscoll [1,21].…”

Section: Introductionmentioning

confidence: 99%

A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

et al. 2014

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We present a finite element modeling (FEM) implementation for solving the forward problem in electroencephalography (EEG). The solution is based on Helmholtz's principle of reciprocity which allows for dramatically reduced computational time when constructing the leadfield matrix. The approach was validated using a 4-shell spherical model and shown to perform comparably with two current state-of-the-art alternatives (OpenMEEG for boundary element modeling and SimBio for finite element modeling).We applied the method to real human brain MRI data and created a model with five tissue types: white matter, grey matter, cerebrospinal fluid, skull, and scalp. By calculating conductivity tensors from diffusion-weighted MR images, we also demonstrate one of the main benefits of FEM: the ability to include anisotropic conductivities within the head model. Root-mean square deviation between the standard leadfield and the leadfield including white-matter anisotropy showed that ignoring the directional conductivity of white matter fiber tracts leads to orientation-specific errors in the forward model. Realistic head models are necessary for precise source localization in individuals. Our approach is fast, accurate, open-source and freely available online.

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“…For standard CG-FEM, several different source models have been proposed, such as the partial integration [12], [17], [19], the Saint-Venant [2], [20], the Whitney or Raviart Thomas [18], [37] or the subtraction approach [13], [38]. In principle, the presented method is applicable to any given source model.…”

Section: A Source Modelmentioning

confidence: 99%

“…An eccentricity value of 0 denotes the center of the sphere and a value of 1 a location at the boundary of the inner compartment. Because it is well known that numerical errors increase with increasing eccentricity (a reasoning for this effect has been given in [38]), the chosen eccentricities were scaled logarithmically with increasing eccentricity and range from 0.1666 to 0.9939. The latter corresponds to a distance of only 0.48 mm to the inner sphere surface and thus very high eccentricity (where thus also higher numerical errors have to be expected [38]).…”

Section: G Sourcesmentioning

confidence: 99%

“…Because it is well known that numerical errors increase with increasing eccentricity (a reasoning for this effect has been given in [38]), the chosen eccentricities were scaled logarithmically with increasing eccentricity and range from 0.1666 to 0.9939. The latter corresponds to a distance of only 0.48 mm to the inner sphere surface and thus very high eccentricity (where thus also higher numerical errors have to be expected [38]). With regard to the application, distances between 1 mm (eccentricity of 0.9872) and 2.5 mm (0.9678) or 3 mm (0.9615) seem to be the most important, because, depending on the location, the cortex has a thickness of about 2 to 6 mm [50] and source locations should be chosen to be in the middle of the grey matter compartment.…”

Section: G Sourcesmentioning

confidence: 99%

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The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem

Nusing

Wolters

Brinck

et al. 2016

IEEE Trans. Biomed. Eng.

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Abstract-Objective: 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. Methods: 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 multi-layer 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. Results: The given results show convergence and indicate a good overall accuracy of the UDG-FEM approach. 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. Conclusion: The UDG-FEM approach is an accurate, flexible and promising method to solve the EEG forward problem. Significance: This study shows the first application of the UDG-FEM approach to the EEG forward problem.

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Numerical Mathematics of the Subtraction Method for the Modeling of a Current Dipole in EEG Source Reconstruction Using Finite Element Head Models

Cited by 85 publications

References 25 publications

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation

A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem

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