On the numerical accuracy of the boundary element method (EEG application)

Meijs, J. W. H.; Weier, O.W.; Peters, M.J.; Oosterom, A. van

doi:10.1109/10.40805

Cited by 282 publications

(178 citation statements)

References 19 publications

Supporting

Mentioning

169

Contrasting

Unclassified

Order By: Relevance

“…First, to specifically evaluate the inverse procedure, we assumed that there were no errors in the EEG and MEG forward solutions. Currently, the MEG forward solution is more accurate than the EEG forward solution, owing to the fact that the MEG forward solution requires only the inner skull surface and does not depend on the conductivities of the various tissue types in the brain [Hamalainen and Sarvas, 1989;Meijs et al, 1987Meijs et al, , 1989. If errors in the head model are included, which is likely to be the case with the currently available head models, the EEG accuracy will worsen relative to the MEG accuracy.…”

Section: Discussionmentioning

confidence: 99%

“…The computation of the MEG forward solution has been shown to only require the inner skull boundary to achieve an accurate solution [Hamalainen and Sarvas, 1989;Meijs et al, 1987Meijs et al, , 1989. The EEG forward solution computation requires the specification of boundaries between brain and skull, skull and scalp, scalp and air, and the relative conductivities of each of those regions.…”

Section: Forward Solutionmentioning

confidence: 99%

“…Specifically, there are fundamental differences between the forward solution accuracy required by EEG and MEG, with MEG requiring a simpler model [Hamalainen and Sarvas, 1989;Meijs et al, 1987Meijs et al, , 1989. Therefore, one would expect better accuracy for experimental MEG data using the more accurate MEG head model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Monte Carlo simulation studies of EEG and MEG localization accuracy

Liu¹,

Dale²,

Belliveau³

2002

Hum. Brain Mapp.

View full text Add to dashboard Cite

Both electroencephalography (EEG) and magnetoencephalography (MEG) are currently used to localize brain activity. The accuracy of source localization depends on numerous factors, including the specific inverse approach and source model, fundamental differences in EEG and MEG data, and the accuracy of the volume conductor model of the head (i.e., the forward model). Using Monte Carlo simulations, this study removes the effect of forward model errors and theoretically compares the use of EEG alone, MEG alone, and combined EEG/MEG data sets for source localization. Here, we use a linear estimation inverse approach with a distributed source model and a realistic forward head model. We evaluated its accuracy using the crosstalk and point spread metrics. The crosstalk metric for a specified location on the cortex describes the amount of activity incorrectly localized onto that location from other locations. The point spread metric provides the complementary measure: for that same location, the point spread describes the mis-localization of activity from that specified location to other locations in the brain. We also propose and examine the utility of a "noise sensitivity normalized" inverse operator. Given our particular forward and inverse models, our results show that 1) surprisingly, EEG localization is more accurate than MEG localization for the same number of sensors averaged over many source locations and orientations; 2) as expected, combining EEG with MEG produces the best accuracy for the same total number of sensors; 3) the noise sensitivity normalized inverse operator improves the spatial resolution relative to the standard linear estimation operator; and 4) use of an a priori fMRI constraint universally reduces both crosstalk and point spread. Hum. Brain Mapping 16:47-62, 2002.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Forward Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Monte Carlo simulation studies of EEG and MEG localization accuracy

Liu¹,

Dale²,

Belliveau³

2002

Hum. Brain Mapp.

View full text Add to dashboard Cite

show abstract

“…Many authors have already discussed and improved the BEM (Geselowitz, 1967;Hämäläinen and Sarvas, 1989;Meijs et al, 1989;Oostendorp and van Oosterom, 1989;Cuffin, 1990;Fletcher et al, 1995;Yvert et al, 1995;Ferguson and Stroink, 1997;Fuchs et al, 1998Fuchs et al, , 2001Musha and Okamoto, 1999;Frijns et al, 2000). The BEM requires a description of the compartment surfaces by closed triangle meshes with a limited number of nodes.…”

Section: Introductionmentioning

confidence: 99%

A standardized boundary element method volume conductor model

Fuchs¹,

Kastner²,

Wagner³

et al. 2002

Clinical Neurophysiology

881

575

View full text Add to dashboard Cite

Objectives: We used a 3-compartment boundary element method (BEM) model from an averaged magnetic resonance image (MRI) data set (Montreal Neurological Institute) in order to provide simple access to realistically shaped volume conductor models for source reconstruction, as compared to individually derived models. The electrode positions were transformed into the model's coordinate system, and the best fit dipole results were transformed back to the original coordinate system. The localization accuracy of the new approach was tested in a comparison with simulated data and with individual BEM models of epileptic spike data from several patients.Methods: The standard BEM model consisted of a total of 4770 nodes, which describe the smoothed cortical envelope, the outside of the skull, and the outside of the skin. The electrode positions were transformed to the model coordinate system by using 3-5 fiducials (nasion, left and right preauricular points, vertex, and inion). The transformation consisted of an averaged scaling factor and a rigid transformation (translation and rotation). The potential values at the transformed electrode positions were calculated by linear interpolation from the stored transfer matrix of the outer BEM compartment triangle net. After source reconstruction the best fit dipole results were transformed back into the original coordinate system by applying the inverse of the first transformation matrix.Results: Test-dipoles at random locations and with random orientations inside of a highly refined reference BEM model were used to simulate noise-free data. Source reconstruction results using a spherical and the standardized BEM volume conductor model were compared to the known dipole positions. Spherical head models resulted in mislocation errors at the base of the brain. The standardized BEM model was applied to averaged and unaveraged epileptic spike data from 7 patients. Source reconstruction results were compared to those achieved by 3 spherical shell models and individual BEM models derived from the individual MRI data sets. Similar errors to that evident with simulations were noted with spherical head models. Standardized and individualized BEM models were comparable.Conclusions: This new approach to head modeling performed significantly better than a simple spherical shell approximation, especially in basal brain areas, including the temporal lobe. By using a standardized head for the BEM setup, it offered an easier and faster access to realistically shaped volume conductor models as compared to deriving specific models from individual 3-dimensional MRI data. q

show abstract

“…Ᏺ was calculated using the "boundary element method" (BEM) for a three-shell realistic head model (Geselowitz, 1967; Hä mä lä inen and Sarvas, 1989;Meijs et al, 1989;de Munck, 1992;Schlitt et al, 1995;Ferguson and Stroink, 1997;Buchner et al, 1997). A structural MR image of the head was segmented (Ashburner and Friston, 1997) and divided into three volumes with homogeneous isotropic conductivity: the brain, the skull, and the scalp volume.…”

Section: Head and Source Modelmentioning

confidence: 99%

Systematic Regularization of Linear Inverse Solutions of the EEG Source Localization Problem

2002

View full text Add to dashboard Cite

Distributed linear solutions of the EEG source localization problem are used routinely. Here we describe an approach based on the weighted minimum norm method that imposes constraints using anatomical and physiological information derived from other imaging modalities to regularize the solution. In this approach the hyperparameters controlling the degree of regularization are estimated using restricted maximum likelihood (ReML). EEG data are always contaminated by noise, e.g., exogenous noise and background brain activity. The conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimization of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to prior constraints. Here we introduce a systematic approach to this regularization problem, in the context of a linear observation model we have described previously. In this model, basis functions are extracted to reduce the solution space a priori in the spatial and temporal domains. The basis sets are motivated by knowledge of the evoked EEG response and information theory. In this paper we focus on an iterative "expectationmaximization" procedure to jointly estimate the conditional expectation of the source distribution and the ReML hyperparameters on which this solution rests. We used simulated data mixed with real EEG noise to explore the behavior of the approach with various source locations, priors, and noise levels. The results enabled us to conclude: (i) Solutions in the space of informed basis functions have a high face and construct validity, in relation to conventional analyses. (ii) The hyperparameters controlling the degree of regularization vary largely with source geometry and noise. The second conclusion speaks to the usefulness of using adaptative ReML hyperparameter estimates. © 2002 Elsevier Science (USA)

show abstract

On the numerical accuracy of the boundary element method (EEG application)

Cited by 282 publications

References 19 publications

Monte Carlo simulation studies of EEG and MEG localization accuracy

Monte Carlo simulation studies of EEG and MEG localization accuracy

A standardized boundary element method volume conductor model

Systematic Regularization of Linear Inverse Solutions of the EEG Source Localization Problem

Contact Info

Product

Resources

About