Factors affecting the accuracy of the boundary element method in the forward problem. I. Calculating surface potentials

Ferguson, A.S.; Stroink, G.

doi:10.1109/10.641342

Cited by 58 publications

(31 citation statements)

References 24 publications

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“…In [38], de Munck and Peters consider the more general case of anisotropic conductivities, and the infinite series is substituted with one which converges more rapidly. Recent empirical work on closed-form approximations by Berg and Scherg [3], and related theoretical studies by Zhang [52], describe a valid method for approximating the infinite series with as few as three evaluations of scaled forms of the single shell model (13) and (14). For a given -shell head model, these so-called "Berg parameters" [52] can be designated as (see [3] and [52] for definitions).…”

Section: B Eeg Spherically Symmetric Conductormentioning

confidence: 99%

EEG and MEG: forward solutions for inverse methods

Mosher

Leahy

Lewis

1999

IEEE Trans. Biomed. Eng.

746

536

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Abstract-A solution of the forward problem is an important component of any method for computing the spatio-temporal activity of the neural sources of magnetoencephalography (MEG) and electroencephalography (EEG) data. The forward problem involves computing the scalp potentials or external magnetic field at a finite set of sensor locations for a putative source configuration. We present a unified treatment of analytical and numerical solutions of the forward problem in a form suitable for use in inverse methods. This formulation is achieved through factorization of the lead field into the product of the moment of the elemental current dipole source with a "kernel matrix" that depends on the head geometry and source and sensor locations, and a "sensor matrix" that models sensor orientation and gradiometer effects in MEG and differential measurements in EEG. Using this formulation and a recently developed approximation formula for EEG, based on the "Berg parameters," we present novel reformulations of the basic EEG and MEG kernels that dispel the myth that EEG is inherently more complicated to calculate than MEG. We also present novel investigations of different boundary element methods (BEM's) and present evidence that improvements over currently published BEM methods can be realized using alternative error-weighting methods. Explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries are included.Index Terms-Boundary element method (BEM), electroencephalogram (EEG), forward model, head modeling, realistic head model, spherical head model.

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Section: B Eeg Spherically Symmetric Conductormentioning

confidence: 99%

EEG and MEG: forward solutions for inverse methods

Mosher

Leahy

Lewis

1999

IEEE Trans. Biomed. Eng.

746

536

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“…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

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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)

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“…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

897

575

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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

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Factors affecting the accuracy of the boundary element method in the forward problem. I. Calculating surface potentials

Cited by 58 publications

References 24 publications

EEG and MEG: forward solutions for inverse methods

EEG and MEG: forward solutions for inverse methods

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

A standardized boundary element method volume conductor model

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