Fast realistic modeling in bioelectromagnetism using lead‐field interpolation

With the increasing availability of surface extraction techniques for magnetic resonance and x-ray computed tomography images, realistic head models can be readily generated as forward models in the analysis of electroencephalography (EEG) and magnetoencephalography (MEG) data. Inverse analysis of this data, however, requires that the forward model be computationally efficient. We propose two methods for approximating the EEG forward model using realistic head shapes. The 'sensor-fitted sphere' approach fits a multilayer sphere individually to each sensor, and the 'three-dimensional interpolation' scheme interpolates using a grid on which a numerical boundary element method (BEM) solution has been precomputed. We have characterized the performance of each method in terms of magnitude and subspace error metrics, as well as computational and memory requirements. We have also made direct performance comparisons with traditional spherical models. The approximation provided by the interpolative scheme had an accuracy nearly identical to full BEM, even within 3 mm of the inner skull surface. Forward model computation during inverse procedures was approximately 30 times faster than for a traditional three-shell spherical model. Cast in this framework, high-fidelity numerical solutions currently viewed as computationally prohibitive for solving the inverse problem (e.g. linear Galerkin BEM) can be rapidly recomputed in a highly efficient manner. The sensor-fitting method has a similar one-time cost to the BEM method, and while it produces some improvement over a standard three-shell sphere, its performance does not approach that of the interpolation method. In both methods, there is a one-time cost associated with precomputing the forward solution over a set of grid points.

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“…We note also the recent publication by Yvert et al (2000), who describe a similar methodology with results consistent with ours.…”

Section: Introductionsupporting

confidence: 91%

Rapidly recomputable EEG forward models for realistic head shapes

et al. 2001

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“…The computational performance of our implementation is about a factor of 60 slower than using analytical spherical models, but is still sufficient for most applications. By linear interpolation of a precomputed leadfield matrix of the standardized BEM model (Yvert et al, 2001) the computational speed could still be increased (work in progress). The sBEM approximation offers an easier and faster access to realistically shaped volume conductor models as compared to individual models and relieves the use of individual 3D MRI data for the BEM model setup.…”

Section: Discussionmentioning

confidence: 99%

A standardized boundary element method volume conductor model

Fuchs¹,

Kastner²,

Wagner³

et al. 2002

Clinical Neurophysiology

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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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“…Because these models take a long time to compute given location parameters; in practice, one might compute the lead-field function using a lookup table, where lead-fields are pre-computed for dipoles on a grid. The lead-fields for locations between grid points can then be interpolated, as shown in Yvert et al (2001). In a similar vein, it is also possible to incorporate parameters of the forward model into the full model (Fig.…”

Section: Discussionmentioning

confidence: 99%

Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG

et al. 2008

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In magneto-and electroencephalography (M/EEG), spatial modelling of sensor data is necessary to make inferences about underlying brain activity. Most source reconstruction techniques belong to one of two approaches: point source models, which explain the data with a small number of equivalent current dipoles and distributed source or imaging models, which use thousands of dipoles. Much methodological research has been devoted to developing sophisticated Bayesian source imaging inversion schemes, while dipoles have received less such attention. Dipole models have their advantages; they are often appropriate summaries of evoked responses or helpful first approximations. Here, we propose a variational Bayesian algorithm that enables the fast Bayesian inversion of dipole models. The approach allows for specification of priors on all the model parameters. The posterior distributions can be used to form Bayesian confidence intervals for interesting parameters, like dipole locations. Furthermore, competing models (e.g., models with different numbers of dipoles) can be compared using their evidence or marginal likelihood. Using synthetic data, we found the scheme provides accurate dipole localizations. We illustrate the advantage of our Bayesian scheme, using a multi-subject EEG auditory study, where we compare competing models for the generation of the N100 component. © 2007 Elsevier Inc. All rights reserved. Keywords: EEG; MEG; Equivalent current dipole; Variational Bayes IntroductionThe analysis of evoked responses using magneto-and electroencephalography (M/EEG) can proceed in several ways. If one is interested in inferring the locations of M/EEG generators within brain space, one has to solve the inverse spatial problem (Baillet et al., 2001). There are two main approaches to estimating sources from observed sensor data. The first assumes that sensor data can be explained by a small set of equivalent current dipoles. The inversion of this model amounts to a nonlinear optimization problem, because the forward model is nonlinear in dipole location (Mosher et al., 1992). Recently, the source reconstruction problem has been addressed by placing many dipoles in brain space, and using constraints on the solution to make it unique; for example (Baillet and Garnero, 1997;Mattout et al., 2006;Phillips et al., 2005). This approach is attractive, because it produces images of brain activity comparable to other imaging modalities and it eschews subjective constraints on the inversion. For imaging solutions, most constraints can be motivated by anatomical and physiological arguments, e.g., smoothness constraints and approximate location priors, based on regional activity in functional magnetic resonance imaging (fMRI). Traditional few-dipole solutions, however, are usually regarded as depending too much on user-specified modelling decisions; like the number of dipoles and their initial locations. Mathematically, it can be argued that the inversion of dipole models is a harder problem than inversion of distributed models, becaus...

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Fast realistic modeling in bioelectromagnetism using lead‐field interpolation

Cited by 25 publications

References 34 publications

Rapidly recomputable EEG forward models for realistic head shapes

Rapidly recomputable EEG forward models for realistic head shapes

A standardized boundary element method volume conductor model

Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG

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