Manfred Fuchs

A standardized boundary element method volume conductor model.

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 models 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.

Linear and nonlinear current density reconstructions.

Minimum norm algorithms for EEG source reconstruction are studied in view of their spatial resolution, regularization, and lead-field normalization properties, and their computational efforts. Two classes of minimum norm solutions are examined: linear least squares methods and nonlinear L1-norm approaches. Two special cases of linear algorithms, the well known Minimum Norm Least Squares and an implementation with Laplacian smoothness constraints, are compared to two nonlinear algorithms comprising sparse and standard L1-norm methods. In a signal-to-noise-ratio framework, two of the methods allow automatic determination of the optimum regularization parameter. Compensation methods for the different depth dependencies of all approaches by lead-field normalization are discussed. Simulations with tangentially and radially oriented test dipoles at two different noise levels are performed to reveal and compare the properties of all approaches. Finally, cortically constrained versions of the algorithms are applied to two epileptic spike data sets and compared to results of single equivalent dipole fits and spatiotemporal source models.

An improved boundary element method for realistic volume-conductor modeling

An improved boundary element method (BEM) with a virtual triangle refinement using the vertex normals, an optimized auto solid angle approximation, and a weighted isolated problem approach is presented. The performance of this new approach is compared to analytically solvable spherical shell models and highly refined reference BEM models for tangentially and radially oriented dipoles at different eccentricities. The lead fields of several electroencephalography (EEG) and magnetoencephalography (MEG) setups are analyzed by singular-value decompositions for realistically shaped volume-conductor models. Dipole mislocalizations due to simplified volume-conductor models are investigated for EEG and MEG examinations for points on a three dimensional (3-D) grid with 10-mm spacing inside the conductor and all principal dipole orientations. The applicability of the BEM in view of the computational effort is tested with a standard workstation. Finally, an application of the new method to epileptic spike data is studied and the results are compared to the spherical-shells approximation.

Improving source reconstructions by combining bioelectric and biomagnetic data

OBJECTIVES A framework for combining bioelectric and biomagnetic data is presented. The data are transformed to signal-to-noise ratios and reconstruction algorithms utilizing a new regularization approach are introduced. METHODS Extensive simulations are carried out for 19 different EEG and MEG montages with radial and tangential test dipoles at different eccentricities and noise levels. The methods are verified by real SEP/SEF measurements. A common realistic volume conductor is used and the less well known in vivo conductivities are matched by calibration to the magnetic data. Single equivalent dipole fits as well as spatio-temporal source models are presented for single and combined modality evaluations and overlaid to anatomic MR images. RESULTS Normalized sensitivity and dipole resolution profiles of the different EEG/MEG acquisition systems are derived from the simulated data. The methods and simulations are verified by simultaneously measured somatosensory data. CONCLUSIONS Superior spatial resolution of the combined data studies is revealed, which is due to the complementary nature of both modalities and the increased number of sensors. A better understanding of the underlying neuronal processes can be achieved, since an improved differentiation between quasi-tangential and quasi-radial sources is possible.

Evaluation of sLORETA in the presence of noise and multiple sources.

The standardized Low Resolution Brain Electromagnetic Tomography method (sLORETA) can be used to compute statistical maps from EEG and MEG data that indicate the locations of the underlying source processes with low error. These maps are derived by performing a location-wise inverse weighting of the results of a Minimum Norm Least Squares (MNLS) analysis with their estimated variances. In this contribution, we evaluate the performance of the method under the presence of noise and with multiple, simultaneously active sources. It is shown that the sLORETA method localizes well, as compared to other linear approaches such as MNLS and LORETA. However, simultaneously active sources can only be separated if their fields are distinct enough and of similar strength. In the context of a strong or superficial source, weak or deep sources remain invisible, and nearby sources of similar orientation tend not to be separated but interpreted as one source located roughly in between.

Inverse localization of electric dipole current sources in finite element models of the human head

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 the 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.

Boundary element method volume conductor models for EEG source reconstruction

OBJECTIVES The boundary element method (BEM) approximates the different compartments of volume conductor models by closed triangle meshes with a limited number of nodes. The shielding effect of the weakly conducting skull layer of the human head leads to decreasing potential gradients from the inside to the outside. Thus, there may be an optimum distribution of nodes to the compartments for a given number of nodes corresponding to a fixed computational effort, resulting in improved accuracy as compared to standard uniform distributions. METHODS Spherical and realistically shaped surfaces are approximated by 500, 1000, 2000, and 3000 nodes, each leading to BEM models with 1500-9000 nodes in total. Electrodes are placed on extended 10/20-system positions. Potential distributions of test-dipoles at 4000 random positions within the innermost compartment are calculated. Dipoles are then fitted using 192 different models to find the optimum node distribution. RESULTS Fitted dipole positions for all BEM models are evaluated to show the dependency of the averaged and maximum localization errors on their node distributions. Dipoles close to the innermost boundary exhibit the largest localization errors, which mainly depend on the refinement of this compartments triangle mesh. CONCLUSIONS More than 500 nodes per compartment are needed for reliable BEM models. For a state-of-the-art model consisting of 6000 nodes overall, the best model consists of 3000, 2000, and 1000 nodes from the inside to the outside.

Development of volume conductor and source models to localize epileptic foci.

Summary: There is increasing interest in mapping and source reconstruction from electrocorticoencephalographic (ECoG) grid data and comparison to surface EEG evaluations of epileptic patients. ECoG mapping onto three-dimensional renderings of the individual cortical anatomy derived from magnetic resonance images and computed tomography (CT) is performed after coregistration of anatomical and functional coordinate systems. Source reconstructions from ECoG and EEG are compared using different source models and realistically shaped volume conductor models. Realistically shaped volume conductor models for EEG source reconstruction are a prerequisite for improved localization accuracy. Individual boundary element method (BEM) models derived from MRI represent the “gold standard” and can approximate isotropic homogeneous head compartments and thus give an improved description of the head shape as compared with classical oversimplifying spherical shell models. Anisotropic volume conduction properties of the bone layer or the white matter fibers can be described by the finite element method (FEM); unfortunately, these models require a huge computational effort and are thus not used in daily applications. To avoid this computational effort, head models derived from an averaged MRI dataset can be used. Highly refined models with a large number of nodes and thus better numerical accuracy can be used by this approach, because the setup is performed only once and the decomposed models or precomputed leadfield matrices are saved for later application. Individual image data are not at all needed, if an overlay of the reconstruction results with the anatomy is not desired. With precomputed leadfield matrices and linear interpolation techniques, at least standardized BEM and FEM volume conductor models derived from averaged MRI datasets can achieve the same computational speed as analytical spherical models. The smoothed cortical envelope is used as a realistically shaped single-shell volume conductor model for ECoG source reconstruction, whereas three-compartment BEM-models are required for EEG. The authors describe how to localize ECoG-grid electrode positions and how to segment the cortical surface from coregistered magnetic resonance and CT images. Landmark-based coregistration is performed using common fiducials in both image modalities. Another more promising automatic approach is based on mutual three-dimensional volume gray-level information. The ECoG electrode positions can be retrieved from three-dimensional CT slices manually using cursors in thresholded images with depth information. Alternatively, the smoothed envelope of the cortical surface segmented from the MRI is used to semiautomatically determine the grid electrode positions by marking the four corners and measuring distances along the smoothed surface. With extended source patches for cortically constrained scans and current density reconstructions, results from ECoG and surface EEG data were compared. Single equivalent dipoles were used to explain the EEG far fields, and results were compared with the original current density distributions explaining the ECoG data. The authors studied the performance of spherical and realistically shaped BEM volume conductor models for EEG and ECoG source reconstruction in spherical and nonspherical parts of the head with simulations and measured epileptic spike data. Only small differences between spherical and realistically shaped models were found in the spherical parts of the head, whereas realistically shaped models are superior to spherical approximations in both single-shell ECoG and three-shell EEG cases in the nonspherical parts, such as the temporal lobe areas. The ECoG near field is more complicated to interpret than the surface EEG far field and cannot be explained in general by simple equivalent dipoles. However, from simulations with realistically shaped volume conductor models and cortically constrained source models, the authors studied how the bone and skin layer act as spatial low pass filters that smooth and simplify the surface EEG maps generated by much more complicated-looking source configurations derived from measured ECoG data.

Source analysis of median nerve and finger stimulated somatosensory evoked potentials: Multichannel simultaneous recording of electric and magnetic fields combined with 3d-MR tomography

SummaryAt the current state of technology, multichannel simultaneous recording of combined electric potentials and magnetic fields should constitute the most powerful tool for separation and localization of focal brain activity. We performed an explorative study of multichannel simultaneous electric SEPs and magnetically recorded SEFs. MEG only sees tangentially oriented sources, while EEG signals include the entire activity of the brain. These characteristics were found to be very useful in separating multiple sources with overlap of activity in time. The electrically recorded SEPs were adequately modelled by three equivalent dipoles located: (1) in the region of the brainstem, modelling the P14 peak at the scalp, (2) a tangentially oriented dipole, modelling the N20-P20 and N30-P30 peaks, and part of the P45, and (3) a radially oriented dipole, modelling the P22 peak and part of the P45, both located in the region of the somatosensory cortex. Magnetically recorded SEFs were adequately modelled by a single equivalent dipole, modelling the N20-P20 and N30-P30 peaks, located close to the posterior bank of the central sulcus, in area 3b (mean deviation: 3 mm). The tangential sources in the electrical data were located 6 mm on average from the area 3b. MEG and EEG was able to locate the sources of finger stimulated SEFs in accordance with the somatotopic arrangement along the central fissure. A combined analysis demonstrated that MEG can provide constraints to the orientation and location of sources and helps to stabilize the inverse solution in a multiple-source model of the EEG.

Fast visual evoked potential input into human area V5

STUDIES of the human visual cortex have demonstrated that an area for motion processing (V5) is located in the lateral occipito-temporal cortex. To study the timing of arrival of signals in V5 we recorded multi-channel visual evoked potentials (VEPs) to checkerboard stimuli. We then applied dipole source analysis which was computed on a grand average of 10 subjects, and on five individual subjects, respectively. We demonstrate an early VEP component with onset before 30 ms and with a peak around 45 ms, located in the vicinity of V5. This early component was independent of a second activity, which started around 50 ms and peaked around 70 ms, and was located within the striate cortex (V1). These results provide further evidence for a very fast input to V5 before activation of V1.