Feasibility of Equivalent Dipole Models for Electroencephalogram-Based Brain Computer Interfaces.

This article examines the localization errors of equivalent dipolar sources inverted from the surface electroencephalogram in order to determine the feasibility of using their location as classification parameters for non-invasive brain computer interfaces. Inverse localization errors are examined for two head models: a model represented by four concentric spheres and a realistic model based on medical imagery. It is shown that the spherical model results in localization ambiguity such that a number of dipolar sources, with different azimuths and varying orientations, provide a near match to the electroencephalogram of the best equivalent source. No such ambiguity exists for the elevation of inverted sources, indicating that for spherical head models, only the elevation of inverted sources (and not the azimuth) can be expected to provide meaningful classification parameters for brain-computer interfaces. In a realistic head model, all three parameters of the inverted source location are found to be reliable, providing a more robust set of parameters. In both cases, the residual error hypersurfaces demonstrate local minima, indicating that a search for the best-matching sources should be global. Source localization error vs. signal-to-noise ratio is also demonstrated for both head models.

Similarities between simulated spatial spectra of scalp EEG, MEG and structural MRI.

Electrical dipoles oriented perpendicular to the cortical surface are the primary source of the scalp EEGs and MEGs. Thus, in particular, gyri and sulci structures on the cortical surface have a definite possibility to influence the EEGs and MEGs. This was examined by comparing the spatial power spectral density (PSD) of the upper portion of the human cortex in MRI slices to that of simulated scalp EEGs and MEGs. The electrical activity was modeled with 2,650 dipolar sources oriented normal to the local cortical surface. The resulting scalp potentials were calculated with a finite element model of the head constructed from 51 segmented sagittal MR images. The PSD was computed after taking the fast Fourier transform of scalp potentials. The PSD of the cortical contour in each slice was also computed. The PSD was then averaged over all the slices. This was done for sagittal and coronal view both. The PSD of EEG and MEG showed two broad peaks, one from 0.05 to 0.22 cycles/cm (wavelength 20-4.545 cm) and the other from 0.22 to 1.2 cycles/cm (wavelength 4.545-0.834 cm). The PSD of the cortex showed a broad peak from 0.08 to 0.32 cycles/cm (wavelength 12.5-3.125 cm) and other two peaks within the range of 0.32 to 0.9 cycles/cm (wavelength 3.125-1.11 cm). These peaks are definitely due to the gyri structures and associated larger patterns on the cortical surface. Smaller peaks in the range of 1-3 cycles/cm were also observed which are possibly due to sulci structures. These results suggest that the spatial information was present in the EEG and MEG at the spatial frequencies of gyri. This also implies that the practical Nyquist frequency for sampling scalp EEGs should be 3.0 cycles/cm and an optimal interelectrode spacing of about 3 mm is needed for extraction of cortical patterns from scalp EEGs in humans.

Application of quasi-static magnetic reciprocity to finite element models of the MEG lead-field.

The reconstruction of neuronal current sources from magneto- and/or electroencephalography (MEG/EEG) measurements is referred to as an inverse problem. A precursor to most inverse algorithms is a forward transfer, or lead-field, matrix, in which the rows correspond to MEG and/or EEG measurement sites, and each column captures the linear response to a particular unit source. Simple models of the head, such as concentric spheres, result in analytic expressions for the lead-field. More realistic head models, such as those based on medical imagery, require numeric simulations. A straightforward, though inefficient, way to obtain the lead-field is to perform one forward simulation for each source, resulting in one column of the lead-field. For MEG/EEG inverse problems, however, the potential sources (rows) far outnumber the measurement sites (columns). Two approaches have been described for computing the EEG lead-field with a number of forward simulations equal to the number of measurement rows, rather than the number of source columns. One of these approaches is based on the principle of electric reciprocity, and the other approach is based on linear-algebraic manipulations of the forward problem. For the MEG lead-field, only a linear-algebraic approach has been described for numeric approaches such as the finite element method. This paper describes a reciprocal approach for the MEG lead-field and discusses implementation details for both approaches.

Influence of head models on neuromagnetic fields and inverse source localizations.

BACKGROUND: The magnetoencephalograms (MEGs) are mainly due to the source currents. However, there is a significant contribution to MEGs from the volume currents. The structure of the anatomical surfaces, e.g., gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the MEGs and the inverse source localizations. This was examined in detail with three different human head models. METHODS: Three finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissuetype model, (3) the Model 3 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. The lead fields and MEGs due to dipolar sources in the motor cortex were computed for all three models. The dipolar sources were oriented normal to the cortical surface and had a dipole moment of 100 microA meter. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. A set of 100 trial inverse runs was made covering the 3 cm cube motor cortex area in a random fashion. The Model 1 was used as a reference model. RESULTS: The reference model (Model 1), as expected, performed best in localizing the sources in the motor cortex area. The Model 3 performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The contour plots of the magnetic fields on top of the head were also different for all three models. The magnetic fields due to source currents were larger in magnitude as compared to the magnetic fields of volume currents. DISCUSSION: These results indicate that the complexity of head models strongly influences the MEGs and the inverse source localizations. A more complex head model performs better in inverse source localizations as compared to a model with lesser tissue surfaces.

Efficient localization of synchronous EEG source activities using a modified RAP-MUSIC algorithm.

Synchronization across different brain regions is suggested to be a possible mechanism for functional integration. Noninvasive analysis of the synchronization among cortical areas is possible if the electrical sources can be estimated by solving the electroencephalography inverse problem. Among various inverse algorithms, spatio-temporal dipole fitting methods such as RAP-MUSIC and R-MUSIC have demonstrated superior ability in the localization of a restricted number of independent sources, and also have the ability to reliably reproduce temporal waveforms. However, these algorithms experience difficulty in reconstructing multiple correlated sources. Accurate reconstruction of correlated brain activities is critical in synchronization analysis. In this study, we modified the well-known inverse algorithm RAP-MUSIC to a multistage process which analyzes the correlation of candidate sources and searches for independent topographies (ITs) among precorrelated groups. Comparative studies were carried out on both simulated data and clinical seizure data. The results demonstrated superior performance with the modified algorithm compared to the original RAP-MUSIC in recovering synchronous sources and localizing the epileptiform activity. The modified RAP-MUSIC algorithm, thus, has potential in neurological applications involving significant synchronous brain activities.

Influence of head models on EEG simulations and inverse source localizations.

BACKGROUND: The structure of the anatomical surfaces, e.g., CSF and gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the scalp potentials and the inverse source localizations. This was examined in detail with four different human head models. METHODS: Four finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissue-type model, (3) the Model 3 was derived from the Model 1 in which the conductivities of gray matter and CSF were set equal to the white matter, i.e., a nine tissue-type model, (4) the Model 4 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. How model complexity influences the EEG source localizations was also studied with the above four finite element models of the head. The lead fields and scalp potentials due to dipolar sources in the motor cortex were computed for all four models. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. The inverse analysis was performed by adding uncorrelated Gaussian noise to the scalp potentials to achieve a signal to noise ratio (SNR) of -10 to 30 dB. The Model 1 was used as a reference model. RESULTS: The reference model, as expected, performed the best. The Model 3, which did not have the CSF layer, performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The scalp potentials were also most affected by the lack of CSF geometry in the Model 3. The MLEs for the Model 4 were also larger than the Model 1 and 2. The Model 4 and the Model 3 had similar MLEs in the SNR range of -10 dB to 0 dB. However, in the SNR range of 5 dB to 30 dB, the Model 4 has lower MLEs as compared with the Model 3. DISCUSSION: These results indicate that the complexity of head models strongly influences the scalp potentials and the inverse source localizations. A more complex head model performs better in inverse source localizations as compared to a model with lesser tissue surfaces. The CSF layer plays an important role in modifying the scalp potentials and also influences the inverse source localizations. In summary, for best results one needs to have highly heterogeneous models of the head for accurate simulations of scalp potentials and for inverse source localizations.

Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction.

This paper presents a new algorithm called Standardized Shrinking LORETA-FOCUSS (SSLOFO) for solving the electroencephalogram (EEG) inverse problem. Multiple techniques are combined in a single procedure to robustly reconstruct the underlying source distribution with high spatial resolution. This algorithm uses a recursive process which takes the smooth estimate of sLORETA as initialization and then employs the re-weighted minimum norm introduced by FOCUSS. An important technique called standardization is involved in the recursive process to enhance the localization ability. The algorithm is further improved by automatically adjusting the source space according to the estimate of the previous step, and by the inclusion of temporal information. Simulation studies are carried out on both spherical and realistic head models. The algorithm achieves very good localization ability on noise-free data. It is capable of recovering complex source configurations with arbitrary shapes and can produce high quality images of extended source distributions. We also characterized the performance with noisy data in a realistic head model. An important feature of this algorithm is that the temporal waveforms are clearly reconstructed, even for closely spaced sources. This provides a convenient way to estimate neural dynamics directly from the cortical sources.

Efficient electromagnetic source imaging with adaptive standardized LORETA/FOCUSS.

Functional brain imaging and source localization based on the scalp's potential field require a solution to an ill-posed inverse problem with many solutions. This makes it necessary to incorporate a priori knowledge in order to select a particular solution. A computational challenge for some subject-specific head models is that many inverse algorithms require a comprehensive sampling of the candidate source space at the desired resolution. In this study, we present an algorithm that can accurately reconstruct details of localized source activity from a sparse sampling of the candidate source space. Forward computations are minimized through an adaptive procedure that increases source resolution as the spatial extent is reduced. With this algorithm, we were able to compute inverses using only 6% to 11% of the full resolution lead-field, with a localization accuracy that was not significantly different than an exhaustive search through a fully-sampled source space. The technique is, therefore, applicable for use with anatomically-realistic, subject-specific forward models for applications with spatially concentrated source activity.

Spatial resolution improvement of 3D EIT images by the shrinking sLORETA-FOCUSS algorithm.

This paper describes the use of the shrinking sLORETA-FOCUSS algorithm to improve the spatial resolution of three-dimensional (3D) EIT images. Conventional EIT yields inaccurate, low spatial resolution images, due to noise, the low sensitivity of boundary voltages to inner conductivity perturbations and a limited number of boundary voltage measurements. The focal underdetermined system solver (FOCUSS) algorithm produces a localized energy solution based on the weighted minimum-norm least-squares (MNLS) solution. It was successfully applied for the spatial resolution improvement of EIT images of simulated and tank data for a 2D homogeneous circular disc. However, due to the fact that a 3D mesh system contains many more elements, much more memory is required to store the weighting matrix. In order to extend the work to 3D, the shrinking-FOCUSS method is utilized to shrink the solution space as well as the weighting matrix in each iteration step. The solution of the standardized low resolution electromagnetic tomography algorithm (sLORETA) is adopted as the initial estimate of the shrinking-FOCUSS. The effectiveness is verified by implementing the new algorithm on tank data for a three-dimensional homogeneous sphere.

A recursive algorithm for the three-dimensional imaging of brain electric activity: Shrinking LORETA-FOCUSS.

Estimation of intracranial electric activity from the scalp electroencephalogram (EEG) requires a solution to the EEG inverse problem, which is known as an ill-conditioned problem. In order to yield a unique solution, weighted minimum norm least square (MNLS) inverse methods are generally used. This paper proposes a recursive algorithm, termed Shrinking LORETA-FOCUSS, which combines and expands upon the central features of two well-known weighted MNLS methods: LORETA and FOCUSS. This recursive algorithm makes iterative adjustments to the solution space as well as the weighting matrix, thereby dramatically reducing the computation load, and increasing local source resolution. Simulations are conducted on a 3-shell spherical head model registered to the Talairach human brain atlas. A comparative study of four different inverse methods, standard Weighted Minimum Norm, L1-norm, LORETA-FOCUSS and Shrinking LORETA-FOCUSS are presented. The results demonstrate that Shrinking LORETA-FOCUSS is able to reconstruct a three-dimensional source distribution with smaller localization and energy errors compared to the other methods.

Ellipsoidal refinement of the regularized inverse: performance in an anatomically realistic EEG model.

Functional brain imaging and source localization based on the scalp's potential field requires a solution to the inverse electrostatic problem. This is an underdetermined problem with many solutions. Minimum norm and regularization methods involving the norm are often used, but generally give solutions in which current is widely distributed. One method for reducing the spatial distribution of a solution is to apply it iteratively within the bounds of a shrinking ellipsoid. This paper compares the performance of this approach with an exhaustive search at various noise levels using a numeric simulation of the electroencephalogram in a realistic conductor model. The results show that inverting a single dipolar source with a location accuracy comparable to an exhaustive search requires in the range of 5 to 10 dB higher signal-to-noise ratio.

Dipole models for the EEG and MEG.

The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite-element and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.