Estimating cortical potentials from scalp EEG's in a realistically shaped inhomogeneous head model by means of the boundary element method

Estimation of cortical dipole sources by equivalent dipole layer imaging and independent component analysis

We explored suitable estimation method for equivalent dipole sources in the brain. In a previous study, we solved an inverse problem that estimated an equivalent dipole-layer distribution from the scalp electroencephalogram by a spatio-temporal inverse filters constructed with parametric projection filter. In the present study, we estimated equivalent dipole sources from dipole layer distributions. Moreover, to identify the number, position, and moment of equivalent dipole sources, we separated each dipole layer distribution using independent component analysis (ICA). The performance of the proposed estimation method was evaluated by computer simulation and human experimental studies in an inhomogeneous three-concentric sphere head model. The present simulation results indicated that the equivalent dipole sources was accurately estimated by ICA and dipole imaging. We also applied the proposed method to human visual evoked potential.

Cortical potential imaging of movement-related potentials using parametric Wiener filter in realistic-shaped head model

Suitable spatial filters were explored for inverse estimation of cortical potential imaging from the scalp electroencephalogram. The effects of incorporating signal and noise covariance into inverse procedures were examined by computer simulations and experimental study. The parametric Wiener filter (PWF) was applied to an inhomogeneous three-sphere head model under various signal and noise conditions. We also examined estimation methods for the signal covariance in PWF. The present simulation results suggest that the PWF with modified matrix transformation method has better performance. The proposed methods were applied to self-paced movement-related potentials In order to identify the anatomic substrate locations of neural generators in realistic head model. The proposed methods demonstrated that the contralateral premotor cortex was preponderantly activated In relation to movement performance.

Evaluation of cortical imaging techniques based on somatosensory evoked potentials

In the present study we evaluate the performance of several inverse algorithms for reconstructing the cortical current density distributions from scalp EEG recordings. The direct cortical SEP recordings in a patient were used as a gold standard to assess the performance of the numerical algorithms. The present results suggest that L(1)-norm methods gave the most accurate results in terms of cortical current density imaging of brain responses invoked by somatosensory stimulation.

On the estimation of the number of dipole sources in EEG source localization

OBJECTIVE

The purpose of the present study was to determine the number of the equivalent dipole sources corresponding to the scalp EEG using the information criterion method based on the instantaneous-state modeling.

METHODS

A three-concentric-spheres head model was used to represent the head volume conductor. The Powell algorithm was used to solve the inverse problem of estimating the equivalent dipoles from the scalp EEG. The information criterion with different penalty functions was used to determine the dipole number. Computer simulations were conducted to evaluate effects of various parameters on the estimation of dipole number.

RESULTS

The present results suggest that the present method is able to estimate the number of equivalent current dipoles (ECDs) from instantaneous scalp EEG measurements, and that increase in the electrode number can improve the accuracy of estimation of the ECD number. For two ECDs, the best performance of estimation with 20% white noise were 85%, 92% and 94%, when 64, 128 and 256 electrodes are used, respectively. When there are 3 ECDs, the present results suggest that using 256 electrodes gave up to 82% estimation accuracy. The present simulation results also indicate that the accuracies of identification are similar when the minimum distance between dipoles is either 1 or 2 cm, which was used in the simulation. It was also found that the different penalty functions used in the information criterion method could have substantial influence on the estimation accuracy.

CONCLUSIONS

The present method can estimate the number of ECDs from instantaneous scalp EEG distribution for up to three dipoles.

SIGNIFICANCE

The successful estimation of the number of ECDs will play an important role in expanding the applicability of dipole source localization to multiple sources.

Resistor mesh model of a spherical head: Part 2: A review of applications to cortical mapping

A resistor mesh model (RMM) has been validated with reference to the analytical model by consideration of a set of four dipoles close to the cortex. The application of the RMM to scalp potential interpolation was detailed in Part 1. Using the RMM and the same four dipoles, the different methods of cortical mapping were compared and have shown the potentiality of this RMM for obtaining current and potential cortical distributions. The lead-field matrices are well-adapted tools, but the use of a square matrix of high dimension does not permit the inverse solution to be improved in the presence of noise, as a regularisation technique is necessary with noisy data. With the RMM, the transfer matrix and the cortical imaging technique proved to be easy to implement. Further development of the RMM will include application to more realistic head models with more accurate conductivities.

Low resolution brain electromagnetic tomography in a realistic geometry head model: a simulation study

It is of importance to localize neural sources from scalp recorded EEG. Low resolution brain electromagnetic tomography (LORETA) has received considerable attention for localizing brain electrical sources. However, most such efforts have used spherical head models in representing the head volume conductor. Investigation of the performance of LORETA in a realistic geometry head model, as compared with the spherical model, will provide useful information guiding interpretation of data obtained by using the spherical head model. The performance of LORETA was evaluated by means of computer simulations. The boundary element method was used to solve the forward problem. A three-shell realistic geometry (RG) head model was constructed from MRI scans of a human subject. Dipole source configurations of a single dipole located at different regions of the brain with varying depth were used to assess the performance of LORETA in different regions of the brain. A three-sphere head model was also used to approximate the RG head model, and similar simulations performed, and results compared with the RG-LORETA with reference to the locations of the simulated sources. Multisource localizations were discussed and examples given in the RG head model. Localization errors employing the spherical LORETA, with reference to the source locations within the realistic geometry head, were about 20-30 mm, for four brain regions evaluated: frontal, parietal, temporal and occipital regions. Localization errors employing the RG head model were about 10 mm over the same four brain regions. The present simulation results suggest that the use of the RG head model reduces the localization error of LORETA, and that the RG head model based LORETA is desirable if high localization accuracy is needed.

Estimation of in vivo human brain-to-skull conductivity ratio from simultaneous extra- and intra-cranial electrical potential recordings

OBJECTIVE

The present study aims to accurately estimate the in vivo brain-to-skull conductivity ratio by means of cortical imaging technique. Simultaneous extra- and intra-cranial potential recordings induced by subdural current stimulation were analyzed to get the estimation.

METHODS

The effective brain-to-skull conductivity ratio was estimated in vivo for 5 epilepsy patients. The estimation was performed using multi-channel simultaneously recorded scalp and cortical electrical potentials during subdural electrical stimulation. The cortical imaging technique was used to compute the inverse cortical potential distribution from the scalp recorded potentials using a 3-shell head volume conductor model. The brain-to-skull conductivity ratio, which leads to the most consistent cortical potential estimates with respect to the direct intra-cranial measurements, is considered to be the effective brain-to-skull conductivity ratio.

RESULTS

The present estimation provided consistent results in 5 human subjects studied. The in vivo effective brain-to-skull conductivity ratio ranged from 18 to 34 in the 5 epilepsy patients.

CONCLUSIONS

The effective brain-to-skull conductivity ratio can be estimated from simultaneous intra- and extra-cranial potential recordings and the averaged value/standard deviation is 25+/-7.

SIGNIFICANCE

The present results provide important experimental data on the brain-to-skull conductivity ratio, which is of significance for accurate brain source localization using piece-wise homogeneous head models.

A second-order finite element algorithm for solving the three-dimensional EEG forward problem

A finite element algorithm has been developed to solve the electroencephalogram (EEG) forward problem. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models. The present algorithm has been evaluated by means of computer simulations, by comparing with analytic solutions in a multi-spheres concentric head model. The developed finite element method (FEM) algorithm has also been applied to address questions of interest in the EEG forward problem. The present simulation study indicates that the second-order FEM provides substantially enhanced numerical accuracy and computational efficiency, as compared with the first-order FEM for comparable numbers of tetrahedral elements. The anisotropic conductivity distribution of the head tissue can be taken into account in the present FEM algorithm. The effects of dipole eccentricity, size of finite elements and local mesh refinement on solution accuracy are also addressed in the present simulation study.

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.

An alternative subspace approach to EEG dipole source localization

In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist.

Effect of Electrode Density and Measurement Noise on the Spatial Resolution of Cortical Potential Distribution

The purpose of the present study was to examine the spatial resolution of electroencephalography (EEG) by means of inverse cortical EEG solution. The main interest was to study how the number of measurement electrodes and the amount of measurement noise affects the spatial resolution. A three-layer spherical head model was used to obtain the source-field relationship of cortical potentials and scalp EEG field. Singular value decomposition was used to evaluate the spatial resolution with various measurement noise estimates. The results suggest that as the measurement noise increases the advantage of dense electrode systems is decreased. With low realistic measurement noise, a more accurate inverse cortical potential distribution can be obtained with an electrode system where the distance between two electrodes is as small as 16 mm, corresponding to as many as 256 measurement electrodes. In clinical measurement environments, it is always beneficial to have at least 64 measurement electrodes.

Equivalent physical models and formulation of equivalent source layer in high-resolution EEG imaging

In high-resolution EEG imaging, both equivalent dipole layer (EDL) and equivalent charge layer (ECL) assumed to be located just above the cortical surface have been proposed as high-resolution imaging modalities or as intermediate steps to estimate the epicortical potential. Presented here are the equivalent physical models of these two equivalent source layers (ESL) which show that the strength of EDL is proportional to the surface potential of the layer when the outside of the layer is filled with an insulator, and that the strength of ECL is the normal current of the layer when the outside is filled with a perfect conductor. Based on these equivalent physical models, closed solutions of ECL and EDL corresponding to a dipole enclosed by a spherical layer are given. These results provide the theoretical basis of ESL applications in high-resolution EEG mapping.

Spatio-temporal cortical source imaging of brain electrical activity by means of time-varying parametric projection filter

In the present study, we explore suitable spatio-temporal filters for inverse estimation of an equivalent dipole-layer distribution from the scalp electroencephalogram (EEG) for imaging of brain electric sources. We propose a time-varying parametric projection filter (tPPF) for the spatio-temporal EEG analysis. The performance of this tPPF algorithm was evaluated by computer simulation studies. An inhomogeneous three-concentric-spheres model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to represent equivalently brain electric sources and estimated from the scalp potentials. The tPPF filter was tested to remove time-varying noise such as instantaneous artifacts caused by eyes-blink. The present simulation results indicate that the proposed time-variant tPPF method provides enhanced performance in rejecting time-varying noise, as compared with the time-invariant parametric projection filter.

High-resolution EEG: cortical potential imaging of interictal spikes

BACKGROUND

It is of clinical importance to localize pathologic brain tissue in epilepsy. Noninvasive localization of cortical areas associated with interictal epileptiform spikes may provide important information to facilitate presurgical planning for intractable epilepsy patients.

METHODS

A cortical potential imaging (CPI) technique was used to deconvolve the smeared scalp potentials into the cortical potentials. A 3-spheres inhomogeneous head model was used to approximately represent the head volume conductor. Five pediatric epilepsy patients were studied. The estimated cortical potential distributions of interictal spikes were compared with the subsequent surgical resections of these same patients.

RESULTS

The areas of negativity in the reconstructed cortical potentials of interictal spikes in 5 patients were consistent with the areas of surgical resections for these patients.

CONCLUSIONS

The CPI technique may become a useful alternative for noninvasive mapping of cortical regions displaying epileptiform activity from scalp electroencephalogram recordings.

Estimation of Active Cortical Current Source Regions Using a Vector Representation Scanning Approach

The objective of this article is to present a framework for cortical current source reconstruction that extracts a center and magnitude of electrical brain activity from EEG signals. High-resolution EEG recordings, a subject-specific MRI-based electromagnetic boundary element method (BEM) model, and a channel reduction technique are used. This new geometric measure combines the magnitude and spatial location of electrical brain activity of each of the identified subsets of channels into a three-dimensional resultant vector. The combination of the two approaches constitutes a source reconstruction scanning technique that provides a real-time estimation of cortical centers that can be tracked over time. Simulations demonstrate that the ability of this method to find the best-fit cortical location is more robust both in terms of accuracy and precision than traditional approaches for single-source conditions. Experimental validation demonstrates its ability to localize and separate cortical activity in plausible sites for two different motor tasks. Finally, this method provides a statistical measure to compare electrical brain activity associated with different motor tasks.

Boundary element method-based cortical potential imaging of somatosensory evoked potentials using subjects' magnetic resonance images

A boundary element method-based cortical potential imaging technique has been developed to directly link the scalp potentials with the cortical potentials with the aid of magnetic resonance images of the subjects. First, computer simulations were conducted to evaluate the new approach in a concentric three-sphere inhomogeneous head model. Second, the corresponding cortical potentials were estimated from the patients' preoperative scalp somatosensory evoked potentials (SEPs) based on the boundary element models constructed from subjects' magnetic resonance images and compared to the postoperative direct cortical potential recordings in the same patients. Simulation results demonstrated that the cortical potentials can be estimated from the scalp potentials using different scalp electrode configurations and are robust against measurement noise. The cortical imaging analysis of the preoperative scalp SEPs recorded from patients using the present approach showed high consistency in spatial pattern with the postoperative direct cortical potential recordings. Quantitative comparison between the estimated and the directly recorded subdural grid potentials resulted in reasonably high correlation coefficients in cases studied. Amplitude difference between the estimated and the recorded potentials was also observed as indexed by the relative error, and the possible underlying reasons are discussed. The present numerical and experimental results validate the boundary element method-based cortical potential imaging approach and demonstrate the feasibility of the new approach in noninvasive high-resolution imaging of brain electric activities from scalp potential measurement and magnetic resonance images.

An equivalent current source model and laplacian weighted minimum norm current estimates of brain electrical activity

We have developed a method for estimating the three-dimensional distribution of equivalent current sources inside the brain from scalp potentials. Laplacian weighted minimum norm algorithm has been used in the present study to estimate the inverse solutions. A three-concentric-sphere inhomogeneous head model was used to represent the head volume conductor. A closed-form solution of the electrical potential over the scalp and inside the brain due to a point current source was developed for the three-concentric-sphere inhomogeneous head model. Computer simulation studies were conducted to validate the proposed equivalent current source imaging. Assuming source configurations as either multiple dipoles or point current sources/sinks, in computer simulations we used our method to reconstruct these sources, and compared with the equivalent dipole source imaging. Human experimental studies were also conducted and the equivalent current source imaging was performed on the visual evoked potential data. These results highlight the advantages of the equivalent current source imaging and suggest that it may become an alternative approach to imaging spatially distributed current sources-sinks in the brain and other organ systems.

High-resolution EEG: on the cortical equivalent dipole layer imaging

BACKGROUND

Brain electrical activity is a spatio-temporally distributed process. Cortical imaging techniques have been developed to reconstruct cortical activity from the scalp electroencephalographic or magnetoencephalographic measurements. Several cortical imaging approaches, such as the epicortical potentials and a dipole layer accounting for the cortical activity, have been used to represent brain electrical activity.

METHODS

A closed cortical dipole layer source model is used to equivalently represent brain electrical activity. The relationship between the primary brain electrical sources and the cortical equivalent dipole layer is derived from the theory of electromagnetics. Computer simulation studies were conducted using a 3-concentric-sphere head model to validate the proposed theory. The cortical equivalent dipole layer imaging approach was tested in both computer simulation and human visual evoked potential (VEP) experiments.

RESULTS

The strength of the cortical equivalent dipole layer is shown to be proportional to the electrical potential over the same surface generated by primary electrical sources, had the outer medium been replaced by air. The proposed theory was validated by computer simulation in a discrete system. Simulation and VEP experimental studies suggest the feasibility of applying the cortical equivalent dipole layer imaging approach for brain imaging.

CONCLUSIONS

The cortical equivalent dipole layer model can equivalently represent the primary brain electrical sources throughout the entire brain surrounded by the dipole layer. The strength of the cortical equivalent dipole layer due to primary sources can be directly calculated according to the theory developed in the present study.

A study of equivalent source techniques for high-resolution EEG imaging

High-resolution EEG imaging has been an important topic in recent EEG research, and much work has been done on the two equivalent source imaging techniques: the equivalent distributed dipole-layer source imaging technique (EST) and the equivalent multipole source imaging technique (SAT). In this paper we first develop a forward density formula for a spherical equivalent distributed dipole layer of an arbitrary dipole in a three-concentric-sphere head model. It is clarified using the derived forward formula that the equivalent dipole-layer source and equivalent multipole source are interrelated in theory. Finally, simulation comparisons are conducted, the results of which suggest that EST has a higher spatial resolution than SAT when both of them are implemented by a truncated singular value decomposition algorithm. This is due to the different singularities of the inversion equations involved in the two techniques. An empirical VEP data study also shows that EST is better than SAT in providing higher spatial resolution EEG imaging.

A cortical potential imaging analysis of the P300 and novelty P3 components

The P300 and Novelty P3 are positive components of the event related brain potential (ERP) with a latency of at least 300 ms, which are manifestations of brain activity evoked by deviant events. Spencer et al. [1999, 2001] demonstrated that these are two distinct components, both of which may be elicited, with different amplitudes, by both rare and novel events. However, the locations of the intracranial sources of the components remain unknown. We describe the application of cortical potential imaging (CPI) analysis to the data described by Spencer et al. [1999]. The ERPs were recorded from 15 healthy subjects presented with auditory oddball sequences. Cortical potential maps (CPMs) were reconstructed from the scalp potential maps (SPMs) corresponding to the P300 and Novelty P3 components by deblurring the smoothing effect of the head volume conductor. The reconstructed CPMs, derived from the SPMs by means of the CPI, showed localized areas of activity distributed in both the frontal and parietal lobes; the parietal region was active throughout the period of the late positivities. The reconstructed CPMs associated with novel events showed prominent activity at the frontal lobe (Novelty P3) followed by progressively pronounced parietal lobe activity (P300), and these two components can be well separated by the CPMs. These analyses show how the CPI can be used to relate the scalp electrical recordings to the underlying brain activity.