A computer simulation study of cortical imaging from scalp potentials

Channel interpolation in TMS-EEG: a quantitative study towards an accurate topographical representation

The co-registration of transcranial magnetic stimulation and electroencephalography (TMS-EEG) is emerging as a successful technique for causally exploring cortical mechanisms and connections. However, various artefacts could affect TMS-EEG signals. Correct artefacted channels reconstruction is crucial to obtain accurate topographical representation and consequently accurate inverse problem solution, in order to map in a proper way the global brain responses after the stimulation of one particular brain region of interest. In this paper, we discuss the problem of artefacted channels interpolation in TMS-EEG signals. Aim of the study was to investigate two different interpolation methods evaluating their performance in two datasets: one constituted by 19 EEG channels montage (low-density spatial resolution) and the other one by 60 EEG channels montage (high-density spatial resolution). In addition, these evaluations took place in two different contexts of application: after the averaging of TMS Evoked Potentials (TEPs) in a time interval to obtain a global information in the considered range, and at fixed latencies 100 ms and 300 ms after the TMS stimulus. The results showed that the global reconstruction error was lower at fixed latencies for the high-density electrodes spatial resolution montage.

High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.

Localized cortical dipole imaging using a small number of electrodes based on independent component analysis

The spatial resolution of scalp potential mapping is limited because of low conductivity of a skull. Cortical dipole layer imaging has been proposed as a method to visualize brain electrical activity with high spatial resolution. According to this method, about 100 electrodes were required to measure whole brain electrical activity. In the present study, we investigated simplified cortical dipole imaging with a small number of electrodes. The density of electrodes and the spatial resolution are in a trade-off relation. Thus, the number of electrodes was reduced by limiting the visualization region of interest, without lowering the density of electrodes. Moreover, independent component analysis was applied to the multiple signal sources to extract an attention signal from the other signals and noise. In simulation, even if the number of electrodes was reduced to 25, the obtained results were almost equivalent to the case with whole brain electrodes. The proposed method was applied to human experimental data of movement-related potential. We confirmed that the proposed method provided high resolution cortical dipole imaging with localized distribution.

Noninvasive imaging of the high frequency brain activity in focal epilepsy patients

High-frequency (HF) activity represents a potential biomarker of the epileptogenic zone in epilepsy patients, the removal of which is considered to be crucial for seizure-free surgical outcome. We proposed a high frequency source imaging (HFSI) approach to noninvasively image the brain sources of the scalp-recorded HF EEG activity. Both computer simulation and clinical patient data analysis were performed to investigate the feasibility of using the HFSI approach to image the sources of HF activity from noninvasive scalp EEG recordings. The HF activity was identified from high-density scalp recordings after high-pass filtering the EEG data and the EEG segments with HF activity were concatenated together to form repetitive HF activity. Independent component analysis was utilized to extract the components corresponding to the HF activity. Noninvasive EEG source imaging using realistic geometric boundary element head modeling was then applied to image the sources of the pathological HF brain activity. Five medically intractable focal epilepsy patients were studied and the estimated sources were found to be concordant with the surgical resection or intracranial recordings of the patients. The present study demonstrates, for the first time, that source imaging from the scalp HF activity could help to localize the seizure onset zone and provide a novel noninvasive way of studying the epileptic brain in humans. This study also indicates the potential application of studying HF activity in the presurgical planning of medically intractable epilepsy patients.

Effect of brain-to-skull conductivity ratio on EEG source localization accuracy

The goal of this study was to investigate the influence of the brain-to-skull conductivity ratio (BSCR) on EEG source localization accuracy. In this study, we evaluated four BSCRs: 15, 20, 25, and 80, which were mainly discussed according to the literature. The scalp EEG signals were generated by BSCR-related forward computation for each cortical dipole source. Then, for each scalp EEG measurement, the source reconstruction was performed to identify the estimated dipole sources by the actual BSCR and the misspecified BSCRs. The estimated dipole sources were compared with the simulated dipole sources to evaluate EEG source localization accuracy. In the case of considering noise-free EEG measurements, the mean localization errors were approximately equal to zero when using actual BSCR. The misspecified BSCRs resulted in substantial localization errors which ranged from 2 to 16 mm. When considering noise-contaminated EEG measurements, the mean localization errors ranged from 8 to 18 mm despite the BSCRs used in the inverse calculation. The present results suggest that the localization accuracy is sensitive to the BSCR in EEG source reconstruction, and the source activity can be accurately localized when the actual BSCR and the EEG scalp signals with high signal-to-noise ratio (SNR) are used.

Cortical dipole imaging using truncated total least squares considering transfer matrix error

Cortical dipole imaging has been proposed as a method to visualize electroencephalogram in high spatial resolution. We investigated the inverse technique of cortical dipole imaging using a truncated total least squares (TTLS). The TTLS is a regularization technique to reduce the influence from both the measurement noise and the transfer matrix error caused by the head model distortion. The estimation of the regularization parameter was also investigated based on L-curve. The computer simulation suggested that the estimation accuracy was improved by the TTLS compared with Tikhonov regularization. The proposed method was applied to human experimental data of visual evoked potentials. We confirmed the TTLS provided the high spatial resolution of cortical dipole imaging.

High-resolution Functional Source and Impedance Imaging

Functional imaging has played a significant role in bettering our understanding of mechanisms of brain function and dysfunctions. We review recent research on electrophysiological neuroimaging, multimodal neuroimaging integrating functional MRI with EEG, and our development of magnetoacoustic tomography with magnetic induction for high resolution impedance imaging. Examples from research of our group will be shown to illustrate the concepts. The extensive work being pursued by a number of investigators suggests the promise of functional neuroimaging in imaging neural activity from noninvasive measurements.

Objective evaluation of somatic sensation for mechanical stimuli by means of cortical dipole layer imaging

In clinical situations, the objective evaluation of somatic sensations is expected without a patient's subjective opinions to reduce social problems such as those related to lawsuits for nerve injuries and malingering. In this study, the somatosensory evoked potential (SEP) using the mechanical stimulations of the tactile sensation was measured and analyzed in spatiotemporal domains. The spatial resolution of SEP maps was improved by application of cortical dipole layer imaging. The experimentally obtained results suggest that the spatiotemporal distributions of the SEPs reflect the differences for positions, strengths, and patterns of somatosensory stimulations.

Cortical potential imaging of somatosensory evoked potential induced by mechanical stimulation

The objective evaluation of somatic sensations is expected without a patient's subjective opinions to reduce social problems such as those related to lawsuits for nerve injuries or malingering. In this study, the somatosensory evoked potential (SEP) using the mechanical stimulations of the tactile sensation was measured and analyzed in spatiotemporal domains. The cortical potential mapping projected onto the realistic-shaped model was estimated to improve the spatial resolution of the SEP maps by application of cortical dipole layer imaging. The experimentally obtained results suggest that the spatiotemporal distributions of the SEPs reflect the differences for positions, strengths, and patterns of somatosensory stimulations.

Cortical potential imaging of somatosensory evoked potentials by means of the boundary element method in pediatric epilepsy patients

The aim of the present study was to assess the feasibility of identifying the primary hand sensory area and central sulcus in pediatric patients using the cortical potential imaging (CPI) method from the scalp recorded somatosensory evoked potentials (SEPs). The CPI method was used to reconstruct the cortical potential distribution from the scalp potentials with the boundary element (3-layer: scalp, skull and brain) head model based on MR images of individual subjects. The cortical potentials estimated from the pre-operative scalp SEPs of four pediatric patients, were compared with the post-op subdural SEP recordings made in the same subjects. Estimated and directly recorded cortical SEP maps showed comparable spatial patterns on the cortical surface in four patients (spatial correlation coefficient >0.7 in the SEP spikes). For two of four patients, the estimated waveforms correlated significantly to the waveforms obtained by direct cortical recordings. The present results demonstrated the feasibility of the cortical potential imaging approach in noninvasive imaging spatial distribution and temporal waveforms of cortical potentials for pediatric patients. These also suggest that the CPI method may provide a promising means of estimating the cortical potential and noninvasive localizing the central sulcus to aid surgical planning for pediatric patients.

Influence of white matter anisotropic conductivity on EEG source localization: comparison to fMRI in human primary visual cortex

OBJECTIVE

The goal of this study was to experimentally investigate the influence of the anisotropy of white matter (WM) conductivity on EEG source localization.

METHODS

Visual evoked potentials (VEP) and fMRI data were recorded from three human subjects presented with identical visual stimuli. A finite element method was used to solve the EEG forward problems based on both anisotropic and isotropic head models, and single-dipole source localization was subsequently performed to localize the source underlying the N75 VEP component.

RESULTS

The averaged distances of the localized N75 dipole locations in V1 between the isotropic and anisotropic head models ranged from 0 to 6.22+/-2.83mm. The distances between the localized dipole positions and the centers of the fMRI V1 activations were slightly smaller when using an anisotropic model (7.49+/-1.35-15.70+/-8.60mm) than when using an isotropic model (7.65+/-1.30-15.31+/-9.18mm).

CONCLUSIONS

Anisotropic models incorporating realistic WM anisotropic conductivity distributions do not substantially improve the accuracy of EEG dipole localization in the primary visual cortex using experimental data obtained using visual stimulation.

SIGNIFICANCE

The present study represents the first attempt using a human experimental approach to assess the effects of WM anisotropy on EEG source analysis.

EEG/MEG source imaging: methods, challenges, and open issues

We present the four key areas of research-preprocessing, the volume conductor, the forward problem, and the inverse problem-that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization.

High-resolution cortical dipole layer imaging based on noise covariance matrix

We have investigated the suitable spatial filters for inverse estimation of cortical dipole imaging from the scalp electroencephalogram. The effects of incorporating statistical information of noise into inverse procedures were examined by computer simulations and experimental studies. The parametric projection filter (PPF) was applied to an inhomogeneous three-sphere volume conductor head model. The noise covariance matrix was estimated by applying independent component analysis (ICA) to the scalp potentials. Moreover, the sampling method of the noise information was examined for calculating the noise covariance matrix. The simulation results suggest that the spatial resolution was improved while the effect of noise was suppressed by including the separated noise at the time instant of imaging and by adjusting the number of samples according to the signal to noise ratio.

Multimodal functional neuroimaging: integrating functional MRI and EEG/MEG

Noninvasive functional neuroimaging, as an important tool for basic neuroscience research and clinical diagnosis, continues to face the need of improving the spatial and temporal resolution. While existing neuroimaging modalities might approach their limits in imaging capability mostly due to fundamental as well as technical reasons, it becomes increasingly attractive to integrate multiple complementary modalities in an attempt to significantly enhance the spatiotemporal resolution that cannot be achieved by any modality individually. Electrophysiological and hemodynamic/metabolic signals reflect distinct but closely coupled aspects of the underlying neural activity. Combining fMRI and EEG/MEG data allows us to study brain function from different perspectives. In this review, we start with an overview of the physiological origins of EEG/MEG and fMRI, as well as their fundamental biophysics and imaging principles, we proceed with a review of the major advances in the understanding and modeling of neurovascular coupling and in the methodologies for the fMRI-EEG/MEG simultaneous recording. Finally, we summarize important remaining issues and perspectives concerning multimodal functional neuroimaging, including brain connectivity imaging.

Three-dimensional brain current source reconstruction from intra-cranial ECoG recordings

We have investigated 3-dimensional brain current density reconstruction (CDR) from intracranial electrocorticogram (ECoG) recordings by means of finite element method (FEM). The brain electrical sources are modeled by a current density distribution and estimated from the ECoG signals with the aid of a weighted minimum norm estimation algorithm. A series of computer simulations were conducted to evaluate the performance of ECoG-CDR by comparing with the scalp EEG based CDR results. The present computer simulation results indicate that the ECoG-CDR provides enhanced performance in localizing single dipole sources which are located in regions underneath the implanted subdural ECoG grids, and in distinguishing and imaging multiple separate dipole sources, in comparison to the CDR results as obtained from the scalp EEG under the same conditions. We have also demonstrated the applicability of the present ECoG-CDR method to estimate 3-dimensional current density distribution from the subdural ECoG recordings in a human epilepsy patient. Eleven interictal epileptiform spikes (seven from the frontal region and four from parietal region) in an epilepsy patient undergoing surgical evaluation were analyzed. The present promising results indicate the feasibility and applicability of the developed ECoG-CDR method of estimating brain sources from intracranial electrical recordings, with detailed forward modeling using FEM.

Estimation of signal and noise covariance using ICA for high-resolution cortical dipole imaging

Suitable spatial filters were explored for inverse estimation of cortical dipole imaging from a scalp electroencephalogram. Computer simulations were used to examine the effects of incorporating statistical information of signal and noise into inverse procedures. Actually, the parametric projection filter (PPF) and parametric Wiener filter (PWF) were applied to an inhomogeneous three-sphere head model. The signal and noise covariance matrices were estimated by applying independent component analysis (ICA) to the scalp potentials. The simulation results described herein suggest that the PPF using differential noise between EEG and separated signal were equivalent to those obtained using the method with actual noise. Moreover, the PWF using separated signals has better performance than traditional inverse techniques.

Spatio-temporal EEG dipole estimation by means of a hybrid genetic algorithm

EEG source localization can be considered as a nonlinear optimization process. In the present study, a hybrid genetic algorithm (HGA) is introduced, which combines genetic and local search strategies to overcome the disadvantages of conventional genetic algorithm and local optimization methods. This HGA algorithm was used to localize two dipoles from scalp EEG, and yielded localization accuracy range of 0.95 cm-1.55 cm when the noise level is within 15%, which is better than the Simplex and GA algorithms in localizing multiple dipoles.

Effect of measurement noise and electrode density on the spatial resolution of cortical potential distribution with different resistivity values for the skull

The purpose of the present theoretical study was to examine the spatial resolution of electroencephalography (EEG) by means of the accuracy of the inverse cortical EEG solution. The study focused on effect of the amount of measurement noise and the number of electrodes on the spatial resolution with different resistivity ratios for the scalp, skull and brain. The results show that if the relative skull resistivity is lower than earlier believed, the spatial resolution of different electrode systems is less sensitive to the measurement noise. Furthermore, there is then also greater advantage to be obtained with high-resolution EEG at realistic noise levels.

Integration of EEG/MEG with MRI and fMRI

EEG and MEG are important functional neuroimaging modalities for studying the temporal dynamics of neural activities and interactions, but the accurate localization of neural activities still remains a challenging problem. Combining EEG/MEG with MRI or/and functional MRI (fMRI) holds promise to significantly increase the spatial resolution of electromagnetic source imaging, and at the same time, allows tracing the rapid neural processes and information pathways within the brain, which cannot be achieved using these modalities in isolation. In this paper, we review some recent progresses in multimodal neuroimaging, with special emphasis on the integration of EEG, MEG with MRI and fMRI. Some examples are shown to illustrate the importance of the combined source analysis in clinical and experimental studies.

A cortical potential imaging study from simultaneous extra- and intracranial electrical recordings by means of the finite element method

In the present study, we have validated the cortical potential imaging (CPI) technique for estimating cortical potentials from scalp EEG using simultaneously recorded electrocorticogram (ECoG) in the presence of strong local inhomogeneity, i.e., Silastic ECoG grid(s). The finite element method (FEM) was used to model the realistic postoperative head volume conductor, which includes the scalp, skull, cerebrospinal fluid (CSF) and brain, as well as the Silastic ECoG grid(s) implanted during the surgical evaluation in epilepsy patients, from the co-registered magnetic resonance (MR) and computer tomography (CT) images. A series of computer simulations were conducted to evaluate the present FEM-based CPI technique and to assess the effect of the Silastic ECoG grid on the scalp EEG forward solutions. The present simulation results show that the Silastic ECoG grid has substantial influence on the scalp potential forward solution due to the distortion of current pathways in the presence of the extremely low conductive materials. On the other hand, its influence on the estimated cortical potential distribution is much less than that on the scalp potential distribution. With appropriate numerical modeling and inverse estimation techniques, we have demonstrated the feasibility of estimating the cortical potentials from the scalp EEG with the implanted Silastic ECoG gird(s), in both computer simulations and in human experimentation. In an epilepsy patient undergoing surgical evaluation, the cortical potentials were reconstructed from the simultaneously recorded scalp EEG, in which main features of spatial patterns during interictal spike were preserved and over 0.75 correlation coefficient value was obtained between the recorded and estimated cortical potentials. The FEM-based CPI technique provides a means of connecting the simultaneous recorded ECoG and the scalp EEG and promises to become an effective tool to evaluate and validate CPI techniques using clinic data.

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.

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.

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.

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 method to standardize a reference of scalp EEG recordings to a point at infinity

The effect of an active reference in EEG recording is one of the oldest technical problems in EEG practice. In this paper, a method is proposed to approximately standardize the reference of scalp EEG recordings to a point at infinity. This method is based on the fact that the use of scalp potentials to determine the neural electrical activities or their equivalent sources does not depend on the reference, so we may approximately reconstruct the equivalent sources from scalp EEG recordings with a scalp point or average reference. Then the potentials referenced at infinity are approximately reconstructed from the equivalent sources. As a point at infinity is far from all the possible neural sources, this method may be considered as a reference electrode standardization technique (REST). The simulation studies performed with assumed neural sources included effects of electrode number, volume conductor model and noise on the performance of REST, and the significance of REST in EEG temporal analysis. The results showed that REST is potentially very effective for the most important superficial cortical region and the standardization could be especially important in recovering the temporal information of EEG recordings.

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.

High-resolution EEG mappings: a spherical harmonic spectra theory and simulation results

Shown first is the equivalence between the multiple expansion (ME) of the brain electrical generator and the spherical harmonic spectra (SHS) of the potential generated by the electrical generator in an infinite volume conductor. Based on the equivalence, the SHS and the spatial filters which connect the SHS with the ME are deduced, in a concentric 3 sphere conductor and for the 5 EEG source mappings. They are cortical potential mapping (CPM), scalp Laplacian mapping (LM), pseudo-cortical potential mapping (PCPM), equivalent dipole layer mapping (EDM) and equivalent charge layer mapping (ECM). The theoretical simulation study of the spatial filters and mappings indicate that all 5 mappings provide higher resolution imaging maps of brain electrical activity than the scalp potential map. In the inverse problem, a spherical spline fit algorithm is provided to reconstruct the SHS of the scalp recording potential, and then the SHS and maps of the 5 mappings are reconstructed by utilizing the spatial filters and the SHS of the scalp potential. The results indicate that the correlativity order between a reconstructed map and the actual cortical potential map is CPM > or = EDM > PCPM > LM > ECM. An empirical VEP data study shows that any one of the 5 mappings also provides higher spatial resolution than the scalp potential map.

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

Cortical potentials are estimated from scalp potentials using a realistically shaped inhomogeneous head model, by means of the boundary element method (BEM). A new adaptive algorithm has been developed to achieve high accuracy to link directly the cortical potentials to the scalp potentials in a realistically shaped inhomogeneous head model including the thin low-conductivity skull layer. Computer simulations using a concentric three-spheres head model have tested this approach. The present study demonstrates that the cortical potentials can be directly estimated from the scalp potentials using the BEM in a realistically shaped inhomogeneous head model.