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

On the concordance between electrical source imaging, anatomical and functional neuroimaging in patients with focal epilepsy

OBJECTIVE

Limited knowledge exists regarding how electrical source imaging (ESI) of interictal epileptiform discharges (IEDs) aligns with findings from other neuroimaging modalities. This study investigates the relationships of interictal ESI with MRI, 18FDG PET, SISCOM, and voxel-based morphometry (VBM) during presurgical evaluation of drug-resistant epilepsy (DRE).

METHODS

A cross-sectional study evaluated the concordance of IED locations from ESI using various inverse solutions (CLARA, LAURA, LORETA, SLORETA, SWLORETA, SSLOFO) with MRI lesions, 18FDG PET, SISCOM, and VBM grey matter abnormalities. The role of ESI in presurgical evaluation of DRE was assessed.

RESULTS

Significant relationships were identified between the localization and distribution of IEDs identified by ESI and the various sets of neuroimages. SLORETA and SWLORETA exhibited the highest concordance and interlobar associations with MRI, 18FDG PET and SISCOM. The main cluster of IEDs proved helpful in locating the epileptogenic zone (EZ).

CONCLUSIONS

The distribution of IEDs identified by the ESI technique exhibited a high degree of significant relationships with other neuroimaging sources. Its use may prove valuable in defining the epileptogenic zone.

SIGNIFICANCE

Combining ESI of IEDs with other neuroimaging techniques may be useful in the presurgical evaluation of DRE.

Forearm muscle activity estimation based on anatomical structure of muscles

Estimation of muscle activity using surface electromyography (sEMG) is an important non-invasive method that can lead to a deeper understanding of motor-control strategies in humans. Measurement using multiple active electrodes is necessary to estimate not only surface muscle activity but also deep muscle activity in dynamic motion. In this paper, we propose a method for estimating muscle activity of dynamic motions based on anatomical knowledge of muscle structures. To estimate muscle activity, a large number of signal sources are set in the muscle model, and connections between the signal sources are defined a priori based on the anatomical structure of the muscles. The signal source activities are first estimated by minimizing the Kullback-Leibler divergence with a continuity cost. Then, the muscle activity is computed from the signal source activity. In the experiments, five healthy participants performed five types of motion and the forearm sEMG was measured with 20-channel active electrodes. The estimation results for these motions were visualized in four dimensions as the three-dimensional position of the muscle over time. The results showed that the estimation was accurate, with a reproduction rate of 95% for the measured sEMG and continuity of the muscle activity. In addition, the results suggest the advantage of the proposed method over the conventional approaches in terms of estimating the muscle activity for both dynamic and abnormal motions.

Function Based Brain Modeling and Simulation of an Ischemic Region in Post-Stroke Patients using the Bidomain

BACKGROUND

Several studies have shown that post-stroke patients develop divergent activity in the sensorimotor areas of the affected hemisphere of the brain compared to healthy people during motor tasks. Proper mathematical models will help us understand this activity and clarify the associated underlying mechanisms. New Method. This research describes an anatomically based brain computer model in post-stroke patients. We simulate an ischemic region for arm motion using the bidomain approach. Two scenarios are considered: a healthy subject and a post-stroke patient with motion impairment. Next, we limit the volume of propagation considering only the sensorimotor area of the brain. Comparison with existing methods. In comparison to existing methods, we combine the use of the bidomain for modeling the propagation of the electrical activity across the brain volume with functional information to limit the volume of propagation and the position of the expected stimuli, given a specific task. Whereas just using the bidomain without limiting the functional volume, propagates the electrical activity into non-expected areas.

RESULTS

To validate the simulation, we compare the activity with patient measurements using functional near-infrared spectroscopy during arm motion (n=5) against controls (n=3). The results are consistent with empirical measurements and previous research and show that there is a disparity between position and number of spikes in post-stroke patients in contrast to healthy subjects.

CONCLUSIONS

These results hold promise in improving the understanding of brain deterioration in stroke patients and the re-arrangement of brain networks. Furthermore, shows the use of functionality based brain modeling.

Non-invasive Seizure Localization with Ictal Single-Photon Emission Computed Tomography is Impacted by Preictal/Early Ictal Network Dynamics

OBJECTIVE

More than one third of children with epilepsy have medically intractable seizures. Promising therapies, including targeted neurostimulation and surgery, depend on accurate localization of the epileptogenic zone. Ictal perfusion Single-Photon Emission Computed Tomography (SPECT) can localize the seizure focus noninvasively, with comparable accuracy to that of invasive EEG. However, multiple factors including seizure dynamics may affect its spatial specificity.

METHODS

Using subtracted ictal from interictal SPECT and scalp EEG from 118 pediatric epilepsy patients (40 of whom had surgery after the SPECT studies), information theoretic measures of association and advanced statistical models, this study investigated the impact of preictal and ictal brain network dynamics on SPECT focality.

RESULTS

Network dynamics significantly impacted the SPECT localization ~30 s before to ~45 s following ictal onset. Distributed early ictal connectivity changes, indicative of a rapidly evolving seizure, were negatively associated with SPECT focality. Spatially localized connectivity changes later in the seizure, indicating slower seizure propagation, were positively associated with SPECT focality. In the first ~60 s of the seizure, significantly higher network connectivity was estimated in an area overlapping with the area of hyperperfusion. Finally, ~75% of patients with Engel class 1a/1b outcomes had SPECTs that were concordant with the resected area.

CONCLUSION

Slowly evolving seizures are more likely to be accurately imaged with SPECT, and the identified focus may overlap with brain regions where significant topological changes occur.

SIGNIFICANCE

Measures of preictal/early ictal network dynamics may help optimize the SPECT localization, leading to improved surgical and neurostimulation outcomes in refractory epilepsy.

Imaging brain source extent from EEG/MEG by means of an iteratively reweighted edge sparsity minimization (IRES) strategy

Estimating extended brain sources using EEG/MEG source imaging techniques is challenging. EEG and MEG have excellent temporal resolution at millisecond scale but their spatial resolution is limited due to the volume conduction effect. We have exploited sparse signal processing techniques in this study to impose sparsity on the underlying source and its transformation in other domains (mathematical domains, like spatial gradient). Using an iterative reweighting strategy to penalize locations that are less likely to contain any source, it is shown that the proposed iteratively reweighted edge sparsity minimization (IRES) strategy can provide reasonable information regarding the location and extent of the underlying sources. This approach is unique in the sense that it estimates extended sources without the need of subjectively thresholding the solution. The performance of IRES was evaluated in a series of computer simulations. Different parameters such as source location and signal-to-noise ratio were varied and the estimated results were compared to the targets using metrics such as localization error (LE), area under curve (AUC) and overlap between the estimated and simulated sources. It is shown that IRES provides extended solutions which not only localize the source but also provide estimation for the source extent. The performance of IRES was further tested in epileptic patients undergoing intracranial EEG (iEEG) recording for pre-surgical evaluation. IRES was applied to scalp EEGs during interictal spikes, and results were compared with iEEG and surgical resection outcome in the patients. The pilot clinical study results are promising and demonstrate a good concordance between noninvasive IRES source estimation with iEEG and surgical resection outcomes in the same patients. The proposed algorithm, i.e. IRES, estimates extended source solutions from scalp electromagnetic signals which provide relatively accurate information about the location and extent of the underlying source.

3-dimensional brain source imaging by means of laplacian weighted minimum norm estimate in a realistic geometry head model

We investigated the source localization performance of the Laplacian weighted minimum norm (LWMN) estimate technique in a realistic geometry (RG) head model in the present study. We simulated current sources at different brain regions with various noise levels. The present results show there is no obvious depth dependency on the three-dimensional (3D) source estimation. The average source localization error over all simulated cases is about 10 mm. The tangential sources exhibit larger localization errors than the radial sources when they are close to the epicortical surface. The localization error will increase when the noise level increases. The LWMN technique was applied to source imaging of motor potentials induced by finger movement in a human subject. Both activities in the motor and premotor cortex, which are related to the execution and coordinating of the finger movement, were reconstructed by the LWMN technique. The present study suggests that LWMN has great ability in 3D sources 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.

Sparse source imaging in electroencephalography with accurate field modeling

We have developed a new L1-norm based generalized minimum norm estimate (GMNE) and have fully characterized the concept of sparseness regularization inherited in the proposed algorithm, which is termed as sparse source imaging (SSI). The new SSI algorithm corrects inaccurate source field modeling in previously reported L1-norm GMNEs and proposes that sparseness a priori should only be applied to the regularization term, not to the data term in the formulation of the regularized inverse problem. A new solver to the newly developed SSI has been adopted and known as the second-order cone programming. The new SSI is assessed by a series of simulations and then evaluated using somatosensory evoked potential (SEP) data with both scalp and subdural recordings in a human subject. The performance of SSI is compared with other L1-norm GMNEs and L2-norm GMNEs using three evaluation metrics, i.e., localization error, orientation error, and strength percentage. The present simulation results indicate that the new SSI has significantly improved performance in all evaluation metrics, especially in the metric of orientation error. L2-norm GMNEs show large orientation errors because of the smooth regularization. The previously reported L1-norm GMNEs show large orientation errors due to the inaccurate source field modeling. The SEP source imaging results indicate that SSI has the best accuracy in the prediction of subdural potential field as validated by direct subdural recordings. The new SSI algorithm is also applicable to MEG source imaging.

A novel sparse source imaging in reconstructing extended cortical current sources

We have developed a new sparse source imaging (SSI) method with the use of the L1-norm in EEG inverse problems to reconstruct extended cortical current sources. The new SSI method explores the sparseness in cortical current density variation maps (the transform domain) other than in the cortical current density maps (the original domain) from previously reported SSI methods. The new SSI is assessed by a series of computer simulations. The performance of SSI is compared with the well-known L2-norm MNE using the AUC metric. Our present simulation data indicate that the new SSI has significantly improved performance in reconstructing extended cortical current sources and estimating their cortical extents. The L2-norm MNE shows relatively poor performance in the same source imaging tasks. The new SSI method is also applicable to MEG source imaging.

L1-norm and L2-norm neuroimaging methods in reconstructing extended cortical sources from EEG

We have previously reported a new sparse neuroimaging method (i.e. VB-SCCD) using the L1-norm optimization technology to solve EEG inverse problems. The new method distinguishes itself from other reported L1-norm methods since it explores the sparseness in a transform domain rather than in the original source domain. In the present study, we conducted a Monte Carlo simulation study to compare the performance of VB-SCCD and other two popular L2-norm neuroimaging methods (i.e. wMNE and cLORETA) in reconstructing extended cortical neural electrical activations. Our simulation data suggests that the VB-SCCD method is able to reconstruct extended cortical sources with the overall high accuracy. It has significantly higher accuracy, less number of false alarms and less number of missing sources when studying complex brain activations (up to 5 simultaneous sources). This new sparse neuroimaging method is thus promising to have many valuable applications in neuroscience and neurology problems. It is also applicable to MEG neuroimaging.

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.

Noninvasive imaging of bioimpedance distribution by means of current reconstruction magnetic resonance electrical impedance tomography

We have developed a novel magnetic resonance electrical impedance tomography (MREIT) algorithm-current reconstruction MREIT algorithm-for noninvasive imaging of electrical impedance distribution of a biological system using only one component of magnetic flux density. The newly proposed algorithm uses the inverse of Biot-Savart Law to reconstruct the current density distribution, and then, uses a modified J-substitution algorithm to reconstruct the conductivity image. A series of computer simulations has been conducted to evaluate the performance of the proposed current reconstruction MREIT algorithm with simulation settings for breast cancer imaging applications, with consideration of measurement noise, current injection strength, size of simulated tumors, spatial resolution, and position dependency. The present simulation results are highly promising, demonstrating the high spatial resolution, high accuracy in conductivity reconstruction, and robustness against noise of the proposed algorithm for imaging electrical impedance of a biological system. The present MREIT method may have potential applications to breast cancer imaging and imaging of other organs.

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.

Lp norm iterative sparse solution for EEG source Localization

How to localize the neural electric activities effectively and precisely from the scalp EEG recordings is a critical issue for clinical neurology and cognitive neuroscience. In this paper, based on the spatial sparse assumption of brain activities, proposed is a novel iterative EEG source imaging algorithm, Lp norm iterative sparse solution (LPISS). In LPISS, the lp (p < or =1) norm constraint for sparse solution is integrated into the iterative weighted minimum norm solution of the underdetermined EEG inverse problem, and it is the constraint and the iteratively renewed weight that forces the inverse problem to converge to a sparse solution effectively. The conducted simulation studies with comparison to LORETA and FOCUSS for various dipoles configurations confirmed the validation of LPISS for sparse EEG source localization. Finally, LPISS was applied to a real evoked potential collected in a study of inhibition of return (IOR), and the result was consistent with the previously suggested activated areas involved in an IOR process.

Review on solving the forward problem in EEG source analysis

Background

The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.

Methods

While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.

Results

It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.

Conclusion

Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

EEG source imaging: correlating source locations and extents with electrocorticography and surgical resections in epilepsy patients

SUMMARY

It is desirable to estimate epileptogenic zones with both location and extent information from noninvasive EEG. In the present study, the authors use a subspace source localization method (FINE), combined with a local thresholding technique, to achieve such tasks. The performance of this method was evaluated in interictal spikes from three pediatric patients with medically intractable partial epilepsy. The thresholded subspace correlation, which is obtained from FINE scanning, is a favorable marker, which implies the extents of current sources associated with epileptic activities. The findings were validated by comparing the results with invasive electrocorticographic (ECoG) recordings of interictal spike activity. The surgical resections in these three patients correlated well with the epileptogenic zones identified from both EEG sources and ECoG potential distributions. The value of the proposed noninvasive technique for estimating epileptiform activity was supported by satisfactory surgery outcomes.

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.

Ictal source analysis: localization and imaging of causal interactions in humans

We propose a new integrative approach to characterize the structure of seizures in the space, time, and frequency domains. Such characterization leads to a new technical development of ictal source analysis for the presurgical evaluation of epilepsy patients. The present new ictal source analysis method consists of three parts. First, a three-dimensional source scanning procedure is performed by a spatio-temporal FINE source localization method to locate the multiple sources responsible for the time evolving ictal rhythms at their onsets. Next, the dynamic behavior of the sources is modeled by a multivariate autoregressive process (MVAR). Lastly, the causal interaction patterns among the sources as a function of frequency are estimated from the MVAR modeling of the source temporal dynamics. The causal interaction patterns indicate the dynamic communications between sources, which are useful in distinguishing the primary sources responsible for the ictal onset from the secondary sources caused by the ictal propagation. The present ictal analysis strategy has been applied to a number of seizures from five epilepsy patients, and their results are consistent with observations from either MRI lesions or SPECT scans, which indicate its effectiveness. Each step of the ictal source analysis is statistically evaluated in order to guarantee the confidence in the results.

Evaluation of cortical current density imaging methods using intracranial electrocorticograms and functional MRI

OBJECTIVE

EEG source imaging provides important information regarding the underlying neural activity from noninvasive electrophysiological measurements. The aim of the present study was to evaluate source reconstruction techniques by means of the intracranial electrocorticograms (ECoGs) and functional MRI.

METHODS

Five source imaging algorithms, including the minimum norm least square (MNLS), LORETA with L(p)-norm (p equal to 1, 1.5 and 2), sLORETA, the minimum L(p)-norm (p equal to 1 and 1.5; when p=2, the MNLS method is mathematically equivalent to the minimum L(p)-norm) and L(1)-norm (the linear programming) methods, were evaluated in a group of 10 human subjects, in a paradigm with somatosensory stimulation. Cortical current density (CCD) distributions were estimated from the scalp somatosensory evoked potentials (SEPs), at approximately 30 ms following electrical stimulation of median nerve at the wrist. Realistic geometry boundary element head models were constructed from the MRIs of each subject and used in the CCD analysis. Functional MRI results obtained from a motor task and sensory stimulation in all subjects were used to identify the central sulcus, motor and sensory areas. In three patients undergoing neurosurgical evaluation, ECoGs were recorded in response to the somatosensory stimulation, and were used to help determine the central sulcus and the sensory cortex.

RESULTS

The CCD distributions estimated by the L(p)-norm and LORETA-L(p) methods were smoother when the p values were high. The LORETA based on the L(1)-norm performed better than the LORETA-L(2) method for imaging well localized sources such as the P30 component of the SEP. The mean and standard deviation of the distance between the location of maximum CCD value and the central sulcus, estimated by the minimum L(p)-norm (with p equal to 1), L(1)-norm (the Linear programming) and LORETA-L(p) (with p equal to 1) methods, were 4, 7, 7 mm and 3, 4, 2 mm, respectively (after converting into Talairach coordinates). The mean and standard deviation of the aforementioned distance, estimated by the MNLS, LORETA with L(p)-norm (p equal to 1.5 and 2.0), sLORETA and the minimum L(p)-norm (p equal to 1.5) methods, were over 11 mm and 6 mm, respectively.

CONCLUSIONS

The present experimental study suggests that L(1)-norm-based algorithms provide better performance than L(2) and L(1.5)-norm-based algorithms, in the context of CCD imaging of well localized sources induced by somatosensory electrical stimulation of median nerve at the wrist.

Spatial resolution of EEG cortical source imaging revealed by localization of retinotopic organization in human primary visual cortex

The aim of the present study is to investigate the spatial resolution of electroencephalography (EEG) cortical source imaging by localizing the retinotopic organization in the human primary visual cortex (V1). Retinotopic characteristics in V1 obtained from functional magnetic resonance imaging (fMRI) study were used as reference to assess the spatial resolution of EEG since fMRI can discriminate small changes in activation in visual field. It is well known that the activation of the early C1 component in the visual evoked potential (VEP) elicited by pattern onset stimuli coincides well with the activation in the striate cortex localized by fMRI. In the present experiments, we moved small circular checkerboard stimuli along horizontal meridian and compared the activations localized by EEG cortical source imaging with those from fMRI. Both fMRI and EEG cortical source imaging identified spatially correlated activity within V1 in each subject studied. The mean location error, between the fMRI-determined activation centers in V1 and the EEG source imaging activation peak estimated at equivalent C1 components (peak latency: 74.8+/-10.6 ms), was 7 mm (25% and 75% percentiles are 6.45 mm and 8.4 mm, respectively), which is less than the change in fMRI activation map by a 3 degrees visual field change (7.8 mm). Moreover, the source estimates at the earliest major VEP component showed statistically good correlation with those obtained by fMRI. The present results suggest that the spatial resolution of the EEG cortical source imaging can correctly discriminate cortical activation changes in V1 corresponding to less than 3 degrees visual field changes.

Spatio-temporal EEG source localization using a three-dimensional subspace FINE approach in a realistic geometry inhomogeneous head model

The subspace source localization approach, i.e., first principle vectors (FINE), is able to enhance the spatial resolvability and localization accuracy for closely-spaced neural sources from EEG and MEG measurements. Computer simulations were conducted to evaluate the performance of the FINE algorithm in an inhomogeneous realistic geometry head model under a variety of conditions. The source localization abilities of FINE were examined at different cortical regions and at different depths. The present computer simulation results indicate that FINE has enhanced source localization capability, as compared with MUSIC and RAP-MUSIC, when sources are closely spaced, highly noise-contaminated, or inter-correlated. The source localization accuracy of FINE is better, for closely-spaced sources, than MUSIC at various noise levels, i.e., signal-to-noise ratio (SNR) from 6 dB to 16 dB, and RAP-MUSIC at relatively low noise levels, i.e., 6 dB to 12 dB. The FINE approach has been further applied to localize brain sources of motor potentials, obtained during the finger tapping tasks in a human subject. The experimental results suggest that the detailed neural activity distribution could be revealed by FINE. The present study suggests that FINE provides enhanced performance in localizing multiple closely spaced, and inter-correlated sources under low SNR, and may become an important alternative to brain source localization from EEG or MEG.

Estimation of number of independent brain electric sources from the scalp EEGs

In electromagnetic source analysis, many source localization strategies require the number of sources as an input parameter (e.g., spatio-temporal dipole fitting and the multiple signal classification). In the present study, an information criterion method, in which the penalty functions are selected based on the spatio-temporal source model, has been developed to estimate the number of independent dipole sources from electromagnetic measurements such as the electroencephalogram (EEG). Computer simulations were conducted to evaluate the effects of various parameters on the estimation of the source number. A three-concentric-spheres head model was used to approximate the head volume conductor. Three kinds of typical signal sources, i.e., the damped sinusoid sources, sinusoid sources with one frequency band and sinusoid sources with two separated frequency bands, were used to simulate the oscillation characteristics of brain electric sources. The simulation results suggest that the present method can provide a good estimate of the number of independent dipole sources from the EEG measurements. In addition, the present simulation results suggest that choosing the optimal penalty function can successfully reduce the effect of noise on the estimation of number of independent sources. The present study suggests that the information criterion method may provide a useful means in estimating the number of independent brain electrical sources from EEG/MEG measurements.

3D source localization of interictal spikes in epilepsy patients with MRI lesions

The present study aims to accurately localize epileptogenic regions which are responsible for epileptic activities in epilepsy patients by means of a new subspace source localization approach, i.e. first principle vectors (FINE), using scalp EEG recordings. Computer simulations were first performed to assess source localization accuracy of FINE in the clinical electrode set-up. The source localization results from FINE were compared with the results from a classic subspace source localization approach, i.e. MUSIC, and their differences were tested statistically using the paired t-test. Other factors influencing the source localization accuracy were assessed statistically by ANOVA. The interictal epileptiform spike data from three adult epilepsy patients with medically intractable partial epilepsy and well-defined symptomatic MRI lesions were then studied using both FINE and MUSIC. The comparison between the electrical sources estimated by the subspace source localization approaches and MRI lesions was made through the coregistration between the EEG recordings and MRI scans. The accuracy of estimations made by FINE and MUSIC was also evaluated and compared by R(2) statistic, which was used to indicate the goodness-of-fit of the estimated sources to the scalp EEG recordings. The three-concentric-spheres head volume conductor model was built for each patient with three spheres of different radii which takes the individual head size and skull thickness into consideration. The results from computer simulations indicate that the improvement of source spatial resolvability and localization accuracy of FINE as compared with MUSIC is significant when simulated sources are closely spaced, deep, or signal-to-noise ratio is low in a clinical electrode set-up. The interictal electrical generators estimated by FINE and MUSIC are in concordance with the patients' structural abnormality, i.e. MRI lesions, in all three patients. The higher R(2) values achieved by FINE than MUSIC indicate that FINE provides a more satisfactory fitting of the scalp potential measurements than MUSIC in all patients. The present results suggest that FINE provides a useful brain source imaging technique, from clinical EEG recordings, for identifying and localizing epileptogenic regions in epilepsy patients with focal partial seizures. The present study may lead to the establishment of a high-resolution source localization technique from scalp-recorded EEGs for aiding presurgical planning in epilepsy patients.

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.

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.

Evaluation of different cortical source localization methods using simulated and experimental EEG data

Different cortical source localization methods have been developed to directly link the scalp potentials with the cortical activities. Up to now, these methods are the only possible solution to noninvasively investigate cortical activities with both high spatial and time resolutions. However, the application of these methods is hindered by the fact that they have not been rigorously evaluated nor compared. In this paper, the performances of several source localization methods (moving dipoles, minimum Lp norm, and low resolution tomography (LRT) with Lp norm, p equal to 1, 1.5, and 2) were evaluated by using simulated scalp EEG data, scalp somatosensory evoked potentials (SEPs), and upper limb motor-related potentials (MRPs) obtained on human subjects (all with 163 scalp electrodes). By using simulated EEG data, we first evaluated the source localization ability of the above methods quantitatively. Subsequently, the performance of the various methods was evaluated qualitatively by using experimental SEPs and MRPs. Our results show that the overall LRT Lp norm method with p equal to 1 has a better source localization ability than any of the other investigated methods and provides physiologically meaningful reconstruction results. Our evaluation results provide useful information for choosing cortical source localization approaches for future EEG/MEG studies.

Electrical localization of neural activity in the dorsal horn of the spinal cord: a modeling study

Intraspinal microstimulation is a means of eliciting coordinated motor responses for restoration of function. However, detailed maps of the neuroanatomy of the human spinal cord are lacking, and it is not clear where electrodes should be implanted. We developed an electrical approach to localize active neurons in the spinal cord using potentials recorded from the surface of the spinal cord. We evaluated this localization method using an analytical model of the spinal cord and two previously developed inverse algorithms (standardized low resolution brain electromagnetic tomography (sLORETA) and a locally optimal source (LOS) method). The results support electrical source localization as a feasible imaging approach for localizing (within 300 microm) active neurons in the spinal cord. The LOS method could localize the source when 16 recording electrodes were placed on the dorsolateral aspect of the cord and the noise level was 2%. When recording electrodes were positioned around the entire circumference of the spinal cord, either localization method could localize the source, even at 15% noise. Finally, localization error was not sensitive to inaccuracies in the expected electrode positions or the electrical parameters of the forward model, but was sensitive to a geometrical modification of the forward model in one case.

EEG source imaging

OBJECTIVE

Electroencephalography (EEG) is an important tool for studying the temporal dynamics of the human brain's large-scale neuronal circuits. However, most EEG applications fail to capitalize on all of the data's available information, particularly that concerning the location of active sources in the brain. Localizing the sources of a given scalp measurement is only achieved by solving the so-called inverse problem. By introducing reasonable a priori constraints, the inverse problem can be solved and the most probable sources in the brain at every moment in time can be accurately localized.

METHODS AND RESULTS

Here, we review the different EEG source localization procedures applied during the last two decades. Additionally, we detail the importance of those procedures preceding and following source estimation that are intimately linked to a successful, reliable result. We discuss (1) the number and positioning of electrodes, (2) the varieties of inverse solution models and algorithms, (3) the integration of EEG source estimations with MRI data, (4) the integration of time and frequency in source imaging, and (5) the statistical analysis of inverse solution results.

CONCLUSIONS AND SIGNIFICANCE

We show that modern EEG source imaging simultaneously details the temporal and spatial dimensions of brain activity, making it an important and affordable tool to study the properties of cerebral, neural networks in cognitive and clinical neurosciences.

The magnetic field inside special conducting geometries due to internal current

In view of recent attempts to directly and noninvasively detect the neuromagnetic field, we derive an analytic formula for the magnetic field inside a homogeneous conducting sphere due to a point current dipole. It has a similar structure to a well-known formula for the field outside any spherically symmetric conductivity profile. For a radial dipole, the field on the inside has a very simple expression. A symmetry argument is given as to why the field of a radial dipole vanishes outside a spherical conductor. Illustrative plots of the magnetic field are presented for a radial and a tangential dipole; the slope of the tangential component of the magnetic field is discontinuous at the surface of the sphere. A spherical conductor having three concentric regions is discussed; and we also derive an analytic formula for the magnetic field inside a homogeneous infinite half space.

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.

High-resolution EEG mapping: an equivalent charge-layer approach

Brain electrical signal is one of the windows to understanding neural activities. Various high-resolution imaging techniques have been developed to reveal the electrical activities underneath the cortical surface from scalp electroencephalographic recordings, such as scalp Laplacian, cortical surface potential, equivalent charge layer (ECL) and equivalent dipole layer (EDL). In this work, we develop forward density formulae for the ECL and the EDL of neural electric sources in a 4-concentric-sphere head model, and compare ECL with EDL in theory, simulation and real evoked data tests. The results confirm that the ECL map may be of higher spatial resolution than the EDL map.

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.