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

Electroencephalographic Source Reconstruction by the Finite-Element Approximation of the Elliptic Cauchy Problem

OBJECTIVE

This paper develops a novel approach for fast and reliable reconstruction of EEG sources in MRI-based head models.

METHODS

The inverse EEG problem is reduced to the Cauchy problem for an elliptic partial-derivative equation. The problem is transformed into a regularized minimax problem, which is directly approximated in a finite-element space. The resulting numerical method is efficient and easy to program. It eliminates the need to solve forward problems, which can be a tedious task. The method applies to complex anatomical head models, possibly containing holes in surfaces, anisotropic conductivity, and conductivity variations inside each tissue. The method has been verified on a spherical shell model and an MRI-based head.

RESULTS

Numerical experiments indicate high accuracy of localization of brain activations (both cortical potential and current) and rapid execution time.

CONCLUSION

This study demonstrates that the proposed approach is feasible for EEG source analysis and can serve as a rapid and reliable tool for EEG source analysis.

SIGNIFICANCE

The significance of this study is that it develops a fast, accurate, and simple numerical method of EEG source analysis, applicable to almost arbitrary complex head models.

Power Dissipation and Surface Charge in EEG: Application to Eigenvalue Structure of Integral Operators

OBJECTIVE

To demonstrate the role of surface charge and power dissipation in the analysis of EEG measurements.

METHODS

The forward EEG problem is formulated in terms of surface charge density. Using bounds based on power dissipation, the integral equations for forward solutions are shown to satisfy bounds on their eigenvalue structure.

RESULTS

We show that two physical variables, dissipated power and the accumulated charge at interfaces, can be used in formulating the forward problem. We derive the boundary integral equations satisfied by the charge and show their connection to the integral equations for the potential that are known from other approaches. We show how the dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in EEG boundary element methods. Using the eigenvalue structure, we propose a new method for the solution of the forward problem, where the integral kernels are regularized by the exclusion of eigenvectors associated to a finite range of eigenvalues. We demonstrate the method on a head model with realistic shape.

CONCLUSION

The eigenvalue analysis of the EEG forward problem is given a clear interpretation in terms of power dissipation and surface charge density.

SIGNIFICANCE

The use of these variables enhances our understanding of the structure of EEG, makes connection with other techniques and contributes to the development of new analysis algorithms.

Sparse EEG Source Localization Using LAPPS: Least Absolute l-P (0 < p < 1) Penalized Solution

OBJECTIVE

The electroencephalographic (EEG) inverse problem is ill-posed owing to the electromagnetism Helmholtz theorem and since there are fewer observations than the unknown variables. Apart from the strong background activities (ongoing EEG), evoked EEG is also inevitably contaminated by strong outliers caused by head movements or ocular movements during recordings.

METHODS

Considering the sparse activations during high cognitive processing, we propose a novel robust EEG source imaging algorithm, LAPPS (Least Absolute -P (0 < p < 1) Penalized Solution), which employs the -loss for the residual error to alleviate the effect of outliers and another -penalty norm (p=0.5) to obtain sparse sources while suppressing Gaussian noise in EEG recordings. The resulting optimization problem is solved using a modified ADMM algorithm.

RESULTS

Simulation study was performed to recover sparse signals of randomly selected sources using LAPPS and various methods commonly used for EEG source imaging including WMNE, -norm, sLORETA and FOCUSS solution. The simulation comparison quantitatively demonstrates that LAPPS obtained the best performances in all the conducted simulations for various dipoles configurations under various SNRs on a realistic head model. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS obtained sparse activations consistent with previous findings revealed by EEG and fMRI.

CONCLUSION

This study demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators.

SIGNIFICANCE

This method alleviates the effect of noise and recovers sparse sources while maintaining a low computational complexity due to the cheap matrix-vector multiplication.

Long-term impacts of prenatal synthetic glucocorticoids exposure on functional brain correlates of cognitive monitoring in adolescence

The fetus is highly responsive to the level of glucocorticoids in the gestational environment. Perturbing glucocorticoids during fetal development could yield long-term consequences. Extending prior research about effects of prenatally exposed synthetic glucocorticoids (sGC) on brain structural development during childhood, we investigated functional brain correlates of cognitive conflict monitoring in term-born adolescents, who were prenatally exposed to sGC. Relative to the comparison group, behavioral response consistency (indexed by lower reaction time variability) and a brain correlate of conflict monitoring (the N2 event-related potential) were reduced in the sGC exposed group. Relatedly, source localization analyses showed that activations in the fronto-parietal network, most notably in the cingulate cortex and precuneus, were also attenuated in these adolescents. These regions are known to subserve conflict detection and response inhibition as well as top-down regulation of stress responses. Moreover, source activation in the anterior cingulate cortex correlated negatively with reaction time variability, whereas activation in the precuneus correlated positively with salivary cortisol reactivity to social stress in the sGC exposed group. Taken together, findings of this study indicate that prenatal exposure to sGC yields lasting impacts on the development of fronto-parietal brain functions during adolescence, affecting multiple facets of adaptive cognitive and behavioral control.

Back-Projection Cortical Potential Imaging: Theory and Results

Electroencephalography (EEG) is the single brain monitoring technique that is non-invasive, portable, passive, exhibits high-temporal resolution, and gives a directmeasurement of the scalp electrical potential. Amajor disadvantage of the EEG is its low-spatial resolution, which is the result of the low-conductive skull that "smears" the currents coming from within the brain. Recording brain activity with both high temporal and spatial resolution is crucial for the localization of confined brain activations and the study of brainmechanismfunctionality, whichis then followed by diagnosis of brain-related diseases. In this paper, a new cortical potential imaging (CPI) method is presented. The new method gives an estimation of the electrical activity on the cortex surface and thus removes the "smearing effect" caused by the skull. The scalp potentials are back-projected CPI (BP-CPI) onto the cortex surface by building a well-posed problem to the Laplace equation that is solved by means of the finite elements method on a realistic head model. A unique solution to the CPI problem is obtained by introducing a cortical normal current estimation technique. The technique is based on the same mechanism used in the well-known surface Laplacian calculation, followed by a scalp-cortex back-projection routine. The BP-CPI passed four stages of validation, including validation on spherical and realistic head models, probabilistic analysis (Monte Carlo simulation), and noise sensitivity tests. In addition, the BP-CPI was compared with the minimum norm estimate CPI approach and found superior for multi-source cortical potential distributions with very good estimation results (CC >0.97) on a realistic head model in the regions of interest, for two representative cases. The BP-CPI can be easily incorporated in different monitoring tools and help researchers by maintaining an accurate estimation for the cortical potential of ongoing or event-related potentials in order to have better neurological inferences from the EEG.

Math anxiety: Brain cortical network changes in anticipation of doing mathematics

Following our previous work regarding the involvement of math anxiety (MA) in math-oriented tasks, this study tries to explore the differences in the cerebral networks' topology between self-reported low math-anxious (LMA) and high math-anxious (HMA) individuals, during the anticipation phase prior to a mathematical related experiment. For this reason, multichannel EEG recordings were adopted, while the solution of the inverse problem was applied in a generic head model, in order to obtain the cortical signals. The cortical networks have been computed for each band separately, using the magnitude square coherence metric. The main graph theoretical parameters, showed differences in segregation and integration in almost all EEG bands of the HMAs in comparison to LMAs, indicative of a great influence of the anticipatory anxiety prior to mathematical performance.

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.

Resting-state test-retest reliability of a priori defined canonical networks over different preprocessing steps

Resting-state functional connectivity analysis has become a widely used method for the investigation of human brain connectivity and pathology. The measurement of neuronal activity by functional MRI, however, is impeded by various nuisance signals that reduce the stability of functional connectivity. Several methods exist to address this predicament, but little consensus has yet been reached on the most appropriate approach. Given the crucial importance of reliability for the development of clinical applications, we here investigated the effect of various confound removal approaches on the test-retest reliability of functional-connectivity estimates in two previously defined functional brain networks. Our results showed that gray matter masking improved the reliability of connectivity estimates, whereas denoising based on principal components analysis reduced it. We additionally observed that refraining from using any correction for global signals provided the best test-retest reliability, but failed to reproduce anti-correlations between what have been previously described as antagonistic networks. This suggests that improved reliability can come at the expense of potentially poorer biological validity. Consistent with this, we observed that reliability was proportional to the retained variance, which presumably included structured noise, such as reliable nuisance signals (for instance, noise induced by cardiac processes). We conclude that compromises are necessary between maximizing test-retest reliability and removing variance that may be attributable to non-neuronal sources.

Beta-Band Functional Connectivity is Reorganized in Mild Cognitive Impairment after Combined Computerized Physical and Cognitive Training

Physical and cognitive idleness constitute significant risk factors for the clinical manifestation of age-related neurodegenerative diseases. In contrast, a physically and cognitively active lifestyle may restructure age-declined neuronal networks enhancing neuroplasticity. The present study, investigated the changes of brain's functional network in a group of elderly individuals at risk for dementia that were induced by a combined cognitive and physical intervention scheme. Fifty seniors meeting Petersen's criteria of Mild Cognitive Impairment were equally divided into an experimental (LLM), and an active control (AC) group. Resting state electroencephalogram (EEG) was measured before and after the intervention. Functional networks were estimated by computing the magnitude square coherence between the time series of all available cortical sources as computed by standardized low resolution brain electromagnetic tomography (sLORETA). A statistical model was used to form groups' characteristic weighted graphs. The introduced modulation was assessed by networks' density and nodes' strength. Results focused on the beta band (12-30 Hz) in which the difference of the two networks' density is maximum, indicating that the structure of the LLM cortical network changes significantly due to the intervention, in contrast to the network of AC. The node strength of LLM participants in the beta band presents a higher number of bilateral connections in the occipital, parietal, temporal and prefrontal regions after the intervention. Our results show that the combined training scheme reorganizes the beta-band functional connectivity of MCI patients. ClinicalTrials.gov Identifier: NCT02313935 https://clinicaltrials.gov/ct2/show/NCT02313935.

Correspondence of electroencephalography and near-infrared spectroscopy sensitivities to the cerebral cortex using a high-density layout

This study investigates the correspondence of the cortical sensitivity of electroencephalography (EEG) and near-infrared spectroscopy (NIRS). EEG forward model sensitivity to the cerebral cortex was calculated for 329 EEG electrodes following the 10-5 EEG positioning system using a segmented structural magnetic resonance imaging scan of a human subject. NIRS forward model sensitivity was calculated for the same subject using 156 NIRS source-detector pairs selected from 32 source and 32 detector optodes positioned on the scalp using a subset of the 10-5 EEG positioning system. Sensitivity correlations between colocalized NIRS source-detector pair groups and EEG channels yielded R = 0.46 ± 0.08. Groups of NIRS source-detector pairs with maximum correlations to EEG electrode sensitivities are tabulated. The mean correlation between the point spread functions for EEG and NIRS regions of interest (ROI) was R = 0.43 ± 0.07. Spherical ROIs with radii of 26 mm yielded the maximum correlation between EEG and NIRS averaged across all cortical mesh nodes. These sensitivity correlations between EEG and NIRS should be taken into account when designing multimodal studies of neurovascular coupling and when using NIRS as a statistical prior for EEG source localization.

Neuroelectrical correlates of trustworthiness and dominance judgments related to the observation of political candidates

The present research investigates the neurophysiological activity elicited by fast observations of faces of real candidates during simulated political elections. We used simultaneous recording of electroencephalographic (EEG) signals as well as galvanic skin response (GSR) and heart rate (HR) as measurements of central and autonomic nervous systems. Twenty healthy subjects were asked to give judgments on dominance, trustworthiness, and a preference of vote related to the politicians' faces. We used high-resolution EEG techniques to map statistical differences of power spectral density (PSD) cortical activity onto a realistic head model as well as partial directed coherence (PDC) and graph theory metrics to estimate the functional connectivity networks and investigate the role of cortical regions of interest (ROIs). Behavioral results revealed that judgment of dominance trait is the most predictive of the outcome of the simulated elections. Statistical comparisons related to PSD and PDC values highlighted an asymmetry in the activation of frontal cortical areas associated with the valence of the judged trait as well as to the probability to cast the vote. Overall, our results highlight the existence of cortical EEG features which are correlated with the prediction of vote and with the judgment of trustworthy and dominant faces.

Node accessibility in cortical networks during motor tasks

Recent findings suggest that the preparation and execution of voluntary self-paced movements are accompanied by the coordination of the oscillatory activities of distributed brain regions. Here, we use electroencephalographic source imaging methods to estimate the cortical movement-related oscillatory activity during finger extension movements. Then, we apply network theory to investigate changes (expressed as differences from the baseline) in the connectivity structure of cortical networks related to the preparation and execution of the movement. We compute the topological accessibility of different cortical areas, measuring how well an area can be reached by the rest of the network. Analysis of cortical networks reveals specific agglomerates of cortical sources that become less accessible during the preparation and the execution of the finger movements. The observed changes neither could be explained by other measures based on geodesics or on multiple paths, nor by power changes in the cortical oscillations.

Reconstructing spatially extended brain sources via enforcing multiple transform sparseness

Accurate estimation of location and extent of neuronal sources from EEG/MEG remain challenging. In the present study, a new source imaging method, i.e. variation and wavelet based sparse source imaging (VW-SSI), is proposed to better estimate cortical source locations and extents. VW-SSI utilizes the L1-norm regularization method with the enforcement of transform sparseness in both variation and wavelet domains. The performance of the proposed method is assessed by both simulated and experimental MEG data, obtained from a language task and a motor task. Compared to L2-norm regularizations, VW-SSI demonstrates significantly improved capability in reconstructing multiple extended cortical sources with less spatial blurredness and less localization error. With the use of transform sparseness, VW-SSI overcomes the over-focused problem in classic SSI methods. With the use of two transformations, VW-SSI further indicates significantly better performance in estimating MEG source locations and extents than other SSI methods with single transformations. The present experimental results indicate that VW-SSI can successfully estimate neural sources (and their spatial coverage) located in close areas while responsible for different functions, i.e. temporal cortical sources for auditory and language processing, and sources on the pre-bank and post-bank of the central sulcus. Meantime, all other methods investigated in the present study fail to recover these phenomena. Precise estimation of cortical source locations and extents from EEG/MEG is of significance for applications in neuroscience and neurology.

A Graph theoretical approach to study the organization of the cortical networks during different mathematical tasks

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it's local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network's weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha's network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.

Functional brain network organisation of children between 2 and 5 years derived from reconstructed activity of cortical sources of high-density EEG recordings

There is increasing interest in applying connectivity analysis to brain measures (Rubinov and Sporns, 2010), but most studies have relied on fMRI, which substantially limits the participant groups and numbers that can be studied. High-density EEG recordings offer a comparatively inexpensive easy-to-use alternative, but require channel-level connectivity analysis which currently lacks a common analytic framework and is very limited in spatial resolution. To address this problem, we have developed a new technique for studies of network development that overcomes the spatial constraint and obtains functional networks of cortical areas by using EEG source reconstruction with age-matched average MRI templates (He et al., 1999). In contrast to previously reported channel-level analysis, this approach provides information about the cortical areas most likely to be involved in the network as well as their functional relationship (Babiloni et al., 2005; De Vico Fallani et al., 2007). In this study, we applied source reconstruction with age-matched templates to task-free high-density EEG recordings in typically-developing children between 2 and 6 years of age (O'Reilly, 2012). Graph theory was then applied to the association strengths of 68 cortical regions of interest based on the Desikan-Killiany atlas. We found linear increases of mean node degree, mean clustering coefficient and maximum betweenness centrality between 2 years and 6 years of age. Characteristic path length was negatively correlated with age. The correlation of the network measures with age indicates network development towards more closely integrated networks similar to reports from other imaging modalities (Fair et al., 2008; Power et al., 2010). We also applied eigenvalue decomposition to obtain functional modules (Clayden et al., 2013). Connection strength within these modules did not change with age, and the modules resembled hub networks previously described for MRI (Hagmann et al., 2010; Power et al., 2010). The high temporal resolution of EEG additionally allowed us to distinguish between frequency bands potentially reflecting dynamic coupling between different neural oscillators. Generally, network parameters were similar for networks based on different frequency bands, but frequency band did emerge as a significant factor for clustering coefficient and characteristic path length. In conclusion, the current analysis shows that source reconstruction of high-density EEG recordings with appropriate head models offers a valuable tool for estimating network parameters in studies of brain development. The findings replicate the pattern of closer functional integration over development described for other imaging modalities (Fair et al., 2008; Power et al., 2010).

Consumer nueroscience: a new area of study for biomedical engineers

In scientific literature, the most accepted definition of consumer neuroscience or neuromarketing is that it is a field of study concerning the application of neuroscience methods to analyze and understand human behavior related to markets and marketing exchanges. First, it might seem strange that marketers would be interested in using neuroscience to understand consumer's preferences. Yet in practice, the basic goal of marketers is to guide the design and presentation of products in such a way that they are highly compatible with consumer preferences. To understand consumers preferences, several standard research tools are commonly used by marketers, such as personal interviews with the consumers, scoring questionnaries gathered from consumers, and focus groups. The reason marketing researchers are interested in using brain imaging tools instead of simply asking people for their preferences in front of marketing stimuli, arises from the assumption that people cannot (or do not want to) fully explain their preference when explicitly asked. Researchers in the field hypothesize that neuroimaging tools can access information within the consumer's brain during the generation of a preference or the observation of a commercial advertisement. The question of will this information be useful in further promoting the product is still up for debate in marketing literature. From the marketing researchers point of view, there is a hope that this body of brain imaging techniques will provide an efficient tradeoff between costs and benefits of the research. Currently, neuroscience methodology includes powerful brain imaging tools based on the gathering of hemodynamic or electromagnetic signals related to the human brain activity during the performance of a relevant task for marketing objectives. These tools are briefly reviewed in this article.

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.

High-resolution EEG analysis of power spectral density maps and coherence networks in a proportional reasoning task

Proportional reasoning is very important logical skill required in mathematics and science problem solving as well as in everyday life decisions. However, there is a lack of studies on neurophysiological correlates of proportional reasoning. To explore the brain activity of healthy adults while performing a balance scale task, we used high-resolution EEG techniques and graph-theory based connectivity analysis. After unskilled subjects learned how to properly solve the task, their cortical power spectral density (PSD) maps revealed an increased parietal activity in the beta band. This indicated that subjects started to perform calculations. In addition, the number of inter-hemispheric connections decreased after learning, implying a rearrangement of the brain activity. Repeated performance of the task led to the PSD decrease in the beta and gamma bands among parietal and frontal regions along with a synchronization of lower frequencies. These findings suggest that repetition led to a more automatic task performance. Subjects were also divided in two groups according to their scores on the test of logical thinking (TOLT). Although no group differences in the accuracy and reaction times were found, EEG data showed higher activity in the beta and gamma bands for the group that scored better on TOLT. Learning and repetition induced changes in the pattern of functional connectivity were evident for all frequency bands. Overall, the results indicated that higher frequency oscillations in frontal and parietal regions are particularly important for proportional reasoning.

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.

On the use of EEG or MEG brain imaging tools in neuromarketing research

Here we present an overview of some published papers of interest for the marketing research employing electroencephalogram (EEG) and magnetoencephalogram (MEG) methods. The interest for these methodologies relies in their high-temporal resolution as opposed to the investigation of such problem with the functional Magnetic Resonance Imaging (fMRI) methodology, also largely used in the marketing research. In addition, EEG and MEG technologies have greatly improved their spatial resolution in the last decades with the introduction of advanced signal processing methodologies. By presenting data gathered through MEG and high resolution EEG we will show which kind of information it is possible to gather with these methodologies while the persons are watching marketing relevant stimuli. Such information will be related to the memorization and pleasantness related to such stimuli. We noted that temporal and frequency patterns of brain signals are able to provide possible descriptors conveying information about the cognitive and emotional processes in subjects observing commercial advertisements. These information could be unobtainable through common tools used in standard marketing research. We also show an example of how an EEG methodology could be used to analyze cultural differences between fruition of video commercials of carbonated beverages in Western and Eastern countries.

Simultaneous estimation of cortical activity during social interactions by using EEG hyperscannings

In this paper we show how the possibility of recording simultaneously the cerebral neuroelectric activity in different subjects (EEG hyperscanning) during the execution of different tasks could return useful information about the "internal" cerebral state of the subjects. We present the results obtained by EEG hyperscannings during ecological task (such as the execution of a card game) as well as that obtained in a series of couples of subjects during the performance of the Prisoner's Dilemma Game. The simultaneous recordings of couples of interacting subjects allows to observe and to model directly the neural signature of human interactions in order to understand the cerebral processes generating and generated by social cooperation or competition. Results obtained in a study of different groups recorded during the card game revealed a larger activity in prefrontal and anterior cingulated cortex in different frequency bands for the player that leads the game when compared to other players. Results collected in a population of 10 subjects during the performance of the Prisoner's Dilemma suggested that the most consistently activated structure is the orbitofrontal region (roughly described by the Brodmann area 10) during the condition of competition in both the tasks. It could be speculated whether the pattern of cortical connectivity between different cortical areas in different subjects could be employed as a tool for assessing the outcome of the task in advance.

OpenMEEG: opensource software for quasistatic bioelectromagnetics

Background

Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages.

Methods

We have run a benchmark study in the field of electro- and magneto-encephalography, in order to compare the accuracy of OpenMEEG with other freely distributed forward solvers. We considered spherical models, for which analytical solutions exist, and we designed randomized meshes to assess the variability of the accuracy. Two measures were used to characterize the accuracy. the Relative Difference Measure and the Magnitude ratio. The comparisons were run, either with a constant number of mesh nodes, or a constant number of unknowns across methods. Computing times were also compared.

Results

We observed more pronounced differences in accuracy in electroencephalography than in magnetoencephalography. The methods could be classified in three categories: the linear collocation methods, that run very fast but with low accuracy, the linear collocation methods with isolated skull approach for which the accuracy is improved, and OpenMEEG that clearly outperforms the others. As far as speed is concerned, OpenMEEG is on par with the other methods for a constant number of unknowns, and is hence faster for a prescribed accuracy level.

Conclusions

This study clearly shows that OpenMEEG represents the state of the art for forward computations. Moreover, our software development strategies have made it handy to use and to integrate with other packages. The bioelectromagnetic research community should therefore be able to benefit from OpenMEEG with a limited development effort.

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.

Noninvasive cortical imaging of epileptiform activities from interictal spikes in pediatric patients

Improved non-invasive localization of the epileptogenic foci prior to epilepsy surgery would improve surgical outcome in patients with partial seizure disorders. A critical component for the identification of the epileptogenic brain is the analysis of electrophysiological data obtained during ictal activity from prolonged intracranial recordings. The development of a noninvasive means to identify the seizure onset zone (SOZ) would thus play an important role in treating patients with intractable epilepsy. In the present study, we have investigated non-invasive imaging of epileptiform activity in patients with medically intractable epilepsy by means of a cortical potential imaging (CPI) technique. Eight pediatric patients (1M/7F, ages 4-14 years) with intractable partial epilepsy were studied. Each patient had multiple (6 to 14) interictal spikes (IIS) subjected to the CPI analysis. Realistic geometry boundary element head models were built using each individual's MRI in order to maximize the imaging precision. CPI analysis was performed on the IISs, and extrema in the estimated CPI images were compared with SOZs as determined from the ictal electrocorticogram (ECoG) recordings, as well as the resected areas in the patients and surgical outcomes. The distances between the maximum cortical activities of the IISs reflected by the estimated cortical potential distributions and the SOZs were determined to quantitatively evaluate the performance of the CPI in localizing the epileptogenic zone. Ictal ECoG recordings revealed that six patients exhibited a single epileptogenic focus while two patients had multiple foci. In each patient, the CPI results revealed an area of activity overlapping with the SOZs as identified by ictal ECoG. The distance from the extreme of the CPI images at the peak of IIS to the nearest intracranial electrode associated with the onset of the ictal activity was evaluated for each patient and the averaged distance was 4.6mm. In the group of patients studied, the CPI imaged epileptogenic foci were within the resected areas. According to the follow-up of the eight patients included, two were seizure free and six had substantial reduction in seizure frequency. These promising results demonstrate the potential for noninvasive localization of the epileptogenic focus from interictal scalp EEG recordings. Confirmation of our results may have a significant impact on the process of presurgical planning in pediatric patients with intractable epilepsy by dramatically reducing or potentially eliminating the use of intracranial recording.

Brain activity during the memorization of visual scenes from TV commercials: an application of high resolution EEG and steady state somatosensory evoked potentials technologies

The aim of this study was to elucidate if the TV commercials that were remembered by the subjects after their observation within a documentary elicited particular brain activity when compared to the activity generated during the observation of TV commercials that were forgotten. High resolution EEG recordings were performed in a group of 10 healthy subjects with the steady state somatosensory evoked potentials (SSSEPs) technique, in which a series of light electrical stimulation at the left wrist were delivered at the frequency of 20Hz. The brain activity was indexed by the phase delay of the EEG spectral responses at 20Hz with respect to the stimulus delivering and evaluated at the scalp level as well as at the cortical surface using several regions of interest coincident with the Brodmann areas (BAs). Results suggest that the cerebral processes involved during the observation of TV commercials that were remembered by the population examined (RMB dataset) are generated by the posterior parietal cortices and the prefrontal areas, rather bilaterally. These results are compatible with previously results obtained in literature by using MEG and fMRI devices during similar experimental tasks. High resolution EEG is able to summarize, with the use of SSSEPs methodologies, the behavior of the estimated cortical networks subserving the proposed memory tasks. It is likely that such tool could play a role in the next future for the investigation of the neural substrates of the human behavior in decision-making and recognition tasks.

The track of brain activity during the observation of TV commercials with the high-resolution EEG technology

We estimate cortical activity in normal subjects during the observation of TV commercials inserted within a movie by using high-resolution EEG techniques. The brain activity was evaluated in both time and frequency domains by solving the associate inverse problem of EEG with the use of realistic head models. In particular, we recover statistically significant information about cortical areas engaged by particular scenes inserted within the TV commercial proposed with respect to the brain activity estimated while watching a documentary. Results obtained in the population investigated suggest that the statistically significant brain activity during the observation of the TV commercial was mainly concentrated in frontoparietal cortical areas, roughly coincident with the Brodmann areas 8, 9, and 7, in the analyzed population.

Assessing the memorization of TV commercials with the use of high resolution EEG: a pilot study

The present work intends to evaluate the functional characteristics of the cerebral network during the successful memory encoding of TV commercials. We estimated the functional networks in the frequency domain from a set of high-resolution EEG data. High resolution EEG recordings were performed in a group of healthy subjects and the cortical activity during the observation of TV commercials was evaluated in several regions of interest coincident with the Brodmann areas (BAs). Summarizing the main results of the present study, a sign of the memorization of a particular set of TV commercials have been found in a group of investigated subjects with the aid of advanced modern tools for the acquisition and the processing of EEG data. The cerebral processes involved during the observation of TV commercials that were remembered successively by the population examined (RMB dataset) are generated by the posterior parietal cortices and the prefrontal areas, rather bilaterally and are irrespective of the frequency bands analyzed. Such results are compatible with previously results obtained from EEG recordings with superficial electrodes as well as with the brain activations observed with the use of MEG and fMRI devices.

Cortical imaging of event-related (de)synchronization during online control of brain-computer interface using minimum-norm estimates in frequency domain

It is of wide interest to study the brain activity that correlates to the control of brain-computer interface (BCI). In the present study, we have developed an approach to image the cortical rhythmic modulation associated with motor imagery using minimum-norm estimates in the frequency domain (MNEFD). The distribution of cortical sources of mu activity during online control of BCI was obtained with the MNEFD. Contralateral decrease (event-related desynchronization) and ipsilateral increase (event-related synchronization) are localized in the sensorimotor cortex during online control of BCI in a group of human subjects. Statistical source analysis revealed that maximum correlation with movement imagination is localized in sensorimotor cortex.

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.

Cortical activation mapping of epileptiform activity derived from interictal ECoG spikes

PURPOSE

To develop and evaluate a new cortical activation mapping (CAM) method to obtain the neuronal activation sequences from the cortical potential distributions.

METHODS

Interictal electrocorticogram (ECoG) recordings were analyzed for eight pediatric epilepsy patients to find the cortical activation maps, which were compared with the patients' seizure-onset zones identified from ictal ECoG recordings. Various relations between the local activation time and cortical potential were assumed. The most effective relation was determined by accessing their capability to predict the seizure-onset zone. Computer simulations using a moving dipole source model were also conducted to test the present approach in imaging the propagated cortical activity.

RESULTS

In both clinical data analysis and computer simulations, the maximal amplitude proved to be the most effective criterion with which to determine the local cortical activation time. The present method successfully predicted the seizure-onset zone in seven of eight patients by the CAM analysis of ECoG-recorded interictal spikes (IISs). For patients with multiple seizure foci, each focus can be revealed by analyzing IISs with different spatial patterns.

CONCLUSIONS

The time difference between spike peaks of the interictal events in the leading channel and other channels can be effectively defined as the local cortical activation time. The cortical activation mapping method based on this time latency can be used to predict the seizure-onset zones, suggesting that the present CAM method is useful to assist the presurgical evaluation for the epilepsy patients.

Estimation of in vivo brain-to-skull conductivity ratio in humans

The electrical conductivity value of the human skull is important for biophysics research of the brain. In the present study, the human brain-to-skull conductivity ratio was estimated through in vivo experiments utilizing intra-cranial electrical stimulation in two epilepsy patients. A realistic geometry inhomogeneous head model including the implanted silastic grids was constructed with the aid of the finite element method, and used to estimate the conductivity ratio. Averaging over 49 sets of measurements, the mean value and standard deviation of the brain-to-skull conductivity ratio were found to be 18.7 and 2.1, respectively.

Effects of holes on EEG forward solutions using a realistic geometry head model

Holes in the skull and the scalp are associated with intracranial monitoring procedures. The purpose of the present study is to evaluate the effects of holes on extracranial electroencephalogram (EEG) and intracranial electrocorticogram (ECoG) recordings. The finite difference method (FDM) was used to model the head volume conductor with a hole of varying size. A current dipole was used to simulate the brain electrical activity with varying locations within the brain. The effects of the holes were assessed by comparing the forward potential distributions with and without a hole. The present computer simulation results indicate that the effect of a hole on the scalp EEG and ECoG recordings strongly depends on the dipole location and orientation. For a superficial radial dipole located under a hole of radius ranging from 5 mm to 40 mm, the relative error (RE) varies from 0.99% to 93.07% for the EEG and from 0.025% to 16.72% for the ECoG. The correlation coefficient (CC) varies from 99.99% to 21.1% and from 100% to 99.75% for the EEG and EcoG, respectively. For radial dipoles, the strongest effect on the EEG and ECoG occurs when the dipole is located below the center of the hole, while for tangential dipoles, the strongest effect occurs when the dipole is located below the border of the hole. The effect of a hole on the EEG is much larger than upon the ECoG.

A fast method to derive realistic FEM models based on BEM models

A fast method for constructing a FEM head model based on the relevant BEM head model is presented. The method has been evaluated and shown to provide an alternative means of deriving FEM head models. The availability of such fast method would facilitate the realistic head modeling for EEG/MEG research.

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.

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 new magnetic resonance electrical impedance tomography (MREIT) algorithm: the RSM-MREIT algorithm with applications to estimation of human head conductivity

We have developed a new magnetic resonance electrical impedance tomography (MREIT) algorithm, the RSM-MREIT algorithm, for noninvasive imaging of the electrical conductivity distribution using only one component of magnetic flux density. The proposed RSM-MREIT algorithm uses the response surface methodology (RSM) algorithm for optimizing the conductivity distribution through minimizing the errors between the measured and calculated magnetic flux densities. A series of computer simulations has been conducted to assess the performance of the proposed RSM-MREIT algorithm to estimate electrical conductivity values of the scalp, the skull and the brain tissue, in a three-shell piecewise homogeneous head model. Computer simulation studies were conducted in both a spherical and realistic-geometry head model with a single variable (the brain-to-skull conductivity ratio) and three variables (the conductivity of the brain, the skull, and the scalp). The relative error between the target and estimated head conductivity values was less than 12% for both the single-variable and three-variable simulations. These promising simulation results demonstrate the feasibility of the proposed RSM-MREIT algorithm in estimating electrical conductivity values in a piecewise homogeneous head model of the human head, and suggest that the RSM-MREIT algorithm merits further investigation.

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.