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

One Definition to Join Them All: The N-Spherical Solution for the EEG Lead Field

Albeit its simplicity, the concentric spheres head model is widely used in EEG. The reason behind this is its simple mathematical definition, which allows for the calculation of lead fields with negligible computational cost, for example, for iterative approaches. Nevertheless, the literature shows contradictory formulations for the electrical solution of this head model. In this work, we study several different definitions for the electrical lead field of a four concentric spheres conduction model, finding that their results are contradictory. A thorough exploration of the mathematics used to build these formulations, provided in the original works, allowed for the identification of errors in some of the formulae, which proved to be the reason for the discrepancies. Moreover, this mathematical review revealed the iterative nature of some of these formulations, which allowed us to develop a formulation to solve the lead field in a head model built from an arbitrary number of concentric, homogeneous, and isotropic spheres.

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.

A Comparative Study on the Dynamic EEG Center of Mass with Different References

One of the most fundamental issues during an EEG study is choosing an available neutral reference. The infinity zero reference obtained by the reference electrode standardization technique (REST) has been recommended and used for its higher accuracy. This paper examined three traditional references, the average reference (AR), the linked mastoids reference (LM), and REST, in the study of the EEG center of mass (CM) using simulated and real ERPs. In the simulation, the relative error of REST was the smallest among the references. As for the ERP data with the visual oddball paradigm, the dynamic CM trajectory and its traveling velocity obtained by REST characterized three typical stages in spatial domain and temporal speed metrics, which provided useful information in addition to the distinct ERP waveform in the temporal domain. The results showed that the CM traveling from the frontal to parietal areas corresponding to the earlier positive components (i.e., P200 and P250), stays temporarily at the parietal area corresponding to P300 and then returns to the frontal area during the recovery stage. Compared with REST, AR, and LM not only changed the amplitude of P300 significantly but distorted the CM trajectory and its instantaneous velocity. As REST continues to provide objective results, we recommend that REST be used in future EEG/ERP CM studies.

How Different EEG References Influence Sensor Level Functional Connectivity Graphs

Highlights: Hamming Distance is applied to distinguish the difference of functional connectivity networkThe orientations of sources are testified to influence the scalp Functional Connectivity Graph (FCG) from different references significantlyREST, the reference electrode standardization technique, is proved to have an overall stable and excellent performance in variable situations. The choice of an electroencephalograph (EEG) reference is a practical issue for the study of brain functional connectivity. To study how EEG reference influence functional connectivity estimation (FCE), this study compares the differences of FCE resulting from the different references such as REST (the reference electrode standardization technique), average reference (AR), linked mastoids (LM), and left mastoid references (LR). Simulations involve two parts. One is based on 300 dipolar pairs, which are located on the superficial cortex with a radial source direction. The other part is based on 20 dipolar pairs. In each pair, the dipoles have various orientation combinations. The relative error (RE) and Hamming distance (HD) between functional connectivity matrices of ideal recordings and that of recordings obtained with different references, are metrics to compare the differences of the scalp functional connectivity graph (FCG) derived from those two kinds of recordings. Lower RE and HD values imply more similarity between the two FCGs. Using the ideal recording (IR) as a standard, the results show that AR, LM and LR perform well only in specific conditions, i.e., AR performs stable when there is no upward component in sources' orientation. LR achieves desirable results when the sources' locations are away from left ear. LM achieves an indistinct difference with IR, i.e., when the distribution of source locations is symmetric along the line linking the two ears. However, REST not only achieves excellent performance for superficial and radial dipolar sources, but also achieves a stable and robust performance with variable source locations and orientations. Benefitting from the stable and robust performance of REST vs. other reference methods, REST might best recover the real FCG of EEG. Thus, REST based FCG may be a good candidate to compare the FCG of EEG based on different references from different labs.

Non-linear Analysis of Scalp EEG by Using Bispectra: The Effect of the Reference Choice

Bispectral analysis is a signal processing technique that makes it possible to capture the non-linear and non-Gaussian properties of the EEG signals. It has found various applications in EEG research and clinical practice, including the assessment of anesthetic depth, the identification of epileptic seizures, and more recently, the evaluation of non-linear cross-frequency brain functional connectivity. However, the validity and reliability of the indices drawn from bispectral analysis of EEG signals are potentially biased by the use of a non-neutral EEG reference. The present study aims at investigating the effects of the reference choice on the analysis of the non-linear features of EEG signals through bicoherence, as well as on the estimation of cross-frequency EEG connectivity through two different non-linear measures, i.e., the cross-bicoherence and the antisymmetric cross-bicoherence. To this end, four commonly used reference schemes were considered: the vertex electrode (Cz), the digitally linked mastoids, the average reference, and the Reference Electrode Standardization Technique (REST). The reference effects were assessed both in simulations and in a real EEG experiment. The simulations allowed to investigated: (i) the effects of the electrode density on the performance of the above references in the estimation of bispectral measures; and (ii) the effects of the head model accuracy in the performance of the REST. For real data, the EEG signals recorded from 10 subjects during eyes open resting state were examined, and the distortions induced by the reference choice in the patterns of alpha-beta bicoherence, cross-bicoherence, and antisymmetric cross-bicoherence were assessed. The results showed significant differences in the findings depending on the chosen reference, with the REST providing superior performance than all the other references in approximating the ideal neutral reference. In conclusion, this study highlights the importance of considering the effects of the reference choice in the interpretation and comparison of the results of bispectral analysis of scalp EEG.

Impact of the reference choice on scalp EEG connectivity estimation

OBJECTIVE

Several scalp EEG functional connectivity studies, mostly clinical, seem to overlook the reference electrode impact. The subsequent interpretation of brain connectivity is thus often biased by the choice of a non-neutral reference. This study aims at systematically investigating these effects.

APPROACH

As EEG reference, we examined the vertex electrode (Cz), the digitally linked mastoids (DLM), the average reference (AVE), and the reference electrode standardization technique (REST). As a connectivity metric, we used the imaginary part of the coherency. We tested simulated and real data (eyes-open resting state) by evaluating the influence of electrode density, the effect of head model accuracy in the REST transformation, and the impact on the characterization of the topology of functional networks from graph analysis.

MAIN RESULTS

Simulations demonstrated that REST significantly reduced the distortion of connectivity patterns when compared to AVE, Cz, and DLM references. Moreover, the availability of high-density EEG systems and an accurate knowledge of the head model are crucial elements to improve REST performance, with the individual realistic head model being preferable to the standard realistic head model. For real data, a systematic change of the spatial pattern of functional connectivity depending on the chosen reference was also observed. The distortion of connectivity patterns was larger for the Cz reference, and progressively decreased when using the DLM, the AVE, and the REST. Strikingly, we also showed that network attributes derived from graph analysis, i.e. node degree and local efficiency, are significantly influenced by the EEG reference choice.

SIGNIFICANCE

Overall, this study highlights that significant differences arise in scalp EEG functional connectivity and graph network properties, in dependence on the chosen reference. We hope that our study will convey the message that caution should be used when interpreting and comparing results obtained from different laboratories using different reference schemes.

Why do we need to use a zero reference? Reference influences on the ERPs of audiovisual effects

Using ERPs in the audiovisual stimulus, the current study is the first to investigate the influence of the reference on experimental effects (between two conditions). Three references, the average reference (AR), the mean mastoid (MM), and a new infinity zero reference (IR), were comparatively investigated via ERPs, statistical parametric scalp mappings (SPSM), and LORETA. Specifically, for the N1 (170-190 ms), the SPSM results showed an anterior distribution for MM, a posterior distribution for IR, and both anterior and posterior distributions for AR. However, the circumstantial evidence provided by LORETA is consistent with SPSM of IR. These results indicated that the newly developed IR could provide increased accuracy; thus, we recommend IR for future ERP studies.

Diffuse optical cortical mapping using the boundary element method

Cortical mapping, also called optical topography is a new medical imaging modality which allows the non-invasive investigation of the outer layers of the cortex. This technique is challenging and the geometry of the subject is very often over-simplified. We aim here to localize activated regions of an anatomically accurate brain. A Boundary Element Method is used for the forward model. The reconstruction of perturbations in the absorption coefficient is demonstrated in a geometrically realistic simulation and in vivo. These results show that diffuse optical imaging of the head can provide reliable activity maps when anatomical data is available.

Neuroelectric source imaging using 3SCO: a space coding algorithm based on particle swarm optimization and l0 norm constraint

The electroencephalogram (EEG) neuroelectric sources inverse problem is usually underdetermined and lacks a unique solution, which is due to both the electromagnetism Helmholtz theorem and the fact that there are fewer observations than the unknown variables. One potential choice to tackle this issue is to solve the underdetermined system for a sparse solution. Aiming to the sparse solution, a novel algorithm termed 3SCO (Solution Space Sparse Coding Optimization) is presented in this paper. In 3SCO, after the solution space is coded with some particles, the particle-coded space is compressed by the evolution of particle swarm optimization algorithm, where an l0 constrained fitness function is introduced to guarantee the selection of a suitable sparse solution for the underdetermined system. 3SCO was first tested by localizing simulated EEG sources with different configurations on a realistic head model, and the comparisons with minimum norm (MN), LORETA (low resolution electromagnetic tomography), l1 norm solution and FOCUSS (focal underdetermined system solver) confirmed that a good sparse solution for EEG source imaging could be achieved with 3SCO. Finally, 3SCO was applied to localize the neuroelectric sources in a visual stimuli related experiment and the localized areas were basically consistent with those reported in previous studies.

A new method of spatio-temporal topographic mapping by correlation coefficient of K-means cluster

It would be of the utmost interest to map correlated sources in the working human brain by Event-Related Potentials (ERPs). This work is to develop a new method to map correlated neural sources based on the time courses of the scalp ERPs waveforms. The ERP data are classified first by k-means cluster analysis, and then the Correlation Coefficients (CC) between the original data of each electrode channel and the time course of each cluster centroid are calculated and utilized as the mapping variable on the scalp surface. With a normalized 4-concentric-sphere head model with radius 1, the performance of the method is evaluated by simulated data. CC, between simulated four sources (s (1)-s (4)) and the estimated cluster centroids (c (1)-c (4)), and the distances (Ds), between the scalp projection points of the s (1)-s (4) and that of the c (1)-c (4), are utilized as the evaluation indexes. Applied to four sources with two of them partially correlated (with maximum mutual CC = 0.4892), CC (Ds) between s (1)-s (4) and c (1)-c (4) are larger (smaller) than 0.893 (0.108) for noise levels NSR</= 0.2; Applied to four sources with two of them completely correlated, CC (Ds) between s (1)-s (4) and c (1)-c (4) are larger (smaller) than 0.97367 (0.1898) for a random noise level NSR</= 0.2; Applied to 128, 64 and 32 recording electrodes, CC (Ds) between s (1)-s (4) and c (1)-c (4) are larger (smaller) than 0.9557 (0.4251) for a random noise level NSR = 0.15; And applied to the cases of spatially overlapped scalp activities, CC (Ds) between s (1)-s (4) and c (1)-c (4) are larger (smaller) than 0.9083 (0.4329) for a random noise level NSR = 0.15. Finally, the method successfully decomposed the ERPs collected in a spatial selective attention experiment into three clusters located at left, right occipital and frontal. The estimated vectors of the contra-occipital area demonstrate that attention to the stimulus location produces increased amplitude of the P1 and N1 components over the contra-occipital scalp. The estimated vector in the frontal area displays two large processing negativity waves around 100 ms and 250 ms when subjects are attentive, and there is a small negative wave around 140 ms and a P300 when subjects are unattentive. The results of simulations and real Visual Evoked Potentials (VEPs) data demonstrate the validity of the method in mapping correlated sources. This method may be an objective, heuristic and important tool to study the properties of cerebral, neural networks in cognitive and clinical neurosciences.

The effect of reference choices on the spatio-temporal analysis of brain evoked potentials: the use of infinite reference

Reference is a very virtual issue in EEG and ERP. Understanding the difference of various references will make the applications more confident. In this work, somatosensory evoked potential (SEP) with stimulation on the right hand was studied. The SEP spatio-temporal analysis was conducted comparatively on six references, left mastoid (contralateral mastoid reference, CM), right mastoid (ipsilateral mastoid reference, IM), linked mastoids (LM), average reference (AR), vertex reference (Cz) and the infinity reference (IR) newly proposed in 2001. Among the six, CM is the one used in actual recordings, and the other five are obtained by off-line re-referencing. The comparison is conducted on four selected components (P30 ms, P40 ms, N90 ms and P230 ms) in both temporal and spatial aspects. The results show that references may have a distinct influence on the amplitudes of the scalp potentials, with relative error at some electrodes larger than 500%, and for some electrodes it may even change the polarity. Pair-wise multiple comparison (Tukey test) shows that the differences of peak values among various references are very significant (P<0.001) between Cz and IR\CM\IM\LM, and significant (P<0.01) between Cz and AR for component N90 ms; very significant (P<0.001) between Cz and IR\CM\IM\LM\AR, significant between IMLM and AR (P<0.01), CM and AR (P<0.05) for component P230 ms. The amplitude value order is CM/IM> or =LM>IR>AR>Cz. The two-ways (the six references vs. the four Peaks) repeated measures ANOVA test shows the effect of different references depends on various components; there is a statistically significant interaction between reference and the peak (P=<0.001). While for the spatial map of the potential amplitude, references will not affect the amplitude map shape if the color-bar is selected automatically, but if a fixed color-bar is chosen for data of various references, they may show some differences. These results mean a common reference is important for producing a comparable result between labs. As IR is theoretically a constant reference, we recommend it as the common choice in the future.

The use of standardized infinity reference in EEG coherency studies

The study of large scale interactions in the brain from EEG signals is a promising method for the identification of functional networks. However, the validity of a large scale parameter is limited by two factors: the use of a non-neutral reference and the artifactual self-interactions between the measured EEG signals introduced by volume conduction. In this paper, we propose an approach to study large scale EEG coherency in which these factors are eliminated. Artifactual self-interaction by volume conduction is eliminated by using the imaginary part of the complex coherency as a measure of interaction and the Reference Electrode Standardization Technique (REST) is used for the approximate standardization of the reference of scalp EEG recordings to a point at infinity that, being far from all possible neural sources, acts like a neutral virtual reference. The application of our approach to simulated and real EEG data shows that the detection of interaction, as opposed to artifacts due to reference and volume conduction, is a goal that can be achieved from the study of a large scale parameter.

Removal of the ocular artifacts from EEG data using a cascaded spatio-temporal processing

Eye movements and blinks may produce unusual voltage changes in human electroencephalogram (EEG). These effects may spread across scalp and mask brain signals. In this paper, a cascaded spatio-temporal processing procedure (CAST) is presented to remove artifact electrooculogram (EOG). Firstly a discrete equivalent distributed source on the cortical surface is reconstructed from the contaminated scalp recordings by a linear minimum norm estimation (i.e. a spatial analysis step). Then, the equivalent sources of EOG are identified by principal component analysis (PCA) of the equivalent distributed source time series (i.e. a temporal analysis step). Finally, the EOG-corrected scalp EEG is reconstructed from the equivalent distributed source where EOG components have been removed. The effectiveness of CAST is confirmed by the application to actual scalp data and a detailed comparative study.

Influence of the scalp thickness on the intracranial contribution to rheoencephalography

In spite of the great efforts made by the scientific community, up to now there is no agreement about the rheoencephalography (REG) capability to reflect cerebral blood flow (CBF). Moreover, a standard procedure and the optimal electrode arrangement have not been established yet. In a previous study, we found, using a classical four-shell spherical model of the head and solving it by numerical methods that, theoretically, there could exist an electrode arrangement to register an REG II free of extracranial contribution. In this paper, we have studied the influence of scalp thickness on the intracranial contribution to REG II. The study has been performed by solving the head model, using in this case analytical methods, and then estimating the partial contribution of CBF pulsatility to REG for a given set of scalp thicknesses. Although our theoretical results validate the previous finding and suggest that, in some cases, an optimal electrode arrangement to register REG II exists, such an arrangement, and even its existence, is very sensitive to the subject's scalp thickness. According to this, there could not exist a universal electrode arrangement suitable for all individuals to register an REG II free of extracranial contribution, since it depends on the subject's physical constitution. This fact could explain the lack of agreement in the literature about REG interpretation.

A study on the reference electrode standardization technique for a realistic head model

One oldest technical problem in EEG practice is the effect of an active reference on EEG recording, and it is especially important for identifying the temporal information of EEG recordings. To solve this problem, a reference electrode standardization technique (REST) has been proposed for a concentric three-sphere head model. REST, based on an equivalent distributed source model, reconstructs the potential with a reference at infinity from the potential with a scalp point reference or with the average reference. In this paper, investigated was the REST for a realistic head model. The results of simulation studies show that the potential reconstruction for the realistic head model is more sensitive to noise than that for the concentric three-sphere head model, so a regularized inverse by truncated singular value decomposition was introduced. The results confirm that REST is still an efficient method even for a realistic head model especially for the most important superficial cortex region.

High-resolution electroencephalogram (EEG) mapping: scalp charge layer

The neural electrical signal related to the human brain function is one of the tracks to understanding ourselves. Various electroencephalogram imaging techniques have been developed to reveal spatial information on neural activities in the brain from scalp recordings, such as Laplacian, equivalent source layer and potential. Physically, these methods may be classified into two categories: scalp surface or cortical surface based techniques. In this work, the focus is on the scalp surface based equivalent charge layer (ECL), with a comparison to the scalp potential with different references and scalp Laplacian (SL). The contents include theoretical analysis and numeric evaluation of simulated data and real alpha (8-12 Hz) data. The results confirm the fact that SL and ECL are of higher spatial resolution than various scalp potential maps, and for SL and ECL, SL is of higher resolution but more sensitive to noise.

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

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