High-resolution EEG mapping: a radial-basis function based approach to the scalp Laplacian estimate

Which Reference Should We Use for EEG and ERP practice?

Which reference is appropriate for the scalp ERP and EEG studies? This unsettled problem still inspires unceasing debate. The ideal reference should be the one with zero or constant potential but unfortunately it is well known that no point on the body fulfills this condition. Consequently, more than ten references are used in the present EEG-ERP studies. This diversity seriously undermines the reproducibility and comparability of results across laboratories. A comprehensive review accompanied by a brief communication with rigorous derivations and notable properties (Hu et al. Brain Topogr, 2019. https://doi.org/10.1007/s10548-019-00706-y ) is thus necessary to provide application-oriented principled recommendations. In this paper current popular references are classified into two categories: (1) unipolar references that construct a neutral reference, including both online unipolar references and offline re-references. Examples of unipolar references are the reference electrode standardization technique (REST), average reference (AR), and linked-mastoids/ears reference (LM); (2) non-unipolar references that include the bipolar reference and the Laplacian reference. We show that each reference is derived with a different assumption and serves different aims. We also note from (Hu et al. 2019) that there is a general form for the reference problem, the 'no memory' property of the unipolar references, and a unified estimator for the potentials at infinity termed as the regularized REST (rREST) which has more advantageous statistical evidence than AR. A thorough discussion of the advantages and limitations of references is provided with recommendations in the hope to clarify the role of each reference in the ERP and EEG practice.

Local and Widely Distributed EEG Activity in Schizophrenia With Prevalence of Negative Symptoms

We evaluated EEG frequency abnormalities in resting state (eyes closed and eyes open) EEG in a group of chronic schizophrenia patients as compared with healthy subjects. The study included 3 methods of analysis of deviation of EEG characteristics: genuine EEG, current source density (CSD), and group independent component (gIC). All 3 methods have shown that the EEG in schizophrenia patients is characterized by enhanced low-frequency (delta and theta) and high-frequency (beta) activity in comparison with the control group. However, the spatial pattern of differences was dependent on the type of method used. Comparative analysis has shown that increased EEG power in schizophrenia patients apparently concerns both widely spatially distributed components and local components of signal. Furthermore, the observed differences in the delta and theta range can be described mainly by the local components, and those in the beta range mostly by spatially widely distributed ones. The possible nature of the widely distributed activity is discussed.

Reconstruction of electroencephalographic data using radial basis functions

OBJECTIVE

In this paper we introduce a new interpolation method to use for scalp potential interpolation. The predictive value of this new interpolation technique (the multiquadric method) is compared to commonly used interpolation techniques like nearest-neighbour averaging and spherical splines.

METHODS

The method of comparison is cross-validation, where the data of one or two electrodes is predicted by the rest of the data. The difference between the predicted and the measured data is used to determine two error measures. One is the maximal error in one interpolation technique and the other is the mean square error. The methods are tested on data stemming from 30 channel EEG of 10 healthy volunteers.

RESULTS

The multiquadric interpolation methods performed best regarding both error measures and have been easier to calculate than spherical splines.

CONCLUSION

Multiquadrics are a good alternative to commonly used EEG reconstruction methods.

SIGNIFICANCE

Multiquadrics have been widely used in reconstruction on sphere-like surfaces, but until now, the advantages have not been investigated in EEG reconstruction.

Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial review

Despite the recognition that the surface Laplacian may counteract adverse effects of volume conduction and recording reference for surface potential data, electrophysiology as a discipline has been reluctant to embrace this approach for data analysis. The reasons for such hesitation are manifold but often involve unfamiliarity with the nature of the underlying transformation, as well as intimidation by a perceived mathematical complexity, and concerns of signal loss, dense electrode array requirements, or susceptibility to noise. We revisit the pitfalls arising from volume conduction and the mandated arbitrary choice of EEG reference, describe the basic principle of the surface Laplacian transform in an intuitive fashion, and exemplify the differences between common reference schemes (nose, linked mastoids, average) and the surface Laplacian for frequently-measured EEG spectra (theta, alpha) and standard event-related potential (ERP) components, such as N1 or P3. We specifically review common reservations against the universal use of the surface Laplacian, which can be effectively addressed by employing spherical spline interpolations with an appropriate selection of the spline flexibility parameter and regularization constant. We argue from a pragmatic perspective that not only are these reservations unfounded but that the continued predominant use of surface potentials poses a considerable impediment on the progress of EEG and ERP research.

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.

Principal components analysis of Laplacian waveforms as a generic method for identifying ERP generator patterns: I. Evaluation with auditory oddball tasks

OBJECTIVE

To evaluate the effectiveness and comparability of PCA-based simplifications of ERP waveforms versus their reference-free Laplacian transformations for separating task- and response-related ERP generator patterns during auditory oddball tasks.

METHODS

Nose-referenced ERPs (31 sites total) were recorded from 66 right-handed adults during oddball tasks using syllables or tones. Response mode (left press, right press, silent count) and task was varied within subjects. Spherical spline current source density (CSD) waveforms were computed to sharpen ERP scalp topographies and eliminate volume-conducted contributions. ERP and CSD data were submitted to separate covariance-based, unrestricted temporal PCAs (Varimax) to disentangle temporally and spatially overlapping ERP and CSD components.

RESULTS

Corresponding ERP and CSD factors were unambiguously related to known ERP components. For example, the dipolar organization of a central N1 was evident from factorized anterior sinks and posterior sources encompassing the Sylvian fissure. Factors associated with N2 were characterized by asymmetric frontolateral (tonal: frontotemporal R > L) and parietotemporal (phonetic: parietotemporal L > R) sinks for targets. A single ERP factor summarized parietal P3 activity, along with an anterior negativity. In contrast, two CSD factors peaking at 360 and 560 ms distinguished a parietal P3 source with an anterior sink from a centroparietal P3 source with a sharply localized Fz sink. A smaller parietal but larger left temporal P3 source was found for silent count compared to button press. Left or right press produced opposite, region-specific asymmetries originating from central sites, modulating the N2/P3 complex.

CONCLUSIONS

CSD transformation is shown to be a valuable preprocessing step for PCA of ERP data, providing a unique, physiologically meaningful solution to the ubiquitous reference problem. By reducing ERP redundancy and producing sharper, simpler topographies, and without losing or distorting any effects of interest, the CSD-PCA solution replicated and extended previous task- and response-related findings.

SIGNIFICANCE

Eliminating ambiguities of the recording reference, the combined CSD-PCA approach systematically bridges between montage-dependent scalp potentials and distinct, anatomically-relevant current generators, and shows promise as a comprehensive, generic strategy for ERP analysis.

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.

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.

The theoretical relation of scalp Laplacian and scalp current density of a spherical shell head model

The theoretical relation between the scalp Laplacian (SL) and the scalp current density (SCD) is derived for a spherical shell head model. The result shows that they are related by a function of spatial frequency. For practically available low spatial frequencies, they are approximately linearly related to each other, so the SL estimate may be considered as an approximate SCD estimate in practice.