A study of equivalent source techniques for high-resolution EEG imaging

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.

Analytical expressions for the transfer matrix to standardize scalp potentials to infinity reference

A procedure based on the multiple expansion of the brain electrical generator is used here to derive analytical expressions for the transfer matrix necessary to obtain potentials referenced to infinity. Its features include: avoidance of computations that involve a large number of discrete dipole sources; faster evaluation compared to the use of the dipole layer; and a transparency showing the parameters that constitute the transfer matrix. The paper also proposes the construction of the standardization matrix without the use of the general inverse of a non-symmetrical matrix.

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.

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.

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

OBJECTIVES

The present study addressed a new scalp Laplacian mapping (LM) algorithm.

METHODS

Using a radial-basis function (RBF) as the interpolation basis function, and the smallest arc length on the surface of a spherical head model as the distance measure between two measurement sites, a new RBF based approach to LM is formulated.

RESULTS

With simulated data and empirical data, comparison between the new RBF based approach and the spherical spline function (SSF) based approach was conducted in a 4-concentric spheres head model, and the results show that the RBF based approach is better than the SSF based approach to LM.

CONCLUSIONS

The new RBF based approach to LM provides an additional efficient way for the neural electrical activities imaging.

Source potential mapping: a new modality to image neural electric activities

A new neural electric imaging modality-source potential mapping (SPM)-is presented here, which images the neural sources by the potential produced by the sources in a homogeneous infinite conducting medium. Compared with the extant cortical surface potential mapping (CPM). SPM is a more direct reflection of the sources and is a simpler physical model, thus assuring easy understanding. The simulations show that SPM has a slightly higher spatial resolution than CPM and the calculation of SPM is more economical than that of CPM.

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

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