Estimating cortical activity from VEPS with the shrinking ellipsoid inverse

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.

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

We have developed a method for estimating the three-dimensional distribution of equivalent current sources inside the brain from scalp potentials. Laplacian weighted minimum norm algorithm has been used in the present study to estimate the inverse solutions. A three-concentric-sphere inhomogeneous head model was used to represent the head volume conductor. A closed-form solution of the electrical potential over the scalp and inside the brain due to a point current source was developed for the three-concentric-sphere inhomogeneous head model. Computer simulation studies were conducted to validate the proposed equivalent current source imaging. Assuming source configurations as either multiple dipoles or point current sources/sinks, in computer simulations we used our method to reconstruct these sources, and compared with the equivalent dipole source imaging. Human experimental studies were also conducted and the equivalent current source imaging was performed on the visual evoked potential data. These results highlight the advantages of the equivalent current source imaging and suggest that it may become an alternative approach to imaging spatially distributed current sources-sinks in the brain and other organ systems.

High-resolution EEG: on the cortical equivalent dipole layer imaging

BACKGROUND

Brain electrical activity is a spatio-temporally distributed process. Cortical imaging techniques have been developed to reconstruct cortical activity from the scalp electroencephalographic or magnetoencephalographic measurements. Several cortical imaging approaches, such as the epicortical potentials and a dipole layer accounting for the cortical activity, have been used to represent brain electrical activity.

METHODS

A closed cortical dipole layer source model is used to equivalently represent brain electrical activity. The relationship between the primary brain electrical sources and the cortical equivalent dipole layer is derived from the theory of electromagnetics. Computer simulation studies were conducted using a 3-concentric-sphere head model to validate the proposed theory. The cortical equivalent dipole layer imaging approach was tested in both computer simulation and human visual evoked potential (VEP) experiments.

RESULTS

The strength of the cortical equivalent dipole layer is shown to be proportional to the electrical potential over the same surface generated by primary electrical sources, had the outer medium been replaced by air. The proposed theory was validated by computer simulation in a discrete system. Simulation and VEP experimental studies suggest the feasibility of applying the cortical equivalent dipole layer imaging approach for brain imaging.

CONCLUSIONS

The cortical equivalent dipole layer model can equivalently represent the primary brain electrical sources throughout the entire brain surrounded by the dipole layer. The strength of the cortical equivalent dipole layer due to primary sources can be directly calculated according to the theory developed in the present study.

High-resolution EEG mappings: a spherical harmonic spectra theory and simulation results

Shown first is the equivalence between the multiple expansion (ME) of the brain electrical generator and the spherical harmonic spectra (SHS) of the potential generated by the electrical generator in an infinite volume conductor. Based on the equivalence, the SHS and the spatial filters which connect the SHS with the ME are deduced, in a concentric 3 sphere conductor and for the 5 EEG source mappings. They are cortical potential mapping (CPM), scalp Laplacian mapping (LM), pseudo-cortical potential mapping (PCPM), equivalent dipole layer mapping (EDM) and equivalent charge layer mapping (ECM). The theoretical simulation study of the spatial filters and mappings indicate that all 5 mappings provide higher resolution imaging maps of brain electrical activity than the scalp potential map. In the inverse problem, a spherical spline fit algorithm is provided to reconstruct the SHS of the scalp recording potential, and then the SHS and maps of the 5 mappings are reconstructed by utilizing the spatial filters and the SHS of the scalp potential. The results indicate that the correlativity order between a reconstructed map and the actual cortical potential map is CPM > or = EDM > PCPM > LM > ECM. An empirical VEP data study shows that any one of the 5 mappings also provides higher spatial resolution than the scalp potential map.

Common spatial subspace decomposition applied to analysis of brain responses under multiple task conditions: a simulation study

A method, called common spatial subspace decomposition, is presented which can extract signal components specific to one condition from multiple magnetoencephalography/electroencephalography data sets of multiple task conditions. Signal matrices or covariance matrices are decomposed using spatial factors common to multiple conditions. The spatial factors and corresponding spatial filters are then dissociated into specific and common parts, according to the common spatial subspace which exists among the data sets. Finally, the specific signal components are extracted using the corresponding spatial filters and spatial factors. The relationship between this decomposition and spatio-temporal source models is described in this paper. Computer simulations suggest that this method can facilitate the analysis of brain responses under multiple task conditions and merits further application.