Pedro A. Valdes-Sosa

Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis

Abstract Finding the means to efficiently summarize electroencephalographic data has been a long-standing problem in electrophysiology. A popular approach is identification of component modes on the basis of the time-varying spectrum of multichannel EEG recordings—in other words, a space/frequency/time atomic decomposition of the time-varying EEG spectrum. Previous work has been limited to only two of these dimensions. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) have been used to create space/time decompositions; suffering an inherent lack of uniqueness that is overcome only by imposing constraints of orthogonality or independence of atoms. Conventional frequency/time decompositions ignore the spatial aspects of the EEG. Framing of the data being as a three-way array indexed by channel, frequency, and time allows the application of a unique decomposition that is known as Parallel Factor Analysis (PARAFAC). Each atom is the tri-linear decomposition into a spatial, spectral, and temporal signature. We applied this decomposition to the EEG recordings of five subjects during the resting state and during mental arithmetic. Common to all subjects were two atoms with spectral signatures whose peaks were in the theta and alpha range. These signatures were modulated by physiological state, increasing during the resting stage for alpha and during mental arithmetic for theta. Furthermore, we describe a new method (Source Spectra Imaging or SSI) to estimate the location of electric current sources from the EEG spectrum. The topography of the theta atom is frontal and the maximum of the corresponding SSI solution is in the anterior frontal cortex. The topography of the alpha atom is occipital with maximum of the SSI solution in the visual cortex. We show that the proposed decomposition can be used to search for activity with a given spectral and topographic profile in new recordings, and that the method may be useful for artifact recognition and removal.

Intracerebral Sources of Human Auditory-Evoked Potentials

Evoked potentials to brief 1,000-Hz tones presented to either the left or the right ear were recorded from 30 electrodes arrayed over the head. These recordings were submitted to two different forms of source analysis: brain electric source analysis (BESA) and variable-resolution electromagnetic tomography (VARETA). Both analyses showed that the dominant intracerebral sources for the late auditory-evoked potentials (50–300 ms) were in the supratemporal plane and lateral temporal lobe contralateral to the ear of stimulation. The analyses also suggested the possibility of additional sources in the frontal lobes.

Invariant reversible QEEG effects of anesthetics

Continuous recordings of brain electrical activity were obtained from a group of 176 patients throughout surgical procedures using general anesthesia. Artifact-free data from the 19 electrodes of the International 10/20 System were subjected to quantitative analysis of the electroencephalogram (QEEG). Induction was variously accomplished with etomidate, propofol or thiopental. Anesthesia was maintained throughout the procedures by isoflurane, desflurane or sevoflurane (N = 68), total intravenous anesthesia using propofol (N = 49), or nitrous oxide plus narcotics (N = 59). A set of QEEG measures were found which reversibly displayed high heterogeneity of variance between four states as follows: (1) during induction; (2) just after loss of consciousness (LOC); (3) just before return of consciousness (ROC); (4) just after ROC. Homogeneity of variance across all agents within states was found. Topographic statistical probability images were compared between states. At LOC, power increased in all frequency bands in the power spectrum with the exception of a decrease in gamma activity, and there was a marked anteriorization of power. Additionally, a significant change occurred in hemispheric relationships, with prefrontal and frontal regions of each hemisphere becoming more closely coupled, and anterior and posterior regions on each hemisphere, as well as homologous regions between the two hemispheres, uncoupling. All of these changes reversed upon ROC. Variable resolution electromagnetic tomography (VARETA) was performed to localize salient features of power anteriorization in three dimensions. A common set of neuroanatomical regions appeared to be the locus of the most probable generators of the observed EEG changes.

Estimating brain functional connectivity with sparse multivariate autoregression

There is much current interest in identifying the anatomical and functional circuits that are the basis of the brains computations, with hope that functional neuroimaging techniques will allow the in vivo study of these neural processes through the statistical analysis of the time-series they produce. Ideally, the use of techniques such as multivariate autoregressive (MAR) modelling should allow the identification of effective connectivity by combining graphical modelling methods with the concept of Granger causality. Unfortunately, current time-series methods perform well only for the case that the length of the time-series Nt is much larger than p, the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging for which relatively short time-series are measured over thousands of voxels. Methods are introduced for dealing with this situation by using sparse MAR models. These can be estimated in a two-stage process involving (i) penalized regression and (ii) pruning of unlikely connections by means of the local false discovery rate developed by Efron. Extensive simulations were performed with idealized cortical networks having small world topologies and stable dynamics. These show that the detection efficiency of connections of the proposed procedure is quite high. Application of the method to real data was illustrated by the identification of neural circuitry related to emotional processing as measured by BOLD.

Effects of spatial selective attention on the steady-state visual evoked potential in the 20-28 Hz range.

Steady-state visual evoked potentials (SSVEPs) were recorded from the scalp of subjects who attended to a flickering LED display in one visual field while ignoring a similar display (flickering at a different frequency) in the opposite visual field. The flicker frequencies were 20.8 Hz in the left-field display and 27.8 Hz in the right-field display. The SSVEP to the flicker in either field was enhanced in amplitude when attention was directed to its location. The scalp distribution of this SSVEP enhancement was narrowly focused over the posterior scalp contralateral to the visual field of stimulation. A source analysis using Variable Resolution Electromagnetic Tomography (VARETA) indicated that the source current densities for the SSVEP attention effect had a focal origin in the contralateral parieto-occipital cortex.

Effective connectivity: Influence, causality and biophysical modeling

This is the final paper in a Comments and Controversies series dedicated to “The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution”. We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener–Akaike–Granger–Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.

Bayesian model averaging in EEG/MEG imaging.

In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular low-resolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA).

3D Statistical Parametric Mapping of EEG Source Spectra by Means of Variable Resolution Electromagnetic Tomography (VARETA)

This article describes a new method for 3D QEEG tomography in the frequency domain. A variant of Statistical Parametric Mapping is presented for source log spectra. Sources are estimated by means of a Discrete Spline EEG inverse solution known as Variable Resolution Electromagnetic Tomography (VARETA). Anatomical constraints are incorporated by the use of the Montreal Neurological Institute (MNI) probabilistic brain atlas. Efficient methods are developed for frequency domain VARETA in order to estimate the source spectra for the set of 103–105 voxels that comprise an EEG/MEG inverse solution. High resolution source Z spectra are then defined with respect to the age dependent mean and standard deviations of each voxel, which are summarized as regression equations calculated from the Cuban EEG normative database. The statistical issues involved are addressed by the use of extreme value statistics. Examples are shown that illustrate the potential clinical utility of the methods herein developed.

Feature-selective attention enhances color signals in early visual areas of the human brain

We used an electrophysiological measure of selective stimulus processing (the steady-state visual evoked potential, SSVEP) to investigate feature-specific attention to color cues. Subjects viewed a display consisting of spatially intermingled red and blue dots that continually shifted their positions at random. The red and blue dots flickered at different frequencies and thereby elicited distinguishable SSVEP signals in the visual cortex. Paying attention selectively to either the red or blue dot population produced an enhanced amplitude of its frequency-tagged SSVEP, which was localized by source modeling to early levels of the visual cortex. A control experiment showed that this selection was based on color rather than flicker frequency cues. This signal amplification of attended color items provides an empirical basis for the rapid identification of feature conjunctions during visual search, as proposed by “guided search” models.

Model driven EEG/fMRI fusion of brain oscillations

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post‐synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL‐algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL‐innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible. Hum Brain Mapp, 2009.