Multi-Scale Neural Sources of EEG: Genuine, Equivalent, and Representative. A Tutorial Review.

A biophysical framework needed to interpret electrophysiological data recorded at multiple spatial scales of brain tissue is developed. Micro current sources at membrane surfaces produce local field potentials, electrocorticography, and electroencephalography (EEG). We categorize multi-scale sources as genuine, equivalent, or representative. Genuine sources occur at the micro scale of cell surfaces. Equivalent sources provide identical experimental outcomes over a range of scales and applications. In contrast, each representative source distribution is just one of many possible source distributions that yield similar experimental outcomes. Macro sources ("dipoles") may be defined at the macrocolumn (mm) scale and depend on several features of the micro sources-magnitudes, micro synchrony within columns, and distribution through the cortical depths. These micro source properties are determined by brain dynamics and the columnar structure of cortical tissue. The number of representative sources underlying EEG data depends on the spatial scale of neural tissue under study. EEG inverse solutions (e.g. dipole localization) and high resolution estimates (e.g. Laplacian, dura imaging) have both strengths and limitations that depend on experimental conditions. The proposed theoretical framework informs studies of EEG source localization, source characterization, and low pass filtering. It also facilitates interpretations of brain dynamics and cognition, including measures of synchrony, functional connections between cortical locations, and other aspects of brain complexity.

EEG functional connectivity, axon delays and white matter disease.

OBJECTIVE: Both structural and functional brain connectivities are closely linked to white matter disease. We discuss several such links of potential interest to neurologists, neurosurgeons, radiologists, and non-clinical neuroscientists. METHODS: Treatment of brains as genuine complex systems suggests major emphasis on the multi-scale nature of brain connectivity and dynamic behavior. Cross-scale interactions of local, regional, and global networks are apparently responsible for much of EEG's oscillatory behaviors. Finite axon propagation speed, often assumed to be infinite in local network models, is central to our conceptual framework. RESULTS: Myelin controls axon speed, and the synchrony of impulse traffic between distant cortical regions appears to be critical for optimal mental performance and learning. Several experiments suggest that axon conduction speed is plastic, thereby altering the regional and global white matter connections that facilitate binding of remote local networks. CONCLUSIONS: Combined EEG and high resolution EEG can provide distinct multi-scale estimates of functional connectivity in both healthy and diseased brains with measures like frequency and phase spectra, covariance, and coherence. SIGNIFICANCE: White matter disease may profoundly disrupt normal EEG coherence patterns, but currently these kinds of studies are rare in scientific labs and essentially missing from clinical environments.

Neocortical dynamics due to axon propagation delays in cortico-cortical fibers: EEG traveling and standing waves with implications for top-down influences on local networks and white matter disease.

The brain is treated as a nested hierarchical complex system with substantial interactions across spatial scales. Local networks are pictured as embedded within global fields of synaptic action and action potentials. Global fields may act top-down on multiple networks, acting to bind remote networks. Because of scale-dependent properties, experimental electrophysiology requires both local and global models that match observational scales. Multiple local alpha rhythms are embedded in a global alpha rhythm. Global models are outlined in which cm-scale dynamic behaviors result largely from propagation delays in cortico-cortical axons and cortical background excitation level, controlled by neuromodulators on long time scales. The idealized global models ignore the bottom-up influences of local networks on global fields so as to employ relatively simple mathematics. The resulting models are transparently related to several EEG and steady state visually evoked potentials correlated with cognitive states, including estimates of neocortical coherence structure, traveling waves, and standing waves. The global models suggest that global oscillatory behavior of self-sustained (limit-cycle) modes lower than about 20 Hz may easily occur in neocortical/white matter systems provided: Background cortical excitability is sufficiently high; the strength of long cortico-cortical axon systems is sufficiently high; and the bottom-up influence of local networks on the global dynamic field is sufficiently weak. The global models provide "entry points" to more detailed studies of global top-down influences, including binding of weakly connected networks, modulation of gamma oscillations by theta or alpha rhythms, and the effects of white matter deficits.

Top-down influences on local networks: basic theory with experimental implications.

The response of a population of cortical neurons to an external stimulus depends not only on the receptive field properties of the neurons, but also the level of arousal and attention or goal-oriented cognitive biases that guide information processing. These top-down effects on cortical neurons bias the output of the neurons and affect behavioral outcomes such as stimulus detection, discrimination, and response time. In any physiological study, neural dynamics are observed in a specific brain state; the background state partly determines neuronal excitability. Experimental studies in humans and animal models have also demonstrated that slow oscillations (typically in the alpha or theta bands) modulate the fast oscillations (gamma band) associated with local networks of neurons. Cross-frequency interaction is of interest as a mechanism for top-down or bottom up interactions between systems at different spatial scales. We develop a generic model of top-down influences on local networks appropriate for comparison with EEG. EEG provides excellent temporal resolution to investigate neuronal oscillations but is space-averaged on the cm scale. Thus, appropriate EEG models are developed in terms of population synaptic activity. We used the Wilson-Cowan population model to investigate fast (gamma band) oscillations generated by a local network of excitatory and inhibitory neurons. We modified the Wilson-Cowan equations to make them more physiologically realistic by explicitly incorporating background state variables into the model. We found that the population response is strongly influenced by the background state. We apply the model to reproduce the modulation of gamma rhythms by theta rhythms as has been observed in animal models and human ECoG and EEG studies. The concept of a dynamic background state presented here using the Wilson-Cowan model can be readily applied to incorporate top-down modulation in more detailed models of specific cortical systems.

Neocortical dynamics at multiple scales: EEG standing waves, statistical mechanics, and physical analogs.

The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model.

Implications of white matter correlates of EEG standing and traveling waves.

This letter addresses the recent paper titled "White matter architecture rather than cortical surface area correlates with the EEG alpha rhythm" (Valdés-Hernández et al., 2009) and takes issue with some of its conclusions. I suggest here that the standing wave model cited by the authors provides a robust connection to a restricted class of genuine EEG experiments. The alpha band actually consists of a mixture of distinct phenomena; the standing wave model applies only to the distributed and coherent (global) part. New approaches are suggested that may either refute or support competing dynamic models of EEG and can have major impacts on the experimental design of new cognitive studies.

Identification of wave-like spatial structure in the SSVEP: comparison of simultaneous EEG and MEG.

Steady-state visual-evoked potentials/fields (SSVEPs/SSVEFs) are used in cognitive and clinical electroencephalogram (EEG) and magnetoencephalogram (MEG) studies because of their excellent signal-to-noise ratios and relative immunity to artifact. Steady-state paradigms are also used to characterize preferred frequencies of dynamic neocortical processes. In this study, SSVEPs and SSVEFs were simultaneously recorded while subjects viewed checkerboard patterns alternating (black to white, white to black) with fixed driving frequency between 2 and 20 Hz. Distinct peaks in SSVEP/SSVEF power were observed in the theta (4-8 Hz) and upper alpha (10-14 Hz) bands. A distinct peak in SSVEP power was also observed in the beta band (between 15 and 20 Hz) which had no counterpart in the MEG. One-dimensional spatial spectra indicate that distinct large-scale source distributions contribute to SSVEP power in the upper alpha band in the form of long wavelength (lambda>20 cm) traveling waves propagating from occipital to prefrontal electrodes. In the beta band, spatial spectra and SSVEF indicate that long-wavelength source distributions over posterior and anterior regions form standing wave patterns. These results suggest that simple models of SSVEP based on a single dipole source in the occipital lobe are inadequate to explain the dynamic spatial patterns of SSVEP magnitude and phase. Theoretical models of SSVEP should include multiple local and distributed sources and exhibit both traveling and standing wave dynamics.

EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics.

We contrasted coherence estimates obtained with EEG, Laplacian, and MEG measures of synaptic activity using simulations with head models and simultaneous recordings of EEG and MEG. EEG coherence is often used to assess functional connectivity in human cortex. However, moderate to large EEG coherence can also arise simply by the volume conduction of current through the tissues of the head. We estimated this effect using simulated brain sources and a model of head tissues (cerebrospinal fluid (CSF), skull, and scalp) derived from MRI. We found that volume conduction can elevate EEG coherence at all frequencies for moderately separated (<10 cm) electrodes; a smaller levation is observed with widely separated (>20 cm) electrodes. This volume conduction effect was readily observed in experimental EEG at high frequencies (40-50 Hz). Cortical sources generating spontaneous EEG in this band are apparently uncorrelated. In contrast, lower frequency EEG coherence appears to result from a mixture of volume conduction effects and genuine source coherence. Surface Laplacian EEG methods minimize the effect of volume conduction on coherence estimates by emphasizing sources at smaller spatial scales than unprocessed potentials (EEG). MEG coherence estimates are inflated at all frequencies by the field spread across the large distance between sources and sensors. This effect is most apparent at sensors separated by less than 15 cm in tangential directions along a surface passing through the sensors. In comparison to long-range (>20 cm) volume conduction effects in EEG, widely spaced MEG sensors show smaller field-spread effects, which is a potentially significant advantage. However, MEG coherence estimates reflect fewer sources at a smaller scale than EEG coherence and may only partially overlap EEG coherence. EEG, Laplacian, and MEG coherence emphasize different spatial scales and orientations of sources.

Comparison of the effect of volume conduction on EEG coherence with the effect of field spread on MEG coherence.

We analyzed models of volume conduction and magnetic field spread to account for aspects of spatial structure in electroencephalographic (EEG) and magnetoencephalographic (MEG) coherence. The head volume conduction model consisted of three confocal ellipsoids, representing three layers (brain, skull, and scalp) with different tissue conductivities, while the magnetic field model follows from the Biot-Savart law in a spherically symmetric medium. Source models were constructed based on magnetic resonance imaging data from three subjects, approximating neocortical current source distributions as dipoles oriented perpendicular to the local cortical surface. Assuming that every source is uncorrelated to every other source, coherence between sensors due to volume conduction and field-spread effects was estimated. Spatial properties of the model coherences were then compared with simultaneously recorded spontaneous EEG and MEG. In both models and experimental data, EEG and MEG coherence was elevated between closely spaced channels. At very large channel separations, the field-spread effect on MEG coherence appears smaller than the volume conduction effect on EEG coherence. In EEG coherence studies, surface Laplacian methods can be used to remove volume conduction effects. With single-coil magnetometers, MEG coherences are free of field effects only for sensor pairs separated by more than 20 cm. Model coherences resemble most high-frequency (e.g. >20 Hz) data; volume conduction and field-spread effects are independent of frequency, suggesting mostly uncorrelated sources in these bands. High-frequency EEG and MEG coherence can evidently serve as an estimate of coherence effects due to volume conduction and field effects, when source and head models are not available for individual subjects.

Source analysis of EEG oscillations using high-resolution EEG and MEG.

We investigated spatial properties of the source distributions that generate scalp electroencephalographic (EEG) oscillations. The inherent complexity of the spatio-temporal dynamics of EEG oscillations indicates that conceptual models that view source activity as consisting only of a few "equivalent dipoles" are inadequate. We present an approach that uses volume conduction models to characterize the distinct spatial filtering of cortical source activity by average reference EEG, high-resolution EEG, and magnetoencephalography (MEG). By comparing these three measures, we can make inferences about the sources of EEG oscillations without having to make prior assumptions about the sources. We apply this approach to spontaneous EEG oscillations observed with eyes closed at rest. Both EEG and MEG recordings show robust alpha rhythms over posterior regions of the cortex; however, the dominant frequency of these rhythms varies between EEG and MEG recordings. Frontal alpha and theta rhythms are generated almost exclusively by superficial radial dipole layers that generate robust EEG signals but very little MEG signals; these sources are presumably mainly in the gyral crowns of frontal cortex. MEG and high-resolution EEG estimates of alpha rhythms provide evidence of local tangential and radial sources in the posterior cortex, lying mainly on sulcal and gyral surfaces. Despite the detailed information about local radial and tangential sources potentially afforded by high-resolution EEG and MEG, it is also evident that the alpha and theta rhythms receive contributions from non-local source activity, for instance large dipole layers distributed over lobeal or (potentially) even larger spatial scales.

A theoretical basis for standing and traveling brain waves measured with human EEG with implications for an integrated consciousness.

OBJECTIVE: We propose a theoretical framework for EEG and evoked potential studies based on the single postulate that these data are composed of a combination of waves (as this term is used in the physical sciences) and thalamocortical network activity. METHODS: Using known properties of traveling and standing waves, independent of any neocortical dynamic theory, our simple postulate leads to experimental predictions, several of which have now been verified. A mathematical-physiological theory of "brain waves" based on known (but highly idealized) properties of cortical synaptic action and corticocortical fibers is used to support the framework. RESULTS: Brain waves are predicted with links between temporal frequencies and the spatial distributions of synaptic activity. Such dispersion relations, which essentially define more general phenomena as waves, are shown to restrict the spatial-temporal dynamics of synaptic action with many experimental EEG consequences. CONCLUSIONS: The proposed framework accounts for several salient features of spontaneous EEG and evoked potentials. SIGNIFICANCE: We conjecture that wave-like behavior of synaptic action may facilitate interactions between remote cell assemblies, providing an important mechanism for the functional integration underlying conscious experience.

Steady-state visual evoked potentials: distributed local sources and wave-like dynamics are sensitive to flicker frequency.

Steady-state visual evoked potentials (SSVEPs) are used in cognitive and clinical studies of brain function because of excellent signal-to-noise ratios and relative immunity to artifacts. SSVEPs also provide a means to characterize preferred frequencies of neocortical dynamic processes. In this study, SSVEPs were recorded with 110 electrodes while subjects viewed random dot patterns flickered between 3 and 30 Hz. Peaks in SSVEP power were observed at delta (3 Hz), lower alpha (7 and 8 Hz), and upper alpha band (12 and 13 Hz) frequencies; the spatial distribution of SSVEP power is also strongly dependent on the input frequency suggesting cortical resonances. We characterized the cortical sources that generate SSVEPs at different input frequencies by applying surface Laplacians and spatial spectral analysis. Laplacian SSVEPs recorded are sensitive to small changes (1-2 Hz) in the input frequency at occipital and parietal electrodes indicating distinct local sources. At 10 Hz, local source activity occurs in multiple cortical regions; Laplacian SSVEPs are also observed in lateral frontal electrodes. Laplacian SSVEPs are negligible at many frontal electrodes that elicit strong potential SSVEPs at delta, lower alpha, and upper alpha bands. One-dimensional (anterior-posterior) spatial spectra indicate that distinct large-scale source distributions contribute SSVEP power in these frequency bands. In the upper alpha band, spatial spectra indicate the presence of long-wavelength (> 15 cm) traveling waves propagating from occipital to prefrontal electrodes. In the delta and lower alpha band, spatial spectra indicate that long-wavelength source distributions over posterior and anterior regions form standing-wave patterns. These results suggest that the SSVEP is generated by both (relatively stationary) localized sources and distributed sources that exhibit characteristics of wave phenomena.

Dynamic sculpting of brain functional connectivity is correlated with performance.

In this study, we examined the relationship between cortical coupling, reflected in event related partial coherence (ERPC) and cognitive processing speed while subjects performed a set of Raven's Progressive Matrices (RPM), a task used to measure IQ. Fifty-five participants (29 males) performed a computerized version of the RPM where they were required to identify the shape (probe) that is consistent with a matrix of displayed shapes. Participants indicated a match or non-match by pressing a micro-switch with either the right or left hand. The steady state visually evoked potential (SSVEP) was elicited by a 13 Hz uniform visual flicker superimposed over the visual fields and the SSVEP event-related coherence (SSVEP-ERPC) calculated for all 2016 unique electrode pairs. The linear correlation between SSVEP-ERPC and processing speed (the inverse of reaction time) was calculated for all electrode pairs for all time points during the 3 sec interval that the probes were on the screen. Using correlation coeffident thresholds corresponding to p=0.001 we identified those electrode pairs where SSVEP-ERPC or neural synchronization was significantly correlated with processing speed. At a point 0.8 sec before the appearance of the probe we observed that the synchronization between specific prefrontal, frontal and central sites was correlated with processing speed. We suggest that this relationship may reflect the efficiency of working memory processes and speed of information processing.

Fronto-parietal evoked potential synchronization is increased during mental rotation.

We used steady state visually evoked potential event related partial coherence (SSVEP-ERPC) to examine the SSVEP synchronization between brain regions while 22 males undertook a sequential version of the Shepard and Metzler mental rotation task. Compared to the 60 degrees rotation, the 180 degrees rotation was associated with increased synchronization between bilateral prefrontal and parieto-occipital sites, between left frontal and right parietal sites and between bilateral parietal and occipital sites. We suggest that the increased synchronization between prefrontal and parieto-occipital regions may be associated with the working memory components of the task, while the left frontal to right parietal synchronization may represent the increased interaction between these regions thought to occur in a variety of visuo-motor tasks.

Implications of recording strategy for estimates of neocortical dynamics with electroencephalography.

Neocortical dynamics evidently involves very complex, nonlinear processes including top-down and bottom-up interactions across spatial scales. The dynamics may also be strongly influenced by global (periodic) boundary conditions. The primary experimental measure of human neocortical dynamics at short time scales ( approximately few ms) is the scalp electroencephalogram (EEG). It is shown that different recording and data analysis strategies are sensitive to different parts of the spatial spectrum. Thus experimental measures of system dynamics (e.g., correlation dimension estimates) can generally be expected to depend on experimental method. These ideas are illustrated in two ways: a large scale, quasilinear theory of neocortical dynamics in which standing wave phenomenon occur with predicted frequencies in the general range of EEG, and a relatively simple nonlinear physical system consisting of a linear string with attached nonlinear springs. The string/springs system is integrated numerically to illustrate transitions from periodic to chaotic behavior as mesoscopic nonlinear influences dominate macroscopic linear effects. The implications of these results for new theories of neocortical dynamics, experimental estimates of dynamic properties, and cognitive EEG studies are considered.