Ramesh Srinivasan

Electric Fields of the Brain: The Neurophysics of EEG

1. The physics-EEG interface 2. Fallacies in EEG 3. An overview of electromagnetic fields 4. Electric fields and currents in biological tissue 5. Current sources in a homogeneous and isotropic medium 6. Current sources in inhomogeneous and isotropic media 7. Recording strategies, reference issues, and dipole localization 8. High-resolution EEG 9. Measures of EEG dynamic properties 10. Spatial-temporal properties of EEG 11. Neocortical dynamics, EEG, and cognition APPENDICES A. Introduction to the calculus of vector fields B. Quasi-static reduction of Maxwells equations C. Surface magnetic field due to a dipole at an arbitrary location in a volume conductor D. Derivation of the membrane diffusion equation E. Solutions to the membrane diffusion equation F. Point source in a five layered plane medium G. Radial dipole and dipole layer inside the 4-sphere model H. Tangential dipole inside concentric spherical shells I. Spherical harmonics J. The spline Laplacian K. Impressed currents and cross-scale relations in volume conductors L. Outline of neocortical dynamic global theory

A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging

Two different methods to improve the spatial resolution of EEG are discussed: the surface Laplacian (e.g., current source density) and cortical imaging (e.g., spatial deconvolution). The former methods tend to be independent of head volume conductor model, whereas the latter methods are more model-dependent. Computer simulation of scalp potentials due to either a few isolated sources or 4200 distributed cortical sources and studies of actual EEG data both indicate that the two methods provide similar estimates of cortical potential distribution. Typical correlation coefficients between either spline-Laplacian or cortical image and simulated (calculated) cortical potential are in the 0.8-0.95 range, depending partly on CSF thickness. By contrast, correlation coefficients between simulated scalp and cortical potential are in the 0.4-0.5 range, suggesting that high resolution methods provide much better estimates of cortical potential than is obtained with conventional EEG. The two methods are also applied to steady-state visually evoked potentials and spontaneous EEG. Correlation coefficients obtained from real EEG data are in the same general ranges as correlations obtained from simulations. The new high resolution methods can provide a dramatic increase in the information content of EEG and appear to have widespread application in both clinical and cognitive studies.

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.

Spatial filtering and neocortical dynamics: estimates of EEG coherence

The spatial statistics of scalp electroencephalogram (EEG) are usually presented as coherence in individual frequency bands. These coherences result both from correlations among neocortical sources and volume conduction through the tissues of the head. The scalp EEG is spatially low-pass filtered by the poorly conducting skull, introducing artificial correlation between the electrodes. A four concentric spheres (brain, CSF, skull, and scalp) model of the head and stochastic field theory are used here to derive an analytic estimate of the coherence at scalp electrodes due to volume conduction of uncorrelated source activity, predicting that electrodes within 10-12 cm can appear correlated. The surface Laplacian estimate of cortical surface potentials spatially bandpass filters the scalp potentials reducing this artificial coherence due to volume conduction. Examination of EEG data confirms that the coherence estimates from raw scalp potentials and Laplacians are sensitive to different spatial bandwidths and should be used in parallel in studies of neocortical dynamic function.

EEG coherency II: experimental comparisons of multiple measures.

OBJECTIVE A concentric spheres model was used in an earlier paper to estimate the effects of volume conduction, reference electrode and spatial filtering on different EEG coherence measures. EEG data are used here to verify theoretical predictions. METHODS Three EEG data sets were: (1) 64 channel, recorded during 7 alternating periods of resting and mental calculation. (2) 128 channel, for comparison of eyes open versus eyes closed coherence. (3) 128 channel, recorded during deep sleep (stages 3 and 4) and REM. RESULTS The directions of large scale (lobeal) coherency changes between brain states are relatively independent of coherence measure. However, coherence between specific electrode pairs is sensitive to method and frequency. Average reference and digitally linked mastoids provide reasonable semi-quantitative estimates of large-scale neocortical source coherence. Close bipolar, Laplacian, and dura image methods remove most reference electrode and volume conduction distortion, but may underestimate coherence by spatial filtering. CONCLUSION Each EEG coherence method has its own potential sources of error and provides coherence estimates for different neural population sizes located in different locations. Thus, studies of coherence and brain state should include several different kinds of estimates to take full advantage of information in recorded signals.

Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials

SummaryThe electroencephalogram (EEG) is recorded by sensors physically separated from the cortex by resistive skull tissue that smooths the potential field recorded at the scalp. This smoothing acts as a low-pass spatial filter that determines the spatial bandwidth, and thus the required spatial sampling density, of the scalp EEG. Although it is better appreciated in the time domain, the Nyquist frequency for adequate discrete sampling is evident in the spatial domain as well. A mathematical model of the low-pass spatial filtering of scalp potentials is developed, using a four concentric spheres (brain, CSF, skull, and scalp) model of the head and plausible estimates of the conductivity of each tissue layer. The surface Laplacian estimate of radial skull current density or cortical surface potential counteracts the low-pass filtering of scalp potentials by shifting the spatial spectrum of the EEG, producing a band-passed spatial signal that emphasizes local current sources. Simulations with the four spheres model and dense sensor arrays demonstrate that progressively more detail about cortical potential distribution is obtained as sampling is increased beyond 128 channels.

Estimating the spatial Nyquist of the human EEG

The discrete sampling of the brain’s electrical field at the scalp surface with individual recording sensors is subject to the same sampling error as the discrete sampling of the time series at any one sensor with analog-to-digital conversion. Unlike temporal sampling, spatial sampling is intrinsically discrete, so that the post hoc application of analog anti-aliasing filters is not possible. However, the skull acts as a low-pass spatial filter of the brain’s electrical field, attenuating the high spatial frequency information. Because of the skull’s spatial filtering, a discrete sampling of the spatial field with a reasonable number of scalp electrodes is possible. In this paper, we provide theoretical and experimental evidence that adequately sampling the human electroencephalograph (EEG) across the full surface of the head requires a minimum of 128 sensors. Further studies with each of the major EEG and event-related potential phenomena are required in order to determine the spatial frequency of these phenomena and in order to determine whether additional increases in sensor density beyond 128 channels will improve the spatial resolution of the scalp EEG.

Spatial structure of the human alpha rhythm: global correlation in adults and local correlation in children

OBJECTIVE The maturation of the neocortex during childhood and adolescence involves dramatic increases in white-matter volume. EEG recordings from children and adults were examined to determine whether there are associated changes in spatial properties of dynamic processes in the neocortex. METHODS Spontaneous eyes-closed and eyes-open EEG were recorded at 128 electrodes in 20 children aged 6-11 years and 23 adults aged 18-23 years. The surface Laplacian algorithm was applied to improve the spatial resolution of each electrode. Power and coherence were used to characterize the spatial structure of the alpha rhythm. A stochastic field model was used to eliminate coherences that are inflated due to volume conduction. RESULTS In adults, the alpha rhythm is characterized by very high coherence between distant electrodes. The children demonstrated reduced anterior power and coherence between anterior and posterior electrodes at the peak alpha frequency in comparison to the adults. The Laplacian alpha rhythm demonstrated much higher power in the children at both anterior and posterior electrodes, but was weakly correlated between electrodes. CONCLUSIONS The maturation of neocortex in late childhood involves increased global correlation by long-range corticocortical connections. The local correlation that contributes power to each electrode, independent of other electrodes, is reduced as the global correlation increases.

Steady-State Visual Evoked Potentials: Distributed Local Sources and Wave-Like Dynamics Are Sensitive to Flicker Frequency

Summary: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.

Resting-state cortical connectivity predicts motor skill acquisition

Many studies have examined brain states in an effort to predict individual differences in the capacity for learning, with overall moderate results. The present study investigated how measures of cortical network function acquired at rest using dense-array EEG (256 leads) predict subsequent acquisition of a new motor skill. Brain activity was recorded in 17 healthy young subjects during 3min of wakeful rest prior to a single motor skill training session on a digital version of the pursuit rotor task. Practice was associated with significant gains in task performance (% time on target increased from 24% to 41%, p<0.0001). Using a partial least squares regression (PLS) model, coherence with the region of the left primary motor area (M1) in resting EEG data was a strong predictor of motor skill acquisition (R(2)=0.81 in a leave-one-out cross-validation analysis), exceeding the information provided by baseline behavior and demographics. Within this PLS model, greater skill acquisition was predicted by higher connectivity between M1 and left parietal cortex, possibly reflecting greater capacity for visuomotor integration, and by lower connectivity between M1 and left frontal-premotor areas, possibly reflecting differences in motor planning strategies. EEG coherence, which reflects functional connectivity, predicts individual motor skill acquisition with a level of accuracy that is remarkably high compared to prior reports using EEG or fMRI measures.