Paul L. Nunez

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

Neocortical Dynamics and Human EEG Rhythms

1: Paul Nunez: Quantitative states of neocortex. 2: Paul Nunez: Towards a physics of neocortex. 3: Paul Nunez: Mind, brain and EEG. 4: Kenneth L. Pilgreen: Physiological, medical and cognitive correlates of EEG. 5: Fernando H. Lopes da Silva: Dynamics of electrical activity of the brain, local networks and modulating systems. 6: Richard B. Silberstein: Steady state visually evoked potentials, brain resonance and cognitive processes. 7: Alan Gevins and Brian Cutillo: Neuroelectric measures of mind. 8: Paul Nunez: Discrete linear systems of physics and brain. 9: Paul Nunez: Continuous linear systems of physics and brain. 10: Paul Nunez: Nonlinear phenomena and chaos. 11: Paul Nunez: Global contribution to EEG dynamics. 12: Paul Nunez: Experimental connections between EEG data and the global wave theory. 13: Lester Ingber: Statistical mechanics of multiple scales of neocortical interactions

Spatial-temporal structures of human alpha rhythms: theory, microcurrent sources, multiscale measurements, and global binding of local networks

A theoretical framework supporting experimental measures of dynamic properties of human EEG is proposed with emphasis on distinct alpha rhythms. Robust relationships between measured dynamics and cognitive or behavioral conditions are reviewed, and proposed physiological bases for EEG at cellular levels are considered. Classical EEG data are interpreted in the context of a conceptual framework that distinguishes between locally and globally dominated dynamic processes, as estimated with coherence or other measures of phase synchronization. Macroscopic (scalp) potentials generated by cortical current sources are described at three spatial scales, taking advantage of the columnar structure of neocortex. New EEG data demonstrate that both globally coherent and locally dominated behavior can occur within the alpha band, depending on narrow band frequency, spatial measurement scale, and brain state. Quasi‐stable alpha phase structures consistent with global standing waves are observed. At the same time, alpha and theta phase locking between cortical regions during mental calculations is demonstrated, consistent with neural network formation. The brain‐binding problem is considered in the context of EEG dynamic behavior that generally exhibits both of these local and global aspects. But specific experimental designs and data analysis methods may severely bias physiological interpretations in either local or global directions. Hum. Brain Mapping 13:125–164, 2001.

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.

On the Relationship of Synaptic Activity to Macroscopic Measurements: Does Co-Registration of EEG with fMRI Make Sense?

A two-scale theoretical description outlines relationships between brain current sources and the resulting extracranial electric field, recorded as EEG. Finding unknown sources of EEG, the so-calledg “inverse problem”, is discussed in general terms, with emphasis on the fundamental non-uniqueness of inverse solutions. Hemodynamic signatures, measured with fMRI, are expressed as voxel integrals to facilitate comparisons with EEG. Two generally distinct cell groups (1 and 2), generating EEG and fMRI signals respectively, are embedded within the much broader class of synaptic action fields. Cell groups 1 and 2 may or may not overlap in specific experiments. Implications of this incomplete overlap for co-registration studies are considered. Each experimental measure of brain function is generally sensitive to a different kind of source activity and to different spatial and temporal scales. Failure to appreciate such distinctions can exacerbate conflicting views of brain function that emphasize either global integration or functional localization.

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.

The Spline-Laplacian in clinical neurophysiology : A method to improve EEG spatial resolution

An important goal of EEG research is to obtain practical methods to improve the spatial resolution of scalp-recorded potentials, i.e., to make surface data more accurately represent local underlying brain sources. This goal may be somewhat different from that of “localizing brain activity with EEG,” since the latter approach often involves prior assumptions about the nature of sources. In this paper, we demonstrate the spline-Laplacian, a relatively new approach that can yield dramatic improvement in spatial resolution when average electrode spacing is less than about 3 cm. This approach is mostly independent of assumptions about sources and models of the head. The demonstration involves computer simulations, evoked potentials, normal spontaneous EEG, and epileptic spikes.

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.

The brain wave equation: a model for the EEG

Abstract Both spontaneous and evoked potentials measured on the surface of the head are believed due to postsynaptic potentials in vertically oriented neurons in the cortex. Potential differences between surface locations at any given time are due to the instantaneous difference in synaptic activity between the corresponding vertical regions. Because of the high correlation of activity between regions separated by distances large compared to the radius of influence of single neurons, communication between these locations must be by means of action potentials. In order to quantify the dynamics of interaction of 10 10 cortical neurons, use is made of the concept of a neural mass. The neural mass consists of sufficiently large number of neurons so as to exhibit certain average properties which are independent of its exact inner circuitry. An integral wave equation is derived to describe the spatial-temporal variation of cortical potential. Solutions are obtained indicating that electrical oscillations, which are independent of the location and time history of subcortical input, can persist in the cortex. The nature of these oscillations depends on the relative abundance of excitatory and inhibitory connections between neural masses and on the physiological state of the brain. The latter is partially determined by velocity distribution functions for action potential propagation. A dispersion relation for brain waves is shown to exist for certain ranges of the connection parameters. In some limiting cases, weakly damped waves occur with ω = ck , where c refers to a characteristic velocity for the distribution functions. Preliminary experiments indicate qualitative agreement with this result.