Paul Nunez

• Tulane University

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. Treatment of brains as genuine complex systems suggests major emphasis on the multi-scale nature of brain connectivity and...

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, experimen...

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 o...

This chapter aims to provide the basic information needed for effective users of electric- or magnetic-field recording methods in brain-computer interface research and development. It addresses the generation, distribution, and detection of these fields on micro-, meso-, and macroscales, thereby accounting for the multiscale structure of brain tiss...

In this chapter, human brains are treated as preeminent complex systems with consciousness assumed to emerge from dynamic interactions within and between brain subsystems. Given this basic premise, the chapter first focuses on general brain features underlying such complexity and, by implication, the emergence of consciousness. Next, it outlines so...

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 syste...

Kayser and Tenke (2010) provide a nice history and editorial review of the critical EEG reference electrode issue and critique of REST, the reference electrode standardization technique, apparently first implemented by Yao (Yao, 2001; Yao et al, 2005; Qin et al, 2010). For many years, EEG scientists seemed to insist (based on both word and deed) th...

In the early 1990s, Wolf Singer advanced a very provocative idea: Different features of an animal’s world are represented by distinct cell assemblies that can be bound together by oscillatory synchrony (Singer 1993; Singer and Gray 1995). In particular, simultaneous recordings from animal visual, association, somatosensory, and motor areas reveal t...

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...

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...

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 proce...

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,...

Human brains exhibit complex dynamic behaviour measured by external recordings of electric (EEG) and magnetic fields (MEG). These data reveal synaptic field oscillations in neocortex at millisecond temporal and centimetre spatial scales. We suggest that the neural networks underlying behaviour and cognition may be viewed as embedded in these synapt...

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. Using known properties of traveling and standing waves, independent of any neocortical dynamic theory, our...

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...

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...

This chapter demonstrates the relationship of current sources to recorded potentials in volume conductors using a simple salt water fish tank experiment consisting of a dipole current source and separate measuring circuit. In such a conductive medium, the behavior of potentials is determined only by the geometric arrangement of current sources and...

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 requ...

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 synchronizat...

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° rotation, the 180° rotation was associated with increased synchronization between bi...

We demonstrate an application of spherical harmonic decomposition to the analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to the analysis of hemispherical, irregularly sampled data. Spatial sampling requirements and performance of the methods are quantified using simulated data. The analysis is...

The steady state visually evoked potential (SSVEP) elicited by a diffuse 13-Hz visual flicker was recorded from 64 scalp sites in 30 subjects performing a low and high demand version of an object working memory task. During the perceptual component of the task, the SSVEP amplitude was reduced at left and right parieto-occipital sites. During the ho...

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 interp...

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, measur...

A general conceptual framework for large-scale neocortical dynamics based on data from many laboratories is applied to a variety of experimental designs, spatial scales, and brain states. Partly distinct, but interacting local processes (e.g., neural networks) arise from functional segregation. Global processes arise from functional integration and...

EEG and synaptic action fields provide experimental and theoretical entry points into brain complexity. Such entry is distinguished from the core system of cell assemblies assumed to underlie cognitive processing. The global theory of synaptic action predicts several new properties of EEG, providing limited penetration into brain complexity.

We present high-resolution path-integral calculations of a previously developed model of short-term memory in neocortex. These calculations, made possible with supercomputer resources, supplant similar calculations made in L. Ingber, Phys. Rev. E 49, 4652 (1994), and support coarser estimates made in L. Ingber, Phys. Rev. A 29, 3346 (1984). We also...

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. Three EEG data sets were: (1) 64 channel, recorded during 7 alternating periods of resting and mental calculati...

Human brains are information processing systems of vast complexity. Over the past century and especially over the past few decades, our understanding of brain function at small scales has grown substantially. For example, we know many new properties of neurotransmitters, synapses, membranes, and neurons. Higher brain functions involving the thought...

The author discusses a conceptual framework emphasizing spatial scales. He considers the following topics: experimental EEG and mental states; the neocortex; local/global theory of large-scale neocortical dynamics; experimental connections to theory

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 artifici...

A conceptual framework for neocortical dynamic behavior is proposed to embrace brain theories applied to different experimental designs, spatial scales, and brain states. Neocortical dynamics and correlated behavioral/cognitive brain states are viewed as distinct, but interacting local (regionally specific) processes and globally coherent dynamics....

Several methodological issues which impact experimental design and physiological interpretations in EEG coherence studies are considered, including reference electrode and volume conduction contributions to erroneous coherence estimates. A new measure, `reduced coherency', is introduced as the difference between measured coherency and the coherency...

Well-posed questions about information processing may require physiologically based, quantitative models of large scale neocortical dynamic function. “Synchronization” of this dynamics can be viewed in different contexts of the binding problem.

Several methodological issues which impact experimental design and physiological interpretations in EEG coherence studies are considered, including reference electrode and volume conduction contributions to erroneous coherence estimates. A new measure, `reduced coherency', is introduced as the difference between measured coherency and the coherency...

The 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 a...

Multiscale dynamics, linear approximations, global boundary conditions, experimental verification, and global influences on local cell assemblies are considered in the context of Wright & Liley's work. W&L provide a nice introduction to these issues and a reasonable simulation of intermediate scale dynamics, but the model does not adequately simula...

Summary form only given. An overview and evaluation of various methods of spatial analysis of EEG and evoked potentials are presented. Topics include multiple scales of neural sources, spline-generated surface Laplacians, and representation of surface potentials by orthogonal functions

A two-dimensional time-dependent Duffing oscillator model of macroscopic neocortex exhibits chaos for some ranges of parameters. We embed this model in moderate noise, typical of the context presented in real neocortex, using PATHINT, a non-Monte-Carlo path-integral algorithm that is particularly adept in handling nonlinear Fokker-Planck systems. T...

The surface Laplacian estimate (i.e., current source density) as obtained with spline functions is evaluated in the context of some recent controversies concerning high resolution EEG and source localization. In simulation studies, the spline-Laplacian provides much better estimates of cortical surface potential than is obtained from raw scalp pote...

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...

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...

Spline generated surface Laplacians are introduced as an effective method for estimating neocortical source activity at moderate scales. The method appears to be robust to the unavoidable perturbations of measured potentials and errors of head geometry and resistivity that are certain to occur in clinical or research settings. In particular, we hav...

Mathematically simulated data is used to obtain direct comparisons of the accuracies of spline/Laplacian and cortical imaging algorithms in predicting cortical potential. Even though the two approaches have quite different theoretical bases, the two methods provide nearly identical estimates of cortical activity at scales greater than about 2 or 3...

First Page of the Article

A bshuct- The EEG as classically recorded is influenced by the activity at the reference electrode. The nearest-neighbor Laplacian is a method that removes the ef€ect of the reference electrode by representing the current activity under the recording electrode. In this study coherence was obtained from EEG recorded from four Merent scalp Imtions. D...

An investigation into the relationship between scalp recorded EEG data and the underlying source generators using an analytic three concentric spheres model is presented. Correlation coefficients were computed for scalp potential and scalp Laplacian due to randomly distributed conical sources using electrode pairs of varying separation. Direct comp...

Current topographical mapping methods and problems associated with mapping are reviewed, and one approach for improving the spatial resolution of scalp recorded EEGs is detailed. In particular, techniques for interpolating the potential distribution and estimating the surface Laplacian from multichannel data are presented and applied to human evoke...

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 as...

Three-dimensional finite-element models provide a method to study the relationship between human scalp potentials and neural current sources inside the brain. A new formulation of dipole-like current sources is developed here. Finite-element analyses based on this formulation are carried out for both a three-concentric-spheres model and a human-hea...

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 as...

A three dimensional digitizer was used to locate 62 positions on an electrode cap placed on the heads of nine subjects. Nonlinear regression methods were used to obtain the best fit sphere, ellipsoid, and perturbed ellipsoid. RMS errors varied from approximately 1 cm to 2 mm, depending on subject and surface chosen. The spherical coordinates of the...

A "picture book" of surface potentials, Laplacians, and magnetic fields due to distributed, neocortical sources is presented. The mathematically simulated data is based on 4200 current sources at the macrocolumn scale. Estimated scalp surface maps are based on the three-concentic spheres model of the head. Emphasis is placed on the effects of sampl...

Present brain topographic mapping methods utilize scalp potentials. However, scalp potentials are affected by two variables; (1) the nature and distribution of current sources; and (2) the conductive properties of the head. Since volume conductive properties vary and are still not fully understood, potential-based methods are sensitive to differenc...

The human neocortex is a complex physical and biological system that processes information at multiple spatial and temporal scales. This paper describes a statistical physics methodology to bridge several of these scales which are of current experimental interest. We propose specific algorithms to calculate neuronal processes underlying electroence...

Relationships between neural current sources recorded at different spatial and temporal scales are considered. A number of computer simulations using a three-concentric spheres model of the head are used to illustrate relationships between distributed neocortical sources at the macrocolumn scale and resulting scalp potentials. Computer simulations...

A theory of neocortical interactions is developed involving both local delays (PSP rise and decay times) and global delays due to finite velocity of action potentials in corticocortical fibers. The theory is based on plausible assumptions regarding input/output relations in neocortical columns and realistic neural parameters. The simultaneous exist...

The use of spline-generated Laplacians was investigated for several types of evoked potentials. Potentials were recorded from several subjects and spline-fitted to a sphere generated, using nonlinear regression techniques, from digitized head coordinate values. This preliminary study confirms that the topological maps of the surface Laplacian are m...

The cooperative efforts of physical and biological scientists over the past half century have resulted in a tentative, first order understanding of biological membranes and the behavior of single neurons. Nevertheless, recent work has further exposed the neuron as a highly complex system whose behavior is likely to be the subject of study for many...

Simulated and real visual evoked EEG data were used to study the use of empirical orthogonal functions to describe spatial EEG properties. Sixteen channels of EEG data were recorded from the back of the head during visual checkerboard stimulation. From these data the sum of cross products was obtained at discrete time intervals before and after the...

Given the complexity of neocortical source activity which largely determines observed EEG phenomena, it is of interest to categorize four types of sources. Whereas dipole localization methods are generally applicable only to one of these types, methods to improve spatial resolution apply to all four types of sources. The four types are: type I, loc...

A method is suggested to estimate the local skull resistance function G (¿, o) from surface potential measurements due to a known dipole-like source in the brain. That is, the classical boundary value problem is overspecified by knowledge of both the source and surface potential so that properties of the volume conductor may be estimated. The func...

The theoretical basis for magnetic field recording (MEG) methods is briefly summarized. Lines of constant radial magnetic field on a spherical surface, which are typically used in MEG applications to locate sources, are shown for various multiple dipole sources. It is shown that the usual localization methods are subject to relatively large error i...