Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude

Extraction and localization of mesoscopic motor control signals for human ECoG neuroprosthetics

Electrocorticogram (ECoG) recordings for neuroprosthetics provide a mesoscopic level of abstraction of brain function between microwire single neuron recordings and the electroencephalogram (EEG). Single-trial ECoG neural interfaces require appropriate feature extraction and signal processing methods to identify and model in real-time signatures of motor events in spontaneous brain activity. Here, we develop the clinical experimental paradigm and analysis tools to record broadband (1Hz to 6kHz) ECoG from patients participating in a reaching and pointing task. Motivated by the significant role of amplitude modulated rate coding in extracellular spike based brain-machine interfaces (BMIs), we develop methods to quantify spatio-temporal intermittent increased ECoG voltages to determine if they provide viable control inputs for ECoG neural interfaces. This study seeks to explore preprocessing modalities that emphasize amplitude modulation across frequencies and channels in the ECoG above the level of noisy background fluctuations in order to derive the commands for complex, continuous control tasks. Preliminary experiments show that it is possible to derive online predictive models and spatially localize the generation of commands in the cortex for motor tasks using amplitude modulated ECoG.

Intelligence and EEG current density using low-resolution electromagnetic tomography (LORETA)

The purpose of this study was to compare EEG current source densities in high IQ subjects vs. low IQ subjects. Resting eyes closed EEG was recorded from 19 scalp locations with a linked ears reference from 442 subjects ages 5 to 52 years. The Wechsler Intelligence Test was administered and subjects were divided into low IQ (< or =90), middle IQ (>90 to <120) and high IQ (> or =120) groups. Low-resolution electromagnetic tomographic current densities (LORETA) from 2,394 cortical gray matter voxels were computed from 1-30 Hz based on each subject's EEG. Differences in current densities using t tests, multivariate analyses of covariance, and regression analyses were used to evaluate the relationships between IQ and current density in Brodmann area groupings of cortical gray matter voxels. Frontal, temporal, parietal, and occipital regions of interest (ROIs) consistently exhibited a direct relationship between LORETA current density and IQ. Maximal t test differences were present at 4 Hz, 9 Hz, 13 Hz, 18 Hz, and 30 Hz with different anatomical regions showing different maxima. Linear regression fits from low to high IQ groups were statistically significant (P < 0.0001). Intelligence is directly related to a general level of arousal and to the synchrony of neural populations driven by thalamo-cortical resonances. A traveling frame model of sequential microstates is hypothesized to explain the results.

On-line Detection of Perceptual Signatures in Multichannel ECoG

Neocortical ECoG studies have unveiled the presence of active states - spatial patterns of amplitude modulation- in the beta- gamma ranges in the presence of conditioned stimuli that resemble cinematographic frames. These sequences of active frames emerge with abrupt phase resettings, followed by resynchronization and stabilization over channels, and magnified intensity. An online pattern recognizer that captures the spatial and spectral characteristics of the active frames is presented. The results of detection are confirmed via high occurrences of pragmatic information, defined by the ratio of pattern intensity to pattern stability.

Definitions of state variables and state space for brain-computer interface : Part 2. Extraction and classification of feature vectors

The hypothesis is proposed that the central dynamics of the action-perception cycle has five steps: emergence from an existing macroscopic brain state of a pattern that predicts a future goal state; selection of a mesoscopic frame for action control; execution of a limb trajectory by microscopic spike activity; modification of microscopic cortical spike activity by sensory inputs; construction of mesoscopic perceptual patterns; and integration of a new macroscopic brain state. The basis is the circular causality between microscopic entities (neurons) and the mesoscopic and macroscopic entities (populations) self-organized by axosynaptic interactions. Self-organization of neural activity is bidirectional in all cortices. Upwardly the organization of mesoscopic percepts from microscopic spike input predominates in primary sensory areas. Downwardly the organization of spike outputs that direct specific limb movements is by mesoscopic fields constituting plans to achieve predicted goals. The mesoscopic fields in sensory and motor cortices emerge as frames within macroscopic activity. Part 1 describes the action-perception cycle and its derivative reflex arc qualitatively. Part 2 describes the perceptual limb of the arc from microscopic MSA to mesoscopic wave packets, and from these to macroscopic EEG and global ECoG fields that express experience-dependent knowledge in successive states. These macroscopic states are conceived to embed and control mesoscopic frames in premotor and motor cortices that are observed in local ECoG and LFP of frontoparietal areas. The fields sampled by ECoG and LFP are conceived as local patterns of neural activity in which trajectories of multiple spike activities (MSA) emerge that control limb movements. Mesoscopic frames are located by use of the analytic signal from the Hilbert transform after band pass filtering. The state variables in frames are measured to construct feature vectors by which to describe and classify frame patterns. Evidence is cited to justify use of linear analysis. The aim of the review is to enable researchers to conceive and identify goal-oriented states in brain activity for use as commands, in order to relegate the details of execution to adaptive control devices outside the brain.

The place of 'codes' in nonlinear neurodynamics

A key problem in cognitive science is to explain the neural mechanisms of the rapid transposition between stimulus energy and abstract concept--between the specific and the generic--in both material and conceptual aspects, not between neural and psychic aspects. Three approaches by researchers to a solution in terms of neural codes are considered. Materialists seek rate and frequency codes in the interspike intervals of trains of action potentials induced by stimuli and carried by topologically organized axonal lines. Cognitivists refer to the symbol grounding problem and search for symbolic codes in firings of hierarchically organized feature-detector neurons of phonemes, lines, odorants, pressures, etc., that object-detector neurons bind into representations of probabilities of stimulus occurrence. Dynamicists seek neural correlates of stimuli and associated behaviors in spatial patterns of oscillatory fields of dendritic activity that self-organize and evolve as trajectories through high-dimensional brain state space; the codes are landscapes of chaotic attractors. Unlike codes in DNA and the periodic table, these codes have neither alphabet nor syntax. They are epistemological metaphors required by experimentalists to measure neural activity and by engineers to model brain functions. Here I review the central neural mechanisms of olfaction as a paradigm for use of codes to explain how brains create cortical activities that mediate sensation, perception, comprehension, prediction, decision, and action or inaction.

P1 and traveling alpha waves: evidence for evoked oscillations

The hypothesis is tested whether the P1 of the event-related potential (ERP) component behaves like an evoked, traveling alpha wave. This hypothesis is based on different kinds of evidence showing, e.g., that-after undergoing phase reorganization-frequencies in the broad alpha range become synchronized (aligned) in absolute phase and contribute significantly to the generation of the P1. We investigated data from a Stroop task in which subjects had to respond only to the color and ignore the meaning of the presented words. Analyzing topographical phase relationships expressed in terms of traveling speed (with respect to Pz as trailing site) revealed that a systematic posterior to anterior traveling pattern appeared only in the broad time window of the P1-N1 complex and in the extended alpha frequency range. The obtained findings are consistent with the oscillatory ERP model and suggest that the P1 component may be considered a manifestation of an evoked, traveling alpha wave. We assume that the P1 reflects a top-down process in a sense that traveling alpha waves control or "gate" the direction of information processing in the brain.

Definitions of state variables and state space for brain-computer interface : Part 1. Multiple hierarchical levels of brain function

Neocortical state variables are defined and evaluated at three levels: microscopic using multiple spike activity (MSA), mesoscopic using local field potentials (LFP) and electrocorticograms (ECoG), and macroscopic using electroencephalograms (EEG) and brain imaging. Transactions between levels occur in all areas of cortex, upwardly by integration (abstraction, generalization) and downwardly by differentiation (speciation). The levels are joined by circular causality: microscopic activity upwardly creates mesoscopic order parameters, which downwardly constrain the microscopic activity that creates them. Integration dominates in sensory cortices. Microscopic activity evoked by receptor input in sensation induces emergence of mesoscopic activity in perception, followed by integration of perceptual activity into macroscopic activity in concept formation. The reverse process dominates in motor cortices, where the macroscopic activity embodying the concepts supports predictions of future states as goals. These macroscopic states are conceived to order mesoscopic activity in patterns that constitute plans for actions to achieve the goals. These planning patterns are conceived to provide frames in which the microscopic activity evolves in trajectories that adapted to the immediate environmental conditions detected by new stimuli. This circular sequence forms the action-perception cycle. Its upward limb is understood through correlation of sensory cortical activity with behavior. Now brain-machine interfaces (BMI) offer a means to understand the downward sequence through correlation of behavior with motor cortical activity, beginning with macroscopic goal states and concluding with recording of microscopic MSA trajectories that operate neuroprostheses. Part 1 develops a hypothesis that describes qualitatively the neurodynamics that supports the action-perception cycle and derivative reflex arc. Part 2 describes episodic, "cinematographic" spatial pattern formation and predicts some properties of the macroscopic and mesoscopic frames by which the embedded trajectories of the microscopic activity of cortical sensorimotor neurons might be organized and controlled.

The sometimes pernicious role of theory in science

The role of theory in science is discussed in the context of understanding brain function. Historically, theories of brain functions have oscillated between localization and anti-localization beliefs. In the last 50 years, the important discoveries of the ascending reticular activating system (ARAS), feature extracting neurons and synaptic growth led many to orthodoxy. Research became more and more focused upon the elements comprising the nervous system and their interconnections. The mainstream belief became that many brain functions including consciousness were localized, certain kinds of brain injuries produced irreversible functional deficits. Contrary scientific challenges were discouraged by the omnipresence of such theory. Examples of theoretical "Einstellungen" in the areas of ARAS, coma, treatment of brain injuries and consciousness are given, as well as signs that the pendulum is swinging back to an approach to the system as a whole rather than a focus on its parts.

S-transform time-frequency analysis of P300 reveals deficits in individuals diagnosed with alcoholism

OBJECTIVE

Decomposition of event-related potential (ERP) waveforms using time-frequency representations (TFR's) is becoming increasingly common in electrophysiology. The P300 potential is an important component of the ERP waveform and has been used to study cognition as well as psychiatric disorders such as alcoholism. In this work, we aim to further understand the nature of the event-related oscillation (ERO) components which form the P300 wave and how these components may be used to differentiate alcoholic individuals from controls.

METHODS

The S-transform decomposition method is used to derive TFR's from single trial and trial-averaged ERP data acquired during a visual oddball task. These TFR's are averaged within time and frequency windows to provide ERO measures for further investigation. ERO measures are compared with conventional ERP amplitude measures using correlation analyses. Statistical analyses was performed with MANOVA and stepwise logistic regressions to contrast an age-matched sample of control (N=100) and alcoholic male subjects (N=100).

RESULTS

The results indicate that the P300 waveform, elicited using infrequent salient stimuli, is composed of frontal theta and posterior delta activations. The frontal theta activation does not closely correspond to any of the conventional ERP components and is therefore best analyzed using spectral methods. Between group comparisons and group predictions indicate that the delta and theta band ERO's, which underlie the P300, show deficits in the alcoholic group. Additionally, each band contributes unique information to discriminate between the groups.

CONCLUSIONS

ERO measures which underlie and compose the P300 wave provide additional information to that offered by conventional ERP amplitude measures, and serve as useful genetic markers in the study of alcoholism.

SIGNIFICANCE

Studying the ERP waveform using time-frequency analysis methods opens new avenues of research in electrophysiology which may lead to a better understanding of cognitive processes, lead to improved clinical diagnoses, and provide phenotypes/endophenotypes for genetic analyses.

Fine spatiotemporal structure of phase in human intracranial EEG

OBJECTIVE

To transfer to the clinic for humans the technology and theory for high-resolution EEG analysis that have been developed in the laboratory with animals.

METHODS

EEGs were recorded at high spatial resolution from a 1 x 1 cm 8 x 8 electrode array on the right inferior temporal gyrus of a patient undergoing preoperative monitoring for epilepsy surgery. Cosines were fitted to EEG segments to measure frequency and phase and compute location, size, latency, phase velocity, duration, and recurrence rate of radially symmetric spatial patterns called phase cones. The Hilbert transform was also used to get high temporal resolution.

RESULTS

In the awake state, the power spectral density (PSD) showed power-law decrease in log power with log frequency at 1/falpha, alpha approximately 2, but with peaks in the standard empirical ranges. The phase in beta and gamma ranges had spatial gradients in conic form. Resetting of these stable spatial patterns of phase cones was spatially coincident at intermittent discontinuities ('phase slip') recurring at theta rates. Cones had half power diameters from 2 to 50+ mm; their durations had power-law distributions with values ranging from 6 to 300+ ms depending on length of the analysis window. In slow wave sleep PSD decreased at 1/falpha, alpha approximately 3,with loss of beta-gamma spectral peaks and diminished or absent oscillations and spatiotemporal phase structure.

CONCLUSIONS

Spatiotemporal structures in awake human and rabbit EEG showed striking similarities. The only clear differences were ascribable to differing scales of measurement. These fine spatiotemporal structures of EEG were diminished or lost in slow wave sleep.

SIGNIFICANCE

The fine structure indicates that neocortical stability is sustained at self-organized criticality; that synaptic input in the awake state drives neocortex away from criticality causing beta-gamma oscillations in re-stabilizing 'neural avalanches'; and that diminished input in slow wave sleep allows return toward criticality but with some added risk of instability and seizure.

Imaging human EEG dynamics using independent component analysis

This review discusses the theory and practical application of independent component analysis (ICA) to multi-channel EEG data. We use examples from an audiovisual attention-shifting task performed by young and old subjects to illustrate the power of ICA to resolve subtle differences between evoked responses in the two age groups. Preliminary analysis of these data using ICA suggests a loss of task specificity in independent component (IC) processes in frontal and somatomotor cortex during post-response periods in older as compared to younger subjects, trends not detected during examination of scalp-channel event-related potential (ERP) averages. We discuss possible approaches to component clustering across subjects and new ways to visualize mean and trial-by-trial variations in the data, including ERP-image plots of dynamics within and across trials as well as plots of event-related spectral perturbations in component power, phase locking, and coherence. We believe that widespread application of these and related analysis methods should bring EEG once again to the forefront of brain imaging, merging its high time and frequency resolution with enhanced cm-scale spatial resolution of its cortical sources.

A cognitive architecture that combines internal simulation with a global workspace

This paper proposes a brain-inspired cognitive architecture that incorporates approximations to the concepts of consciousness, imagination, and emotion. To emulate the empirically established cognitive efficacy of conscious as opposed to non-conscious information processing in the mammalian brain, the architecture adopts a model of information flow from global workspace theory. Cognitive functions such as anticipation and planning are realised through internal simulation of interaction with the environment. Action selection, in both actual and internally simulated interaction with the environment, is mediated by affect. An implementation of the architecture is described which is based on weightless neurons and is used to control a simulated robot.

Towards a proper estimation of phase synchronization from time series

In experimental synchronization studies a continuous phase variable is commonly estimated from a scalar time series by means of its representation on the complex plane. The aim is to obtain a pair of functions [A(t), phi(t)] defining its instantaneous amplitude and phase, respectively. However, any arbitrary pair of functions cannot be considered as the amplitude and the phase of the real observable. Here, we point out some criteria that the pair [A(t), phi(t)] must observe to unambiguously define the instantaneous amplitude and phase of the observed signal. In this work, we illustrate how the complex representation may fail if the signal possesses a multi-component or a broadband spectra. We also point out a practical procedure to test whether a signal, not displaying a single oscillation at a unique frequency, has a narrow-band behavior. Implications for the study of phase interdependencies are illustrated and discussed. Phase dynamics estimated from electric brain activities recorded from an epileptic patient are also discussed.

Synergetics of brain function

Several brain functions such as movement coordination and visual perception are analysed in terms of synergetics, an interdisciplinary field of research dealing with spontaneous pattern formation. Accordingly, the brain is conceived as a self-organizing system operating close to instabilities where its activities are governed by collective variables, the order parameters, that enslave the individual parts, i.e., the neurons. In this approach, emphasis is laid on qualitative changes of behavioral and neuronal activities. These concepts are substantiated by detailed experimental and theoretical studies of the coordination of finger movements by direct observation of their changes and MEG measurements. In its main part, this paper deals with visual pattern recognition. Using general properties of order parameters, at the phenomenological level bistability, hysteresis and oscillations of visual perception can be modelled. Then, at the microscopic level, a network of pulse-coupled neurons is treated, where the dynamics of the dendritic currents as well as the axonic pulses (spikes) are taken into account. Both pulse-synchronization as well as pattern recognition are treated. In the high pulse frequency limit the attractor network of the synergetic computer is recovered. In the next step, the concept of quasi-attractors is mathematically formulated where due to saturation of attention attractors are closed. Depending on incoming signals, the visual system thus wanders from quasi-attractor to quasi-attractor. The paper includes an interpretation of consciousness in terms of order parameters as well as a discussion on linearity versus nonlinearity, the binding problem, and the psychological "present".

A cinematographic hypothesis of cortical dynamics in perception

The aim of this study was to measure and classify spatial patterns in sensory cortical EEGs relating to conditioned stimuli (CSs) in order to test the hypothesis, based on clinical reports, that cortical dynamics is not continuous but operates in steps that resemble frames in a cinema. Recent advances in the application of the Hilbert Transform to intracranial recordings of the EEG in animals have revealed markers for repetitive phase transitions in neocortex at frame rates in the theta band. The frames were sought in multichannel EEGs that had been recorded from 8x8 high-density arrays that were fixed on primary sensory cortices of rabbits trained to discriminate visual, auditory or somatic conditioned stimuli with reinforcement (CS+) or without (CS-). Localization of frames in EEGs was by use of a new index, H(e)(t), called "pragmatic information". Each spatial pattern was represented by a feature vector from the 64 analytic amplitudes at a maximal value of H(e)(t) from the Hilbert transform and expressed as a 64x1 feature vector specifying a point in 64-space. Classification with respect to CS+/- was by calculation of Euclidean distances of points from centers of gravity of clusters after preprocessing by nonlinear mapping. Stable spatial patterns were found in the form of amplitude modulation (AM) of aperiodic waveforms that included all channels. The impact of a CS on a sensory neocortex reorganized background EEG into two types of sequential patterns of coordinated activity, initially local and modality-specific, later global. The initial stage of phase transitions required 3-7 ms. Large-scale cortical activity then reorganized itself repeatedly and reliably over relatively immense cortical distances within the cycle duration of the center frequency of oscillation. The size, texture, timing, and duration of the AM patterns support the hypothesis that these frames may provide the basis for multisensory percepts (Gestalts).

Origin, structure, and role of background EEG activity. Part 4: Neural frame simulation

OBJECTIVE

To develop a method for simulating background EEG based on the premise that the self-organized activity from synaptic interaction among populations of neurons creates sustained fluctuations that can be modeled with the filtered output of a random number generator.

METHODS

The logarithm of the amplitude of activity was weighted in accordance with 1/f, the log frequency in both temporal (PSD(T)) and spatial (PSD(X)) power spectral densities. The activity was spatially smoothed by volume conduction. Further deviation from full randomness was by sustained spatial coherence averaging 25% of total power. The departure from the background state to an active state, as seen in the awake EEG, was simulated by adding segments that were 90% correlated while attenuating by 50% the uncorrelated background activity in those segments. Spatial amplitude modulation was imposed on the correlated noise to create signals that simulated AM patterns.

RESULTS

The statistical properties of the EEG that were replicated (Freeman, 2004a,b, 2005) included the PSD(T), PSD(X), point spread function (PSF), partitioning of the variance with PCA, and the percentages of correct classification of AM patterns.

CONCLUSIONS

The origin of background EEG was traced to self-sustaining mutual excitation among pyramidal cells creating stable noise that was filtered by self-organized criticality to give 1/f(2) PSD, by inhibitory feedback to give oscillations in the classic clinical bands, and by volume conduction to give smoothing. The essential change that identified a frame in EEG was transient synchrony by phase transition among cortical populations in beta and gamma bands of the PSD(T).

SIGNIFICANCE

This simulation can provide test data with which to optimize techniques for noninvasively extracting information from the EEG for diagnosis and treatment evaluation of neuropsychiatric disorders and for operation by paraplegics of prosthetic devices.

Information-based modeling of event-related brain dynamics

We discuss the theory and practice of applying independent component analysis (ICA) to electroencephalographic (EEG) data. ICA blindly decomposes multi-channel EEG data into maximally independent component processes (ICs) that typically express either particularly brain generated EEG activities or some type of non-brain artifacts (line or other environmental noise, eye blinks and other eye movements, or scalp or heart muscle activity). Each brain and non-brain IC is identified with an activity time course (its 'activation') and a set of relative strengths of its projections (by volume conduction) to the recording electrodes (its 'scalp map'). Many non-articraft IC scalp maps strongly resemble the projection of a single dipole, allowing the location and orientation of the best-fitting equivalent dipole (or other source model) to be easily determined. In favorable circumstances, ICA decomposition of high-density scalp EEG data appears to allow concurrent monitoring, with high time resolution, of separate EEG activities in twenty or more separate cortical EEG source areas. We illustrate the differences between ICA and traditional approaches to EEG analysis by comparing time courses and mean event related spectral perturbations (ERSPs) of scalp channel and IC data. Comparing IC activities across subjects necessitates clustering of similar Ics based on common dynamic and/or spatial features. We discuss and illustrate such a component clustering strategy. In sum, continued application of ICA methods in EEG research should continue to yield new insights into the nature and role of the complex macroscopic cortical dynamics captured by scalp electrode recordings.

From synchronous neuronal discharges to subjective awareness?

For practical clinical purposes, as well as because of their deep philosophical implications, it becomes increasingly important to be aware of contemporary studies of the brain mechanisms that generate subjective experiences. Current research has progressed to the point where plausible theoretical proposals can be made about the neurophysiological and neurochemical processes which mediate perception and sustain subjective awareness. An adequate theory of consciousness must describe how information about the environment is encoded by the exogenous system, how memories are stored in the endogenous system and released appropriately for the present circumstances, how the exogenous and endogenous systems interact to produce perception, and explain how consciousness arises from that interaction. Evidence assembled from a variety of neuroscience areas, together with the invariant reversible electrophysiological changes observed with loss and return of consciousness in anesthesia as well as distinctive quantitative electroencephalographic profiles of various psychiatric disorders, provides an empirical foundation for this theory of consciousness. This evidence suggests the need for a paradigm shift to explain how the brain accomplishes the transformation from synchronous and distributed neuronal discharges to seamless global subjective awareness. This chapter undertakes to provide a detailed description and explanation of these complex processes by experimental evidence marshaled from a wide variety of sources.

NDN, VOLUME TRANSMISSION, AND SELF-ORGANIZATION IN BRAIN DYNAMICS

Fields of neural activity are seen in synchronized oscillations that are detected at mesoscopic scales in syntheses of multicellular recordings of action potentials and electroencephalograms (EEGs) over broad areas of cerebral cortex. The waves often have large-scale, highly textured spatial patterns of cortical activity, formed in the context of associative learning under classical and operant conditioning in rabbits. The patterns show spatial amplitude modulation of shared oscillations of carrier waves in the beta and gamma ranges of the EEG, with recurrence at frame rates in the alpha and theta ranges. The frames also show spatial phase modulation that is inconsistent with driving of the oscillations by focal pacemakers. The hypothesis is developed that the synchronization manifests continuous distributions of activity in cortical neuropil that modulate firings of selected neural networks embedded in the neuropil. Five interactive agencies have been postulated to explain the mechanism for the field synchrony: electric fields; magnetic fields; electromagnetic fields (radio waves); diffusion chemical gradients; and order parameters that control self-organization of large populations of neurons by widespread synaptic interaction constituting negative and positive feedback. Only the last interactive agency fits the data. The points are emphasized that these field patterns in frames require interactive neural dynamics that is modulated in respect to global operations mediating arousal, attention, selective emotional stance, wake, sleep, learn, habituate, dishabituate, etc., and that these operations require differing but complementary fields that form by massive parallel feed-forward architectures of brainstem neuromodulatory nuclei. An example is given using histamine of the neural discharges of brainstem nuclei that do not require fine spatiotemporal texturing of their firing; they operate by nonsynaptic release of neuromodulators that effect changes in background state, such that textured patterns of cortical activity can form and update in flexible adaptations of brains to their environments. These systems instantiate volume transmission by nonsynaptic diffusion transmission, in concert with the self-organization of the textured neural activity that supports cognition.

Metastability, instability, and state transition in neocortex

Mesoscopic patterns of neural activity were sought in multichannel EEGs of rabbits that were trained to respond to conditioned stimuli (CSs) in visual, auditory and somatic modalities. Spatiotemporal patterns were sought of oscillations in the beta and gamma ranges. The techniques required for preprocessing EEGs in search of global patterns were diametrically opposed to those needed for localization of modular EEG signals. Frames were found in the form of intermittent spatial patterns of phase and amplitude modulation (AM and PM) of carrier waves in beta and gamma ranges that served to classify EEG frames with respect to CSs. A model based on the intentional action-perception cycle is proposed to complement the information processing model.

The use of stationarity and nonstationarity in the detection and analysis of neural oscillations

Using available signal (i.e., spectral and time-frequency) analysis methods, it can be difficult to detect neural oscillations because of their continuously changing properties (i.e., nonstationarities) and the noise in which they are embedded. Here, we introduce fractally scaled envelope modulation (FSEM) estimation which is sensitive specifically to the changing properties of oscillatory activity. FSEM utilizes the fractal characteristic of wavelet transforms to produce a compact, two-dimensional representation of time series data where signal components at each frequency are made directly comparable according to the spectral distribution of their envelope modulations. This allows the straightforward identification of neural oscillations and other signal components with an envelope structure different from noise. For stable oscillations, we demonstrate how partition-referenced spectral estimation (PRSE) removes the noise slope from spectral estimates, yielding a level estimate where only peaks signifying the presence of oscillatory activity remain. The functionality of these methods is demonstrated with simulations and by analyzing MEG data from human auditory brain areas. FSEM uncovered oscillations in the 9- to 12-Hz and 15- to 18-Hz ranges whereas traditional spectral estimates were able to detect oscillations only in the former range. FSEM further showed that the oscillations exhibited envelope modulations spanning 3-7 s. Thus, FSEM effectively reveals oscillations undetectable with spectral estimates and allows the use of EEG and MEG for studying cognitive processes when the common approach of stimulus time-locked averaging of the measured signal is unfeasible.

Empirical mode decomposition of field potentials from macaque V4 in visual spatial attention

Empirical mode decomposition (EMD) has recently been introduced as a local and fully data-driven technique for the analysis of non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. In this article we consider the application of EMD to the analysis of neuronal activity in visual cortical area V4 of a macaque monkey performing a visual spatial attention task. We show that, by virtue of EMD, field potentials can be resolved into a sum of intrinsic components with different degrees of oscillatory content. Low-frequency components in single-trial recordings contribute to the average visual evoked potential (AVEP), whereas high-frequency components do not, but are identified as gamma-band (30-90 Hz) oscillations. The magnitude of time-varying gamma activity is shown to be enhanced when the monkey attends to a visual stimulus as compared to when it is not attending to the same stimulus. Comparison with Fourier analysis shows that EMD may offer better temporal and frequency resolution. These results support the idea that the magnitude of gamma activity reflects the modulation of V4 neurons by visual spatial attention. EMD, coupled with instantaneous frequency analysis, is demonstrated to be a useful technique for the analysis of neurobiological time-series.

Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions

We model the dynamical behavior of the neuropil, the densely interconnected neural tissue in the cortex, using neuropercolation approach. Neuropercolation generalizes phase transitions modeled by percolation theory of random graphs, motivated by properties of neurons and neural populations. The generalization includes (1) a noisy component in the percolation rule, (2) a novel depression function in addition to the usual arousal function, (3) non-local interactions among nodes arranged on a multi-dimensional lattice. This paper investigates the role of non-local (axonal) connections in generating and modulating phase transitions of collective activity in the neuropil. We derived a relationship between critical values of the noise level and non-locality parameter to control the onset of phase transitions. Finally, we propose a potential interpretation of ontogenetic development of the neuropil maintaining a dynamical state at the edge of criticality.

A field-theoretic approach to understanding scale-free neocortical dynamics

A mesoscopic field-theoretic approach is compared with neural network and brain imaging approaches to understanding brain dynamics. Analysis of high spatiotemporal resolution rabbit electroencephalogram (EEG) reveals neural fields in the form of spatial patterns in amplitude (AM) and phase (PM) modulation of gamma and beta carrier waves that serve to classify EEGs from trials with differing conditioned stimuli (CS+/-). Paleocortex exemplified by olfactory EEG has one AM-PM pattern at a time that forms by an input-dependent phase transition. Neocortex shows multiple overlapping AM-PM patterns before and during presentation of CSs. Modeling suggests that neocortex is stabilized in a scale-free state of self-organized criticality, enabling cooperative domains to form virtually instantaneously by phase transitions ranging in size from a few hypercolumns to an entire hemisphere. Self-organized local domains precede formation of global domains that supervene and contribute global modulations to local domains. This mechanism is proposed to explain Gestalt formation in perception.

Origin, structure, and role of background EEG activity. Part 3. Neural frame classification

OBJECTIVE

To show that cortical responses to conditioned stimuli (CS) include intermittently induced spatial patterns of amplitude modulation (AM) of beta-gamma oscillation called frames.

METHODS

EEGs were recorded from 8x8 high-density arrays fixed on primary sensory cortices of rabbits trained to discriminate CS with reinforcement (CS+) from those without (CS-). EEG frames were located with a pragmatic information index, H(e). The spatial patterns of the first 3 frames on each of 37-40 trials were measured by the square of 64 analytic amplitudes from the Hilbert transform to give points in 64-space. The questions were asked: Did the frames from CS+ trials and CS- trials differ within each sequential group? Did the 3 frames differ from each other (form 3 clusters of points)?

RESULTS

EEG frames that were identified by high H(e) had AM patterns that could be classified with respect to CS+ and CS- well above chance levels. Two stages of correct frame classification occurred on each trial: 40-130 ms after CS onset with a gamma carrier frequency, and 450-550 ms with a beta carrier frequency. Peak power in the beta frames was double that in gamma frames, and mean pattern surface area of beta frames was nearly 4-fold greater.

CONCLUSIONS

Under the impact of a CS on a sensory neocortex, the background EEG activity reorganized in sequential frames of coordinated activity, first local and modality-specific, thereafter global.

SIGNIFICANCE

The size, texture and duration of these AM patterns indicate that spatial patterns of human beta frames may be accessible with high-density scalp arrays for correlation with phenomenological reports by human subjects.

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

OBJECTIVE

To explain spontaneous EEG through measurements of spatiotemporal patterns of phase among beta-gamma oscillations.

METHODS

High-density 8 x 8 intracranial arrays were fixed over sensory cortices of rabbits. EEGs were spatially low pass filtered, temporally bandpass filtered and segmented in overlapping windows stepped at 2 ms. Phase was measured with the cosine as the temporal basis function, using both Fourier and Hilbert transforms to compensate for their respective limitations. Spatial patterns in 2D phase surfaces were measured with the geometric form of the cone as the spatial basis function.

RESULTS

Two fundamental state variables were measured at each digitizing step in the 64 EEGs: the rate of change in phase with time (frequency) and the rate of change in phase with distance (gradient). The parameters of location, diameter, duration, and phase velocity of the cone of phase were derived from these two state variables. Parameter distributions including recurrence intervals extending into the low theta range were fractal; the mean values varied with window duration and interelectrode distance.

CONCLUSIONS

The formation of spatial amplitude patterns began with state transitions that were documented by phase discontinuities and phase cones. The multiplicity of overlapping cones indicated that sensory neocortices maintained a scale-free state of self-organized criticality (SOC) in each hemisphere as the basis for its rapid integration of sensory input with prior learning stored in cortical synaptic webs. Further evidence came from the fractal properties of the phase parameters and the self-similarity of phase patterns in the ms/mm to m/s ranges.

SIGNIFICANCE

These EEG data suggest that neocortical dynamics is analogous to the dynamics of self-stabilizing systems, such as a sand pile that maintains its critical angle by avalanches, and a pan of boiling water that maintains its critical temperature by bubbles that release heat. Beta-gamma oscillations stem from the ability of neocortex to maintain its stability under continuous sensory bombardment. Modeling implies that the critical parameter of neocortex (analogous to angle of repose or temperature) is the mean firing rates of neurons that are homeostatically regulated by refractory periods everywhere at all times in cortex. The advantage of SOC in perception may be the ability it gives neocortex to generate instantaneous global state transitions (avalanches, bubbles) large enough to include the multiple sensory areas that are necessary to form gestalts (multisensory percepts).