Elsevier

Clinical Neurophysiology

Volume 115, Issue 9, September 2004, Pages 2089-2107
Clinical Neurophysiology

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

https://doi.org/10.1016/j.clinph.2004.02.028Get rights and content

Abstract

Objective: To explain spontaneous EEG through measurements of spatiotemporal patterns of phase among beta–gamma oscillations.

Methods: High-density 8×8 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).

Introduction

Human perception takes place in rapid frames that engage voluminous sensory input in situations, such as a feeling about the shoulders when trying on a new coat, an understanding that a friend is angry or frightened, a flash of recognition of the identity and state of mind of a parent with one word on the telephone, and so on. Brains are usually in states of arousal and expectancy before the arrival of stimuli. These states are normally prerequisite for perception. EEG and MEG from humans and animals in such states give evidence of background spatiotemporal waves of potential that flicker ceaselessly all over the head, like the background noise of traffic, wind and surf. How might neurons create these background oscillations through interactions, and how might these waves contribute to phenomenological experiences before, during and after expected stimuli?

Recent efforts to open background activity to exploration have included recording scalp EEG with a high-density electrode array (Freeman et al., 2003a, Freeman et al., 2003b, Freeman et al., 2003c) and analyzing the signals with the Hilbert transform (Freeman et al., 2003a). The unprecedented spatial and temporal resolution afforded by these new techniques, which were developed from research on rabbit brains, revealed remarkably detailed patterns in the seemingly featureless chaotic oscillations in electrical potential found everywhere over the scalp. Most striking was the widespread synchrony in oscillations at frequencies broadly distributed over the beta–gamma range that were aperiodically re-initialized at intervals corresponding to rates in the theta–alpha range. The distances across which the waves were synchronized varied among subjects and across samples, ranging up to 189 mm (the length of the array). Evidence was found for textures of amplitude at the scale of the gyri, 1–3 cm in length, indicating synchrony that extended across multiple gyri and sulci. Temporally the synchrony was interrupted but then re-established in phase jumps. Each jump lasted only a few milliseconds and recurred at irregular intervals, yet successive jumps were nearly simultaneous, even over long distances. In subjects at rest with eyes closed the episodes of desynchronization on average were correlated with the alpha rhythm. In subjects holding their eyes open or intentionally tensing their scalp to introduce EMG, the mean repetition rate often appeared in the theta range.

A provisional explanation for these episodic patterns in scalp EEG was based on studies of spatiotemporal patterns of intracranial EEG in rabbits with high-density electrode arrays fixed surgically over the primary sensory areas (Barrie et al., 1996, Viana Di Prisco and Freeman, 1985). The olfactory bulb and neocortical areas were found to generate spatial patterns of amplitude modulation (‘AM patterns’) of oscillations in the gamma and beta ranges, respectively. The patterns lasted 80–100 ms and recurred at rates in the theta–delta range (Freeman and Barrie, 2000). Each AM pattern expressed a short-lasting state of the cortex, which formed by an abrupt change in the cortical dynamics known as a state transition. Each state transition had two steps. First was the very rapid spread of re-initialization of the phase of the beta–gamma activity (Freeman, 2001); second was the stabilization and increase in amplitude of the AM pattern in 24–34 ms (Freeman, 2003b, Freeman and Burke, 2003; Part 1). These phase-locked spatial patterns in the EEG revealed organizations of cortical activity that were termed ‘wave packets’ (Freeman, 1975, Freeman, 2003b). Successive wave packets resembled frames in a black/white cinema with successive spatial patterns held briefly. The AM patterns observed in sensory areas were statistically related to conditioned stimuli (CS), not so much to the features of the stimuli as to the categories of the stimuli (Ohl et al., 2001) that constituted the meanings of the stimuli for the animals (Freeman, 2003a).

Multiple mini-arrays fixed over the visual, auditory, somatic, olfactory and entorhinal areas detected multicortical events that involved all 3 neocortical sensory cortices and the limbic and olfactory areas (Freeman and Burke, 2003, Freeman et al., 2003c). The onsets were virtually simultaneous (Freeman and Rogers, 2003). That finding led to a search for episodic re-synchronization in scalp EEG, which might give evidence of similar widespread state transitions in human cortex (Freeman et al., 2003a). The conclusion was reached that in both animals and humans the neocortex generated temporally discontinuous, broad spatial patterns that had the requisite sizes, durations, and repetition rates to qualify as candidates for Gestalts, the frames of meaning in perception (Freeman, 2003a).

In contrast to the olfactory EEG, which provided an obvious relation of bursts of activity to respiration (Freeman, 1975), visual inspection of the multichannel EEG recordings from intracranial electrode arrays on neocortex (Fig. S1.1 in Part 1) gave no clues to the temporal locations of the sequential neocortical states and the transitions by which they emerged (Barrie et al., 1996). In both structures it appeared that responses to stimuli might take the form of abrupt re-organizations of background activity into patterns that were selected by stimuli following state transitions that were triggered by the stimuli. Therefore, re-examination of extant data was undertaken here to answer the question, what is the neural mechanism that sustains background activity in brains and in particular gives the EEG its dynamic properties? The aperiodic oscillations for many years have been regarded as dendritic ‘noise’ (Bullock, 1969, Elul, 1972) that is best removed by time-locked averaging of responses to stimuli (event related potentials, ERP). However, EEG has too much informative structure to be so lightly dismissed (Watters, 2000). The approach taken here to explain the ‘spontaneous’ EEG is to measure the distributions of phase defined at frequencies in the beta–gamma range in multichannel EEG signals, and to calculate the rates of change in phase with time and distance. A companion report (Freeman, 2004, Part 1) deals with the amplitude distributions. The large data base needed for the study consisted of EEG records derived from high-density arrays implanted over sensory cortices in rabbits that were then trained to discriminate CS in a classical aversive paradigm (Barrie et al., 1996).

These data were interpreted in the context of the theory of self-organization in nonlinear systems operating far from equilibrium. The term ‘self-organizing’ means that a complex system with many interacting elements, such as an area of cortex with many synaptically interactive neurons, develops its own set of preferred states, which it constructs and modifies by changing its connections in accordance with certain rules. In the case of cortex these are the well-known rules of learning. The term ‘nonlinear’ means that small inputs can give large outputs and vice versa; the proportionality and additivity of outputs to inputs of linear systems does not hold. Physiologists are familiar in principle with nonlinearity in terms of paired-shock testing in search of facilitation and depression, thresholds and refractory periods. Operating ‘far from equilibrium’ means that normal cortex does not go to rest, as an isolated nerve cell does when it is deprived of input; instead, cortex continually boils with background activity that requires metabolic energy that is supported by a steady supply of oxygen and glucose and removal of waste heat and carbon dioxide.

EEG background activity, which is not truly ‘spontaneous’, has several statistical properties that are characteristic of self-organizing systems; they are fractal, scale-free, and self-similar. The distributions of the sizes and durations of events are fractal (Mandelbrot, 1983), not normal. Whereas events in normal distributions have means and standard deviations that are independent of the dimensions of the tools of measurement, events in fractal distributions have means that tend to be equal to the standard deviations, and both mean and standard deviation (SD) decrease with decreasing size of the measuring tool. Systems that are characterized by fractal distributions of their properties are called and ‘scale-free’ (Wang and Chen, 2003). The classic example is the length of the coastline of England, which varies with the size of the measuring stick from kilometers to microns. In histograms the distributions are not bell-shaped but have maximal numbers at minimal dimensions. Small, brief structures and events have the same appearance and proportions as large, long-lasting events. This property is called ‘self-similarity’. It is often applied to anatomical structures such as dendrites, in which branchlets far from the cell body have the same appearance as branches close in. The spectra of EEG signals often show the 1/f power-law distribution across frequencies (Freeman et al., 2003a, Freeman et al., 2003b, Freeman et al., 2003c), which is an example of self-similarity (Hwa and Ferree, 2002, Pereda et al., 1998, Watters, 2000). The self-similarity of events in a scale-free network offers a key to understanding how cortical gamma synchronization can be reinitialized by a state transition over much of a human cerebral hemisphere (Figs. S1.12 and S1.13 in Part 1) without impediment by sulci in under a quarter cycle duration of a gamma wave (Freeman et al., 2003a). This time frame is as rapid as the re-set of phase over the much smaller rabbit olfactory bulb (Freeman and Baird, 1987).

All these properties point to a special kind of self-organization, which is termed self-organized criticality (‘SOC’, Bak, 1996, Jensen, 1998). The structural properties of axons and dendrites have already have been shown to be fractal (Braitenberg and Schüz, 1991). If the distributions of the spatial and temporal measurements of the EEG data can be shown to be fractal, then the basis for relations between the animal and human EEG may become apparent through self-similarity (Fig. S1.13 in Part 1). Most importantly, SOC might explain how human cerebral hemispheres can reorganize their activity patterns almost instantly over distances that can exceed the dimensions of most dendritic arbors by 2–3 orders of magnitude and perhaps thereby ‘bind’ (von der Malsburg, 1983) the sensory information that is held transiently in multiple widely dispersed areas almost instantly into Gestalts.

Section snippets

Experimental animals and EEG recording

A cursory description has been given in the preceding report, Part 1, of the methods by which the EEG data were acquired from rabbits that were conditioned to discriminate visual, auditory, or somatic CS in a classical aversive paradigm. EEG signals were recorded from high-density 8×8 epidural arrays over one of the 3 cortices in each of two rabbits totaling 6 sessions. Electrode spacing averaged 0.79 mm giving an array window of 5.6×5.6 mm. Sampling after analog filtering at 0.1–100 Hz was at

Measurement of phase gradients with the Fourier method

Reliable convergence of nonlinear regression in fitting the cosine basis function to the EEG segments (Appendix 2.A) was enabled by preprocessing: editing, temporal bandpass filtering (Appendix 1.A, Part 1) preceded by spatial low pass filtering (Appendix 1.B, Part 1), and segmentation in short-, medium- and long window durations. Each overlapping window stepped at 2 ms yielded two phase surfaces expressed in 8×8 matrices. Detailed analysis was undertaken of the phase surface incorporating the

EEG phase data and the concept of self-organized criticality

Phase is easily understood as a difference between the times of zero crossings of two EEG components at the same frequency. The concept is readily generalized to multiple EEG signals by computing the spatial ensemble average and measuring the time difference between each signal and the average as a common reference. It is not difficult to treat aperiodic waveforms as sums of component frequencies, giving a phase distribution for each component and each pair of locations. This empirical approach

Acknowledgements

This study was supported by grant MH 06686 from the National Institute of Mental Health, and by grants NCC 2-1244 from the National Aeronautics and Space Administration EIA-0130352 from the National Science Foundation to Robert Kozma. Programming was by Brian C. Burke. Essential contributions to surgical preparation and training of animals, data acquisition, and data analysis by John Barrie, Gyöngyi Gaál, and Linda Rogers are gratefully acknowledged.

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