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

Abstract

Objective: To explain spontaneous EEG through measurements of spatiotemporal patterns of phase among beta-gamma oscillations.Methods: High-density 8x8 intracranial arrays were fixed over sensory cortices of rabbits. EEGs were spatially low pass filtered, temporally band pass 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 2-D 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 phase 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. Betagamma 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 phase transitions (avalanches, bubbles) large enough to include the multiple sensory areas that are necessary to form Gestalts (multisensory percepts).Background EEG analytic phase 3Walter J Freeman

Natural world physical, brain operational, and mind phenomenal space–time

“…Observations of EEG signal show that it is characterized by the more or less stable (quasistationary) episodes and sudden changes in amplitude [226,257,258], frequency [243,244] and phase [259][260][261][262]. Such abrupt changes in one or several of these EEG characteristics (amplitude, frequency or phase) mark a brief state of indeterminacy -transition (we will return to this in Section 4.2).…”

Power spectral density changes and language lateralization during covert object naming tasks measured with high-density EEG recordings

“…The notation PSDt is used to emphasize that it is the power spectral density of the time-domain EEG data and it is different from the spatial power spectral density (PSDx or PSDz) of scalp EEG data. Such notations are becoming very common in the EEG literature [13,14]. …”

Dynamics of human neocortex that optimizes its stability and flexibility

“…The Hilbert transform was used to get two essential quantities in each frame: the rate of change in phase with time (the frequency ω in rad/sec or Hz) and the rate of change in phase with distance (the gradient γ in rad/mm) [Freeman, 2004a]. Use of the Hilbert transform required further data preprocessing in four steps: (i) selecting 5 s blocks by visual editing; (ii) computing PSD T (Fig.…”

“…Details and rationales have been published previously Freeman, 2005]. The phase measurements by the Hilbert transform were cross-validated by phase measurements using Fourier decomposition, within the limits of each method on temporal resolution [Freeman, 2004a].…”

“…This well-known "spontaneous" background EEG has been conventionally treated as "noise" and removed by averaging over multiple trials to derive event-related potentials that are postulated to signify cortical responses to impulse inputs like clicks, flashes, and so on. Avoiding time averaging enabled measurement of remarkable spatiotemporal structures in patterns of phase and amplitude in the background EEG [Freeman, 2004a[Freeman, ,b, 2005. The behaviorally related EEG patterns with CS were formed by phase transitions from the background attentive state to a state of categorizing the CS [Ohl, Scheich and Freeman, 2001;Ohl et al, 2003;Freeman, 2005], and their contents were mostly derived from pre-existing activity in the background relating to categories of stimuli and not from the stimulus-evoked activity.…”