EEG analytic amplitude 1

Objective: To explain the neural mechanisms of spontaneous EEG by measuring the spatiotemporal patterns of synchrony among beta-gamma oscillations during perception. Methods: EEGs were measured from 8x8 (5.6x5.6 mm) arrays fixed on the surfaces of primary sensory areas in rabbits that were trained to discriminate visual, auditory or tactile conditioned stimuli (CSs) eliciting conditioned responses (CRs). EEG preprocessing was by (i) band pass filtering to extract the beta-gamma range (deleting theta-alpha); (ii) low-pass spatial filtering (not high-pass Laplacians used for localization), (iii) spatial averaging (not time averaging used for evoked potentials), and (iv) close spacing of 64 electrodes for simultaneous recording in each area (not sampling single signals from several areas); (v) novel algorithms were devised to measure synchrony and spatial pattern stability by calculating variances among patterns in 64-space derived from the 8x8 arrays (not by fitting equivalent dipoles). These methodological differences are crucial for the proposed new perspective on EEG. Results: Spatial patterns of beta-gamma EEG emerged following sudden jumps in cortical activity called “phase transitions”. Each transition began with an abrupt phase re-setting to a new value on every channel, followed sequentially by re-synchronization, spatial pattern stabilization, and a dramatic increase in pattern amplitude. State transitions recurred at varying intervals in the theta range. A novel parameter was devised to estimate the perceptual information in the beta-gamma EEG, which disclosed 2 to 4 patterns with high information content in the CS-CR interval on each trial; each began with a phase transition and lasted ~.1 s. Conclusions: The function of each primary sensory neocortex was discontinuous; discrete spatial patterns occurred in frames like those in cinema. The frames before and after the CSCR interval had low content. Significance: Derivation and interpretation of unit data in studies of perception might benefit from using multichannel EEG recordings to define distinctive epochs that are demarcated by phase transitions of neocortical dynamics in the CS-CR intervals, particularly in consideration of the possibility that EEG may reveal recurring episodes of exchange and sharing of perceptual information among multiple sensory cortices. Simultaneously recorded, multichannel beta-gamma EEG might assist in the interpretation of images derived by fMRI, since high beta-gamma EEG amplitudes imply high rates of energy utilization. The spatial pattern intermittency provides a tag to distinguish gamma bursts from contaminating EMG activity in scalp recording in order to establish beta-gamma recording as a standard clinical tool. Finally, EEG cannot fail to have a major impact on brain theory. Background EEG analytic amplitude 3 Walter J Freeman Table 1. Symbol List for Part 1 and Part 2 General N Number of electrodes, channels and signals in high-density EEG recording; when subscripted, N, number of qualifying phase cones Δt digitizing interval in ms w window length in T ms, also expressed as window order T in number of bins at Δt t time of midpoint of moving window in ms T elapsed time within the moving window, specified as window order in number of bins AM amplitude modulation in space of a beta or gamma carrier wave PM phase modulation in space of a beta or gamma carrier wave SDj,T(t) standard deviation of a variable in j-th channel over a time window, w, centered at t SDT(t) average of SDj,T(t) over 64 channels over a time window, w, centered at t SDX(t) standard deviation of a variable over an array of channels at one point in time, t Fourier method Vi(t) amplitude of the Fourier components within a moving window fi frequency in Hz of the EEG from the Fourier components by nonlinear regression of the i-th component on the j-th channel in a window φi,j(t) phase in radians of the EEG from the Fourier components by nonlinear regression of the i-th component on the j-th channel in a window φk(t) shuffled phase in radians in a control by randomization PSDT temporal power spectral density PSDX spatial power spectral density fo cut-off frequency in Hz of a temporal filter fx cut-off frequency in c/mm of a spatial filter, usually Gaussian Hilbert method vj(t) EEG from the j-th channel after spatial and temporal band pass filtering, also the real part of the Hilbert transform v(t) spatial ensemble average of vj(t) over N channels v’j(t) the imaginary part of the EEG from the j-th channel after spatial and temporal band pass filtering and the Hilbert transform v’(t) spatial ensemble average of v’j(t) over N channels Vj(t) vector given by the real and imaginary parts Aj(t) analytic amplitude from the Hilbert transform at the j-th channel A(t) mean analytic amplitude over N channels Pj(t) analytic phase in radians for the j-th channel from the Hilbert transform by the MATLAB atan2 function without unwrapping P(t) mean analytic phase in radians over Pj(t) from N channels pi(t) analytic phase in radians from the Hilbert transform by the MATLAB atan function after unwrapping p(t) mean unwrapped phase over pi(t) from N channels Δpj(t) successive analytic phase differences were calculated from pj(t) by the atan function after unwrapping ω(t) time-varying instantaneous frequency in rad/s from Δpj(t) divided by Δt Background EEG analytic amplitude 4 Walter J Freeman CAPD coordinated analytic phase differences (Freeman, Burke and Holmes, 2003) Measures derived from analytic amplitude in Part 1. Aj(t) analytic amplitude squared waveform on the j-th channel at intervals of Δt A(t) spatial ensemble average of Aj(t) over the 64 channels in the window, w. of length T SDj,T(t) standard deviation of the j-th signal Aj,T(t) in the window, w SDT mean of the N values of SDj,T(t) in window, w SDT standard deviation of the mean wave form A(t) in window, w Re(t) ratio of the SDT of the mean signal to the mean SDT of the N signals, a measure of synchrony among a collection of aperiodic “chaotic” wave forms, giving an indirect estimate of the order parameter, k A(t) a normalized spatial pattern of amplitude that is formed by N channels of EEG designating a point in N-space that is evaluated by an Nx1 vector De(t) change in normalized spatial pattern given by Euclidean distance between successive points separated by Δt, given by the vector length between A (t) and A (t-1) ki,j feedback gain coefficient between the i-th and j-th populations; an estimator of the order parameter that is the intensity of synaptic interaction in populations of cortical neurons and that is symbolized in models by the nonlinear gain Δk an estimator of a change in order parameter and ki,j with Δt that is approximated by De E(t) an estimator of free energy that is approximated by A(t) from the square of the EEG current, i(t), estimated from the potential difference, v(t), established by its passage across fixed tissue specific resistance, r: i = v / r ΔE change in free energy in Δt at t, approximated by A(t) He pragmatic information provided by a pattern, A, where He = ΔE / Δk ~ A/ De Parameters of cones fitted to phase by Fourier [φi,j(t)] or Hilbert [Pj(t)] method in Part 2 x, y the coordinates of the phase cone from the center of the array at xo, yo in mm Φo(t) height of the fitted cone above the plane of fit (the pial surface of the cortex) in radians Φj(t) value of phase at the j-th electrode from the fitted cone in radians γ(t) gradient of phase cone in radians/mm at time, t in ms γk average phase gradient over the duration of a stable phase cone in radians/mm Wx spatial wavelength in mm/radian fN average frequency over the N-th qualifying phase cone in Hz from Fourier method ωN average analytic frequency over N-th qualifying phase cone in rad/s from Hilbert method Wt temporal wavelength in ms/radian β phase velocity in m/s Dx half-power diameter of phase cone in mm Background EEG analytic amplitude 5 Walter J Freeman