Fine Temporal Resolution of Analytic Phase Reveals Episodic Synchronization by State Transitions in Gamma EEGs

Abstract

The analytic signal given by the Hilbert transform applied to an electroencephalographic (EEG) trace is a vector of instantaneous amplitude and phase at the temporal resolution of the digitizing interval (here 2 ms). The transform was applied after band-pass filtering for extracting the gamma band (20–80 Hz in rabbits) to time series from up to 64 EEG channels recorded simultaneously from high-density arrays giving spatial “windows” of 4 × 4 to 6 × 6 mm onto the visual, auditory, or somatosensory cortical surface. The time series of the analytic phase revealed phase locking for brief time segments in spatial patterns of nonzero phase values from multiple EEG that was punctuated by episodic phase decoherence. The derivative of the analytic phase revealed spikes occurring not quite simultaneously (within ±4 ms) across arrays aperiodically at mean rates in and below the theta range (3–7 Hz). Two measures of global synchronization over a group of channels were derived from analytic phase differences between pairs of channels on the same area of cortex. One was a synchronization index expressing phase locking. The other was a decoherence index estimating the variance in phase among multiple channels. Spectral analyses of the indices indicated that decoherence events recurred aperiodically at rates in and below the theta range of the EEGs. The results provide support for the hypothesis that neurons in mesoscopic neighborhoods in sensory cortices self-organize their activity by synaptic interactions into wave packets that have spatial patterns of amplitude (AM) and phase (PM) modulation of their spatially coherent carrier waves in the gamma range and that form and dissolve aperiodically at rates in and below the theta range. Each AM pattern is formed by a nonlinear state transition in the cortical dynamics, as shown by spikes in the derivative. Phase locking within each PM pattern is not at zero phase lag but over a fixed distribution of phase values that is consistent with the radially symmetric phase gradients already reported called “phase cones” detected by Fourier-based methods. The insight is suggested that sensory cortices are bistable comparably to cardiac dynamics, with a diastolic state that accepts sensory input and an abrupt transition to a systolic state that transmits perceptual output. Further support for this inference will require improvements in methods for temporal resolution of the times of onset of spatial patterns of phase modulation.