Measurement of phase gradients in the EEG

Previous research has shown that spatio-temporal waves in the EEG are generally of long spatial wavelength and form smooth patterns of phase gradients at particular time-samples. This paper describes a method to measure smooth phase gradients of long spatial wavelength in the EEG. The method depends on the global pattern of phase at a given frequency and time and is therefore robust to variations, over time, in phase-lag between particular sites. Phases were estimated in the EEG signal using wavelet or short time-series Fourier methods. During an auditory oddball task, phases across the scalp tend to fall within a limited circular range, a range that is not indicative of phase-synchrony nor waves with multiple periods. At times the phases tended to maintain a spatially and temporally ordered relationship. The relative phases were analysed using three phase gradient basis functions, providing a measure of the amount of variance explained, across the electrodes, by smooth changes in relative phase from a single minimum or single maximum. The data from 586 adult subjects were analysed and it was found that the probability of phase gradient events varies with time and frequency in the stimulus-locked average, and with task demands. The temporal extent of spatio-temporal waves was measured by detecting smoothly changing patterns of phase latencies across the scalp. The specific spatial pattern and timing of phase gradients correspond closely to the latency distributions of certain ERPs.