Journal of Neuroscience Methods 156 (2006) 111–128 Measurement of phase gradients in the EEG D.M. Alexander a,b,∗ , C. Trengove a,b , J.J. Wright c , P.R. Boord d , E. Gordon a,d,e a Brain Resource Company and Brain Resource International Database, PO Box 737, Broadway, Sydney, 2007 NSW, Australia b Faculty of Information Technology, University of Technology, PO Box 123, Broadway NSW 2007, Australia c The Liggins Institute, University of Auckland, 2-6 Park Avenue, Grafton 1001, Auckland, New Zealand d Brain Dynamics Centre, Acacia House, Westmead Hospital, PO Box 533, Wentworthville, NSW 2145, Australia e Brain Dynamics Centre, Westmead Millenium Institute and Department of Psychological Medicine, University of Sydney, PO Box 533, Wentworthville, NSW 2145, Australia Received 23 November 2005; received in revised form 4 February 2006; accepted 13 February 2006 Abstract 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. © 2006 Elsevier B.V. All rights reserved. Keywords: Electroencephalogram; Brain dynamics; Phase gradient; Auditory oddball; Spatio-temporal waves 1. Introduction 1.1. Spatio-temporal waves in the cortex Spatio-temporal waves in the gamma band have been mea- sured in visual, auditory, somatic and olfactory areas of the cortex (Eckhorn et al., 2001; Freeman and Barrie, 2000). Related findings have been made for waves in the alpha band (Roelfsema et al., 1997). In a review of earlier research on waves in the EEG, Hughes (1995a) suggest that abnormal mental states may be associated with alpha waves travelling in the posterior-anterior direction. EEG waves have also been described propagating from lateral to midline sites, or vice versa, depending on the subject’s task ∗ Corresponding author. Tel.: +61 2 9211 7120; fax: +61 2 9211 2710. E-mail address: dalex@brainresource.com (D.M. Alexander). (resting, calculation, emotional or pain experience; Hughes et al., 1995b). Ribary et al. (1991), using magneto-encephalogram (MEG), described an anterior to posterior spatio-temporal wave in the gamma band that occurs during the processing of auditory stimuli. In the EEG, anterior to posterior phase gradients in the alpha band have been recorded during a resting condition (Ito et al., 2005; Nunez et al., 2001). A posterior to anterior phase gra- dient in the alpha band has been recorded in response to steady state visual stimulation (Burkitt et al., 2000) and during a visual memorization task (Schack et al., 1999). Theta band travelling waves have been implicated in the transfer of visual information from long-term memory to working memory. Retrieval attempts are associated with an anterior to posterior wave motion, with a reversal to a posterior to anterior wave motion upon success- ful retrieval (Sauseng et al., 2002). Travelling waves have been detected during sleep that show a variety of behaviours, but more often originate in prefrontal–orbitofrontal regions and propagate posteriorly (Massimini et al., 2004). 0165-0270/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2006.02.016