EMPIRICAL MODE DECOMPOSITION OF EEG SIGNALS FOR SYNCHRONISATION ANALYSIS C. M. Sweeney-Reed 1 , A. O. Andrade 1 , S. J. Nasuto 1 1 Department of Cybernetics, School of Systems Engineering, University of Reading, Reading, UK C.M.Sweeney@rdg.ac.uk, A.D.O.Andrade@rdg.ac.uk, S.J.Nasuto@rdg.ac.uk Abstract – Synchronisation has been proposed as the mechanism for the dynamic integration of neuronal activity required to produce coherent cognitive acts. The detailed study of brain dynamics is expected to enhance understanding of how cognition takes place. In this paper, we introduce a novel method of detection of synchronisation between EEG signals by using empirical mode decomposition (EMD), which decomposes a signal into components known as Intrinsic Mode Functions (IMFs). The results, using simulated signals, suggest that the IMFs may be used to determine the particular frequency bandwidths in which synchronisation phenomena occur. I. INTRODUCTION Physiological, neuro-imaging, and neuropsycho- logical studies provide evidence of anatomical and functional specialisation of the brain [1]. The integration of the activity of these separate regions to produce a coherent, conscious cognitive act may take place through emergence of transient dynamical neural ensembles mediated by synchrony [1]. A neural assembly is thought to arise by formation of dynamic links, comprising preferential interactions among a particular subgroup of neurons firing synchronously over multiple frequency bands [1, 2]. Assemblies may form over large as well as local scales and are thought to last for the 50-200 ms required for a cognitive act to take place [1] . In this paper, we introduce the application of Empirical Mode Decomposition (EMD) to the detection of synchronisation in EEG signals. EMD is a tool for analysis of nonlinear, nonstationary time series [3], and its application is therefore appropriate for EEG analysis. It decomposes a signal, based on the local, characteristic time scale of the data, into a finite number of intrinsic mode functions (IMFs) [3]. It is shown from the analysis of synthetic EEG signals that IMFs may provide an alternative way of studying neuronal synchrony. II. METHODS A. EEG Data It is often assumed that synchronisation between different EEG sources may take place over narrow frequency bands. Thus we simulated such a situation by using real EEG data which were subsequently processed to produce synthetic signals reminiscent of EEG but with the desired synchrony pattern. The EEG data were recorded at the University of Graz during imagined finger movements [4]. The study reported in this article used two EEG channels from a single subject in one trial, recorded for 9 s and sampled at 128 Hz. B. Simulation of EEG signal As stated above, two independent signals were required, with a period of synchronisation in a particular frequency band. The 1 st EEG channel, x, and the 2 nd , y, were bandpass filtered, using a 4 th order Butterworth filter, to obtain the 4-7 Hz frequency band from each. These were then synchronised for a period of 500 ms, using a model adapted from [5], described in Eq. 2: y x z ) 1 ( ε ε − + = Eq. 2 where z is a vector which is coupled to x, and ε is the coupling coefficient. ε begins at 2500 ms. Its value increases gradually from 0 to 1, then back to 0. When ε equals 0, z equals y, so there is no synchrony with x. When ε equals 1, z is equal to x, giving complete synchrony between z and x. 500 ms was chosen, to give a high degree of synchrony over a timescale of physiological relevance (50-200 ms) [1]. x and y were then made orthogonal during the times before and after the period in which the synchronisation was introduced. Each data sequence, x and y, was divided into 18 windows. Window 5 begins at 2500 ms, so it was excluded from this stage. For each of the other windows (1-4 and 6-18), a vector q, which was to be orthogonal to x, was created, by projection onto y. q is defined in Eq. 1: x x x y x y q ⋅ − = T T Eq. 1 The 1 st channel of EEG data, x, was then used as Signal 1. To create window 5 for Signal 2, the frequency band greater than 7 Hz and the band less than 4 Hz from y, and the 4-7 Hz vector that was synchronised during window 5 with its counterpart in Signal 1, were summed to produce an auxiliary vector. Summation was used, as the Fourier transform is a linear transformation, so the properties are preserved. Signal 2 was then built by concatenating the data from windows 1-4 of q, then the data from window 5 of the auxiliary vector, then windows 6-18 of q. This resulted in a Signal 2 that is independent of Signal 1, except in the 4-7 Hz band, where synchrony increases, then decreases, over a period of 2500ms to 3000ms. C. Empirical Mode Decomposition EMD can be used to decompose any time series into a finite number of functions called intrinsic mode functions (IMFs). These have been defined by Huang et al as a class of functions satisfying two conditions [3]. Firstly, in the whole data set, the number of extrema and zero crossings must be equal or differ by a maximum of one. Secondly, the mean value of the envelope defined by the local maxima, and that defined by the local minima, must equal zero at any point. The above conditions ensure that the IMFs may have a physical meaning, and they enable visualisation of the signal in different time scales.