Technical Note Synchronization likelihood with explicit time-frequency priors T. Montez, a,b, ⁎ K. Linkenkaer-Hansen, c B.W. van Dijk, a and C.J. Stam a a Department of Clinical Neurophysiology and MEG Centre, VU University Medical Center, Amsterdam, The Netherlands b Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Portugal c Center for Neurogenomics and Cognitive Research (CNCR), Department of Experimental Neurophysiology, Vrije Universiteit Amsterdam, The Netherlands Received 24 November 2005; revised 29 May 2006; accepted 25 June 2006 Available online 3 October 2006 Cognitive processing requires integration of information processed simultaneously in spatially distinct areas of the brain. The influence that two brain areas exert on each others activity is usually governed by an unknown function, which is likely to have nonlinear terms. If the functional relationship between activities in different areas is domi- nated by the nonlinear terms, linear measures of correlation may not detect the statistical interdependency satisfactorily. Therefore, algo- rithms for detecting nonlinear dependencies may prove invaluable for characterizing the functional coupling in certain neuronal systems, conditions or pathologies. Synchronization likelihood (SL) is a method based on the concept of generalized synchronization and detects nonlinear and linear dependencies between two signals (Stam, C.J., van Dijk, B.W., 2002. Synchronization likelihood: An unbiased measure of generalized synchronization in multivariate data sets. Physica D, 163: 236–241.). SL relies on the detection of simultaneously occurring patterns, which can be complex and widely different in the two signals. Clinical studies applying SL to electro- or magnetoence- phalography (EEG/MEG) signals have shown promising results. In previous implementations of the algorithm, however, a number of parameters have lacked a rigorous definition with respect to the time- frequency characteristics of the underlying physiological processes. Here we introduce a rationale for choosing these parameters as a function of the time-frequency content of the patterns of interest. The number of parameters that can be arbitrarily chosen by the user of the SL algorithm is thereby decreased from six to two. Empirical evidence for the advantages of our proposal is given by an application to EEG data of an epileptic seizure and simulations of two unidirectionally coupled Hénon systems. © 2006 Elsevier Inc. All rights reserved. Keywords: Nonlinear dynamics; Generalized synchronization; Synchroniza- tion likelihood; EEG; MEG; Time-delay embedding; Functional connectivity Introduction Cognition depends on coordinated neuronal activity in spatially distinct areas of the brain (Varela et al., 2001). Two central issues in cognitive neuroscience are to detect the brain areas that interact during various tasks and to reveal the nature of their interaction. It is natural to assume that the coordination of activity or exchange of information between brain areas gives rise to a statistical interdependence between the activities in these areas. In other words, we may reveal the spatial functional connectivity underlying cognitive processing by mapping the statistical interdependencies between time series of neuronal data recorded from different anatomical locations (Lee et al., 2003). The evidence suggests that functional interactions are mediated by synchronization of oscillations and that the frequency content of these oscillations has some specificity to the function that they serve (Sarnthein et al., 1998; von Stein and Sarnthein, 2000; Varela et al., 2001). Nevertheless, neuronal activity patterns may be related through nonlinear functions including strongly transient or cross-frequency phase locking (Friston, 2000; Stam et al., 2003; Palva et al., 2005a). To detect statistical interdependencies that are not governed by simple linear functions, so-called “nonlinear methods” are required. Many coupling measures for detecting linear and nonlinear interdependencies have been proposed (for a review, see Stam, 2005). Currently, there is no consensus on how to best detect non- linear interdependencies in neurophysiological data (Quiroga et al., 2002; David et al., 2004). In fact, different algorithms have been shown to detect nonlinear interactions between brain regions (Stam et al., 2003). The most general form of interaction between two dynamical systems is generalized synchronization, where the state of a response system Y is a function of the state of the driver system X: Y = F(X)(Rulkov et al., 1995). For neural systems, this implies that if a given area generates a specific pattern of activity (X) at different times, the functionally connected brain areas are likely to generate specific patterns of activity F(X) at those same points in time. Note that the patterns in the different areas may be widely different because of the potentially nonlinear coupling that governs the functional relationships (in other words, F may be a nonlinear www.elsevier.com/locate/ynimg NeuroImage 33 (2006) 1117 – 1125 ⁎ Corresponding author. MEG Centre, VU University Medical Center, P.O. Box 7057, 1007 MB Amsterdam, The Netherlands. Fax: +31 20 444 4816. E-mail address: t.montez@vumc.nl (T. Montez). Available online on ScienceDirect (www.sciencedirect.com). 1053-8119/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2006.06.066