Topographic Organization of Nonlinear Interdependence in Multichannel Human EEG M. Breakspear* , † , ‡ ,1 and J. R. Terry§ *Brain Dynamics Centre, Westmead Hospital, Westmead, NSW, 2145, Australia; †School of Physics, Faculty of Science, ‡Department of Psychological Medicine, Faculty of Medicine, University of Sydney, NSW, 2008, Australia; and §Department of Mathematics, University of Queensland, St. Lucia, Queensland, 4072, Australia Received October 18, 2001 This paper investigates the spatial organization of nonlinear interactions between different brain re- gions in healthy human subjects. This is achieved by studying the topography of nonlinear interdepen- dence in multichannel EEG data, acquired from 40 healthy human subjects at rest. An algorithm for the detection and quantification of nonlinear interdepen- dence is applied to four pairs of bipolar electrode derivations to detect posterior and anterior inter- hemispheric and left and right intrahemispheric in- terdependences. Multivariate surrogate data sets are constructed to control for linear coherence and finite sample size. Nonlinear interdependence is shown to occur in a small but statistically robust number of epochs. The occurrence of nonlinear interdependence in any region is correlated with the concurrent pres- ence of nonlinear interdependence in other regions at high levels of significance. The strength, direction and topography of the interdependences are also corre- lated. For example, posterior interhemispheric inter- dependence from right-to-left is strongly correlated with right intrahemispheric interdependence from back-to-front. There is a subtle change in these corre- lations when subjects open their eyes. These results suggest that nonlinear interdependence in the human brain has a specific topographic organization which reflects simple cognitive changes. It sometimes occurs as an isolated phenomenon between two brain re- gions, but often involves concurrent interdepen- dences between multiple brain regions. © 2002 Elsevier Science (USA) INTRODUCTION Investigations of synergistic activity between differ- ent brain regions have generally employed linear mea- sures of interdependence such as the coherence func- tion. For example, Acherman et al. (1998) used the coherence function to illustrate strong coherence of sleep spindles across the scalp, and sleep-stage depen- dent changes in regional coherence. Recent advances in time series analysis now permit the examination of EEG data for evidence of nonlinear interdependence. Several papers have employed these techniques to il- lustrate strong nonlinear interdependence between scalp (Le Van Quyen et al., 1999) and intracortical (Arnhold et al., 1999) EEG channels prior to and dur- ing epileptic seizures. It appears that in temporal lobe epilepsy, for example, the epileptic focus slaves the dynamics in other brain regions through a type of nonlinear synchronization. The appearance of strong nonlinear interdependence presumably reflects abnor- mally strong synchronization of neuronal activity aris- ing in pathological brain tissue. The contribution of synchronous cortical activity to normal cognitive functions has been studied in a vari- ety of experimental designs (e.g., Gray et al., 1989; Stopfer et al., 1989; Miltner et al., 1999; Rodriguez et al., 1999; Haig et al., 2000). Synchronization has been proposed as a mechanism of achieving functional inte- gration between specialized neural networks respond- ing to different aspects of a single sensory stimulus (Singer, 1995). To what extent do nonlinear mecha- nisms contribute to functional integration during cog- nitive activities? Friston (1997) suggested that nonlin- ear forms of neural interdependence may in fact play a crucial role in large-scale neural cooperation. Specifi- cally, nonlinear coupling may facilitate integration be- tween distributed neural systems each exhibiting dis- tinct local activity. The coherence function, however, is only sensitive to shared activity confined to the same narrow band frequency domains (such as 40 Hz gamma activity). We recently studied nonlinear interdepen- dence between posterior bipolar EEG leads (O 1 P 3 /O 2 P 4 ) in 40 normal subjects, using a mutual nonlinear pre- diction algorithm and multivariate surrogate data sets (Breakspear et al., 2001). Statistical analysis revealed strong evidence for weak and irregular nonlinear in- 1 To whom correspondence and reprint requests should be ad- dressed. Fax: 61-2-9635-7734. E-mail: mbreak@physics.usyd.edu.au. NeuroImage 16, 822– 835 (2002) doi:10.1006/nimg.2002.1106 822 1053-8119/02 $35.00 © 2002 Elsevier Science (USA) All rights reserved.