Interdependence of EEG signals: linear vs. nonlinear associations and the significance of time delays and phase shifts.

To investigate the degree of interdependence of EEG signals, we have to use signal analysis methods. Three of these are described and their performance is compared: the cross-correlation (coherence and phase), the average amount of mutual information (AAMI) or the normalized AAMI, also called transmission coefficient T, and the correlation ratio h2 that is a general measure of nonlinear fit between any two signals. The three methods were applied to simulated and real signals in order to put in evidence how nonlinear relationships may affect differently these three measures of association. The nature of the interdependence between EEG signals is not characterized only by the degree of association, but also by the corresponding phase relationship. A basic question is whether such a phase shift can be interpreted as a transmission delay. However, a fundamental problem is that a phase shift may be difficult to interpret in terms of a biophysical model. A procedure is described in order to solve this problem. This involves computing the phase spectrum between the pair of signals, estimating the gain of the corresponding linear transfer function and the associated minimum phase. By subtracting the minimum phase from the phase spectrum, a corrected phase function can be obtained. From the slope of this phase function, a transmission delay can be estimated. This procedure is illustrated by applications to simulated and real EEG signals. It is demonstrated that from phase shifts we may estimate transmission delays between at least certain classes of EEG signals. In this way we can asses, unambiguously, how the transmission of information between different brain sites develops.