Functional relationship between cerebral structures: from linear to non-linear.

Two kinds of methods are available in order to assess the functional relationships between different cerebral structures from the analysis of EEG signals: linear and non-linear methods. In this paper, we describe didactically the methodological bases of signal processing. After recalling the significance of the fundamental parameters of a sine wave: frequency, amplitude and phase, we show, from a first example about an epileptic seizure propagation, how a linear variation between phase and frequency can be interpreted as a small time difference between two EEG channels. This linear method hypothesises that these two signals are respectively the input and the output of a linear system. Then, we point out the limits of this method and we introduce non-linear methods. Among the latter, a recent approach introduces a realistic model of EEG which try to relate signal measured quantities to relations between underlying structures which produce them. (C) 2002 Editions scientifiques et medicales Elsevier SAS.