We report here on a first attempt to settle the methodological controversy between advocates of two alternative reconstruction approaches for temporal dynamics in brain signals: the single‐channel method (using data from one recording site and reconstructing by time‐lags), and the multiple‐channel method (using data from a spatially distributed set of recordings sites and reconstructing by means of spatial position). For the purpose of a proper comparison of these two techniques, we computed a series of EEG‐like measures on the basis of well‐known dynamical systems placed inside a spherical model of the head. For each of the simulations, the correlation dimension estimates obtained by both methods were calculated and compared, when possible, with the known (or estimated) dimension of the underlying dynamical system. We show that the single‐channel method fails to reliably quantify spatially extended dynamics, while the multichannel method performs better. It follows that the latter is preferable, given the known spatially distributed nature of brain processes. Hum. Brain Mapping 5:26–47, 1997. © 1997 Wiley‐Liss, Inc.

Entropy of neuronal dynamics was computed using nonlinear forecasting methods and multichannel reconstruction. These methods were tested using numerical simulations and applied to neuro-electrical data in normal and pathological conditions.

We present a procedure to quantify spatio-temporal dynamics applied here to brain surface recordings during three distinct cognitive tasks. The method uses 19 sites of EEG recording as spatial embedding for the reconstruction of trajectories, global and local linear indices, and non-linear forecasting methods to quantify the global and local information loss of the dynamics (K-entropy). We show that K-entropy can differentiate between raw and multivariate phase random surrogate data in a significant percentage of EEG segments, and that relevant non-linear indices are best studied in time segments not longer than 4 s. We also find a certain complementarity between local non-linear and linear indices for the discrimination between the three cognitive tasks. Moreover, localized projections onto electrode site of K-entropy provide a new kind of brain mapping with functional significance.

Key words: Non-linear forecasting, Electroencephalogram, K-entropy, Spatio-temporal dynamics

Mathematical models are helpful in the understanding of diseases through the use of dynamical indicators. A previous study has shown that brain activity can be characterized by a decrease of dynamical complexity in depressive subjects. The present paper confirms and extends these conclusions through the use of recent methodological advances: first episode and recurrent patients strongly differ in their dynamical response to therapeutic interventions. These results emphasize the need for clinical follow-ups to avoid recurrence and the necessity of specific therapeutic intervention in the case of recurrent patients.