On the intrinsic time scales involved in synchronization: a data-driven approach

We address the problem of detecting, from scalar observations, the time scales involved in synchronization of complex oscillators with several spectral components. Using a recent data-driven procedure for analyzing nonlinear and nonstationary signals [Huang, Proc. R. Soc. London A 454, 903 (1998)], we decompose a time series in distinct oscillation modes which may display a time varying spectrum. When applied to coupled oscillators with multiple time scales, we found that motions are captured in a finite number of phase-locked oscillations. Further, in the synchronized state distinct phenomena as phase slips, anti-phase or perfect phase locking can be simultaneously observed at specific time scales. This fully data-driven approach (without a priori choice of filters or basis functions) is tested on numerical examples and illustrated on electric intracranial signals recorded from an epileptic patient. Implications for the study of the build-up of synchronized states in nonstationary and noisy systems are pointed out.     

Nonlinear EEG Changes Associated with Clinical Improvement in Depressed Patients

Assuming that the depressive syndrome could be related to a cerebral dynamical disease, we attempted to describe in a longitudinal and quantitative manner the modifications of brain electrical activity during depressive episodes treatment. This study tested whether mood improvement during therapy (pharmacological treatment or electroconvulsive therapy) is related to concomitant modifications of brain dynamics. The evolution of brain activity and mood were measured, every two days during treatment for three depressed patients and over three weeks for a control subject. Complexity of brain electrical activity was computed for each site of recording (EEG with 31 electrodes), leading to maps of complexity; depressive mood modulations were quantified using a self-assessment scale. The results show a specific organization of depressed patients' brain dynamics compared to the control's dynamics. Moreover, covariations between nonlinear changes in brain dynamics and mood improvement are observed during the remission of depressive episodes.     

Nonlinear EEG Changes in a 48-Hour Cyclic Manic-Depressive Patient

This research report presents the case study of a 48-hour cyclic manicdepressive patient which further demonstrates the association between nonlinear EEG characteristics and mood variations as previously reported by Thomasson et al. (2000). The evolution of brain dynamics and mood were daily measured during a week. Global complexity of brain electrical activity was estimated by a nonlinear index (entropy) and mood modulations were evaluated by a clinical self-assessment scale (BfS'). Illustrating the concept of dynamical disease, a significant co-variation between the nonlinear EEG index and mood evolution (Spearman correlation coefficient = 0.92, p = .008) was observed. This result strengthens the previous ones and demonstrates a clear association between nonlinear brain dynamics and state of mind in psychopathology.