Résumé : Major Depressive Disorder (MDD) is exceedingly prevalent and considered to be one of the leading cause of disability worldwide. Depression is also a heterogeneous disorder characterized by complex diagnotic approaches with a lack of diagnostic biomarker, an inconsistent response to treatment, no established mechanism, and affecting multiple physiological systems such as endocrine, immunological and cardiovasular as well.

The growing impact of the analysis of complex signals on biology and medicine is fundamentally changing our view of living organisms, physiological systems, and disease processes. In this endeavour, the basic challenge is to reveal how the coordinated, dynamical behavior of cells and tissues at the macroscopic level, emerges from the vast number of random molecular interactions at the microscopic level. In this way, the fundamental questions could be: (i) how physiological systems function as a whole, (ii) how they transduce and process dynamical information, (iii) how they respond to external stimuli, and mostly (iv), how they change during a pathological processus.

These challenges are of interest from a number of perspectives including basic modeling of physiology and practical bedside approaches to medical and risk stratification.

The general purpose of this thesis, therefore, is to study physiological time series to provide a new understanding of sleep dynamics in health, specifically as they apply to the pathological condition of MDD. More precisely: (1) to quantitatively characterize the complex, nonlinear behaviour of cardiovascular (ECG) and electroencephalographic (EEG) time series during sleep, in health and in MDD. This project will test the hypotheses that both the sleep EEG and ECG detects reorganization in the system dynamics in patient suffering from depression. (2) To develop new diagnostic and prognostic tests for MDD, by detecting and extracting “hidden information” in the ECG and EEG datasets.

Three different methods are introduced in this thesis for the analysis of dynamical systems. The first one, detrended fluctuation analysis, can reveal the presence of long-term correlations ("memory" in the physiological system) even when embedded in non-stationary time series. Graph theoretical measures were then applied to test whether disrupting an optimal pattern ["small-world network"] of functional brain connectivity underlies depression. Finally, multiscale entropy method, which is aimed at quantifying the complexity of the systems' output resulting from the presence of irregular structures on multiple scales, was applied on the ECG signal.

The results indicate that healthy physiologic systems, measured through the EEG and the ECG signals, are the most complex. According to the decomplexification theory, the depressive disease model exhibits a loss of system complexity, with potential important applications in the development and testing of basic physiologic models, of new diagnostic and prognostic tools in psychiatry, and of clinical risk stratification.