06 Mai – Thesis defense - Alexandre Guillet

14 h Amphi G / Building A29 | University of Bordeaux (Talence campus)

Revisiting statistical physics tools for the complex time-frequency characterization of physiological signals.

An analytical tool for the observation of the dynamics of living organisms is developed in this thesis, and applied to the study of interactions between the cardiac, respiratory and neural systems based on human recordings during sleep. These physiological signals are peculiar and complex: each recording is unique, non-stationary and cannot be reproduced.  To solve this issue, a time-frequency analysis of physiological signals, based on analytic wavelets also called ``time-frequency atoms'', is proposed. The first part A of this thesis introduces this formalism, highlighting the adequacy of the log-normal wavelet in that context, the importance of the associated quality factor $Q$ and its correspondence with the Heisenberg uncertainty principle. Extending this approach to the estimation of the time-frequency coherence of physiological signals, we separate temporal from spectral resolutions in order to introduce statistical degrees of freedom in this analysis. To assist the observation of physiological interactions between different sources, we define a generic family of complex rate estimators capturing both the modulations of the instantaneous frequency and amplitude, in a spectral band of interest. The second part B illustrates this methodology on physiological signals from polysomnography databases. The rich specificities of fluctuating rhythms contained in electrocardiograms (ECG), breathing signals and electroencephalograms (EEG) are thoroughly discussed to validate the generic estimation of the time-frequency coherence between pairs of recordings or their rate transformations. We compare the effectiveness of wide-band and narrow-band estimators in retrieving heart rate modulations, relative to a reference extraction method. From coherent cardiac and respiratory modulations, we observe three distinct scales of interaction: a fast one at the fundamental breathing frequency (RSA), a slow and less rhythmic one and an even slower one, regulating cardio-respiratory rates. In the wavelet framework, we propose an original time-dependent representation of the frequency ratios of cardiac and breathing rhythms that turns out very effective for tracking signatures of sleep apnea, rapid eye movement (REM) phases, and deep sleep stages. This approach of the cardio-respiratory coupling also offers a new perspective to detect synchronization episodes of cardio-respiratory coupling and their temporal fluctuations. The neural activity during sleep is introduced from the time-frequency analysis of EEG signals, and their characteristic sequences of multi-band power density and coherence patterns. Finally, we gather cardio-respiratory rates and neural magnitude signals and compare them in pairs in terms of time-frequency coherence. From an extensive analysis of 2650 recordings from a large polysomnography database, we point out the increased amplitude and coherence of slow apneic modulations, systematically emerging as a spectral peak as compared to a flat baseline without apnea. We also show that apnea is concomitant with a strong coherence reduction of the fast RSA cardio-respiratory interaction and the very slow neuro-respiratory interaction. This study paves the way to new developments, outlined in the end of this thesis, such as the detection of sleep spindles from the phase of the sigma EEG band, and the coherence of their amplitude with slow delta oscillations during deep sleep.

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