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A New Novel Synchronization Index of Brain Networks in Hyperbolic EEG Dynamics

The functional connectivity ofbrain connectivity changes its pattern over time i.e. dynamics, even in the resting state with an infinite number of degrees of freedom with local couplings. Recently, quantifying the level of synchrony has received considerable attention. We hypothesized that time-varying instantaneous phase synchronization over local couplings are defined in hyperbolic space and different brain regions can identify failures, flexibility, and stability in network dynamics.Our goal is to understand the phase synchronization changes of the beta-gamma band, and in addition, to investigate Shannon entropy based on phase synchronization stability. Whole EEG dynamics from local phase synchronizations was used to detect treatment resistance from both hemispheres in OCD patients. Temporal filtering and Hilbert transforms were performed to infer beta-gamma band phase difference activity from the EEG brain dynamics.Then, the response beta-gamma band phase stability was quantified using a new phase synchronization index (PSI). Results indicated significantly changed phase synchronization of the response and non-response to treatment, patients in OCD patients in F7 electrode. Greater phase fluctuations of beta-gamma synchronizations in treatment resistance OCD is claiming phase deficiencies within neural populations.This study first provides experimental and theoretical support for characterizing cycle structure depends on the non-Euclidian dynamics of neural phase synchrony caused by disturbances of underlying neurotransmitter systems, as reflected in different normal and disease states.

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