Estimating global phase synchronization by quantifying multivariate mutual information and detecting network structure

In neuroscience, phase synchronization (PS) is a crucial mechanism that facilitates information processing and transmission between different brain regions. Specifically, global phase synchronization (GPS) characterizes the degree of PS among multivariate neural signals. In recent years, several GPS methods have been proposed. However, they primarily focus on the collective synchronization behavior of multivariate neural signals, while neglecting the structural difference between oscillator networks. Therefore, in this paper, we introduce a method named total correlation-based synchronization (TCS) to quantify GPS intensity by examining network organization. To evaluate the performance of TCS, we conducted simulations using the Rössler model and compared it to three existing methods: circular omega complexity, hyper-torus synchrony, and symbolic phase difference and permutation entropy. The results indicate that TCS outperforms the other methods at distinguishing the GPS intensity between networks with similar structures. And it offers insight into the separation and integration behavior of signals during synchronization. Furthermore, to validate this method with experimental data, TCS was applied to analyze the GPS variation of multichannel stereo-electroencephalography (SEEG) signals recorded from onset zones of patients with temporal lobe epilepsy. It was observed that the termination of seizures was associated with the increased GPS and the integration of brain regions. Taken together, TCS offers an alternative way to measure GPS of multivariate signals, which may shed new lights on the mechanism of brain functions and neurological disorders, such as learning, memory, epilepsy, and Alzheimer's disease.