Entropy-based measure for assessing global synchronicity in EEG signals

Neuronal oscillations and their inter-areal synchronisation are fundamental for brain function and cognitive processes. While electrophysiological recordings, such as electroencephalography (EEG), provide invaluable insights, existing quantitative methodologies for assessing neuronal synchrony often focus on pairwise interactions, thereby limiting a comprehensive understanding of global network coordination. This study proposes principal component (PC)-entropy, a novel multichannel synchronisation metric designed to quantify the global degree of synchrony within brain signals. PC-entropy is a hybrid measure derived from Principal Component Analysis and Shannon entropy, specifically by applying normalised entropy to the eigenvalues obtained from data covariance. This approach effectively translates the distribution of variance across principal components into a synchrony measure, ranging from 0 (perfect synchrony) to 1 (complete desynchronisation), and is notably robust to variations in the number of recording channels.We validated PC-entropy using synthetic data from the Kuramoto model, including non-isofrequency signals, demonstrating its efficacy in assessing synchronisation. Subsequently, we applied PC-entropy to diverse human EEG datasets. Our results indicate its capacity to detect changes in synchrony preceding epileptic seizure onset, differentiate between sleep stages, reflect levels of consciousness in coma patients, and distinguish performance in arithmetic tasks.PC-entropy offers a valuable and sensitive tool for assessing global brain synchrony. It provides a new dimension for understanding functional connectivity and various physiological states, extending beyond the limitations of pairwise analyses and conventional spectral approaches.