# A principal component entropy metric for assessing global synchronicity in EEG signals

## TL;DR

This paper introduces a new method called PC-entropy to measure global brain synchrony using EEG signals, which can detect changes in neural coordination during sleep, epilepsy, coma, and cognitive tasks.

## Contribution

The novel PC-entropy metric combines principal component analysis and entropy to assess global EEG synchrony, overcoming limitations of pairwise methods.

## Key findings

- PC-entropy effectively detects neural synchrony changes during sleep and differentiates NFLE patients from controls.
- The metric reflects consciousness levels in coma patients and distinguishes arithmetic task performance.
- PC-entropy is robust to variations in the number of recording channels and validated using synthetic and real EEG data.

## Abstract

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 in EEG 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. PC-entropy was then applied to three human EEG datasets, demonstrating its utility in detecting neural synchrony changes during sleep, differentiating nocturnal frontal lobe epilepsy (NFLE) patients from controls, reflecting consciousness levels in coma patients, and distinguishing arithmetic task performance. 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.