Reassessing Global Field Synchronization as a Phase-Synchrony EEG Metric: Mathematical Review and Empirical Counterexamples With Implications for Wearable Pain Monitoring.

BACKGROUND: Integrative pain care emphasizes longitudinal monitoring to personalize multimodal treatment and reduce medication-related risk. Wearable electroencephalography (EEG) could enable scalable, real-time neurophysiological tracking but requires connectivity features that are computationally simple and mechanistically valid. Global field synchronization (GFS) is widely used and often interpreted as a global phase-synchrony index, yet its construct validity remains unclear. OBJECTIVE: To evaluate whether GFS validly represents EEG phase synchronization and discuss implications for wearable monitoring in integrative pain management. METHODS: We conducted construct validation using (i) synthetic Fourier-domain multichannel data designed to generate counterexamples and (ii) empiricalresting-state EEG data from healthy subjects (32 channels, eyes closed). Phase dispersion was quantified by circular standard deviation (CSD). Simulations assessed GFS-CSD correspondence under rotations (0°-180°) and scaling (1-5). Empirical EEG analyses computed GFS and CSD across 1-50 Hz and evaluated their relationships by frequency band. RESULTS: In simulations, GFS was invariant to rotations that substantially changed CSD but varied strongly with scaling, whereas CSD changed minimally, indicating that GFS and phase dispersion can dissociate. In empirical resting-state EEG, an expected inverse relationship between GFS and CSD was not consistently observed across delta, theta, alpha, beta, or gamma bands. At a single frequency, examples showed that similar GFS values could correspond to markedly different phase patterns depending on the point cloud's location and distribution. CONCLUSIONS: GFS does not generally serve as a valid proxy for EEG phase synchronization, thereby limiting its mechanistic interpretation as a wearable connectivity biomarker. For integrative pain monitoring and decision support, rigorous construct validation should precede clinical translation, and alternative phase-based indices with real-world robustness are needed.