Complex-valued Phase Synchrony Reveals Directional Coupling in FMRI and Tracks Medication Effects

Understanding interactions in complex systems requires capturing the relative timing of coupling, not only its strength. Phase synchronization captures this timing, yet most methods either reduce the phase to its cosine or collapse it into scalar indices such as the phase-locking value, discarding relative timing. We propose a complex-valued phase synchrony (CVPS) framework that estimates phase with an adaptive Gabor wavelet and preserves both cosine and sine components. Simulations confirm that CVPS recovers true phase offsets and tracks non-stationary dynamics more faithfully than Hilbert-based methods. Because antipsychotics are known to modulate the timing of cortical interactions, they provide a rigorous context to evaluate whether CVPS can capture such pharmacological effects. CVPS further reveals cortical neuro-hemodynamic drivers, with occipital-to-parietal and prefrontal-to-striatal lead--lag flows consistent with known receptor targets, confirming its ability to capture pharmacological timing. CVPS, therefore, offers a robust, generalizable framework for detecting relative timing in complex systems such as the brain.