Fig. 1: Schematic diagram of heart-brain variational phase-amplitude coupling framework.

A The data acquisition procedure. EEG and ECG are directly acquired from the polysomnography (PSG) equipment. R-peaks are extracted from ECG signals, and the RR interval time series is constructed from continuous adjacent R-peaks. B Decompose EEG (in blue) and RR intervals (in red) time series into intrinsic mode functions (IMFs). EEG oscillations are decomposed into IMFs in several spectral sub-bands, such as δ (0.5 ~ 4 Hz), θ (4 ~ 8 Hz), α (8 ~ 13 Hz), and β (13 ~ 30 Hz); while RR intervals are decomposed into mainly LF (0.04 ~ 0.15 Hz) and HF (0.15 ~ 0.4 Hz) sub-bands of heart rate variability (HRV). C Perform Hilbert transform on IMFs of EEG and RR intervals to obtain instantaneous amplitudes and phases, respectively. D Calculate modulation index between the instantaneous phase and amplitude time series derived from IMFs of EEG and RR intervals. E Generate surrogate data to perform permutation testing on MI. The z-score threshold is set at α < 0.05. F Visualize heart-brain variational phase-amplitude coupling results in a phase-amplitude frequency plane. Figure components incorporate illustrations from Servier Medical Art (CC BY 4.0).