Modified Fourier-Domain Transfer Entropy for Cardiovascular Analysis: Insights Into Aging Mechanisms

The causality between heart period (HP) and systolic arterial pressure (SAP) within the 0.04-0.4 Hz frequency band is a critical aspect of cardiovascular system dynamics. In this study, we introduce a novel method named Modified Multiscale Fourier-domain Transfer Entropy (MMFTE). As an extension of the Fourier-domain Transfer Entropy (FTE), the MMFTE method is designed to analyze causal interactions within specific frequency ranges across multiple time and frequency scales. Simulation results demonstrate that MMFTE is more sensitive in detecting weak coupling and exhibits greater robustness to variations in data length compared to the traditional FTE method. Analysis of the cardiovascular data further reveals that MMFTE provides a detailed characterization of the coupling between HP and SAP. Specifically, elderly subjects show significantly reduced coupling in both the low- and high-frequency bands compared to young subjects, across multiple time and frequency scales. Moreover, MMFTE produces lower p-values in both coupling directions than FTE (HP-to-SAP: 0.0027 vs. 0.0054; SAP-to-HP: 0.0021 vs. 0.0229) and identifies significant differences across a broader range of scales, indicating improved effectiveness in distinguishing between young and elderly subjects. This study develops a method for estimating causality across multiple scales, offering a new perspective for exploring cardiovascular interactions.