A Novel Approach to Pulse Coupling Analysis: Frank Copula Transfer Entropy for Finger–Wrist PPG Signals

Pulse diagnosis is a fundamental component of Traditional Chinese Medicine (TCM), yet manual palpation suffers from subjectivity. In recent years, research on objective pulse signal acquisition via wearable sensors has indeed garnered significant attention. Wrist-based pulse acquisition, while aligned with traditional TCM practice, often suffers from limitations in wearability and signal stability, posing challenges to its global applicability. In contrast, fingertip photoplethysmography (PPG) sensors offer advantages in comfort and usability, yet the physiological relationship between fingertip and wrist pulse signals remains unclear. To address this gap, we propose a multi-channel PPG acquisition system capable of simultaneously capturing high-fidelity signals from the three traditional pulse-diagnostic palpation locations (PLs) on the wrist (Cun, Guan, and Chi) and two fingertips (index and middle fingers). To further analyze the coupling relationship between fingertip and wrist pulse signals, this study proposes a coupling analysis method—Frank Copula Transfer Entropy (FCTE)—which integrates Frank Copula theory with traditional Transfer Entropy (TE) to quantitatively evaluate the coupling strength while revealing underlying causal interactions. Experimental results demonstrate that compared to conventional TE methods, the FCTE approach exhibits superior performance in two critical aspects: (1) enhanced accuracy in time-delay estimation between finger-wrist PPG signals, achieving a physiologically plausible delay of 345 ms, and (2) significant improvement in TE values from 1.117 to 2.143 (p