Topological Prior Vector for quantifying PPG waveform morphology: Metrological characteristics and a hemodynamic state monitoring demonstration

Abstract

Photoplethysmography (PPG) waveform analysis for wearable monitoring remains challenging because waveform quantification is easily affected by noise, sampling variability, fiducial-point uncertainty, and strong inter-subject differences. To address this problem, we propose the Topological Prior Vector (TPV), a deterministic 33-dimensional descriptor that transforms persistent-homology-derived topology into an explicitly defined and reproducible statistical representation of global PPG morphology. Unlike rhythm-oriented variability metrics or fiducial-dependent waveform indices, TPV summarizes the structural organization of delay-embedded pulse trajectories through fixed statistical summaries of birth, death, lifetime, dispersion, complexity, and entropy. We evaluate TPV from a measurement-oriented perspective by examining repeatability, perturbation robustness, and statistical sensitivity to waveform variation on two public datasets. The results show that TPV preserves stable within-subject morphology profiles and remains consistent under controlled signal degradation. In addition, TPV exhibits state-dependent statistical associations across blood-pressure-defined groups, with clearer monotonic tendencies in normotensive conditions and attenuated relationships in hypertensive conditions, suggesting that waveform-topology coupling is regime-dependent rather than uniformly linear. As an initial downstream validation for normotensive versus hypertensive state discrimination, TPV was further evaluated using conventional tree-based classifiers. In intra-subject and inter-subject settings, Random Forest achieved AUCs of 0.83 and 0.75, respectively, while LightGBM yielded AUCs of 0.80 and 0.779, supporting the representational utility of TPV across different classifier choices. These findings suggest that TPV is best understood not as a direct physiological surrogate, but as a compact, reproducible, and measurement-oriented statistical descriptor for profiling global waveform structure under wearable sensing uncertainty.