Attractor-Vascular Coupling Theory: Formal Grounding and Empirical Validation for AAMI-Standard Cuffless Blood Pressure Estimation from Smartphone Photoplethysmography

This work proposes Attractor-Vascular Coupling Theory (AVCT), a mathematical framework showing that cardiac attractor geometry encodes blood pressure (BP) information sufficient for AAMI-standard estimation, and validates the theory through a calibrated cuffless BP model using photoplethysmography (PPG). AVCT is grounded in Cardiac Stability Theory and operationalized using Takens delay embedding and attractor morphology extraction. Two theorems, one proposition, and one corollary formally justify the use of PPG attractor features for BP estimation and predict the feature-importance hierarchy. A LightGBM model trained on pulse transit time (PTT) and Cardiac Stability Index (CSI) attractor features under single-point calibration was evaluated using strict leave-one-subject-out cross-validation (LOSO-CV) on 46 subjects from BIDMC ICU (n = 9) and VitalDB surgical data (n = 37), comprising 29,684 windows. The model achieved systolic BP (SBP) mean absolute error (MAE) of 2.05 mmHg and diastolic BP (DBP) MAE of 1.67 mmHg, with correlations r = 0.990 and r = 0.991, satisfying the AAMI/IEEE SP10 requirement of MAE below 5 mmHg. Median per-subject MAE was 1.87/1.54 mmHg, and 70%/76% of subjects individually satisfied AAMI criteria. A PPG-only ablation using nine smartphone attractor features matched the ECG+PPG model within 0.05 mmHg, demonstrating that clinical-grade BP tracking is achievable using only a smartphone camera while surpassing prior generalized LOSO-CV results using fewer sensors. All four AVCT predictions were quantitatively confirmed, with 91.5% error reduction from uncalibrated to calibrated estimation (epsilon_cal = 0.915). Unlike post-hoc explainable AI methods, AVCT predicts features satisfying the architectural faithfulness criterion of the Explainable-AI Trustworthiness (EAT) framework and grounding BP estimation in nonlinear dynamical systems theory.

Cardiac Stability Theory: An Axiomatically Grounded Framework for Continuous Cardiac Health Monitoring via Smartphone Photoplethysmography

We present Cardiac Stability Theory (CST), an axiomatically grounded framework formally defining cardiovascular health as a stability margin around a cardiac dynamical attractor. From four axioms we derive the Cardiac Stability Index (CSI), a composite scalar in [0,1] integrating the largest Lyapunov exponent, recurrence determinism, and signal entropy via time-delay embedding. The ECG-based model (CSISurrogateV2, CNN-Transformer) achieves $R^2=0.8788$, MAE$=0.0234$ on PTB-XL (21,799 recordings). We extend CSI to smartphone PPG via Complementary Domain Transfer (CDT): CSISurrogateV2 generates pseudo-labels for the BUT PPG dataset (48 recordings, 12 subjects), training TinyCSINet (122,849 parameters), achieving MAE$=0.0557$, $ρ=0.660$ on the held-out test set ($n=1065$ windows) at ${<}30$ ms mobile latency. CDT is validated on BIDMC, Welltory, and RWS-PPG. Paired validation on 5,035 BIDMC windows yields $r=0.454$ ($ρ=0.485$, $p<10^{-295}$), confirming correlated cardiac stability across modalities. CSI is negatively correlated with age (slope $= -0.000225$ CSI/year, PTB-XL), discriminates atrial fibrillation from normal sinus rhythm (AUROC$=0.89$), and is robust under Perturbation Invariance Training (max AUC drop 1.65\%). We derive HeartSpan, a longitudinal stability metric relative to population age norms, enabling continuous non-invasive cardiac monitoring from commodity smartphones for longevity tracking and cardiac risk stratification.