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

TL;DR

This paper introduces Cardiac Stability Theory (CST), a formal framework for assessing cardiovascular health using smartphone PPG, deriving a stability index (CSI) that correlates with age, detects arrhythmias, and enables continuous non-invasive monitoring.

Contribution

It presents a novel axiomatically grounded framework and a composite stability index (CSI) for cardiac health assessment via smartphone PPG, validated across multiple datasets.

Findings

CSI achieves high correlation with ECG-based models (R^2=0.8788)

CSISurrogateV2 and TinyCSINet effectively estimate cardiac stability from PPG

CSI discriminates atrial fibrillation with AUROC=0.89 and correlates with age

Abstract

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$=0.0557$, $\rho=0.660$ 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 $r=0.454$ ($\rho=0.485$, $p<10^{-295}$), 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.