用数学框架定义心脏健康稳定性，手机拍照就能测心律风险
Cardiac Stability Theory: An Axiomatically Grounded Framework for Continuous Cardiac Health Monitoring via Smartphone Photoplethysmography
- 基于四个公理构建心脏稳定性指数，融合动力学特征
- 手机光体积变化图可精准预测稳定性，误差仅0.0557，延迟低于30毫秒
- 能连续监测心跳稳定度，适合长期心健康追踪和风险预警
我们提出心脏稳定性理论（CST），一个基于公理的框架，将心血管健康形式化为围绕心脏动力学吸引子的稳定性裕度。从四个公理推导出心脏稳定性指数（CSI），是一个[0,1]区间内的复合标量，通过时延嵌入整合最大李雅普诺夫指数、递归确定性和信号熵。基于心电图的模型CSISurrogateV2（CNN-Transformer）在PTB-XL数据集（21,799条记录）上达到R²=0.8788，MAE=0.0234。我们将CSI扩展至智能手机光电容积脉搏波（PPG），采用互补域迁移（CDT）：CSISurrogateV2为BUT PPG数据集（48条记录，12名受试者）生成伪标签，训练出小型模型TinyCSINet（122,849参数），在保留测试集（1065个窗口）上实现MAE=0.0557，ρ=0.660，移动端延迟小于30毫秒。CDT在BIDMC、Welltory和RWS-PPG上均验证有效。在BIDMC上配对验证5,035个窗口，相关系数r=0.454（ρ=0.485，p<10⁻²⁹⁵），证实多模态间的心脏稳定性高度相关。CSI与年龄负相关（斜率=-0.000225 CSI/年，PTB-XL），可区分房颤与正常窦性心律（AUROC=0.89），且在扰动不变训练下鲁棒性强（最大AUC下降1.65%）。我们推导出HeartSpan，一种相对于人群年龄基准的纵向稳定性指标，使消费级智能手机实现持续非侵入式心脏健康监测，支持长寿追踪与心血管风险分层。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。