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.

翻译：本文提出吸引子-血管耦合理论（AVCT），该数学框架表明心脏吸引子几何结构编码了足以满足AAMI标准估计的血压信息，并通过基于光电容积描记术（PPG）的校准无袖带血压模型验证了该理论。AVCT以心脏稳定性理论为基础，利用Takens延迟嵌入和吸引子形态提取技术进行操作化。两个定理、一个命题和一个推论形式化地论证了利用PPG吸引子特征进行血压估计的合理性，并预测了特征重要性层级。使用基于脉搏传输时间（PTT）和心脏稳定性指数（CSI）吸引子特征训练的LightGBM模型，采用单点校准方法，对来自BIDMC ICU（n=9）和VitalDB手术数据（n=37）共46名受试者进行严格留一受试者交叉验证（LOSO-CV），共计29,684个窗口。该模型实现的收缩压（SBP）平均绝对误差（MAE）为2.05 mmHg，舒张压（DBP）MAE为1.67 mmHg，相关系数r分别为0.990和0.991，满足AAMI/IEEE SP10要求的MAE低于5 mmHg。每位受试者的中位MAE为1.87/1.54 mmHg，其中70%/76%的受试者个体满足AAMI标准。仅使用九个智能手机吸引子特征的PPG消融模型与心电图+PPG模型的性能差距在0.05 mmHg以内，表明仅使用智能手机摄像头即可实现临床级血压跟踪，同时以更少的传感器超越此前广义LOSO-CV的结果。所有四项AVCT预测均得到定量验证，从无校准到校准估计的误差降低了91.5%（ε_cal=0.915）。与事后可解释性人工智能方法不同，AVCT预测的特征满足可解释人工智能可信度（EAT）框架的架构保真度标准，并将血压估计奠基于非线性动力系统理论。