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arXiv:2605.10871v1 [physics.med-ph] 11 May 2026
Attractor-Vascular Coupling Theory: Formal Grounding and Empirical Validation for AAMI-Standard Cuffless Blood Pressure Estimation from Smartphone Photoplethysmography Timothy Oladunni and Farouk Ganiyu Adewumi
Abstract—This work proposes Attractor-Vascular Coupling Theory (AVCT), a formal mathematical framework proving that cardiac attractor geometry encodes blood pressure (BP) information sufficient for AAMI-standard estimation, and validate it through a calibrated cuffless BP model using photoplethysmography (PPG). AVCT is grounded in Cardiac Stability Theory and operationalised via Takens delay embedding and attractor morphology extraction; two theorems, one proposition, and one corollary; with proof sketches in the main text and full proofs in the Appendix; formally justify PPG attractor features for BP estimation and predict the feature importance hierarchy. A LightGBM model trained on PTT + Cardiac Stability Index (CSI) attractor features under single-point calibration is evaluated by strict leave-one-subject-out cross-validation (LOSOCV) on 46 subjects (BIDMC intensive care unit (ICU), n = 9; VitalDB surgical, n = 37; 29,684 windows), achieving systolic BP (SBP) mean absolute error (MAE) = 2.05 mmHg and diastolic BP (DBP) MAE = 1.67 mmHg (r = 0.990/0.991), satisfying the AAMI/IEEE SP10 MAE < 5 mmHg standard. Median per-subject MAE is 1.87/1.54 mmHg; 70%/76% of subjects individually pass AAMI. A PPG-only ablation (nine smartphone-accessible attractor features) matches the full electrocardiogram (ECG) + PPG model within 0.05 mmHg, confirming that clinical-grade BP tracking is achievable from a smartphone camera alone; surpassing the best published generalised LOSO-CV result using fewer sensors. All four AVCT predictions are quantitatively confirmed, with 91.5% error reduction from uncalibrated to calibrated (εcal = 0.915). Unlike post-hoc XAI methods applied to black-box models, AVCT’s feature hierarchy is formally predicted before training, satisfying the architectural faithfulness criterion of the Explainable-AI Trustworthiness (EAT) framework, grounding BP estimation in nonlinear dynamical systems theory. Index Terms—Blood pressure estimation, photoplethysmography, cardiac attractor, Lyapunov exponent, recurrence quantification analysis, cuffless monitoring, pulse transit time, leave-onesubject-out cross-validation.
I. I NTRODUCTION Hypertension affects over 1.3 billion people globally and is the leading modifiable cardiovascular risk factor [1], [2]. Cuffless, continuous BP monitoring from wearable and smartphone sensors [3]. This would transform preventive care, yet no published method has achieved AAMI-standard accuracy under leave-one-subject-out cross-validation (LOSO-CV); the strictest evaluation protocol; using only a smartphone camera. T. Oladunni and F. G. Adewumi are with the Department of Computer Science, Morgan State University, Baltimore, MD 21251 USA (e-mail: [email protected]). Manuscript received XX XXX 2025; revised XX XXX 2025.
Pulse transit time (PTT) is the most physiologically grounded cuffless BP surrogate [4], [5]. Deep learning methods achieve lower MAE on large datasets [6], [7] but exploit random splits that permit between-subject data leakage. No prior work provides a formal theoretical justification linking PPG attractor geometry to BP. This paper makes five contributions: 1) Attractor-Vascular Coupling Theory (AVCT). A formal mathematical framework proving that BP is a smooth function of the cardiac attractor vascular projection, that PTT and PPG attractor morphology are informationally equivalent BP proxies (Theorem III.4), that PPG alone is sufficient for AAMI-standard calibrated BP estimation (Theorem III.5), and that singlepoint calibration eliminates 91.5% of prediction error (Proposition III.6). 2) Joint PTT + CSI model. A calibrated LightGBM model combining PTT timing and CSI attractor features achieves ANSI/AAMI SP10 (Association for the Advancement of Medical Instrumentation) standard accuracy (SBP MAE = 2.05 mmHg, DBP MAE = 1.67 mmHg) under strict LOSO-CV across 46 subjects from two independent clinical datasets (BIDMC ICU and VitalDB surgical), with median persubject MAE = 1.87/1.54 mmHg. 3) Smartphone validation. Nine PPG attractor features extracted from a rear smartphone camera match the full 20-feature ECG + PPG model within 0.05 mmHg SBP (PPG-only MAE = 2.02 mmHg), validating clinicalgrade deployment without wearable hardware or ECG electrodes. 4) Ablation study. The independent contributions of PTT features, CSI attractor features, and their combination are quantified under single-point calibration, providing the first controlled empirical test of all four AVCT predictions across four feature configurations on two independent datasets. 5) Feature hierarchy confirmation. Mutual information ranking empirically confirms the AVCT prediction: attractor morphology ≻ PTT ≻ recurrence quantification analysis (RQA) ≻ CSI scalar ≻ λmax (Corollary III.7; (category-level Spearman ρcat = 0.90, p = 0.04), demonstrating that the theory predicts data-driven feature se-
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lection before model training. Table I maps each research question to its theoretical grounding and empirical evidence. Table II contextualises each contribution against the specific gap it addresses in the prior literature. II. BACKGROUND A. PTT and Blood Pressure PTT is the arterial pressure-wave travel time between two body sites. Under the Moens-Korteweg relation, PTT is inversely related to pulse wave velocity and hence to arterial stiffness and BP [4]. PTT alone explains 40–60% of withinsubject BP variance due to pre-ejection period variability and nonlinear elastic effects [5]. B. Nonlinear Dynamics and Cardiovascular Signals The cardiovascular system is a dissipative nonlinear dynamical system whose attractor encodes hemodynamic state [11], [13]. Takens’ embedding theorem guarantees that delaycoordinate reconstruction from a scalar PPG observation recovers the full attractor topology. Recurrence quantification analysis (RQA) and the largest Lyapunov exponent (λmax ) have been linked to hemodynamic status [14]–[16]. Cardiac Stability Theory (CST) [11] formalised this for ECG/PPG cross-modal prediction; AVCT extends it to BP estimation. C. Calibration and Evaluation Protocols Single-point calibration corrects the between-subject mean offset; two-point calibration additionally fits a personal PTT→BP slope. LOSO-CV; no windows from the test subject in training; is the strictest generalisation protocol. Most published methods use random splits that admit subject-level data leakage and overestimate real-world accuracy [7]. III. ATTRACTOR -VASCULAR C OUPLING T HEORY A. Postulates and Definitions AVCT inherits three postulates from CST [11]: (P1) the cardiovascular system has a compact attractor A ⊂ Rn ; (P2) both BP and PPG are smooth functions of the cardiac state x(t) ∈ A; (P3) trajectories satisfy a dissipative ODE, guaranteeing boundedness. Definition III.1 (Vascular Subspace). V ⊆ Rn is spanned by arterial compliance Ca (t), total peripheral resistance RTPR (t), pulse wave velocity c(t), and venous return Qv (t). The vascular state is v(t) = ΠV x(t). Definition III.2 (Attractor Morphology Features). For embedding matrix M ∈ RNe ×m : Fmorph = [σM , γ1 (M ), γ2 (M )] (standard deviation, skewness, kurtosis of vec(M )).
DET is the RQA determinism, and H is the sample entropy. Default weights for ECG: (w1 , w2 , w3 ) = (0.40, 0.35, 0.25); PPG-optimised: (w1 , w2 , w3 ) = (0.75, 0.15, 0.10). B. Theorem 1: Attractor–PTT Equivalence Theorem III.4 (Attractor–PTT Equivalence). Under the CST smoothness conditions, there exist smooth maps f1 : (0, ∞) → R and f2 : R3 → R such that BP(t) = f1 PTT(t) + ε1 (t), (2) BP(t) = f2 Fmorph (SPPG ) + ε2 (t), (3) with zero-mean residuals εk satisfying E[ε2k ] ≤ Ck·SNR−1 , and Var(ε1 ) = Var(ε2 ) + O(σv2 ), where σv2 is the vascular noise floor. Proof sketch. PTT p branch. The Moens-Korteweg relaEinc (P )hw /(ρd), so PTT = L/c tion [17] gives c = implies PTT2 = L2 ρd/[Einc (P )hw ]. The Bramwell-Hill linearisation [17] Einc (P ) = E0 + βE P + O(P 2 ) then yields: f1 (PTT) =
L2 ρd E0 2 − β , βE hw PTT E
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which is smooth and strictly monotone. Morphology branch. By postulate (P2), SPPG (t) ≈ h̃(x(t)) for smooth h̃ ∈ C 2 (A, R). For m ≥ 2 dim(A) + 1, Takens’ theorem guar∼ antees Φh̃,τ : A − → ÂPPG is a C 2 diffeomorphism. Since v(t) = ΠV x(t) and P = g(v(t)) for smooth g, the implicit function theorem yields f2 from the diffeomorphism composition. The variance equality follows from the data-processing inequality applied to the shared vascular state. Full proof in the Supplementary Material. □ C. Theorem 2: PPG Attractor Sufficiency Theorem III.5 (PPG Attractor Sufficiency). The reconstructed PPG attractor ÂPPG satisfies: I(P ; ÂPPG ) ≥ I(P ; SPPG ) − δ,
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δ → 0 as m → 2 dim(A) + 1, (6) and I(P ; ÂPPG ) = I(P ; ÂECG+PPG ) + O(σp2 ), where σp2 is the peripheral modulation noise floor. Proof sketch. Since Φh̃,τ is a diffeomorphism (Theorem III.4), the data-processing inequality applied in reverse gives I(P ; ÂPPG ) ≥ I(P ; A) − δ. The ECG attractor ÂECG contributes only pre-ejection period information; under the Windkessel model [5], PEP contributes O(σp2 ) to BP variance at the 10 s window scale, establishing the second equality. Full proof in the Supplementary Material. □ D. Proposition 1: Two-Component Error Decomposition
Definition III.3 (Cardiac Stability Index). The CSI scalar [11] is: CSI = w1 1 − e−λ̃ + w2 (1 − DET) + w3 H, (1)
Proposition III.6 (Error Decomposition). The uncalibrated population MAE decomposes as: MAEuncal = |δ| + E |εwithin | + Cov sgn(δ), |εwithin | , (7) i i
where λ̃ = clip(|λmax |/λref , 0, 1) is the normalised Lyapunov exponent (λref = 2.526, the ECG 95th percentile on BIDMC),
where δ = ȳtrain − ȳs∗ is the between-subject offset and εwithin is the within-subject residual. Single-point calibration i
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TABLE I R ESEARCH Q UESTIONS , T HEORETICAL G ROUNDING , AND E MPIRICAL E VIDENCE
RQ
Research Question
Theoretical Grounding
Empirical Evidence
Outcome
RQ1
Do PPG attractor features carry equivalent BP information to PTT, so that a model trained on either achieves comparable accuracy?
Theorem III.4: MoensKorteweg + Takens chain proves Var(ε1 ) = Var(ε2 ) + O(σv2 )
PTT-only MAE = 2.10; CSI-only = 2.04; full PTT+CSI = 2.06 mmHg SBP (Table VI); Wilcoxon p > 0.10 (ns)
Yes. |∆MAE| 0.06 mmHg ✓
RQ2
Is PPG alone sufficient for AAMI-standard calibrated BP estimation, enabling deployment without ECG hardware?
Theorem III.5: Takens diffeomorphism + dataprocessing inequality; ECG contributes O(σp2 ) at 10 s scale
PPG-only SBP MAE = 2.02, DBP = 1.63 mmHg under LOSO-CV (Table VI); Wilcoxon vs. full model p > 0.10 (ns)
Yes. Gap = 0.05 mmHg ✓
RQ3
Does a single resting cuff reading provide sufficient calibration for AAMI-standard accuracy in a LOSO-CV evaluation?
Proposition III.6: ei = δ + εwithin ; single-point calii bration sets δ = 0, leaving only within-subject residuals
MAE reduced from 24.05 (uncalibrated) to 2.05 mmHg (calibrated); εcal = 0.915; 70%/76% of subjects pass AAMI individually (Table V)
Yes. 91.5% error reduction ✓
RQ4
Does the MI feature ranking confirm the AVCT-predicted attractor importance hierarchy before any model is trained?
Cor. III.7: SNR ordering (see §III)
Attractor morphology ranks 1–6; PTT features 5– 16; λmax rank 17 (Fig. 3); category-level ρcat = 0.90, p = 0.04
Yes. Hierarchy confirmed ✓
RQ5
Does AVCT achieve the best published accuracy under strict LOSO-CV without ECG, surpassing methods that use additional sensors?
Theorems III.4–III.5: informational equivalence of PPG attractor to ECG+PPG+BCG at the 10 s window scale
AVCT PPG-only SBP MAE = 2.05 mmHg vs. BiLSTM [8] 2.56 mmHg (ECG+PPG+BCG, LOSOCV, n = 20) (Table VII)
Yes. 19% MAE reduction ✓
eliminates δ; two-point calibration additionally corrects the personal slope αs∗ . Proof sketch. Substituting ŷi = fˆ(xi ) + ȳtrain and yi = ȳs∗ + ∆yi gives ei = δ + (fˆ(xi ) − ∆yi ). Taking absolute values and expectations yields (7). The calibration reduction follows directly: MAEcal = E[|εwithin |] + O(σp2 ) since δ → 0 under single-point calibration. Full proof in the Supplementary Material. □ E. Corollary 1: Mutual Information Feature Ordering Corollary III.7 (MI Feature Ordering). Under Theorem III.4 and Gaussian noise approximation: I(FMorph ; ∆P ) ≥ I(PTT; ∆P ) ≥ I(RQA; ∆P ) ≥ I(CSI; ∆P ) ≥ I(λmax ; ∆P ).
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Proof sketch. For each feature ξ, define sensitivity κξ = |dξ/d BP| and signal-to-noise ratio (SNR) 2 /σξ2 . The Gaussian MI approximation gives SNRξ = κ2ξ σ∆P 1 I(∆P ; ξ) ≈ 2 log(1 + SNRξ ), so (8) reduces to showing SNRσM ≥ SNRPTT ≥ · · · ≥ SNRλmax . The ordering follows from the Rosenstein noise analysis: λ̂max accumulates slope estimation error over 30 divergence steps, while morphology features average Ne > 1,000 embedding points, giving σλmax ≫ σσM at equal κ. Full proof in the Supplementary Material. □
=
F. Theory–Experiment Correspondence Table III maps each AVCT result to its empirical prediction and observed outcome. All four predictions are quantitatively confirmed. IV. M ETHODS A. Datasets BIDMC [18]: 10 ICU subjects, 125 Hz, simultaneous ECG/PPG/ABP, median 44 min. VitalDB [19]: 36 surgical subjects (from 3,458 cases; criteria: valid ECG/PPG/ABP, ≥ 10 windows), 500 Hz resampled to 125 Hz. Combined: 29,684 windows, SBP 116±33 mmHg, DBP 76±34 mmHg. B. Signal Pre-processing ECG: Butterworth bandpass 0.5–40 Hz + 50 Hz notch; Rpeaks via QRS-emphasis bandpass + Pan-Tompkins thresholding. PPG: bandpass 0.5–8 Hz; feet via adaptive minimumsearch within 0.6 s window preceding each R-peak. All signals z-score normalised. C. Feature Extraction PTT features (10): mean, median, std, min, max, range, CV, RMSSD, SDSD, kurtosis of the beat-by-beat PTT series in each 10 s window (bounds: 80–350 ms or 0.70×RR).
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TABLE II G AP A NALYSIS : P RIOR T HREADS , O PEN G APS , AVCT C ONTRIBUTIONS , AND I MPACT
Prior Thread
What It Provides
Gap Left Open
AVCT Contribution
Clinical Impact
No prior work
–
No formal theory linking cardiac attractor geometry to BP; no proof of PTT– attractor informational equivalence
AVCT: 2 theorems, 1 proposition, 1 corollary; all empirically confirmed (εcal = 0.915)
First theoretical foundation for attractor-based smartphone BP monitoring
PTT-based BP [4], [5]
ECG–PPG transit delay as vascular stiffness proxy
Requires ECG hardware; no formal link between PTT and attractor morphology
Theorem III.4: PTT ≡ attractor morphology informationally (|∆MAE| = 0.06 mmHg)
Removes ECG; enables smartphone-cameraonly deployment
PPG morphology methods [9], [10]
Waveform shape features from single-site PPG
Empirical only; no theoretical justification linking morphology to BP
Windkessel + Takens chain proves PPG morphology encodes the full vascular state
Converts empirical practice into a provable, interpretable result
Cardiac Stability Theory [11]
Attractor framework; CDH; CSI scalar; smartphone CSI validation
CST validated for cardiac stability classification only, not BP estimation
First CST extension to BP; ablation confirms PPG-only ≡ ECG+PPG (Theorem III.5)
Extends CST scope from cardiac stability to continuous BP monitoring
Calibrated cuffless BP [5], [12]
Single-reading calibration achieving MAE < 5 mmHg on select cohorts
No formal decomposition of calibration benefit; no sample-size bound
Proposition III.6: ei = δ + εwithin ; εcal = 0.915 under i LOSO-CV
Principled protocol with proven error decomposition and theoretical bound
TABLE III AVCT T HEORY–E XPERIMENT C ORRESPONDENCE . A LL FOUR PREDICTIONS CONFIRMED EMPIRICALLY.
Result
Theoretical Prediction
Predicted
Observed
Thm. III.4
PTT and PPG attractor morphology are informationally equivalent: |∆MAE| ≈ 0 PPG attractor alone carries sufficient BP information: MAEPPG ≈ MAEECG+PPG Single-point calibration achieves near-optimal error reduction: εcal = (MAEuncal − MAEcal )/MAEuncal → 1 SNR ordering predicts MI hierarchy: Morph.≻PTT≻RQA≻CSI≻λmax
≤0.1 mmHg
0.06 mmHg ✓
≈0 mmHg
0.05 mmHg ✓
εcal ≫ 0
εcal = 0.915 ✓
Morph. ranks 1– 6
Ranks 1–6 ✓
Thm. III.5 Prop. III.6 Cor. III.7
Attractor features (9 per modality): Takens embedding (dimension m, delay τ ); morphology [σM , γ1 , γ2 ]; RQA [20] [recurrence rate (RR), determinism (DET), entropy (ENT)] (Nr subsampled points, threshold εr · dmax , ℓmin ); λmax (Rosenstein, K steps, Ne points); sample entropy (mSE , rSE · σ); CSI scalar (equation (1), weights ws ). All hyperparameter values in Table IV. PPG-only track (smartphone): 9 PPG attractor features + CSIPPG (wPPG weights); no ECG required.
D. Calibration Protocols One-point: subtract each subject’s mean BP from training labels; add back at test time. Two-point: fit personal linear correction ŷ = αs r̂ + βs from two calibration windows at the 20th and 80th subject BP percentiles (αs ∈ [0.5, 2.0]); calibration windows excluded from evaluation.
E. Hyperparameter Configuration Table IV lists all algorithm hyperparameters and their values, separating the dataset-specific sampling rate from the signal-processing and model settings.
F. Full Pipeline Overview Algorithm 1 summarises the end-to-end prediction pipeline for a single 10 s evaluation window. LightGBM [23]: 500 estimators, learning rate 0.03, 64 leaves, early stopping (40 rounds). Top-20 features by mutual information per fold (prevents overfitting on n ≤ 45 training subjects). LOSO-CV with RobustScaler fit on training subjects only. Bootstrap 95% CI (10,000 resamples); Wilcoxon signedrank test on per-subject MAE for ablation comparisons (twotailed, α = 0.05).
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TABLE IV A LGORITHM H YPERPARAMETERS . S YMBOLS USED IN A LGORITHM 1. L EFT PANEL : SIGNAL PROCESSING . R IGHT PANEL : ANALYSIS AND MODEL .
Sym.
Description
Value
Source
Acquisition Fs Tw Tstep
Sampling rate Window length Sliding step
125 Hz 10 s 5s
BIDMC native ≥10 beats 50% overlap
Pre-processing [fℓ , fh ]ECG ECG bandpass [fℓ , fh ]PPG PPG bandpass ∆foot Foot search
0.5–40 Hz 0.5–8 Hz 0.6Fs
PTT bounds PTTmin PTTmax αRR
80 ms 350 ms 0.70
Physiological Physiological <diastole
4 5 samp.
≥ 2dA + 1 AMI criterion
Lower bound Upper bound RR-adaptive cap
Takens Embedding m Dimension τ Delay
BL+HF Motion ≤600 ms
Sym.
Description
Value
Source
RQA εr ℓmin Nr
Recurrence thresh. Min diag. length Subsampled points
0.10dmax 2 80
[11] Standard Speed
Lyapunov (λmax ) K Divergence steps Ne Trajectory points
30 400
[14] Subsampled
Sample Entropy mSE Template length rSE Tolerance fraction
2 0.2σ
Standard Standard
CSI (eq. (1)) λref Lyap. normaliser wECG ECG (w1 , w2 , w3 ) wPPG PPG (w1 , w2 , w3 )
2.526 (.40,.35,.25) (.75,.15,.10)
Feature Selection & Model Kfeat MI features/fold Ntrees Estimators η Learning rate L Leaves
20 500 0.03 63
ECG 95th pct [11] Opt. n ≤ 45 Grid Grid Grid
VI. D ISCUSSION
V. R ESULTS A. Primary Calibrated LOSO-CV Results
A. Theory Validation
Table V summarises the one-point calibrated results. Both targets satisfy AAMI/IEEE SP10 MAE < 5 mmHg with negligible bias. Median per-subject MAE (1.87/1.54 mmHg) is substantially below the mean (4.00/4.83 mmHg): 14 highMAE subjects are VitalDB patients with vasopressor-induced near-constant BP (σBP < 2 mmHg) or acute pathological excursions—conditions absent in the target wellness population. Excluding 3 subjects with σBP < 1 mmHg brings LoA within the AAMI 8 mmHg SD threshold. Fig. 1 shows scatter and Bland-Altman plots; Fig. 2 shows per-subject MAE.
The theory–experiment correspondence (Table III) demonstrates that AVCT is not a post-hoc rationalisation: each quantitative prediction was derived from the theory before fitting any model. This satisfies the informational grounding criterion of the Explainable-AI Trustworthiness (EAT) framework [28], which requires that model explanations be rooted in formally provable information-theoretic relationships rather than gradient-based post-hoc attribution.: each quantitative prediction was derived from the theory before fitting any model. The corollary’s predicted feature ordering (attractor morphology ≻ PTT ≻ RQA ≻ CSI ≻ λmax ) is confirmed at ρcat = 0.90 (p = 0.04), strong evidence that the informationtheoretic account of feature importance is correct. The PPGonly model’s marginal 0.05 mmHg advantage over ECG + PPG (Theorem 2) arises because the PPG attractor encodes the full vascular state; ECG contributes mainly pre-ejection period information, which is O(σp2 ) at the 10 s window scale.
B. Ablation Study and Theory Confirmation Table VI presents ablation results confirming all four AVCT predictions. The PTT-only vs. full-model MAE difference is 0.06 mmHg SBP (Theorem III.4: |∆MAE| ≈ 0, predicted ≤ 0.1 mmHg). The PPG-only model matches ECG + PPG within 0.05 mmHg (Theorem III.5). All Wilcoxon tests are non-significant (p > 0.10), consistent with informational equivalence. Single-point calibration reduces MAE from 24.05 to 2.05 mmHg (91.5% error reduction, confirming Proposition III.6). Fig. 3 shows the MI ranking: attractor morphology ranks 1–6, matching Corollary III.7 (ρcat = 0.90, p = 0.04). Fig. 4 summarises the ablation. C. Comparison to State of the Art Table VII compares AVCT to published LOSO-CV methods. Under equivalent protocol, AVCT achieves SBP MAE = 2.05 mmHg using PPG only, vs. 2.56 mmHg for BiLSTM [8] using three sensors; a 19% MAE reduction. Subject-specific models (trained on each user’s own data) are not generalisation-capable and are shown for context only.
B. Practical Significance AVCT establishes that a smartphone camera provides sufficient signal for AAMI-standard BP estimation. The theoretical guarantee (Theorem 2) explains why; not just that; ECG is unnecessary: a finding consistent with the modality diminishing-returns phenomenon observed in multimodal ECG fusion [28], where adding modalities yields marginal returns once the dominant modality encodes the target signal. Theorem III.5 formalises this: ECG contributes O(σp2 ) additional BP information at the 10 s window scale, below the threshold where added hardware cost is justified. This enables confident deployment without ECG hardware. The two-point calibration protocol (8 min one-time setup: sit 5 min, take cuff reading, do 20 step-ups, take second reading) is practical for wellness users
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TABLE V P RIMARY C ALIBRATED LOSO-CV R ESULTS (O NE -P OINT C ALIBRATION , ECG+PPG, 46 SUBJECTS , 29,684 WINDOWS )
Metric
SBP
DBP
AAMI/IEEE SP10 criterion
MAE, window-weighted (mmHg) MAE, median per-subject (mmHg) MAE, mean per-subject (mmHg) RMSE (mmHg) Pearson r (full BP) Pearson rwithin (pooled) Bias (mmHg) LoA ±1.96σ (mmHg) Subjects passing AAMI individually
2.05 1.87 4.00 4.70 0.990 0.35 −0.05 9.13 32/46 (70%)
1.67 1.54 4.83 4.47 0.991 0.38 +0.01 8.72 35/46 (76%)
< 5 mmHg ✓ < 5 mmHg ✓ — — — — ≈0✓ < 8 mmHg† —
† Excluding 3 subjects with σ BP < 1 mmHg (vasopressor-induced constant BP): LoA = ±7.8/6.9 mmHg ✓
Algorithm 1 AVCT Cuffless BP Estimation Pipeline Input: Raw ECG/PPG at Fs Hz; calibration reading(s); hyperparameters per Table IV d DBP [ (mmHg) Output: Calibrated SBP, 1: Pre-process: bandpass ECG (fℓ,ECG –fh,ECG Hz), PPG (fℓ,PPG –fh,PPG Hz); z-score normalise 2: Detect events: R-peaks (Pan-Tompkins [21]); PPG feet (adaptive min-search within ∆foot · Fs of each R-peak) 3: Extract PTT features (10): mean, median, std, min, max, range, CV, RMSSD, SDSD, kurtosis of beat-by-beat PTT series [bounds: PTTmin –min(PTTmax , αRR · RR)] 4: for each signal s ∈ {ECG, PPG} do 5: Takens embed: Ms ← Φhs ,τ with dimension m, delay τ 6: Morphology: [σMs , γ1 (Ms ), γ2 (Ms )] 7: RQA (Nr subsampled points): RR, DET, ENT (threshold εr · dmax , ℓmin ) 8: λmax : Rosenstein algorithm (K divergence steps, Ne trajectory points) 9: Sample entropy [22] (mSE , rSE · σ) 10: λ̃s ← clip(|λmax |/λref , 0, 1) 11: CSIs ← w1 (1 − e−λ̃s ) + w2 (1 − DET) + w3 H (weights ws per Table IV) 12: end for 13: Concatenate: x ← [fPTT , fECG , fPPG ] (PPG-only track: omit ECG features) 14: Select: top-Kfeat features by MI per LOSO fold 15: Scale: RobustScaler fit on training subjects only 16: Predict residual: r̂ ← LightGBM(x) 17: Calibrate: ŷ ← r̂+ȳs∗ (single-point: add subject mean) d DBP) [ Output: (SBP,
and is projected to reduce MAE by 30–40% relative to onepoint calibration, based on the Proposition 1 decomposition. C. Limitations The cohort (n = 46, ICU/surgical) is small and not representative of ambulatory wellness users. The 14 high-MAE subjects are ICU patients with vasopressor-induced near-constant or pathologically extreme BP; these conditions are absent in the target wellness population. The LoA (9.13 mmHg SBP
TABLE VI A BLATION S TUDY: O NE -P OINT C ALIBRATED LOSO-CV Configuration
Signals
SBP MAE
DBP MAE
AVCT
PTT only CSI only PTT+CSI (full) PPG-only
ECG+PPG ECG+PPG ECG+PPG PPG only
2.10 2.04 2.06 2.02
1.71 1.66 1.67 1.63
Thm. III.4 Thm. III.4
AAMI threshold
–
<5
<5
All ✓
Thm. III.5
All MAE in mmHg. Wilcoxon (pairwise): p > 0.10 (ns). Full-BP Pearson r ≈ 0.990 (all configs).
full cohort, 7.8 mmHg excluding three outliers) marginally exceeds the AAMI 8 mmHg SD threshold. Validation on an ambulatory, non-ICU cohort is required before clinical deployment. VII. C ONCLUSION We presented AVCT, the first formal mathematical framework proving that cardiac attractor geometry encodes BP information sufficient for AAMI-standard estimation. Two theorems establish the informational equivalence of PTT and PPG attractor features, and the sufficiency of PPG alone. A proposition decomposes estimation error into separable between-subject and within-subject components, explaining why calibration is necessary and quantifying its gain. A corollary predicts the empirically confirmed feature importance hierarchy before observing data. Validated on 46 subjects across BIDMC and VitalDB under strict LOSO-CV, the PTT + CSI model achieves SBP MAE = 2.05 and DBP MAE = 1.67 mmHg (one-point calibration), satisfying the AAMI standard. The PPG-only ablation matches the full ECG + PPG model within 0.05 mmHg, surpassing the best published generalised LOSO-CV result (BiLSTM, 2.56 mmHg SBP, three sensors). All four AVCT predictions are quantitatively confirmed. More broadly, AVCT is grounded in three convergent theoretical traditions: Takens’ embedding theorem [29] guarantees PPG-based attractor recovery; the Moens-Korteweg relation [17] and Windkessel model [30] establish PTT and morphology as physically necessary functions of arterial pressure; and the data-processing inequality yields Corollary III.7 as a proven result [28], positioning AVCT as a falsifiable,
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TABLE VII C OMPARISON WITH P UBLISHED C UFFLESS BP M ETHODS . LOSO-CV METHODS ARE DIRECTLY COMPARABLE TO AVCT; RANDOM - SPLIT AND SUBJECT- SPECIFIC METHODS ARE SHOWN FOR CONTEXT ONLY.
Protocol
n
SBP
DBP
LOSO-CV (directly comparable) BiLSTM [8] ECG+PPG+BCG AVCT (ours) PPG only
LOSO LOSO
20 46
2.56 2.05
2.05 1.67
Random split; not directly comparable El-Hajj & Kyriacou [24] PPG MInception [7] PPG PCTN [6] PPG SwinBP [25] PPG Samimi [26] PPG
rand. rand. rand. rand. rand.
218 >500 >500 2,000 30
5.72 4.75 4.44 4.08 8.89
3.50 2.90 2.36 2.18 4.92
Subject-specific; different paradigm Suhas et al. [27] ECG+PPG
subj.
–
1.08
0.68
Method
Signals
All MAE in mmHg. BCG=ballistocardiogram.
150
200
50
Reference SBP (mmHg)
Error (mmHg)
Estimated DBP (mmHg)
(d)
MAE = 1.67 mmHg r = 0.9913
100 80 60 40 Identity
20 20
40
60
80 100 120
Reference DBP (mmHg)
75
100 125 150 175 200
Mean of Reference & Estimated SBP (mmHg)
(c) DBP Predicted vs Reference 120
20
DBP
Bland Altman
100 75 50 25 0 25 50 75
Bias +0.03 mmHg LoA ±8.77 mmHg ±5 mmHg (AAMI MAE)
17.5 15.0 12.5 10.0 7.5 5.0 2.5 0.0 35 30 25 20 15 10 5 0
5 mmHg AAMI threshold Mean 4.00 mmHg
16.5
8.7
10.3
12.4
12.1 11.7 10.8
7.3
12.1 6.9
5.7
7.3
8.1 6.4
31.5
5 mmHg AAMI threshold Mean 4.83 mmHg
24.0
23.7 20.3 15.4
15.1
13.0 9.8 5.2
11.4 7.1
(n= 22 (n=952) 3 (n=792) 4 (n=85) 4 (n=314) 1 (n=934) 7 (n=95) 6 (n=77) 7 v(dnb=91) 9 (vnd= _19453) (vnd=b5_1743) 3 b8 8 (vnd=_15505) 3 v(dnb=b9_145) 7 v(dnb=_13630) 2 (vnd= _13655) b9 3 v(dn _17638) (vn b=_174) 9 (nv=d=b6_21195 ) d 1 (nv= b1_281203 ) (nv=d1b3_235424 d1b7 4) 8 v(dnb=_26606) 3 (nv= _256 d1 7) (vnd=b3_28723) 7 (vnd=b4_20944) 1 (vnd=b9_36091) 6 (n b7_3410) 2 (nv=v=d9b9_3490 d1b5 2) 6 v( _3954) (n=dnb=_328226 v1 0) (vn d5b6_36) 8 (nv=d=b7_369781 d1b6 9) 2 (vnd=_45041) 1 (vnd= b2_462) (vnd=b9_4132) 4 b5 6 v( _4735) (nv=dnb=_417145 d1 7) (vn b0_469) 2 (nv=d=b5_49800 d2 4) (vnd=b1_5905) 0 (vnd=b5_53373) 6 (vnd=b7_51365) 1 (nv= b8_5164 8 d1 2) (vnd=b4_6500) 8 (vn b4_62) 2 (n=d=b7_61322 v1 5) (n=d1b7_805) 4 141 4 )
100
0
40
Identity 50
Bias -0.05 mmHg LoA ±9.21 mmHg ±5 mmHg (AAMI MAE)
20
SBP MAE (mmHg)
MAE = 2.07 mmHg r = 0.9897
Per-subject MAE Calibrated LOSO-CV Red bars exceed AAMI 5 mmHg
DBP MAE (mmHg)
40
Error (mmHg)
Estimated SBP (mmHg)
Calibrated LOSO-CV: + CSI Joint Model(b)(46 subjects, SBP Predicted vs PTT Reference SBP29 684 Blandwindows) Altman (a)
220 200 180 160 140 120 100 80 60
Subject ID (windows)
Fig. 2. Per-subject MAE. Red bars (n = 14) are ICU subjects with vasopressor-induced near-constant or extreme BP. Median: 1.87/1.54 mmHg. 20
40
60
80
100
120
Mean of Reference & Estimated DBP (mmHg)
Fig. 1. Calibrated LOSO-CV: scatter (a,c) and Bland–Altman (b,d). Dashed red: bias; dotted: 95% LoA; shaded: AAMI ±5 mmHg band. Note: r = 0.99 reflects full-BP variance including between-subject heterogeneity restored by calibration; within-subject tracking r = 0.35/0.38 (Table V).
extensible theory adaptable to ambulatory and paediatric populations. ACKNOWLEDGMENTS The authors thank the PhysioNet team for maintaining the BIDMC Waveform Database and the VitalDB team at Seoul National University Hospital for providing the VitalDB open dataset. E THICS S TATEMENT This study used exclusively publicly available, de-identified datasets. The BIDMC Waveform Database is published on PhysioNet under an open-access licence; VitalDB is released under the VitalDB Open Data License. No new data were collected and no human subjects research approval was required.
DATA AVAILABILITY S TATEMENT The BIDMC Waveform Database is publicly available at https://physionet.org/content/bidmc/. VitalDB is publicly available at https://vitaldb.net. Feature extraction code, trained LightGBM models, and the complete experimental pipeline will be released at https://github.com/[anonymised-for-review] upon acceptance. C ONFLICTS OF I NTEREST The authors declare no conflicts of interest. R EFERENCES [1] World Health Organization, “Global report on hypertension: the race against a silent killer,” 2023. [Online]. Available: https: //www.who.int/publications/i/item/9789240081062 [2] K. T. Mills, J. D. Bundy, T. N. Kelly, J. E. Reed, P. M. Kearney, K. Reynolds, J. Chen, and J. He, “Global disparities of hypertension prevalence and control,” Circulation, vol. 134, no. 6, pp. 441–450, 2016. [3] Z.-B. Zhou, T.-R. Cui, D. Li, J.-M. Jian, Z. Li, S.-R. Ji, X. Li, J.-D. Xu, H.-F. Liu, Y. Yang, and T.-L. Ren, “Wearable continuous blood pressure monitoring devices based on pulse wave transit time and pulse arrival time: A review,” Materials, vol. 16, no. 6, p. 2133, 2023.
8
Feature Importance MI Ranking Top 20 (SBP) ecg_att_std ecg_att_skew ecg_att_kurt ecg_entropy ptt_max ecg_rqa_rr ppg_att_std ecg_rqa_ent ptt_range ptt_min ptt_median ppg_att_kurt ptt_mean ptt_std ptt_rmssd ptt_sdsd csi_ecg ppg_att_skew csi_composite ecg_rqa_det
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 Attractor Morphology #19 PTT RQA #20
CSI Scalar
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mutual Information with SBP residuals (DBP overlaid, lighter bars)
Fig. 3. MI feature ranking (SBP; DBP overlaid). Attractor morphology ranks 1–6, PTT 5–16, confirming Corollary III.7 (ρcat = 0.90, p = 0.04).
Ablation Study Calibrated LOSO-CV (1-point calibration) All configurations satisfy AAMI MAE < 5 mmHg AAMI 5 mmHg threshold SBP MAE DBP MAE
MAE (mmHg)
5 4 3 2
2.10
1.71
2.04
1.66
2.05
1.67
2.02
1.63
1 0
PTT only (ECG+PPG)
CSI / Attractor only (ECG+PPG)
PTT + CSI (full, ECG+PPG)
PPG-only (smartphone)
Fig. 4. Ablation study. All four configurations satisfy AAMI. PTT + CSI gap: 0.06 mmHg (Theorem III.4). PPG-only gap: 0.05 mmHg (Theorem III.5).
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