A Multidimensional Data-Driven Hybrid Transformer Framework for Non-invasive Continuous Blood Pressure Prediction

• Cuff-based BP methods provide intermittent measurements and are constrained by discomfort, bulkiness, and operational demands for long-term monitoring.Source: §1 · p. 1
• PTT links ECG cardiac activation to peripheral PPG pulse arrival and is widely used as a BP surrogate, while auxiliary descriptors can improve estimation precision.Source: §1 · pp. 1–2
• The proposed pipeline fuses ECG/PPG-derived physiological descriptors with demographic features instead of feeding raw waveform samples directly into the model.Source: §1 · p. 2
• MSEM integrates Transformer, KAN, and XGBoost branches to capture complementary temporal, nonlinear, and tabular representations of hemodynamic variation.Source: §1 · p. 2
• DCFD unifies the branches using differential multi-head attention to reduce redundancy and improve cross-branch fusion efficiency.Source: §1 · p. 2
• The composite robust regression objective jointly optimizes DBP and SBP using weighted error, focal-style, quantile, Huber, regularization, and auxiliary-supervision terms.Source: §1 · p. 2

• PTT-only models are sensitive to individual differences and vascular compliance, motivating augmentation with PPG morphology, intensity descriptors, and waveform-based learning.Source: §2 · p. 2

CNNs and RNNs

• CNNs learn local waveform patterns, while RNNs model historical dependencies but rely on serial computation that can limit very long-range temporal modeling.Source: §2.1 · pp. 2–3

Transformers and Generative Models

• Transformer-based approaches use self-attention for cuffless BP estimation and waveform synthesis, with recent models combining attention with multiscale, Fourier, or graph-based representations.Source: §2.1 · p. 3

Multimodal Data Fusion

• ECG/PPG fusion is regarded as a strategy for improving robustness against motion artifacts and sensor-specific noise.Source: §2.2 · p. 3

Feature-, Decision-, and Model-level Fusion

• Feature-level fusion can overlook nonlinear cross-modal interactions, whereas decision-level fusion aggregates outputs from independent models.Source: §2.2 · p. 3

Gap Analysis

• Real-world deployment remains constrained by protocol realism, calibration drift, population diversity, fairness reporting, subject variability, calibration needs, and wearable resource costs.Source: §2.3 · pp. 3–4

Proposed Direction

• The proposed hybrid framework combines KAN with differential-attention fusion to enhance integration of multibranch features.Source: §2.3 · p. 4

Problem Definition

• Each input contains L = 10 consecutive feature records and F = 8 variables, while the target contains subsequent-record DBP and SBP references.Source: §3.1 · p. 4

Overall Framework

• The framework integrates waveform and metadata construction, physiological descriptor derivation, feature-sequence construction, and hybrid Transformer prediction with composite optimization.Source: §3.2 · p. 4
• MSEM and DCFD together model temporal dependencies, nonlinear hemodynamic characteristics, and cross-branch feature interactions.Source: §3.2 · p. 4, §3.3 · p. 4

Encoding and Branches

• The encoding stage removes missing observations, standardizes eight inputs using training-partition statistics, and normalizes each window temporally for neural branches.Source: §3.3.1 · p. 4
• The Transformer main head uses mean-pooled temporal representations, KAN models nonlinear relationships from the flattened window, and XGBoost supplies a tabular estimate from window statistics.Source: §3.3.1 · p. 4

MSEM

• The MSEM combines Transformer, KAN, and XGBoost branches to model complementary temporal, nonlinear, and tabular representations.Branch projections create common tokens for downstream fusion.Source: Figure 1 · p. 5

DCFD

• The DCFD applies differential attention, fused representation learning, token-weighted aggregation, and gated residual correction to integrate branch outputs.The neural correction is added to the two-dimensional XGBoost baseline estimate.Source: §3.3.2 · p. 5

Preprocessing and feature engineering

• The upstream pipeline uses filtering, robust normalization, polarity correction, and fiducial detection to derive timing and morphology features from synchronized ECG and PPG.PTT, the PPG foot-to-peak interval, RR interval, and HR are defined from ECG R-peaks and PPG landmarks.Source: §3.3.2 · p. 6, §3.6 · p. 7

Model-ready inputs

• The model input is a standardized 10-step sequence containing six physiological descriptors plus age and body weight, rather than raw waveform samples.The physiological variables include PTT, foot-to-peak interval, heart rate, maximum PPG slope, RI, and SD time.Source: §3.3.2 · p. 6, §3.6 · p. 7

Data preparation and limitations

• Complete-case filtering removed 9 of 53,630 rows with missing weight, while the analytical table retained physiologically unusual values without retrospective exclusion.The retained table included two rows with SBP ≤ DBP and extreme reflection-index values.Source: §3.4 · p. 6

Composite robust loss

• The composite objective jointly optimizes DBP and SBP using target-weighted squared errors, scheduled focal-style and quantile penalties, early Huber stabilization, and regularization.Learnable target-specific scales adjust the relative DBP and SBP squared-error contributions; the Huber term is active for the first ten epochs.Source: §3.8 · p. 8

Experimental protocol

• The shared 53,621-observation table used an 80%/10%/10% segment split, but subject identifiers were unavailable, so the test set was not subject-disjoint.Windows from different segments of the same subject could therefore occur across partitions.Source: §4.1 · p. 9

Baseline comparison

• 3.74 mmHg was the lowest DBP SD, with the narrowest 95% LoA of [-6.93, 7.74] mmHg among compared methods.DBP accuracies were 87.95%, 98.48%, and 99.01% at ≤5, ≤10, and ≤15 mmHg.Source: §4.3 · p. 11
• 5.95 mmHg was the lowest SBP SD, while the proposed model achieved the narrowest SBP 95% LoA of [-13.25, 10.06] mmHg and highest threshold accuracies.SBP accuracies were 70.75%, 94.36%, and 98.11% at the three thresholds, although XGBoost had the bias closest to zero at -0.60 mmHg.Source: §4.3 · p. 11
• Compared with XGBoost, the hybrid reduced SBP SD from 7.10 to 5.95 mmHg and improved ≤10 mmHg accuracy from 87.23% to 94.36%.Its SBP LoA also narrowed from [-14.52, 13.32] to [-13.25, 10.06] mmHg.Source: §4.3 · p. 11

Ablation study

• Removing XGBoost increased DBP SD from 3.74 to 12.00 mmHg and SBP SD from 5.95 to 23.43 mmHg, producing much wider LoA intervals.The ablation supports XGBoost as a statistical anchor in the hybrid residual framework.Source: §4.4 · p. 12
• Removing KAN reduced SBP ≤10 mmHg accuracy from 94.36% to 40.07%, while removing MHDA reduced it to 42.62%.The MHDA ablation also widened SBP LoA to [-17.37, 37.27] mmHg, whereas the KAN ablation widened it to [-22.43, 36.95] mmHg.Source: §4.4 · p. 12
• The full model had the narrowest DBP and SBP LoA intervals among reduced variants and the best SBP cumulative accuracy at all three thresholds.Its DBP ≤5 and ≤10 mmHg accuracies were also best, despite a slightly higher DBP ≤15 mmHg accuracy for one reduced variant.Source: §4.4 · p. 12

Agreement analysis

• Bland–Altman analysis showed biases of 0.41 mmHg for DBP and −1.60 mmHg for SBP, with unadjusted 95% LoA of [-6.93, 7.74] and [-13.25, 10.06] mmHg.These are descriptive per-window estimates for 2,431 test windows, which are not statistically independent because of repeated subjects and adjacent windows.Source: §4.2 · p. 10, §4.5 · p. 13

• The proposed framework achieved the best overall agreement-oriented performance among the compared continuous BP estimation models.It explicitly combines six ECG/PPG-derived descriptors with age and body weight, unlike end-to-end waveform models that rely solely on latent feature extraction.Source: §5.1 · p. 16
• The model met numerical AAMI mean-error and standard-deviation criteria and numerical BHS Grade A percentage thresholds on the held-out test set.These comparisons motivate formal clinical validation but do not constitute compliance testing, device validation, or certification.Source: §5.2 · p. 16
• MIMIC-III ICU data may not represent ambulatory conditions, where motion artifacts can reduce signal quality and robustness requires further validation.The authors also note that periodic calibration could further improve long-term accuracy and propose validation on real-world wearable datasets.Source: §5.3 · p. 16
• The segment-level split allowed segments from the same subject to appear in different partitions, potentially producing more optimistic generalization estimates than subject-disjoint evaluation.Subject mapping was reconstructed later for cohort accounting but was not used to alter the established partitions.Source: §5.3 · p. 16
• Future evaluation should use a de novo subject-disjoint split defined before scaling and window construction, together with external-cohort validation.Source: §5.3 · p. 17
• The complete-case pipeline lacked prespecified physiological-range exclusions or RI clipping, and the influence of retained extreme values was not quantified through retrained sensitivity analysis.Future work should compare results with and without physiologically justified quality-control exclusions.Source: §5.3 · p. 17
• Reported SD and Bland–Altman limits of agreement are descriptive per-window estimates because temporally adjacent and repeated observations were not analyzed with subject-clustered inference.The 2,431 test windows therefore should not be interpreted as subject-level precision estimates.Source: §5.3 · p. 17

• The framework models standardized 10-step sequences of six ECG/PPG-derived descriptors and two demographic covariates using hybrid Transformer components with complementary XGBoost and KAN representations.Source: §6 · p. 17
• On MIMIC-III, the model achieved the best overall agreement-oriented performance among the compared baselines.The reported numerical AAMI and BHS comparisons were obtained on a segment-level test set.Source: §6 · p. 17
• The numerical AAMI and BHS comparisons are descriptive and do not constitute formal compliance testing or device certification.The conclusion calls for prespecified quality-control rules, repeated-measures inference, de novo subject-disjoint evaluation, and external-cohort validation.Source: §6 · p. 17

• The analysis used de-identified physiological and linked demographic data from the MIMIC-III Waveform and Clinical Databases.Source: Ethical statement · p. 17
• No participants were recruited and no new physiological or clinical data were collected by the authors.Source: Ethical statement · p. 17

• The authors declare no competing interests.Source: Conflict of interest · p. 18
• Author contributions covered conceptualization, methodology, software, data curation, validation, analysis, visualization, supervision, resources, and manuscript preparation.Source: Conflict of interest · p. 18
• All authors reviewed and approved the final manuscript.Source: Conflict of interest · p. 18