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Nonlinear Cuff-less Blood Pressure Estimation of Healthy Subjects Using Pulse Transit Time and Arrival Time

Amirhossein Esmaili, Mohammad Kachuee, Mahdi Shabany

arXiv:1812.00544v2eess.SP

TL;DR

Continuous cuff-less BP monitoring is desirable, but the BP–PTT relationship varies between individuals and requires calibration. This paper proposes an elastic-tube nonlinear estimator calibrated for each subject using PTT or PAT, and reports that PAT performs better for SBP estimation while PTT performs better for DBP estimation.

  • Problem

    Continuous cuff-less BP monitoring is desirable, but the BP–PTT relationship is individual-specific and requires calibration for each person.

    Source: §I · p. 1

  • Method

    The method uses an elastic-tube-based nonlinear BP estimator with subject-specific calibration and PTT or PAT derived from PCG or ECG and PPG signals.

    Source: §I · p. 2

  • Results

    PAT provides more precise SBP estimations, while PTT performs better for DBP estimations.

    Source: B. PAT Versus PTT · p. 6, §VII · p. 9

  • Takeaways & Limitations

    The proposed nonlinear estimator using either PTT or PAT can be employed for accurate estimation of SBP and DBP.

    Source: §VII · p. 9

    Subjects were generally young and healthy, and this homogeneous dataset may affect results; broader age ranges and subjects with cardiovascular diseases remain future study directions.

    Source: §VI · p. 9

Abstract

from arXiv · show

This paper presents a novel blood pressure (BP) estimation method based on pulse transit time (PTT) and pulse arrival time (PAT) to estimate the systolic BP (SBP) and the diastolic BP (DBP). A data acquisition hardware is designed for high-resolution sampling of phonocardiogram (PCG), photoplethysmogram, and electrocardiogram (ECG). PCG and ECG perform as the proximal timing reference to obtain PTT and PAT indices, respectively. In order to derive a BP estimator model, a calibration procedure, including a supervised physical exercise, is conducted for each individual, which causes changes in their BP, and then, a number of reference BPs are measured alongside the acquisition of the signals per subject. It is suggested to use a force-sensing resistor that is placed under the cuff of the BP reference device to mark the exact moments of reference BP measurements, which are corresponding to the inflation of the cuff. Additionally, a novel BP estimator nonlinear model, based on the theory of elastic tubes, is introduced to estimate the BP using PTT/PAT values precisely. The proposed method is evaluated on 32 subjects. Using the PTT index, the correlation coefficients for SBP and DBP estimation are 0.89 and 0.84, respectively. Using the PAT index, the correlation coefficients for SBP and DBP estimation are 0.95 and 0.84, respectively. The results show that the proposed method, exploiting the introduced nonlinear model with the use of PAT index or PTT index, provides a reliable estimation of SBP and DBP.

I. INTRODUCTION

Continuous, cuff-less blood pressure monitoring is desirable, but blood pressure’s relationship to pulse timing varies between individuals. This paper introduces an elastic-tube-based nonlinear estimator and individual calibration using PTT or PAT.

I. INTRODUCTION

  • Hypertension increases risks of ischemic heart disease, heart failure, and aortic aneurysms, supporting the need for continuous BP monitoring.The passage reports hypertension prevalence of about 26% among men and 23% among women.Source: §I · p. 1
  • Cuff-based non-invasive methods cannot provide beat-to-beat monitoring and can be slow and inconvenient, motivating continuous, non-invasive, cuff-less measurement.Cuff inflation and deflation take about one minute per measurement and occlude arterial blood flow.Source: §I · p. 1
  • The BP–PTT relation is individual-specific, so estimating it requires a calibration procedure with reference BP measurements for each person.The proposed method also considers PAT, which includes a pre-ejection period in addition to PTT.Source: §I · p. 1
  • Prior work often assumed a linear PTT/PAT–BP relation, while earlier nonlinear work used globally determined parameters across subjects with different physical properties.The paper states that the nonlinear relation’s parameters depend on individual vessel and blood properties.Source: §I · p. 2
  • The proposed nonlinear estimator uses PTT or PAT with subject-specific parameters derived through individual calibration.PCG and ECG provide proximal timing references for PTT and PAT, respectively, while PPG provides the distal reference.Source: §I · p. 2

II. BACKGROUND

The background derives an individual BP–PTT relationship by modeling vessels as elastic tubes. It then describes how calibration data determine model parameters and how PAT can serve as an alternative timing measure.

A. The Relationship between BP and PTT

  • The elastic-tube model makes vessel elasticity and compliance pressure-dependent, providing the physical basis for a nonlinear BP–PTT relationship.The model treats vessel-wall elastic modulus as pressure-dependent and derives compliance as a function of pressure.Source: A. The Relationship between BP and PTT · p. 2
  • Wave propagation in the elastic-tube model yields PTT for a tube of length l, with the resulting BP–PTT relation depending on individual-specific parameters.The paper describes solving that relation for BP as a function of PTT.Source: A. The Relationship between BP and PTT · p. 2
  • PAT can replace PTT for cuff-less BP estimation and is defined as PTT plus the pre-ejection period.The pre-ejection period is the time for the myocardium to raise pressure enough to open the aortic valve and start forcing blood out of the ventricle.Source: A. The Relationship between BP and PTT · p. 2
  • Calibration pairs reference BP measurements with corresponding PTT/PAT values to determine the parameters of the nonlinear estimator for each individual.The paper also describes deriving the relation through subject-specific parameters a0, a1, and a2.Source: A. The Relationship between BP and PTT · p. 2

B. PTT/PAT Measurement Method

The measurement method forms PTT and PAT by pairing proximal cardiac timing references with selected PPG points in the same cardiac cycle. The proximal reference distinguishes the two indices.

B. PTT/PAT Measurement Method

  • PTT is calculated as distal minus proximal time, using the PCG S1 peak as the proximal reference because it approximately marks when the pressure wave leaves the heart.S1 and S2 are dominant PCG sounds; S1 corresponds to mitral and tricuspid valve closure.Source: B. PTT/PAT Measurement Method · pp. 2–3
  • PAT uses the ECG R peak instead of PCG S1 as the proximal reference, so corresponding PAT values equal PTT values plus a PEP offset.The figure depicts the different PTT variations and their corresponding PAT values.Source: Figure 1 · p. 3, B. PTT/PAT Measurement Method · p. 3
  • PPG onset, maximum-slope point, or systolic peak can provide the distal timing reference, producing corresponding f, d, and p variants of PTT and PAT.The selected PPG point is taken from the same cardiac cycle as the proximal reference.Source: B. PTT/PAT Measurement Method · p. 3

III. DATA COLLECTION METHODOLOGY

The acquisition setup synchronously records PCG, PPG, ECG, and cuff-pressure signals alongside reference BP measurements. A force-sensing resistor (FSR) under the cuff marks measurement timing for calibration.

III. DATA COLLECTION METHODOLOGY

  • Four separate ADC channels synchronously record PCG, PPG, ECG, and FSR signals at 1 kHz.Data are sent to a portable computer in one-second frames; the calibration procedure compensates for constant channel offsets.Source: A. Hardware Setup · p. 3
  • The setup combines a custom acquisition board, portable computer, and commercial BP monitor with green reflectance PPG, ECG, and chest-mounted PCG sensors.The reference device is an automatic Omron M3 monitor.Source: A. Hardware Setup · p. 3
  • The FSR sits beneath the BP cuff to measure instantaneous cuff pressure and identify reference-measurement times.PPG is recorded from the left hand while BP is measured on the right to reduce measurement effects on the PPG signal.Source: A. Hardware Setup · p. 3

B. Data Acquisition Procedure

Calibration data were collected from healthy subjects after supervised exercise, with repeated BP references acquired alongside the vital signals. The processing pipeline preprocesses signals before extracting PTT/PAT values for nonlinear SBP and DBP estimation.

B. Data Acquisition Procedure

  • 32 healthy subjects, aged 21–50, completed a supervised three-minute run at 8 km/h to perturb BP before calibration measurements.After exercise, subjects sat still while repeated reference BPs and signals were collected; calibration took about 15 minutes and was performed once per subject.Source: B. Data Acquisition Procedure · pp. 3–4

IV. PROCESSING PIPELINE

  • The processing pipeline preprocesses acquired signals, extracts PTT/PAT values corresponding to reference BP measurements, then estimates SBP and DBP with the nonlinear model.The preprocessing, feature extraction, calibration, and estimation were implemented in Python using scikit-learn for regression training.Source: §IV · p. 4

A. Preprocessing on the Signals

Signal preprocessing uses filtering and normalization before PTT/PAT measurement. The measurement pipeline aligns signals to cuff-reference times, delineates cardiac features, and averages timing values for calibration.

A. Preprocessing on the Signals

  • All four signals are median-filtered with a five-millisecond window, statically normalized, and filtered with forward-backward IIR to avoid phase shifts.The forward-backward application produces a fixed zero-phase response while reducing impulsive noise.Source: A. Preprocessing on the Signals · p. 4
  • FSR signals receive low-pass filtering, while the other acquired signals receive band-pass filtering designed to retain their main content.Table I is identified as the source of the filter specifications.Source: A. Preprocessing on the Signals · p. 4, Table I · p. 5

B. PTT/PAT Measurement and Post-Processing

  • The FSR signal identifies cuff inflation, deflation, and BP-read moments; t3 divides the vital signals into intervals paired with reference measurements.PTT/PAT values are then calculated from the corresponding intervals.Source: B. PTT/PAT Measurement and… · p. 5
  • Each interval is split into equal-sized windows containing at least two complete cardiac cycles, and each window is scaled to values between zero and one.The example window is about 2.5 seconds.Source: B. PTT/PAT Measurement and… · p. 5, Figure 5 · p. 5
  • ECG R-peaks are identified using the signal and its first derivative, while PCG S1/S2 peaks are assigned by their positions relative to the PPG systolic peak.Windows with unreliable proximal or distal delineation are excluded from analysis.Source: B. PTT/PAT Measurement and… · p. 5, Figure 6 · p. 5, Figure 7 · p. 5
  • Averaged window-level PTT/PAT values are paired with reference BPs to estimate subject-specific model parameters.Table II is designated to present SBP and DBP estimation results using the proposed nonlinear estimator.Source: B. PTT/PAT Measurement and… · pp. 5–6, Table II · p. 6

C. Model Creation

The nonlinear BP-PTT model is fitted to each subject’s calibration data using gradient descent. The procedure initializes parameters from a simplified model and least-squares estimates before iterative updates.

C. Model Creation

  • Gradient descent fits the nonlinear BP-PTT relation using the collected calibration data.Analytical derivatives of the model are used to update its parameters recursively.Source: C. Model Creation · p. 6
  • The initial parameter choice sets a1 to 0, simplifying the BP-PTT relation before fitting.The derivatives are calculated with respect to the calibration model parameters.Source: C. Model Creation · p. 6
  • Least squares estimates a0 and a2, then gradient descent iteratively determines a0, a1, and a2 for each individual.The procedure uses an appropriate learning rate, such as 0.01.Source: C. Model Creation · p. 6

V. RESULTS

Evaluation leaves out one reference BP and its associated PTT/PAT value per subject, fits the model to the remaining pairs, and tests on the held-out pair.

V. RESULTS

  • For each subject, one reference BP and associated PTT/PAT pair is held out while the nonlinear model is trained on the remaining pairs.The model estimates BP from the held-out pair’s PAT or PTT index, and the estimate is compared with its reference BP.Source: §V · p. 6
  • Each subject contributes 5 or 6 extracted reference BP and PAT/PTT pairs, yielding 5 or 6 BP estimates per subject.Source: §V · p. 6
  • The evaluation comprises 173 BP estimations across 32 subjects.Source: §V · p. 6

A. Comparison between different distal timing references on the PPG signal

The paper compares PPG distal timing points and then compares PAT with PTT using PPGd. Across both indices, estimation errors and confidence intervals are reported alongside correlations and subgroup comparisons.

A. Comparison between different distal timing references on the PPG signal

  • PPGf yields inferior estimation to other PPG characteristic points, while PPGd and PPGp perform nearly the same for SBP and DBP.The model parameters are calibrated separately for each individual.Source: A. Comparison between different distal… · p. 6

B. PAT Versus PTT

  • PAT performs better than PTT for SBP estimation, whereas PTT gives higher DBP estimation accuracy than PAT.The comparison uses PPGd as the distal timing reference.Source: B. PAT Versus PTT · p. 6
  • Most SBP and DBP estimation errors lie within ±10 mmHg and are distributed around zero.Fig. 8 shows the error histograms for PTTp or PATp estimates.Source: B. PAT Versus PTT · p. 6, Figure 8 · p. 7
  • For target ranges of 106–197 mmHg SBP and 51–93 mmHg DBP, PTT and PAT limits of agreement are reported for both targets.Fig. 9 presents Bland–Altman plots; PTT limits are −0.28 ± 1.96×9.44 mmHg for SBP and 1.03 ± 1.96×5.15 mmHg for DBP, while PAT limits are 0.12 ± 1.96×6.15 mmHg and 1.31 ± 1.96×5.36 mmHg, respectively.Source: B. PAT Versus PTT · p. 7, Figure 9 · p. 7
  • With PPGd as the distal reference, SBP correlation is 0.89 for PTT and 0.95 for PAT, while DBP correlation is 0.84 for both indices.Fig. 10 presents the estimation-versus-target regression plots.Source: B. PAT Versus PTT · p. 7, Figure 10 · p. 7
  • Across 10 mmHg target intervals, the authors describe the 95% confidence intervals as reasonable and say they approximate intervals for new patients within the studied BP ranges.Fig. 11 shows the intervals for SBP and DBP.Source: B. PAT Versus PTT · p. 8, Figure 11 · p. 8
  • No significant male–female accuracy differences are observed; SBP MAEs are 6.50 versus 5.86 mmHg for PTT and 4.76 versus 4.64 mmHg for PAT.For DBP, male-versus-female MAEs are 3.85 versus 4.00 mmHg using PTT and 4.34 versus 4.57 mmHg using PAT.Source: B. PAT Versus PTT · p. 8

C. Comparison with Other Works

The authors compare the proposed method with prior PTT- and PAT-based estimators and report higher correlation-based accuracy. On their own dataset, it also outperforms a reimplementation of by correlation values.

C. Comparison with Other Works

  • Compared by correlation coefficients, the proposed method’s PTT- and PAT-based estimations are reported as more encouraging than other methods for both SBP and DBP.The authors particularly note the DBP results relative to prior studies.Source: C. Comparison with Other Works · p. 8
  • On the authors’ dataset, the proposed model has higher estimation accuracy by r values than the model from, evaluated using a 17-subject training group and 15-subject test group.The comparison uses one-point calibration for, with the first PAT/reference-BP pair per subject used for calibration and the rest for evaluation.Source: C. Comparison with Other Works · p. 8

VI. DISCUSSIONS AND LIMITATIONS

The proposed nonlinear estimator produced useful SBP and DBP correlations, with PAT performing better for SBP and PTT for DBP. The authors qualify these findings by noting intervention-dependent PAT behavior, brachial-artery vasomotor effects, and the cohort’s generally young, healthy profile.

VI. DISCUSSIONS AND LIMITATIONS

  • PAT may track BP more accurately when exercise moves PEP and PTT in the same direction, but interventions moving them oppositely can adversely affect PAT-based results.The authors explain that exercise was used to provide varied calibration points; the opposite-direction intervention effect is a stated qualification.Source: §VI · pp. 8–9
  • Table III comparison values include unreported or unestimable entries, plot-based approximations, and an RMSE-for-MAE substitution in one cited study.The table note also identifies a comparison that applies the model from to this paper’s dataset.Source: §VI · p. 9, Table III · p. 9
  • Brachial-artery stiffness and PTT/PAT values may vary with vasomotor tone, not only with BP; central PPG has been suggested to reduce this effect.The paper notes that most studies have not incorporated this factor into the PTT–BP estimation model.Source: §VI · p. 9
  • The study’s generally young, healthy cohort may affect results; the authors identify more heterogeneous subjects, cardiovascular disease, and wider age ranges as future study directions.They note that cardiovascular disease can involve heart-rate variation that may make valid PTT and PAT extraction infeasible.Source: §VI · p. 9

VII. CONCLUSION

  • The conclusion reports that FSR synchronization of reference BP measurements with vital signals significantly improved calibration.The estimator’s parameters are determined separately for each subject through calibration.Source: §VII · p. 9
  • PAT-based estimation produced better SBP correlations, while PTT performed better for DBP; PPGd or PPGp could provide better correlations for both targets.The conclusion reports that either index can be used with the proposed nonlinear estimator for SBP and DBP estimation.Source: §VII · p. 9
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