A method for blood pressure hydrostatic pressure correction using wearable inertial sensors and deep learning

Abstract

Cuffless noninvasive blood pressure (BP) measurement could enable early unobtrusive detection of abnormal BP patterns, but when the sensor is placed on a location away from heart level (such as the arm), its accuracy is compromised by variations in the position of the sensor relative to heart level; such positional variations produce hydrostatic pressure changes that can cause swings in tens of mmHg in the measured BP if uncorrected. A standard method to correct for changes in hydrostatic pressure makes use of a bulky fluid-filled tube connecting heart level to the sensor. Here, we present an alternative method to correct for variations in hydrostatic pressure using unobtrusive wearable inertial sensors. This method, called IMU-Track, analyzes motion information with a deep learning model; for sensors placed on the arm, IMU-Track calculates parameterized arm-pose coordinates, which are then used to correct the measured BP. We demonstrated IMU-Track for BP measurements derived from pulse transit time, acquired using electrocardiography and finger photoplethysmography, with validation data collected across 20 participants. Across these participants, for the hand heights of 25 cm below or above the heart, mean absolute errors were reduced for systolic BP from 13.5 ± 1.1 and 9.6 ± 1.1 to 5.9 ± 0.7 and 5.9 ± 0.5 mmHg, respectively, and were reduced for diastolic BP from 15.0 ± 1.0 and 11.5 ± 1.5 to 6.8 ± 0.5 and 7.8 ± 0.8, respectively. On a commercial smartphone, the arm-tracking inference time was ~134 ms, sufficiently fast for real-time hydrostatic pressure correction. This method for correcting hydrostatic pressure may enable accurate passive cuffless BP monitors placed at positions away from heart level that accommodate everyday movements.

Keywords: Biomedical engineering; Cardiology.

Fig. 1. Overview of IMU-Track.

A Overview of how a non-zero hydrostatic pressure P_h contributes to transmural pressure P_t (i.e., by adding to the arterial pressure P_a, the quantity of interest). For example, for a BP sensor placed on an arm, lowering the arm increases P_t and PWV, and decreases the PTT measured compared to the case of a BP sensor at heart level. PWV and PTT relationships to arm levels below heart level, near heart level, and above heart level are illustrated. B Illustration of a commercial method for correcting for P_h, based on an initial calibration procedure where the reference sensors (at heart and fingers) are placed at the same vertical level, followed by continued hydrostatic pressure correction using a fluid-filled tube relative pressure sensor that connects heart level to the finger. C Overview of approach for P_h tracking. The approach uses wrist-based inertial sensors and a deep learning model to infer parameterized arm orientation, which is then used to calculate P_h to correct errors that result from height differences between BP sensors using an analytical biomechanics wave model. D Diagram illustrating changes in P_h along the arm relative to the heart. The arrows represent the pulse wave traveling down the arm, with arrow length corresponding to PWV magnitude. E PTT calculation from ECG and PPG waveforms. F Block diagram of the deep learning-assisted model and BP prediction pipeline. Arm pose is estimated from a wrist-based IMU and a deep learning model based on measurements from IMU and a parametrized arm-pose coordinate system; this arm pose information is used to calculate hydrostatic pressure (P_h). PTT is measured using ECG and PPG. A prediction of BP is made using an analytical pressure wave propagation model with inputs of PTT and P_h following person-specific calibration to calculate fitting coefficients. Pink denotes IMU for estimating P_h, and blue denotes devices for measuring PTT. G The devices used in this study were one lead ECG, finger PPG, and wrist-mounted IMU.

Fig. 2. Tracking of arm pose from a single wrist-based IMU using parametrized arm-pose coordinate system and deep learning.

A Schematic diagram showing a parameterized model for arm pose. Positive θ indicates moving the corresponding limb upward. B Deep learning architecture diagram for tracking upper arm orientation (θ_u). The inputs at each timestep are forearm acceleration and orientation (i.e., yaw, pitch θ_f, and roll) represented as a unit quaternion. These inputs are fed through a fully connected (FC) layer followed by two bidirectional LSTM (BiLSTM) layers. The latent feature vector for the current timestep is then passed through a final FC layer to predict the upper arm orientation quaternion, normalized to the unit norm. The orientation quaternion is finally used to calculate θ_u. (C) Histogram of absolute errors for θ_u prediction for the model pretrained on the Virginia Tech Natural Motion Dataset alone (“pretrained”) and after fine-tuning on in-house training data (“fine-tuned”). D Time series of predicted and measured θ_u for a representative participant from a test fold. E Mean inference time for the arm-tracking model with 32- and 8-bit weight precision when run on a commercial smartphone. The dashed line indicates the cardiac cycle duration for a heart rate of 240 beats per minute (BPM). Data were represented as mean ± standard error of the mean (n = 50 for 32-bit and 8-bit).

Fig. 3. Changes in PTT induced by hydrostatic pressure, as modeled analytically and experimentally validated.

A Relationship between pressure and simulated PTT. A solid black line indicates simulated PTT without P_h effects. Dashed blue and orange lines indicate simulated PTT with P_h minimized and maximized via straight up and down poses, respectively. B Left: heatmap of simulated PTTs for constant BP over all possible arm pose configurations. Positive pitch indicates moving the corresponding limb upward. Right: projection of heatmap simulation with arm pose converted to hand height. A solid line indicates simulated PTT with average P_h effects (i.e., where θ_u = θ_f). Dashed blue and orange lines indicate simulated PTT with P_h minimized and maximized, respectively. C Across n = 20 participants, box plots of measured PTT were taken at different hand heights. Each measurement was the participant’s time-averaged PTT for the indicated height (for h = −25, 0, and 25 cm, n = 20, 20, and 19, respectively). Significance determined by mixed-effects model followed by Dunnett post hoc test. For h = −25 vs h = 0 cm, ****P < 0.0001; for h = 0 vs h = 25 cm, ****P < 0.0001. Individual trajectories in Supplementary Fig. 5. D Across n = 20 participants, box plots of h-stratified MAE for best-fit PTT predictions generated using the uncorrected and corrected models, with or without PEP, compared to the measured reference. Each measurement was the participant’s time-averaged MAE for the indicated h. The diagrams above show an illustrative example of the arm pose corresponding to each group (for h = -25, 0, and 25 cm, n = 16, 20, and 15, respectively). Significance determined by mixed-effects model followed by Šídák post hoc test; **P < 0.01; ns, not significant). Individual trajectories in Supplementary Fig. 7. E Repeated measures Bland-Altman plots for the best-fit PTT predictions from the uncorrected (top) and corrected model (bottom) compared to the measured reference across time-averaged participant and height pairs (n = 51; 2 to 3 measurements from each of the 20 participants). The X-axis shows the average of prediction and reference, and the y-axis shows the difference between prediction and reference. The solid line indicates the mean difference, and the dashed line indicates 95% LoA. The enlarged version shows the values of h in Supplementary Fig. 8. F A representative participant’s time series of measured and predicted hand height (top); corresponding time series of PTT predicted using the uncorrected and corrected models compared to the measured reference (bottom). Time series of representative participants PTT prediction error in Supplementary Fig. 10. For (C, D), the box represents the interquartile range, with the horizontal line at the median value. The vertical lines extend to the maximum and minimum data points within 1.5 × IQR.

Fig. 4. Prediction of BP with correction for hydrostatic pressure error.

A Box plots of h-stratified MAE for DBP (middle) and SBP (bottom) predictions generated using the uncorrected and corrected model compared to the measured reference across 20 subjects with n = 19, 20, and 19 measurements for heights of h = −25, 0, and 25 cm, respectively. Each measurement was the participant’s time-averaged MAE for the indicated h. The box represents the interquartile range, with the horizontal line at the median value. The vertical lines extend to the maximum and minimum data points within 1.5 × IQR. The diagrams (top) show an illustrative example of an arm pose corresponding to each group. Significance determined by mixed-effects model followed by Šídák post hoc test. (DBP: for h = -25 cm, ****P < 0.0001; for h = 0 cm, *P = 0.0356; for h = 25 cm, **P = 0.0096. SBP: for h = -25 cm, ****P < 0.0001; for h = 0 cm, *P = 0.0284; for h = 25 cm, **P = 0.0051). Individual trajectories in Supplementary Figs. 13 and 14. B, C Repeated measures Bland-Altman plots using the uncorrected and corrected model compared to the measured reference for DBP (D) and SBP (E) prediction across time-averaged participant and height pairs (n = 58; 2 to 3 measurements from each of the 20 participants). The X-axis shows the average of prediction and reference, and the y-axis shows the difference between prediction and reference. The solid line indicates the mean difference, and the dashed line indicates 95% LoA. Enlarged versions showing the values of h in Supplementary Figs. 15,16. D A representative participant’s time series of measured and predicted hand height (top); corresponding time series of DBP and SBP predicted using the uncorrected and corrected models compared to the measured reference (bottom). Time series of representative participant’s BP prediction error in Supplementary Fig. 17. E Participant-aggregated MAE over time for DBP (top) and SBP (bottom) predictions using the uncorrected and corrected model. The first 4 min of data were used for calibrating the models, while the following 8 min were used for prediction. Data were represented as mean ± standard error of the mean (n = 13 to 20 for each point, across the 20 subjects).