BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet

TL;DR

This work develops BP-DeepONet, a physics-informed DeepONet that learns the operator mapping physiological signals to arterial blood pressure waveforms by embedding the 1D Navier–Stokes equations with Windkessel boundary conditions and time-periodicity. It introduces BP-DeepONet and a meta-learning variant that supports sample-specific hyper-parameters, enabling continuous ABP waveform prediction across locations in an arterial segment using outlet measurements only. The methods achieve favorable accuracy on both simulated data (PINN validation) and real clinical data (MIMIC), with the meta-version delivering strong SBP/DBP/MBP predictions and IEEE-grade assessments. These results support cuffless, cuff-free ABP monitoring with physically consistent waveforms and pave the way for more complex arterial geometries and architectures in future work.

Abstract

Cardiovascular diseases (CVDs) are the leading cause of death worldwide, with blood pressure serving as a crucial indicator. Arterial blood pressure (ABP) waveforms provide continuous pressure measurements throughout the cardiac cycle and offer valuable diagnostic insights. Consequently, there is a significant demand for non-invasive and cuff-less methods to measure ABP waveforms continuously. Accurate prediction of ABP waveforms can also improve the estimation of mean blood pressure, an essential cardiovascular health characteristic. This study proposes a novel framework based on the physics-informed DeepONet approach to predict ABP waveforms. Unlike previous methods, our approach requires the predicted ABP waveforms to satisfy the Navier-Stokes equation with a time-periodic condition and a Windkessel boundary condition. Notably, our framework is the first to predict ABP waveforms continuously, both with location and time, within the part of the artery that is being simulated. Furthermore, our method only requires ground truth data at the outlet boundary and can handle periodic conditions with varying periods. Incorporating the Windkessel boundary condition in our solution allows for generating natural physical reflection waves, which closely resemble measurements observed in real-world cases. Moreover, accurately estimating the hyper-parameters in the Navier-Stokes equation for our simulations poses a significant challenge. To overcome this obstacle, we introduce the concept of meta-learning, enabling the neural networks to learn these parameters during the training process.

Figures (15)

• Figure 1: Filtered ECG and PPG signals in 10 seconds.
• Figure 2: Illustration of the pulse pressure amplification in arterial systems.
• Figure 3: Simplification of the three-dimensional model to one-dimensional model. The vessel is assumed to be a straight cylinder, and each axial cross-section is circular.
• Figure 4: Structures of the fully connected network and the residual network.
• Figure 5: Structures of the DeepONet and FNO.

Theorems & Definitions (3)

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