Uncovering near-wall blood flow from sparse data with physics-informed neural networks

Abstract

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular disease, yet they are challenging to quantify with high fidelity. Patient-specific computational and experimental measurement of WSS suffers from uncertainty, low resolution, and noise issues. Physics-informed neural networks (PINN) provide a flexible deep learning framework to integrate mathematical equations governing blood flow with measurement data. By leveraging knowledge about the governing equations (herein, Navier-Stokes), PINN overcomes the large data requirement in deep learning. In this study, it was shown how PINN could be used to improve WSS quantification in diseased arterial flows. Specifically, blood flow problems where the inlet and outlet boundary conditions were not known were solved by assimilating very few measurement points. Uncertainty in boundary conditions is a common feature in patient-specific computational fluid dynamics models. It was shown that PINN could use sparse velocity measurements away from the wall to quantify WSS with very high accuracy even without full knowledge of the boundary conditions. Examples in idealized stenosis and aneurysm models were considered demonstrating how partial knowledge about the flow physics could be combined with partial measurements to obtain accurate near-wall blood flow data. The proposed hybrid data-driven and physics-based deep learning framework has high potential in transforming high-fidelity near-wall hemodynamics modeling in cardiovascular disease.

ModalPINN: an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors

“…This could help predict local wall shear stress with a better accuracy, which is of interest for drag estimation or for application in bio-medical applications. For instance, Arzani et al [44] use PINNs to estimate near-wall blood flows and wall shear stress which are linked to cardiovascular diseases. The differences of convergence of higher frequency mode shapes can also be explained from a computational point of view: higher frequency modes display smaller structures than low frequency modes.…”

Physics-informed neural networks (PINNs) for fluid mechanics: A review

“…In [15], the vanilla PINN was proposed to infer the unknown parameters (e.g., the coefficient of the convection term) in the NS equations based on velocity measurements for the 2D flow over a cylinder. Following this work, PINNs were then applied to various flows [10,11,12,13,14,42,43,44,45,46,47,48,49], covering the applications on compressible flows [13], biomedical flows [14,42,50], turbulent convection flows [48], free boundary and Stefan problems [47], etc. The main attractive advantage of PINNs in solving fluid mechanics problems is that a unified framework (shown in Fig.…”

Physics-informed neural networks for solving Reynolds-averaged Navier$\unicode{x2013}$Stokes equations

“…PINNs have been used to simulate vortex-induced vibrations (Raissi et al, 2019b) and to tackle ill-posed inverse fluid mechanics problems (Raissi et al, 2020). Moreover, PINNs have been employed for super-resolution and denoising of 4Dflow magnetic resonance imaging (MRI) (Fathi et al, 2020) and prediction of near-wall blood flow from sparse data (Arzani et al, 2021). Recently, Jin et al (2021) showed the applicability of PINNs for the simulation of turbulence directly, where good agreement was obtained between the direct numerical simulation (DNS) results and the PINNs simulation results.…”