  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.
