Data-driven near-wall blood flow and wall shear stress modeling with physics-informed neural networks

High fidelity quantification of near-wall blood flow and wall shear stress (WSS) in diseased arteries is challenging. Experimental limitations in the quantification of WSS, uncertainty in computational models, and the complex multi-directional behavior in WSS vector fields challenge accurate WSS modeling. Physics-informed neural networks (PINN) provide a flexible machine learning framework to integrate mathematical equations such as Navier-Stokes with sparse measurement data. In this work, we demonstrate how PINNs can quantify WSS by leveraging sparse blood flow data collected away from the wall, which are easier to measure experimentally. We challenge the framework by not providing inlet and outlet boundary condition data. PINN combines the governing blood flow equations with the provided sparse velocity data away from the wall to obtain WSS. We demonstrate examples in 2D and 3D idealized stenosis and aneurysm models. Finally, inspired by the classical analytical Womersley solution for pulsatile flow in tubes, we demonstrate the application of Fourier features for efficient extension of the PINN approach to pulsatile blood flow problems.