In this study, we use physics-informed neural networks (PINNs) to assimilate the turbulent mean flow fields from Cartesian time-resolved three-dimensional phase-contrast magnetic resonance imaging [known as four-dimensional (4D) flow MRI] measurements in an in vitro axis-symmetric stenosis. 4D flow has emerged as a prominent tool for the hemodynamic assessment of cardiovascular pathologies such as aortic stenosis. However, the standard, Cartesian-based 4D flow acquisitions suffer from displacement artifacts and limited spatiotemporal resolution, which bias the quantification of the velocity field. The goal of this study is to enhance noisy 4D flow measurements by correcting the displacement artifact and assimilating the mean pressure and Reynolds stresses. We consider a transitional stenotic flow that exhibits flow separation. In the first step, a PINN is trained on noisy phase-contrast MRI time-averaged velocity data and informed by the continuity equation. The validation against synchronized single-point imaging (Sync SPI) MRI experimental data reveals a substantial reduction of the displacement artifact and effective denoising. This PINN-corrected mean velocity field is used to assimilate the mean pressure and Reynolds stresses by training a PINN based on the Reynolds-averaged Navier–Stokes (RANS) equations closed with the Spalart–Allmaras turbulence model. The mean pressure and Reynolds stress assimilations are validated using a numerical RANS dataset and then applied to experimental 4D flow data. Our results demonstrate that PINNs are effective for post-processing 4D flow measurements. They enable displacement error correction, data denoising, and identifying unknown quantities. Such post-processing can bridge the quality gap between short acquisition-time standard 4D flow and Sync SPI measurements.
