Flow-Rate-Constrained Physics-Informed Neural Networks for Flow Field Error Correction in Four-Dimensional Flow Magnetic Resonance Imaging

In this study, we present enhanced physics-informed neural networks (PINNs), which were designed to address flow field errors in four-dimensional flow magnetic resonance imaging (4D Flow MRI). Flow field errors, typically occurring in high-velocity regions, lead to inaccuracies in velocity fields and flow rate underestimation. We proposed incorporating flow rate constraints to ensure physical consistency across cross-sections. The proposed framework included optimization strategies to improve convergence, stability, and accuracy. Artificial viscosity modeling, projecting conflicting gradients (PCGrad), and Euclidean norm scaling were applied to balance loss functions during training. The performance was validated using 2D computational fluid dynamics (CFD) with synthetic error, in-vitro 4D flow MRI mimicking aortic valve, and in-vivo 4D flow MRI from patients with aortic regurgitation and aortic stenosis. This study demonstrated considerable improvements in correcting flow field errors, denoising, and super-resolution. Notably, the proposed PINNs provided accurate flow rate reconstruction in stenotic and high-velocity regions. This approach extends the applicability of 4D flow MRI by providing reliable hemodynamics in the post-processing stage.