PI-GNN: Physics-Informed Graph Neural Network for Super-Resolution of 4D Flow MRI

Assessment of cardiovascular and neurovascular disease requires precise measurement of hemodynamic parameters for effective diagnosis and prognosis. Variations in velocity gradients are correlated with changes in the pressure gradient, a key hemodynamic biomarker, necessitating a super-resolved velocity field. We introduce PI-GNN (Physics-Informed Graph Neural Networks) that combines the strengths of Graph Neural Network (GNN) and Navier-Stokes equations as physical laws of fluid dynamics to enhance the resolution of 4D flow MRI. We employed the capacity of Graph Neural Networks (GNNs) to process unstructured Computational Fluid Dynamics (CFD) data for super-resolution tasks. GNNs, inherently size-agnostic, effectively capture both local and global features. This unique suitability is further enhanced by incorporating terms from the Navier-Stokes equations as edge features within their message-passing mechanisms. We trained, evaluated, and tested PI-GNN using high-fidelity simulated Computational Fluid Dynamics (CFD) data in a phantom model of vascular stenosis. Subsequent testing of our proposed network on in vitro 4D flow MRI data exhibited commendable precision in velocity field estimation for super-resolution. Our approach has the potential to impact broader fluid dynamics research to reduce computation time with applications in cardiovascular and biological systems.