Deep Physics-Informed Super-Resolution of Cardiac 4D-Flow MRI

4D-flow magnetic resonance imaging (MRI) provides non-invasive blood flow reconstructions in the heart. However, low spatio-temporal resolution and significant noise artefacts hamper the accuracy of derived haemodynamic quantities. We propose a physics-informed super-resolution approach to address these shortcomings and uncover hidden solution fields. We demonstrate the feasibility of the model through two synthetic studies generated using computational fluid dynamics. The Navier-Stokes equations and no-slip boundary condition on the endocardium are weakly enforced, regularising model predictions to accommodate network training without high-resolution labels. We show robustness to each type of data degradation, achieving normalised velocity RMSE values of under 16% at extreme spatial and temporal upsampling rates of 16\times and 10\times respectively, using a signal-to-noise ratio of 7.