SMURF: Scalable method for unsupervised reconstruction of flow in 4D flow MRI

We introduce SMURF, a scalable and unsupervised machine learning method for simultaneously segmenting vascular geometries and reconstructing velocity fields from 4D flow MRI data. SMURF models geometry and velocity fields using multilayer perceptron-based functions incorporating Fourier feature embeddings and random weight factorization to accelerate convergence. A measurement model connects these fields to the observed image magnitude and phase data. Maximum likelihood estimation and subsampling enable SMURF to process high-dimensional datasets efficiently. Evaluations on synthetic, in vitro, and in vivo datasets demonstrate SMURF's performance. On synthetic internal carotid artery aneurysm data derived from CFD, SMURF achieves a quarter-voxel segmentation accuracy across noise levels of up to 50%, outperforming the state-of-the-art segmentation method by up to double the accuracy. In an in vitro experiment on Poiseuille flow, SMURF reduces velocity reconstruction RMSE by approximately 34% compared to raw measurements. In in vivo internal carotid artery aneurysm data, SMURF attains nearly half-voxel segmentation accuracy relative to expert annotations and decreases median velocity divergence residuals by about 31%, with a 27% reduction in the interquartile range. These results indicate that SMURF is robust to noise, preserves flow structure, and identifies patient-specific morphological features. SMURF advances 4D flow MRI accuracy, potentially enhancing the diagnostic utility of 4D flow MRI in clinical applications.