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

TL;DR

SMURF tackles the challenge of performing high-resolution, unsupervised segmentation and velocity reconstruction from 4D flow MRI by representing geometry and velocity with separate modified MLPs that incorporate Fourier feature embeddings and Random Weight Factorization. A unified measurement model couples these fields to observed magnitude and velocity data, enabling simultaneous segmentation and flow reconstruction from either or both data modalities, under a maximum-likelihood objective with subsampling for scalability. Across synthetic, in vitro, and in vivo datasets, SMURF achieves sub-voxel segmentation accuracy (e.g., a quarter-voxel error on synthetic ICA aneurysm data) and substantial velocity-reconstruction improvements (e.g., RMSE reductions of up to ~34% in Poiseuille flow and notable reductions in velocity-divergence residuals in vivo). The results indicate SMURF’s robustness to noise, its ability to preserve flow structure, and its potential to enhance clinical diagnostics by providing automatic, high-resolution, patient-specific hemodynamic insights without requiring labeled data.

Abstract

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.

Figures (7)

• Figure 1: Visualization of velocity fields at peak systole for the synthetic ICA aneurysm dataset, showing true velocities (left column), measured velocities (top row), and SMURF-reconstructed velocities (bottom row), all overlaid on the true geometry.
• Figure 2: Segmentation comparison for the synthetic ICA aneurysm 4D flow model at increasing noise levels (5%, 20%, 50%), showing ground truth (gray) with overlaid segmentations from PCD (magenta), SDM (blue), and SMURF (red).
• Figure 3: Quantitative comparison of segmentation accuracy for PCD, SDM, and SMURF methods across varying noise levels. (a) Mean normalized $L^2$-error; (b–d) Segmentation performance evaluated using Accuracy, F1 Score, and Jaccard Index (see Table \ref{['tab:seg_scores']}). The X-axis for the first row of plots matches that of the second row.
• Figure 4: Quantitative evaluation of SMURF's velocity reconstruction for the synthetic ICA aneurysm dataset. (a) Velocity magnitude errors for raw and reconstructed fields across 5%, 10%, and 20% noise levels; (b) Comparison of raw and reconstructed velocity fields using RMSE, SSIM, and cosine similarity metrics across different noise levels.
• Figure 5: In vitro Poiseuille flow experimental validation. (a) Expert-segmented geometry overlaid with PCD, SDM, and SMURF segmentation results; (b) Axial section velocity visualization comparing raw velocity measurements with expert segmentation (top row) versus SMURF-reconstructed velocities and geometry (bottom row); (c) Evaluation of segmentation accuracy using volumetric classification scores (see Table \ref{['tab:seg_scores']}); (d) Normalized $L^2$-error violin plots quantifying deviation of predicted segmentations from expert annotation.