Unsupervised 4D Flow MRI Velocity Enhancement and Unwrapping Using Divergence-Free Neural Networks

2026-03-31

AI Summary

This work addresses key challenges in 4D Flow MRI—namely high noise levels in velocity fields, phase aliasing, and violations of mass conservation—by introducing DAF-FlowNet, an unsupervised neural network that uniquely embeds a divergence-free physical prior directly into its architecture. By parameterizing the velocity field as the curl of a vector potential, the method inherently enforces the incompressibility constraint while simultaneously performing denoising and phase unwrapping. A cosine-based data consistency loss enables joint image enhancement and unwrapping in a single stage, eliminating the need for explicit regularization tuning. Evaluated on both synthetic and in vivo patient data, DAF-FlowNet substantially outperforms existing approaches, reducing velocity errors by up to 15%, decreasing residual aliased voxels by 72%, and significantly improving mass conservation fidelity in blood flow.

Abstract

This work introduces an unsupervised Divergence and Aliasing-Free neural network (DAF-FlowNet) for 4D Flow Magnetic Resonance Imaging (4D Flow MRI) that jointly enhances noisy velocity fields and corrects phase wrapping artifacts. DAF-FlowNet parameterizes velocities as the curl of a vector potential, enforcing mass conservation by construction and avoiding explicit divergence-penalty tuning. A cosine data-consistency loss enables simultaneous denoising and unwrapping from wrapped phase images. On synthetic aortic 4D Flow MRI generated from computational fluid dynamics, DAF-FlowNet achieved lower errors than existing techniques (up to 11% lower velocity normalized root mean square error, 11% lower directional error, and 44% lower divergence relative to the best-performing alternative across noise levels), with robustness to moderate segmentation perturbations. For unwrapping, at peak velocity/velocity-encoding ratios of 1.4 and 2.1, DAF-FlowNet achieved 0.18% and 5.2% residual wrapped voxels, representing reductions of 72% and 18% relative to the best alternative method, respectively. In scenarios with both noise and aliasing, the proposed single-stage formulation outperformed a state-of-the-art sequential pipeline (up to 15% lower velocity normalized root mean square error, 11% lower directional error, and 28% lower divergence). Across 10 hypertrophic cardiomyopathy patient datasets, DAF-FlowNet preserved fine-scale flow features, corrected aliased regions, and improved internal flow consistency, as indicated by reduced inter-plane flow bias in aortic and pulmonary mass-conservation analyses recommended by the 4D Flow MRI consensus guidelines. These results support DAF-FlowNet as a framework that unifies velocity enhancement and phase unwrapping to improve the reliability of cardiovascular 4D Flow MRI.

Problem

• 4D Flow MRI
• velocity enhancement
• phase unwrapping
• noise
• aliasing

Innovation

• divergence-free neural network
• unsupervised learning
• 4D Flow MRI
• phase unwrapping
• velocity enhancement