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

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.

Enhancing Hemodynamic Parameter Estimations: Nonlinear Blood Behavior in 4D Flow MRI

Hemodynamic parameters have been estimated assuming a Newtonian constant viscosity, even when blood exhibits shear-thinning behavior. This article investigates the influence of blood rheology and hematocrit percentage on estimating Wall Shear Stress (WSS) and Energy Loss ($E_L$) at different time instants of the cardiac cycle, as well as the Oscillatory Shear Index (OSI). We specifically focus on a hematocrit-dependent power-law non-Newtonian model, considering a wide range of hematocrit values. The rheological parameters are obtained from experimentally fitted data reported previously. This study contributes to understanding the impact of blood rheology on hemodynamic parameter estimations using both in-silico and in-vivo aortic 4D Flow magnetic resonance images. Across all cases, we systematically compared WSS, $E_L$, and OSI parameters using Newtonian and power-law models, highlighting the crucial role of blood rheology in accurately assessing cardiovascular diseases.