4D Flow MRI Velocity Enhancement and Unwrapping Using Divergence-Free Neural Networks
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The purpose of this study is to enhance and unwrap 4D flow MRI estimations by embedding the divergence-free principle into a neural network. Current methods for optimizing divergence-free 4D flow MRI often lose precision when applied to varying flow types or algorithmic adjustments. In this work, we introduce a vector potential formulation as an inductive bias within a neural network, allowing it to predict only divergence-free velocity fields. This ensures that the network produces the best-fitting divergence-free velocity field for the data without the need to balance physics regularization. We employ a fully connected neural network that takes the spatial coordinates of the entire volume as input to estimate the vector potential. The velocity field is then computed using automatic differentiation. Additionally, Fourier feature encoding is applied to the input coordinates to mitigate spectral bias in the neural network. To further improve velocity predictions, we minimized a loss function designed to enhance velocities, even in the presence of wrapping artifacts. To assess the performance of the divergence free network we generated A 4D flow MRI image by applying the signal equation for gradient-echo using computational fluid dynamics simulations of a vascular model of the aorta. Our network outperformed robust divergence-free methods, such as divergence free wavelets4, and 4DFlowNet5, in both normalized root mean square velocity error and directional error. Moreover, for aliased velocities, our method resulted in the fewest remaining wrapped voxels compared to traditional unwrapping methods for 4D flow MRI. We also implemented our method on in-vivo data for patients with hypertrophic cardiomyopathy achieving excellent reduction in divergence and wrapping artifacts. In conclusion, our divergence-free neural network formulation successfully enhanced 4D Flow MRI data, even in the presence of wrapping artifacts. Compared to other methods, our approach does not require balancing physics regularization in the training function, leading to better generalization.
