Comparison of divergence-free algorithms for 3D MRI with three-directional velocity encoding

Summary Two divergence-free algorithms (finite difference and radial basis functions) are evaluated for improving the flow visualization quality of PC-VIPR 4D flow data. Both methods improve streamline length, with the finite difference method performing slightly better. Background The velocity-to-noise ratio in 4D MR Flow acquisitions can suffer, particularly for low velocity segments, because the velocity encoding settings are adjusted to the highest velocities in the volume. Blood is essentially incompressible so vascular velocity fields should be divergence free. Therefore, any remaining divergence in an acquired 3D or 4D MR flow dataset can be assumed to originate from image noise, which can be reduced by imposing divergence free conditions. Several methods have been proposed to reconstruct a divergence free velocity vector field, yet to our knowledge no comparison studies exist to explore their properties in flow MRI data. This study compares two methods in their effectiveness at improving flow visualizations, the finite difference method (FDM)[1] and the radial basis function (RBF)[2] based approach, which differ in their handling of noise and boundary conditions. Methods MR flow data were acquired in a straight tube flow phantom and the internal carotid arteries of a volunteer on a clinical 3T scanner with a 3D radially undersampled acquistion (PC-VIPR)[3]. Time resolved PCVIPR images were acquired as follows: scan time: 6 min acquired isotropic spatial resolution: 0.68 mm, TR/TE = 8.3/2.9 ms, temporal resolution: 39.5 ms. The FDM algorithm is solved with a fast Fourier solver for the Poisson equation. The RBF algorithm includes a normalized convolution, and is solved using iterative least squares. The quality of the resulting flow fields was quantified by average streamline lengths and streamline counts that extended from the emitter plane to a distal portion in the flow phantom or vessel. Data fidelity was measured by comparing flow values pre and post processing in the emitter and analysis planes. Results