Enhancing the Velocity Data From 4D Flow MR Images by Reducing its Divergence

Velocity measurements from 4D flow MRI are prone to be affected by several imperfections of the MR system. Assuming that blood is incompressible, we propose a novel method for enhancing the velocity field by reducing its divergence. To enhance the velocity data, we added a corrector velocity to each voxel such that the divergence is minimized. The method was validated using an analytical Womersley flow model for different settings of resolution and noise levels. The performance of the proposed method was also assessed in volunteers and patients. Results demonstrated a significant reduction of the divergence depending on the size of the regularization term, obtaining a reduction close to 50% of the mean divergence with negligible modification of flow parameters. Remarkably, we found that the reduction of the divergence, in percentage, was independent of volunteers, resolution or noise.