Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing.

Divergence-free smoothing with wall treatment (DFSwt) method is proposed for processing with four-dimensional (4D) flow magnetic resonance imaging (MRI) data of blood flows to enhance the quality of flow field with physical constraints. The new method satisfies the no-slip wall boundary condition and applies wall function of velocity profile for better estimating the velocity gradient in the near-wall region, and consequently improved wall shear stress (WSS) calculation against the issue of coarse resolution of 4D flow MRI. In the first testing case, blood flow field obtained from 4D flow MRI is well smoothed by DFSwt method. A great consistency is observed between the post-processed 4D flow MRI data and the computational fluid dynamics (CFD) data in the interested velocity field. WSS has an apparent improvement due to the proposed near-wall treatment with special wall function comparing to the result from original 4D flow MRI data or the DFS-processed data with no wall function. The other five cases also show the same performance that smoothed velocity field and improved WSS estimation are achieved on 4D flow MRI data optimized by DFSwt. The improvements will benefit the study of hemodynamics regarding the determination of location or the potential possibility of lesions.