Comparison of divergence-free filters for cardiac 4D PC-MRI data

Abstract

4D PC-MRI enables the measurement of time-resolved blood flow directions within a 3D volume. These data facilitate a comprehensive qualitative and quantitative analysis. However, noise is introduced, e.g., due to inhomogeneous magnetic field gradients. Blood is commonly assumed as a non-Newtonian fluid, thus, incompressible, and divergence should be zero. Divergence-free filters enforce this model assumption and have been shown to improve data quality. In this paper, we compare binomial smoothing and three of these techniques: The finite difference method (FDM), divergence-free radial basis functions (DFRBF) and divergence-free wavelets (DFW). The results show that average and maximum velocities tend to decrease, while average line lengths tend to increase slightly. We recommend FDM or DFW divergence-free filtering as an optional pre-processing step in 4D PC-MRI processing pipelines, as they have feasible computation times of few seconds.