Robust three-dimensional phase unwrapping algorithm for phase contrast magnetic resonance velocity imaging

Conclusions

In neither 2D nor 3D is it possible to find where the undersampling has happened from the measured wrapped phase distribution alone. Such information is lost in the sampling process, which is also responsible for the creation of the singularities. Therefore, it is necessary to make use of additional information about the physics of the problem.

In the particular case of CINE-MRI, the pulsatile nature of the flow produces a sudden acceleration that can result in temporal undersampling and PSLs with singularities oriented perpendicular to the time axis, that require a surface with its normal in the direction of the time axis. This sudden increase in velocity may then result in spatial undersampling near the vessel wall, forming loops that require a branch surface located along the wall and whose normal is perpendicular to the time axis. These considerations, taken with an approximate form for the relevant Navier-Stokes equation, resulted in three criteria for the branch cut placement algorithm that, when implemented manually allowed even one-voxel errors to be prevented. An unfortunate consequence of this observation however is that it is not possible to find a universal approach that solves all possible undersampled 3D phase distributions.