A comparison of phase unwrapping methods in velocity-encoded MRI for aortic flows

The phase of a MRI signal is used to encode the velocity of blood flow. Phase unwrapping artifacts may appear when aiming to improve the velocity-to-noise ratio (VNR) of the measured velocity field. This study aims to compare various unwrapping algorithms on ground-truth synthetic data generated using computational fluid dynamics (CFD) simulations.

We compare four different phase unwrapping algorithms on two different synthetic datasets of four-dimensional flow MRI and 26 datasets of 2D PC-MRI acquisitions including the ascending and descending aorta. The synthetic datasets are constructed using CFD simulations of an aorta with a coarctation, with different levels of spatiotemporal resolutions and noise. The error of the unwrapped images was assessed by comparison against the ground truth velocity field in the synthetic data and dual-VENC reconstructions in the in vivo data.

Using the unwrapping algorithms, we were able to remove aliased voxels in the data almost entirely, reducing the L2-error compared to the ground truth by 50%-80%. Results indicated that the best choice of algorithm depend on the spatiotemporal resolution and noise level of the dataset. Temporal unwrapping is most successful with a high temporal and low spatial resolution ( $$  ms, $$  mm), reducing the L2-error by 70%-85%, while Laplacian unwrapping performs better with a lower temporal or better spatial resolution ( $$ ms, $$ mm), especially for signal-to-noise ratio (SNR) 12 as opposed to SNR 15, with an error reduction of 55%-85% compared to the 50%-75% achieved by the Temporal method. The differences in performance between the methods are statistically significant.

The temporal method and spatiotemporal Laplacian method provide the best results, with the spatiotemporal Laplacian being more robust. However, single- $$ methods only situationally and not generally reach the performance of dual- $$ unwrapping methods.