4 D Gradient Based Phase Unwrapping for PC-MR Flow Data

Introduction: 4D PC MRI has emerged as a promising approach for hemodynamic evaluation of larger vascular territories. One of the major problems associated with volumetric phase contrast MRI is the large dynamic range of velocities of interest and the potential risk of velocity aliasing in areas of higher velocities. While correcting a wrapped voxel is easily accomplished by adding or subtracting multiples of 2π, determining which voxels are wrapped is challenging. There is a large body of research on the phase unwrapping problem, spanning many different imaging modalities and generally following a path-based or least-squares cost function based algorithm [1]. Many of the path-following methods are challenged with regular PC MR data that contain noise, sharp jumps at vessel walls between static and moving spins, or undersampling artefacts in accelerated acquisitions. The vast majority of phase unwrapping algorithms operate in 2 dimensions, with some approaches for processing in 3 dimensions [2], or in the temporal dimension [3], or a combination of 2D and temporal dimension [4]. Here we demonstrate a novel phase unwrapping method that utilizes a gradient approach in 4 dimensions, space and time. Algorithm: Blood flow through a vessel is inherently continuous in space and time, so as voxel size and temporal resolution approach zero, the gradient between voxels in these directions also approach zero. As voxel size and temporal resolution increase, the gradients involved become larger and the process of differentiating normal flow patterns from those with wrapped phase values becomes more challenging.