Vector-field analysis for phase contrast magnetic resonance angiography

Phase contrast magnetic resonance angiography (PC MRA) is a noninvasive method that creates volume images of moving tissue (such as blood) in the body. PC MRA datasets are velocity-vector fields that describe the direction and magnitude of tissue flow at every voxel (volume element). Previous methods for visualization of PC MRA data have relied on the speed component of the velocity vectors, which are multiplied by the MR-signal intensity (this suppresses noise from low intensity background, such as air). The intensity-weighted speed is projected using maximum intensity projection (MIP). However, MIP images have numerous limitations due to the projection geometry that can amplify noise in the projected image obscuring small vessels that present slow flow.;In this dissertation, I develop, implement and test a method that combines orientation and speed of velocity vectors to classify and visualize PC MRA data. The method is based on mixture models of the statistical distributions of PC MRA observations in regions of flow and background. The statistical model of noisy PC MRA combines MR-signal intensity, speed, and the relative orientations of neighboring voxels to create a single probability-of-flow metric.;The vector-difference distribution (VDD) describes the expected distribution of orientations in sets of neighboring voxels in regions of flow and background. I implement and test the mixture models in a program called VDD-SEM. For simulated noisy PC MRA images, VDD-SEM distinguishes flow from background and stationary tissue, for signal-to-noise ratios (SNRs) of between 5 and 10. I create probabilistic MIP (PMIP) images by performing MIP on the intensity-weighted speed data weighted by probability-of-flow data. Evaluation of PMIP of physical phantoms shows a significant reduction of the background intensities when compared to MIP. Finally, analysis of the behavior of VDD-SEM reveals that the sensitivity for identification of flow in low-flow regions depends entirely on the VDD component of the mixture models. I conclude that the orientation of PC MRA vector fields may provide an alternative method for visualizing PC MRAs.