Probabilistic 4D blood flow tracking and uncertainty estimation.

Phase-Contrast (PC) MRI utilizes signal phase shifts resulting from moving spins to measure tissue motion and blood flow. Time-resolved 4D vector fields representing the motion or flow can be derived from the acquired PC MRI images. In cardiovascular PC MRI applications, visualization techniques such as vector glyphs, streamlines, and particle traces are commonly employed for depicting the blood flow. Whereas these techniques indeed provide useful diagnostic information, uncertainty due to noise in the PC-MRI measurements is ignored, which may lend the results a false sense of precision. In this work, the statistical properties of PC MRI flow measurements are investigated and a probabilistic flow tracking method based on sequential Monte Carlo sampling is devised to calculate flow uncertainty maps. The theoretical derivations are validated using simulated data and a number of real PC MRI data sets of the aorta and carotid arteries are used to demonstrate the flow uncertainty mapping technique.