Tracking of cyclic motion with phase‐contrast cine MR velocity data

A method of computing trajectories of objects by using velocity data, particularly as acquired with phase‐contrast magnetic resonance (MR) imaging, is presented. Starting from a specified location at one time point, the method recursively estimates the trajectory. The effects of measurement noise and eddy current‐induced velocity offsets are analyzed. When the motion is periodic, trajectories can be computed by integrating in both the forward and backward temporal directions, and a linear combination of these trajectories minimizes the effect of velocity offsets and maximizes the precision of the combined trajectory. For representative acquisition parameters and signal‐to‐ noise ratios, the limitations due to measurement noise are acceptable. In a phantom with reciprocal rotation, the measured and true trajectories agreed to within 3.3%. Sample trajectory estimates of human myocardial regions are encouraging.