Optimal processing of velocity images for tracking of moving material [myocardial MRI]

Several algorithms are analyzed for determining the trajectory of a particle in motion given cine magnetic resonance (MR) phase contrast (PC) velocity field data. The PC velocity field is usually measured in a fixed frame of reference (spatial coordinates) and must be transformed to the velocity in material coordinates, i.e., the velocity experienced by individual points in the medium. The material velocity field can then be integrated to yield the trajectory of a particular point. Therefore, to determine the trajectory of a particular point, the given spatial velocity field must be transformed to the material velocity field. Although there exists a mathematical relationship that maps velocity fields in spatial coordinates to material coordinates, this mapping can be applied only if particle trajectories are known. This observation readily suggests an iterative solution, which the author presents, using an optimization technique