Flow Velocity and Acceleration Mapping

If the nuclei are displaced by a flow field, their positions on the gradient axis become time dependent  

This phase shift depends on x0, vx0 and ax0 at the same time, i.e., on the parameters needed for spin density, velocity and acceleration mapping, respectively. In order to distinguish the three quantities of interest, more sophisticated gradient pulse sequences have been designed, resulting in phase shifts that essentially depend only on a single parameter or a selection of parameters. 

For many systems and flow fields, the position dependent term dominates the phase shift while the velocity dependent term is still significantly larger than the acceleration dependent term. As a direct consequence, terms with a higher order of t than the term including the parameter to be evaluated may often be neglected, 

Another type of flow artifact is due to voxel inflow and outflow problems large velocities make a spin leave its designated voxel in the time between signal encoding and signal readout. As the traveled distance d and the velocity v are related by the expression d = vt, it is obvious that the effect is more severe, the smaller the voxel size is. Slow velocities, on the other hand, may be masked by diffusive displacements. 

3 Velocity Mapping of Strongly Heterogeneous Flow Velocity Fields 

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