Measurement of bulk and random directional velocity fields by NMR imaging.

A formalism for the multidimensional measurement of velocity fields in liquids by nuclear magnetic resonance (NMR) is introduced. We assume that the velocity at any point within a flow field is given by a superposition of two velocity components. The first one is taken to represent the mean bulk velocity within a voxel and the second component is assumed to be random directional such as one may find in the capillary beds or porous materials. We show that the random directional flow leads to an extra dephasing of the nuclear magnetization in addition to molecular diffusion and spin-spin relaxation (T2) processes. The coherent bulk flow introduces a phase distortion in the NMR images. A procedure for measuring the spin density as well as the two velocity fields is described.