Measurement of mean and variance of velocity fields within each voxel by NMR imaging

If a flow field exists within an object that is being imaged, there could be a velocity spectrum in each voxel due to the finite voxel size. Consequently, the mean value and the variance of velocity in each voxel can be defined and used to describe the velocity spectrum. An NMR (nuclear magnetic resonance) imaging technique for performing the spatially resolved measurement of the mean value and the variance of velocity as well as the conventional spin density is proposed. A theoretical formalism and experimental results are presented and show good agreement. This technique is expected to be useful in the spatially resolved measurement of random directional flow, such as the fluid flow in living tissue and through porous materials.<>