A novel MRI framework for the quantification of any moment of arbitrary velocity distributions

MRI can measure several important hemodynamic parameters but might not yet have reached its full potential. The most common MRI method for the assessment of flow is phase-contrast MRI velocity mapping that estimates the mean velocity of a voxel. This estimation is precise only when the intravoxel velocity distribution is symmetric. The mean velocity corresponds to the first raw moment of the intravoxel velocity distribution. Here, a generalized MRI framework for the quantification of any moment of arbitrary velocity distributions is described. This framework is based on the fact that moments in the function domain (velocity space) correspond to differentials in the Fourier transform domain (kv-space). For proof-of-concept, moments of realistic velocity distributions were estimated using finite difference approximations of the derivatives of the MRI signal. In addition, the framework was applied to investigate the symmetry assumption underlying phase-contrast MRI velocity mapping; we found that this assumption can substantially affect phase-contrast MRI velocity estimates and that its significance can be reduced by increasing the velocity encoding range.