q-Space MR Propagator in Partially-Restricted, Axially-Symmetric and Isotropic Environments

Evren Ozarslan¹, Cheng Guan Koay, Peter J. Basser

Diffusion may lead to non-symmetric propagators, which can be mapped from the complex-valued MRI signal. Because the true diffusion propagator obeys the reciprocity property, both forward and backward Fourier transforms can be employed, leading to propagators with different meanings. Depending on the geometry, Fourier transform in one direction may provide a more intuitive representation of the geometry than the other. In axially-symmetric and isotropic environments, having one-dimensional data is sufficient to reconstruct higher-dimensional propagators. In these environments, other transforms can be employed, which may make information, otherwise obscured by the one-dimensional Fourier transform, visible.