Measuring microscopic anisotropy with diffusion magnetic resonance: From material science to biomedical imaging

Diffusion magnetic resonance provides a non-invasive probe of material structure at the micro-scale in porous media including emulsions, rocks, catalysts and biological tissue. The quantification of microscopic anisotropy aims to reflect the size and shape of individual pores, separating the effect of their orientation distribution in the imaging voxel, which is of great importance in many applications. The single diffusion encoding (SDE) sequence, which consists of a pair of diffusion gradients applied before and after the refocusing pulse in a spin-echo preparation, is the standard pulse sequence for acquiring diffusion MRI data. SDE sequences, which have one gradient orientation per measurement, have been used in various studies to estimate microscopic anisotropy, mainly assuming that the underlying substrate consists of identical pores. In order to discriminate between more complex systems, which may include pores of various sizes and shapes, more sophisticated techniques which use diffusion gradients with varying orientation within one measurement, such as double diffusion encoding, isotropic encoding or q-space trajectory imaging, have been proposed in the literature. In addition to the these techniques which aim to estimate microscopic anisotropy, a different approach to characterize pore shape directly is to take the inverse Fourier transform of the reciprocal pore shape function which can be measured with diffusion gradients that are highly asymmetric. This work provides a review of various diffusion magnetic resonance techniques which have been proposed in the literature to measure the microscopic shape of pores, both in material science as well as in biomedical imaging.