Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the q-vector

Abstract. Diffusion NMR and MRI methods building on the classic pulsed gradient spin echo sequence are sensitive to many aspects of translational motion, including time/frequency-dependence (“restriction”), anisotropy, and flow, which leads to ambiguities when interpreting experimental data from complex heterogeneous materials such as living biological tissues. Higher specificity to restriction or anisotropy can be obtained with, respectively, oscillating gradient or tensor-valued encoding which nevertheless both have some sensitivity to the property not being of direct interest. Here we propose a simple scheme derived from the “double rotation” technique in solid-state NMR to generate a family of modulated gradient waveforms allowing for comprehensive exploration of the two-dimensional frequency-anisotropy space and convenient investigation of both restricted and anisotropic diffusion with a single multidimensional acquisition protocol. The method is demonstrated by measuring multicomponent isotropic Gaussian diffusion in simple liquids, anisotropic Gaussian diffusion in a polydomain lyotropic liquid crystal, and restricted diffusion in a yeast cell sediment.