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

Diffusion NMR and MRI methods building on the classic pulsed gradient spin-echo sequence are sensitive to many aspects of translational motion, including time and frequency dependence ("restriction"), anisotropy, and flow, leading to ambiguities when interpreting experimental data from complex heterogeneous materials such as living biological tissues. While the oscillating gradient technique specifically targets frequency dependence and permits control of the sensitivity to flow, tensor-valued encoding enables investigations of anisotropy in orientationally disordered materials. 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 2D frequency-anisotropy space and convenient investigation of both restricted and anisotropic diffusion with a single multidimensional acquisition protocol, thereby combining the desirable characteristics of the oscillating gradient and tensor-valued encoding techniques. 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.