2D correlation of isotropic and anisotropic diffusion

By measuring the translational diffusion of water via NMR, we can non-invasively probe the structure of porous materials like lyotropic liquid crystals, cements, and brain tissue. In diffusion NMR, these materials can be described as a collection of microscopic domains, where the water diffusion is described by a diffusion tensor, and whose ensemble average defines the macroscopic diffusion tensor. The eigenvalues of the macroscopic tensor are affected by microscopic properties such as the pores sizes, or the anisotropy of the pore space, and macroscopic properties like the orientation dispersion of domains. However, in conventional techniques such as diffusion-encoding with the Stejskal-Tanner sequence, the effects of those properties are entangled.

Inspired by solid-state NMR techniques, we have recently introduced a triple PGSE sequence that provides isotropic diffusion weighting [1] , a scheme where the signal decay is independent of the effects of anisotropy and orientation. Said pulse sequences also allow for typical directional diffusion-encoding. Still within the field of solid-state NMR, we can find an extension of the typical magic-angle spinning experiment called variable-angle spinning (VAS) [2] . In VAS, the angle between the axis of rotation and the external magnetic field is varied, thus allowing for a correlation between the isotropic and anisotropic chemical shifts.

Capitalizing on the aforementioned works, we present a new experimental protocol designed to separate the contributions from domains with different isotropic diffusivities. Using a pulse sequence similar to the one described in [1], we define a 2D parameterization of the diffusion-encoding tensor that correlates isotropic and anisotropic diffusion, in analogy with the VAS experiment [2] . To validate our protocol, we performed proof-of-principle experiments on assemblies of materials with known diffusion properties. More precisely, the method was tested on phantoms where a central core filled with a liquid crystal in the hexagonal phase was surrounded by a yeast suspension with two isotropic diffusion components. Sparse decomposition of the data yields a 2D map of isotropic and anisotropic diffusivities wherein each of the components is clearly resolved.

Furthermore, we think that our method could serve as a basis to experimental protocols capable of quantifying the volume fraction of different structural components of the brain.