Microscopic kurtosis tensor invariants and DDE 4-fold angular modulation in human brain diffusion MRI

Motivation: dMRI signal at moderate diffusion-weightings $$$\sim\,b^2$$$ has contributions from intrinsic (microstructural) kurtosis, and from heterogeneity of compartments. Goal(s): To separate all kurtosis sources and provide a complete set of tensor invariants for a most general distribution of non-Gaussian compartments. Approach: We decompose double diffusion encoding (DDE) signal into irreducible spherical tensor components via harmonic analysis on the rotation group manifold, a 3-dimensional sphere $$$\mathbb{S}^3$$$. Results: We find a complete set of 18(covariances) + 12(microscopic-kurtosis)=33 independent rotational invariants at $$$b^2$$$ level. Impact: We observe for the first time a 4-fold angular modulation of double diffusion encoding signal in the human brain in vivo. This validates the presence of higher-order tensor anisotropies in brain microstructure, which we fully quantify at the $$$b^2$$$ level.