Quantifying changes of axonal shape in traumatic brain injury with time-dependent diffusion

Motivation: Interpreting diffusion MRI (dMRI) in terms of brain tissue micro-geometry. Goal(s): To identify cellular features that govern diffusion measurements among myriads of parameters specifying tissue microstructure. Approach: We found how axonal micro-geometry is manifested in a dMRI measurement by analytically solving the diffusion equation in a tube with a randomly varying cross-section. Results: We identify a specific power-law approach of the time-dependent diffusion coefficient along the axon to its long-time limit. The average inverse cross-section and the variance of long-range cross-sectional fluctuations govern the diffusive dynamics. We quantify changes in these non-trivial geometrical features, associated with axonal beading, in a rat TBI model. Impact: Beading is a characteristic feature of numerous neurodegenerative diseases triggered by different pathological conditions and injuries. Here, we detect geometrical changes in the axonal micro-geometry, accessible via the along-tract diffusivity from the diffusion tensor using clinically feasible diffusion weightings.