Coarse-graining with time-dependent diffusion reveals signatures of demyelination and axonal loss

Motivation: Time-dependent diffusion $$$D(t)$$$ is sensitive to brain microstructure. Using Monte Carlo (MC) simulations, $$$D(t)$$$ has been shown to provide information about structural changes caused by pathological conditions. Goal(s): To establish the relation between the parameters of $$$D(t)$$$ and the extra-axonal space geometry. Approach: We solve the Fick-Jacobs equation in the effective medium framework, connect $$$D(t)$$$ to correlations of density and local diffusivity, and validate with Monte-Carlo simulations. Results: Time-dependence of $$$D(t)$$$ is quantitatively related to geometric characteristics of axonal packing, demyelination and axonal loss. Impact: By coarse-graining the extra-axonal space, time-dependent diffusion explores the geometry relevant for demyelination and axonal loss, enabling quantifying axonal microstructure.