Quantifying unmyelinated axons from time-dependent radial kurtosis in brain white matter

Motivation: Unmyelinated axons have been largely overlooked in white matter modeling Goal(s): To demonstrate that unmyelinated axonal water fraction can be estimated from radial kurtosis $$$K^\perp(t)$$$ measured at varying diffusion times. Approach: By means of the KÄrger model, we derived an equation that relates exchange time, myelinated and unmyelinated axonal water fractions with $$$K^\perp(t)$$$ Results: Using Monte Carlo simulations, we demonstrate good agreement between our derived equation and $$$K^\perp(t)$$$, and accurate estimation of the unmyelinated axon water fraction. Impact: Unmyelinated axon density changes in development, aging, and neurodegenerative diseases such as multiple sclerosis. Estimation of the unmyelinated axon fraction from time dependent kurtosis could lead to new biomarkers for diagnosis and prognosis, as well as to assess remyelination.