Singular Behavior of Time-Dependent Diffusion in a Fiber Bundle Geometry Due to a Disordered Packing

Lauren Burcaw¹, Els Fieremans², Dmitry S. Novikov¹

We demonstrate that disorder in the packing geometry of a fiber bundle, such as an axonal tract, is crucial for the time-dependent diffusion. Using fiber phantom measurements and Monte Carlo simulations, we uncover a logarithmic singular behavior at long times, which makes the time dependence of diffusion in the extra-axonal space more pronounced than that coming from water confined inside axons. This singularity translates into linear-in-frequency dependence of OGSE diffusion coefficient at small frequencies, which again dominates over that from confined spaces. As a result, incorporating disorder in axonal packing is crucial for modeling and characterization of axonal tracts.