Exploiting Non-Gaussian Phase Distributions to Model Micron-Scale Restricted Diffusion

Leigh A. Johnston¹, ², David Wright, ²³, Iven M. Mareels¹

A model of cylindrically restricted diffusion is derived through analytic combination of non-Gaussian phase distribution, applicable to the micron-size axon compartments and diffusion characteristics of mammalian white matter, with an assumed parametric form for the cylinder radii probability density function. The resultant model is presented as an alternative to the AxCaliber method of Assaf et al (2008) that obviates the need for truncation of Bessel functions to solve. We apply the restricted diffusion form in a two-compartment model to two experimental datasets, rat auditory nerve and sheep brain, and demonstrate its ability to infer axon diameter densities.