  Diffusion MRI measures of the human brain provide key insight into
microstructural variations across individuals and into the impact of central
nervous system diseases and disorders. One approach to extract information from
diffusion signals has been to use biologically relevant analytical models to
link millimetre scale diffusion MRI measures with microscale influences. The
other approach has been to represent diffusion as an anomalous process and
infer information from the different anomalous diffusion equation parameters.
How parameters of various anomalous diffusion models vary with age in the human
brain white matter has not been investigated. We perform the tests within a
general continuous time random walk framework, in which temporal jump lengths
and structural barriers to diffusion are considered. We outline the
formulations for the super-diffusion (i.e., stretched exponential),
sub-diffusion, quasi-diffusion and fractional Bloch-Torrey models with respect
to the continuous time random walk expression. We also provide a direct link
between diffusion kurtosis and the sub-diffusion model and demonstrate
mathematical equivalence between parameters. 7T diffusion weighted MRI data in
the age range 19-67 was used in this study, particularly focusing on the corpus
callosum. Anomalous diffusion model parameters were found to show trends with
aging, and interestingly, our investigations led to a new robust technique for
generating maps of diffusion kurtosis.
