A Textile Anisotropic Brain Imaging Phantom incorporating textile water filled hollow fibers (taxons with inner/outer diameter 12/34 micron) is used to examine time-dependent diffusion. In this study, impermeable hollow tubes (taxons) with 12-micron diameter are used to test the relationship between axial and radial diffusivities with diffusion time (Δ) for a given taxon packing density. An inverse relationship of radial diffusivity with diffusion time (Δ) is established. A constant relationship of axial diffusivity with diffusion time is established. The dependence of these relationships on packing density is then tested and the radial diffusivity relationship is shown to vary with packing density.