Diffusion MRI (dMRI) has been established as a useful tool to obtain voxel-level
information on the tissue micro-structure. An important quantity measured in
dMRI is the apparent diffusion coefficient (ADC), and it has been well
established by in-vivo brain imaging experiments that the ADC depends
significantly on the diffusion time. We derive an explicit formula for
the time-dependent ADC, and, using the ADCs at multiple diffusion times and gradient directions, we
estimate the surface to volume ratio, the eigenvalues and the first
moment of the dominant eigen-functions associated to the geometry of the biological cells.