  Porous or biological materials comprise a multitude of micro-domains
containing water. Diffusion-weighted magnetic resonance measurements are
sensitive to the anisotropy of the thermal motion of such water. This
anisotropy can be due to the domain shape, as well as the (lack of) dispersion
in their orientations. Averaging over measurements that span all orientations
is a trick to suppress the latter, thereby untangling it from the influence of
the domains' anisotropy on the signal. Here, we consider domains whose
anisotropy is modeled as being the result of a Hookean (spring) force, which
has the advantage of having a Gaussian diffusion propagator while still
retaining the fact of finite spatial range for the diffusing particles.
Analytical expressions for the powder-averaged signal under this assumption are
given for so-called single and double diffusion encoding schemes, which
sensitize the MR signal to the diffusive displacement of particles in,
respectively, one or two consecutive time intervals.
