  In this work, the time evolution of the free induction decay caused by the
local dipole field of a spherical magnetic perturber is analyzed. The
complicated treatment of the diffusion process is considered by the
strong-collision approximation that allows a determination of the free
induction decay in dependence of the underlying microscopic tissue parameters
such as diffusion coefficient, sphere radius and susceptibility difference. The
interplay between susceptibility- and diffusion-mediated effects yields several
dephasing regimes of which, so far, only the classical regimes of motional
narrowing and static dephasing for dominant and negligible diffusion,
respectively, were extensively examined. Due to the asymmetric form of the
three-dimensional dipole field for spherical objects, the free induction decay
exhibits a complex component in contradiction to the cylindrical case, where
the symmetric local two-dimensional dipole field only causes a purely real
induction decay. Knowledge of the shape of the corresponding frequency
distribution is necessary for the evaluation of more sophisticated pulse
sequences and a detailed understanding of the off-resonance distribution allows
improved quantification of transverse relaxation.
