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In this work, the time evolution of the free induction decay caused by thelocal dipole field of a spherical magnetic perturber is analyzed. Thecomplicated treatment of the diffusion process is considered by thestrong-collision approximation that allows a determination of the freeinduction decay in dependence of the underlying microscopic tissue parameterssuch as diffusion coefficient, sphere radius and susceptibility difference. Theinterplay between susceptibility- and diffusion-mediated effects yields severaldephasing regimes of which, so far, only the classical regimes of motionalnarrowing and static dephasing for dominant and negligible diffusion,respectively, were extensively examined. Due to the asymmetric form of thethree-dimensional dipole field for spherical objects, the free induction decayexhibits a complex component in contradiction to the cylindrical case, wherethe symmetric local two-dimensional dipole field only causes a purely realinduction decay. Knowledge of the shape of the corresponding frequencydistribution is necessary for the evaluation of more sophisticated pulsesequences and a detailed understanding of the off-resonance distribution allowsimproved quantification of transverse relaxation.

Freier Induktionszerfall und Linienform im dreidimensionalen magnetischen Dipolfeld