# Freier Induktionszerfall und Linienform im dreidimensionalen magnetischen Dipolfeld

## TL;DR

This paper analyzes the free induction decay caused by a spherical magnetic dipole in a 3D field, considering tissue parameters and diffusion effects, revealing complex decay behavior due to asymmetry.

## Contribution

It introduces a model for the free induction decay in 3D dipole fields considering diffusion and susceptibility effects, extending understanding beyond classical regimes.

## Key findings

- Identification of complex decay components due to asymmetry
- Dependence of decay on tissue parameters and diffusion
- Enhanced understanding of off-resonance frequency distribution

## Abstract

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.