  Purpose: To investigate the effect of anisotropic magnetic microstructure on
the measurable Larmor frequency offset in media with heterogeneous magnetic
susceptibility. Specific objectives were (i) validation of recently developed
theory for the case of fast diffusion and (ii) investigation of the transition
between the regimes of fast and slow diffusion. Methods: Monte Carlo
simulations in synthetic media. Results: Simulations demonstrate a perfect
agreement with the previously developed theory for fast diffusion. Beyond this
regime, the frequency offset shows a pronounced dependence on the medium
microarchitecture and the diffusivity of NMR-reporting spins in relation to the
magnitude of the susceptibility-induced magnetic field. Conclusion: While the
effect of myelin in brain white matter is commonly treated assuming efficient
diffusion narrowing, this regime does not hold for larger cells or higher
magnetic susceptibility. In such a case, the effect essentially deviates from
the prediction based on the assumption of diffusion narrowing.
