The larmor frequency shift in magnetically heterogeneous media depends on their mesoscopic structure

Abstract

Purpose: Recent studies have addressed the determination of the NMR precession frequency in biological tissues containing magnetic susceptibility differences between cell types. The purpose of this study is to investigate the dependence of the precession frequency on medium microstructure using a simple physical model. Theory: This dependence is governed by diffusion of NMR-visible molecules in magnetically heterogeneous microenvironments. In the limit of fast diffusion, the precession frequency is determined by the average susceptibility-induced magnetic field, whereas in the limit of slow diffusion it is determined by the average local phase factor of precessing spins. Methods: The main method used is Monte Carlo simulation of isotropic suspensions of impermeable magnetized spheres. In addition, NMR spectroscopy was performed in aqueous suspensions of polystyrene microbeads. Results: The precession frequency depends on the structural organization of magnetized objects in the medium. Monte Carlo simulations demonstrated a nonmonotonic transition between the regimes of fast and slow diffusion. NMR experiments confirmed the transition, but were unable to confirm its precise form. Results for a given pattern of structural organization obey a scaling law. Conclusion: The NMR precession frequency exhibits a complex dependence on medium structure. Our results suggest that the commonly assumed limit of fast water diffusion holds for biological tissues with small cells. Magn Reson Med 79:1101–1110, 2018. © 2017 International Society for Magnetic Resonance in Medicine.