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

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.

Distributions of discrete spherical particles with a constant susceptibility can lead to echo time dependent phase shifts which deviate from theories.

PURPOSE: When an object contains a distribution of discrete magnetic inclusions with a constant susceptibility, the MRI signal inside the object may no longer be determined analytically by assuming that the object is uniform or magnetic inclusions are completely random. Through simulations and experiments with spherical particles inside cylinders, this work is to study the signal behavior in the static dephasing regime. METHODS: MRI complex images of long cylinders containing spherical particles with different arrangements were simulated and compared to similar experimental phantom data. All experiments were designed for the static dephasing regime so that diffusion was neglected. RESULTS: Several factors can lead to different phase shifts over echo time. These include numbers of particles per image voxel, particle arrangements, and Gibbs ringing effects. Purely random arrangements of particles in simulations can agree with a revised theoretical formula at short echo times, but quasi-random arrangements of particles do not agree with the theory. In addition, close to half of experimental results show deviations from the theory and the quasi-random arrangements of particles can explain those experimental results. Simulated R2' values are about the same for different cylinder orientations but increase when random particle arrangement is restricted toward lattice. Nonetheless, as expected, phase distributions outside and far away from each cylinder are independent of any factor affecting phase inside and behave as if they are from a cylinder with a uniform bulk susceptibility. CONCLUSION: Phase over echo time inside an object containing discrete spheres can be nonlinear and deviate from current theories in the static dephasing regime. Phase outside the object can be used to accurately determine its magnetic moment and bulk susceptibility without a priori knowledge of the spherical particle distribution inside the object. These results can be extended to the subcortical gray matter and suggest that in vivo susceptibility quantification will need to be re-thought.

White matter shifts in MRI: Rehabilitating the Lorentz sphere in magnetic resonance.

A thorough exposition and analysis of the role of the Lorentz sphere in magnetic resonance is presented from the fundamental standpoint of macroscopic magnetostatics. The analysis will be useful to those interested in understanding susceptibility and chemical shift contributions to frequency shifts in magnetic resonance. Though the topic is mature, recent research on white matter shifts in the brain promotes the notion of replacing the Lorentz sphere with a generalized Lorentzian cylinder, and has put into question the long standing spherical approach when elongated structures are present. The cavity shape issue can be resolved by applying Helmholtz's theorem, which can be expressed in a differential and an integral formulation. The general validity of the Lorentz sphere for any situation is confirmed. Furthermore, a clear exposition of the "generalized approach" is offered, using the language of Lorentz's theory. With the rehabilitation of the Lorentz sphere settled, one must consider alternative contributions to white matter shifts and a likely candidate is the effect of molecular environment on chemical shifts.