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 R 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.