Access Type

Open Access Dissertation

Date of Award

January 2018

Degree Type


Degree Name



Biomedical Engineering

First Advisor

Yu-Chung Norman Cheng

Second Advisor

E Mark Haacke


Simulating signal behavior in Magnetic Resonance imaging (MRI) is often a necessary step in being able to understand how signal relates to certain physiological parameters. One such parameter of interest in the body is magnetic susceptibility since it is related to iron content. The bulk magnetic susceptibility of an object is a property that describes how magnetized it becomes when placed in an external magnetic field. When the bulk susceptibility of an object arises from the presence of discrete magnetic inclusions, the MRI phase signal inside the object can no longer be determined analytically by assuming it has a continuous susceptibility. This phase will depend on the microstructure of the inclusions and requires either simulations or some other analytical modeling which makes assumptions about the microstructure. Under static dephasing conditions, if the discrete inclusions are spherical particles and randomly dispersed, then a known frequency shift will affect the phase signal. It has also recently been shown that this shift can vary depending on the volume fraction and clustering of the particles. The main focus dissertation is to demonstrate that spherical particles inside an object can lead to non-linear phase behavior which is not describable by a signal frequency shift, while the phase outside the object behaves as if it were continuous. This makes the phase outside the object a more reliable source for susceptibility quantification, as it does not depend on the microstructure of the object.

This dissertation consists of three major research projects. The first explores different static dephasing simulation model parameters to predict MRI phase from different quasi-random arrangements of spherical particles. Guidelines are established on the required size of the modeled particles and how many are needed per simulated MRI voxel to obtain precise and accurate results. It is also shown how restricting the randomness of particles affects the simulated voxel phase and R2' values. The second research project uses these guidelines to simulate long cylinders made up of discrete spherical particles. Both random and quasi-random particle arrangements were used. Input parameters for these simulations were taken from experimental phantom data which also consisted of cylinders that contain mixtures of nanoparticles and polystyrene beads, separately. Phase inside the cylinders, bulk susceptibility quantified from phase outside them, and R2' were compared between simulation and experiment. In most cases, the averaged phase inside the simulated and experimental cylinders agree with the theoretical shift for static dephasing regime, while one experimental case agrees better with the quasi-random arrangement. The predicted large variation of phase values from having low numbers or particles per voxel was seen in experiment. The R2' from simulations was generally higher than the quantified R2* from experiment. Bulk susceptibilities of simulated and experimental cylinders were in good agreement and shown to be insensitive to particle arrangement. This supports the reliability of using outside phase for quantification. In the third research project, this concept of using outside phase as an accurate reflection of bulk susceptibility was applied to clusters of iron-tagged stem cells. It was shown how the magnetic moment of the cluster should can be used to determine the number of cells there.