Access Type

Open Access Dissertation

Date of Award

January 2015

Degree Type


Degree Name



Biomedical Engineering

First Advisor

Yu-Chung N. Cheng

Second Advisor

E. M. Haacke


Purpose: The purpose of this PhD work is to develop a method for accurately quantifying effective magnetic moments and susceptibility of either cylindrical or spherical-like small objects from magnetic resonance imaging (MRI). A standard 3D gradient echo sequence with only one echo time is intended for our approach to measure the effective magnetic moment of a given object of interest. For the quantification of the susceptibility in the cylindrical objects at different orientations, a standard 3D gradient echo sequence with only one or two echo times is needed.

Methods: Our method is to sum over complex MR signals around the object and equates those sums to equations derived from the magnetostatic theory. With those equations, our method is able to determine the center of the object with subpixel precision. By rewriting those equations, the effective magnetic moment or susceptibility of the object becomes the only unknown to be solved. The uncertainty of quantified effective magnetic moment and susceptibility of the object is derived from the error propagation method. For the object without having signal, if it is also imaged in the spin echo sequence, the volume of the object can be measured from spin echo images, the susceptibility difference between the object and its surrounding can be further quantified from the effective magnetic moment. If the cylindrical object has signal such as veins, the susceptibility of this object can be quantified by rearranging the equation with the known effective magnetic moment and the spin density surrounding the object. Numerical simulations, a variety of air straw, glass beads, and the gadolinium doped straw in phantom studies with different MR imaging parameters from a 1.5T and 3.0T machines have been conducted to test the robustness of this method. This method also quantified the magnetic moments and susceptibility of cerebral veins in human images from a 3.0T and 4.0T machines.

Results: Quantified effective magnetic moments and susceptibility differences from different imaging parameters and methods all agree with each other within two standard deviations of estimated uncertainties.

Conclusion: CISSCO method is developed to accurately quantify the effective magnetic moment and susceptibility of a given small object of interest. Most results are accurate within 10% of true values and roughly half of the total results are accurate within 5% of true values using very reasonable imaging parameters. Our method is minimally affected by the partial volume, dephasing, and phase aliasing effects.