Magnetic Moment Quantifications of Small Spherical Objects in MRI
Purpose: The purpose of this work is to develop a method for accurately quantifying effective magnetic moments of 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. Methods: Our method sums 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 of the object becomes the only unknown to be solved. Each quantified effective magnetic moment has an uncertainty that is derived from the error propagation method. If 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. Numerical simulations, a variety of glass beads in phantom studies with different MR imaging parameters from a 1.5 T machine, and measurements from a SQUID (superconducting quantum interference device) based magnetometer have been conducted to test the robustness of our method. 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: An MRI method is developed to accurately quantify the effective magnetic moment 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. Our next goal is to apply this method to in vivo studies.