Efficient Experimental Design for Measuring Magnetic Susceptibility of Arbitrarily Shaped Materials by MRI

Purpose: The purpose of this study is to develop a simple method to measure magnetic susceptibility of arbitrarily shaped materials through MR imaging and numerical modeling. Materials and Methods: Our 3D printed phantom consists of a lower compartment filled with a gel (gel part) and an upper compartment for placing a susceptibility object (object part). The $B_0$ maps of the gel with and without the object were reconstructed from phase images obtained in a 3T MRI scanner. Then, their difference was compared with a numerically modeled $B_0$ map based on the geometry of the object, obtained by a separate MRI scan of the object possibly immersed in an MR-visible liquid. The susceptibility of the object was determined by a least-squares fit. Results: A total of 18 solid and liquid samples were tested, with measured susceptibility values in the range of -12.6 to 28.28 ppm. To confirm accuracy of the method, independently obtained reference values were compared with measured susceptibility when possible. The comparison revealed that our method can determine susceptibility within approximately 5%, likely limited by the object shape modeling error. Conclusion: The proposed gel-phantom-based susceptibility measurement may be used to effectively measure magnetic susceptibility of MR-compatible samples with an arbitrary shape, and can enable development of various MR engineering parts as well as test biological tissue specimens.