SU‐FF‐I‐87: Qualifying Magnetic Moments in Small Cylindrical Objects by Complex Sum Method

Purpose: Our ultimate goal is to quantify magnetic moments of small cylindrical objects in‐vivo from MR images, without any a priori information. We want to achieve this goal with the complex sum method [1,2]. Methods: Simulation procedures and the experimental setups were described in [1]. The magnetic moment is defined as . The magnetic moment of an object is proportional to the phase values around the object in MR phase images. Three concentric circles were chosen on a phase image with radii R 1 , R 2 and R 3 . In the simulations, if the magnetic moment is known in advance, the phase values around the object can be used to determine the radii, using formulas in [3]. Each radius has to be larger than the size of the phase aliasing area[2]. Knowing the radii can be used to determine the magnetic moment of the object [2]. We also study the uncertainties of the magnetic moment with the presence of both systematic and thermal noises through error propagation methods. A gel image is also analyzed. Results: For the uncertainty studies, we found that the phase combination (φ 1 ,φ 2 ,φ 3 )=(3,2,1), in units of radians, leads to an uncertainty of the magnetic moment within 3% of the expected moment, which seems to be the lowest uncertainty. Using this phase combination and the known magnetic moment −5.78 ppm‐mm 2 from gel data [1], we were able to determine those three radii and then solve the magnetic moment between the gel‐air interface. The result is −5.53 ppm‐mm 2 which is within 5% uncertainty of the expected value. Conclusions: We have shown that the current method is feasible of extracting the magnetic moment of a small cylindrical object within good accuracy.