SU‐FF‐I‐87: Qualifying Magnetic Moments in Small Cylindrical Objects by Complex Sum Method
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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 R1, R2 and R3. 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 (φ1,φ2,φ3)=(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‐mm2 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‐mm2 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.
