A Hybrid Field-Harmonics Approach for Passive Shimming Design in MRI

This paper presents a new passive shimming (PS) design scheme for the correction of static magnetic-field inhomogeneities in magnetic resonance imaging (MRI) systems. In MRI, the PS procedure usually employs magnetic-field-based or harmonic-based methods to find an optimal iron-piece configuration to improve the uniformity of the static magnetic field in the imaging region. For the field-based PS technique, the peak-to-peak field inhomogeneity is minimized, and the harmonic components are inherently unconstrained; in the harmonic-based scheme, selected unwanted harmonics are minimized, and the overall field uniformity is consequently reduced. The field approach usually provides good field homogeneity but lacks flexibility in managing all terms of spherical harmonic field expansion; the harmonic approach is capable of controlling targeted low-order harmonic terms but can have difficulty in producing optimal overall field homogeneity and in controlling high-order harmonics. The new algorithm proposed herein attempts to combine the strengths of these two methods for a better PS solution. During the PS implementation, an explicit expression of the system matrix with both the field and harmonic sensitivities is generated, and then, an optimization procedure is performed for the determination of shim-piece thicknesses and locations. A case study presented shows that the hybrid method provides good quality, flexible solutions for controlling individual harmonic impurities, and also overall field uniformity. This method is not only applicable to conventional MRI magnets, but also, its flexibility means that it can be easily used to shim unconventional electromagnets.