High-order MR shimming: a simulation study of the effectiveness of competing methods, using an established susceptibility model of the human head

The first step in the process of shimming a magnetic field is to characterize it by obtaining a field map and decomposing that map into a convenient set of basis functions. The strength of each member of the set is then calculated. Finally, a set of correction elements which generate fields corresponding to the same spatial distribution as the basis functions is energized so that the sum of their fields and the error fields is substantially zero. The basis functions used typically are solutions to Laplace’s equation and have been shown to be very effective when the region of interest is substantially free space. This paper addresses issues associated with shimming the magnetic field in a region in which there is a distribution of materials with different susceptibilities and which therefore is not free space. In such a region, Laplace’s equation is no longer valid and in principle cannot be used to describe the magnetic field there. It is demonstrated that in spite of this, the same set of basis functions suffices for analyzing the field and the same set of elements suffices for correcting the field. The motivation for this study stems from the need to improve the magnetic field homogeneity when biological specimens are being imaged by magnetic resonance. In particular, this paper describes a study carried out by various simulated shimming strategies to improve the uniformity of the magnetic field over a multitissue model of susceptibility of the human head. The topics of magnetic susceptibility, the effect of shimming on MR images, shimming hardware and shimming methods are briefly reviewed. Two slices of the human head model were selected for detailed study, both offset inferior to the origin and including the base of the brain and the anterior sinus. The results of the study include comparisons between the strategies of global shimming, local slice-selective shimming and combinations of the two; the effects of shimming to various orders of spherical harmonics; and the effects of rotation and displacement of the head with respect to the shim frame of reference.