An improved passive shimming approach to design correction iron pieces for high field MRI

This paper proposes a new passive shimming method to design correction iron pieces for compensating field impurities generated by the main magnets of high field magnetic resonance imaging (MRI) for human body imaging. First, the relationship formula of a magnetic dipole to any field point in space is established. Then, a sensitivity matrix in the form of spherical harmonic expansions can be set up based on the contribution of each shim piece to each field point. Next, an optimization procedure of linear programming is applied to determine the location and thickness of the ferromagnetic shim pieces. This is different from the previous methods that consider that all magnetic moments for each magnetized iron piece are located only at its central position, which may cause some intrinsic errors. This method takes the shim piece's volume into account and gives more accurate results in a sensitivity matrix by means of integration in the azimuthal and axial directions while the radial (thickness) direction remains constant. Finally, a case study combining the analytical method and a 3D finite element analysis simulation demonstrates that the new approach provides better results in terms of homogeneity. The method presented can also be used to design passive shims for various practical MRI applications.