A Novel Target-Field Approach to Design Bi-Planar Shim Coils for Permanent-Magnet MRI

A novel target-field approach for designing bi-planar gradient and shim coils of restricted radius for use with permanent-magnet MRI systems is presented in this article. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic held whose z-component follows a chosen spherical harmonic function. Mathematical expressions that relate the harmonic terms in the surface current distribution to spherical harmonic terms in the field expansion are established and then used in a simple matrix inversion approach to design a range of shim coils. The expressions providing a spherical harmonic decomposition of the field components produced by a particular current distribution are novel. The results can be used to design bi-planar shim coils of restricted radius that will generate a field variation that follows a certain spherical harmonic over a reasonably-sized volume. A stream function was utilized to obtain the discrete wire distribution on the coil plane. This method does not require the setting of the target-field points. Through an analysis of the matrix equations in terms of condition numbers, we show that this novel approach has no ill-conditioned problems. (C) 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 29-38, 2010Chemistry, PhysicalInstruments & InstrumentationPhysics, Atomic, Molecular & ChemicalSpectroscopySCI(E)3ARTICLE129-3837