A novel target‐field approach to design bi‐planar shim coils for permanent‐magnet MRI

Abstract

AbstractA 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 field 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. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 29–38, 2010