Finite-length shim coil design using a fourier series minimum inductance and minimum power algorithm

Abstract

High field magnetic resonance (MR) imaging and spectroscopy are sensitive to magnetic field inhomogeneities caused by susceptibility differences between tissues, bone, and air. These inhomogeneities cause MR image artifacts and line broadening in MR spectra. To correct for these inhomogeneities, specialized shim coils are used in combination with the usual gradient systems. To produce realistic coils for use in human or small-animal studies, direct control over the length of the coils is necessary. In this article, a simple method for the design of shim coils of arbitrary order and with predetermined length is presented. The method is based on a simple Fourier series expansion of the current density and either power or inductance can be minimized subject to a series of field constraints. The method is mathematically simple, easy to implement and computationally fast. A quantitative comparison of figures of merit for inductance and resistance was made as a function of shim coil length. Coils of 40 cm diameter were designed with lengths of 50, 60, 80, and 100 cm. Comparison of results obtained using the two design methods across all shim axes and coil lengths indicate very little performance difference between the two methods. The decreased complexity of the minimum power designs appears to outweigh any small benefits obtainable using the minimum inductance algorithm for the range of coils investigated. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 245–253, 2010.