A stream function method for gradient coil design

Abstract

A new design approach for the construction of gradient coils for magnetic resonance imaging is presented. The theoretical formulation involves a constraint cost function between the desired field in a particular region of interest in space and an almost arbitrarily defined surface that carries the current configuration based on Biot-Savart's integral equation. An appropriate weight function in conjunction with linear approximation functions permits the transformation of the problem formulation into a linear matrix equation whose solution yields discrete current elements in terms of magnitude and direction within a specified coil surface. Numerical predictions and comparisons with practical measurements for the Gx, Gy, Gz gradient coils underscore the success of this approach in terms of achieving highly linear fields while maintaining low parasitic fields and low inductances. © 2005 Wiley Periodicals, Inc.