3D gradient coil design for open MRI systems

Existing gradient coil design methods typically require some predetermined surface to be specified upon which the precise locations of coil windings are optimised with respect to gradient homogeneity and other measures of coil performance. In contrast, in this paper an analytic inverse method is presented for the theoretical design of 3D gradient coils in which the precise 3D geometry of the coils is obtained as part of the optimisation process. This method has been described previously for cylindrical wholebody gradients and is extended here for open MRI systems. A 3D current density solution is obtained using Fourier series combined with Tikhonov regularisation. The examples presented involve a minimum power penalty function and an optional shielding constraint. A discretised set of 3D coil windings is obtained using an equi-flux streamline seeding method. Results for an unshielded example display a concentration of windings within the portion of the coil volume nearest the imaging region and looped return path windings taken away from this region. However, for a shielded example the coil windings are found to lie almost exclusively on biplanar surfaces, suggesting that this is the optimum geometry for a shielded minimum power open coil.