Theoretical design of 3D gradient coils

Introduction: Gradient coil design is constrained by the important coil parameters of inductance, efficiency and field homogeneity [1]. Additional secondary concerns include reducing the induction of eddy currents and peripheral nerve stimulation, patient claustrophobia and acoustic noise [2]. The search for optimal coil geometries to address various combinations of these design criteria has resulted in a wide variety of coil structures to be presented in the literature (eg [3], [4]). These recent designs deviate away from the established cylindrical or bi-planar, primary plus shield coil set; however, despite the associated methods often being applicable to arbitrary geometry, this geometry must still be chosen prior to the method being implemented. A method is presented here for the theoretical design of transverse gradient coils that allows full freedom to be explored within 3D solution space. That is, the coil windings are not constrained to lie on some predetermined surface, but are instead found as part of the optimisation process. Interest lies primarily with the optimum geometry of the coil windings in obtaining a linear gradient field, with coil inductance, efficiency and shielding being secondary concerns in this preliminary work.