An inverse design method for 3D toroidal gradient coils

Introduction: Traditional gradient coil design is typically constrained to cylindrical, planar, spherical or conical surfaces. Gradient coil geometry is important in arriving at optimal trade-offs between gradient homogeneity, coil efficiency and inductance [1]. Additional concerns such as the induction of eddy currents and peripheral nerve stimulation, patient claustrophobia and acoustic noise have dictated novel coil structures and design methods (eg [2], [3]). However, these methods ordinarily demand that the geometry of the gradient coils be specified prior to optimisation. While et al. [4] present a method for designing fully 3D transverse gradient coils, in which the precise geometry is obtained as part of the optimisation process. This method solves for a 3D current density vector and obtains coil windings using a priority streamline seeding technique. Results are found to display an interesting general geometric form involving sets of closed loops plus spiral-type coils, and lie approximately on the surfaces of sets of elliptical tori. However, despite displaying excellent gradient homogeneity, coil efficiency is low due to the small number of windings and increasing this number results in an unattractive design in terms of manufacturability. The aim of the subsequent work presented here is to use the 3D windings of [4] as a guide for choosing appropriate elliptical torus current density surfaces for which to repeat the gradient field optimisation. It is envisaged that this will provide a transverse gradient coil with a similar optimal geometric form to that of [4], but one that is easy to manufacture via machine etching and should also offer much greater freedom in regards to optimising the trade-off between coil efficiency, inductance and field error.