Design method of transverse gradient coils based on nonuniform rational B-spline (NURBS) curves.

Purpose: To propose a hybrid transverse gradient coil design method that leverages current density-based methods and nonuniform rational B-spline (NURBS) curves to optimize the performance and manufacturability of gradient coils.

Methods: Our method begins by generating an initial wire configuration using a density-based method. Then, we fit NURBS curves to the configuration, and adjust the control parameters of these curves to meet performance requirements. To ensure adequate spacing and even distribution of wires, an objective function utilizing the sigmoid function to modulate the distances between adjacent wires is constructed. Critical factors including gradient efficacy, linearity, eddy current, and torque, are incorporated as constraints. The piecewise nature of the curves provides the flexibility to independently control specific segments without impacting others.

Results: We validated our method by designing three shielded transverse gradient coils: a whole-body coil, an ultra-short whole-body coil, and an ultra-short asymmetric head coil. The primary design objectives were to improve linearity and maintain gradient efficiency. All optimized coils demonstrated significant linearity across large diameters of spherical volumes (DSVs), while gradient efficiency, eddy currents, and torque were well-balanced. The objective function effectively managed the wire concentrations required for high linearity, ensuring even wire arrangement and adequate spacing. We leveraged the flexibility of the curves to individually tailor wire paths for specific objectives, such as preventing interference between coils and passive shimming and accommodating wire connections and cooling circuits.

Conclusion: This method provides a versatile and effective approach for designing high-performance and manufacturable gradient coils.