A volumetric finite-difference method for the design of three-dimensional, arbitrary-structured MRI gradient coil

Generalized magnetostatic target field method for shielded magnetic field coils in a separable coordinate system

A theoretical method is described to analytically calculate a pair of surface current densities, which produce a desired static magnetic field in one region of the space and zero magnetic field in another. The analysis is based on the known relationship between a surface current density and a stream function, the equivalence of stream functions and surface magnetic dipole density, and the scalar potential representation of the associated magnetic field in free space. From these relations, we formulate the magnetostatic problem, which is often treated as a vector field problem, as a scalar field problem in which a two-dimensional scalar field (stream function) is related to a three-dimensional one (magnetic scalar potential) via the differentiation of the electrostatic Green's function 1/|r-rs|. It is shown that, in a coordinate system in which a separated form of the Green's function exists (separable coordinate system), there exists a simple relationship between a harmonic component of a stream function and a harmonic component of the magnetic scalar potential. The method is applied to calculate idealized surface current patterns for actively shielded, linear gradient field coils in the Cartesian, cylindrical, and spherical coordinates.

Design of an insertable cone-shaped gradient coil matrix for head imaging with a volumetric finite-difference method

Matrix gradient coils have received increasing interest in generating arbitrary-shaped magnetic fields for various magnetic resonance imaging applications. In this paper, a novel cone-shaped matrix gradient coil is proposed to design a multifunctional insertable system for head imaging. Using a volumetric finite-difference-based method, the matrix coil is designed to have comprised several coil elements that can implement localized imaging and control eddy current, dissipated power, and minimum wire gap. With the lowest total dissipated power, various current configurations are selected to generate multiple gradient fields within a large, spheroidal region of interest (ROI) and two small spherical sub-ROIs. The numerical computation results show that the designed matrix coil offers high flexibility in generating a local gradient field capable of improving the local resolution. In addition, with enhanced coil performance, the cone-shaped structure provides a patient-friendly solution for head imaging.