Application of engineering analysis techniques to the design of Magnetic Resonance Imaging (MRI) coils

Abstract

In this paper, we develop a new approach to analysing and designing the gradient coils for magnetic resonance imaging (MRI) scanners for medical applications. More specifically, a novel higher-order BEM which satisfies the continuity equation for the current density is proposed. We also present solution procedures for applying this method to the inverse problem whereby the divergence-free surface current distribution in the gradient coil is deduced from knowledge of the magnetic flux density in a prescribed region of interest. The novel BEM proposed is a non-traditional one, in the sense that the collocation points are given by the vertices of the triangular elements only and not all the BEM nodes used to define the boundary elements. Furthermore, the degree of the interpolation is one degree less than that of the geometry of the triangular elements employed, so that (for example) the linear boundary elements involve constant interpolation for the surface current density. Moreover, the present method can be easily extended in order to obtain any desired degree of the interpolation for the surface current density. Within the inverse problem, care must be taken to employ the optimal value of the Tikhonov regularisation parameter. Results are presented relating to various geometries of coil, obtained using linear, quadratic and cubic variants of the boundary element formulation; those obtained using the quadratic and cubic elements agree almost precisely, while those from the linear elements exhibit small differences from those of the higher-order formulations. © 2008 IOP Publishing Ltd.