Application of engineering analysis techniques to the design of Magnetic Resonance Imaging (MRI) coils L. Marin 1 , H. Power 1 , R.W. Bowtell 2 , C. Cobos Sanchez 2 , A.A. Becker 1 , P. Glover 2 and I.A. Jones 1 1 School of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, UK 2 Sir Peter Mansfield Magnetic Resonance Centre, School of Physics and Astronomy, The University of Nottingham, Nottingham Park, Nottingham NG7 2RD, UK 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 sur- face 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. Keywords : Inverse problem; Regularization; Divergence-free BEM; Magnetic resonance imaging (MRI) 1. Introduction MRI is a non-invasive technique for imaging the human body, which has revolutionised the field of diagnostic medicine. MRI relies on the generation of highly controlled magnetic fields that are es- sential to the process of image production. In particular, an extremely homogeneous, strong, static field is required to polarize the sample and provide a uniform frequency of precession, while pure field gradients (which are required separately along the direction of the static field and in two perpendicular directions) are needed to encode the spatial origin of signals. The field gradients are generated by carefully arranged wire distributions generally placed on cylindrical surfaces surrounding the imaging subject, known as gradient coils [1-3]. The objective of the research reported here is to provide a computational tool to enable more complex geometries of gradient coil to be designed. This involves two stages, beginning with the de- velopment of a so-called direct boundary element method which enables the magnetic field distribution to be calculated from a known current distribution on a chosen geometry of coil. This approach is then incorporated into an inverse technique in which the desired distribution of magnetic field is used to calculate the current distribution necessary to achieve it. The project was originated in response to an EPSRC initiative to promote collaboration between engineers and physicists, and in order to provide tools to improve the design of MRI equipment. Those involved in the project include two physicists, an electrical engineer, three mechanical engineers and a mathematician. Unusually for such a collaboration, the project involves the application of engineering techniques to the solution of a physics-based problem, rather than the use of specialist techniques from physics to solve an engineering problem. Engineering and Physics—Synergy for Success IOP Publishing Journal of Physics: Conference Series 105 (2008) 012004 doi:10.1088/1742-6596/105/1/012004 c  2008 IOP Publishing Ltd 1