The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of t...The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.展开更多
基金the National Natural Science Foundation of China under grant No.51675506.JGK acknowledges support from an EU2020 FET grant(737043 TiSuMR)the Deutsche Forschungsgesellschaft(DFG)(grant KO 1883/20-1 Metacoils)funding within the framework of the German Excellence Initiative under grant EXC 2082“3D Matter Made to Order”,from the VirtMat initiative“Virtual Materials Design”,and from an ERC Synergy Grant(951459,HiSCORE),European Union.
文摘The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.
