The Calculation of the Susceptibility-Induced Magnetic Field from 3D NMR Images with Applications to Trabecular Bone

Abstract A method is described for computing the induced magnetic field caused by the susceptibility difference of two materials. Arbitrary surfaces derived from 3D NMR images were modeled with triangular elements of constant magnetic surface-charge density. The boundary elements were generated by means of a surface triangulation method that is typically used for displaying 3D images. The induced field was computed from the charged triangles using a hierarchical multipole algorithm. Validation of the technique on a spherical object showed excellent agreement with the analytical solution. The method was applied to computing histograms of the induced fields in specimens of trabecular bone. A 76 × 76 × 76 3D array of image voxels resulted in 322,169 triangles and required ∼70 minutes on a Sun Sparc 10 workstation to compute the field at 100,000 locations. The width of the induced field distributions was found to be narrowest when the polarizing field was parallel to the principal orientation of the trabeculae, confirming previous experimental findings. The method is applicable to other structures in which susceptibility-induced fields are of interest, such as capillary networks or blood cells.