The use of the boundary element method to compute MR image distortions caused by tissue susceptibility

The clinical applicability of MR images is restricted by geometrical distortions caused by magnetic susceptibility differences between air and tissue. Here, the authors describe a method to compute these kind of distortions in spin echo MR images. Starting from the Boundary Element method (BEM) and the assumption that the susceptibilities are small, a formula is derived to compute the distorted magnetic field. This formula is efficient when the magnetic field is needed at a limited number of points, e.g. to compute geometrical distortions of a set of markers. The maximum difference between the BEM solution and the analytical solution for a sphere was 0.053 ppm of the static field. The method was applied to simulate the displacement vector field of the surface of a human head. The distortions can be as large as 3 mm for points just outside the surface of the head when a gradient strength of 3 mT/m is used. Within the head the distortion can be described accurately as a linear scaling in the axial direction