Theoretically calculating the
field, given a matter distribution,
allows modelling of MRI signal dropout, interaction of
and motion
effects, manipulation of
using active and weakly magnetic passive
shims, respiration effects, etc. Existing methods for calculating
use full finite element calculations [1,2] or
approximate solutions to Maxwell's equations given either surface models of
matter interfaces [3,4], voxel-based
elements [5] or Fourier representations [6].
By using a perturbation approach to solving Maxwell's
equations [7], a linear first-order solution can be
found which is fast and appropriate for most MR imaging applications.
In addition, the perturbation method allows the magnitude of the
errors to be calculated, and hence the accuracy and appropriateness
of the method to be estimated for various applications.