A method of inverse calculation for regions of small susceptibility variations

The paper considers the determination, from a knowledge of the perturbation of a constant incident field, the susceptibility of regions where the susceptibility is 0.01 to 10 ppm different from the majority of the space of interest. This is pertinent to magnetic resonance imaging (MRI), and is an inverse problem. Two forward methods of calculating the B field are considered. First, the normal finite element method and secondly, the method of considering the induced polarity in the region of enhanced susceptibility, and calculating the difference field. The accuracies of the methods are explored and the induced polarity method is chosen for the inverse calculation. An iterative technique for inverse calculation is described utilising knowledge of the geometry of the problem, which is available from an MR plot. The numerical work is validated using experimental data from an MR imaging machine