A Perturbation Method for $\hbox{$\mathrm{B}_0$}$ Field Calculations of Non-Conductive Objects

FMRIB Technical Report TR04MJ1
(A related paper is published in Magnetic Resonance in Medicine)

Mark Jenkinson, James Wilson and Peter Jezzard

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK

Abstract:

Inhomogeneous $\mathrm{B}_0$ fields produce artifacts in MR images including signal dropout and spatial distortion. We present a perturbative method for calculating the $\mathrm{B}_0$ field to first order (error is second order). The perturbation parameter is the susceptibility difference between brain tissue and air: around 10 ppm. This method is advantageous as it is sufficiently accurate for most purposes, can be implemented as a simple convolution with a volumetric matter model, and is linear. Furthermore, the method is simple to use and can quickly calculate the field for any orientation of an object using a set of precalculated basis images.