Geometrical image transformation to compensate for MRI distortions

This paper reports that magnetic resonance imaging (MRI), begin one of the most promising neuro-imaging modalities in medical diagnosis, suffers from spatial inaccuracy when it comes to high precision processes such as neuro-stereotactic surgery. Spatial distortions of several millimeters are possible. The distortion originates from the fact that highly controllable magnetic fields are used to encode the positions of the spins. When the fields are perturbed by unknown interferences such as the para- and/or dia-magnetism of the patient or inhomogeneity in the main field, the spatial encoding becomes inaccurate. However, the distortions are not without helpful characteristics. For instance, using a SE pulse sequence, one may observe that the distortion vectors are collinear, they are along an axis which is determined by the gradients, and the integral of image intensity between homologous coaxial points is unaffected by the inhomogeneity. With such an observation, we propose a method that uses a pair of images from the same object that are acquired using a set of gradients having a prescribed relationship. While these two images are both distorted, a set of independent, first order, ordinary differential equations have been derived to relate the two images