Numerical determination of the susceptibility caused geometric distortions in magnetic resonance imaging

The goal of this work is the design of highly accurate surgical navigation methods purely based on magnetic resonance imaging. In this context we numerically examine the geometrical distortions which occur in magnetic resonance imaging. We extend an existing method for computing magnitude and direction of distortions for any internal point. In particular, a multi-grid approach for a fast and efficient calculation of the static magnetic field throughout the imaging volume is presented and compared to the analytical solution for simple geometries. We found that shifts in the range of up to 2.5 mm occur in MRI of femur bones with 1.5 Tesla. Our new method was implemented and has been found capable of accurately correcting for geometrical distortions within reasonable computing times. In particular, we show that the registration accuracy for mutual information (MI) based MR-CT fusion can be much improved. Thus the value of the optimization functional in MI registration for MR-CT substantially increases after our distortion correction.