Mapping gradient nonlinearity and miscalibration using diffusion-weighted MR images of a uniform isotropic phantom

Abstract

Purpose: To use diffusion measurements to map the spatial dependence of the magnetic field produced by the gradient coils of an MRI scanner with sufficient accuracy to correct errors in quantitative diffusion MRI (DMRI) caused by gradient nonlinearity and gradient amplifier miscalibration. Theory and Methods: The field produced by the gradient coils is expanded in regular solid harmonics. The expansion coefficients are found by fitting a model to a minimum set of diffusion-weighted images of an isotropic diffusion phantom. The accuracy of the resulting gradient coil field maps is evaluated by using them to compute corrected b-matrices that are then used to process a multi-shell diffusion tensor imaging (DTI) dataset with 32 diffusion directions per shell. Results: The method substantially reduces both the spatial inhomogeneity of the computed mean diffusivities (MD) and the computed values of the fractional anisotropy (FA), as well as virtually eliminating any artifactual directional bias in the tensor field secondary to gradient nonlinearity. When a small scaling miscalibration was purposely introduced in the x, y, and z, the method accurately detected the amount of miscalibration on each gradient axis. Conclusion: The method presented detects and corrects the effects of gradient nonlinearity and gradient gain miscalibration using a simple isotropic diffusion phantom. The correction would improve the accuracy of DMRI measurements in the brain and other organs for both DTI and higher order diffusion analysis. In particular, it would allow calibration of MRI systems, improving data harmony in multicenter studies.