A Model-based Method for Retrospective Correction of Geometric Distortions in Diffusion-weighted EPI

The self-diffusion tensor may be calculated from several echo-planar image acquisitions preceded by different diffusion gradients. Unfortunately, these diffusion gradients cause geometric distortion that must be corrected before estimation of the tensor. In the present paper we suggest and implement a method for retrospective correction of these distortions firmly based on a physical model for the diffusion-weighted images. This method simultaneously estimates subject movement and distortion parameters by finding the set of parameters that minimizes residual error when fitting data to the diffusion tensor model. We show how this notion can be formalized as a quadratic form thereby facilitating the implementation of a rapid algorithm. In addition, we suggest models for how distortions vary with slice position and gradient direction that allow us to substantially reduce the dimensionality of the parameter space. Our results indicate that we are able to estimate both eddy current-induced distortion and subject movement directly from the data without need of any additional measurements.