Correction of gradient echo images for first and second order macroscopic signal dephasing using phase derivative mapping

Gradient echo techniques are often hampered by signal dephasing due to macroscopic phase perturbations because of system imperfections (shimming) or object induced perturbations of the magnetic field (hemorrhagic lesions, calcified tissue, air-tissue interfaces). Many techniques have been proposed to reduce the effects of macroscopic phase variations. Among these techniques are tuned pulse sequences, fitting techniques and reconstruction algorithms. These methods, however, suffer from one or more of the following draw-backs: they require longer acquisition times, require additional acquisitions, compensate only locally, can only be applied to multi-gradient echo data or may result in inaccurate results. In this work a generally applicable post-processing technique is presented to evaluate and compensate signal alterations invoked by first and second order macroscopic phase incoherences. In this technique, the derivatives of the signal phase are determined by applying the Fourier derivative theorem on the complex data. As a result, the phase derivatives are obtained without phase unwrapping and without compromising the resolution. The method is validated for single and multi-echo acquisitions by experiments on a co-axial cylinder phantom with known macroscopic field disturbances. The potential of the method is demonstrated on a multi-gradient echo acquisition on the head of a human volunteer. In general a first order correction is shown to be sufficient, however higher order correction is found to be beneficial near sharp transitions of the magnetic field. (C) 2011 Elsevier Inc. All rights reserved.