Generalized reconstruction of phase contrast MRI: Analysis and correction of the effect of gradient field distortions

Abstract

To characterize gradient field nonuniformity and its effect on velocity encoding in phase contrast (PC) MRI, a generalized model that describes this phenomenon and enables the accurate reconstruction of velocities is presented. In addition to considerable geometric distortions, inhomogeneous gradient fields can introduce deviations from the nominal gradient strength and orientation, and therefore spatially-dependent first gradient moments. Resulting errors in the measured phase shifts used for velocity encoding can therefore cause significant deviations in velocity quantification. The true magnitude and direction of the underlying velocities can be recovered from the phase difference images by a generalized PC velocity reconstruction, which requires the acquisition of full three-directional velocity information. The generalized reconstruction of velocities is applied using a matrix formalism that includes relative gradient field deviations derived from a theoretical model of local gradient field nonuniformity. In addition, an approximate solution for the correction of one-directional velocity encoding is given. Phase contrast MRI (PC-MRI) is widely used to assess blood flow and tissue motion. This technique relies on the measurement of changes in the signal phase due to flow or motion in the presence of known linear magnetic gradient fields (1-5).Although it is well known that nonuniformity in magnetic field gradients can cause significant image warping and require correction, little has been reported about the impact of spatial gradient field distortions on velocity encoding.In PC-MRI, these imperfections introduce errors in velocity measurements by affecting the first moments used to encode flow or motion. Any error in strength or direction of the local gradient from its ideal value is directly reflected in the strength or direction in the first-order gradient moments and thus in the velocity encoding. Therefore, gradient field distortions can lead to considerable deviations between the designed encoding and the actual encoding in PC-MRI. The true gradient field demonstrates deviations not only from the nominal gradient strength but also from the intended gradient direction, and thus affects not only the magnitude of encoded velocities but also the velocity encoding direction. In some recent high-performance gradient systems, the coil size was reduced to limit dB/dt and amplifier power. As a result, gradient uniformity has become even more degraded.Currently, based on the deviations of the actual gradient from the desired uniform gradient, the spatial image distortions in magnitude and phase images are retrospectively corrected by image unwarping algorithms, e.g., with algorithms included in the image reconstruction software (7-18). The velocity-encoded information is moved to its correct location, but the error in velocity encoding due to the local field deviation still persists.In this work we demonstrate the effect of imperfect gradient fields on velocities measured with PC-MRI. Observed errors are directly...

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