Characterizing and correcting gradient errors in non-cartesian imaging: Are gradient errors linear time-invariant (LTI)?

Non-Cartesian and rapid imaging sequences are more sensitive to scanner imperfections such as gradient delays and eddy currents. These imperfections vary between scanners and over time and can be a significant impediment to successful implementation and eventual adoption of non-Cartesian techniques by scanner manufacturers. Differences between the k-space trajectory desired and the trajectory actually acquired lead to misregistration and reduction in image quality. While early calibration methods required considerable scan time, more recent methods can work more quickly by making certain approximations. We examine a rapid gradient calibration procedure applied to multiecho three-dimensional projection reconstruction (3DPR) acquisitions in which the calibration runs as part of every scan. After measuring the trajectories traversed for excitations on each of the orthogonal gradient axes, trajectories for the oblique projections actually acquired during the scan are synthesized as linear combinations of these measurements. The ability to do rapid calibration depends on the assumption that gradient errors are linear and time-invariant (LTI). This work examines the validity of these assumptions and shows that the assumption of linearity is reasonable, but that gradient errors can vary over short time periods (due to changes in gradient coil temperature) and thus it is important to use calibration data matched to the scan data.