Spiral k-space trajectories have been investigated by many researchers as a more efficient alternative to widely-used rectilinear (Cartesian) trajectories, offering advantages in terms of acquisition speed, reduced sensitivity to motion and shorter minimum echo times [1]. Nonetheless, despite many research studies demonstrating promising results, spiral trajectories have yet to become available among the standard techniques offered on commercial MR scanners. In this regard, a practical limitation is that, compared to Cartesian trajectories, the quality of imaging results for spiral trajectories is much more dependent on gradient-system fidelity. This limitation has often been addressed by measuring the actual (vs. theoretical) k-space trajectory of a specific implementation (i.e., selected orientation, FOV, etc.) for use in image reconstruction; however, this approach is impractical for widespread application of spiral imaging. Tan and Meyer [2] proposed a method of characterizing scanner performance for spiral trajectories, which can be used to perform a model-based correction at image reconstruction, applicable to freely chosen imaging parameters. The purpose of this work was to apply this characterization method to a variety of scanner models to assess, across scanners, the consistency of characterization parameters and the ability of the method to yield high-quality spiral images on the different scanners.The scanner characterization procedure was based on 15 image datasets (5 from each of the primary axes) acquired from a spherical phantom using a prototype pulse sequence (total acquisition time < 8 min). These were processed with a MATLAB script to yield, in addition to measured k-space trajectories, gradient delays and eddy-current terms for each axis that can be incorporated into reconstruction for trajectory correction [2]. This procedure was applied to 11 scanners, including 1.5T scanners (MAGNETOM Dot Avanto, Siemens Healthcare; MAGNETOM Aera, Siemens Healthcare) and 3T scanners (MAGNETOM Skyra, Siemens Healthcare; MAGNETOM Prisma, Siemens Healthcare), and 2 software levels. To assess the degree to which image quality was improved by incorporating model-based trajectory correction into the reconstruction, the root mean squared error (RMSE) was calculated for images reconstructed based on measured k-space trajectories (gold standard) compared to those reconstructed using theoretical trajectories corrected for nominal isotropic gradient delays, for anisotropic gradient delays from system characterization, and for anisotropic gradient delays plus eddy-current terms from system characterization.

Across all scanners, the variation (standard deviation) of the gradient delays along the three physical axes ranged from 0.3 to 0.9 ms. Some of this variation would be expected to arise from the different models of gradient systems among scanners. For example, considering only seven 3T scanners, the variation of gradient delays was smaller, ranging from 0.1 to 0.4 ms. The eddy-current terms were relatively small among all scanners (reflecting that the baseline eddy-current compensation performed well for the spiral waveforms), although there were systematic differences among scanner models. Considering again the seven 3T scanners, the maximum coefficient of variance for eddy-current terms was less than 10% and the mean was 7%. Comparing model-based reconstruction to reconstruction using measured trajectories, anisotropic gradient delays alone provided an average reduction of 3.4% in RMSE relative to nominal isotropic delays, and anisotropic gradient delays plus eddy current terms provided an average reduction of 37.3% in RMSE. Thus, the gradient delays on these systems were relatively isotropic.

Visually, it was difficult to discern differences between spiral images reconstructed using measured trajectories and those reconstructed using model-based parameters including gradient delays and eddy-current terms for each axis. Representative images are shown comparing transverse (Fig. 1), coronal (Fig. 2) and sagittal (Fig. 3) images from measured trajectories to the corresponding images from model-based trajectory correction. The difference images illustrate the small remaining error between the two image sets. The eddy-current terms corrected image scaling errors resulting from variations in the magnitude of the gradient transfer function as a function of gradient temporal frequency [3]. Spiral abdominal images of a volunteer are shown in Fig. 4.

Characterization of gradient-system performance on 11 MR scanners yielded only minor variation in parameter values among scanners, and in all cases model-based correction of spiral trajectories yielded very similar image results to reconstruction based on measured trajectories. The calibration results for a particular scanner were stable over time, and the calibration results were similar for this group of scanners. These results suggest that model-based reconstruction may represent a viable approach for obtaining high-quality spiral images without the need for characterization of specific spiral-trajectory implementations. Nonetheless, future work is needed to verify the approach on additional MR scanners, and for a wide variety of spiral-trajectory implementations (orientation, FOV, spatial resolution, number of interleaves, etc.).