Purpose

The 3D stack-of-stars trajectory acquisition is widely used in liver and abdominal imaging applications because of its relative insensitivity to object motion compared with Cartesian trajectory, as well as its higher acquisition efficiency compared to 3D radial trajectory. However, one drawback compared to a Cartesian acquisition is its sensitivity gradient delays. Due to this problem, the acquired k-space data might not perfectly match the designed trajectory. As self-gated motion signals are derived from the central k-space data, it would be vulnerable to the induced k-space misalignment. More importantly, gradient delays affect not only the image quality but also the accuracy of motion state estimation. Several approaches for correcting the gradient delay have been proposed in the past. One method is to measure the exact k-space location by using pre-scan or extra hardware^1,2. Research⁵ shows that gradient delay might vary over time, some pre-calibration method might not estimate the correct delay. Another way is to calculate the delay by using acquired data^3,4,9 without extra calibration. Block’s work⁴, used the spokes acquired at opposing orientations to estimate the gradient delay for x and y direction, then estimated delay for different direction spokes based on these two estimations. In this work, based on similar idea from Block’s work, we extended it to 3D trajectory. In addition, we estimated gradients delays for each acquisition direction instead of linear combining x and y delay components.

Methods

We assume that the gradient delay-induced k-space misalignment in the opposing orientation acquisitions were the same or similar. The correction process work flow is shown in Figure 1. Firstly, opposing orientation acquisition spokes are paired and transformed in projection domain through a Fourier transform. Then, phase differences between paired spokes are calculated and transformed back to k-space. The shift of peak from the center is the compensated phase for the paired acquisition spokes. To reduce the noise effect and error measurement, low pass filter is applied after the correction shift. An adult volunteer was scanned under IRB approval using a 3D T1-FFE sequence with a free-breathing acquisition (TR/TE 4.35 ms 1.20ms, voxel resolution 1 x 1 x 1.5mm, FOV 40 x 40 x 12.5cm). The sequence was implemented on a 3T MR system (Philips Healthcare) equipped with a 16-channel torso coil. Data processing and reconstruction steps are shown in Figure 2. Firstly, the proposed delay correction process was applied to the raw data. Then, central k-space data were selected to calculate the self-gated motion signal. After that, FLICM (fuzzy local information C-Means)⁷ segmentation method is used to extract the motion state curve and data are evenly binned to 4 motion states based on the curve position. Finally, motion resolved images are reconstructed by using iterative reconstruction with a total variation constraint along motion states, similar to XD-GRASP framework⁶ via BART (Berkeley Advanced Reconstruction Toolbox)⁸.

Results

Figure 3 shows the self-gated signals calculated from the raw data before and after correcting the central k-space data for gradient delay. The proposed method removes most of the intensity inhomogeneity in the self-gated signals caused by gradient delay. Then the respiration motion can be easily delineated with the proposed segmentation method with any intensity inhomogeneity correction. Figure 4 shows the motion binning signals calculated from the segmentation results based on both corrected and uncorrected data. The arrows point to errors in the binning signal due to the uncorrected gradient delay that cause a mismatch between the data and its motion state. After the gradient delay correction, the binning is largely improved. Figure 5 shows the reconstruction results with and without gradient delay correction. The proposed method improves the sharpness of the liver and some vessels inside liver because the binning process groups the motion corrupted data in the correct motion state. In addition, most of the intensity inhomogeneity and streaking artifacts caused by gradient delay are removed after the correction.

Conclusion and Discussion

In this work, we proposed a workflow to improve motion correction by correcting the gradient delay induced k-space misalignment. From the result, we found that proposed method improved both self-gated motion estimation and the overall reconstruction image quality. This workflow could also be extended to other applications using the 3D stack-of-star and conventional 2D radial trajectory.

Acknowledgements

Authors would like to thank Wenwen Jiang, Jonathan Tamir, and Peng Cao for their comments and suggestions.

References

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