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Retrospective gradient delay correction in multi-shot multi-echo rosette acquisition
Alexey V. Dimov1, Nanyque A. Boyd2, Keigo Kawaji2,3, and Timothy J. Carroll1

1Radiology, University of Chicago, Chicago, IL, United States, 2Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, United States, 3Medicine, University of Chicago, Chicago, IL, United States

### Synopsis

Rosette k-space sampling is an attractive tool for a variety of applications such QSM, DCE, etc. However, as many non-Cartesian acquisition schemes, rosette is highly susceptible to the system-specific gradient delays. We present a robust technique utilizing intrinsic symmetries of multi-shot rosettes, which allows to reconstruct images with minimal artifacts due to misalignment of the k-space points.

### Target audience

Researchers interested in non-cartesian MRI

### Purpose

The Rosette k-space sampling [1] (Fig. 1) is an attractive approach for a variety of applications such Quantitative Susceptibility Mapping (QSM), Dynamic Contrast Enhanced MRI, as well as any $R_2$ or $R_2^*$ mapping approaches. However, the Rosette sampling is highly susceptible to the system-specific gradient delays, off-resonance, and resultant trajectory errors [2]. While iterative correction approach can be employed with the joint estimation of magnitude, phase, and $R_2^*$, such approaches are potentially time-consuming. In this work, we present a robust technique that utilizes intrinsic rotational symmetries of a multi-shot Rosette pulse sequence design, which can thereby allow reconstruction of images with reduced artifacts caused by the misalignment of the sampled points along the measured trajectory.

### Methods

The proposed method utilizes intrinsic symmetries in multi-shot multi-echo rosette with even number of acquired arms. In particular, for any $i<N/2$, arms $i$ and $i+N/2$ are traversing the center of the k-space in the opposite directions and in tangential manner (Fig 2). Under ideal conditions, values measured along the rosette spokes belonging to these arms should be aligned in the k-space center. If, however, imperfect gradient timing is present, spokes’ phase and magnitude profiles will differ by a noticeable shift $\delta$ (Fig 3). This shift can be estimated through a cross-correlation of analysis of the tangential spokes and eliminated prior gridding.The algorithm of the proposed correction method can be summarized as follows:

1. Split $N$ arms into $N/2$ arm pairs
2. For each resulting pair of spokes $\{S_1, S_2\}$, calculate correlation $c = FT\{|S_1|\}\cdot FT\{|\tilde{S_2}|\}^*$. Here "~" denotes inversion ("flip") of the spoke points, and $FT\{\}$ is Fourier transform.
3. Estimate slope $\alpha$ in the phase of $c$
4. Shift each of the spokes by $\frac{L\alpha}{4\pi}$

Experimental validation

2D multi-shot rosette sequence was implemented on a 3T MR platform (Philips Achieva). A phantom dataset was acquired using a 64-arm rosette sequence (FOV = 22 cm, Slice thickness = 5 mm, # Slices = 1, TR = 24-30 ms, TE = 0.8-1.2ms, 24 echoes). No parallel imaging was used. A volunteer data was additionally acquired using similar scan parameters.The gridding reconstruction, implemented offline using MATLAB (The Mathworks, Natick, MA) with CUDA-PTX graphical processing unit acceleration (NVIDIA, Santa Clara, CA) of the original data and data corrected using the proposed technique was performed. Image magnitude, phase, and presence of off-resonance artifacts was examined using region-of-interest analysis.

### Results

Figure 4shows the images reconstructed by both methods from the phantom data, and results of field inhomogeneity estimation based on 20 consecutive rosette echoes. The proposed correlation-based method successfully eliminated artificial intensity modulation present in the magnitude, as well as fringe lines in the phase of the gridded images. Phase of individual echo images demonstrates linear behavior which allows for estimation of a high-quality field map. Processed volunteer data demonstrates similar level of quality in resulting images.Inspection of the post-correction k-space (Fig 5) showed accurate alignment of the k-space profiles of different rosette arms.

### Discussion and conclusions

We demonstrate the feasibility of a simple algorithm for retrospective correction of system-dependent gradient delays that does not require additional data acquisition. The proposed method demonstrated reliable performance and allowed artifact-free reconstruction of multiple consecutive multi-shot rosette echoes, making rosette applicable for fast mapping of the inhomogeneity field. The method can be easily generalized to the cases of rosettes with odd number of arms, as well as other self-intersecting trajectories (e.g., radial), and EPI.

### Acknowledgements

No acknowledgement found.

### References

1. Noll DC, et.al., Magn Reson Med. 1998 May;39(5):709-16
2. Peters DC, et al., Magn Reson Med. 2003 Jul;50(1):1-6.

### Figures

Figure 1. Structure of a multi-echo multi-arm rosette

Figure 2. Rosette trajectory in k-space. Note the tangential passing of two rosette arms at each crossing of the k-space origin.

Figure 3. (a) Crossing of the k-space center by a set of rosette spokes’ pairs; (b) Magnitude and (c) phase profiles of the spokes. Note the shift δ in the data prior the correction.

Figure 4. Comparison of results of processing of the original and corrected phantom data, and results of reconstruction from the corrected volunteer data.

Figure 5. Magnitude and phase profiles of the spokes after correction. Notice that the shift due to gradient delays was successfully eliminated.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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