### Synopsis

Respiratory motion during MRI scan causes inconsistencies in the acquired k-space data providing strong blurring artifacts in the reconstructed images. In this work, a new method ( respiratory motion corrected GROG followed by L+S reconstruction for free breathing Golden-Angle Radial DCE-MRI) is presented.The proposed method is tested on 3-T free-breathing Golden angle radial DCE liver MRI data. The proposed method is compared with the conventional L+S reconstruction model. The proposed method provides 90% improvement in Artefact Power and 42% in RMSE as compared to conventional L+S reconstruction at acceleration factor 8.

### Introduction:

In free breathing dynamic MRI,k-space data is acquired in different respiratory positions, which results in strong blurring artefacts in the reconstructed images 1.Simplest approach to avoid respiratory motion is: (i) breath-hold data acquisition (ii)use of navigator signals that increases the patient discomfort and prolongs scan time 2,3. Low-Rank plus Sparse (L+S) reconstruction with effective separation of the background and dynamic components proposed by Otazo et.al. to reconstruct the unalised dynamic MR images 4.The L+S technique combines the idea of parallel MRI(pMRI),Compressed sensing(CS) and Principal Component Analysis(PCA) to reconstruct under-sampled MR images. L+S reconstruction is mathematically formulated as 4:

$$min L,S 1/2 ||G.E (L+S) -y||2 + λL||L||*s||S||1$$

where y is the under-sampled k-space data acquired from the MRI scanner, T is the temporal Total-Variation operator, E is the multi coil Encoding operator, λL and λs are the regularization parameters.G represents the gridding operation which converts non-Cartesian data onto Cartesian grid. Conventional L+S uses Fessler gridding to convert the radial data to a Cartesian grid 5.

In the proposed method, Golden-angle radial liver perfusion data is first sorted into time frames. Motion signal is extracted by using self-navigator properties of this Golden angle radial data 6. This data is gridded onto a Cartesian grid using SC GROG gridding 7,8.The resulting gridded data contains incoherent artifacts that are removed using L+S reconstruction.

### Methods:

This work proposes a respiratory motion corrected GROG based L+S reconstruction with effective separation of the background and dynamic components for free breathing Golden-Angle Radial DCE-MRI data. In the proposed method, initially a motion signal is directly extracted from the center of the Golden angle radial k-space data 6. Golden-angle radial data is first sorted into time frames and binned into multiple motion states. The self-calibrated GROG (SC-GROG) gridding is applied to map the motion compensated Golden angle radial data on a Cartesian grid 9. Finally, L+S reconstruction is applied on the motion corrected GROG gridded data to get the final solution image.Figure 1 shows a flow chart of the proposed method.

### Results and Discussions:

The proposed method is tested on free-breathing Golden angle radial DCE data acquired with 3-T Siemens scanner at New York University 2.The data acquisition parameters are: 512 readouts, 1144 radial spokes and 12 receiver coils. In order to generate a dynamic series, 96 adjacent spokes are grouped into one time point, these frames are further divided into 4 respiratory states. This data is gridded onto a Cartesian grid by using SC-GROG, corresponding Cartesian data size is : .The Nyquist sampling rate for this case is 512×π/2 =800,corresponding simulated Acceleration factor (AF) is 8.3 2. Figure 2 shows the reconstruction results. Left, middle and right hepatic veins are not clearly visible in the conventional L+S reconstruction (Figure 2a), while they can be clearly seen in the reconstruction results of the proposed method(Figure 2b).

AP and RMSE values of the reconstructed images for both the standard L+S and proposed methods are given in Table 1. The results show that the proposed method by incorporating motion correction frame work in L+S reconstruction outperforms conventional L+S method. For example there is 90% improvement in AP and 42% improvement in RMSE in the reconstruction results of the proposed method for Golden angle radial data at AF=8.

### Conclusion:

In this work a respiratory motion corrected GROG based L+S reconstruction model with effective separation of Land S components for free breathing Golden-Angle Radial DCE-MRI data is proposed. The results show good quality reconstructed images with motion correction as compared to the conventional L+S approach.

### Acknowledgements

No acknowledgement found.

### References

1. Usman M, Atkinson D, Odille F, et al. Motion corrected compressed sensing for free-breathing dynamic cardiac MRI. Magn Reson Med. 2013;70(2):504-516.

2. Feng L, Grimm R, Block KT, et al. Golden-angle radial sparse parallel MRI: Combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI. Magn Reson Med. 2014;72(3):707-717. doi:10.1002/mrm.24980.

3. Feng L, Axel L, Chandarana H, Block KT, Sodickson DK, Otazo R. XD-GRASP: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing. Magn Reson Med. 2016;75(2):775-788. doi:10.1002/mrm.25665.

4. Otazo R, Candès E, Sodickson DK. Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components. Magn Reson Med. 2015;73(3):1125-1136.

5. Fessler JA. On NUFFT-based gridding for non-Cartesian MRI. J Magn Reson. 2007;188(2):191-195.

6. Feng L, Huang C, Shanbhogue K, Sodickson DK, Chandarana H, Otazo R. RACER-GRASP: Respiratory-weighted, aortic contrast enhancement-guided and coil-unstreaking golden-angle radial sparse MRI. Magn Reson Med. 2018;80(1):77-89.

7. Aslam I, Najeeb F, Omer H. Accelerating MRI Using GROG Gridding Followed by ESPIRiT for Non-Cartesian Trajectories. Appl Magn Reson. September 2017:1-18.

8. Seiberlich N, Breuer FA, Blaimer M, Barkauskas K, Jakob PM, Griswold MA. Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG). Magn Reson Med. 2007;58(6):1257-1265.

9. Wright KL, Hamilton JI, Griswold MA, Gulani V, Seiberlich N. Non-Cartesian parallel imaging reconstruction. J Magn Reson Imaging. 2014;40(5):1022-1040.

### Figures

Figure 1. Flow graph of Respiratory Motion Corrected GROG based L+S reconstruction for free breathing Golden-angle radial MRI (Proposed Method).

Figure 2. Reconstruction results (a) Conventional L+S reconstruction (b) The proposed method. The left, middle and right hepatic veins (shown by indicating arrows) are not clearly visible in (a) while they can be clearly seen in (b).

Table 1. Reconstruction results of the proposed method and conventional L+S reconstruction in terms of AP and RMSE for 3-T Golden angle radial data at AF=8.

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