Ahmad Hussain^{1}, Faisal Najeeb^{1}, Ibtisam Aslam^{1}, Hammad Omer^{1}, and Mujahid Nisar^{1}

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}:

$$ min _{L,S }1/2 ||G.E (L+S) -y||_{2} + λ_{L}||L||_{*} +λ_{s}||S||_{1 }$$

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, λ_{L} and λ_{s} 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:**

**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:**

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.