Low rank and sparsity on MR-based PET motion correction using simultaneous PET/MRI: a patient study
Yixin Ma1, Yoann Petibon2, Joyita Dutta2, Xucheng Zhu3, Rong Guo1, Georges El Fakhri2, Kui Ying1, and Jinsong Ouyang2

1Key laboratory of Particle and Radiation Imaging, Ministry of Education, Tsinghua University, Beijing, China, People's Republic of, 2Center for Advanced Medical Imaging Sciences, Division of Nuclear Medicine and Molecular Imaging, Department of Imaging, Massachusetts General Hospital, Boston, MA, United States, 3UCSF/UC Berkeley Bioengineering Graduate Group, University of California Berkeley, Berkeley, CA, United States

### Synopsis

In this work, we exploited the low-rank and sparse properties of dynamic MRI data to accelerate the MR acquisition and assessed its impact on MR-based PET respiratory motion using a PET/MR oncologic patient study. PET/MR motion correction workflow was accomplished, and good performance of partially sampled MR based motion correction attests the possibility of faster PET/MR data acquisition and better lesion estimation.

### PURPOSE

Respiratory motion is a major source of image quality degradation in whole-body PET imaging. MR-based PET motion correction using simultaneous PET/MR offers a solution to this problem.1 However, one major hurdle for the adoption of this motion correction approach is the long time needed for the acquisition of fully sampled MR data in all motion phases. In this work, we exploited the low-rank and sparse properties of dynamic MRI data to accelerate the MR acquisition and assessed its impact on MR-based PET respiratory motion correction using a PET/MR oncologic patient study.

### MATERIALS AND METHODS

Fig. 1 shows the flow chart of simultaneous PET/MR data acquisition and motion correction approach.

A. PET/MR data acquisition and binning: A patient with known thoracic lesions was injected with 12.5mCi of FDG and scanned on a whole-body simultaneous PET-MR scanner (Siemens Biography mMR). First, a 4-tissue class PET attenuation map was acquired during a breath-hold using a Dixon sequence. List-mode PET acquisition started simultaneously with attenuation map acquisition. To track respiratory motion, the Golden-angle RAdial Navigated Gradient Echo (GRANGE) MR sequence was used with the following acquisition parameters: Flip Angle=30°, TR=3.3ms/slice, bandwidth=1kHZ/pixel, 24 coronal slices, slice thickness= 8mm, 4000 radial lines per slice, 256 samples per radial line. The simultaneously acquired MR k-space and PET list-mode data were then binned into 10 gates, which contain same number of PET events, using the histogram-guided, diaphragm amplitude measured by the navigator.2

B. MR reconstruction and motion fields estimation: A low-rank and sparse matrix decomposition algorithm,3 which decomposes image matrix by enforcing low-rank in the background matrix $L$ as well as sparsity in the innovation components $S$, was used to reconstruct respiratory-gated partially sampled MR k-space data with acceleration factor (AF) = 2, 4. The same algorithm was also applied to the fully sampled k-space data (i.e., AF=1). The following cost function was minimized: $$min\frac{1}{2}{\parallel E(L+S)-d \parallel}^2_2+\lambda_L\parallel L\parallel_*+\lambda_S\parallel TS\parallel_1$$Where $E$ is the non-uniform fast Fourier transform (NUFFT, J.A. Fessler, 2009) operation for the radial trajectories, $T$ is total variance operation, $\lambda_L$ =0.01, $\lambda_S$ = 0.005 maximum of image. Optimal reconstruction parameters were determined empirically to ensure that the reconstructed images did not exhibit streaking artifacts and that the motion between respiratory phases was well preserved. To estimate respiratory motion fields, non-rigid B-spline registration (Chun S Y, 2009) with enforcement of the invertibility of the estimated transformation was applied to the reconstructed MR images to obtain motion fields.

C. PET reconstruction and attenuation map correction: The resulting motion fields were incorporated into the system matrix $P_t$ of a modified OSEM PET reconstruction algorithm such that, $P_t=NA_tGM_t$, where $M_t$ is MR based deformation operator (respiratory motion fields), $G$ is the forward-projection operator, $A_t$ includes attenuation effect, where motion-dependent attenuation map are generated by warping the reference attenuation map in all respiratory phases using the respiratory motion fields, and $N$ contains detector normalization factors.4 PET image reconstruction was performed without motion correction and with motion correction using the motion fields calculated at various AFs.

### RESULTS

Fig. 2(a) shows the reconstructed end-inspiration and end-expiration MR coronal slices at different acceleration factors (1, 2 and 4). Line profiles drawn along the head-feet direction in the reconstructed, MR end-inspiration and end-expiration images are shown in Fig. 2(b) and (c) respectively. As can be seen, low-rank and sparse matrix decomposition using under-sampling of the k-space data yields comparable MR image quality to fully sampled data. In addition, the motion fields between gates were well preserved. Fig. 3 shows motion corrected PET images reconstructed with motion fields obtained from various acceleration factors. Line profiles shown in Fig. 3(e) indicate that at AF=1 motion correction yields 29.7% increase in tumor peak intensity as compared to the motion uncorrected PET image. Tumor volume, which was computed with a threshold of 50% of its peak intensity, is reduced by 29.4%, 32.5%, 28.5% using AF=1,2 and 4, respectively, as compared to no motion correction.

### DISCUSSION

We used low-rank and sparse matrix decomposition to accelerate the MR acquisition for MR-based PET motion correction. We applied our approach to a patient PET-MR study and showed that an acceleration factor of 4 can be achieved without compromising the performance of MR-based PET motion correction.

### Acknowledgements

The authors would like to thank Massachusetts General Hospital for PET/MR data acquisition in patient study. We would also like to thank Dr. Ricardo Otazo (CAI2R, New York University) for L+S reconstruction code and Dr. J.A.Fessler for NUFFT code.

### References

1. Judenhofer M S, Wehrl H F, Newport D F, et al. Simultaneous PET-MRI: a new approach for functional and morphological imaging[J]. Nature medicine, 2008, 14(4): 459-465.

2. Dutta J, Huang C, Li Q, et al. Pulmonary imaging using respiratory motion compensated simultaneous PET/MR[J]. Medical physics, 2015, 42(7): 4227-4240.

3. Otazo R, Candès E, Sodickson D K. Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components[J]. Magnetic Resonance in Medicine, 2015, 73(3): 1125-1136.

4. Petibon Y, Huang C, Ouyang J, et al. Relative role of motion and PSF compensation in whole-body oncologic PET-MR imaging[J]. Medical physics, 2014, 41(4): 042503.

### Figures

Fig. 1 Work flow of MR based PET motion correction using simultaneous PET/MR

Fig. 2 L+S reconstructed coronal MR images at different acceleration factors (AF=1,2 and 4) for end inspiration (left) and end expiration (right) phases and line profiles taken in the (b) end-inspiration and (c) end-expiration images.

Fig. 3 PET coronal slices reconstructed using (a) no motion correction (No MC) and motion correction (MC) using (b) fully-sampled (c) 2-fold and (d) 4-fold acceleration, with zoomed-in FOV. (e) Line profiles taken across the lesion for No MC, MC AF=1, AF=2 and AF=4.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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