### 4539

Accelerated T2 mapping based on Bloch signal-model with fixed rank and sparsity constraints
Daniel Grzeda1, Meirav Galun2, Noam Omer1, Tamar Blumenfeld-Katzir1, Dvir Radunsky1, Ricardo Otazo3, and Noam Ben-Eliezer1,4,5

1Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel, 2Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, 3Departments of Medical Physics and Radiology, Memorial Sloan Kettering Cancer Center, New York, NY, United States, 4Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel, 5Center for Advanced Imaging Innovation and Research (CAI2R), New-York University Langone Medical Center, New York, NY, United States

### Synopsis

Quantification of T2 values is valuable for a wide range of research applications and clinical pathologies. Multi-echo spin echo (MESE) protocols offer significantly shorter scan-times, at the cost of strong contamination from stimulated and indirect echoes. The echo-modulation-curve (EMC) algorithm, can efficiently overcome these limitations to produce accurate T2 values. In this work we propose a new reconstruction algorithm based on Sparsity and Fixed Rank constraints, denoted as SPARK. We compare our method against GRAPPA and show its superiority in the quantitative evaluation of T2 values from highly undersampled data.

### Introduction

Quantification of T2 values is valuable for a wide range of research applications and clinical pathologies1–3. The use of single spin-echo (SSE) protocol is unpractical due to its extensive scan time. Multi-echo spin echo (MESE) protocols offer significantly shorter scan-times and lower diffusion effects, at the cost of strong contamination from stimulated and indirect echoes4. The echo-modulation-curve (EMC) algorithm, can efficiently overcome these limitations to produce accurate T2 values, which are moreover reproducible across scanners and scan settings5.

Further acceleration of quantitative mapping can be achieved by undersampling the spatial or temporal domains, requiring designated reconstruction algorithms, and involving prior information on the signal model6–8.

Low-rank plus Sparse (L+S) signal-decomposition was recently introduced as a powerful tool for reconstructing undersampled dynamic MR images and has been demonstrated to enhance standard compressed sensing6. It was shown that enforcing a fixed rank constraint along with sparsity constraints may outperform L+S, fixed rank only, or sparse only methods8.

In this work, the EMC model provides us the signal’s rank, which is necessary to perform an iterative reconstruction of highly undersampled MESE data using sparse and fixed low-rank constraints to achieve highly accelerated mapping of quantitative T2 values. We denote the suggested approach as SPARK (SPArsity and fixed RanK).

### Methods

MRI scans: Two datasets were scanned using a standard MESE sequence with fully sampled k-space. Brain imaging was done using a 16-channel receiver coil and calf scans were obtained using a flexible 4-channel receiver coil and 4 additional coils embedded in the scanner bed. Scan parameters for both datasets were: NEchoes=30; TE/TR=10/3000 ms, slice thickness=3 mm; in-plane resolution=1.1x1.1 mm2 (brain), and 1.3x1.3 mm2 (calf). Only the first 20 echoes contained significant information and used during reconstruction.
Postprocessing: Images were reconstructed from retrospectively under sampled k-spaces using our proposed method and standard GRAPPA. Reconstruction was performed by solving the following optimization problem: $[L,S]=argmin_{L\in C, S}\frac{1}{2}||d-E(L+S) ||^2_2 + \lambda||S||_1$, where E is the acquisition operator, d is the under-sampled k-t data and is the set of matrices of fixed rank r5. The Identity transform was used to enforce sparsity in the image domain of S. Fixed rank value was estimated from the simulated EMC data prior to reconstruction, and variable density schemes were used following the Compressed Sensing (CS) framework3,4,6.
Following the iterative reconstruction, T2 maps were generated on a pixel-by-pixel basis using the EMC algorithm.
Analysis: Mean ± standard deviation of T2 values were calculated for regions of interest within each anatomy, and relative errors were calculated with respect to the fully sampled results.

### Results

T2 values in the brain were estimated for acceleration factors 2...5 in the putamen, head of caudate nucleus, thalamus and white matter fascicles, with reference T2 values (mean ± SD) of 62.48±2.7, 66.5±3.0, 66.17±3.4 and 56.28±2.0 ms, respectively. The SD of SPARK’s evaluated T2 values are similar to those of the fully sampled data (3.4, 2.4, 3.3 and 2.1% at acceleration x5), ensuring high precision at all acceleration factors and outperforming the conventional acceleration method, GRAPPA, whose precision decreases from acceleration factor 3 and above, and is an order of magnitude larger at factor x5 (24.4, 23.4, 23.8 and 17.8% at acceleration x5). Mean relative errors at acceleration factor x5 at the mentioned regions in the brain GRAPPA and SPARK reconstruction are 32.1, 28.7, 26.4, 25.3% and 3.9, 3.4, 4.3, 3.1%, respectively.

T2 values in the calf were estimated for the same acceleration factors in the tibialis anterior, gastrocnemius, soleus, peronari longus and flexor longus muscles, with reference T2 values (mean ± SD) of 30.6±2.9, 32.6±7.9, 35.0±6.3, 41.6±6.6 and 32.3±3.3 ms, respectively. The mean relative errors at acceleration factor x5 at the mentioned regions in the calf muscle of GRAPPA and SPARK are 18.4, 62.8, 50.6, 39.5, 49.1% and 3.0, 3.8, 5.3, 3.1, 4.4%, respectively.

### Discussion

Our results demonstrate that the combination of EMC and SPARK reconstruction achieves high accuracy and precision in T2 quantification across different anatomies and for a range of acceleration factors. The SPARK algorithm’s performance on undersampled data is in good agreement with the standard reconstruction from fully sampled data, provided we perform tuning of the following parameters: λ for sparsity, c for singular value thresholding and r for rank truncation. We have found that accurate results can be achieved for fixed ranks of 5-10, hence being less sensitive to the exact rank of the data. Future work on SPARK aims to improve its robustness to the selection of tuning parameters.

### Acknowledgements

ISF 2009/17; NIH NIBIB Biomedical Technology Resource Center (P41EB017183)

### References

1. Eitel I, Friedrich MG. T2-weighted cardiovascular magnetic resonance in acute cardiac disease. J Cardiovasc Magn Reson. 2011;13(1):13. doi:10.1186/1532-429X-13-13

2. Lund H, Jønsson A, Andresen J, Rostrup E, Paulson OB, Sørensen PS. Cognitive deficits in multiple sclerosis: correlations with T2 changes in normal appearing brain tissue. Acta Neurol Scand. 2012;125(5):338-344. doi:10.1111/j.1600-0404.2011.01574.x

3. Siemonsen S, Mouridsen K, Holst B, et al. Quantitative T2 Values Predict Time From Symptom Onset in Acute Stroke Patients. Stroke. 2009;40(5):1612-1616. doi:10.1161/STROKEAHA.108.542548

4. Noam B-E, K. SD, Tobias BK. Rapid and accurate T2 mapping from multi–spin‐echo data using Bloch-simulation-based reconstruction. Magn Reson Med. 73(2):809-817. doi:10.1002/mrm.25156

5. Shepherd TM, Kirov II, Charlson E, et al. New rapid, accurate T2 quantification detects pathology in normal-appearing brain regions of relapsing-remitting MS patients. NeuroImage Clin. 2017;14:363-370. doi:10.1016/J.NICL.2017.01.029

6. 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. 2014;73(3):1125-1136. doi:10.1002/mrm.25240

7. Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58(6):1182-1195.

8. Lior W, L. MK, C. EY, Mark C. PEAR: PEriodic And fixed Rank separation for fast fMRI. Med Phys. 44(12):6166-6182. doi:10.1002/mp.12599

9. Tsai CM, Nishimura DG. Reduced aliasing artifacts using variable-density k-space sampling trajectories. Magn Reson Med. 2000;43(3):452-458.

### Figures

Figure 1: Comparison of brain T2 maps at x5 acceleration. (a) Reference fully sampled map. (b) GRAPPA reconstruction. (c) SPARK reconstruction, c = 0.7, lambda S = 10-1.5, r = 15. (d) Scanned anatomy with segmented regions: R1- putamen, R2- head of caudate nucleus, R3- thalamus, R4- white matter fascicles.

Figure 2: Comparison of calf T2 maps at x4 acceleration. (a) Reference fully sampled map. (b) GRAPPA reconstruction. (c) SPARK reconstruction, c = 0.7, lambda S = 0.01, r = 7. (d) Scanned anatomy with segmented regions: R1- Tibialis Anterior, R2- Gastrocnemius, R3- Soleus, R4- Peronari Longus, R5- Flexor Longus.

Figure 3: Relative error per acceleration factor in the brain. (a) SPARK’s Mean Rel. Err. varies from 2.6-4.8%, while GRAPPA varies from 1.9-18.9%. (b) SPARK’s Rel. Err. SD varies from 3.56-15.1%, while GRAPPA varies from 3.9-25.1%.

Figure 4: Relative error per acceleration factor in the calf. (a) SPARK’s Mean Rel. Err. varies from 3.9-6.6%, while GRAPPA varies from 5.3-38.6%. (b) SPARK’s Rel. Err. SD varies from 11.3-19.8%, while GRAPPA varies from 23.1-65.5%.

Figure 5: Mean T2 values at manually segmented regions. (a) White Matter Fascicles, (b) Thalamus, (c) Tibialis Anterior Muscle, (d) Gastrocnemius Muscle. T2 values in SPARK reconstruction are consistently more accurate than GRAPPA reconstruction values across anatomies and acceleration factors.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
4539