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Accelerating Bi-exponential T1ρ mapping using SCOPE
Yuanyuan Liu1, Yanjie Zhu1, Jing Cheng1, Weitian Chen2, Xin Liu1, and Dong Liang1,3

1Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, 2Department of Imaging and Interventional Radiology, The Chinese University of Hong Kong, Shatin, Hong Kong, China, 3Research center for Medical AI, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

### Synopsis

Mono-exponential T mapping requires 4 or 5 T-weighted images with different spin lock times (TSLs) to obtain the T maps, while bi-exponential T mapping requires a larger number of TSLs, which further prolongs the acquisition time. In this work, we develop a variable acceleration rate undersampling strategy to reduce the total scan time. A signal compensation strategy with low-rank plus sparse model was used to reconstruct the T-weighted images. We provide the reconstructed images and the estimated T maps at an acceleration factor up to 6.1 in fast bi-exponential T mapping.

### INTRODUCTION

T relaxation is normally described by a mono-exponential model1-5. However, compartmentation of tissues may lead to bi-exponential or multi-exponential T relaxation behavior in certain tissues. Several previous studies have reported that bi-exponential T relaxation can potentially provide more information than a mono-exponential relaxation6-9. However，bi-exponential T mapping requires a larger number of spin-lock times (TSLs), which further prolongs the acquisition time. Compressed sensing has shown significant performance in fast quantitative T mapping10-14. In this work, we extend our previous fast T mapping method (SCOPE)14 to bi-exponential model, referred to as bio-SCOPE.

### METHODS

In bi-exponential T mapping,the T parameters can be estimated using the bi-exponential model:

$$M=M_0{((1-\alpha)\exp{(-TSL_k/T_{1\rho s})}+\alpha\exp{(-TSL_k/T_{1\rho l})})}_{k=1,2,...,N}\ \ \ \ \ \ \ \ \ \ \ \ \ [1]$$where M is the image intensity obtained at varying TSLs;M0 is the baseline image intensity ;TSLk is the kth spin-lock time;α is the fraction of long relaxation component;T1ρs and T1ρl denote the short and long bi-exponential T relaxation times; N is the total TSL number.

The reconstruction model can be expressed as follows:

$$min{||L||_*}+\lambda||S||_1 \ \ \ \ s.t.\ \ C(X)=L+S,E(X)=d\ \ \ \ \ \ \ \ [2]$$

where $||L||_*$ is the nuclear norm of the low-rank matrix L;$||S||_1$is the $\ell_1$-norm of the sparse matrix S; X is the image series; λ is a regularization parameter; d is the undersampled k-space data; C(∙) performs pixel-wise signal compensation; E is the encoding operator15,16.Here, the compensation coefficient for signal compensation is calculated by:

$$Coef=1/{((1-\alpha)\exp{(-TSL_k/T_{1\rho s})}+\alpha\exp{(-TSL_k/T_{1\rho l})})}_{k=1,2,...,N}\ \ \ \ \ \ \ \ \ \ \ \ \ [3]$$

The solving strategy is shown in Figure 1. The image series is first compensated by an initial compensation coefficient calculated from the T maps estimated from the fully sampled central k-space. Iterative hard thresholding of the singular values of L and a modified soft-thresholding of the entries of S are used to solve the optimization problem in Eq. [2]. T-weighted images are reconstructed using L+S followed by data consistency. New T maps are estimated from the reconstructed images using the bi-exponential model described in Eq.[1], and then used to update the compensation coefficient. The reconstruction and signal compensation coefficient updating steps are repeated alternately until convergence.

Evaluation

All MR data were acquired on a 3T scanner (Trio, SIEMENS, Germany) using a twelve-channel head coil. Brain T mapping datasets were acquired from a healthy volunteer (male, age 26, IRB proved, written informed consent obtained) using a spin-lock embedded turbo spin-echo (TSE) sequence. Imaging parameters were: TR/TE=4000ms/9ms, spin-lock frequency 500 Hz, echo train length 16, FOV=230 mm2, matrix size =384 × 384, slice thickness 5 mm, and 16 T-weighted images were acquired with TSLs =1, 2, 4, 6, 8, 10, 12, 15, 20, 25, 30, 40, 50, 60, 70, and 80 ms. The acquired data was retrospectively undersampled with a variable rate undersampling scheme (shown in Figure 2). T-weighted images were reconstructed by bio-SCOPE and L+S methods15.

### RESULTS and DISCUSSION

Figure 3 shows the reconstructed T-weighted images using bio-SCOPE and L+S methods at net acceleration factors (R) of 4.6, 5.3, and 6.1. At R=4.6, all reconstructed images are comparable with the reference, which were reconstructed from the fully sampled k-space data. However, aliasing artifacts (green arrows) are observed on the images reconstructed by the L+S method at higher acceleration factors, i,e, R=5.3 and 6.1. Figure 4 shows the reference T maps derived from fully sampled k-space data and the T maps estimated from the reconstructed images using bio-SCOPE at R=4.6. The T maps derived from bio-SCOPE were comparable to the reference.

### CONCLUSION

The proposed method, bio-SCOPE can reconstruct the T-weighted image series from highly undersampled k-sapce data, and thereby significantly reduce the scan time of bi-exponential Tmapping.

### Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under grant nos. 61771463 and 61471350, National Key R&D Program of China nos. 2017YFC0108802.

### References

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### Figures

Figure 1. The flow diagram of the proposed method for bi-exponential Tmapping.

Figure 2. The proposed variable rate undersampling mask in the ky-TSL space for net acceleration factor R=5.3.The acceleration rates for short TSLs are lower than those for long TSLs (R=[4,4,4.8,4.8,4.8,4.8,4.8,4.8,6,6,6,6,6,6,6,6]). The percentages of fully sampled k-space center lines also vary for different TSLs ([0.13, 0.13, 0.12, 0.12, 0.1, 0.1, 0.1, 0.1, 0.1, 0.09, 0.09, 0.09, 0.08, 0.08, 0.08, 0.08]).

Figure 3. The reconstructed T-weighted images at TSL=1ms,8ms and 40ms for net acceleration factor of R=4.6 (a), R=5.3 (b) and R=6.1 (c). The reference images were obtained from the fully sampled k-space data. Aliasing artifacts (green arrows) can be observed using the L+S method at higher acceleration factors(R=5.3 and R=6.1).

Figure 4. (a) The T maps estimated from the reconstructed images using bio-SCOPE at R=4.6 and (b) the reference T maps derived from fully sampled k-space data.

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