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Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH
Xiaoqing Wang1, Sebastian Rosenzweig1, Nick Scholand1, H. Christian M. Holme1, and Martin Uecker1

1Department of Interventional and Diagnostic Radiology of the University Medical Center Göttingen, Göttingen, Germany

### Synopsis

Recent advances in real-time MRI and model-based reconstructions have enabled single-slice T1 mapping within a single inversion recovery. To allow fast multi-slice T1 mapping, this work employs radial simultaneous multi-slice (SMS) schemes and develops an SMS model-based reconstruction approach for high-resolution multi-slice T1 mapping based on single-shot inversion recovery FLASH. In comparison to conventional multi-slice approaches, the proposed SMS model-based reconstruction achieves high resolution (0.75 x 0.75 x 5 mm3) T1 maps for three slices of the brain within 4 s with a higher precision and a better preservation of image details.

### Introduction

Model-based reconstruction is one of the most efficient ways to accelerate quantitative MRI by estimating parameter maps directly from undersampled k-space, bypassing the intermediate image reconstruction and pixel-wise fitting steps completely. Simultaneous multi-slice (SMS) techniques have been used to accelerate MR imaging with a multi-slice coverage [1-3]. To further enable fast multi-slice T1 mapping, this work develops an SMS model-based reconstruction approach for high-resolution multi-slice T1 mapping based on single-shot inversion recovery (IR) radial FLASH. Validations of the proposed method have been performed on phantom and human brain studies.

### Theory & Methods

The IR SMS radial FLASH together with a conventional spoke-interleaved multi-slice data acquisition scheme [4] are demonstrated in Figure 1. Two SMS sampling strategies are illustrated: spokes aligned (middle) or distributed with a golden angle (right) among partitions. While the former allows decoupling the reconstructions into single-slices, providing an SNR benefit over the conventional multi-slice acquisition, the latter makes use of the actual advantage of SMS - acceleration by sensitivity encoding in the direction perpendicular to the slices [1,2] . The model-based reconstruction [5] is then extended to jointly estimate parameter maps and coil sensitivity maps for all the slices for the latter case. The estimation of unknowns is formulated as a nonlinear inverse problem, where the forward model, $\small F$, mapping all the unknowns $\small x$ to the measured data $\small y$, can be written as: $$\small F:x \mapsto \mathbf{P}{\Xi}\left( \begin{array}{c} \mathcal{F}\{ \mathbf {c}^{1} \cdot \mathbf{M}^{1}\} \\ \vdots \\ \mathcal{F}\{ \mathbf{c}^{Q} \cdot \mathbf{M}^{Q}\} \end{array}\right), \quad \text{with} \quad \mathcal{F}\{\mathbf{c}^{q} \cdot \mathbf{M}^{q}\}:=\left( \begin{array}{c} \mathcal{F}\{ c^{q}_{1} \cdot M_{t_{1}}^{q}(M_{ss}, M_{0}, R_{1}^{*}) \} \\ \vdots \\ \mathcal{F}\{c^{q}_{N} \cdot M_{t_{1}}^{q}(M_{ss}, M_{0}, R_{1}^{*}) \} \\ \mathcal{F}\{c^{q}_{1} \cdot M_{t_{2}}^{q}(M_{ss}, M_{0}, R_{1}^{*}) \} \\ \vdots \\ \mathcal{F}\{c^{q}_{N} \cdot M_{t_{n}}^{q}(M_{ss}, M_{0}, R_{1}^{*})\} \\ \end{array}\right), \quad q\in \{1,\cdots, Q\}.$$

$\small \mathbf{P}$ is the sampling pattern, $\small \Xi$ is the encoding matrix, which is a Fourier‐matrix as in [2]. $\small \mathbf{c}^{q}$ are the coil sensitivity maps for $\small q$th slice. $\small Q$ is the number of partitions/slices. $\small M_{t_{k}}^{q}$ represents the relaxation model for the $\small q$th slice following: $\small M_{t_{k}}^{q} = M^{q}_{ss} - ( M^{q}_{ss} + M^{q}_{0})\cdot e^{-t_{k} \cdot {R^{*}_{1}}^q }$ and $\small x = (x^{1}, \cdots, x^{Q})^{\intercal}$ with $\small x^{q} = (M^{q}_{ss}, M^{q}_{0}, {R^{*}_{1}}^q, c^{q}_{1},\cdots, c^{q}_{N})^{\intercal}$. The unknown $\small x$ is then reconstructed by solving the following regularized nonlinear inverse problem:

$$\small \hat{x} = \text{argmin} \|F(x) -y \|_{2}^{2} + \alpha \sum_{q=1}^{Q}R(x^{q}_{\mathbf{p}}) + \beta \sum_{q=1}^{Q}U(x^{q}_{\mathbf{c}})$$

where $\small R(\cdot)$ is the joint wavelet regularization in the parameter dimension, $\small U({\cdot})$ is a Sobolev norm to enforce the smoothness of coil sensitivity maps as in [6]. $\small \alpha$ and $\small \beta$ are regularization parameters for parameter maps $\small x_{\mathbf{p}}$ and coil sensitivity maps $\small x_{\mathbf{c}}$, respectively. Similar to [5], the above nonlinear problem is solved using the IRGNM-FISTA algorithm.

All the MRI measurements were conducted on a Magnetom Skyra 3T (Siemens Healthineers, Erlangen, Germany) scanner. Both phantom and brain measurements employed a 20‐channel head/neck coil. 2 subjects with no known illness were recruited. Written informed consent was obtained from both subjects prior to MRI. The acquisition parameters are: FOV 192 $\times$ 192 mm2, slice thickness 5 mm (10 mm distance between slices), spatial resolution 0.75 $\times$ 0.75 mm2, TR/TE 3.6 / 2.33 ms, nominal flip angle 6o and total acquisition time 4 s. All data processing was done offline and implemented with BART [7].

### Results

Figure 2 shows T1 maps of an experimental phantom obtained by model-based reconstructions from single-slice and (simultaneous) multi-slice acquisitions, respectively. All data were reconstructed using the same regularization parameters. Both visual inspection and quantitative results in Table 1 reveal that SMS based approaches produce T1 maps with less noise than the conventional multi-slice method. The SMS golden-angle based method has a better performance than the SMS aligned based method. Figure 3 then compares high-resolution T1 maps, enlarged views, and difference maps of the human brain (same section) obtained by single-slice and three multislice acquisition schemes in 4 s. In line with phantom results, both SMS based methods produce T1 maps with less noise. The SMS golden-angle scheme appears slightly better at preserving image details which are indicated by the white arrow than the other methods.

### Discussion & Conclusion

In this work, simultaneous multi-slice techniques together with a multi-slice model-based reconstruction approach are developed to allow simultaneous multi-slice T1 mapping based on single-shot IR radial FLASH. Initial results on phantom and human brain studies have demonstrated a better performance of the SMS golden-angle scheme combined with model-based reconstructions than the other multi-slice approaches. More clinical applications of the proposed method, such as multi-slice abdominal and cardiac T1 mapping, will be further explored in future studies.

### Acknowledgements

No acknowledgement found.

### References

[1]. Barth M, Breuer F, Koopmans PJ, Norris DG, Poser BA. Simultaneous multislice (SMS) imaging techniques. Magn Reson Med 2016;75:63–81.

[2]. Rosenzweig S, Holme H, Wilke R, Voit D, Frahm J, Uecker M. Simultaneous Multi-Slice Reconstruction Using Regularized Nonlinear Inversion: SMS-NLINV, Magn Reson Med. 2018;79:2057–2066.

[3]. Hilbert T, Schulz J, Bains L, Marques JP, Meuli R, Thiran JP, Krueger G, Norris DG, and Kober T. Fast Quantitative T2 Mapping using Simultaneous-Multi-Slice and Model-Based Reconstruction. In Proceedings of the 24th Annual Meeting of ISMRM, Singapore, 2016. p.0500.

[4]. Wang X, Voit D, Roeloffs V, Uecker M, and Frahm J. Fast Interleaved Multislice T1 Mapping: Model-Based Reconstruction of Single-Shot Inversion-Recovery Radial FLASH. Comput Math Methods Med, 2018:2560964, 2018. https://doi.org/10.1155/2018/2560964.

[5]. Wang X, Roeloffs V, Klosowski J, Tan Z, Voit D, Uecker M and Frahm J. Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH. Magn Reson Med 2018;79:730–740.

[6]. Uecker M, Hohage T, Block KT, Frahm J. Image reconstruction by regularized nonlinear inversion – joint estimation of coil sensitivities and image content. Magn Reson Med 2008;60:674–682.

[7]. Uecker M, Ong F, Tamir J, Bahri D, Virtue P, Cheng J, Zhang T, Lustig M. Berkeley advanced reconstruction toolbox. In Proceedings of the 23rd Annual Meeting of ISMRM, Toronto, Canada, 2015. p. 2486.

### Figures

Figure 1. Multi-slice data acquisition schemes for inversion recovery radial FLASH. Three slices and a multiband factor of 3 are demonstrated. a. (Left) Conventional interleaved data acquisition scheme. (Middle) SMS spoke-aligned and (Right) spokes distributed by a golden-angle among partitions. b. Combined spoke distribution for the first 7 TRs for all schemes.

Figure 2. Model-based single-slice and 3-slice T1 maps 4 s (top) and difference maps relative to the single-slice acquisition for an experimental phantom.

Table 1. T1 relaxation times (ms, mean ± SD) for an experimental phantom (Figure 2).

Figure 3. Model-based single-slice and 3-sliceT1 maps 4 s (top), magnified views (middle), and difference maps relative to the single-slice acquisition for the human brain. The white arrows indicate a better preservation of image details by the SMS golden-angle based approach.

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