Xiaoqing Wang^{1}, Sebastian Rosenzweig^{1}, Nick Scholand^{1}, H. Christian M. Holme^{1}, and Martin Uecker^{1}

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 mm^{3}) T1 maps for three slices of the brain within 4 s with a higher precision and a better preservation of image details.

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 mm^{2}, slice thickness 5 mm (10 mm distance between slices), spatial resolution 0.75 $$$ \times $$$ 0.75 mm^{2}, TR/TE 3.6 / 2.33 ms, nominal flip angle 6^{o} and total acquisition time 4 s. All data processing was done offline and implemented with BART [7].

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.

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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.