Introduction

$$$T_1~$$$as a biomarker is of high interest in clinical applications$$$^1$$$, but conventionally its accessibility is limited by time-consuming acquisitions$$$^2$$$. Those become especially challenging in motion-affected organs such as the heart. Conventional myocardial $$$T_1$$$ mapping therefore utilizes gated acquisitions over multiple heartbeats during a breath-hold and has been restricted on single-slice applications.

In this abstract, we develop a time-efficient multi-slice$$$~T_1~$$$mapping technique. We combine a single-shot IR-FLASH sequence incorporating radial slice-interleaved SMS readouts with NLINV subspace reconstruction to achieve acquisition times of 4 seconds for 6 or 9 slices. The technique is demonstrated in a phantom, brain and cardiac experiment.

Methods

Sequence
The proposed multi-slice IR-FLASH sequence starts with a non-selective inversion followed by interleaved SMS excitations and radial readouts. The $$$n$$$ slice-interleaved SMS acquisitions with a multiband factor $$$m$$$ are specified as SMS$$$n$$$x$$$m$$$. Each of the $$$n$$$ SMS groups is sampled with the same pattern, with distinct samples in partition dimension utilizing an angle based on the golden-ratio between two consecutive spokes per group. (Figure$$$~1$$$)

Reconstruction
The underlying Look-Locker signal model in voxel$$$~r$$$
$$M(t,r)~=~M_{ss}(r)~-~(M_{ss}(r)~+~M_{0}(r))~e^{-t/T_1^*(r)}$$
is linearized in a subspace spanned by $$$N_c=4$$$ basis functions
$$M(\boldsymbol{x_p}(r),t)~\approx~\sum_c^{N_c}~\boldsymbol{x_c}(r)~B_c(t),$$
with the model parameters $$$\boldsymbol{x_p}(r)=(M_0, M_{ss}, T_1^*)^T$$$ and the respective subspace coefficients $$$\boldsymbol{x_c}(r)$$$. The basis functions are determined with a PCA from a simulated dictionary with different physical parameter combinations$$$^3$$$.

Coefficient maps $$$\boldsymbol{x_c}$$$ are reconstructed independently per SMS groups with the developed algorithm, a subspace version of SMS-NLINV$$$^{4,5}$$$.
The nonlinear forward operator
$$\textit{F}:~\boldsymbol{x}~=~(\boldsymbol{x_c},~\boldsymbol{c})~\to~\mathcal{P}~{\Xi} \mathcal{F}~\mathcal{D}~\mathcal{B}~(\boldsymbol{x_c}~\odot~\boldsymbol{c})$$
maps the unknown coil sensitivities $$$\boldsymbol{c}$$$ and coefficient maps $$$\boldsymbol{x_c}$$$ to the acquired k-space data $$$\boldsymbol{y}$$$. Here, $$$\odot$$$ is the element-wise product, $$$\mathcal{B}$$$ the basis operator, $$$\mathcal{D}$$$ a temporal mask selecting diastolic data, $$$\mathcal{F}$$$ the Fourier transform, $$$\Xi$$$ the SMS-encoding matrix and $$$\mathcal{P}$$$ the radial sampling pattern.
The resulting nonlinear inverse problem
$$\hat{\boldsymbol{x}}~=~\arg~\min_{\boldsymbol{x}}~||F(\boldsymbol{x})-\boldsymbol{y}||^2_2~+~\alpha~||\boldsymbol{x_c}||^2_2~+~\alpha~||W\boldsymbol{c}||^2_2$$
incorporates a Sobolev weighting matrix$$$~W$$$ and is solved by an iteratively regularized Gauss Newton method$$$^4$$$.
After reconstruction of $$$\boldsymbol{x_c}$$$, the physical parameters are pixel-wise fitted in the linear subspace
$$\hat{\boldsymbol{x_p}}~=~\arg~\min_{\boldsymbol{x_p}}~||\mathcal{B}^H~\mathcal{DB}\boldsymbol{x_c}~-~\mathcal{B}^H~\mathcal{D}\mathcal{M}(\boldsymbol{x_p})||_2^2~.$$
Finally, the Look-Locker correction $$$T_1~=~M_0/M_{ss}~T_1^*~+~2~T_d$$$ with delay time $$$T_d$$$ is applied to obtain the $$$T_1~$$$map$$$^6$$$.

All reconstruction steps were implemented in the Berkeley advanced reconstruction toolbox (BART)$$$^7$$$.

Acquisition
The evaluation of the sequence was performed in a NIST-phantom and brain with SMS3x3, and demonstrated for myocardial mapping with SMS2x3.
All MRI experiments were performed on a 3T Magnetom Vida (Siemens Healthineers, Erlangen, Germany). Each IR-FLASH consists of 1080 spokes acquired at $$$T_R=3.6~ms$$$.
SMS3x3 was quantitatively evaluated in the NIST-phantom where reference values were determined with a gold-standard IR-SE sequence. To validate the gated IR-FLASH sequence, temporal patterns $$$\mathcal{D}$$$ corresponding to heart-rates of 60 and 100 bpm are defined, with data reduction matching the cardiac example.
Cardiac measurements were conducted during exhaled breath-hold and the ECG-trigger was set to start the inversion in early diastolic phase. Systolic data ($$$\approx 40\%$$$) was discarded in order to exclude motion-affected samples$$$^8$$$.
All measurements were performed with a slice thickness of $$$6~mm$$$ and slice gap for SMS$$$n$$$x$$$m$$$ of$$$~50\%$$$. The in-plane resolution was chosen to be $$$0.86~mm^2$$$ and $$$1.25~mm^2~$$$(cardiac).

Results & Discussion

Figure$$$~2$$$ presents the NIST-phantom experiment. The reconstruction of the SMS3x3 IR-FLASH data is compared to a $$$T_1~$$$gold-standard mapping (IR-SE). In the corresponding Bland-Altman plot the bias across a wide range of $$$T_1$$$ is lower than 10 ms. The proposed technique can acquire accurate $$$T_1~$$$maps of $$$9~$$$slices in the phantom.
The results of the brain measurements are presented in Figure$$$~3$$$. One representative slice of the SMS3x3 stack is quantitatively compared to the corresponding single-slice IR-FLASH reference. A difference of $$$\approx~2\%~$$$in the ROI analysis can be observed in white and gray matter. Figure$$$~3B$$$ shows a similar quality across the whole volume demonstrating the applicability of SMS3x3 to estimate 9$$$~T_1~$$$maps of different slices in the brain using the proposed method.
In Figure$$$~4$$$, a reference cardiac single-slice$$$~T_1~$$$map is compared to the extracted corresponding slice from a SMS1x3 and the SMS2x3 acquisition. The resolution is decreased compared to the brain due to the constraint of balancing the available data per partition/slice and the spatial coverage of the larger heart volume. In Figure 4D$$$~T_1~$$$maps of a whole-heart are presented with an in-plane resolution of $$$1.25~mm^2$$$. While the sharpness and quality decreases, the rapid acquisition of up to 6 $$$T_1~$$$maps in a single-shot is promising.

Conclusion

In this work, we combined a single-shot IR-FLASH acquisition incorporating an interleaved SMS excitation and radial readout with a subspace-based NLINV reconstruction. With the proposed method, multi-slice $$$T_1~$$$maps were reconstructed from datasets acquired within $$$4~s$$$. The accuracy is validated in a phantom and brain experiment. The cardiac results demonstrate promising results for single-shot whole-heart myocardial $$$T_1~$$$mapping.

Acknowledgements

Funded by the DZHK (German Centre for Cardiovascular Research). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2067/1- 390729940