Introduction

MR parameter quantification enables advanced characterization of tissue and facilitates longitudinal studies^1-4. However, MR parameter estimation techniques typically require excessive acquisition time, hence they often do not lend themselves to routine clinical application. Herein, we propose a rapid parameter estimation technique that provides distortion-free and co-registered T₁, T₂, M₀, B₀ and B₀ maps.

Method

Acquisition & Reconstruction
The proposed mapping of T₁, T₂, M₀ and B₁ inhomogeneity is based on simultaneously acquired spin- and stimulated-echo signals from three-90° RF pulse sequence^5,6. Figure 1(a) shows the proposed pulse sequence, where EPI technique is used for rapidly encoding spin- and stimulated-echo contrasts. The acquired echo signals are formulated as follows:
$$S_{SE}=M_{0}\cdot(1-e^{-TR_{eff}^{prev}/T_{1}})\cdot sin⁡(B_{1}\cdot \frac{\pi}{2})\cdot sin^{2}⁡(B_{1}\cdot \frac{\pi}{4})\cdot e^{-TE/T_{2}}~~~~~[1]$$
$$S_{STE}=\frac{1}{2}\cdot M_{0}\cdot(1-e^{-TR_{eff}^{prev}/T_{1}})\cdot sin^{3}⁡(B_{1}\cdot \frac{\pi}{2})\cdot e^{-TM/T_{1}}\cdot e^{-TE/T_{2}}~~~~~[2]$$
where TE is the echo time, TM is the mixing time, and $$$TR_{eff}^{prev}=TR^{prev}-\frac{TE^{prev}}{2}-TM^{prev}$$$ is the effective TR of the previous acquisition.
In order to eliminate the geometric distortion in the EPI readout, we introduce blip-up/down acquisition (BUDA) and reconstruction⁷. BUDA acquires two shots of EPI with opposite phase encoding directions. With this set of opposite-polarity images, B₀ field map can be estimated⁸. BUDA reconstruction incorporates the estimated field inhomogeneity into parallel imaging forward model and employs Hankel structured low-rank constraint^9-11 to exploits similarities between the opposite-polarity images while mitigating potential shot-to-shot phase variation as follows:
$$\min_{I}\sum_{t=1(blip-up)}^{2(blip-down)}‖F_{t}ECI_{t}-k_{t} ‖_{2}^{2}+\lambda‖\mathcal{H}(I)‖_{*}~~~~~[3]$$
where $$$F_{t}$$$ is Fourier operator in $$$t^{th}$$$ shot, $$$E$$$ is field inhomogeneity map, $$$C$$$ is coil sensitivities estimated from distortion-free gradient-echo calibration data using ESPIRiT¹², $$$𝑘_{𝑡}$$$ is k-space data for $$$t^{th}$$$ shot, $$$\mathcal{H}(\cdot)$$$ is the block-Hankel representation and $$$𝐼$$$ is the distortion-free image.
While using a larger TM provides T₁ sensitivity, this increases the dead time between the second and the third RF pulses and reduces the acquisition efficiency. We incorporate an echo-shifting approach⁶ to ensure high sampling efficiency, where the mixing time is used for acquiring spin echo data from different slice locations as shown in Figure 1(c).

Parameter estimation
We introduce two methods for estimating T₁, T₂, M₀ and B₁. First approach is an analytic method with dictionary matching and nonlinear least square fitting, whereas the second approach uses unsupervised neural network-based optimization.

Analytic fitting: We take the signal ratio between stimulated and spin echoes to eliminate T₂ decay effect and spin density component.
$$\frac{S_{STE}}{S_{SE}}=\frac{1}{2}\cdot\left\{\frac{sin⁡(B_{1}\cdot \frac{\pi}{2})}{sin⁡(B_{1}\cdot \frac{\pi}{4})}\right\}^{2}\cdot e^{-TM/T_{1}}~~~~~[4]$$
The ratio follows simple exponential decay with respect to TM. T₁ and B₁ are estimated from these ratio images. Rapid initial estimates for T₁ and B₁ are first obtained by Bloch-simulated dictionary matching and the values are used as seed point for subsequent nonlinear least-square fitting. The estimated T₁ and B₁ values are plugged in the spin echo signal equation, which now only contains T₂ and M₀ components and follows simple exponential decay with respect to TE. T₂ and M₀ are estimated by nonlinear least-square fitting after an interim dictionary matching. With the prior knowledge that B₁ field is spatially smooth, B₁ is estimated by polynomial fitting and T₁ is re-estimated using the estimated B₁ to improve estimation performance.

Unsupervised deep neural network for parameter estimation: In order to exploit spatial relations between neighboring voxels, we propose a convolutional neural network-based parameter quantification method. Input of the quantification network is a set of spin- and stimulated-echo images for various TE and TM. The quantification network produces T₁, T₂, M₀ maps as output. A residual network is used as the quantification network. Starting from these output T₁, T₂, M₀ maps and the polynomial fitted B₁, spin- and stimulated-echo signals are synthesized by Bloch generator as Eqs [1-2]. The signal difference between the input images and the synthesized images is utilized as loss function, thereby obviating the need for any additional ground truth information during the estimation of network weights.
$$Loss=|SE-SE_{syn}|+\lambda|STE-STE_{syn}|~~~~~[5]$$
$$$\lambda$$$ is the regularizing parameter for compensating signal intensity difference between spin echo and stimulated echo signals.

Result

Phantom experiments and in vivo MRI experiments were conducted on 3T MRI scanner (Siemens Magnetom Verio) to validate the proposed method. The proposed simultaneous spin echo and stimulated echo acquisition was performed with five combinations of TE and TM.
Parameter estimation results of phantom experiments with the proposed method and reference methods are shown in Figure 3 and those of in vivo brain experiments are shown in Figure 4 and 5. As shown in the parameter estimation results, geometric distortion are corrected by the proposed BUDA-STEAM. In terms of T₁ and T₂ values, the proposed and reference methods show similar results even though the proposed method took shorter time for acquisition, total 25sec for the phantom experiment and 50sec for the in vivo experiment. The estimated results with the analytic fitting and the neural network-based estimation are similar for all parameters of T₁, T₂, B₁, and M₀. The neural network-based estimation provides noise-robust MR parameters owing to the fact that the convolutional network takes information of spatially adjacent voxels into account.

Discussion & Conclusion

The proposed BUDA-STEAM parameter estimation method enables acquisition of distortion-corrected, co-registered T₁, T₂, M₀, B₁ and B₀ maps, within a short acquisition time using a three-90° pulse sequence and BUDA reconstruction. In addition, the parameter estimation using unsupervised neural network optimization provided noise-robust results from this rapid acquisition.

Acknowledgements

This research was supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant number : HI14C1135) and MIT-Korea - KAIST Seed Fund of MIT International Science and Technology Initiatives (MISTI).