Congbo Cai^{1}, Chao Wang^{2}, Xinghao Ding^{2}, Shuhui Cai^{2}, Zhong Chen^{2}, and Jianhui Zhong^{3}

Overlapping-echo detachment (OLED) planar imaging sequence can provide reliable T2 mapping within milliseconds even under continuous object motion. A detachment algorithm based on the sparsity and structure similarity constraints has been used to separate the echo signals to form T2 map. However, the effectiveness of separation is limited and the reconstruction is time consuming. Here, an end-to-end deep convolutional network based on deep residual network was introduced. The results of simulation and in vivo human brain show that it can reconstruct T2 mapping efficiently and reduce the reconstruction time from minutes to milliseconds after deep residual network is trained.

The OLED sequence is
shown in Fig. 1. Three echo signals with different T_{2}
weighting are obtained in the same k-space within a single shot:

\begin{cases}S_{1}(TE_{1})=\frac{1}{2}\int_{\overrightarrow{r}}\rho(\overrightarrow{r})|\sin\alpha\cos\alpha|(1-\cos\beta)e^{-TE_{1}/T_{2}(\overrightarrow{r})}d\overrightarrow{r} \ \ \ \ \ \ \ \ \ \ ,first -spin- echo \\S_{2}(TE_{2})=\frac{1}{4}\int_{\overrightarrow{r}}\rho(\overrightarrow{r})|\sin\alpha|(1+\cos\alpha)(1-\cos\beta)e^{-TE_{2}/T_{2}(\overrightarrow{r})}d\overrightarrow{r} \ , second- spin- echo\\S_{3}(TE_{1})=\frac{1}{4}\int_{\overrightarrow{r}}\rho(\overrightarrow{r})|\sin\alpha|(1-\cos\alpha)(1-\cos\beta)e^{-TE_{1}/T_{2}(\overrightarrow{r})}d\overrightarrow{r} \ , double-spin-echo\end{cases}

The details of the traditional
reconstruction method can be found in our previous report [4]. For deep learning,
a residual network with 14 parameter layers was used. In the network, all pooling
operations were removed to preserve spatial information. Stochastic
gradient descent (SGD) was used with the weight decay of 10^{-10},
momentum of 0.9 and mini-batch size of 16. We started with a learning rate of
0.1, divided it by 10 at 3×10^{4}
and 6×10^{4}
iterations, and terminated training at 10^{5} iterations. The filter
size was 3×3,
and the filter number was 64. No augmentation was used. The batch normalization
(BN) was adopted right after each convolution and before activation. The output
size was 64×64.
The training dataset was obtained
from the simulation of OLED sequence using the SPROM software developed by our
group. Fig. 2(a) shows the input image and Fig. 2(b) shows the
corresponding label image. In the simulations possible non-ideal experimental
conditions were considered fully, and guided image filtering applied [6]. The
training dataset included 100 images, and a 64×64 crop was randomly sampled
from an image (256×256). The human brain
experiments were performed on a whole-body 3T MRI system (MAGNETIOM Trio TIM,
Siemens Healthcare, Erlangen, Germany).

Fig. 1. Single-shot OLED sequence. The first two RF pulses are excitation pulses with flip angle α, the third RF pulse is refocusing pulse with flip angle β. G_{1} and G_{2} are the first and second echo-shifting gradients, and Gcr represents crusher gradients along three directions. n_{1}+n_{2}+n_{3}+n_{4}+6=N, where N is the echo number.

Fig. 2. An example of training dataset from simulation. (a) Amplitude of input image. The acquisition matrix is 128×128, and Fourier transformed to 256×256 by zero padding; (b) The corresponding label image (reference T_{2} mapping).

Fig. 3. Simulated MR images (22×22 cm^{2}). The total scan time is 147.6 ms (for OLED) and 135.9 ms (for EPI) with acquisition matrix = 128×128, sw = 1.42 kHz/pixel. (a) Original OLED image containing two echo signals; (b) Reference T_{2} mapping; (c) T_{2} mapping reconstructed from (a) using traditional regularization-based method (c); (d) T_{2} mapping reconstructed from (a) using DL method; (e) Spin-echo EPI image; (f) T_{2} value trace of (b), (c) and (d) along the red circle line in (e). The trace starts at the three-o’clock position of the circle and runs anticlockwise.

Fig. 4. MR images of human brain. FOV = 22×22 cm^{2}, acquisition matrix = 128×128, 2×GRAPPA acceleration, sw = 751 Hz/pixel, slice thickness = 4 mm, and 17 slices were imaged. For conventional spin-echo sequence (for reference images), 4 different TE values (35, 50, 75 and 90 ms ) were selected, TR = 2.0 s and the total scan time is about 17 mins. Each original OLED image contains two echo signals.