Daiki Tamada^{1}, Ryoichi Kose^{2}, Katsumi Kose^{2}, Hiroshi Onishi^{1}, and Utaroh Motosugi^{1}

Water/fat separation algorithm for two-echo spiral acquisition in the liver was developed using the convolutional neural network (CNN). The processing in the CNN was performed in the sinogram domain. A Bloch simulator was used to simulate the phase error in the k-space caused by the off-resonance components of background and fat. A volunteer study showed the successful water/fat separation using the proposed method without additional echoes of reference scans.

A spiral readout is a promising approach to achieve fast acquisition in the liver. Generally, fat suppression techniques including spectrally-selective saturation pulses are required in spiral imaging because the acquisition with long readout time results in artifact caused by fat components1. However, it is challenging to perform uniform fat suppression in case of inhomogeneous B^{0} and B_{1} field. A chemical shift encoded imaging (CSI) is widely used to achieve uniform water-fat separation in clinical applications^{2,3}. However, the CSI in spiral readout still has the blurring problem.

In this study, we developed a novel water-fat separation technique for spiral readout acquisition using the convolutional neural network (CNN) and the Bloch simulator to overcome the blurring problem.

**Network architecture and training:**

A simple CNN consists of six 1-dimensional (1D) convolution filters (kernel size = 5 with four channels) with rectified linear units (ReLU), followed by a 1D convolution filter (kernel size = 3 with four channels) with hyperbolic function was adopted as shown in Fig. 1. Sinograms of in-phase and out-of-phase k-spaces were used for the input of the network. Finally, the fat sinogram was predicted in the last layer. The water sinogram can be calculated by subtracting it from the in-phase sinogram. The optimization of the network was implemented using the stochastic gradient descent optimizer (learning rate = 0.0025, momentum = 10^{-6}, momentum = 0.9) with 80 epochs. The mean square error was used for the loss function.

**Training datasets: **

A procedure to obtain datasets for the training was summarized in Fig. 2. The datasets were generated from the water and fat MR images acquired using the two-point chemical shift imaging (LAVA-Flex, TR/TE1/TE2 = 3.9/1.2/2.4 ms, flip angle = 12°, matrix = 512×512, acquisition matrix = 320×224, FOV = 33-40 cm, slice thickness = 3 mm). The k-space datasets were calculated from the images using the Bloch simulator^{4}, which enables realistic simulation of the blurring due to the fat and background off-resonance expressed as below equation.

$$$S(t) = \int \int (W e^{-j2 \pi (k_x(t)x + k_y(t)y)} + F e^{-j2 \pi (k_x(t)x + k_y(t)y)+\phi_f t}) e^{-2 \pi j \phi_0 t} dx dy,$$$

where S is the k-space signal, t is the sampling time, W and F are the water and fat images, k_{x} and k_{y} are the k-space coordinates along x and y, Φ_{0} and Φ_{f} are the background and fat off-resonance frequencies. The fixed T1 and T2 for the water (T1 = 1000 ms, T2 = 60 ms) and fat (T1 = 300 ms, T2 = 80 ms) components were used for the simulation. A spoiled gradient echo sequence (TR/TE1/TE2 = 20/2.2/3.3 ms, matrix = 320×320, FOV = 36 cm) with a 64-shot spiral readout (sampling point = 2048, dwell time = 2 microseconds) was used. The sinogram was derived by applying the Fourier transform to the k-space along the readout direction.

**Experiment**

We tested the proposed method with a volunteer. A 3-tesla clinical MRI scanner (GE Healthcare, Milwaukee, WI) with a 32-channel torso array and a three-echo spiral sequence (TR/TE1/TE2/TE3 = 20/2.2/3.3/4.4 ms, matrix = 320×320, FOV = 36 cm, slice thickness = 5 mm) with the trajectory adopted in the simulation was used. The acquisition was performed within one breath-hold to avoid image misregistration. The two echoes of in-phase (2.2 ms) and out-of-phase (3.3 ms) were used for the water/fat separation using the CNN. For the comparison of reconstruction techniques, water/fat separation using the three echoes (three-point chemical shift imaging: 3P-CSI)^{3} was performed. The reconstruction from the k-space to the image domain for the CNN and the 3P-CSI was implemented using the non-uniform Fourier transform (number of iteration = 15).

[1] Moriguchi, Hisamoto, Jonathan S. Lewin, and Jeffrey L. Duerk. "Dixon techniques in spiral trajectories with off‐resonance correction: a new approach for fat signal suppression without spatial‐spectral RF pulses." Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 50.5 (2003): 915-924.

[2] Dixon, W. Thomas. "Simple proton spectroscopic imaging." Radiology 153.1 (1984): 189-194.

[3] Glover, G. H., and E. Schneider. "Three‐point Dixon technique for true water/fat decomposition with B0 inhomogeneity correction." Magnetic resonance in medicine 18.2 (1991): 371-383.

[4] Kose, Ryoichi, and Katsumi Kose. "BlochSolver: A GPU-optimized fast 3D MRI simulator for experimentally compatible pulse sequences." Journal of Magnetic Resonance 281 (2017): 51-65.

[5] Brodsky, Ethan K., et al. "Generalized k‐space decomposition with chemical shift correction for non‐Cartesian water‐fat imaging." Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 59.5 (2008): 1151-1164.

Fig. 1 The network architecture which predicts fat
component from in-phase and out-of-phase sinograms. All processing in the
network is performed in the sinogram domain.

Fig.2 Procedure to generate datasets for
the training. Sinograms were derived from the k-space datasets calculated using
the Bloch simulator. Off-resonance and sensitivity were included in the
simulation.

Fig.
3 The MSE loss of network optimization.

Fig.
4 Separated fat images using the (a) 3P-CSI and (b) CNN.

Fig.
5 Water images obtained using the (a) 3P-CSI and (b) CNN. The results implied
that the CNN using the Bloch simulator enables sharper image quality.