Tao Zhang^{1}, Yuxin Chen^{2}, Shreyas Vasanawala^{3}, and Ersin Bayram^{1}

Water-fat separation is widely used in many MR applications and is known to be challenging in various situations. Traditionally, region growing, spatial smoothing, and global optimization have been applied in dual echo water-fat separation. These methods require complex-valued images acquired at two echo times and occasionally suffer from global or local swaps due to inaccurate field map estimation. In this work, a deep learning approach for dual echo water-fat separation is investigated.

Dual echo Dixon imaging can be modeled as:

$$$S_1=(W+c_1F)e^{i\phi_1},\\S_2=(W+c_2F)e^{i\phi_2},$$$ (1)

where $$$S_1$$$ and $$$S_2$$$ are pixel-wise complex composite signals acquired at two echo times, $$$W$$$ and $$$F$$$ are real-valued water and fat signal at each image pixel, $$$c_1$$$ and $$$c_2$$$ are dephasing factors for fat with respect to water corresponding to the two echo times, and $$$\phi_1$$$ and $$$\phi_2$$$ are additional phases attributed to field inhomogeneity. There are more unknowns ($$$W$$$, $$$F$$$ and $$$\phi_1$$$/$$$\phi_2$$$) than the number of linear equations, therefore Eq. (1) has multiple solutions. Traditional methods rely on the fact that the underlying field map is smooth to down-select the optimal solution. However, this process can be challenging, and, for certain optimization methods, time-consuming [4-5]. Note that the final solutions for water and fat can be written as functions of $$$S_1$$$ and $$$S_2$$$, although these functions cannot be easily approximated.

$$$W=f_1(S_1,S_2),\\F=f_2(S_1,S_2),$$$ (2)

In this work, we employ a deep neural network to approximate Eq. (2). Furthermore, since neural network can effectively estimate nonlinear functions, we approximate a mapping on magnitude images instead of complex-valued images. For simplicity, we only focus on estimating $$$W=f(|S_1|,|S_2|)$$$ for the rest of this work.

Deep Learning: we applied a modified U-Net neural network (Fig. 1) in this work. U-Net is a popular architecture for image segmentation, in which image pixels are labelled to different tissue types and the functions to be approximated are therefore discrete [6]. In comparison, the water-fat separation problem requires the neural network to approximate a continuous function $$$W=f(|S_1|,|S_2|)$$$. Thus, the loss function for U-Net needs to be carefully chosen. Here, a structural dissimilarity (DSSIM) metric is applied as the loss function [7]. Compared to traditional $$$\ell_2$$$ or $$$\ell_1$$$ loss functions, DSSIM better represents the human perception of images.

Data Preparation: With IRB approval and patient consent, 24 patients were recruited for dual echo Dixon imaging on MR750 3T scanners (GE Healthcare, Waukesha, USA). The imaging parameters were: TE1/TE2 = 2.2/3.3 ms, TR = 6.3-7.3 ms, and bandwidth = $$$\pm$$$ 100kHz. Global optimization [5] was used to obtain water-only images. Two board-certified radiologists reviewed and confirmed no obvious global or local water-fat swaps existed in these water-only images. A total of 9048 2D images from 20 patients were used to train the neural network, with 20% of the images for cross-validation. Another 1696 images from the remaining 4 patients were used for testing. All images were normalized and scaled to a fixed size of 256x256 during preprocessing.

Implementation: The proposed method was implemented in Python using Keras [8] and Tensorflow [9]. U-Net was trained with stochastic gradient descent (learning rate = 0.1, decaying factor = 5e-5, batch size = 16, and Nesterov momentum = 0.9). Training and testing were performed on a standard desktop with a GTX 1080 Nvidia GPU (Nvidia, Santa Clara, USA).

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[2] Xiang Q. Two-point water-fat imaging with partially-opposed-phase (POP) acquisition: an asymmetric Dixon method. Magn Reson Med 2006;56:572-584

[3] Eggers H, Brendel B, Duijndam A, Herigault G. Dual-echo Dixon imaging with flexible choice of echo times. Magn Reson Med 2011;65:96-107

[4] Berglund J, Ahlstrom H, Johansson L, Kullberg J. Two-point Dixon method with flexible echo times. Magn Reson Med 2011;65:994-1004

[5] Zhang T, Chen Y, Bao S, et al. Resolving phase ambiguity in dual-echo Dixon imaging using a projected power method. Magn Reson Med 2017;77:2066-2076

[6] Ronneberger O, Fischer P, Brox T. U-Net: Convoluntional Networks for Biomedical Image Segmentation. arXiv preprint arXiv:1505.04597, 2015

[7] Wang Z, Bovik, A, Sheikh, H, Simoncelli, E. Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 2004;13:600-612

[8] Chollet F, et al. Keras, 2015. https://github.com/fchollet/keras

[9] Abadi M, et al. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. https://www.tensorflow.org

[10] Gong E, Zaharchuk G, Pauly J. Improved Multi-echo Water-fat Separation Using Deep Learning. ISMRM 2017. p5657

Fig. 1 U-Net neural network for dual echo
water-fat separation. Major components of the network are illustrated by
different symbols, including up convolution, max pooling, and convolution with
different kernel sizes and activation functions. The number of feature maps
(also known as the depth of each layer) is shown on top of each layer. The
network takes two 2D images as inputs and generates the corresponding
water-only image as the output.

Fig. 2 Representative images from the
training set. Similar image quality is achieved using deep learning compared to
the traditional method.

Fig. 3 Representative images from the
training set. Similar image quality is achieved using deep learning compared to
the traditional method. Note that deep learning was able to correct minor
water-fat separation inaccuracy from the traditional method (arrowhead).

Fig. 4 Representative images from the test
set. Similar image quality is achieved using deep learning compared to the
traditional method.

Fig. 5 Representative images from the test
set. Similar image quality is achieved using deep learning compared to the
traditional method. Minor water-fat separation inaccuracy was noticed in the
deep learning result (arrowhead).