In our experiments, we used LiTS as our image dataset of liver CT images with tumors, which consisted of only 131 sequences. The size of LiTS was not big enough for the training of deep learning algorithms, such as liver tumor segmentation or classification. To enlarge the LiTS, we chose 4555 2D slices with tumors from 131 sequences of liver CT images. Then, all the images were normalized by using formula (6)
![](data:image/png;base64,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)
valueoriginal and valuenormalized represented the original and normalized image pixels value, respectively. mean indicated the mean value of image pixels, and std indicated the standard deviation of image pixels. Moreover, we specially cut the tumor regions from the liver CT images and built a liver tumor dataset, then we augmented the tumor dataset by flipping, rotating, scaling the original tumor region so that we can create a liver tumor dataset of 50000 slices from the original 4555 slices, which were used as the mask attention map in our method.
The hardware and software configuration of our experiments were shown in Table 1. The quantitative evaluation metric used in our experiments was the peak signal to noise ratio (PSNR). There were four sections in our experiments, including training of our model, quantitative comparison between our method and other state-of-the-art methods, Turing test for synthesized images by radiologists, and the evaluation of the synthetic dataset for the medical image segmentation.
Table 1 Hardware and software configuration of our experiments
Item
|
Configuration
|
Operating system
|
Ubuntu 16.04
|
GPU
|
NVIDIA GeForce GTX 1080
|
CPU
|
Intel Core i5-7500 @3.4GHz
|
Software toolkit
|
Python 2.7;tensorflow 1.1;matlab 2016b
|
Disk
|
500 GB
|
GPU memory
|
8 GB
|
System memory
|
16 GB
|
3.1 Training of our model
The configurations of hyperparameters in our model during the training were shown in Table 2. The proposed MAGAN network was implemented by python 2.7 and TensorFlow 1.1 and trained on a NVIDIA GeForce GTX 1080 GPU using Adam optimizer with a learning rate 0.0002. It cost about ten hours for the whole procedure of the training.
Shown as Fig.5~Fig.9, and we can find that as the number of iterations increased, the performance of the synthesized CT liver images became better and better. After the first iteration of training (in Fig.5), the performance of the synthesized image from the generator network was terrible, for example, most pixels were black, the contour was blurring, intense chessboard effect. All these bad performances indicated that the training had just started, and more iterations were needed. After ten iterations (in Fig.6), the whole image was more clear, the contour was more vivid, but the chessboard effect still existed. After one hundred iterations (in Fig.7), the performance of the synthesized image was much better and closer to the real image, more details can be visualized, human organs were vivid, the chessboard effect was weaker but still existed, whitened regions were not filled with tumor texture. After one thousand iterations (in Fig.8), the chessboard effect disappeared, all details of liver CT were restored, but only part of the whitened regions was filled with tumor texture. After ten thousand iterations (in Fig.9), it was hard to tell differences between synthesized image and real image, all details of liver CT was restored, the chessboard effect disappeared, all the whiten regions were filled with tumor texture.
Table 2 Hyperparameters of our model
parameter
|
value
|
initial learning rate
|
0.0002
|
Adam momentum
|
0.5
|
λ1 in formula (5)
|
100
|
λ2 in formula (5)
|
1
|
exponential decay
|
0.99
|
batch_size
|
1
|
epoch
|
10
|
dropout
|
0.5
|
frequency of saving loss value
|
100
|
frequency of saving model
|
500
|
The loss function of the generator network, discriminator network, and total network during the training were shown in Fig.10, Fig.11, Fig.12, respectively, and we can conclude that the loss functions decreased as the number of iterations increased, and became steady after about 10000 iterations, which indicated that our model performed well during the training.
Results of the synthesized image were shown in Fig.13, three liver tumor images with tumor masks were in the first row, which was used as inputs of our model, and can obtain the synthesized images in the second row. We compared the synthesized images and the real images and calculated the differences between them. The color image of the differences was shown in the fourth row. All these results showed that our method can synthesize liver CT images with tumors, and the synthesized images were almost identical to the real images.
To test the impact of the dilated convolution operators in the MAGAN, we replaced the dilated convolution operators with the regular convolution operators in the contracting path of the generator network and quantitatively compared PSNR of these two GAN networks. And we found that the network with regular convolution operators can provide PSNR of 59.66, while the MAGAN with dilated convolution operators can provide PSNR of 64.72, which indicated the effectiveness of the dilated convolution operators in our network.
To test the impact of the residual connections in the MAGAN, we removed the residual connections and quantitatively compared PSNR of these two GAN networks. And we found that the network without residual connections can provide PSNR of 55.23, while the MAGAN with residual connections can provide PSNR of 64.72, which indicated the effectiveness of the residual connections in our network.
Besides, we can also manually or automatically “add” tumor regions on the healthy liver CT images using our liver tumor dataset of 50000 slices, to create a diseased liver CT image, shown in Fig.14. The healthy liver CT images were in the first row. In the second row, manually changing the pixel values of two regions to white color, which meant that these two regions were the selected tumor regions. Using our method, the results of the synthesized images were shown in the third row. All these results showed that our method can intelligently create liver CT images with tumors based on the healthy liver CT images, and the synthesized diseased images were almost identical to the real ones.
3.2 Quantitative comparison
In this section, we quantitatively compared our method with other seven state-of-the-art medical synthesis methods using the same dataset as ours: (1) atlas-based method[15]; (2) sparse representation (SR) based method; (3) structured random forest with ACM (SRF+)[16]; (4) manipulable object synthesis (MOS)[17]; (5) deep convolutional adversarial networks (DCAN) method[18]; (6) multi-conditional GAN(MC-GAN)[19];(7) mask embedding in conditional GAN (ME-cGAN)[20]. The first four methods were implemented by our group, and the source code of DCAN, MOS, ME-cGAN were downloaded from GitHub (www.github.com/ginobilinie/medSynthesis, www.github.com /HYOJINPARK/MC_GAN, and www.github.com/johnryh/Face_Embedding_GAN ). The results of the quantitative comparison were shown in Table 3, which indicated that our method outperformed the other seven approaches and benefited from attention mechanism, dilated convolution operator, and residual connections.
Table 3 The quantitative comparison between our method and seven other approaches
|
Method
|
Atlas[15]
|
SR
|
SRF+[16]
|
MOS[17]
|
DCAN[18]
|
MC-GAN[19]
|
ME-cGAN[20]
|
our method
|
mean PSNR(dB)
|
45.15
|
49.77
|
55.30
|
60.11
|
58.26
|
59.29
|
61.35
|
64.72
|
3.3 Turing test
To further verify the effectiveness of our method, we did the Turing test. Two experienced radiologists from Shengjing Hospital of China Medical University were asked to classify one hundred liver CT images into two types: real image or synthesized image. The radiologists were not aware of the answer to each image before the Turing test. The one hundred liver CT images consisted of fifty real CT images and fifty synthesized images. The results of the Turing test were shown in Table 4, radiologist #1 made correct judgments for 74% real image slices and 64% synthesized image slices, and radiologist #2 made correct judgments for 84% real image slices and 12% synthesized image slices. The radiologists made correct judgments for most of the real images and maybe psychologically influenced by the existence of a synthesized image, so they made some errors about the real images. Furthermore, the radiologists made difficult judgments for the synthesized images and can’t tell the obvious differences between the real images and the synthesized images. And according to radiologist #1, his most reliable evidence of telling the difference was the color of the tumor region was a little darker than the real ones, which was also the improvement we needed to do in the future. All these results of the Turing test indicated that our method can synthesize liver CT images with a tumor, which were almost identical to the real ones.
Table 4 The Turing test of our method
|
real image
(50 slices)
|
synthesized image
(50 slices)
|
be judged as real images
|
be judged as synthesized images
|
be judged as real images
|
be judged as synthesized images
|
radiologist#1
|
37
|
13
|
18
|
32
|
radiologist#2
|
42
|
8
|
44
|
6
|
3.4 Evaluation of synthetic dataset for medical image segmentation
To evaluate the effectiveness of the synthetic dataset in the training of deep learning models, we used fully-connected network (FCN)[21] to perform the tumor segmentation task in the liver CT images and trained the FCN model using LiTS dataset (images from 131 subjects) and the new dataset obtained by our method (images from 131 real subjects and 865 synthetic subjects). And we used the Dice Index to quantitatively evaluate the performance of the segmentation results from the two trained FCN models. The FCN model trained by the LiTS dataset can provide a Dice value of 0.611 for the tumor segmentation, and the FCN model trained by a new dataset can provide a Dice value of 0.658 for the tumor segmentation. The result indicated that the synthesized liver CT images obtained by the proposed method can effectively enlarge the original dataset, and as the number of images in the dataset increased, the performance of the training of the deep learning model can become better, which resulted in the higher Dice value for the liver tumor segmentation.