Introduction

Breast cancer is the most common cancer in women. In the USA, 40,610 women died due to breast cancer in 2017 [1]. Early detection and treatment are very important for breast cancer patients since 95% of patients with early breast cancer can be cured completely [2]. Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has become an established clinical imaging modality for diagnosis and staging of breast cancer [3, 4]. The sensitivity of breast DCE-MRI is higher than that of mammography, which is the standard screening modality. Especially in dense breast, the sensitivity has been improved from 33–59% with mammography to 71–94% with DCE-MRI [5,6,7,8,9]. However, the specificity of DCE-MRI, which is typically between 30–70%, is lower than that of mammography [10,11,12,13,14].

A computer-aided diagnosis (CAD) scheme [15] is one of the solutions to improve the specificity of breast MRI. The CAD scheme presents the likelihood of malignancy for a lesion on medical image as a “second opinion” in order to assist radiologists’ diagnosis [15,16,17,18]. In our previous study, we developed the CAD scheme for distinguishing between benign and malignant masses on breast DCE-MRI [19]. The CAD scheme was based on the conventional method with the handcrafted features and a classifier. In the CAD scheme, mass region was segmented from DCE-MRI images. Objective features were then extracted from the segmented mass region to distinguish between benign and malignant masses. Therefore, there was a problem that classification performance was strongly dependent on the segmented mass region.

Recently, deep convolutional neural networks (DCNNs) such as AlexNet, ZFNet, VGG16, and GoogLeNet have been applied to classification tasks [20,21,22,23]. The DCNNs have shown greater classification performances than the conventional methods with the handcrafted features and a classifier in an ImageNet Large Scale Visual Recognition Competition (ILSVRC) [24]. The DCNN can extract complex multi-level objective features from input images due to self-learning ability without the segmentation of target [25,26,27]. Therefore, there is not a problem that the classification performance is influenced from the segmented region. As with many studies [18, 28,29,30,31], the classification accuracy of our previous CAD scheme based on the conventional method might be improved by using the DCNN. The well-known DCNN models such as AlexNet, ZFNet, VGG16, and GoogLeNet were constructed for general images with RGB channels. Therefore, those models can be inadequacy in the classification task for medical images with grayscale channel.

The purpose of this study was to determine the optimum architecture of the DCNN models for distinguishing benign from malignant masses on breast DCE-MRI using Bayesian optimization [32,33,34,35]. In this study, we first determined a baseline DCNN model from well-known DCNN models in term of classification performance. The optimum architecture of the DCNN model was clarified by changing the hyperparameters of the baseline DCNN model such as the number of layers, the filter size, and the number of filters using Bayesian optimization. The usefulness of the optimized DCNN model was evaluated by comparing with conventional DCNN models.

Materials and Methods

The use of the following database was approved by the Institutional Review Board at Ritsumeikan University. The database was stripped of all patient identifiers.

Materials

Our database consisted of 56 DCE-MRI examinations—each of which contained five sequential phase images—that were obtained from 56 patients (mean age: 55.8 years, age range: 20–82 years). These DCE-MRI images were acquired with a 3.0 T MR scanner at Hokuto Hospital (Obihiro, Japan) from October 2009 and July 2015. The patients were excluded if they had undergone breast surgery in the past, size of mass was more than 5 cm. It included 30 malignant and 26 benign breast masses. Table 1 shows the patients’ clinical information. All masses underwent 10 G vacuum-assisted biopsy and/or surgical specimen. After the injection of a contrast agent, four post-contrast series of 3D MRI scans and data acquisitions were sequentially performed after a duration of 0 min, 1 min, 2 min, and 4 min. The one pre-contrast and the four post-contrast series generated images with a spatial resolution of 0.7 × 0.7 × 1.2 mm3, with a data matrix of 512 × 512 pixels. Figure 1 shows an example of pre-contrast and four post-contrast DCE-MRI images. Each of five image scan series consisted of 150 image slices.

Table 1 Patients’ clinical information
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Fig. 1
figure 1

Example of DCE-MRI images with a malignant mass before injection of a contrast agent, and after a duration of 0, 1, 2, and 4 min

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Determination of Baseline DCNN Model

To optimize the architecture of DCNN model for distinguishing between benign and malignant masses on DCE-MRI images, we first determined a baseline DCNN model from AlexNet, ZFNet, VGG16, and GoogLeNet in terms of area under the receiver operating characteristic (ROC) curve [36]. Here, we briefly described those DCNN models below.

AlexNet consists of five convolutional layers, three max-pooling layers, and three fully connected layers including cross channel normalization layer, rectified linear unit (ReLU) function, and dropout. The convolutional layer and the max-pooling layer play a role of feature extractor, whereas the fully connected layer plays a role of classifier. The first convolutional layer has 96 filters of size 11 × 11 with a stride of four pixels and padding with two pixels. The second convolutional layer has 256 filters of size 5 × 5. The third, fourth, and fifth convolutional layers have 384, 384, and 256 filters with size of 3 × 3, respectively. The number of the units in the first and second fully connected layer is 4,096, whereas that of the units in the third fully connected layer is same as the number of the classes. In this study, the number of units in the third fully connected layer is two (Benign or Malignant).

ZFNet is similar architecture to AlexNet. The difference between ZFNet and AlexNet is only filter size and stride in first convolutional layer. The filter size of the first convolutional layer in ZFNet is 7 × 7, whereas the stride is two pixels. The other parameters of ZFNet are same as AlexNet.

VGG16 consists of 13 convolutional layers with filter size of 3 × 3, and three fully connected layers including ReLU function and dropout. The configurations of fully-connected layers in VGG16 are the same with AlexNet.

GoogLeNet consists of 22 layers with nine inception layers and one fully connected layer. The inception layer has multiple convolution filters [23].

Optimization of DCNN Architecture with Bayesian Optimization

After the determination of baseline DCNN model with the highest area under the ROC curve (AUC), the hyperparameters such as the number of the convolutional layer, the number of filters, and the filter size were optimized in the baseline DCNN model using Bayesian optimization with Gaussian process [32,33,34,35]. The Bayesian optimization is an algorithm for optimizing hyperparameters in a machine learning. Table 2 shows the search range for each hyperparameter in the DCNN model. When the number of the convolutional layer was − 4, it means to remove the final and the fourth from the last convolutional layer in the baseline DCNN model. On the other hand, when the number of the convolutional layer was + 4, it means to add four convolutional layers after the final convolutional layer. With the number of the convolutional layer, the number of the max-pooling layer, and the number of the fully connected layer were 0, the configuration of the DCNN model was same as the baseline DCNN model.

Table 2 Candidate values for each hyperparameter
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In the Bayesian optimization, four different combinations of hyperparameters were first determined by selecting search value randomly in each hyperparameter. The DCNN model with each combination was then trained independently. With a Gaussian process based on the classification errors for each DCNN model, the combination of hyperparameters was updated to reduce the classification error. By repeating this process 100 times, the optimal combination of hyperparameters was founded efficiently.

Training and Testing of DCNN

The DCNN model was developed and evaluated using MATLAB 2019a on a workstation (CPU: Intel Core i7-7820X processor, RAM: 128 GB, and GPU: NVIDIA GeForce GTX 1080Ti).

A k-fold cross validation method [37] with k = 3 was utilized for the training and testing of the DCNN model. In the method, 56 patients were randomly divided into three groups (A, B, C) so that the number of patients was approximately equal. A group was used for test dataset, whereas the remaining two groups were used for training dataset. This process was repeated three times until every group had been used for test dataset.

The ROIs which include an entire mass were selected from each DCE-MRI image by an experienced radiologist (12 years of experience devoted in breast image diagnosis). For augmenting each training data, each ROI was flipped horizontally and cropped [38] randomly eight times. Thus, the total number of training samples was increased by 16 times. A stochastic gradient descent (SGD) was employed to minimize the loss between the output of the proposed DCNN model and the corresponding teacher signal.

Evaluation of Classification Performance

The classification accuracy, the sensitivity, the specificity, the positive predictive value (PPV), and the negative predictive value (NPV) [39] of the DCNN model were evaluated by using the ensemble average from the testing datasets over the threefold cross validation method. ROC analysis [36] was also used for evaluation of classification performance.

Results

The baseline DCNN model was first determined from AlexNet, ZFNet, VGG16, and GoogLeNet in terms of the AUC. Here, the learning rate, the mini-batch size, and the number of epochs were given by 0.0001, 3, and 15, respectively. The AUC for ZFNet was 0.889, showing to be greater than those for AlexNet (0.867, P = 0.302), VGG16 (0.800, P = 0.050), and GoogLeNet (AUC = 0.827, P = 0.080). Therefore, ZFNet was determined as the baseline DCNN model.

The hyperparameters in the determined baseline DCNN model were optimized using Bayesian optimization. Tables 3 and 4 show the optimal architecture and the parameters determined by Bayesian optimization when each group was used for testing dataset, respectively. The average AUC of the determined DCNN models for three test datasets was 0.945.

Table 3 Optimized DCNN architecture determined by Bayesian optimization
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Table 4 Optimized hyperparameters relating to learning determined by Bayesian optimization
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Figure 2 compares the ROC curve for the proposed DCNN model with those for AlexNet, ZFNet, VGG16, and GoogLeNet. The AUC for the proposed DCNN model (0.945) was significantly higher than those for the other four DCNN models (AlexNet: 0.867, P = 0.015; ZFNet: 0.889, P = 0.026; VGG16: 0.800, P = 0.002, GoogLeNet: 0.827, P = 0.006). Table 5 shows average classification accuracy among five different DCNN models. All evaluation indices for the proposed DCNN model was the highest among the five different DCNN models.

Fig. 2
figure 2

Comparison of the receiver operating characteristic (ROC) curves between proposed DCNN model, AlexNet, ZFNet, VGG16, and GoogLeNet

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Table 5 Comparison of classification accuracy among five different DCNN models
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Figure 3 shows example of correctly classified cases and incorrectly classified cases in DCE-MRI images at 1-min post-contrast. The characteristics of masses incorrectly classified by the proposed DCNN model were as follows: (1) small masses (2 cm or lower in size), (2) malignant masses with regularity in shape, and (3) benign masses with irregularity in shape.

Fig. 3
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Example of correctly classified cases and incorrectly classified cases in DCE-MRI images at 1-min post-contrast

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Discussion

To investigate the usefulness of the proposed DCNN model, we compared with the classification performance with our previous method based on the handcrafted features and a classifier [19]. In the previous method, ROI which included an entire mass was selected manually on the DCE-MRI image. The mass region was determined automatically by applying Otsu’s method [40]. Quadratic discriminant analysis (QDA) was employed to distinguish between benign and malignant masses. The four handcrafted features were used for the input of the QDA. With the previous method, the average classification accuracy, the sensitivity, the specificity, the PPV, and the NPV were 75.0% (42/56), 76.7% (23/30), 73.1% (19/26), 76.7% (23/30), and 73.1% (19/26), respectively. Figure 4 compares the ROC curve for the proposed DCNN model with that for the previous method. The AUC for the proposed DCNN model was significantly greater than that for the previous method (0.810, P = 0.01). These results would imply that the features extracted automatically from the proposed DCNN model were more useful for distinguishing between benign and malignant masses when compared with handcrafted features manually obtained in our previous method.

Fig. 4
figure 4

Comparison of the receiver operating characteristic (ROC) curves between the proposed DCNN model and the previous method

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With the proposed DCNN model, the classification accuracy, sensitivity, specificity, PPV, and NPV for 34 masses smaller than 2 cm were 88.2% (30/34), 84.6% (11/13), 90.5% (19/21), 84.6% (11/13), and 90.5% (19/21), whereas those for 22 masses larger than 2 cm were 100% (22/22), 100% (17/17), 100% (5/5), 100% (17/17), and 100% (5/5). We believe that the proposed DCNN model can reduce the number of unnecessary biopsies for masses larger than 2 cm. Patients with masses smaller than 2 cm which are early lesions will be able to undergo follow-up at a short interval. The classification accuracy for those masses might be improved by introducing the differences in growth speed between benign and malignant cases into the proposed method[41,42]. However, further studies are required by use of large data sets to evaluate the computerized method for analysis of changes over time.

In this study, a strategy for optimizing the hyperparameters in the DCNN model was proposed. It is very difficult to construct suitable DCNN model for classification tasks from scratch, because the combination of hyperparameters in the DCNN is infinite. In the proposed strategy, we determined baseline DCNN model from well-known DCNN models, and then optimized architecture and the other parameters of the baseline DCNN model for breast mass classification task using Bayesian optimization. With this strategy, we could easily construct suitable DCNN architecture according to tasks. In the fact, this study has shown that the proposed DCNN model achieved better classification accuracy than that of our previous method and well-known DCNN model. Therefore, we believe that this strategy is effective for optimizing DCNN architecture and its parameters in classification task.

There are some limitations in this study. We used only 56 patient data in this study. Thus, we need to evaluate the strategy for optimizing the hyperparameters and the proposed DCNN model in the further study by using larger dataset. Other limitation is that the proposed DCNN model used two-dimensional (2D) ROIs as the input. In clinical practice, radiologists usually diagnose by considering three-dimensional (3D) information on DCE-MRI. Therefore, 3D-based DCNN model might be more appropriate than 2D. However, 3D-based DCNN model has a lot of parameters to train and requires a large number of training data. In this study with a small dataset, 2D-based DCNN model was employed to distinguish between benign and malignant masses. Finally, the DCNN model determined by the Bayesian optimization might not yield the best classification accuracy because the Bayesian optimization does not evaluate all combinations of hyperparameters. However, we believe that Bayesian optimization is useful for effectively determining appropriate hyperparameters of the DCNN model from infinite combinations.

Conclusion

In this study, we developed the CAD scheme to distinguish benign from malignant masses on breast DCE-MRI images by use of the optimal DCNN model determined with Bayesian optimization. The proposed DCNN model achieved high classification accuracy for masses and would be useful in differential diagnoses of masses as a diagnostic aid.