Breast cancer is one of the leading causes of death among women around the globe . Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to complement mammography and ultrasound when evaluating breast cancer, particularly when assessing the extent of cancer before surgery. In some high-risk cases, it is also used for screening.
A significant challenge related to the use of DCE-MRI is the lack of standardized imaging protocols . Different MRI scanners use different parameters, which previous research  has shown to drastically alter image appearance, quality, and even radiological interpretation. When the same patient is imaged using a different scanner or even the same scanner with different scanner parameters, the produced MR images may vary significantly . The inconsistencies present in the radio-frequency (RF) coil produce intensity variations in the underlying tissue across the scanned image . Additionally, varying scanner parameters alters the noise distribution of the images. An illustration of the difference in intensity and noise distribution between images obtained from two different MRI scanner manufacturers (GE Healthcare and Siemens) is illustrated in Fig. 1.
The high degree of inter-scanner variation proves to be a large obstacle for the effective usage of DCE-MRI. In the context of radiomics, where a multitude of features are extracted from images for further processing, the features from different modalities may turn out to be incomparable and rendered useless for classification and prediction. The impact of scanner parameters on breast MRI radiomic features was demonstrated in . Variability in images has been shown to have an impact on the training of deep learning as well . Algorithms trained on images from one scanner may not perform well on exams at a different institution that were acquired using a different scanner. Finally, the inconsistency between images from different scanners may affect the outcome of computer-aided diagnosis and also the interpretation by radiologists. The ability to translate between images acquired by different vendors with different scanner parameters would have tremendous positive consequences. It would enable quantitative comparison of image features across different institutions, and it would also improve generalization as deep models trained on one dataset could still perform inference on new datasets generated by different scanners.
In order to address this issue, we frame the problem of mapping between images generated by different MRI scanners as an application of unpaired image-to-image translation. Most of the literature in the domain of MRI preprocessing[4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] has focused on normalizing intensities but does not account for noise patterns. To our knowledge, no one has yet proposed a method for MRI vendor normalization. This process is challenging because it requires both normalizing the intensity and learn the mapping between the noise patterns. In this work, we present a vendor normalization method that attempts to perform intensity normalization as well as noise distribution mapping between MRIs obtained from different scanners. The major contributions of this work can be summarized as follows:
We present a method for MRI vendor normalization that performs unpaired bidirectional translation between DCE-MRIs produced by different scanner models.
We investigate the challenges of the standard CycleGAN approach for normalization of medical images, primarily the difficulty in maintaining the breast shape and structures within the breast between the original image and the translated image. Then, we propose and evaluate two technical solutions to this issue, as described below.
We propose the incorporation of a mutual information loss with the standard CycleGAN architecture in order to ensure that the structure of the breast and dense tissue is maintained.
We propose a modified discriminator capable to preserve the breast shape as well as the dense tissues and evaluate the effect of changing the field-of-view on the performance.
We present and compare the performance of the proposed vendor normalization methods using both quantitative and qualitative approaches.
We highlight how the proposed work can potentially enable the synthesis of larger and richer data-sets which mitigate issues related to class imbalance.
The remainder of the paper is organized as follows. Section II describes the related work. Section III presents details about the dataset, and the proposed methods are detailed in Section IV. Information about training is furnished in Section V and Section VI presents the metrics for the evaluation of the proposed method. Section VII reports the experimental results and discussions. Finally, Section VIII concludes with a summary.
Ii Related Work
Unlike other imaging modalities, MRIs span a wide, non-linear spectrum of raw intensity values. They lack uniformity and often exhibit high variance between subjects. Even within a single subject, intensity variations of 10-40% have been observed. This heterogeneity makes it difficult to train robust medical image analysis algorithms with MRIs effectively.
In response, various statistical approaches have been proposed for MRI intensity normalization. These include histogram equalization [4, 7], intensity scaling based on regions of interest  and landmarks . However, histogram-based methods rely on discrete approximations of intensity distributions, leading to high levels of inexactness . Meanwhile, obtaining a high level of accuracy with landmark-based algorithms requires obtaining multiple landmarks from various tissue types in the image. Designing algorithms to perform this landmark selection task is difficult and time-consuming .
Another limitation of many MRI normalization methods ,  is that they require auxiliary inputs such as segmentation masks. This adds an intrinsic reliance on the models that perform these preprocessing tasks. Alternatively, few technique  attempts to leverage the physics of MR acquisition in order to develop intensity invariant segmentation algorithms. However, using this type of approach requires integrating explicit physics-based embeddings into the segmentation algorithm, thus limiting this system’s ability to generalize to other downstream tasks.
Additionally, some of the methods discussed above [4, 8, 9] attempt to perform intensity transformation between two fixed imaging settings. That is, they make the assumption that the intensity relationship of the tissues is constant between the target group and the reference group, which is not always true . If the intensity standardization needs to be done for images coming from multiple centers, multiple transforming models need to be established. Resultantly, these methods do not have the ability to process new images that are not from an MR image group that has already been included in their training data. This severely limits their usability.
Recently, GANs have been used in a variety of applications to the domain of medical imaging. Yi et al.  presents a review of GANs’ recent applications to the medical domain. Most of the previous work [19, 20, 21] has focused on using GANs for multimodal translation that in turn, improved diagnosis across several modalities (e.g. PET, CT, MRI). Additionally, GANs have also been used to generate synthetic images  to augment training datasets for algorithms that perform downstream tasks—diagnosis, prognosis, segmentation, and registration. Among GANs, CycleGAN has an intrinsic ambiguity with respect to geometric transformations . It does not take care of the anatomical changes in the transformed images since the shape of training data is arbitrary and the standard discriminator model disregard the changes in anatomical structures as it doesn’t effects the realness of the image. Multimodal translation and synthesis in medical imaging using CycleGAN should ensure shape consistency as anatomical structures are crucial in many computer-aided detection of cancer.
Recently, CycleGAN was used for normalizing MRIs across different scanners. Gao et al.  proposed a universal intensity standardization method for brain MRIs using GANs. Dar et al.  also applied CycleGAN for normalization of brain MRI. However, they failed to learn the noise distribution pattern—e.g. noisy halo around the breast. Another work  have tried to solve the problem by introducing a segmentor model along with CycleGAN networks to ensure shape consistency. However, ground truth is needed to obtain shape consistency loss and ground truth of dense tissues is not available in a typical application. Other papers [19, 20, 21] have used cycleGAN for translation across different modalities (e.g. PET, CT and MRI) with some of the same issues present.
In this article, we present a fully unpaired strategy for image translation using cycleGAN. We address previously unsolved issue of maintaining structure of the organ. Since our method does not rely on availability of registered or even paired images, it is applicable to different organs and not only rigid ones where simple registration is possible.
|GE Healthcare (GE)||Siemens (SE)|
Iii Data-set and Pre-processing
In this study, we experimented with DCE MRI images data obtained using GE Healthcare (GE) and Siemens (SE) scanners (1.5 T) in the axial plane. Our database consisted of 124 subjects: 77 were scanned using a GE Healthcare scanner while the remaining 47 were scanned using a Siemens scanner. Each MR volume contains more than 160 2D axial image slices. The top 1% of pixel values in the entire dataset were assigned the value of 255, and the remaining intensities were linearly scaled to the 0-255 pixel range. The data were randomly divided at the patient level, and 75% were used to produce a training set. Out of the remaining images, 10% were kept as a validation set, and the remaining 90% were used as a test set. Only slices from the middle 50% of each patient volume were used in our study. Details regarding the number of slices used for training, testing, and validation are given in Table I.
In this section, we present various frameworks to perform cross-modal translation between MRI images acquired by GE Healthcare (GE) and Siemens (SE) scanners.
We utilize the CycleGAN —a bidirectional image-to-image translation method—for the transformation between the GE and SE MRIs. It consists of two generators and two discriminators . Each generator has a corresponding discriminator, and they are trained in an adversarial setting in which the two networks compete against each other to fool their counterparts. Fig. 2 illustrates the CycleGAN network configuration where, and are training samples from and , respectively. Generator maps from while maps from .
The discriminator network discriminates between the images generated by the generator and the target image while generator tries to improve the quality of the transformed image so that it can fool the discriminator. Similarly, discriminates between images generated by and the target image , while tries to transform effectively enough to fool . The above task is formulated as a min-max optimization problem.
Iv-A1 Network Architectures
The architecture for the generators is adapted from Johnson et al. . The generator consists of an encoder, transformer, and decoder. The encoder uses convolutional down-sampling to shrink the size of the input representation and increase the number of channels. It is followed by a transformation block which retains the size of representation using residual convolution blocks. Finally, a decoder block is used which upsamples the size of representation using deconvolution.
The discriminator network uses a classical PatchGAN 
. It is a fully convolutional neural network that processes overlapping patches of the input image instead of the entire input image. The output of the discriminator is a matrix of binary classifications of whether each patch is real or fake. A standard PatchGAN has a field of view (FOV), or patch size, of. We also experimented with numerous other discriminator architectures with varying FOV. Those results are detailed in Section VII.
The objective function contains two loss terms: adversarial loss and cyclic loss . The adversarial loss  ensures that the generated images belong to the data distribution of the target domain. The adversarial loss is formulated as below:
The generator tries to minimize the above adversarial loss and the discriminator tries to maximize it. However, the adversarial loss alone is not sufficient enough to produce good target images. The adversarial loss will enforce the transformed output to be of the appropriate domain, but will not enforce the input and output to be recognizably the same. Thus an additional cycle-consistency loss is added to the overall objective. The cycle-consistency loss ensures that the translated image looks like the input image by enforcing and to be inverses of each other i.e. and .
The overall objective is given as below where is the weighting factor for cycle-consistency loss.
Iv-B CycleGAN with Mutual Information
The standard CycleGAN architecture detailed above, when used for translation between GE and SE breast MRIs, may produce results which are unable to preserve the breast shape and tissue characteristics. In order to preserve the breast shape and tissue characteristics, we propose to utilize mutual information maximization between the real images and the generated images, as shown in Fig. 3. Our rationale is that while the intensity and texture of the image may change, high mutual information will indicate that the shape of the breast and the structure of dense tissue remained the same which is desired in our application.
In practice, estimation of mutual information in images is challenging as we only have access to samples rather than the underlying distributions[27, 28]. Additionally, previous sample-based estimators are brittle and do not scale well to higher dimensions . Recently, Mutual Information Neural Estimation (MINE)  was introduced to approximate the mutual information using observed samples even when the true distribution is unknown. Their approach also scales to higher dimensions. Hence, we adopted their method to estimate and maximize mutual information. To the best of our knowledge, the proposed model is the first of its kind to utilize mutual information along with adversarial and cycle-consistency loss.
The mutual information is equivalent to the Kullback-Leibler (KL) divergence between the joint distribution,, and the product of the marginal distributions and , as expressed below
where is defined as,
It uses the Donsker–Varadhan (DV) representation  of KL divergence, which leads to the following definition of approximate mutual information:
The approximate mutual information is obtained by maximizing the lower bound of the objective function shown in eq. 7. The maximization is achieved by using a neural network with parameters . The neural network is optimized using gradient descent to characterise a family of functions which ultimately maximizes the lower bound of the above objective.
To enforce and preserve breast shape and tissue characteristics, we propose to include a mutual information loss in the overall objective as specified below.
where is the weight factor for the mutual information loss.
Iv-C CycleGAN with modified discriminator
We experimented with various fields of view (FOV) —the amount of input that effected a single pixel of an output map. Based on the results, we proposed a modification to the discriminator architecture. The proposed modification was able to prioritize the morphological features of the breast tissue during training. The modified discriminator architecture is shown in Fig. 4
. The proposed discriminator classifies smaller patches () of the image to be real/fake instead of 70*70 patches, as suggested in Isola et al. . A smaller patch size encourages the transformation learned by the generator to maintain sharp, high-frequency detail which is required in order to adequately preserve both the overall structure of the breast and the structure of the dense tissue regions inside the breast. Details about the various architectures with different FOV is presented in Appendix A.
Iv-D CycleGAN with modified discriminator + Mutual Information
We also applied the Mutual Information loss to the modified CycleGAN framework obtained by altering the discriminator architecture.
We optimize the network using mean squared error (MSE) instead of cross-entropy as suggested in Mao et al. . As a result, training becomes more stable and higher quality images are produced. Additionally, to prevent the model from oscillation, the discriminator is fed a history of the 50 most recently generated images rather than solely the most recently generated image. Adam optimizer was used to train the network with learning rate , = 0.5, and = 0.999.
Vi Evaluation Metrics
The quantitative evaluation of the transformed images is difficult in the case of unpaired images  as there is no standard/universal metric to evaluate the accuracy of transformed images . Hence, evaluating the quality of synthesized images is an open and challenging problem for which metrics vary depending on the specific needs of the application. Most previously published work relies either on the visual examination of the transformed images by human subjects or some application-specific metrics. Visual evaluation of the transformed image is still the most common and intuitive method for determining the quality of the transformed images.
In this work, the evaluation of our algorithms was done in two ways. First, we performed a combination of quantitative and qualitative analysis to determine the robustness of the transformation. In the quantitative analysis, we manually annotated a breast mask for 20 images from the test set before and after transformation and used these annotations to compute a Dice coefficient between them. A higher Dice coefficient suggests the breast shape was preserved during the transformation while a lower value suggests distortion in breast shape. In order to evaluate the preservation of dense tissue, we performed qualitative analysis through visual observation to determine whether the shape of the dense tissue was preserved or not.
Secondly, we performed an evaluation of the intensity transformation. Specifically, we manually annotated the dense tissue (10 cases) to estimate the mean intensity value before and after translation. The expectation is that while the mean intensities of dense tissue differ significantly between GE and Siemens before the transformation, they should be similar after the transformation.
Vii Results and Discussion
The result of the proposed vendor normalization using CycleGAN is presented in Fig. 6. Qualitatively, it can also be observed that the standard CycleGAN model is unable to preserve the shape of the breast and dense tissue. Our proposed modified discriminator framework performed the best out of all explored algorithms. A surprising result visible in Fig. 6 is that the introduction of mutual information loss was not even able to preserve the shape of the breast. We analyzed this phenomenon further and we found that it was caused by the noise pattern in GE images. Specifically, the mutual information neural estimator (MINE) network tries to maximizes the mutual information by matching the shape of the breast to the noisy “halo” around the breast, and therefore it increases the size of the breast. Similarly, for the Siemens to GE transformation, it maximizes the mutual information by decreasing the shape of the breast. This is illustrated in Fig. 5.
The proposed modified CycleGAN framework was obtained by modifying the discriminator architecture to put more stress on features pertaining to breast tissue. We experimented with various FOV in the discriminator architecture. The effect of various FOV in the performance is presented in Fig. 7. It can be observed that the FOV frequently modifies the dense tissues of the breast. It also modifies the shape of the breast, which is apparent from the lower Dice coefficients (Table II). A FOV, i.e. PixelGAN, has no effect on spatial statistics and is thus unable to learn the mapping between the noise distributions of the two domains. Additionally, the transformed images look extremely pixelated and exhibit a checkerboard pattern. The performance of a FOV was comparatively better than FOV in terms of preserving the shape of the breast as well the dense tissues. However, after visual inspection, it was observed that a FOV preserves the dense tissue better and produces sharper images as compared to . The Dice coefficients confirmed that the FOV was able to preserve the shape of the breast as well. Additionally, the FOV has fewer parameters. It was for all these reasons that was used as the optimal FOV in the proposed discriminator architecture.
|GE to SE||SE to GE|
Quantitative results are presented in Table III. It can be observed that during GE to Siemens translation, the Dice coefficient of the breast masks is the highest for the CycleGAN framework obtained by modifying the discriminator architecture. It is also apparent from the Table III that applying the mutual information loss to proposed discriminator causes a reduction in Dice coefficient value () due to a decrease in the shape of the breast. However, the standard CycleGAN model and its variant with mutual information both have comparable Dice coefficients. This can be explained by both methods’ inability to preserve the breast shape. Similar observations can be made for the translation between Siemens to GE. This confirms that the modified architecture with the field of view of 34*34 results in superior performance.
|GE to SE||SE to GE|
|Std. CycleGAN + MINE||0.89762||0.05103||0.89486||0.03908|
|Proposed Discrim + MINE||0.90815||0.07137||0.89118||0.07063|
In summary, from a qualitative point of view, it was found that the standard CycleGAN along with mutual information leads to the worst result (See Fig. 6) This was also reflected in the quantitative results, where it achieves almost minimum dice coefficient score. On the other hand, the proposed modified CycleGAN framework obtained by altering the discriminator architecture is able to consistently preserve the dense tissue as well as the breast shape. These observations also align with the quantitative results presented in Table III.
In order to evaluate the intensity transformation, we manually annotated the dense tissue (10 cases) to estimate its mean intensity value before and after translation. The result is presented in Fig 8 where, Fig. 8(a) illustrates the mean intensity distribution of the dense tissue in GE and Siemens before the transformation. It can be observed from Fig. 8(b) that the mean intensity distribution of the original GE is comparable to the transformed Siemens. A similar observation can also be made from Fig. 8(c) for the original Siemens and transformed GE. This demonstrates that the proposed method was able to successfully adjust the intensity of the image as it pertains to dense tissue. It should also be noted that the proposed method not only perform the intensity adjustment but also learns the mapping of noise which is a crucial aspect of vendor normalization. The proposed vendor normalization method will thus potentially increase the robustness of downstream models which do not have access to adequate training data from multiple vendors by synthesizing larger and richer data-sets which will mitigate issues related to class imbalance.
In this article, we have shown that a fully convolutional neural network can be trained to perform vendor normalization by translating between DCE-MRI images generated from different scanners (GE Healthcare & Siemens). In contrast to previous works, our proposed method not only performs intensity normalization but also learns the noise distribution pattern.
Our evaluation showed that the standard CycleGAN when applied to this task, while matching the desired intensity of images, it struggles with recreating the shape of the breast and shape of the dense tissue. This is caused by the limited constraint on the images generated by the GANs and in turn, liberty that it takes to freely generate breast images. In response to this, we proposed two solutions. The first one was to incorporate mutual information into the loss function. Our rationale was that it would ensure that the structure of the breast is maintained between the input and the output of the generator. This first solution did not solve the problem due to a very specific characteristic of the data, which was a noise “halo” around the breast. Incorporating mutual information into a CycleGAN is not a trivial task and we believe that the method of doing so proposed in this paper will be helpful for other similar tasks in medical imaging and beyond. The second solution to the problem of maintaining the structure of the breast that we propose in this paper is a modification to the discriminator. This solution was highly successful for this task as verified by our experiments.
Our study had some limitations. One limitation of this work is that it provides the capability of translation using 2D images only. However, while some effort in network design and parameter optimization is needed, the proposed methods naturally lend themselves to 3D networks. Another limitation is that we tested our algorithm on two vendors only and the number of patients was limited. While we still believe that the dataset used in this study is very representative of the real-life problem faced in analyses of breast MRIs, further studies are needed to show that the proposed method generalizes beyond the data presented here. In summary we proposed a framework for normalization of breast MRIs based on CycleGAN. In response to the challenges with applying this framework, we proposed technical innovations that allowed for this framework to be successfully applied to the task at hand. While the framework was tested using breast MRIs, it naturally lends itself to other medical imaging tasks where no matched data is available.
Appendix A Architectures for discriminator
Discriminator architectures with various field of view is presented in this section. Each model uses a convolution after the last layer to produce a 1-D output of size . InstanceNorm layer was not applied to first layer in each of the architecture. The slope for LeakyReLU was 0.2.
The authors would like to thank Mr. Mateusz Buda for the insightful discussions.
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