Structural magnetic resonance imaging (sMRI) is an essential tool for the clinical care of patients providing details about the anatomical structure of the brain. Segmenting a structural MRI is an important processing step to provide regional tissue volumes and enables subsequent inferences about tissue changes in development, aging and as well as disease. With increasing number of large scale studies and screening programs to detect signs of the disease in early stages it will affect the number of medical images have to be analyzed. Therefore we need fast and accurate enough tools for big data oriented medical research. It will also provide significant benefits for radiologists, neurologists and patients in the medical settings.
Manual labeling is currently gold standard for all kinds of segmentation of medical images. But labeling time cost of an one entire high resolution structural MRI of brain image is about week for an expert which is not acceptable in large scale studies. Furthermore, labeling is usually performed on slices which makes it more consistent along the slice direction. While multi-modal images (T1-weighted, T2-weighted, FLAIR) can provide better tissue contrast to facilitate segmenting, manually performing the same is not only tedious but also more complicated. Therefore, automated methods for segmenting and parcellating the sMRI images are very popular today. Most common tools with strong support community and high success rates MIKHAEL2017 in internal validation are FreeSurfer Desikan2006968 ; Fischl01012004 ; destrieux2010automatic , BrainSuite shattuck2002brainsuite , BrainVISA Geffroy11 . These softwares primarily employ probabilitic methods with priors to solve the problem.
Recently, with the success of end-to-end deep learning approaches using convolutional neural networks (CNNs) identification and segmentation of visual imagery, several new common approaches based on fully convolutional networkslong2015fully , U-Net ronneberger2015u ; cciccek20163d
, Pyramid-long short term memory (LSTM)stollenga2015parallel , dilated convolutions yu2015multi have been developed for segmentation of medical images. These methods can combine multiple sMRI image modalities as input to use different tissue contrast and have the ability to produce fast and accurate prediction. However these methods require substantial amounts of training data, which is often difficult to obtain due to the lack of enough labeled data in medical field.
Fully convolutional networks are a type of CNN where fully connected layers have been replaced by convolutional layers. It allows to predict specific area or volume instead of running CNN with fully connected layers pixel-wise or voxel-wise. This approach has recently been used for segmentation of subcortical regions DOLZ2017 .
U-Net is a generative ladder network consisting of encoder and decoder. This kind of network has been used for visual cortex parcellation 7950666 . In this article, the authors worked with 2D slices and also added additional encoder network for atlas prior, which increases the number of parameters and requires some prior information.
Pyramid-LSTM is a deep neural network based on convolutional LSTM (C-LSTM) layers. To work with 3D volumes it requires 6 C-LSTM layers working with 2D images to scan volume in 6 directions after which it combines output of these C-LSTMs and uses pixel-wise fully connected layers to provide final prediction. This architecture has been used for brain tissue segmentation in MRI images and segmentation of neuronal processes in electron microscopy images.
From simple Fully-convolutional to Pyramid-LSTM, the complexity of neural network architecture is increased with skip-connections in U-Net or C-LSTMs in Pyramid-LSTM. But our MeshNet fedorov2017end has a simple feedforward fully convolutional arhitecture with dilated kernels yu2015multi and we successfully demonstrated its use in gray and white matter segmentation. But this task is simple compared to whole brain atlas segmentation containing more than 50 labels. The atlas segmentation enables more detailed comparing of regional growth curves in gray matter densities sowell2003mapping ; tamnes2009brain or differences in regional gray matter volumes between healthy controls and patients, for example autism redcay2005brain , schizophrenia van2016subcortical and okada2016abnormal .
In this work we extend our MeshNet model to perform atlas segmentation task with 50 cortical, subcortical and cerebellar labels obtained from Freesurfer on open Human Connectome Project (HCP) data and subsequently evaluate the trained models performance in differentiating regional volumes between healthy controls and patients with schizophrenia compared to those obtained using FreeSurfer using a previously published multi-site functional bioinformatics informatics research (fBRIN) data.
2 Materials and Methods
2.1 Feedforward and Convolutional Neural Networks
, known as activation function.
In case of Convolutional Neural Networks instead of matrix multiplication we are using convolution 2 with some kernel .
can be also defined by pooling as max poolingZhouChellappa
, normalization as batch normalizationioffe2015batch or dropout srivastava2014dropout layers.
Convolutional neural networks has some advantages Goodfellow-et-al-2016
compared to MLP. First advantage is local or sparse connectivity. If in MLPs we are connecting every input with every output, here we are applying kernel to only small region of input defined by kernel size, but in deeper layers neurons still indirectly connected to most part of input. How large neuron is connected to input is determined by receptive field, depends on neural network hyperparameters and architecture. Overall local connectivity reduces number of parameters, computational complexity and memory requirements. Second advantage comes from that we are using same kernel over all input, known as parameter sharing. Third advantage is equivariance to translation due to convolutional nature. Other transformations as rotation and scaling requires additional techniques.
2.2 Convolutional Neural Networks for dense prediction
2.2.1 Fully convolutional networks
Fully convolutional neural networks (FCNN) long2015fully are the type of convolutional neural networks where fully connected (FC) layers is replaced by convolutional layers. Fig. 1 visually explains difference between them. Output of FCNN is heatmap, where in 2D case each pixel suggests specific label, whenever neural network with FC layers produces just one label. This kind of networks is suitable for end-to-end learning and pixel-to-pixel segmentation.
U-Net is advancement of fully convolutional networks by adding decoder part to encoder part and connections between them. Example of U-Net architecture is shown on Fig. 2. Encoder uses convolutional layers to shrink image information to compact representation and then decoder using upsampling layers and concatenation connections restores output to initial size of input. Connections are needed to connect representation of decoder with encoder from higher resolution features to produce upsampling, or by another words it allows to flow higher resolution information. U-Net, compared to FCNN, allows to produce segmentation with same size as input image.
2.2.3 Convolutional Neural Network with dilated kernels
Discrete volumetric convolution can be written as
where , , are kernel bounds on , and axis respectively and is the point at which we compute the convolution. We can extend it to make L-Dilated convolution as:
where is dilation factor, is -dilated convolution.
First dilated convolutions using CNNs was introduced in article yu2015multi . Using L-Dilated convolution in CNNs can allow drastically increase receptive field of the neuron, but preserve small amount of parameters. In traditional CNNs to have same receptive field we possibly have to increase depth of neural network or change the kernel size. But this will generate an increased number of parameters to fit, especially in 3D case. Dilated kernels also allows to control receptive field of a neuron while preserving the same number of parameters and depth of neural network.
MeshNet fedorov2017end is feed-forward convolutional neural network with dilated kernels. Every layer of this network create same size feature maps and output in the end as input. Architecture has been inspired by context module of yu2015multi and has been extended to 3D case.
. We also tried to use batch normalization before and after activation function for faster convergence. As activation function we are using ReLU. For weight initialization we have tried identity initialization fromyu2015multi and also xavier initialization glorot2010understanding . To get prediction we are using LogSoftMax activation function after last layer and afterwards maximum value to determine label of the voxel. But overall architecture is the same and scheme of architecture is shown on a Fig. 3
. To train neural network we are using variation of stochastic gradient descent Adamkingma2014adam
to automatically adjust learning rate. For a loss function we have chosen categorical cross-entropy function.
Our workflow with Meshnet is shown in Figure 4. Training worklfow consist from nonoverlap and gaussian subvolume sampling of input T1 or T2 volumes, feeding them to MeshNet, obtaining subvolume prediction by taking argmax of LogSoftMax class channel in every voxel. Final segmentation for testing is obtained by voxel-wise majority voting on accumulated prediction from subvolumes. But last steps as argmax on LogSoftMax and majority voting can be modified by more complicated approaches.
For atlas segmentation we reduced volumetric shape of input to from as we used in our previous work fedorov2017end to fit model in GPU memory and have more features maps in every layer due to increased complexity of the task. Final hyperparameters of the model is shown in Table 1.
|1||3D DC + BN + ReLU||1||1|
|2||3D DC + BN + ReLU||1||1|
|3||3D DC + BN + ReLU||1||1|
|4||3D DC + BN + ReLU||2||2|
|5||3D DC + BN + ReLU||4||4|
|6||3D DC + BN + ReLU||8||8|
|7||3D DC + BN + ReLU + 3D Dropout(p)*||1||1|
|Overall number of parameters||825567|
equal to 1 or 2 if we are using T1 or T1 and T2 respectively. The output of th 8th layer is 50 feature maps, equal to number of regions in our atlas. 3D DC stands for volumetric dilated convolution, BN — Batch Normalization, ReLU — Rectified Linear Unit. *In the 7th layer models can have 3D dropout withand for additional regularization or don’t have it.
For measuring the performance of the models we are calculating DICE coefficient taha2015metrics for measuring spatial overlap and Average Volume Difference (AVD) mendrik2015mrbrains for validating volume values. DICE coefficient is defined as
where is the prediction, — the ground truth, — the true positive value, — the false positive value, — the false negative value. The Average Volume Difference is defined as
where is the prediction volume by model and is the ground truth volume. This metric is sensitive to point positions.
We are also using Macro-averaging zhang2014review approach for comparing overall performance of prediction for different number of subvolumes. Macro-averaging for metric (DICE, AVD) is defined as:
where is number of classes and — metric for class .
2.4.1 Human Connectome Project dataset
The Human Connectome Project (HCP) VANESSEN201362 is an open-access dataset with multi-modal brain imaging data for healthy young-adult subjects. From this dataset we are using T1 and T2 of subjects with slice thickness . These T1 and T2 have been resliced to and padded with zeros to a volume with dimensions , also min-max normalization has been applied. Dataset has been splitted on volumes for training, — validation and — testing.
2.4.2 Function Biomedical Informatics Research Network dataset
The Function Biomedical Informatics Research Network (FBIRN) dataset KEATOR20161074 is an open-access dataset includes multi-modal structural MRI, fMRI, DTI, behavioral data and clinical, demographic assessments. We used T1-weighted MRI scans from FBIRN Phase III and atlas segmentation labels obtained using FreeSurfer 5.3 as in HCP. T2-weighted MRI scans had just axial slices therefore we decided not to use them. Data have been collected on 3.0 Tesla MRI scanners on GE and Siemens platforms at different sites. Overall dataset consist from subjects of which are patients with schizophrenia and — healthy subjects. Subjects are in the age between -. of the subject are males, — females and — unknown. All data has been resliced to thickness, padded with zeros to and min-max normalized to be the same as HCP dataset. For fine-tuning we used 7 subjects (1 subject per site) as training dataset and another 7 subjects as validation dataset therefore subjects are testing set.
2.5 Statistical meta-analysis
In structural studies voxel-based morphometry analysis of MRI images have been used to compare regions of interests (ROIs) in the brain between patient and healthy controls, to find ROI with possible abnormalities. Some previous works are van2016subcortical and okada2016abnormal , related to schizophrenia as FBIRN dataset. Therefore to compare FreeSurfer with proposed method we perform similar meta-analysis.
First, we defined univariate linear regression model for prediction of ROI’s volume:
where is value between to , is for male and — female, is sum of all brain ROIs, and are interactions of and with and
is one-hot encoding ofsites. Volume is measured in number of voxels. This step is adjusting ROI’s volume for age, gender, brain volume and sites.
Secondly, we calculated residuals between true value of ROI’s volume and predicted. Then linear model for repeated measurements ANOVA is defined:
where is residual for ROI after first step, is method used to compute : FreeSurfer or MeshNet, is healthy subject or patient with Schizophrenia, — interaction of and .
To compare methods we inspected significance of covariates and and also Cohen’s d was computed on ROI’s volume residuals after first step between groups.
First we summarize performance of MeshNet on HCP dataset, then present results of a fine-tuned for FBIRN dataset model, trained before on HCP dataset, and statistical comparison of MeshNet with FreeSurfer.
3.1 Segmentation quality and speed performance
3.1.1 Speed performance
Since our model predicts for subvolumes, we measured how long it takes to create whole MRI image segmentation and how well it performs with the amount of subvolumes of , , , , and . Considering Figure 5, model can offer acceptable segmentation with subvolumes running in average 48 seconds for T1 model and in average 50 seconds for T1 and T2 model on GeForce Titan X Pascal 12Gb.
3.1.2 Segmentation quality on HCP
. The model with T1 and T2 as input shows best overall performance. Additional regularization of T1 and T2 model with volumetric dropout before last layer in some classes shows better scores than nondropout model, but model can, for example, in precentral cortex with probability of dropout 0.125 or lateral orbitofrontal cortex with probability of dropout 0.25 can perform poorer than nondropout T1 model, therefore nondropout more stable in overall performance. Same is applicable for T1 model with dropout. Segmentation examples prepared using AFNIcox1996afni for T1 and T1, T2 nondropout models are shown in Figures 8 and 9.
3.1.3 Segmentation quality on FBIRN
Performance on testing subject from FBIRN dataset is shown in Figure 10 and Figure 11. For comparing its performance we also show results on HCP dataset. Segmentation examples is shown in Figures 12. To remind FBIRN dataset has not just healthy subjects, but also patients with schizophrenia. Model shows similar performance by FBIRN dataset’s sites in Figure 13 and Figure 14.
3.2 Statistical comparison
For statistical comparison, first, to prepare data we excluded from FBIRN dataset 14 subjects we had used for fine-tuning as training and validation set and subjects without gender. Then split most of ROIs on right and left hemispheres due disease could affect just one side of brain, calculated for each ROI’s volume and whole brain volume as number of voxels. We ended up with subjects which are by gender females and males and by group healthy controls and patients with schizophrenia. Age is still between 18 to 62. Finally, we performed meta-analysis, described in Section 2.5.
Repeated measurements ANOVA showed that in ROIs (Figure 15) just is significant, therefore it doesn’t matter which method is used and both methods explains group differences. In regions (Figure 16) also interaction is significant, means methods have different slopes, but doesn’t mean that both explain group differences. The covariates and aren’t significant and therefore no differences are in regions (Figure 17). In last regions (Figure 18) the covariate isnt significant, but interaction is significant, means that slopes of method are intercepted. After analyzing Cohen’d we found that in regions Cohen’d of Meshnet is 2 times greater than for FreeSurfer and in regions otherwise. But in most cases of 94 regions Cohen’s d has same direction.
In this paper, we investigated MeshNet as a tool for atlas segmentation of a human MRI brain image trained on a big dataset from the labels obtained using FreeSurfer. Proposed model shows outstanding speed for direct producing of atlas segmentation from raw data, comparable results in segmentation and most important that MeshNet is suitable solution for statistical meta-analysis. Furthermore, proposed model can utilize straightforward second modality T2 as input which leads to better segmentation quality.
Applied to FBIRN dataset MeshNet yeilded similar segmentation quality as on HCP dataset even we just used 7 brains from each site to fine-tune. It should be noted that FBIRN is harder dataset due different MRI machine settings in each site, containing MRI images with rotation, contrast and patients with schizophrenia. Therefore MeshNet is suitable for transfer learning solutions.
4.2 Hyperparameters, training, testing and fine-tuning of Deep Neural Network
To find best model of our network for atlas segmentation we have tried different number of features maps in each layer. From , , , and feature maps per each layer was the optimal number getting the lowest cross-entropy loss. The weight initialization with xavier showed faster convergence and lower cross-entropy loss than with identity from yu2015multi . Batch normalization has showed lower cross-entropy loss if it is before activation function than if it’s after, but it was conversely in gray matter and white matter segmentation task.
Training and testing was performed using nonoverlap and Gaussian distribution subvolume sampling. Nonoverlap sampling was used to be sure we cover whole brain. Gaussian distribution was used due brain is located mostly in the center of MRI image. The center of Gaussian distribution, first, was the middle of the volume, but for better sampling, except model testing step, we used center mass based on the training set. It was located in which lowered our cross-entropy loss. For std of Gaussian distribution we chose due lower cross-entropy loss, before it was
. One training epoch wassubvolumes and model was validated on subvolumes. For providing results in Section 3.1.2 T1 model is epoch old and with dropout and are and epochs respectively, T1 and T2 model — , with dropout — and dropout — . Models with dropout takes more time to train, as expected.
To fine-tune for FBIRN dataset the weights of pretrained on HCP dataset network we run same pipeline for training on HCP, but we reduced learning step of Adam to . We didn’t freezed any earlier layers, due dataset contains some rotations and brains of patients with schizophrenia. One fine-tuning epoch consisted from subvolumes and same amount we used for validation. The FBIRN results were provided in Section 3.1.3 with model fine-tuned on subvolumes.
5 Conclusions and future work
Convolutional Neural Network is a very powerful tool that most likely can solve segmentation problem in neuroimaging but also reduce time needed for processing of large dataset. Therefore the purpose of our work was to create a uncomplicated as U-Net, powerful, generalizable from imperfect labeling, utilizing different neuroimaging modalities, fast and parameter-efficient model. The evidence we got through first work for gray matter and white matter segmentation and this continuation leads that MeshNet is capable for most our needs. Comparing MeshNet performance in statistical meta-analysis showed it as useful tool for large-scale studies. Next each step of modification need careful fine-tunning of hyperparameters and network architecture but the most important evaluating it by performing large-scale studies.
This work was supported by NSF IIS-1318759 and NIH R01EB006841 grants. Data were provided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. FBIRN dataset used for this study were downloaded from the Function BIRN Data Repository (http://fbirnbdr.birncommunity.org:8080/BDR/), supported by grants to the Function BIRN (U24-RR021992) Testbed funded by the National Center for Research Resources at the National Institutes of Health, U.S.A.
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