Glioma Grade Predictions using Scattering Wavelet Transform-Based Radiomics

Glioma grading before the surgery is very critical for the prognosis prediction and treatment plan making. In this paper, we present a novel scattering wavelet-based radiomics method to predict noninvasively and accurately the glioma grades. The multimodal magnetic resonance images of 285 patients were used, with the intratumoral and peritumoral regions well labeled. The wavelet scattering-based features and traditional radiomics features were firstly extracted from both intratumoral and peritumoral regions respectively. The support vector machine (SVM), logistic regression (LR) and random forest (RF) were then trained with 5-fold cross validation to predict the glioma grades. The prediction obtained with different features was finally evaluated in terms of quantitative metrics. The area under the receiver operating characteristic curve (AUC) of glioma grade prediction based on scattering wavelet features was up to 0.99 when considering both intratumoral and peritumoral features in multimodal images, which increases by about 17% compared to traditional radiomics. Such results shown that the local invariant features extracted from the scattering wavelet transform allows improving the prediction accuracy for glioma grading. In addition, the features extracted from peritumoral regions further increases the accuracy of glioma grading.


I. INTRODUCTION
liomas are the most common primary malignant tumors of the central nervous system (CNS), which have high incidence, recurrence, mobility and mortality rate, and how to treat the gliomas effectively is still a challenge. Generally, Gliomas can be classified into low-grade (LGG) and high-grade (HGG) ones [1]. Different grades correspond to Y. Zhu is with the CNRS UMR5220, Inserm U1206, SA Lyon, Université de Lyon, 69000, France. different surgical plans and radiotherapy or chemotherapy strategies. Therefore, accurate grading prediction plays an important role in the treatment-decision making, personalized patient management, and the prognostic evaluation. Currently, biopsy or histopathological assessment after surgery is considered the golden standard for glioma grading [2]. However, such grading means is invasive, time-consuming, painful and useless for those patients not suitable for the surgery. Therefore, developing a noninvasive strategy for grading gliomas precisely is essential.
Medical imaging, especially magnetic resonance imaging (MRI), is a promising noninvasive tool for characterizing the gliomas. The researches showed that contrast-enhanced T1-weighted imaging (T1-CE), diffusion-weighted imaging (DWI) and arterial spin labeling (ASL) imaging have great potential in gliomas grading by noninvasively exploring the heterogeneity of tumors from a microscopic view [3], [4], [5]. Ryu et al. proved that the texture analysis of apparent diffusion coefficient (ADC) map in DWI is useful for evaluating glioma grade [6]. Osamu et al. demonstrated that intravoxel incoherent motion (IVIM) imaging is helpful for differentiating HGG gliomas from LGG gliomas [7]. However, extracting information from a single modality or simple comparison among different modalities is not enough for accurate grading analysis.
Recently, radiomics becomes an emerging non-invasive method to quantify medical images by extracting high throughput image features from multiple imaging modalities, including shapes, textures, wavelet features, etc.[8] [9]. It has been successfully used for phenotypic analysis and prognosis prediction of several tumors [10], [11], [12]. But as far as we known, there are still few works on using radiomics to predict glioma grade. Brynolfsson et al. [13] demonstrated that the gray level co-occurrence matrix (GLCM)-based texture features are useful for glioma grading and prognosis prediction. Following that, Cho et al. showed that the combination of histogram and GLCM-based texture features performed better in distinguishing low-grade and high-grade gliomas [14]. To promote the prediction accuracy, the researchers investigated several feature selection methods and classification models to get a higher prediction accuracy [15], [16], [17].
Image features are the most important factors that influence the prediction ability of radiomics methods. The traditional features used in radiomics were defined by human operators,

Glioma Grade Predictions using Scattering
Wavelet Transform-Based Radiomics Qijian Chen, Lihui Wang*, Li Wang, Zeyu Deng, Jian Zhang and Yuemin Zhu G such as shape, statistical and texture features. These human-defined features are easily influenced by image intensity variation and image deformation, which consequently influences the prediction ability of radiomics. How to extract invariant features to increase the prediction ability of radiomics is still a challenge.
In view of the superiority of scattering wavelet transform (SWT) for the representation of invariant image features [18], we propose to use scattering wavelet features instead of wavelet features to predict noninvasively the glioma grading. In addition, most of radiomics-based glioma grading studies focused on intratumoral regions, such as necrotic, non-enhancing solid and enhancement core of the tumor, the surrounding environment of the tumor remaining unexplored. The surrounding environment of the tumor may provide some unique information which help to glioma grade, so we also propose to take peritumoral into consider.
To evaluate the performance of the proposed method, we firstly extract wavelet and scattering features from different tumor-related regions in the images coming from different imaging modalities, then use several classifiers to predict the glioma grade based on the extracted features, and finally evaluate the prediction performance using various quantitative metrics.

A. Data description
The data used in this work was downloaded from the MICCAI website 2017 targeting for the glioma segmentation challenge [19], [20], [21], which is classified into 75 subjects with LGG (astrocytoma or oligo-astrocytoma) and 210 subjects with HGG (anaplastic astrocytoma and glioblastoma multiforme tumors) based on histological diagnosis. All the subjects were examined with axial T1-weighted, T1-Gd enhanced and T2-weighted images. To overcome the influence of the motions of patients, the skull stripping was performed firstly, followed by the image registration to make sure that the multi-contrast images being strictly matched for the same patient [19], [20], [21]. The spatial resolution of the registered images is 1 mm ×1 mm ×1 mm [22]. The regions of interest were drawn manually by the experienced radiologists, including edema, non-enhancing solid core, necrotic core, and enhancing core. In the present work, to analyze the influence of different tumor regions on the prediction accuracy of glioma grade, for simplicity, we considered that the necrotic core, non-enhancing solid core and enhancing core consists of intratumoral region, and that the edema that excludes intratumoral part constitutes the peritumoral region, as illustrated in Fig. 1.
In addition to the images, the clinical properties of the subjects can be found in the Cancer Genome Atlas (TCGA) [23], as summarized in Table I.

B. Radiomics framework combined with scattering wavelet
Traditional radiomics is composed of four main steps: ROI segmentation, features extraction, features selection, and prediction. Taking into account the insufficiency of wavelet-based features, in the present work, we propose to use scattering wavelet features to replace wavelet-based features to get more meaningful features to promote prediction accuracy. The overall workflow of the proposed radiomics based on scattering wavelet is shown in Fig. 2.  Scttering wavelet is developed based on wavelet transform that is devoted to analyzing images from a multiscale point of view and extracts image features by convolving the variants of mother wavelet and father wavelet with image x . That is where represents the translation, scaling and rotating of mother wavelet with the scaling factor j satisfying that 1 2 2 j J   ( J is the maximum scaling index) and 2 / r l L   denoting the rotation angle of mother wavelet ( L is the maximum number of rotations, 0,1 l L   ), * designates convolution operator. Various mother wavelets can be used to extract the high-frequency information of images. Generally, the father wavelet J  is composed of a series of Gaussian functions and is dedicated to express the low-frequency information of images, It is usually formulated as: with  being expressed by Gaussian function Although the mother wavelet is able to restore image details, it is only translation-invariant at the current scales of 2 j due to its localization properties [24]. In order to extend this translation-invariant property to the biggest scale of x and remain simultaneously the stability for deformation, the average operation at the scale of 2 J is performed by convolving the high-frequency coefficient and the low-frequency filter, namely , j r J x     . However, the result of such convolution is zero because the mother wavelet , j r  and the father wavelet J  are orthogonal. This implies that no information will be generated by averaging directly the high-frequency coefficients. To deal with this issue, a nonlinear operation, namely the modulus of high-frequency coefficients is calculated before the averaging. [25] Then, the translation invariant features can be obtained by From (4), we can see that the high-frequency information is lost after the low-pass filtering. To recover the high-frequency information, wavelet decomposition at larger scale (must be smaller than the biggest scale J ) is performed on the modulus of the current high-frequency coefficient, which can be formulated as However, as mentioned above, such high-frequency information at the current scale is not translation invariant. To keep the translation invariant coefficients, a modulo operation followed by a low-pass filter should be performed again: From (5) and (6), it can be observed that the translation invariants were obtained by implementing the wavelet transformation on the modulus of high-frequency coefficients followed by an averaging operation. This process was called scattering wavelet transform, which can be expressed as: Define the scattering wavelet propagator m U as:   M is the maximum scattering layer. Accordingly, the scattering propagator matrix U can be written as: The corresponding scattering wavelet coefficient 1 , , The detailed expression for During the scattering wavelet decomposition, the scale of scattering wavelet should satisfy 1 2 m j j j J      . According to the above wavelet scattering principle, we extracted the invariant features using the following parameters: the number of scattering wavelet levels is =2 m , the wavelet decomposition scale is =2 J , and the scattering direction at each scale is 4 With such parameter setting, the partial scattering wavelet plot is illustrated in Fig.3, in which the blue, red and green lines represent respectively the scattering wavelet at level of 0, 1 and 2; the black lines indicate the corresponding output at the largest scale J . The outputs consist of the scattering representation of image x . If =2 m , we need to calculate the invariant features 0 S , 1 S and 2 S . According to (9) and (11) The resulted local invariant scattering features is 1 S written as Similarly, the propagation operator for the scattering level 1 is where 0 The corresponding scattering features are Based on the above formulations, if we use two level wavelet scattering, we can get a total of 25 scattering feature maps, and the numbers of 0 S , 1 S and 2 S are 1, 8 and 16, respectively. The outputs of the scattering wavelet network are shown in Fig. 2.

C. Prediction evaluation
The performance of glioma grading prediction with the proposed scattering wavelet-based radiomics and traditional radiomics was evaluated in terms of receiver operating characteristic (ROC) curve, area under curve (AUC), sensitivity, specificity and accuracy. ROC is obtained by plotting true positive rate (TPR) against false positive rate (FPR) at different thresholds in a classifier. AUC indicates the surface under the curve of ROC and specifies the classification accuracy. The bigger the AUC, the more accurate the classification. Sensitivity represents the correct classification rate of positive samples while specificity represents the correct classification rate of negative samples. These metrics allow reflecting the false positive and false negative errors of the prediction models. Since AUC is not sensitive to sample properties such as the unbalance of sample classes, it is often used to evaluate the performance of the classifier for unbalanced dataset.

A. Experimental setup
To objectively compare the glioma grade prediction ability of the proposed radiomics method based on scattering wavelet features with that of traditional radiomics method, experiments with different imaging modalities and different tumor regions were implemented respectively. All experiments were performed and evaluated using the same training and validation datasets and the same 5-fold cross-validation method; 2176 samples were selected as validation datasets and 9738 samples as training datasets. Because the number of HGG and LGG samples was not equal, sample balance was also considered in the training process.
For the traditional radiomics, a total of 335 radiomics features were calculated for each patient, including 7 shape and histogram-based features, and 328 textural features, such as the gray level co-occurrence matrix features, gray run matrix features and multiscale wavelets features. For the wavelet scattering, a total of 54900 features were extracted for each patient, with the scattering direction 4 L  , the wavelet decomposition scale 3 J  and the scattering level 2 m  . Such setting resulted in 61 feature maps of size of 30×30. The above feature extraction programming was implemented in Matlab 2016a [26]. To avoid redundancy and correlation of the large number of radiomics and wavelet scattering-based features, the Partial Least Squares (PLS) regression was used to reduce the feature dimension to 30 [27]. Finally, based on the selected features, three typical classifiers, namely the logistic regression (LR) [28], support vector machine (SVM) and random forest (RF) [29], [30] , were used to predict the glioma grades. The clustering results for the selective features extracted from the wavelet and scattering wavelet are given in Fig. 5, the presentation of the results which is realized using the ConsensusClusterPlus package in bioinformatics analysis software under R language [31] , [32].
It can be clearly observed that the features of all patients can be clustered into two groups, each group sharing the same features. We observe that the two groups clustered with the wavelet features are almost balanced. In contrast, the groups clustered with the scattering wavelet features are unbalanced.
Previous works showed that the performance of radiomics prediction is not only related to the image features in the intratumoral region, but also to the features in the peritumoral regions [33], [34]. In addition, since multiple imaging modalities provide more detailed information to promote prediction accuracy [35], radiomics based on multiple modality images becomes a trend. To fairly evaluate the prediction performance of the proposed scattering wavelet based radiomics, we performed the glioma grading on different tumor regions and imaging modalities using the proposed and traditional radiomics methods, and then quantitatively compared the methods in terms of AUC and other metrics.

B. Quantitative comparison for the glioma grading with different regions
As illustrated in Fig. 1, the labeled region of interests (ROIs) include intratumoral and peritumoral parts. We extracted respectively the wavelet and scattering wavelet features from intratumoral and peritumoral regions. To avoid the influence of imaging modality, in this experiment, only the T1-weighted images were considered. The extracted wavelet and scattering wavelet features were combined with the other radiomics features and were fed into three classifiers, including RF, SVM In these ROC curves, the middle black curve indicates the dividing line with an AUC of 0.5, the green curve the ROC obtained with wavelet features, and the read one the ROC obtained with scattering wavelet features. It can be easily observed that, the glioma grading accuracy using the scattering wavelet features is much better than that using wavelet features, especially for SVM and LR classifiers. In addition, comparing Fig. 5(a) and 5(b) shows that the image features extracted from the peritumoral regions are helpful to promote the glioma grading accuracy.
To further quantitatively compare the prediction performance for glioma grades with different features, the accuracy, sensitivity, specificity and AUC were calculated and given in Table II. Table II shows clearly that the evaluation metrics have much higher values using scattering wavelet features than using wavelet features. In the prediction with intratumoral features, compared to the wavelet-based method, the AUC of scattering-based prediction is increased by about 17.5%, 15.6% and 17.7% for SVM, LR and RF, respectively. As to the prediction with both intratumoral and peritumoral image features, the AUC obtained with scattering-based features is increased by about 11%, 10.2% and 17 % for SVM, LR and RF, respectively. We can see that the features extracted from peritumoral regions can promote the prediction accuracy, especially for the traditional wavelet-based radiomics. In other words, the peritumoral features can decrease the difference in prediction accuracy between the wavelet and scattering-based methods.
C. Quantitative comparison for the glioma grading with different modalities  To investigate the glioma grading performance of wavelet-based and scattering-based features in the multimodal images, we first extracted the image features from T1-weighted, T2-wieghted and T1-enhanced images. Then, glioma grading based on these features was performed with different classifiers. The ROC curves for the classification of glioma grades are given in Fig. 6. We can see that the grading accuracy based on the scattering features extracted from the multi-modal images is still higher than that based on the wavelet features. However, such superiority is not as evident as in the grading with single-modality images.
The corresponding quantitative evaluation results are given in Table III. The features extracted from multimodal images increase indeed the glioma grading accuracy, but the difference in grading AUC based on wavelet and scattering features is not obvious. Nevertheless, the specificity and sensitivity obtained with the scattering features are higher than those obtained with the wavelet features, which verifies that the proposed method decreases simultaneously false positive and false negative errors in glioma grading.

IV. DISCUSSION
The proposed radiomics method is based on using local invariant features from scattering wavelet features instead of traditional wavelet features. The experiments on different tumor regions with different imaging modalities showed that the AUC of the proposed method reaches 0.96 at least, which demonstrates the effectiveness and superiority of the proposed method.
Traditional radiomics methods used the human-defined image features to train classification models. Such features include shapes, textural and statistical information, which are easily affected by image intensity transformation and image deformation. As a result, the prediction accuracy based on these features is influenced. To cope with such problem and in view of the interest of scattering wavelet transform for the extraction of invariant image features, we replaced wavelet features by scattering features to predict glioma grades. The experimental results showed that those invariant features allow us to better represent image properties and thus distinguish more effectively glioma grades. This can be reflected in the feature clustering result, as shown in Fig 6. Considering the distribution of datasets used in this work, with 75 patients with low-grade gliomas and 210 patients with high-grade gliomas, this means that the features extracted from scattering wavelet can represent the data distribution correctly and may be more conducive for glioma grading.
In clinical routine, multimodal imaging is often performed, including T1, T2 and T1-enhanced weighted sequences. These images can provide much more useful and complementary information and therefore the difference between the prediction with wavelet and scattering features is not obvious, as illustrated in Fig. 6. However, in the case of the prediction with a single modality, the features extracted from scattering wavelet are richer and more robust than that from wavelet transform, therefore the proposed method performed much better in the perdition with single modal image.
Although the AUC obtained with our method is greatly increased, there are still several limitations in the present work. Firstly, the dataset used is a public open source dataset, and the training cohort and testing cohort come from the same group. In the future, testing with different cohorts would be interesting to further evaluate the proposed method. Secondly, the number of features obtained using scattering wavelet is extremely large; the feature selection using PLS may lead to the missing of some useful features. Using more effective dimension reduction techniques would then be our future work. Finally, the radiomics prediction being performed on segmented ROIs, the quality of segmentation can influence the subsequent prediction. To deal with this issue and in light of the promising deep learning models [36], we may combine deep learning models and scattering wavelet to achieve glioma grading without the requirement for image segmentation. We have proposed a novel radiomics method to predict noninvasively and accurately glioma grades before surgery. The method is based on the use of local invariant features extracted from scattering wavelet transform instead of conventional wavelet features as used in traditional radiomics methods. The results showed that the high-dimensional image features extracted from scattering wavelet-based radiomics improve greatly the accuracy of glioma grading. In addition, we demonstrated that the peritumoral features are beneficial for glioma grading. All that suggests the potential use of the proposed method for computer-aided glioma diagnosis.