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MPRAD: A Multiparametric Radiomics Framework

Multiparametric radiological imaging is vital for detection, characterization and diagnosis of many different diseases. The use of radiomics for quantitative extraction of textural features from radiological imaging is increasing moving towards clinical decision support. However, current methods in radiomics are limited to using single images for the extraction of these textural features and may limit the applicable scope of radiomics in different clinical settings. Thus, in the current form, they are not capable of capturing the true underlying tissue characteristics in high dimensional multiparametric imaging space. To overcome this challenge, we have developed a multiparametric imaging radiomic framework termed MPRAD for extraction of radiomic features from high dimensional datasets. MPRAD was tested on two different organs and diseases; breast cancer and cerebrovascular accidents in brain, commonly referred to as stroke. The MPRAD framework classified malignant from benign breast lesions with excellent sensitivity and specificity of 87% and 80.5% respectively with an AUC of 0.88 providing a 9%-28% increase in AUC over single radiomic parameters. More importantly, in breast, the glandular tissue MPRAD were similar between each group with no significance differences. Similarly, the MPRAD features in brain stroke demonstrated increased performance in distinguishing the perfusion-diffusion mismatch compared to single parameter radiomics and there were no differences within the white and gray matter tissue. In conclusion, we have introduced the use of multiparametric radiomics into a clinical setting

The texture features extracted are based on several properties inherent to image data, such as, graylevel distribution 4 , inter-voxel relationships [5][6][7][8][9] and shape 10 . The goal of radiomics is to provide a quantitative framework for a "radiological" biopsy of tissue, which could be correlated to the underlying tissue biology. Reviews of several studies that have employed radiomic analysis produced encouraging results for prognosis and diagnosis of different pathologies and imaging modalities in brain, breast, lung, and prostate 1 .
However, the current radiomic methods are based on extraction of textural features from a single image or volume and do not extract the textural features from multimodal or multiparametric datasets consisting of combined imaging sequences. For example, multiparametric magnetic resonance imaging (mpMRI) such as proton density (PD), T2-weighted(T2), T1-weighted(T1), diffusion-weighted (DWI), and perfusion weighted imaging (PWI). These sequences produce different soft tissue contrasts of the tissue, where each imaging sequence provides a specific representation of the tissue based on the underlying physics and gray levels. Integrating the imaging information from different radiological modalities and parameters will provide a more complete view of the underlying tissue characteristics.
Correspondingly, using texture analysis on a high dimensional multi-sequence data would provide information about the "true texture" of the tissue rather than from a single specific point of view. To that end, we developed a multiparametric radiomics imaging (MPRAD) framework for extracting radiomics information from multiparametric and multimodal imaging data.
In the multiparametric setting, we define a tissue signature (TS) that encodes the imaging characteristics of different tissue types for characterization. These different imaging parameters from the tissue signature interact with each other in a high dimensional complex space forming a complex interaction network. Probing the complex interaction network could provide information that was not possible to extract using conventional radiomic methods. The MPRAD framework analyzes both the spatial distribution of the TS, in addition to the complex interaction network within a region of interest (ROI) to compute multiparametric imaging radiomic features. In this paper, we present the theory of the MPRAD framework, develop radiomic features for multi-sequence images and implement the MPRAD framework in two different clinical applications. First, we applied the MPRAD framework to multiparametric breast MRI for classification of benign from malignant lesions and compare the MPRAD results to single image radiomics. Then, the MPRAD framework was applied to multiparametric brain MRI for classification of diffusion-perfusion mismatch in stroke patients [11][12][13][14][15] .

The Tissue Signature
We define a tissue signature that represents a composite feature representation of a tissue type based on the physical modeling of the different imaging. A typical TS is shown in figure 1. Mathematically, for N different imaging parameters, a TS at a voxel position, Sp is defined as a vector of gray level intensity values at that voxel position, p across all the images in the data sequence for different tissue types and is given by the following equation,

= [
(1) , (2) , (3) , … , ( ) ] (1) Figure 1. Illustration of the four different types of multiparametric imaging radiomic features based on first and second order statistical analysis. The tissue signature probability matrix (TSPM) and tissue signature co-occurrence matrix (TSCM) features evaluate the complex interactions between different tissue signatures while the Tissue signature complex interaction network (TSCIN) first order statistics and tissue signature relationship matrix (TSRM) features evaluate the inter-parameter complex interactions.
Where, Ip is the intensity at voxel position, p on each image.

tissue signature probability matrix features
The tissue signature probability matrix (TSPM) characterizes the spatial distribution of tissue signatures within a ROI. The mathematical formulation of TSPM is as follows: Suppose that the intensity values representing each voxel are quantized to G levels, then the total number of possible tissue signatures in a dataset consisting of N images will be equal to . We define a function : → , where T is the set of all tissue signatures in the dataset and M is a N dimensional matrix with edges of length G where each tissue signature is represented as a cell. The function f populates each cell of the matrix M with the frequency of occurrence of the corresponding tissue signature in the set T. The resulting matrix M is called the tissue signature probability matrix (TSPM). The information content of the N dimensional multiparametric imaging dataset ( 1 , 2 , … ) can be analyzed by computing the joint entropy, uniformity, and mutual information of the resultant TSPM 16 . These are defined below.
1. The TSPM entropy, H is given by the following equation (2) 2. The TSPM uniformity, U is given by the following equation 3. The TSPM mutual information, MI is given by can be obtained producing a large number of multiparametric imaging radiomic features.

Tissue signature co-occurrence matrix features
The tissue signature co-occurrence matrix (TSCM) characterizes the spatial relationship between tissue signatures within a ROI. The TSCM is defined similar to the gray level co-occurrence matrix (GLCM) using two input parameters, distance (d) and angle ( ) between the two tissue signature locations 6 . Mathematically, the GLCM between any two tissue signatures, Si and Sj is given by the following equation where ∈ ( ) and | . | denotes the cardinality of a set.
Given a distance, d and angle, ( ), the co-occurrence matrix for all such possible pairs of tissue signatures is given as follows: Here, is the tissue signature co-occurrence matrix. The TSCM can then be analyzed to extract twenty-two different TSCM features using the equations developed by Haralick et al 5 .

Tissue signature complex-interaction network analysis features
The tissue signature complex interaction network (TSCIN) analysis characterizes the complex interactions that define the inter-parametric relationships between different imaging parameters using statistical analysis. The TSCIN features are extracted by transforming a high dimensional multiparametric radiological imaging data into a radiomic feature map using first or higher order statistical analysis of the tissue signature vectors, Sp at each voxel position. The TSCIN feature maps are transformed into a single radiomic quantitative value corresponding to a region of interest using a summary statistical metrics mean, median or standard deviation.

First order TSCIN features
The first order TSCIN features are straightforward and calculated directly from the tissue signature. For example, the TSCIN entropy at a voxel position, p is given by the following equation: Similarly, all the other first order TSCIN features follow.

Second order TSCIN features
The second order TSCIN features characterize the inter-parameter relationship within the tissue signature by computing a TSCIN relationship matrix (TSRM) and are derived below. Mathematically, TSRM for a N dimensional tissue signature at voxel position, p with N imaging sequences quantized to G gray levels is given by the following equation: Here, d represents the distance between the two imaging parameters, I (k) and I (k+d) .
The TSRM is dependent on the relative location of different imaging parameters within the tissue signature. The structure of the TSRM is similar to a G x G gray level co-occurrence matrix, thereby, allowing us to utilize all the twenty-two equations established to extract relevant features from such matrices 5 . All the four classes of the MPRAD features developed in this manuscript are illustrated in figure 1 on an example multiparametric breast MRI dataset.

Digital Phantom
The multiparametric imaging radiomic feature extraction methods developed in this manuscript were tested on the well-known texture phantom from University Southern California (USC) shown in figure   2A and B 7,17 . The texture phantom images consist of a composite mixture of several raw texture images of grass, sand, wool, water, and others derived by Brodatz 18 . Using these composite images,  MPRAD tissue signature model to accurately segment each of the different textures. We applied single image radiomics to each image and MPRAD to stacked images to compare the results from the two methods.

Clinical Data
Informed Consent: All studies in accordance to the institutional guidelines for clinical research under IRB approved protocol by our institution for this retrospective study.

Clinical brain stroke data
Our stroke data set consisted of ten patients (n=10, five women and five men, age=64±19 years) that registration, the PWI images were used as the reference volume for the DWI to be registered to.

Area and Quantitative MRI measurements
The infarcted tissue was segmented from the PWI, DWI, and ADC map using the Eigen filter algorithm 22,23 . The input to Eigen filter algorithm was the selection of white matter, gray matter, cerebrospinal fluid and potential infarcted tissue and the tissue at risk using pixels from each tissue type and respective sequence. The Eigen filter uses a Gram-Schmidt orthonormalization to segment each tissue type. The areas for the tissue at risk and potential infracted tissue were calculated by counting the number of pixels within segmented regions followed by multiplication with the pixel resolution in mm 2 . The ROIs defined by the Eigen filter were overlaid on the ADC map and TTP map to obtain quantitative measurements of the tissue.

MPRAD Radiomic Analysis
Radiomic maps and features were computed by filtering mpMRI images with statistical kernels based on the first order TSPM and TSCIN (e.g. entropy) features and second order TSCM and TSRM features (Haralick's gray level co-occurrence matrix features) described above. The optimal neighborhood and gray level quantization values for filtering were determined by the image resolution, bit depth of the radiological images and empirical analysis of the uniformity and noise within the radiomic maps. The Single radiomic gray level co-occurrence matrix (GLCM) entropy features maps of each MRI parameter. C. The MPRAD RFMs tissue signature co-occurrence matrix (TSCM) and tissue signature complex interaction network (TSCIN) radiomic features. Note, the improved tissue delineation between the different tissue types using MPRAD radiomic parameters of neighborhood and gray level quantization were set to 15x15 with 256 gray levels for synthetic USC texture images, 5x5 and 128 gray levels for breast mpMRI and 3x3 and 32 gray levels for brain mpMRI (DWI and PWI). The ROIs from the different tissue types were segmented and overlaid on the MPRAD maps for quantification of the texture values.

IsoSVM
We developed a new feature embedding and classification framework termed IsoSVM 24 by modifying two machine learning algorithms, Isomap and support vector machine (SVM) 25,26 . This hybrid IsoSVM classifier enables accurate classification of high dimensional data sets. Briefly, the Isomap is a nonlinear dimension reduction algorithm based on the geodesic distance and multidimensional scaling. The SVM is a linear binary classification algorithm that attempts to create a hyperplane that best separates the different groups.

Digital Texture Phantom
The MPRAD features results on each USC composite texture image are shown in figure 2. The reference texture ground truth images provide a method to evaluate the radiomic features from known objects with high texture. From the two composite images, both single and multiparametric radiomic Figure 5. Comparison between the predictive accuracy of the single parameter based radiomics features and multiparametric radiomic features using receiver operating characteristic (ROC) curve analysis. The multiparametric radiomic feature ROC curves (displayed in red) produced area under the ROC curve (AUC) values that were 9%-28% greater than the AUCs obtained for single parameter radiomics (ROC curves displayed in blue). The ROC curve obtained from applying IsoSVM for classification of benign from malignant patients is displayed in black. The area under the ROC curve (AUC) for IsoSVM was obtained at 0.87.
features were able to produce a 100 percent match with the reference images confirming the method on an independent data set ( figure 2 top row). Moreover, the multiparametric radiomic features were able to capture the differences in both shape and intensity distribution of both single parameter radiomic images with excellent detail of the underlying structure. The higher order entropy (GLCM) values for the highlighted subregion in figure 2 were 9.9 and 9.7 for the single radiomic images corresponding to the square and mosaic respectively while the MPRAD TSCM entropy was 10.23.

Multiparametric breast MRI
The set of multiparametric imaging radiomics (MPRAD) features were extracted from one hundred and thirty-eight women with breast lesions that underwent mpMRI scans. The mean age of the patients was 52±11 ranging between 24-80. Of the 138 patients, there were 97 patients with biopsy proven malignancy whereas 41 patients had benign lesions. Figure 3 illustrates both the single and MPRAD feature maps from a patient with a malignant lesion in the upper outer quadrant of the right breast with a benign appearing cyst superior and more medial to the lesion (curved yellow arrow however, there is a striking difference in the textural representation shown by the MPRAD radiomics.
In particular, the cyst is shown with decreased entropy in the MPRAD compared to single radiomic images. The lower entropy in the cyst is consistent with the fact, that the homogenous object has less disorder and hence lower entropy. This is clearly evident when looking at the lesion which has much higher entropy values.

Multiparametric brain MRI
Four MPRAD features were extracted from ten patients with stroke imaged at acute timepoint (<12h).
The mean age of patients was 64±19 ranging between 36-87. Figures 6 and 7 illustrates both the single and multi-parametric radiomic feature maps from the DWI and PWI MRI. As shown in figure 6, there was a striking difference in the textural representation between the single and multi-parametric radiomics images from the DWI and ADC maps. The majority of the single radiomic second order features (GLCM) did not show any significant textural difference between infarcted tissue and tissue at risk on the ADC map. Whereas the same second order multiparametric radiomic features (TSPM) were significantly different for multiparametric complete DWI dataset. These results have been tabulated in  Similarly, multiparametric radiomic values for the TTP and PWI dataset (all parameters, dimensionality >50) demonstrated excellent results for the MPRAD as shown in Figure 7. For example, The MPRAD TSPM Entropy exhibited significant difference between infarcted tissue and potential tissue-at-risk: (6.6±0.5 vs 8.4±0.3, p=0.01). These results are summarized in table 5 detailing the comparison between the single and multiparametric radiomics on PWI. Table 6 summarizes the results from multiparametric radiomics applied to all the parameters.

Discussion
We In breast, consistent with other reports, malignant lesions had increased entropy compared to benign lesions 1 . Importantly, there were no differences in the normal glandular tissue between each group 24 . The MPRAD radiomic features delineated different tissue types better than the single radiomic features, for example, in cysts, normal, and peri-tumoral regions. Finally, the MPRAD demonstrated excellent sensitivity and specificity with increased AUC compared to single radiomic features comparable with those achieved by radiologists.
In stroke patients, predicating stroke outcome is very challenging and the evaluation and treatment are determined by the ability to identify the ischemic penumbra, oligemic and potential salvageable tissue. Ischemic penumbra refers to brain tissue which is at risk for infarction 11,12,27,28 .
Damage to this salvable tissue can be potentially prevented or reversed using thrombolytic therapy 14 . The brain tissue corresponding to ischemic penumbra and oligemia can be identified using advanced MRI parameters of diffusion-weighted imaging (DWI) and perfusion-weighted imaging (PWI) 15,28,29 . the In general, multiparametric imaging for applications such as brain, breast and prostate MRI produces a large number of images (>50) corresponding to each slice location, thereby producing a high dimensional image space. Extracting radiomic features from each image in such datasets may not provide complete information about the tissue. In addition, given the high dimensionality of the dataset, there is an increase in both the computational and space complexity of the radiomic process making radiomics analysis impractical for such cases. The MPRAD framework resolves this issue by extracting radiomic features that not only analyze the progression of tissue texture with time but also evaluate the overall tissue texture in large data sets.
There are, however, some technical limitations to the use the MPRAD in practice. First, there is a need for graphical processor units (GPU) with large memory and user-friendly software for processing. These items may not be currently widely available. More specific to the present study, any assessment of the clinical value of MPRAD network will require additional prospective studies.
These studies would have subsequent follow-up and pathological correlation using MPRAD in breast.
In stroke, these types of studies would provide us with new MPRAD data to potential predict final infraction volume or identify markers of hemorrhagic transformation overtime.
In conclusion, we have demonstrated that MPRAD framework shows a excellent potential in analysis of textural information using multimodal and multiparametric imaging in different clinical settings. With increasing use of multiparametric imaging in clinical setting, MPRAD provides an ideal framework for future clinical decision support systems.

Code availability
Our software will be freely available to academic users after issue of pending patents and a materials research agreement is obtained from the university. Due to University regulations, any patent pending software is not available until a patent is issued.

Data availability
All relevant clinical data are available upon request with adherence to HIPPA laws and the institutions IRB policies.

Acknowledgments:
National Institutes of Health (NIH) grant numbers: 5P30CA006973 (Imaging Response Assessment Team -IRAT), U01CA140204, 1R01CA190299, and The Tesla K40s used for this research was donated by the NVIDIA Corporation.

Author Contributions:
MAJ and VSP developed the concept, performed the testing, algorithm development, statistical methods, and manuscript writing.

Conflict of Interest:
The authors have no conflict of interests.