## 4 Discussion  
We investigated the radiomic features of MRA images associated with the rupture of intracranial aneurysms. Eleven radiomic image features associated with ruptured intracranial aneurysms were selected using LASSO, as shown in Table 2. The 11 features included eight texture features: Energy.1 (GLCM), LLH Variance.1 (GLCM), LLH ZP (GLSZM), HLL ZP (GLSZM), LLH Autocorrelation (GLCM), LLH GLV (GLRLM), HHH ZP (GLSZM), and LLH Contrast (GLCM) (GLCM:4, GLRLM:1, GLSZM:3); and three histogram features: LLL MAD, LLH variance, and uniformity. These basically assessed the voxel-value heterogeneity in the ROI, such as aneurysms, but from different theories. Finally, we chose a combination of three features, Energy.1 (texture/GLCM), LLH Variance.1 (texture/GLCM), and LLH ZP (texture/GLSZM), to achieve the highest AUC of 0.971, accuracy of 0.948, sensitivity of 0.700, and specificity of 0.953. Energy.1 (GLCM) is a measure of squared-voxel-value-wise intensity patterns in an ROI based on the GLCM, which represents the number (or frequency) of co-occurrences  
Figure 4: Scattered plots of image features selected by LASSO for RA and UA training cases: (**a**) 1 st and 2 nd features; (**b**) 3 rd and 4 th features. Figure 5: MRA images of intracranial aneurysms: (**a**) an RA case; (**b**) a UA case. for combinations of two gray levels occurring in neighboring voxels in a specific direction. Variance.1 (GLCM) is a measure of squared-voxel-value-wise variation patterns in the ROI based on the GLCM. The zone percentage (ZP) (GLSZM) is a measure of area-wise variation patterns based on GLSZM, which represents the same voxel-value areas, that is, the number of connected voxels with the same voxel values. The ZP measures the fraction of the number of realized zones and the maximum number of potential zones [26]. Therefore, because voxel values within an ROI have a more spatially coarse heterogeneity, the ZP features could be larger. MAD (histogram) is a measure of the deviation values of all intensity values minus the mean value obtained from the histogram of an ROI. The Variance (histogram) used is that obtained from the histogram of an ROI. Because RA cases may have turbulent flow around the aneurysm centers [27; 28], the intensities around the centers could be lower than that of aneurysm surfaces in MRA images [29; 30] as shown in Figure 5a. This phenomenon could result in a relatively higher Energy.1 (GLCM) and LLH ZP LLH; however, some UA cases overlapped with the RA cases, as shown in Figure 4. Variance.1 (GLCM) and LLL MAD (histogram) showed higher values for some UA cases, as shown in Figure 4, because the UA cases may have higher intensities around centers in MRA images as shown in Figure 5b. There are several reports on the prediction of aneurysm ruptures using radiomics of CTA and DSA, mainly concerning morphological features [9; 10; 11; 12; 13; 14; 15; 16; 17]; however, to the best of our knowledge, no study has been conducted on MRA, and, therefore, our study appears to be the first. Their AUCs ranged from 0.738 to 0.860 in the validation tests, whereas that in our study was 0.977. This study had four limitations. First, we included a small number of UA and RA cases, especially the number of RA cases. Thus, the specificity was high (0.983), but the sensitivity was low (0.700). Therefore, the number of cases should be increased, collecting cases from different institutions to avoid false-negative cases so that the UA and RA cases can have almost the same, and enough, numbers. When collecting them, we should consider various locations (for example, anterior cerebral arteries, posterior cerebral arteries, and posterior communicating artery) and various sizes from <5 mm to >20 mm, which show different hazard ratios to rupture risks [18]. In addition, we should compare the results with and without using the SMOTE to investigate its impact on the final result. Second, a feature selection and machine learning methods were employed in this study.