## 4 Discussion  
In this study, a phantom specifically designed for MRI radiomic studies in the pelvic region was used to investigate the dependency on VOI size of the ability of radiomic features to discriminate between different textures. Three scanners of different manufacturers and different magnetic field strengths were used to perform these assessments, aiming to understand to what extent such dependency may vary across these different settings. Only the radiomic features that had proved to be repeatable at test-retest imaging in a previous study performed on the same images [9] were included in this analysis. As a result, the number of analyzed features was different for the three scanners: 829 for scanner A, 810 for scanner B, and 689 for scanner C (this lower number is likely due to the increased water-fat shift artifact). At the very first level of analysis, performed for each scanner separately, but aggregating the results for all feature classes, imaging filters, and texture couples, the main result emerged indicating that, for any scanner and VOI volume, a non-negligible fraction of features (>70%) was actually able to discriminate the different textures (Figure 3). It was also observed that the smallest volume (0.8 cm\({}^{3}\)) was less discriminative irrespectively of  
Figure 5: Overall percentage of features discriminative at different volumes for each feature class extracted from the original images in scanners A (top left), B (top right), and C (bottom left). At bottom right, coefficient of determination, R-squared, of the percentage of discriminative features explained by the volume for each scanner. the scanner manufacturer and magnetic field strength; this is likely related to the reduced amount of information in the VOI (e.g., number of voxels), which might lead to inadequate sampling of the signal distribution therein, degrading the ability of the features to quantify the texture properties. Another common trend among scanners was the reduction in the proportion of discriminative features when increasing the VOI volume from 20.7 cm\({}^{3}\) to 29.8 cm\({}^{3}\), the latter being the largest VOI drawn in correspondence with the insert edge. In this regard, it might be argued that a slight amount of partial volume effect/background signal was included in the 29.8 cm\({}^{3}\) VOIs, possibly affecting the value of some features, which would have been discriminative otherwise. Finally, in the volume range from 3.3 cm\({}^{3}\) to 20.7 cm\({}^{3}\), an increasing trend in the proportion of discriminative features with volume was found for scanners A and B, supporting the hypothesis that a volume threshold (in terms of volume, or number of voxels) does exist for each feature to become discriminative, whereas noisy results were obtained for scanner C. While the number of features being considered was already different between scanners following the repeatability study performed on [9], the percentage of discriminative features still varied across different scanners. Possible causes for such findings may be the different signal-to-noise ratios between scanners, artifacts affecting different scanners with different magnitudes, system types, e.g., digital versus analog, and coils used. While the aggregated results captured interesting, broad, and succinct information, a more detailed analysis allows a deeper understanding and potentially provides more practical indications. For this reason, the analysis of discriminative features was first stratified, for each scanner, according to feature class, still aggregating data by imaging filters (Figure 4). For scanners A and B, while confirming the lower discriminability of the 0.8 cm\({}^{3}\) volume with respect to the larger volumes across all feature classes, the first-order class distinguished itself for better discrimination, even with the 0.8 cm\({}^{3}\) volume, with \(>\)85% of discriminative features, versus 55-81% for the other classes.