**3. Results**

By varying kVp, one-way ANOVA analysis showed that both nMI and VR metrics significantly changed with kVp between 40 and 60 kVp at a constant 5 mAs. It was also found that nMI changed more prominently than VR in X-ray images with and without HEC, as shown in Figure 5. The Mann–Whitney U test highlighted a significant difference in nMI metrics between any two kVps; however, the VR metrics were not significantly different between 45 to 50 kVp, 45 to 60 kVp, or 50 to 60 kVp in images with and without HEC. Moreover, the nMI metrics were significantly increased after HEC; however, no significant change was noted in the VR metrics at different kVps after HEC.

By varying mAs, one-way ANOVA analysis showed that both nMI and VR metrics also significantly changed with mAs between 5 and 40 mAs at a constant 40 kVp, as shown in Figure 6.

The post-hoc Mann–Whitney U test showed that both nMI and VR were significantly different between any two mAs in the images with and without HEC. The nMI metrics were significantly increased after HEC; however, no significant change was noted in the VR metrics at any of the mAs after HEC. Moreover, the averaged nMI and VR metrics significantly correlated in the images without HEC, as shown in Figure 7.

**Figure 5.** The VR (**A**) and nMI (**B**) metrics changed significantly with kVp, at 5 mAs, before and after HEC.

**Figure 6.** The VR (**A**) and nMI (**B**) metrics changed significantly with mAs, at 40 kVp, before and after HEC.

**Figure 7.** The significant correlation (cc = 0.9129, P < 0.05) between the VR and nMI metrics measured from all exposure parameters in images without HEC.

By varying orientation in the measurement, without HEC, there were significant changes in nMI with orientations between 0 and 180 degrees (the results were symmetric around 180 degrees). However, without HEC, there were no significant changes in VR with orientations between 0 and 180 degrees, as shown in Figure 8. The post-hoc Mann–Whitney U test showed that the nMI metrics were significantly different between two orientations in images with and without HEC. Although the nMI metrics came to be more uniform across different orientations, there remains slight difference in nMI metrics between 30 and 150 degrees.

A posterior-anterior right-hand X-ray image (Figure 9) demonstrated inhomogeneous signal intensity in the anode-cathode direction due to the heel effect, where lower signal intensity (higher X-ray exposure) was noted in the finger than the wrist direction (Figure 9A,C,E). By applying the HEC, the inhomogeneity issue was minimized across the entire image, and small bony structures were more conspicuous in the corrected image than the raw image displayed with an identical window level and width (Figure 9B,D,F). Although the bony structures of the wrist in the raw image can be visualized by adjusting the window level and width, the bony structures of the fingers will be too dark to be visualized. This inhomogeneous issue can be reflected by the inconsistent nMI metrics in radial direction, as shown in Figure 8.

**Figure 8.** *Cont*.

**Figure 8.** The VR (**A**) and nMI (**B**) metrics measured as a function of orientation at 40 kVp and 5 mAs. The VR metrics did not change significantly with orientations, whereas the nMI metrics changed significantly with orientations in the images without HEC.

**Figure 9.** A posterior-anterior right-hand image acquired with 52 kVp and 10 mAs before (**A**,**C**,**E**) and after (**B**,**D**,**F**) HEC. The arrows indicate the bony structures of the lunate that were more conspicuous in the image with (**F**) than without (**E**) HEC.
