**4. Discussion**

In radiography, the heel effect causes less X-ray fluence and higher mean radiation energy in the anode direction, and results in non-uniform image quality. Although there have been some methods proposed to reduce the heel effect [19–21], no suitable method has been presented that can objectively quantify the overall and non-uniform image quality caused by the heel effect. This study designed a CSW phantom for quantification of overall and non-uniform image quality in X-ray radiographs using nMI metrics based on information theory. The nMI metrics were demonstrated to be associated with imaging SNR, contrast, and resolution [13,14]. In the present study, the evaluated image quality was compared between the nMI (CSW phantom) and conventional VR (CDR phantom) metrics in digital X-ray images acquired at various exposure parameters and orientations, and with and without HEC. The results highlight that both metrics significantly changed with kVp (from 40 to 60 kVp at 5 mAs) and mAs (from 5 to 40 mAs at 40 kVp). The overall image quality assessed by nMI and VR metrics exhibited a similar trend with high correlation, suggesting that both metrics are capable of reflecting image quality in digital X-ray images. In addition, the nMI metrics were found to be more sensitive to changes in exposure parameters (kVp and mAs) than the VR metrics. It is postulated that the increased sensitivity is due to the fact the CSW phantom was made of acrylic material and had a small difference in thickness.

It is known that the anode heel effect may lead to heterogeneous X-ray exposure that can deteriorate overall image quality. The results of the present study demonstrated that the heel effect significantly deteriorated the overall image quality. Furthermore, the image quality reflected by the nMI metrics can be significantly improved with HEC in the anode direction; this correction resulted in improved homogeneity of image quality and higher conspicuity of bony structures in the hand X-ray images. However, the conventional VR metrics were not significantly changed with orientations before and after HEC, suggesting that the nMI metrics were more sensitive than the VR metrics to non-uniform image quality.

The insensitivity of VR metrics to detect non-uniformity of image quality was likely attributable to the fact that the disk details were embedded in the central area of the CDR phantom, as shown in Figure 2. Although the centralized disk details in the CDR phantom were suitable for measuring the image quality in the central field of view, the design itself rendered it less sensitive to inhomogeneous image quality that occurred in the outer region. On the contrary, the nMI metrics were calculated from the image of CSW phantom made of acrylic material and with a suitable size that fits the flat panel detector. A previous study showed that the image quality reflected by the correctly identified holes (%) of the CDRAD phantom was more sensitive to changes in exposure parameters than the number of detected details in a CDR phantom [12], suggesting that the acrylic material of the CDRAD phantom was sensitive to changes in signal intensity. Similarly, our results demonstrated that the nMI metrics (CSW phantom) were more sensitive to changes in exposure parameters and orientations than the VR metrics (CDR phantom). The results indicated that the nMI with the CSW phantom could potentially be a quantifiable metric for non-uniform image quality in digital X-ray images.

Some limitations, however, warrant discussion. First, a small range of exposure parameters was utilized in this study. A study using a broader range of exposure parameters may provide more comprehensive comparisons between the two metrics. Second, the nMI metrics with the CSW phantom have an intrinsic disadvantage of less sensitivity to changes in spatial resolution [13]. However, the circular nature of CSW phantom can be used to estimate radial MTF, as proposed by a previous study [27], so in addition to nMI, the CSW phantom can be utilized to evaluate the radial MTF in X-ray images. Third, the CSW phantom was designed with acrylic material, so it may not be suitable to measure the image quality at high kVp and high mAs. A CSW phantom with a combination of aluminum and acrylic materials may be helpful to reflect image quality of X-ray images acquired using clinical parameter settings. Further investigations will be needed to compare the results between phantoms made of different materials.
