# The Role of a DirectDensity(r) CT Reconstruction in a Radiotherapy Workflow: A Phantom Study
## 3 Results
### Mean Calibration Curves  
Figure 6 shows the mean calibration curves at low (Figure 6a) and high (Figure 6b) densities. As expected, the curves related to the standard reconstruction algorithm Qr40 had a strong dependence on the kVp value set during the image acquisition, both at low and high densities, as shown in the graphs to the left of Figure 6. In contrast, the mean calibration curves associated with the reconstruction algorithm DD exhibited this dependence only for densities above 1.82 g/cm\({}^{3}\), which corresponds to the density of the cortical bone, as shown in the middle graphs in Figure 6. The same behavior could be observed for the calibration curves associated with the combined reconstruction DD + iMAR, as shown in the graphs to the right in Figure 6.  
Figure 6: (**a**) The mean calibration curves at densities up to 1.82 g/cm\({}^{3}\) associated with the three different convolution kernels (Qr40 on the left, DD in the middle, and DD + iMAR on the right) used during the reconstruction of the Cheese phantom CT scans with or without the metal inserts. Curves associated with each kVp value, given a convolution kernel, were obtained by averaging the mean HU (or HU\({}_{\text{DD}}\)) value in each ROI over the acquisitions with and without the metal inserts in the Cheese phantom, at the same kVp value. (**b**) The mean calibration curves at densities ranging from 1.82 g/cm\({}^{3}\) to 8 g/cm\({}^{3}\) associated with the three different convolution kernels (Qr40 on the left, DD in the middle, and DD + iMAR on the right) used during the reconstruction of the Cheese phantom CT scans with the metal inserts.  
Figure 7 and Table 4 show the absolute differences in the HU or HUDD in terms of the density between the mean calibration curve built at 80 kVp and the one at 140 kVp for each reconstruction algorithm.  
Given the curve sets associated with the DD and DD + iMAR algorithms at low densities (second and third column of Table 4), no significant difference in the HUDD was found between the 80 kVp and 140 kVp curves (following the IAEA criteria [20]). In contrast, when considering the set of curves associated with the standard reconstruction (first column of Table 4), significant differences in HU involve the ROIs corresponding to the inner bone, B-200 bone, CB2-30%, CB2-50%, and cortical bone equivalent materials.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Insert Name** & **Density (g/cm\({}^{3}\))** & \multicolumn{3}{c}{**Convolution Kernel**} \\ \hline  & & **Qrt0** & **DD** & **DD + iMAR** \\  & & **Abs dHU (dHU\%)** & **Abs dHU (dHU\%)** & **Abs dHU (dHU\%)** \\ \hline LN-300 Lung & 0.30 & 5 (2) & 3 (1) & 5 (2) \\ LN-450 Lung & 0.49 & 0 (0) & 3 (1) & 5 (1) \\ Adipose & 0.94 & 24 (3) & 26 (3) & 25 (3) \\ Breast & 0.98 & 10 (1) & 12 (1) & 14 (1) \\ Solid Water & 1.02 & 9 (1) & 7 (1) & 7 (1) \\ Brain & 1.05 & 23 (2) & 24 (2) & 25 (2) \\ Liver & 1.10 & 7 (1) & 6 (0) & 6 (0) \\ Inner Bone & 1.14 & 116 (10) & 1 (0) & 2 (0) \\ B-200 Bone & 1.15 & 116 (10) & 3 (0) & 3 (0) \\ CB2-30\% & 1.33 & 185 (23) & 22 (2) & 22 (2) \\ CB2-50\% & 1.56 & 368 (21) & 9 (0) & 9 (1) \\ Cortical Bone & 1.82 & 569 (26) & 18 (1) & 22 (1) \\ Titanium & 4.51 & 6068 (76) & 5233 (72) & 5234 (72) \\ Stainless-steel & 8.00 & 12,243 (74) & 10,608 (66) & 10,602 (66) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The absolute and percentage differences (percentage differences between brackets) in the HU or HUDD between the average calibration curve corresponding to the acquisition at 80 kVp and the average calibration curve corresponding to the acquisition at 140 kVp, for each set of curves related to each reconstruction algorithm.  
Figure 7: The absolute difference in HU or HUDD between the average calibration curve corresponding to the acquisition at 80 kVp and the average calibration curve corresponding to the acquisition at 140 kVp, for each set of curves related to each reconstruction algorithm. The curve related to the DD reconstruction (DD) matched the curve related to the combined reconstruction DD + iMAR.