## 4 Discussion  
Understanding the soft tissue changes achieved with orthopedic/orthodontic treatments is of utmost importance in orthodontics. However, the assessment of these changes based on two-dimensional radiological analysis has limitations. Indeed, there is a need for an analysis method able to overcome the limitations of linear and angular measurements that could allow for reliable registration and superimposition of two (or more) three-dimensional facial scans based on a stable reference system. In this study, two new reference systems were compared with one created using CBCT scans as the gold standard. Both reference systems were found to be valid and reliable, and without any difference between growing and non-growing subjects. Indeed, the sagittal plane of both FS reference systems, although not coincident, present a deviation of less than 2 degrees with respect to the CBCT-derived sagittal plane. This difference is similar between the two reference systems at both time points, and between non-growing and growing \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Sagittal FST’Sagittal CBCT**} & \multicolumn{4}{c}{**Sagittal FS2’Sagittal CBCT**} & \multicolumn{4}{c}{**Sagittal FS1’Sagittal FS2**} \\  & **Mean** & **SD** & **95\% CI** & **95\% CI** & **Mean** & **SD** & **95\% CI** & **95\% CI** & **P Value * Mean** & **SD** & **95\% CI** & **95\% CI** & **(LL)** & **UU** \\ \hline Growing T0\({}^{*}\) & 1.94 & 0.93 & 1.57 & 2.30 & 1.71 & 0.79 & 1.40 & 2.01 & 0.232 & 1.42 & 1.08 & 0.99 & 1.83 \\ Growing T1\({}^{*}\) & 1.92 & 0.91 & 1.57 & 2.28 & 1.79 & 0.84 & 1.46 & 2.11 & 0.564 & 1.47 & 1.15 & 1.03 & 1.92 \\ \(\rho\) value § & 0.407 & & & 0.923 & & & & & & & & \\ ICC & 0.998 & & & 0.923 & & & & & 0.926 & & & \\ Non-growing T0\({}^{*}\) & 1.87 & 1.05 & 1.44 & 2.30 & 1.91 & 1.41 & 1.33 & 2.48 & 0.438 & 1.37 & 1.22 & 0.88 & 1.87 \\ Non-growing T1\({}^{*}\) & 1.76 & 1.04 & 1.34 & 2.18 & 1.90 & 1.04 & 1.48 & 2.32 & 0.684 & 1.22 & 1.02 & 0.81 & 1.63 \\ \(\rho\) value § & 0.161 & & & 0.692 & & & & & & 0.936 & & & \\ ICC & 0.997 & & & 0.920 & & & & 0.850 & & & & \\ Total T0\({}^{*}\) & 1.90 & 0.98 & 1.63 & 2.17 & 1.80 & 1.13 & 1.50 & 2.11 & 0.753 & 1.39 & 1.13 & 1.08 & 1.71 \\ Total T1\({}^{*}\) & 1.91 & 0.97 & 1.65 & 2.18 & 1.78 & 0.93 & 1.52 & 2.03 & 0.476 & 1.35 & 1.08 & 1.05 & 1.65 \\ \(\rho\) value § & 0.660 & & & & 0.724 & & & & & 0.777 & & & \\ ICC & 0.997 & & & 0.918 & & & & & & & & \\ \hline \multicolumn{10}{c}{**Coronal FS1’Cronal CBCT**} & \multicolumn{4}{c}{**Coronal FS2’Cronal CBCT**} \\  & **Mean** & **SD** & **95\% CI** & **95\% CI** & **Mean** & **SD** & **95\% CI** & **95\% CI** & **p value *’ & & & \\ \hline Growing T0\({}^{*}\) & 28.14 & 4.40 & 26.44 & 29.85 & 28.13 & 4.40 & 26.42 & 29.84 & 0.372 & & & \\ Growing T1\({}^{*}\) & 28.07 & 4.39 & 26.37 & 29.78 & 28.05 & 4.39 & 26.35 & 29.76 & 0.401 & & & \\ \(\rho\) value § & 0.143 & & & 0.125 & & & & & & & & \\ ICC & 0.999 & & & & 0.999 & & & & & & & \\ Non-growing T0\({}^{*}\) & 23.31 & 4.33 & 21.57 & 25.07 & 23.29 & 4.40 & 21.60 & 24.98 & 0.863 & & \\ Non-growing T1\({}^{*}\) & 23.18 & 4.33 & 21.42 & 24.93 & 23.18 & 4.35 & 21.43 & 24.94 & 0.837 & & \\ \(\rho\) value § & 0.328 & & & & 0.177 & & & & & & & \\ ICC & 0.993 & & & & & & & & & & & \\ Total T0\({}^{*}\) & 25.82 & 4.97 & 24.46 & 27.18 & 25.80 & 4.91 & 24.46 & 27.14 & 0.770 & & \\ Total T1\({}^{*}\) & 25.71 & 4.98 & 24.35 & 27.07 & 25.71 & 4.97 & 24.35 & 27.07 & 0.599 & & & \\ \(\rho\) value § & 0.137 & & & 0.132 & & & & & & & & \\ ICC & 0.997 & & & & 0.999 & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Bias and limits of agreement (LoA) for Bland–Altman plots.