## 4 Discussion  
The digital casts of 43 patients with FPCB and 44 controls were analysed to investigate the asymmetry of the maxillary dento-alveolar and palatal vault regions by measuring transverse and sagittal linear distances and performing superimpositions and 3D analyses. The findings revealed that the study group exhibited a greater degree of asymmetry between the two halves of the maxillary models in both the transverse and sagittal directions compared to the control group. Moreover, the 3D analysis confirmed that the asymmetry of the maxilla in the patients with FPCB was more pronounced than in the control group. Therefore, the null hypothesis was rejected. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**FPCB (\(N=43\))**} & \multicolumn{4}{c}{**Control Group (\(N=44\))**} \\ \hline  & **Median** & **(25 th; 75 th)** & **Min.** & **Max.** & **Median** & **(25 th; 75 th)** & **Min.** & **Max.** & **Diff.** & \(p\) \\ \hline
**DIFF C TW (mm)** & 0.99 & 0.39; 2.09 & 0.02 & 4.08 & 0.54 & 0.26; 0.87 & 0.02 & 1.20 & 0.45 & 0.000 * \\
**DIFF M TW (mm)** & 1.23 & 0.63; 2.14 & 0.02 & 4.19 & 0.50 & 0.27; 0.92 & 0.04 & 2.39 & 0.73 & 0.000 * \\
**DIFF C DEP (mm)** & 1.00 & 0.46; 1.43 & 0.02 & 2.36 & 0.31 & 0.18; 0.43 & 0.01 & 0.88 & 0.69 & 0.000 * \\
**DIFF M DEP (mm)** & 0.95 & 0.50; 1.35 & 0.04 & 2.39 & 0.32 & 0.18; 0.44 & 0.06 & 3.07 & 0.63 & 0.000 * \\
**UM-RP (mm)** & 0.20 & 0.00–0.70 & 0.00 & 1.94 & 0.00 & 0.00–0.00 & 0.00 & 0.5 & 0.2 & 0.000 * \\
**Matching (\%)** & 37.00 & 31.00–46.00 & 18.87 & 61.58 & 51.00 & 42.00–59.00 & 34.01 & 73.08 & \(-\)14.00 & 0.000 * \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics and statistical comparisons of digital model variables between FPCB and CG. Figure 5: **(a,b)**: **(a)** Maximly model 3D analysis of a patient with FPCB; **(b)** Maximly model 3D analysis of a patient in the control group. RGB-coloured scale rod (millimetres) is shown on the right: the top (red) and the bottom (blue) of the scale denote the positive and negative differences in height. Green signifies the tolerance range. Statistical analysis demonstrated that the differences in canine and molar widths and depths between the two sides of the maxilla were significantly larger in the study group compared with the control group (e.g., DIFF M TW was 1.23 mm in the FPCB group and 0.50 in the CG with \(p<0.000\)). This confirmed that patients in the FPCB group presented greater maxillary arch asymmetry in the transverse and sagittal planes compared to control subjects. The difference in transverse and sagittal measurements between the two halves of the maxilla in the study group was approximately 1 mm. However, the interquartile range revealed that, clinically, the asymmetry could reach more relevant values. For instance, the difference in the transverse distance of the molars from the midpalatal raphe (DIFF M TW) was 1.23 mm (IQR 0.63-2.14), and the difference in the sagittal position of the amines between the two halves of the maxilla (DIFF C DEP) was 1.00 mm (IQR 0.46-1.43). Additionally, the upper dental midline showed a deviation from the Raphe plane of 0.20 (IQR 0.00-0.70) in the study group. These findings align with those of [PERSON] [23], who identified and described dento-alveolar asymmetries in the maxilla of patients affected by FPCB. Furthermore, these results support the potential role of dento-alveolar asymmetries as contributing factors in the etiology of an asymmetric malocclusion, as already explored by [PERSON] et al. [24] in Class II subdivision malocclusion. The result of the 3D analysis supported the hypothesis of greater maxillary arch asymmetry in the study group. The percentage of matching--which was obtained from the superimposition of the mirrored models--was significantly lower in the study group (37%) compared to the control group (51%), with the greatest discrepancies observed at the dento-alveolar level. These findings align with those reported by [PERSON] et al.