## 4 Discussion  
In this study, the effects of Twin Block appliance therapy on cephalometric variables and 3D face scans in patients with Class II malocclusion were analyzed. The results of the paired \(t\)-test showed a significant increase in the values of SNB, mandibular length, LsE, and soft tissue mandible length and the protrusion and inclination of lower incisors, while the values of ANB, Wits, ANPG, and overbite and the protrusion of upper incisors to the apical base of the maxilla showed a significant decrease. Other variables did not show \begin{table}
\begin{tabular}{c c c} \hline
**Sample** & **Min (mm)** & **Max (mm)** \\ \hline  
000342 & 14.29 \\ \hline \end{tabular}
\end{table} 
Table 6: Hausdorff distance from reference mesh. Figure 6: Color-coded heat map showing significant changes in the chin, mandible, and lower lip areas. significant changes, including maxillary and mandibular plane angles, and intermaximillary angle, indicating no change in vertical dimensions. An increase in the lower facial third is a favorable response to therapy in Class II patients, and it is mostly attributed to the vertical growth in the condyle and mandibular ramus, without an opening of the mandibular plane angle [7]. These results suggest that Twin Block appliance therapy effectively influenced certain skeletal and soft tissue parameters. Previous studies have indicated that patients with a condylar angle (Co-Go-Me) less than 125.5\({}^{\circ}\) before therapy are likely to exhibit favorable responses to treatment with functional appliances. In the present study, a condylar angle of approximately 119\({}^{\circ}\), both pre- and post-treatment, demonstrated that the use of the Twin Block functional appliance was favorable for treatment outcomes [26]. Comparing the results obtained with previous studies, certain similarities and differences can be observed. The increase in the SNB angle after Twin Block appliance therapy is consistent with findings from other studies, such as those by [PERSON] et al. (2013), [PERSON] et al. (2014), and [PERSON] (2023), indicating sagittal advancement of the mandible and a reduction in the skeletal discrepancy between the mandible and maxilla [27; 28; 29]. Vertical cephalometric parameters did not change significantly after therapy, and as such, did not contribute to masking or emphasizing the sagittal changes. The distance between the reference point of the upper lip (Ls) and Ricketts' esthetic line (Ls:E) increased significantly, contributing to a more optimal facial profile and reduced protrusion of the upper lip. Most of the other related studies support the statistically significant increase in the Ls:E distance, such as those by [PERSON] et al. (2008), [PERSON] et al. (2016), and [PERSON] and [PERSON] (2013) [30; 31; 32]. All of these studies also included a control group, which further strengthens their findings. Although the present study did not include a control group, previous research incorporating a control cohort found no statistically significant differences in skeletal discrepancy or overjet which could be contributed to the growth alone in control subjects [15]. Additionally, another study reported an average mandibular length increase of only 0.3 mm due to natural growth, an amount that was not statistically significant, particularly when compared to the treatment group managed with the Twin Block appliance, which exhibited a statistically significant increase in mandibular length [16], similarly to our findings. Furthermore, the study of maxillomandibular growth in untreated Class II showed that mandibular deficiency will not self-correct during pubertal peak growth [33]. The systematic literature review by [PERSON] et [PERSON] (2006) concluded that two-dimensional measurement methods, such as those based on lateral cephalograms, are not the most optimal approach for evaluating soft tissues, which may explain the contradictory results [34].