## 4 Discussion  
This study used 3D linear and angular measurements to clarify the preoperative anatomical variables affecting the outcome of surgical correction in Class III facial asymmetry. Patients with skeletal Class III malocclusion and facial asymmetry, with a menton deviation greater than 4 mm, were included in this study. According to [PERSON] et al., the perception of asymmetry of a chin deviation of 2 mm to the right and 4 mm to the left is not detected clinically [24]. Alongside that, most individuals, whether dental professionals or laymen, can notice a chin deviation of more than 4 mm [25]. Thus, it is acceptable to define 4 mm of menton deviation relative to MSP as facial asymmetry. The mean preoperative menton deviation in the two groups was 6.52 \(\pm\) 5.36 mm in group S and 8.15 \(\pm\) 4.19 mm in Group A (Table 3). The patients included in our study showed a severe deviation of menton, indicating a greater severity of facial asymmetry. After treatment completion, facial asymmetry significantly improved in all patients, but did not completely resolve. [PERSON] et al. reported that preoperative 3D dentoskeletal variables were not related to subjective visual perceptions of postoperative asymmetry [14]. In the present study, we used a more objective method to define postoperative asymmetry. However, the menton deviation decreased significantly after treatment, and the difference in midline deviation was not appropriate for defining postoperative symmetry and asymmetry. Currently, there is no objective 3D index to represent the degree of facial asymmetry. Therefore, we used the asymmetry index at treatment completion to classify patients into two groups and evaluate the preoperative variables. We observed that only bilateral variables, and not midline variables, significantly affected the surgical outcomes. This may be because midline deviation is already corrected by surgeons with the aid of 3D surgical simulation [10; 11]. For bilateral discrepancy, four variables were observed to significantly affect the surgical outcome: (1) maxillary anterior occlusal canting, (2) maxillary posterior occlusal canting, (3) \(\Delta\)Go to the FHP, and (4) \(\Delta\)mandibular axis to the FHP. These variables indicate the \"roll asymmetry\" of the maxilla and mandible. For maxillary occlusal canting, the greater the preoperative discrepancy, the higher the possibility of residual asymmetry. However, maxillary occlusal canting was corrected well in both groups. [PERSON] et al. found that the odds of presenting with mandibular asymmetry  
Figure 9: Significant correlation of the asymmetry index with preoperative variables. Spearman correlation was used for statistical analysis. The asymmetry index was positively correlated with the six preoperative variables and negatively correlated with five preoperative variables. were significantly higher in the presence of maxillary asymmetry [26]. The mandible is often associated with craniofacial asymmetries, with maxillary asymmetries often secondary to asymmetrical mandibular growth [27]. Severe maxillary canting might indicate more severe deviation of the mandible and more severe asymmetry of the whole face. The occlusal plane canting was usually the result of compensating growth to mandibular asymmetry. The reasons underlying the correlations are not certain and deserve future investigation. Correction of bilateral gonion contour discrepancy is more difficult and relies more on the surgeon's decision-making during surgery. Trimming or contouring the gonion angle or adaptation of the proximal and distal segments all affect the surgical outcome. Presurgical \(\Delta\)Go to MSP did not affect the surgical outcome, but \(\Delta\)Go to the FHP and Go of the deviated side to CP showed a significant between-group difference. This might indicate that the preoperative roll (\(\Delta\)Go to the FHP) and yaw (Go of the deviated side to CP) mandibular asymmetry affects the outcome.