# Morphological Evaluation of Cranium Facial Asymmetry in Class III Malocclusion Patients
## 2 Materials and Methods  
### Research Subjects and Materials  
A total of 60 patients, comprised of 30 patients diagnosed with skeletal mandibular propagnathism with facial asymmetry (asymmetry group) and 30 patients diagnosed with skeletal mandibular propagnathism without facial asymmetry (symmetry group) who visited the Chiba Dental Center of Tokyo Dental College between 2010 and 2020, were included. In all patients, cephalometric X-ray photographs in the lateral, frontal, and axial positions were taken, which were used for cephalometric analysis. The inclusion criteria were skeletal mandibular propagnathism cases with ANB (ANB: an evaluation item of the anteroposterior position of the maxillary and mandibular alveolar bases) of less than 0\({}^{\circ}\)[17] and a Wits appraisal (Wits: an evaluation item of the relative position of the maxilla and mandible) of less than 0 mm [18; 19] in the cephalometric analysis using lateral cephalometric radiographs. In addition, Menton (Menton: the extreme inferior point of the chin) deviation on postero-anterior cephalometric radiographs was defined as 4 mm or more in the asymmetry group and 3 mm or less in the symmetry group [6; 20; 21]. Patients with hereditary or congenital diseases, endocrine and metabolic abnormalities, severe trauma to the maxillofacial cranium, or severe TMJ disorder were excluded. A breakdown of the target population is shown in Table 1.  
The sample size required for this study was considered based on preliminary studies. The effect size was calculated from the measured area, and standard deviation in the cranium, and a significance level of 0.05 and a power of 0.75 were set, resulting in a sample size of 30. Further referencing similar studies, a sample size of 30 was determined to be adequate [20; 21]. Samples were measured for cranial morphology using axial cephalometric radiographs taken before the start of preoperative orthodontic treatment. Axial cephalometric radiographs were taken in the following settings (X-ray tube voltage, 95 kV; X-ray tube current, 100 mA; X-ray irradiation time, 0.16 s). The obtained images were output in DICOM format, and cephalometric analysis and measurements of distances and areas were carried out digitally using cephalometric analysis software (Quick Ceph Studio, Sarasota, FL, USA) and maxillofacial treatment simulation software (Siemens Erlangen, DEU). Measurements in this study were taken by the same evaluator. After 4 weeks, the reference points and reference lines were remeasured, and the intraclass correlation coefficient (ICC; 1, 0, 0.84) was calculated. The study was approved by the Tokyo Dental College Ethics Committee (Approval No.916). Establishment of Reference Points, Reference Lines, and Measurement Items in Cephalometric Radiographs  
Cranial measurements were carried out using axial cephalometric radiographs in all 60 selected cases. The anterior margin of the right and left foramen ovale (Fo: right side--FoR; left side--FoL) was set as the reference point in the axial position cephalometric radiograph to perform the measurement. A line passing through the two points (FoR and FoL) was designated as the FoP and was used as the horizontal reference line. The midpoint between the FoR and FoL on the FoP was set as the FoM. The line passing through the FoM and perpendicular to the FoP was designated as the FoVP, the vertical reference line. In order to compare the anteroposterior and lateral differences in all crania, the cranium was divided between the FoP and FoVP into three sections of 30\({}^{\circ}\) each side. The lengths from the FoM to the divided cranial limb were designated a-e from the right side. The occup of the cranium was also divided in a similar fashion into three sections of 30\({}^{\circ}\) each on the left and right sides, and the cranium was divided into blocks 1-6 from the right side (Figure 1). The length of a-e and the area of blocks 1-6 in all cases were measured.