## 2 Materials and Methods  
Patients who had undergone CBCT imaging at Wonkwang University Dental Hospital in 2019 and satisfied the following conditions were selected: (1) Young adults between the age of 20 and 25, (2) permanent dentition without deciduous teeth or dental implants, (3) no history of root canal treatment in the mandibular molar region with healthy apical tissues, (4) no furcation involvement of mandibular molars, (5) no degenerative changes in the temporomandibular joints, (6) no facial asymmetry, and (7) no orthodontic braces or retainers. CBCT images were acquired using Alphard VEGA (Asahi Roentgen, Kyoto, Japan). Images were taken with 17-s exposure times at a tube voltage of 80 kVp and a tube current of 7 mA. The size of the voxel was 0.39 \(\times\) 0.39 \(\times\) 0.39 mm. Original CBCT data of the 145 patients (84 men, 61 women, mean age: 22.0 \(\pm\) 1.76 years) were stored in digital imaging and communications in medicine format and analyzed using Ondemand3D software (Version 1.0, Cybermed, Seoul, Republic of Korea). Two-dimensional lateral and frontal cephalospors were obtained from the reoriented CBCT images (Figure 1). The following variables were measured on lateral and frontal cephalospors (Figure 2, Table 1): facial height ratio (FHR; S-Go/N-Me), distance from distal root apex of the second mandibular molar to the mandibular plane (D7 MP), ANB angle, sella-nasion to mandibular plane angle (SNMP), palatal plane to mandibular plane angle (PPMP), and the maxilla and  
CBT images were reoriented such that the mandibular occlusal plane passed through the midpoint of the mandibular central incisor edge and right and left mesiobuccal cusps of the mandibular first molar (Figure 1) [2]. The distances between the left and right mandibular molar roots and the inner and outer surfaces of lingual cortical bone were measured (Figure 3). \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Measurements**} & \multicolumn{1}{c}{**Description**} \\ \hline Anterior facial height (AFH) (mm) & Distance from nasion to mention \\ Posterior facial height (PFH) (mm) & Distance from sella to goni \\ Facial height ratio (FHR) (\%) & Ratio of PFH to AFH (PFH/AFH) \\ D7 MP (mm) & Distance from AD7 to mandibular plane \\ ANB (\({}^{\circ}\)) & Angle formed by point A, nasion, and point B \\ SNMP (\({}^{\circ}\)) & Angle between SN plane and mandibular plane \\ PPMP (\({}^{\circ}\)) & Angle between palatal plane and mandibular plane \\ J-J/Ag-Ag ratio (\%) & Ratio of RJ-LJ to RAg-LAg \\ \hline \hline \end{tabular}  
Patients were assigned to hypodivergent (FHR \(\geq\) 69%, \(n\) = 36), normovergent (61% \(\leq\) FHR \(<\) 69%, \(n\) = 80), and hyperdivergent (FHR \(<\) 61%, \(n\) = 29) groups according to FHR (Table 2). This study was approved by the Institutional Review Board (IRB) of Wonkwang University Dental College Hospital (WKDIRB202005-01).  
\end{table} 
Table 1: Linear and angular measurements on lateral and frontal cephalograms. Figure 3: (**A**) The distance between the root and the lingual cortical bone was measured in a plane parallel to the mandibular occlusal plane and 1, 3, and 5 mm away from the apex. (**B**) Schematic diagram showing the distance measured between the root and lingual cortical bone on the axial plane. (a) distance between molar roots and outer lingual cortical bone, (b) distance between molar roots and inner lingual cortical bone.