# Long-Term CBCT Evaluation of Mandibular Third Molar Changes after Distalization in Adolescents
## 2 Materials and Methods
### CBCT Reference Planes and Measurements  
The CBCT imaging results were converted to the Digital Imaging and Communications in Medicine (DICOM) format. These DICOM data were three-dimensionally reconstructed using InVivo software (version 5.3; Anatomage, San Jose, CA, USA) before analyzing. The orientation and measurements were performed by single examiner ([PERSON]). Repeated measurements were calculated to analyze the intraclass correlation coefficient (ICC). The ICC values showed intrarater reliability ranging from 0.92 to 0.95. In addition, 10 cases were measured by another examiner ([PERSON]) to assess the interexaminer reliability using the ICC test; and the results showed 0.99 of good inter-rater reliability. Landmarks were additionally digitized; the mesiobuccal (MB) and distobuccal (DB) cusps and the distance from the MB cusp of mandibular molar to the horizontal, frontal, and sagittal planes were measured. As X-axis, the horizontal plane was defined as the plane passing through the menton and parallel to a plane extending through the right and left mental foramen and pogonion. As Y-axis, the sagittal plane was defined as the plane perpendicular to the horizontal plane at the menton and passing through the B point. As Z-axis, the frontal plane was defined as the plane perpendicular to both planes and passing through the pogonion (Figure 2). Figure 2: Reorientation of X, Y, and Z reference planes using landmarks: menton; gonom; B point; pogonion; mental foramen. The horizontal plane (X-axis) was the plane passing the menton and parallel to a plane extending through the right and left mental foramen and pogonion. The sagittal plane (Y-axis) was perpendicular to the horizontal plane at the menton and passed through the B point. The frontal plane (Z-axis) was perpendicular to both planes and passed through the pogonion. The distances from the MB cusps of mandibular first, second, and third molars to horizontal, sagittal, and frontal planes were measured. The distances from the frontal plane to each MB cusp of the lower posterior teeth were measured parallel to reference line from pogonion to the superior point of mental foramen. The positional changes on each plane were assessed by the distance differences pre- and post- distalization, and after long-term retention (Figure 3A). The angles between the horizontal plane and long axis of first and second molars, which were set as line from the MB cusp to the tip of mesial root, were calculated. The angulation of third molar was defined as the line from midpoint of the crown to that of developing root. The angulation changes of the posterior teeth were analyzed (Figure 3B). Figure 3: _Cont._  
The angles were analyzed between sagittal plane projected on horizontal plane and the crown axis of molars, a line tangential to the MB and DB cusps. The change in rotation of maxillary molars was also measured (Figures 3C and 4). Figure 4: Schematic illustration of the measurements. (a–c) Distance between the MB cusp of each tooth and the frontal plane; (d–f) distance between the MB cusp of each tooth and the horizontal plane; (g–i) angularation of each tooth to the horizontal plane. The first and second molar axis were defined as extending through the MB cusp and apex of the mesial root. The third molar axis was defined and extended through the midpoint of the crown and the mesial and distal endpoint of the developing root. Figure 3: (**A**) Position of the mandibular right first molar: (1) Horizontal plane; (2); frontal plane; (3) the distance from the mesiobuccal cusp to the frontal plane (Z); (4) the distance from the mesiobuccal cusp to the horizontal plane (X). (**B**) Angulation of the mandibular first molar: (5) The angle between the long axis of the first molar (mesiobuccal cusp-mesial root tip) and the horizontal plane (X).