Material and methods

All patient images in this study were collected in the Department of Oral Maxillofacial Surgery and Department of Orthodontics, Peking University School and Hospital of Stomatology. This project was approved by the Biomedical Ethics Committee of Peking University School and Hospital of Stomatology.

After applying the inclusion and exclusion criteria, 69 patients with skeletal Class III malocclusion were included in the sample ( Table I ). The inclusion criteria for the Class III group were as follows: (1) aged at least 16 years; (2) Mongolian; (3) permanent dentition; (4) no prior orthodontic or orthognathic treatment; (5) skeletal Class III (ANB angle, < 0°; Wits appraisal, ≤ –3.6 mm); (6) anterior teeth in crossbite or edge-to-edge position; and (7) MP-SN ≥ 27°. Exclusion criteria included: (1) congenitally missing teeth, retained deciduous teeth, or impacted teeth; (2) severe crowding in posterior teeth; (3) crowns or significant restorations in posterior teeth; (4) maxillary sinus obviously bulging into buccal or lingual alveolar bone of maxillary posterior teeth; (5) severe periodontitis; (6) systemic diseases; and (7) cleft lip or palate, temporomandibular joint disease. In addition, 30 patients with skeletal Class I malocclusion were included with the following inclusion criteria: (1) ANB angle between 0.7° and 4.7°; (2) mandibular deviation < 2 mm; and (3) other inclusion criteria the same as that for skeletal Class III subjects. Exclusion criteria included: (1) severe crowding or crossbite in posterior teeth; (2) crossbite or edge-to-edge position in anterior teeth; and (3) the same exclusion criteria as patients with skeletal Class III malocclusion.

Patients with skeletal Class III malocclusion were further divided into 2 subgroups according to the degree of mandibular deviation from midsagittal plane measured on 3-dimensional CBCT images: (1) group III (asymmetry), which included 39 patients (25 males, 14 females; average age, 20.2 ± 3.00 years) with mandibular deviation more than 4 mm; and (2) group III (symmetry), which included 30 patients (10 males, 20 females; average age, 21.3 ± 4.62 years) with mandibular deviation < 2 mm. Twenty-one patients with mandibular deviation from 2 to 4 mm were excluded from the study. Group I included 30 patients (10 males, 20 females; average age, 22.9 ± 4.16 years) with mandibular deviation < 2 mm. The mandibular deviation was evaluated by menton (Me) deviation to the midsagittal plane. The deviated side was defined as the side Me shifted toward the midsagittal plane, while the other side was defined as the nondeviated side ( Table II ).

The sample size calculation was based on buccal and lingual alveolar bone thickness of maxillary posterior teeth measured at 3 mm apical to the mandibular cementoenamel junction in Sendyk et al study and a standard deviation of 0.6 mm of maxillary second molar was reported. If 0.35 mm was set as clinically relevant difference, a minimum sample size of 20 subjects was required per group to achieve a significant analysis, with a significance level of 0.05 and a statistical power of 90%. The sample size was calculated using the Power Analysis and Sample Size software (version 11; NCSS, Kaysville, Utah).

CBCT images were taken with NewTom Scanner (NewTom AG, Marburg, Germany) set as follows: 15 × 15 cm field of view, 110 kV, 2.81 mA, 3.6-second exposure, with axial slice thickness of 0.3 mm. The CBCT images were saved as digital imaging and communications in medicine format and reconstructed in Dolphin 3D Imaging software (version 11.8; Dolphin Imaging and Management Solutions, Chatsworth, Calif). Landmarks were located with Dolphin software and judged on 3-dimensional sections. The location of each landmark was calculated based on 3-dimensional coordinates. To standardize the orientation of craniofacial structures, 3-dimensional reference planes were set: (1) horizontal plane was defined as Frankfort plane; (2) midsagittal plane was perpendicular to Frankfort plane, passing through nasion and basion point; and (3) coronal plane was perpendicular to the above 2 planes and passing through basion point. Landmarks and reference planes are defined and shown in Table II and Figure 1 .

Reorientation of reference planes.

On long-axis plane, angle between long axis of tooth and midsagittal line was defined as buccolingual inclination of the tooth. Definition and measurement of long axis of teeth are shown in Table III and Figures 2 and 3 . ^{, ,} If a tooth was buccally inclined, inclination angle of the tooth was defined as positive, and if it was lingually inclined, inclination angle was defined as negative.

Location of central fossa and trifurcation of the maxillary first molar. Central fossa point in A, axial; B, coronal; and C, sagittal views. Trifurcation point in D, axial; E, coronal; and F, sagittal views.

Measurement of buccolingual inclination of maxillary posterior teeth. A, in sagittal view, position the vertical reference line ( green ) to obtain the long-axis plane of maxillary first molar; B and C, in the long-axis plane, measure the inclination angle of teeth ( green arrows ).

Buccal and lingual alveolar bone thickness and alveolar width were measured at the level of buccal furcation plane of maxillary first molars. To adjust measurement plane as follows ^, : (1) sagittal view: rotate the section to make long axis of tooth parallel to the vertical reference line ( Fig 4 , A ); (2) coronal view: rotate the section to ensure the horizontal line parallel to the palatal plane and nasal floor ( Fig 4 , B ); (3) axial view: position the section at the level of buccal furcation of maxillary first molar to get the measurement plane ( Fig 4 , C ). Measurements of buccolingual alveolar width and buccal and lingual alveolar bone thickness of teeth are described in Table IV and Figures 4-6 . ^, Dehiscence and fenestration were defined according to the criteria published by Evangelista. If bone defect happened in the measured horizontal plane, the value of bone thickness was marked as zero.

Reorientation of the buccal furcation plane on the right side. A, sagittal view; B, coronal view; and C, axial view.

Measurements of buccolingual alveolar width, and buccal and lingual alveolar bone thickness of maxillary posterior teeth. A, Measurement of buccolingual alveolar width ( green lines ) of maxillary posterior teeth: D6, alveolar with of maxillary first molar; D5, alveolar width of maxillary second premolar; and D4, alveolar width of maxillary first premolar. B, Measurement of buccal and lingual alveolar bone thickness ( green lines ) of maxillary posterior teeth: 6B, buccal alveolar bone thickness of maxillary first molar; 5B, buccal alveolar bone thickness of maxillary second premolar; 4B, buccal alveolar bone thickness of maxillary first premolar; 6L, lingual alveolar bone thickness of maxillary first molar; 5L, lingual alveolar bone thickness of maxillary second premolar; and 4L, lingual alveolar bone thickness of maxillary first premolar. B , buccal alveolar bone thickness; D , distance of buccolingual alvoelar width; L , lingual alveolar bone thickness.

Representative cone-beam computed tomography images of alveolar bone thickness ( yellow lines ) of a patient in group I. Buccal alveolar bone thickness of maxillary first molar: A, axial; and B, coronal views. Lingual alveolar bone thickness of maxillary first molar: C, axial; and D, coronal views. Buccal alveolar bone thickness of maxillary second premolar: E, axial; and F, coronal views. Lingual alveolar bone thickness of maxillary second premolar: G, axial; and H, coronal views.