Subjects

Twenty-seven normal Korean adults with skeletal class I (11 males and 16 females; mean age 24.22 ± 2.91 years), sampled at random, volunteered for this study. Clinical and cephalometric examinations with dental plaster models were used to rule out dysmorphosis and malocclusion. The following inclusion criteria were used for subject collection: native Korean, Angle’s class I molar key and maxillomandibular skeletal relationship with C1–F1 angle of 83–91°, sella–nasion–A point (SNA) angle of 79–85°, sella–nasion–B point (SNB) angle of 76.5–83°, and A point–nasion–B point (ANB) angle of 0–4° (based on Korean norm studies ), full dentition except for permanent third molars and no anterior or posterior crossbite, aesthetically acceptable appearance without facial asymmetry (assessed by two authors, Lee and Park), no previous history of prosthodontic, operative, orthodontic, orthognathic or medical treatment, absence of temporomandibular joint disease or oral functional disturbances, and no history of craniofacial trauma. Informed consent was obtained from each subject and this work was approved by the local ethics committee.

Image acquisition

Each subject underwent CT imaging, with the Frankfort horizontal (FH) line perpendicular to the floor, using a high-speed Advantage CT System (GE Medical Systems, Inc., Milwaukee, WI, USA) employing a high-resolution bone algorithm protocol (200 mA, 120 kV, scanning time 1 s, 1 mm scan thickness, a 512 × 512 pixel reconstruction matrix, and 0.48 mm × 0.48 mm × 1.0 mm voxels). All subjects were asked to close their mouth at the maximum intercuspation. The CT image data were saved in DICOM file format, transferred to a personal computer, and reconstructed to 3D skull images based on the same Hounsfield unit values for bone setting using SimPlant software version 14.0 (Materialise NV, Leuven, Belgium). The subjects also underwent conventional 2D cephalometric radiography with the FH line horizontal to the floor (Cranex 3+ Cep.; Orion-Soredex, Helsinki, Finland): 87 kV, 10 mA, 0.6 s. The 2D cephalometric image data acquired were transferred to a personal computer for 2D analysis using Vceph software version 4.0 (Cybermed, Seoul, Korea).

Reference points, lines, and planes for 2D and 3D architectural and structural analysis

The 2D architectural and structural analyses were performed based on 29 anatomical reference points and 16 lines (C1–C4, F1–F8, d1–d2, occlusal, and mandibular lines; see Supplementary Material Figs. S1a and S2a, Tables S1 and S2). For 3D analysis, the 3D skull model was oriented to the three reference systems, namely the midsagittal (MS), C1 as the axial plane, and F5 as the coronal plane, these being orthogonal to each other (Supplementary Material Fig. S1b insert, Table S2). The construction details for the 2D and 3D analyses are presented in the Supplementary Material. In addition, a plane from the fronto-maxillary point (FM) to the nasopalatine canal point (NP), designated NP-based F1, and one from FM to menton point (Me), designated Me-based F1, were independently constructed to obtain plane F1, corresponding to line F1 between FM, NP, and Me in 2D analysis ( Fig. 1 a–c ).

Construction of F1 in 2D and 3D cephalometric analysis. (a) Line F1 passes through FM, NP, and Me points in 2D lateral cephalometrics. Angle ‘a’ represents the craniofacial angle between line C1 and F1. (b) Plane F1 passing through FM–NP (NP-based F1) differs drastically from that passing through FM–Me (Me-based F1) in the sagittal sectional view in 3D cephalometrics. Angles ‘b’ and ‘c’ indicate, independently, the craniofacial angle between plane C1 and NP-based F1 or Me-based F1, respectively. (c) NP-based and Me-based F1 planes in Fig. 1 b are presented on the 3D model.

Measurements

2D measurements were made of points and lines using Vceph software, and 3D measurements of points and planes using SimPlant software. Cranial and facial angles were measured ( Figs. 1a–c and 2a ): the C1–C2 angle (anterior cranial base angle), C1–C4 angle (posterior cranial base angle), C1–NP-based F1 angle (craniofacial maxillary angle), and C1–Me-based F1 angle (craniofacial mandibular angle). The lengths of C3 and C2, being subdivided into maxillary, mandibular, and craniospinal parts, were also measured, and their proportions were calculated as C3/C2, maxillary part/C2, mandibular part/C2, and craniospinal part/C2 ( Fig. 2 a and b ). Finally the d1–F4 angle (upper incisal angle) and d2–mandibular plane angle (lower incisal angle) were measured ( Fig. 2 c).

Cephalometric measurements of 3D Delaire’s analysis. (a) Angle ‘a’ is the anterior cranial base angle between plane C1 and C2; angle ‘b’ is the posterior cranial base angle between plane C1 and C4; angle ‘c’ is the craniofacial angle between plane C1 and Me-based F1; ‘d’ is the length of the plane between point Sc and a point crossing through C2, C3, and the MS plane. (b) ‘e’ is the maxillary length on plane C2 between mid-M and mid-Pts (superior pterygoid point); ‘f’ is the mandibular length on plane C2 between mid-Pts and mid-Cp (posterior condylar point); ‘g’ is the craniospinal length on plane C2 between mid-Cp and Oi (inferior occipital point). (c) Angle ‘h’ is the upper incisal angle between plane d1 and F4; angle ‘i’ is the lower incisal angle between plane d2 and the mandibular plane.

Statistical analysis and method error

The mean value and standard deviation (SD) for each measurement in both 2D and 3D analyses were calculated, along with the absolute differences between the two methods. A power analysis for the comparison of means was used to determine the validity of the data. The 2D and 3D data were statistically evaluated with Kolmogorov–Smirnov and Shapiro–Wilk tests for normal distribution, and compared using the paired samples t -test at the level of P < 0.05 (except the C1–C4 angle, for which the Wilcoxon signed rank test was used due to the lack of normal distribution) using SPSS software version 18.0 (SPSS Inc., Chicago, IL, USA). Gender differences in the 2D and 3D datasets were also assessed by independent samples t -test.

For the error study, two of the authors (Park and Lee) marked the reference points three times at an interval of 1 week for both the 2D and 3D cephalometric analyses. Intra-observer reliability was evaluated using Dahlberg’s formula and analyzed statistically by intra-class correlation (ICC) with 95% confidence intervals. A paired samples t -test and ICC calculation were also carried out to evaluate inter-observer reliability.