Three-dimensional architectural and structural analysis—a transition in concept and design from Delaire’s cephalometric analysis


The aim of this study was to present a systematic sequence for three-dimensional (3D) measurement and cephalometry, provide the norm data for computed tomography-based 3D architectural and structural cephalometric analysis, and validate the 3D data through comparison with Delaire’s two-dimensional (2D) lateral cephalometric data for the same Korean adults. 2D and 3D cephalometric analyses were performed for 27 healthy subjects and the measurements of both analyses were then individually and comparatively analyzed. Essential diagnostic tools for 3D cephalometry with modified definitions of the points, planes, and measurements were set up based on a review of the conceptual differences between two and three dimensions. Some 2D and 3D analysis results were similar, though significant differences were found with regard to craniofacial angle (C1–F1), incisal axis angles, cranial base length (C2), and cranial height (C3). The discrepancy in C2 and C3 appeared to be directly related to the magnification of 2D cephalometric images. Considering measurement discrepancies between 2D and 3D Delaire’s analyses due to differences in concept and design, 3D architectural and structural analysis needs to be conducted based on norms and a sound 3D basis for the sake of its accurate application and widespread adoption.

Two-dimensional (2D) cephalometric analysis has long been an essential tool in the diagnosis and treatment planning of craniofacial dysmorphosis, as well as for the evaluation of normal craniofacial growth. Among the various cephalometric analyses, architectural and structural craniofacial analysis has attained a unique status due to its evaluation of the mutual balance between the face and cranium on an individual basis. It analyzes the craniofacial architecture and surrounding structures through the geometric allocation of four cranial lines (C1–C4) and eight craniofacial lines (F1–F8) on 2D lateral cephalograms.

Recent advances in imaging technology have led to the transition from 2D to three-dimensional (3D) cephalometrics using computed tomography (CT) scan images. 3D architectural and structural cephalometric analysis is one of the various CT-based 3D cephalometric analyses proposed, and was first introduced by Bettega et al. in 2000. They constructed five planes (C1, F1, F4, F7, and F8) and two lines (F5, chin) using 12 anatomical reference points. A later version of architectural analysis, put forward by Olszewski et al., used 22 anatomical reference points and 13 constructed planes (C1–C3, F1–F8, midsagittal, and chin plane) using commercial 3D software. They defined the reference points and planes successfully and reproducibly based on the main reference points and lines of Delaire’s cephalometrics. Their analysis, however, still showed some limitations, as well as diverging from the original concept of Delaire’s architectural and structural analysis. One limitation was the absence of cranial analysis including cranial height and calvarium-related reference points, such as the summit of the cranium (Sc) and bregma (Br), critical in evaluating the vertical and sagittal growth patterns of the cranium and their relation to the facial architecture. Another limitation lay in the absence of 3D analysis-derived norm data from healthy individuals and their comparison with 2D analysis data, an omission that hinders practical application of their analysis.

3D cephalometric craniofacial analysis is not a simple expansion of 2D analysis using 3D lines and planes. The successful transition from 2D to 3D analysis demands a validation of 3D diagnostic components (points, planes, and measurements), a model orientation in 3D space, and 3D cephalometric norm values, all based on a thorough understanding of the conceptual difference between 2D and 3D. To enable a successful transition from 2D to 3D analysis, we aimed to assess 3D cephalometry by comparing 3D data from normal Korean subjects with 2D data and to suggest a Delaire approach to 3D architectural and structural craniofacial cephalometric analysis using our norm values. We thus review herein 3D-related concepts and present a systematic sequence of 3D cephalometry with norm data from a CT-based 3D architectural and structural analysis of Koreans using modified definitions of the points and planes. A comparison of 3D measurements with traditional 2D cephalometric data for the same individuals is also presented.

Materials and methods


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 ).

Fig. 1
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.


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).

Fig. 2
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.


The measurement results for the 2D and 3D Delaire’s analyses are presented in Tables 1 and 2 . The 3D C1–C2 and C1–C4 angles were 22.62 ± 2.21° and 118.08 ± 2.51°, respectively; their 2D equivalents were almost the same. The C1–NP-based F1 angle was 83.05 ± 2.48° and C1–Me-based F1 angle was 85.94 ± 1.97° in the 3D analysis, while these were 86.12 ± 1.11° (NP-based) and 86.06 ± 1.82° (Me-based) in the 2D analysis. The d1–F4 angle was 115.01° ± 4.56° in 2D and 113.62° ± 5.67° in 3D analysis, and the d2–mandibular plane angle was 94.54° ± 6.39° in 2D and 90.38° ± 5.10° in 3D analysis.

Table 1
Comparison of 2D and 3D cephalometric angular measurement analyses ( N = 27).
Angular measurement (°) 2D (mean ± SD) 3D (mean ± SD) 2D–3D a Intergroup difference ( P -value)
2D–3D b M–F c
C1–C2 22.86 ± 1.89 22.62 ± 2.21 0.74 ± 1.85 0.070 NS (in 2D and 3D)
C1–C4 117.43 ± 2.49 118.08 ± 2.51 0.61 ± 1.89 0.330
C1–NP-based F1 86.12 ± 1.11 83.05 ± 2.48 3.06 ± 2.18 0.000*
C1–Me-based F1 86.06 ± 1.82 85.94 ± 1.97 0.70 ± 1.82 0.795
d1–F4 115.01 ± 4.56 113.62 ± 5.67 3.45 ± 2.31 0.023*
d2–mandibular plane 94.54 ± 6.39 90.38 ± 5.10 5.54 ± 4.35 0.007*
2D, two-dimensional; 3D, three-dimensional; SD, standard deviation; M, male; F, female; NS, not significant ( P ≥ 0.05).

a 2D–3D: absolute difference between 2D and 3D measurements.

b t -Test for paired differences between 2D and 3D analysis, except for C1–C4, where the Wilcoxon signed rank test was used.

c Independent samples t -test for difference between males and females. * P < 0.05, significant.

Table 2
Results of cephalometric linear measurements for 2D and 3D analyses ( N = 27).
Linear measurement 2D (mean ± SD) 3D (mean ± SD) 2D–3D a Intergroup difference ( P -value)
2D–3D b M–F c
C3 height (mm) 151.63 ± 4.55 135.91 ± 4.78 14.81 ± 4.73 0.000* NS (in 2D and 3D)
Maxillary portion (mm) 55.69 ± 2.64 53.23 ± 2.82 2.19 ± 2.40 0.003*
Mandibular portion (mm) 40.51 ± 2.54 34.56 ± 2.06 5.94 ± 1.61 0.029*
Craniospinal portion (mm) 78.41 ± 8.95 72.88 ± 6.37 5.66 ± 6.07 0.000*
C3 height (%) 86.73 ± 4.22 85.67 ± 3.54 1.57 ± 2.78 0.069
Maxillary portion (%) 31.92 ± 1.46 32.79 ± 1.45 1.35 ± 1.00 0.098
Mandibular portion (%) 23.30 ± 1.84 22.20 ± 1.44 1.53 ± 1.00 0.140
Craniospinal portion (%) 44.84 ± 2.93 45.30 ± 2.63 0.82 ± 1.19 0.188
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Jan 19, 2018 | Posted by in Oral and Maxillofacial Surgery | Comments Off on Three-dimensional architectural and structural analysis—a transition in concept and design from Delaire’s cephalometric analysis
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