齒顎矯正協會-TJO

*

Validating the 3D and 2D Mandibular Plane to the Frankfort Plane for Craniofacial Measurement

Jason Jyun-Chen Kuo1,2 , Ellen Wen-Ching Ko2-4
1 Department of Craniofacial Orthodontic, Chang Gung Memorial Hospital, Linkou, Taiwan
2 Graduate institute of Craniofacial and Dental Science, Chang Gung University, Taoyuan, Taiwan
3 Department of Craniofacial Orthodontic, Chang Gung Memorial Hospital, Taipei, Taiwan
4 Craniofacial Research Center, Chang Gung Memorial Hospital, Linkou Taiwan

Running title: 2D and 3D Mandibular Plane Angle

Purpose: This study evaluated whether the three-dimensional (3D) plane-to-plane mandibular plane angle measurement method could be applied in clinical analysis in a manner similar to the application of conventional two-dimensional (2D) cephalometric measurement, regardless of whether patients had symmetrical planes.

Patients and methods: This retrospective study selected 30 patients who had undergone both lateral cephalometric radiography and cone-beam computed tomography (CBCT). The 2D measurement was manually traced from the lateral cephalometric radiographs for the Frankfort horizontal plane line and mandibular plane line (2D FMA). The 3D reconstructions for each patient in the CBCT were evaluated using 3D software and measured using two 3D measurement methods regarding the mandibular plane angle (3D FMA, 3D MP). The Kruskal–Wallis test was used to determine the differences among the three different methods. Dahlberg’s formula was used to determine the intra-examiner reproducibility.

Results: The mandibular plane angle acquired from two-dimensional measurements was larger than that obtained from 3D methods in the two asymmetry groups, and measurements revealed a greater difference in the horizontal asymmetry + vertical asymmetry group compared with the other two groups. However, no statistically significant difference was observed.

Conclusion: The 3D plane-to-plane angle measurement method can be used for analysis in patients with symmetric and asymmetric planes. (Taiwanese Journal of Orthodontics. 31(3): 142-152, 2019)

Keywords:
three-dimensional (3D) cephalometry; mandibular plane angle; Frankfort horizontal plane.
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INTRODUCTION

Two-dimensional (2D) cephalometric radiographs are crucial for orthodontic diagnosis and treatment planning. Several measurement methods have been developed for evaluation of dental, skeletal, and soft tissues. However, 2D cephalometric radiograph measurement demonstrates limitations with respect to size, shape, volume, direction, and landmark identification.
Currently, three-dimensional (3D) cephalometric methods are widely used for orthodontic diagnosis and surgical evaluation because they are more accurate and can provide more information than 2D cephalometry.1 Identifying measurement points in 2D cephalometric radiography is difficult when the landmarks overlap. The errors of landmark identification are lower in 3D cephalometry than in 2D radiography.2,3
Diagnosis of facial divergence is critical for orthodontic treatment planning. Several measurement methods have been developed to facilitate the classification of vertical facial types.4,5 Mandibular plane angle (MPA) is one of the diagnostic criteria used in the analysis of facial pattern in orthodontic patients. Conventional 2D cephalometry usually uses the sellanasion (S-N) line as the reference line for mandibular plane measurement. However, the sella turcica is difficult to mark in 3D because it is located in the center dot of the pituitary gland. Therefore, 3D cephalometry usually uses the Frankfort horizontal (FH) plane instead of SN for MPA measurement.
In terms of 3D cephalometric measurement, mandibular plane is defined differently. Line-to-line, lineto-plane, or plane-to-plane were used in 3D cephalometry to measure the MPA.6–13 Its difference between 2D and 3D cephalometric measurements were compared between 2D MPA to 3D line-to-line MPA,10,11,13,14 or to line-to-plane MPA,11 or to MPA formed by a landmark projected onto the midsagittal plane (Table 1).15
Several studies have reported that using plane-toplane angle method for mandibular plane measurements in 3D cephalometry.6,7,16 Plane-to-plane angle is the easiest to design and does not require projection in 3D cephalometry. It is faster and easier while using 3D software to identify MPA. The 3D plane-to-plane mandibular plane angle is formed by the FH plane and mandibular plane. These planes are composed of bilateral structures and are influenced by asymmetry.17 However, no research has proposed a method for plane-to-plane MPA measurement in asymmetric cases. Therefore, this study evaluated whether the 3D plane-to-plane MPA measurement method could be applied in clinical analysis of patients similar to the conventional 2D cephalometric measurement, regardless of asymmetry.
Table 1

Table 1

Comparison between 2D and 3D mandibular plane measurements. LCR: Lateral cephalometric radiograph, CBCT: Cone-beam computed tomography MPA: Mandibular plane angle FMA: Frankfort mandibular plane angle, SN-MP: Sella-nasion mandibular plane angle

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PATIENTS AND METHODS

This retrospective study used the records of patients between 2016 and 2018, which were retrieved from the database of Chang Gung Craniofacial Center, Taipei and Taoyuan, Taiwan. Thirty adult Taiwanese patients (10 men and 20 women) were included. All of these patients had undergone cone-beam computed tomography (CBCT) and lateral cephalometric radiography (LCR) for diagnosis or surgical evaluation. The present study followed the Declaration of Helsinki on medical protocols and ethics, and the Institutional Review Board of Chang Gung Memorial Hospital approved this study (No. 201900751B0).
The inclusion criteria were Taiwanese adult patients (≥18 years old) who had an absence of craniofacial anomalies (cleft lip and palate, hemifacial microsomia, or congenital muscular torticollis), complete records with clear resolution that were available for evaluation, no history of facial surgery or trauma, and no pathological lesions or severe inflammation.
The three groups were classified according to the 3D image and following criteria (n = 10 patients each): relative symmetry group (menton deviation < 4 mm; gonion discrepancy < 3 mm), horizontal asymmetry group (menton deviation > 4 mm; gonion discrepancy < 3 mm), and horizontal asymmetry (menton deviation > 4 mm) + vertical asymmetry (gonion discrepancy > 3 mm) group.

LCR and CBCT
Head and neck LCR (lateral cephalometric radiograph) and CBCT images were obtained. The resolution of CBCT images was 0.4 × 0.4 × 0.4 mm in voxel size. The patient’s head was positioned with the Frankfort horizontal plane parallel to the ground. Patients were instructed to avoid swallowing, keep their mouth closed, and maintain centric occlusion throughout the scan.

3D model construction and measurement methods
All CBCT images were stored in digital imaging and communication in medicine format and then imported to Simplant® O&O software (Materialise Dental, Leuven, Belgium) to construct 3D skull images for analysis. Each landmark and reference plane were identified and set for this study (Table 2, 3, Figure 1).

Setting of measurement methods after 3D model construction
Every image was measured using the following three methods (Table 4):
(1) 2D FMA (2D Frankfort mandibular plane angle)
    The 2D FMA is formed by the 2D Frankfort horizontal (FH) plane line and 2D mandibular plane line in lateral cephalometry
(2) 3D FMA (3D projected on the midsagittal plane)
    The 3D FH plane was formed by the bilateral orbitale (Or) and the midpoint of the bilateral porion (Po). The midsagittal plane was constructed by connecting the nasion (Na) and basion (Ba) and perpendicular to the FH plane. The FH plane line in this measurement was formed by the 3D FH plane projecting to the midsagittal plane. The 3D bilateral gonion and menton were projected on the midsagittal plane. The 3D FMA (projected on the midsagittal plane) was formed by FH plane line (on midsagittal plane) and projected mandibular plane line (Figure 2, 3).
(3) 3D MP (plane-to-plane)
    The angle between the 3D FH plane and 3D mandibular plane, which was formed by connecting bilateral gonion (Go) and menton (Me) (Figure 4, 5).

Statistical analysis
The Kruskal–Wallis test was used to compare the FMA measurements. For the inter-examiner error assessment, all data were measured twice by the same observer after an interval of 3 weeks. The measurement errors were calculated using the Dahlberg's formula.18 Statistical analysis was performed using SPSS software (version 23.0; IBM).
Figure 1

Figure 1

Landmarks and reference planes of a 3D craniofacial model, frontal view. Or, orbitale; Ba, basion; Go, gonion.

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Figure 2

Figure 2

Bilateral gonion (Go) projecting to the midsagittal plane. Gonion project (blue point), The point formed by the gonion point projected on the midsagittal plane; Gonion (mid) project (red point), The midpoint between the bilateral gonion projected points; Midsagittal plane, the plane perpendicular to the Frankfort horizontal plane and passing through the nasion (Na) and basion (Ba).

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Figure 3

Figure 3

Lateral view of 3D FMA. The 3D bilateral gonion and menton were projected on the midsagittal plane. The 3D FMA was formed by projecting FH plane and mandibular plane line on the midsagittal plane. Mandibular plane was formed by connecting Go mid project to Me project.

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Figure 4

Figure 4

Antero-posterior view of 3D MP. 3D MP, the angle formed between the FH plane and mandibular plane; Frankfort plane, the plane formed by the bilateral orbitale (Or) and midpoint of the bilateral porion (Po); Mandibular plane, the plane passing through the menton (Me) and bilateral gonion (Go).

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Figure 5

Figure 5

Lateral view of 3D MP. 3D MP, the angle between the FH plane and mandibular plane; FH plane, the plane formed by the bilateral orbitale (Or) and midpoint of the bilateral porion (Po); Mandibular plane angle, the plane passing through the menton (Me) and bilateral gonion (Go).

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Table 2

Table 2

Definition of cephalometric landmarks used in the present study.

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Table 3

Table 3

Definition of cephalometric references.

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Table 3

Table 3

Definition of cephalometric references.

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RESULTS

This study recruited 30 patients (each group had 10 patients). Characteristics of the three groups are listed in Table 5. The mean menton deviation was 1.88 mm (SD, 1.18 mm) in the relative symmetry group, 7.03 mm (SD, 1.56 mm) in the horizontal asymmetry group, and 8.59 mm (SD, 2.31 mm) in the horizontal asymmetry + vertical asymmetry group. The mean gonion discrepancy was 1.70 mm (SD, 1.02 mm) in the relative symmetry group, 1.04 mm (SD, 0.95 mm) in the horizontal asymmetry group, and 5.58 mm (SD, 1.00 mm) in the horizontal asymmetry + vertical asymmetry group.
The results of a comparison of different MPA measurements are presented in Table 6. The MPA acquired from 2D measurements (2D FMA group) was larger than that obtained from 3D measurements (3D FMA and 3D MP groups) in the two asymmetry groups. However, a comparison of MPA measurement methods did not reveal any statistically significant difference. When the two 3D measurements were compared, they appeared to be similar in the relative symmetry and horizontal asymmetry groups. Although the measurements revealed a greater difference in the horizontal asymmetry + vertical asymmetry group compared with the other two groups, the difference was not statistically significant. A case of horizontal asymmetry + vertical asymmetry group was illustrated in Figure 6. The MPA measurement of this extreme asymmetry case (menton deviation: 10.8mm, Go discrepancy: 7.3mm) was 20.26° in 2D FMA, 19.29° in 3D FMA, and 19.61° in 3D MP (Table 7).
To evaluate the reproducibility of the measured values, the Dahlberg formula was used for measuring error; the 2D FMA group demonstrated a larger measurement error compared with those of the two 3D measurement method groups (3D FMA, 3D MP). However, no error exceeded 0.5 mm for any measurement (Table 8).
Figure 6

Figure 6

An example of case with extreme asymmetry (menton deviation: 10.8 mm, bilateral Go discrepancy: 7.1 mm).

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Table 5

Table 5

Characteristics of the three groups Gonion (Go) discrepancy: Difference in distance between the bilateral gonions and 3D Frankfort plane. Menton deviation: Distance from the menton to the 3D midsagittal plane; SD: Standard deviation.

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Table 6

Table 6

Descriptive and statistical comparison of 3D and 2D Frankfort mandibular plane angle measurement methods in different groups.

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Table 7

Table 7

Characteristics and measurements of the example of an extreme asymmetry case, as presented in Figure 6.

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Table 8

Table 8

Mean measurement error according to the Dahlberg formula.

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DISCUSSION

This was a pilot study designed to estimate the feasibility of measuring plane-to-plane MPA on a 3D image. Several studies have reported no significant difference and high concordance between 3D and 2D cephalometry. In a comparison of the 2D and 3D CBCT methods, Nalçaci et al. reported no statistically significant difference for the measurements of 12 angles (SNA, SNB, ANB, SND, NA-Pog, AB-NPog, Ns-Ba, IMPA, FMIA, SN Ans-Pns, L1-APog, and L1- NB) but did note a significant difference in the measurements of two angles (U1-NA , U1-SN).19 Yitschaky et al. reported high compatibility between 2D and 3D CT cephalometry in linear and angular measurements, excluding angular measurements that included the sella turcica anatomic landmark.11 Oh et al. compared the angle measurements of 3D reconstructed computed tomography and 2D conventional LCR images. This study discovered that the MPA measured from 2D images was larger than the line-to-line MPA measured on 3D reconstructed computed tomography images for all patients; however, high concordance was still noted.10 Zamora also reported that no statistically significant differences were observed between the angular and linear measurements obtained through LCR and those obtained through CBCT.20 Jung et al. compared 2D and 3D CBCT midsagittal projection cephalometric measurements. Their study noted no significant difference between 3D projected midsagittal plane measurements and 2D cephalometric measurements in patients with plane asymmetry (menton deviation < 2 mm). Although measurements differed after reorientation, these differences were not clinically significant.15 However, the aforementioned studies did not consider the 3D plane-to-plane MPA for measurement and did not conduct comparisons with the facial asymmetry group.
Gateno et al. reported that facial asymmetry affected both 2D and 3D cephalometric measurements. In their study, line-to-line gonial angle (condylion-gonion-menton) measurement was distorted when it was measured using 2D cephalometry, but this distortion was not observed in the 3D measurements. Plane-to-plane occlusal planeFrankfort horizontal angle measurements were distorted in planes with asymmetry in both 2D and 3D cephalometry, although the magnitude of the distortion was larger in 2D cephalometry. In the study conducted by Gateno et al., the 3D occlusal plane-Frankfort horizontal plane-toplane angle was more distorted in roll rotation than in yaw rotation (0.34° distortion in 10° yaw rotation).14
In this study, no significant difference was observed between the measurement values of 2D FMA, 3D FMA and 3D MP, and the difference in mean values between the groups was <0.8°. In extreme case that demonstrated in Figure 6, the difference between 3D FMA and 3D MP was 0.32 mm. According to study of Kamoen et al., the clinical significance error of FMA is 0.8o. 21 The amount of error has no clinical significance at all. Therefore, the differences in our results fall within the clinically acceptable range of measurement error in the range of menton deviation up to 12 mm and Go discrepancy up to 8 mm. Thus, the 3D MP measurement method could be used to analyze patients with symmetric and asymmetric planes.

Our study has several limitations. First, the sample in this pilot study was relatively small and included only 10 patients in each group. Second, patients with facial deformities, such as cleft lip or palate, and a history of facial surgery or trauma were excluded to reduce the identification errors of 2D-LCR tracing. Finally, in the asymmetry group, only menton deviation and bilateral gonion discrepancy were used for classification. More cases could be included in future study to confirm the factors that may affect the methods of 3D MP measurement in asymmetry patients.
Figure 6

Figure 6

An example of case with extreme asymmetry (menton deviation: 10.8 mm, bilateral Go discrepancy: 7.1 mm).

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CONCLUSION

The mandibular plane angle acquired from 2D FMA was larger than in 3D FMA and 3D MP groups in asymmetry patients though the differences did not reach statistical significance. The 3D MPA measurement was influenced by vertical asymmetry rather than horizontal asymmetry. However, the difference was not statistically significant. Therefore, the 3D plane-to-plane angle measurement method can be used for analysis in patients with symmetric and asymmetric facial structures when the asymmetry is confined at a certain range.
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REFERENCES

  1. Adams GL, Gansky SA, Miller AJ, Harrell WE, Jr., Hatcher DC. Comparison between traditional 2-dimensional cephalometry and a 3-dimensional approach on human dry skulls. Am J Orthod Dentofacial Orthop. 2004;126(4):397-409.
  2. Periago DR, Scarfe WC, Moshiri M, Scheetz JP, Silveira AM, Farman AG. Linear accuracy and reliability of cone beam CT derived 3-dimensional images constructed using an orthodontic volumetric rendering program. Angle Orthod. 2008;78(3):387-95.
  3. Brown AA, Scarfe WC, Scheetz JP, Silveira AM, Farman AG. Linear accuracy of cone beam CT derived 3D images. Angle Orthod. 2009;79(1):150-7.
  4. Siriwat PP, Jarabak JR. Malocclusion and facial morphology is there a relationship? An epidemiologic study. Angle Orthod. 1985;55(2):127-38.
  5. Benedicto Ede N, Kairalla SA, Oliveira GM, Junior LR, Rosario HD, Paranhos LR. Determination of vertical characteristics with different cephalometric measurements. Eur J Dent. 2016;10(1):116-20.
  6. Cheung LK, Chan YM, Jayaratne YS, Lo J. Threedimensional cephalometric norms of Chinese adults in Hong Kong with balanced facial profile. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2011;112(2):e56-73.
  7. Park SH, Yu HS, Kim KD, Lee KJ, Baik HS. A proposal for a new analysis of craniofacial morphology by 3-dimensional computed tomography. Am J Orthod Dentofacial Orthop. 2006;129(5):600. e23-34.
  8. Wong RW, Chau AC, Hagg U. 3D CBCT McNamara's cephalometric analysis in an adult southern Chinese population. Int J Oral Maxillofac Surg 2011;40(9):920-5.
  9. Swennen G, Schutyser F, Hausamen JE. ThreeDimensional Cephalometry. A Color Atlas and Manual2005.
  10. Oh S, Kim CY, Hong J. A comparative study between data obtained from conventional lateral cephalometry and reconstructed three-dimensional computed tomography images. J Korean Assoc Oral Maxillofac Surg. 2014;40(3):123-9.
  11. Yitschaky O, Redlich M, Abed Y, Faerman M, Casap N, Hiller N. Comparison of common hard tissue cephalometric measurements between computed tomography 3D reconstruction and conventional 2D cephalometric images. Angle Orthod. 2011;81(1):11-6.
  12. van Vlijmen OJ, Maal T, Berge SJ, Bronkhorst EM, Katsaros C, Kuijpers-Jagtman AM. A comparison between 2D and 3D cephalometry on CBCT scans of human skulls. Int J Oral Maxillofac Surg. 2010;39(2):156-60.
  13. Hariharan A, Diwakar NR, Jayanthi K, Hema HM, Deepukrishna S, Ghaste SR. The reliability of cephalometric measurements in oral and maxillofacial imaging: Cone beam computed tomography versus two-dimensional digital cephalograms. Indian J Dent Res. 2016;27(4):370-7.
  14. Gateno J, Xia JJ, Teichgraeber JF. Effect of facial asymmetry on 2-dimensional and 3-dimensional cephalometric measurements. J Oral Maxillofac Surg. 2011;69(3):655-62.
  15. Jung PK, Lee GC, Moon CH. Comparison of cone-beam computed tomography cephalometric measurements using a midsagittal projection and conventional two-dimensional cephalometric measurements. Korean J Orthod. 2015;45(6):282-8.
  16. Santos R, De Martino JM, Haiter Neto F, Passeri LA. Cone-Beam Computed Tomography-Based ThreeDimensional McNamara Cephalometric Analysis. J Craniofac Surg. 2018;29(4):895-9.
  17. McNamara JA, Jr. A method of cephalometric evaluation. Am J Orthod. 1984;86(6):449-69.
  18. Statistical Methods for Medical and Biological Students. British Medical Journal. 1940;2(4158):358-9.
  19. Nalcaci R, Ozturk F, Sokucu O. A comparison of two-dimensional radiography and three-dimensional computed tomography in angular cephalometric measurements. Dentomaxillofac Radiol. 2010;39(2):100-6.
  20. Zamora N, Llamas JM, Cibrián R, Gandia JL, Paredes V. Cephalometric measurements from 3D reconstructed images compared with conventional 2D images. Angle Orthod. 2011;81(5):856-64.
  21. A. Kamoen, L. Dermaut, R. Verbeeck. The clinical significance of error measurement in the interpretation of treatment results. Eur J Orthod. 2001;23(5):569-78.
Figure 1

Figure 1

Landmarks and reference planes of a 3D craniofacial model, frontal view.
Or, orbitale; Ba, basion; Go, gonion.

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Figure 2

Figure 2

Bilateral gonion (Go) projecting to the midsagittal plane.
Gonion project (blue point), The point formed by the gonion point projected on the midsagittal plane; Gonion (mid) project (red point), The midpoint between the bilateral gonion projected points; Midsagittal plane, the plane perpendicular to the Frankfort horizontal plane and
passing through the nasion (Na) and basion (Ba).

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Figure 3

Figure 3

Lateral view of 3D FMA.
The 3D bilateral gonion and menton were projected on the midsagittal plane. The 3D FMA was formed by projecting FH plane and mandibular plane line on the midsagittal plane. Mandibular plane was formed by connecting Go mid project to Me project.

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Figure 4

Figure 4

Antero-posterior view of 3D MP. 3D MP, the angle formed between the FH plane and mandibular plane; Frankfort plane, the plane formed by the bilateral orbitale (Or) and midpoint of the bilateral porion (Po); Mandibular plane, the plane passing through the menton (Me) and bilateral gonion (Go).

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Figure 5

Figure 5

Lateral view of 3D MP.
3D MP, the angle between the FH plane and mandibular plane; FH plane, the plane formed by the bilateral orbitale (Or) and midpoint of the bilateral porion (Po); Mandibular plane angle, the plane passing through the menton (Me) and bilateral gonion (Go).

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Figure 6

Figure 6

An example of case with extreme asymmetry (menton deviation: 10.8 mm, bilateral Go discrepancy: 7.1 mm).

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Table 1

Table 1

Comparison between 2D and 3D mandibular plane measurements.
LCR: Lateral cephalometric radiograph, CBCT: Cone-beam computed tomography
MPA: Mandibular plane angle FMA: Frankfort mandibular plane angle, SN-MP: Sella-nasion mandibular plane angle

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Table 2

Table 2

Definition of cephalometric landmarks used in the present study.

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Table 3

Table 3

Definition of cephalometric references.

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Table 4

Table 4

Definition of the measurements.

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Table 5

Table 5

Characteristics of the three groups
Gonion (Go) discrepancy: Difference in distance between the bilateral gonions and 3D Frankfort plane.
Menton deviation: Distance from the menton to the 3D midsagittal plane; SD: Standard deviation.

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Table 6

Table 6

Descriptive and statistical comparison of 3D and 2D Frankfort mandibular plane angle measurement methods in different groups.

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Table 7

Table 7

Characteristics and measurements of the example of an extreme asymmetry case, as presented in Figure 6.

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Table 8

Table 8

Mean measurement error according to the Dahlberg formula.

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  1. Adams GL, Gansky SA, Miller AJ, Harrell WE, Jr., Hatcher DC. Comparison between traditional 2-dimensional cephalometry and a 3-dimensional approach on human dry skulls. Am J Orthod Dentofacial Orthop. 2004;126(4):397-409.
  2. Periago DR, Scarfe WC, Moshiri M, Scheetz JP, Silveira AM, Farman AG. Linear accuracy and reliability of cone beam CT derived 3-dimensional images constructed using an orthodontic volumetric rendering program. Angle Orthod. 2008;78(3):387-95.
  3. Brown AA, Scarfe WC, Scheetz JP, Silveira AM, Farman AG. Linear accuracy of cone beam CT derived 3D images. Angle Orthod. 2009;79(1):150-7.
  4. Siriwat PP, Jarabak JR. Malocclusion and facial morphology is there a relationship? An epidemiologic study. Angle Orthod. 1985;55(2):127-38.
  5. Benedicto Ede N, Kairalla SA, Oliveira GM, Junior LR, Rosario HD, Paranhos LR. Determination of vertical characteristics with different cephalometric measurements. Eur J Dent. 2016;10(1):116-20.
  6. Cheung LK, Chan YM, Jayaratne YS, Lo J. Threedimensional cephalometric norms of Chinese adults in Hong Kong with balanced facial profile. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2011;112(2):e56-73.
  7. Park SH, Yu HS, Kim KD, Lee KJ, Baik HS. A proposal for a new analysis of craniofacial morphology by 3-dimensional computed tomography. Am J Orthod Dentofacial Orthop. 2006;129(5):600. e23-34.
  8. Wong RW, Chau AC, Hagg U. 3D CBCT McNamara's cephalometric analysis in an adult southern Chinese population. Int J Oral Maxillofac Surg 2011;40(9):920-5.
  9. Swennen G, Schutyser F, Hausamen JE. ThreeDimensional Cephalometry. A Color Atlas and Manual2005.
  10. Oh S, Kim CY, Hong J. A comparative study between data obtained from conventional lateral cephalometry and reconstructed three-dimensional computed tomography images. J Korean Assoc Oral Maxillofac Surg. 2014;40(3):123-9.
  11. Yitschaky O, Redlich M, Abed Y, Faerman M, Casap N, Hiller N. Comparison of common hard tissue cephalometric measurements between computed tomography 3D reconstruction and conventional 2D cephalometric images. Angle Orthod. 2011;81(1):11-6.
  12. van Vlijmen OJ, Maal T, Berge SJ, Bronkhorst EM, Katsaros C, Kuijpers-Jagtman AM. A comparison between 2D and 3D cephalometry on CBCT scans of human skulls. Int J Oral Maxillofac Surg. 2010;39(2):156-60.
  13. Hariharan A, Diwakar NR, Jayanthi K, Hema HM, Deepukrishna S, Ghaste SR. The reliability of cephalometric measurements in oral and maxillofacial imaging: Cone beam computed tomography versus two-dimensional digital cephalograms. Indian J Dent Res. 2016;27(4):370-7.
  14. Gateno J, Xia JJ, Teichgraeber JF. Effect of facial asymmetry on 2-dimensional and 3-dimensional cephalometric measurements. J Oral Maxillofac Surg. 2011;69(3):655-62.
  15. Jung PK, Lee GC, Moon CH. Comparison of cone-beam computed tomography cephalometric measurements using a midsagittal projection and conventional two-dimensional cephalometric measurements. Korean J Orthod. 2015;45(6):282-8.
  16. Santos R, De Martino JM, Haiter Neto F, Passeri LA. Cone-Beam Computed Tomography-Based ThreeDimensional McNamara Cephalometric Analysis. J Craniofac Surg. 2018;29(4):895-9.
  17. McNamara JA, Jr. A method of cephalometric evaluation. Am J Orthod. 1984;86(6):449-69.
  18. Statistical Methods for Medical and Biological Students. British Medical Journal. 1940;2(4158):358-9.
  19. Nalcaci R, Ozturk F, Sokucu O. A comparison of two-dimensional radiography and three-dimensional computed tomography in angular cephalometric measurements. Dentomaxillofac Radiol. 2010;39(2):100-6.
  20. Zamora N, Llamas JM, Cibrián R, Gandia JL, Paredes V. Cephalometric measurements from 3D reconstructed images compared with conventional 2D images. Angle Orthod. 2011;81(5):856-64.
  21. A. Kamoen, L. Dermaut, R. Verbeeck. The clinical significance of error measurement in the interpretation of treatment results. Eur J Orthod. 2001;23(5):569-78.
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