European Journal of Orthodontics, 2015, 22–27 doi:10.1093/ejo/cju009 Advance Access publication 22 August 2014
Original article
Comparison of the mandibular hinge axis in adult patients with facial asymmetry with and without posterior unilateral crossbite Jun-ichi Takada*, Jun J. Miyamoto*, Toshiaki Yokota*, Takashi Ono** and Keiji Moriyama* *Maxillofacial Orthognathics and **Orthodontic Science, Tokyo Medical and Dental University Graduate School, Japan Correspondence to: Jun J. Miyamoto, Maxillofacial Orthognathics, Graduate School, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8549, Japan. E-mail: [email protected]
Summary Downloaded from by guest on February 10, 2015
Background/Objectives: Although it has been suggested that adult patients with facial asymmetry with posterior unilateral crossbite (PUXB) may have a more tilted mandibular hinge axis (MHA) than those without PUXB, whether craniofacial morphology is associated with the MHA remains unclear. The purpose of this study was to compare the craniofacial morphology and MHA in adult subjects with post-growth facial asymmetry with and without PUXB. Subjects/Methods: Thirty pre-orthodontic patients (PUXB and non-PUXB groups, n = 15 each, 9 females and 6 males, mean age: 23.2 years) participated in the study. The MHA was measured by computerized axiography and duplicated on posteroanterior and submentovertex cephalometric radiographs. Morphological asymmetry was evaluated for both skeletal and dental components and positional deviation of the mandible by cephalometric analysis. The Mann–Whitney U-test and Spearman’s correlation coefficient by rank were used for statistical analysis. The level of statistical significance was set at P 0.001** 0.950 0.901
1.7 2.3 1.1 1.5 1.4 1.0
0.6 0.4 0.3 1.0 1.6 0.2
1.0 1.9 0.6 0.7 2.6 1.0
0.010** 0.004** 0.016** >0.001** 1.000 >0.001**
3.6 4.2 3.9 2.9 5.0 2.2 2.9
–0.5 –1.7 –0.6 –1.2 –1.9 1.9 0.9
2.5 4.5 3.3 2.4 5.6 3.1 2.1
>0.001** 0.015** 0.070 0.983 >0.001** >0.001** >0.001**
3.3 1.4 0.8
1.6 0.7 –0.2
2.6 1.3 0.6
0.108 >0.001** >0.001**
Downloaded from by guest on February 10, 2015
Linear and angular measurements on PA radiographs
26 in morphological assessment by making the FH plane parallel to the film in both the SMV and PA cephalometric assessments (22, 27). Thus, we believe that our methodology for identification of the MHA/IMHA is comparable with that in previous studies.
Comparisons of dentoalveolar and skeletal features between subjects with and without PUXB
Comparisons of the MHA/IMHA between subjects with and without PUXB The method used to study the morphology of the condyle and/ or glenoid fossa that carried suspicion of skeletal asymmetry was mostly cephalometric measurement. A difference between shift-side and non-shift-side condyles in subjects with PUXB in childhood was reported. Moreover, the bilateral difference in the condyle and mandible was corrected after expansion of the maxillary arch using SMV radiographs (21, 22). In this study, functional and anatomical methods were combined to determine the inclination of the MHA/ IMHA. The MHA was significantly tilted superior to the side of the PUXB on the PA radiographs, while the IMHA was significantly
tilted posterior to the side of the PUXB on the SMV radiographs. As mentioned above, the MHA was located inside the condyle. This is in agreement with the findings in a previous study in which adaptive repositioning of the condylar head and glenoid fossa had occurred (9). In another previous study, the mandible of the subjects with PUXB was considered to be rotated in relation to the cranial floor, although there was no mandibular asymmetry (10). The authors suggested that the condylar head and glenoid fossa on the shifted side had been remodelled. In our study, the subjects with PUXB had a greater mandibular deviation (5.8 ± 3.0 mm measured at Me) than that in the study by Brian et al. (10). Therefore, the subjects of our study exhibited both changes in the MHA/IMHA and bony asymmetry of the mandible. Thus, it could be difficult to fully correct yaw axis in adult asymmetry patients in orthognathic surgery. Although the MHA/IMHA was significantly different with and without PUXB, the amount of difference was very small [1.3 degrees of MHA inclination (standard deviation: 1.0) and 1.0 of IMHA (standard deviation: 0.8–0.6)]. In the three-dimensional image analysis, previous studies reported the condyle–fossa relationship ipsilateral to the PUXB is located more posterosuperiorly than that contralateral to the PUXB (35, 36). Consequently, our findings were in line with those in the previous studies. Nevertheless, one should be aware that the clinical application of our findings is limited, because of the small difference.
Conclusions The null hypothesis that there are no differences in the craniofacial morphology or MHA between facially asymmetric adult subjects with and without PUXB was discarded. Rather, the MHA/IMHA in subjects with PUXB was significantly tilted compared with that in subjects without PUXB in both the frontal and horizontal dimensions. Thus, it appears that facially asymmetric adult subjects with malocclusions associated with PUXB exhibit not only mandibular asymmetry but also remodelling of the condylar head and glenoid fossa that accompanies the three-dimensional shifting of the MHA. However, whether there is asymmetry during the pre-growth period in post-growth facially asymmetric patients with PUXB remains unclear. Thus, we would like to clarify the relationship between the craniofacial morphology and MHA in pre-growth facially asymmetric subjects with PUXB in a further study. It is noteworthy that the present study involved simultaneous two-dimensional image analysis with limited accuracy and reliability. It is obvious that further studies should be conducted to clarify the interaction of detailed morphological and functional aspects using three-dimensional image analysis with the greater accuracy and reliability, and serial mandibular movement with our modified approach. This would help with the conclusions of our study, especially those regarding the condylar height and glenoid fossa remodelling.
Funding Grants-in-Aid for Scientific Research Projects from the Japan Society for the Promotion of Science (#22792036, 25862001) and the ‘International Research Center for Molecular Science in Tooth and Bone Diseases’, part of the Japanese Ministry of Education, Global Center of Excellence Program.
Acknowledgements The authors declare no potential conflicts of interest with respect to the authorship and/or publication of this article.
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A previous study compared dentoalveolar and skeletal features between subjects with and without PUXB in childhood, and their findings were similar to those found in adulthood in the present study (22). With regards to dentoalveolar features, there were significant differences in the mandibular arch width in the PA dimension between adult subjects with and without PUXB. Moreover, they reported that in skeletal measurements, there were significant differences in not only the mandibular shift to the cranium but also the relative horizontal position (9). Thus, previous studies have suggested a discrepancy in dental arch width and mandibular asymmetry in subjects with PUXB in childhood (22) and adulthood (9). Although there were no significant dentoalveolar differences in the maxillary width or mandibular arch width, we found that there were significant differences in the L6-U6 between subjects with and without PUXB. Therefore, the present study found discrepancy in the dental arch form as demonstrated in previous studies. Moreover, there were significant differences in the mesiodistal and buccolingual positions (i.e. L6-FP, L6-MSP, and L6-ISL) in the mandibular first molar. For the sample selection, our study excluded subjects with mandibular midline deviation caused by crowding. Thus, the positional difference in the mandibular molar suggests that the mandibular molar was positioned buccodistally on the shifted side, resulting in the bilateral morphological difference in the mandible and glenoid fossa. Skeletal discrepancies in mandibular deviation were revealed between subjects with and without PUXB with reference to the cranium (i.e. Me, Me-MSP, and Sy-Ba) and the maxillary–mandibular relative deviation (i.e. L1/U1), which supports the findings in a previous study (9). Furthermore, there were significant differences in the maxillary (i.e. ANS/MSP and Mx-LO) and occlusal plane (i.e. Op) deviations. Together with the findings in a previous study that reported the achievement of symmetrical condylar positioning after maxillary expansion in juvenile subjects with PUXB, it was suggested that the discrepancy between the maxillary and mandibular arch widths may influence residual symptoms of not only mandibular growth but also maxillary growth (19, 20). However, further longitudinal studies following non-interventional cases of juvenile subjects with PUXB may help to clarify the cause–effect relationship between the morphological and functional aspects of subjects with PUXB.
European Journal of Orthodontics, 2015, Vol. 37, No. 1
J. Takada et al.
References
20. Kurol, J. and Berglund, L. (1992) Longitudinal study and cost-benefit analysis of the effect of early treatment of posterior crossbite in the primary dentition. European Journal of Orthodontics, 14, 173–179. 21. Pinto, A.S., Buschang, P.H., Throckmorton, G.S. and Chen, P. (2001) Morphological and positional asymmetries of young children with functional unilateral posterior crossbite. American Journal of Orthodontics and Dentofacial Orthopedics, 120, 13–20. 22. Kecik, D., Kocadereli, I. and Saatci, I. (2007) Evaluation of the treatment changes of functional posterior crossbite in the mixed dentition. American Journal of Orthodontics and Dentofacial Orthopedics, 131, 202–215. 23. Baccetti, T., Franchi, L. and McNamara, J.A., Jr (2005) The Cervical Vertebral Maturation (CVM) method for the assessment of optimal treatment timing in dentofacial orthopaedics. Seminars in Orthodontics, 11, 119– 129. 24. Cohen, J. (1992) A power primer. Psychological Bulletin, 112, 155–159. 25. Faul, F., Erdfelder, E., Buchner, A. and Lang, A.G. (2009) Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses. Behavior Research Methods, 41, 1149–1160. 26. Gsellmann, B., Schmid-Schwap, M., Piehslinger, E. and Slavicek, R. (1998) Lengths of condylar pathways measured with computerized axiography (CADIAX) and occlusal index in patients and volunteers. Journal of Oral Rehabilitation, 25, 146–152. 27. Forsberg, C.T., Burstone, C.J. and Hanley, K.J. (1984) Diagnosis and treatment planning of skeletal asymmetry with the submental-vertical radiograph. American Journal of Orthodontics and Dentofacial Orthopedics, 85, 224–237. 28. Guilherme, R.P.J., Angelos, M., Donald, G.W., Marcos, R.F. and Arnaldo, P. (2001) Three-dimensional evaluation of skeletal and dental asymmetries in Class II subdivision malocclusions. American Journal of Orthodontics and Dentofacial Orthopedics, 107, 397–400. 29. Uysal, T. and Malkoc, S. (2005) Submentovertex cephalometric norms in Turkish adults. American Journal of Orthodontics and Dentofacial Orthopedics, 128, 724–730. 30. Al-Azemi, R. and Årtun, J. (2012) Posteroanterior cephalometric norms for an adolescent Kuwaiti population. European Journal of Orthodontics, 34, 312–317. 31. Kanomi, R., Hidaka, O., Yamada, C. and Takada, K. (2004) Asymmetry in the condylar long axis first molar rotation. Journal of Dental Research, 83, 109–114. 32. Hashimoto, K., Otsuka, R., Minato, A., Sato-Wakabayashi, M., Takada, J., Ioue-Arai, M., Miyamoto, J.J., Ono, T., Ohyama, K. and Moriyama, K. (2008) Short-term changes in temporomandibular joint function in subjects with cleft lip and palate treated with maxillary distraction osteogenesis. Orthodontics and Craniofacial Research, 11, 74–81. 33. Mantout, B., Giraudeau, A., Perez, C., Ré, J.P. and Orthlieb, J.D. (2008) Technical validation of a computerized condylographic system. International Journal of Stomatology and Occlusion Medicine, 1, 45–50. 34. Han, B., Kang, H., Liu, L., Yi, X. and Li, X. (2010) Comparisons of condylar movements with the functional occlusal clutch and tray clutch recording methods in CADIAX system. International Journal of Oral Science, 2, 208–214. 35. Baek, S.H., Cho, I.S., Chang, Y.I. and Kim, M.J. (2007) Skeletodental factors affecting chin point deviation in female patients with class III malocclusion and facial asymmetry: a three-dimensional analysis using computed tomography. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology, 104, 628–639. 36. Kim, H.O., Lee, W., Kook, Y.A. and Kim, Y. (2013) Comparison of the condyle-fossa relationship between skeletal class III malocclusion patients with and without asymmetry: a retrospective three-dimensional cone-beam computed tomograpy study. The Korean Journal of Orthodontics, 43, 209–217.
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1. Letzer, G.M. and Kronman, J.H. (1967) A posteroanterior cephalometric evaluation of craniofacial asymmetry. Angle Orthodontist, 37, 205–211. 2. Cook, J.T. (1980) Asymmetry of the craniofacial skeleton. British Journal of Orthodontics, 7, 33–38. 3. Severt, T.R. and Proffit, W.R. (1997) The prevalence of facial asymmetry in the dentofacial deformities population at the University of North Carolina. The International Journal of Adult Orthodontics and Orthognathic Surgery, 12, 171–176. 4. Schmid, W., Mongini, F. and Felisio, A. (1991) A computer-based assessment of structural and displacement asymmetries of the mandible. American Journal of Orthodontics and Dentofacial Orthopedics, 100, 19–34. 5. Shigefuji, R., Motohashi, N. and Kuroda, T. (2001) Longitudinal change of molar dental compensation following orthognathic surgery in facial asymmetry patients. Japanese Journal of Jaw Deformity, 11, 11–20. 6. Kusayama, M., Motohashi, N. and Kuroda, T. (2003) Relationship between transverse dental anomalies and skeletal asymmetry. American Journal of Orthodontics and Dentofacial Orthopedics, 123, 329–337. 7. Takada, J.-I., Ono, T., Miyamoto, J.J., Yokota, T. and Moriyama, K. (2011) Association between intraoral pressure and molar position and inclination in subjects with facial asymmetry. European Journal of Orthodontics, 33, 243–249. 8. Pirttiniemi, P., Kantomaa, T. and Lahtela, P. (1990) Relationship between craniofacial and condyle path asymmetry in unilateral posterior crossbite patients. European Journal of Orthodontics, 12, 408–413. 9. Langberg, B.J., Arai, K. and Miner, R.M. (2005) Transverse skeletal and dental asymmetry in adults with unilateral lingual posterior crossbite. American Journal of Orthodontics and Dentofacial Orthopedics, 127, 6–16. 10. Brian, L.O., Cyril, S., Bernard, S. and Ellen, A.B. (1995) An evaluation of mandibular asymmetry in adults with unilateral posterior crossbite. American Journal of Orthodontics and Dentofacial Orthopedics, 107, 394–400. 11. Okeson, J.P. (2007) Management of Temporomandibular Disorders and Occlusion. Mosby, Elsevier, UK, 6th ed., p. 81. 12. Mimura, H. and Deguchi, T. (1994) Relationship between sagittal condylar path and the degree of mandibular asymmetry in unilateral cross-bite patients. The Journal of Craniomandibular Practice, 12, 161–166. 13. Slavicek, R. (1988) Clinical and instrumental functional analysis for diagnosis and treatment planning. Part 7: computer aided axiography. Journal Clinical Orthodontics, 22, 776–787. 14. Slavicek, R. (1989) Clinical and instrumental functional analysis for diagnosis and treatment planning. Part 8: case studies in CADIAX®. Journal Clinical Orthodontics, 23, 42–45. 15. Rekow, E.D., Speidel, T.M. and Koenig, R.A. (1993) Location of the mandibular center of autorotation in maxillary impaction surgery. American Journal of Orthodontics and Dentofacial Orthopedics, 103, 530–536. 16. Nadjmi, N., Mommaerts, M.Y., Abeloos, J.V. and De Clercq, C.A. (1998) Prediction of mandibular autorotation. Journal of Oral and Maxillofacial Surgery, 56, 1241–1247. 17. Wang, Y.C., Ko, E.W., Huang, C.S. and Chen, Y.R. (2006) The inter-relationship between mandibular autorotation and maxillary LeFort I impaction osteotomies. The Journal of Craniofacial Surgery, 17, 898–904. 18. Jamilian, A., Showkatbakhsh, A., Gholami, D. and Kamali, Z. (2009) The relation between pogonion advancement and posterior maxillary impaction. The Journal of Craniofacial Surgery, 20, 841–843. 19. Thilander, B., Wahlund, S. and Lennartsson, B. (1984) The effect of early interceptive treatment in children with posterior crossbite. European Journal of Orthodontics, 6, 25–34.
27
Original article
Comparison of the mandibular hinge axis in adult patients with facial asymmetry with and without posterior unilateral crossbite Jun-ichi Takada*, Jun J. Miyamoto*, Toshiaki Yokota*, Takashi Ono** and Keiji Moriyama* *Maxillofacial Orthognathics and **Orthodontic Science, Tokyo Medical and Dental University Graduate School, Japan Correspondence to: Jun J. Miyamoto, Maxillofacial Orthognathics, Graduate School, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8549, Japan. E-mail: [email protected]
Summary Downloaded from by guest on February 10, 2015
Background/Objectives: Although it has been suggested that adult patients with facial asymmetry with posterior unilateral crossbite (PUXB) may have a more tilted mandibular hinge axis (MHA) than those without PUXB, whether craniofacial morphology is associated with the MHA remains unclear. The purpose of this study was to compare the craniofacial morphology and MHA in adult subjects with post-growth facial asymmetry with and without PUXB. Subjects/Methods: Thirty pre-orthodontic patients (PUXB and non-PUXB groups, n = 15 each, 9 females and 6 males, mean age: 23.2 years) participated in the study. The MHA was measured by computerized axiography and duplicated on posteroanterior and submentovertex cephalometric radiographs. Morphological asymmetry was evaluated for both skeletal and dental components and positional deviation of the mandible by cephalometric analysis. The Mann–Whitney U-test and Spearman’s correlation coefficient by rank were used for statistical analysis. The level of statistical significance was set at P 0.001** 0.950 0.901
1.7 2.3 1.1 1.5 1.4 1.0
0.6 0.4 0.3 1.0 1.6 0.2
1.0 1.9 0.6 0.7 2.6 1.0
0.010** 0.004** 0.016** >0.001** 1.000 >0.001**
3.6 4.2 3.9 2.9 5.0 2.2 2.9
–0.5 –1.7 –0.6 –1.2 –1.9 1.9 0.9
2.5 4.5 3.3 2.4 5.6 3.1 2.1
>0.001** 0.015** 0.070 0.983 >0.001** >0.001** >0.001**
3.3 1.4 0.8
1.6 0.7 –0.2
2.6 1.3 0.6
0.108 >0.001** >0.001**
Downloaded from by guest on February 10, 2015
Linear and angular measurements on PA radiographs
26 in morphological assessment by making the FH plane parallel to the film in both the SMV and PA cephalometric assessments (22, 27). Thus, we believe that our methodology for identification of the MHA/IMHA is comparable with that in previous studies.
Comparisons of dentoalveolar and skeletal features between subjects with and without PUXB
Comparisons of the MHA/IMHA between subjects with and without PUXB The method used to study the morphology of the condyle and/ or glenoid fossa that carried suspicion of skeletal asymmetry was mostly cephalometric measurement. A difference between shift-side and non-shift-side condyles in subjects with PUXB in childhood was reported. Moreover, the bilateral difference in the condyle and mandible was corrected after expansion of the maxillary arch using SMV radiographs (21, 22). In this study, functional and anatomical methods were combined to determine the inclination of the MHA/ IMHA. The MHA was significantly tilted superior to the side of the PUXB on the PA radiographs, while the IMHA was significantly
tilted posterior to the side of the PUXB on the SMV radiographs. As mentioned above, the MHA was located inside the condyle. This is in agreement with the findings in a previous study in which adaptive repositioning of the condylar head and glenoid fossa had occurred (9). In another previous study, the mandible of the subjects with PUXB was considered to be rotated in relation to the cranial floor, although there was no mandibular asymmetry (10). The authors suggested that the condylar head and glenoid fossa on the shifted side had been remodelled. In our study, the subjects with PUXB had a greater mandibular deviation (5.8 ± 3.0 mm measured at Me) than that in the study by Brian et al. (10). Therefore, the subjects of our study exhibited both changes in the MHA/IMHA and bony asymmetry of the mandible. Thus, it could be difficult to fully correct yaw axis in adult asymmetry patients in orthognathic surgery. Although the MHA/IMHA was significantly different with and without PUXB, the amount of difference was very small [1.3 degrees of MHA inclination (standard deviation: 1.0) and 1.0 of IMHA (standard deviation: 0.8–0.6)]. In the three-dimensional image analysis, previous studies reported the condyle–fossa relationship ipsilateral to the PUXB is located more posterosuperiorly than that contralateral to the PUXB (35, 36). Consequently, our findings were in line with those in the previous studies. Nevertheless, one should be aware that the clinical application of our findings is limited, because of the small difference.
Conclusions The null hypothesis that there are no differences in the craniofacial morphology or MHA between facially asymmetric adult subjects with and without PUXB was discarded. Rather, the MHA/IMHA in subjects with PUXB was significantly tilted compared with that in subjects without PUXB in both the frontal and horizontal dimensions. Thus, it appears that facially asymmetric adult subjects with malocclusions associated with PUXB exhibit not only mandibular asymmetry but also remodelling of the condylar head and glenoid fossa that accompanies the three-dimensional shifting of the MHA. However, whether there is asymmetry during the pre-growth period in post-growth facially asymmetric patients with PUXB remains unclear. Thus, we would like to clarify the relationship between the craniofacial morphology and MHA in pre-growth facially asymmetric subjects with PUXB in a further study. It is noteworthy that the present study involved simultaneous two-dimensional image analysis with limited accuracy and reliability. It is obvious that further studies should be conducted to clarify the interaction of detailed morphological and functional aspects using three-dimensional image analysis with the greater accuracy and reliability, and serial mandibular movement with our modified approach. This would help with the conclusions of our study, especially those regarding the condylar height and glenoid fossa remodelling.
Funding Grants-in-Aid for Scientific Research Projects from the Japan Society for the Promotion of Science (#22792036, 25862001) and the ‘International Research Center for Molecular Science in Tooth and Bone Diseases’, part of the Japanese Ministry of Education, Global Center of Excellence Program.
Acknowledgements The authors declare no potential conflicts of interest with respect to the authorship and/or publication of this article.
Downloaded from by guest on February 10, 2015
A previous study compared dentoalveolar and skeletal features between subjects with and without PUXB in childhood, and their findings were similar to those found in adulthood in the present study (22). With regards to dentoalveolar features, there were significant differences in the mandibular arch width in the PA dimension between adult subjects with and without PUXB. Moreover, they reported that in skeletal measurements, there were significant differences in not only the mandibular shift to the cranium but also the relative horizontal position (9). Thus, previous studies have suggested a discrepancy in dental arch width and mandibular asymmetry in subjects with PUXB in childhood (22) and adulthood (9). Although there were no significant dentoalveolar differences in the maxillary width or mandibular arch width, we found that there were significant differences in the L6-U6 between subjects with and without PUXB. Therefore, the present study found discrepancy in the dental arch form as demonstrated in previous studies. Moreover, there were significant differences in the mesiodistal and buccolingual positions (i.e. L6-FP, L6-MSP, and L6-ISL) in the mandibular first molar. For the sample selection, our study excluded subjects with mandibular midline deviation caused by crowding. Thus, the positional difference in the mandibular molar suggests that the mandibular molar was positioned buccodistally on the shifted side, resulting in the bilateral morphological difference in the mandible and glenoid fossa. Skeletal discrepancies in mandibular deviation were revealed between subjects with and without PUXB with reference to the cranium (i.e. Me, Me-MSP, and Sy-Ba) and the maxillary–mandibular relative deviation (i.e. L1/U1), which supports the findings in a previous study (9). Furthermore, there were significant differences in the maxillary (i.e. ANS/MSP and Mx-LO) and occlusal plane (i.e. Op) deviations. Together with the findings in a previous study that reported the achievement of symmetrical condylar positioning after maxillary expansion in juvenile subjects with PUXB, it was suggested that the discrepancy between the maxillary and mandibular arch widths may influence residual symptoms of not only mandibular growth but also maxillary growth (19, 20). However, further longitudinal studies following non-interventional cases of juvenile subjects with PUXB may help to clarify the cause–effect relationship between the morphological and functional aspects of subjects with PUXB.
European Journal of Orthodontics, 2015, Vol. 37, No. 1
J. Takada et al.
References
20. Kurol, J. and Berglund, L. (1992) Longitudinal study and cost-benefit analysis of the effect of early treatment of posterior crossbite in the primary dentition. European Journal of Orthodontics, 14, 173–179. 21. Pinto, A.S., Buschang, P.H., Throckmorton, G.S. and Chen, P. (2001) Morphological and positional asymmetries of young children with functional unilateral posterior crossbite. American Journal of Orthodontics and Dentofacial Orthopedics, 120, 13–20. 22. Kecik, D., Kocadereli, I. and Saatci, I. (2007) Evaluation of the treatment changes of functional posterior crossbite in the mixed dentition. American Journal of Orthodontics and Dentofacial Orthopedics, 131, 202–215. 23. Baccetti, T., Franchi, L. and McNamara, J.A., Jr (2005) The Cervical Vertebral Maturation (CVM) method for the assessment of optimal treatment timing in dentofacial orthopaedics. Seminars in Orthodontics, 11, 119– 129. 24. Cohen, J. (1992) A power primer. Psychological Bulletin, 112, 155–159. 25. Faul, F., Erdfelder, E., Buchner, A. and Lang, A.G. (2009) Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses. Behavior Research Methods, 41, 1149–1160. 26. Gsellmann, B., Schmid-Schwap, M., Piehslinger, E. and Slavicek, R. (1998) Lengths of condylar pathways measured with computerized axiography (CADIAX) and occlusal index in patients and volunteers. Journal of Oral Rehabilitation, 25, 146–152. 27. Forsberg, C.T., Burstone, C.J. and Hanley, K.J. (1984) Diagnosis and treatment planning of skeletal asymmetry with the submental-vertical radiograph. American Journal of Orthodontics and Dentofacial Orthopedics, 85, 224–237. 28. Guilherme, R.P.J., Angelos, M., Donald, G.W., Marcos, R.F. and Arnaldo, P. (2001) Three-dimensional evaluation of skeletal and dental asymmetries in Class II subdivision malocclusions. American Journal of Orthodontics and Dentofacial Orthopedics, 107, 397–400. 29. Uysal, T. and Malkoc, S. (2005) Submentovertex cephalometric norms in Turkish adults. American Journal of Orthodontics and Dentofacial Orthopedics, 128, 724–730. 30. Al-Azemi, R. and Årtun, J. (2012) Posteroanterior cephalometric norms for an adolescent Kuwaiti population. European Journal of Orthodontics, 34, 312–317. 31. Kanomi, R., Hidaka, O., Yamada, C. and Takada, K. (2004) Asymmetry in the condylar long axis first molar rotation. Journal of Dental Research, 83, 109–114. 32. Hashimoto, K., Otsuka, R., Minato, A., Sato-Wakabayashi, M., Takada, J., Ioue-Arai, M., Miyamoto, J.J., Ono, T., Ohyama, K. and Moriyama, K. (2008) Short-term changes in temporomandibular joint function in subjects with cleft lip and palate treated with maxillary distraction osteogenesis. Orthodontics and Craniofacial Research, 11, 74–81. 33. Mantout, B., Giraudeau, A., Perez, C., Ré, J.P. and Orthlieb, J.D. (2008) Technical validation of a computerized condylographic system. International Journal of Stomatology and Occlusion Medicine, 1, 45–50. 34. Han, B., Kang, H., Liu, L., Yi, X. and Li, X. (2010) Comparisons of condylar movements with the functional occlusal clutch and tray clutch recording methods in CADIAX system. International Journal of Oral Science, 2, 208–214. 35. Baek, S.H., Cho, I.S., Chang, Y.I. and Kim, M.J. (2007) Skeletodental factors affecting chin point deviation in female patients with class III malocclusion and facial asymmetry: a three-dimensional analysis using computed tomography. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology, 104, 628–639. 36. Kim, H.O., Lee, W., Kook, Y.A. and Kim, Y. (2013) Comparison of the condyle-fossa relationship between skeletal class III malocclusion patients with and without asymmetry: a retrospective three-dimensional cone-beam computed tomograpy study. The Korean Journal of Orthodontics, 43, 209–217.
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