Mandibular asymmetries and associated factors ... - Angle Orthodontist

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Apr 18, 2018 - Frankfort. Plane passing through the right and left anatomic porion points and the left orbitale point (PoR, .... 516 (43.8). Vertical. 381 (32.3) .... 1997;12:171–176. 3. Sheats RD, McGorray SP, Musmar Q, Wheeler TT, King GJ.

Original Article

Mandibular asymmetries and associated factors in orthodontic and orthognathic surgery patients ´ Guilherme Thiesena; Bruno F. Gribelb; Maria Perpetua M. Freitasc; Donald R. Oliverd; Ki Beom Kime ABSTRACT Objectives: To estimate the prevalence of mandibular asymmetries in orthodontic and orthognathic surgery patients and to investigate demographic and skeletal factors associated with this disharmony. Materials and Methods: Cone-beam computed tomography images of 1178 individuals aged 19 through 60 years with complete dentitions were analyzed. Outcomes were classified as relative mandibular symmetry, moderate asymmetry, and severe asymmetry. Factors recorded included sex, age, side of mandibular deviation, sagittal jaw relationship, vertical skeletal pattern, angle of the cranial base, and maxillary asymmetry. Ordinal logistic regression was used to estimate simple and adjusted odds ratios (OR) for the individuals with moderate and severe mandibular asymmetry, as well as 95% confidence intervals. Results: Prevalence values of 55.2%, 27.2%, and 17.6% were observed for relative mandibular symmetry, moderate asymmetry, and severe asymmetry, respectively. An independent association with the side of mandibular deviation and the presence of maxillary asymmetry was observed, both for subjects with moderate mandibular asymmetry (left side: OR ¼ 1.50; 95% CI: 1.01–2.24 / maxillary asymmetry: OR ¼ 2.07; 95% CI: 1.11–3.76) and for those with severe asymmetry (left side: OR ¼ 2.09; 95% CI: 1.27–3.44 / maxillary asymmetry: OR ¼ 4.93; 95% CI: 2.64–9.20). Conclusions: Moderate and severe mandibular asymmetries were present in 44.8% of the sample, being associated with the side of mandibular deviation and with maxillary asymmetry. (Angle Orthod. 0000;00:000–000.) KEY WORDS: Facial asymmetry; Orthodontics; Orthognathic surgery; Epidemiology

INTRODUCTION Facial embryology usually follows a symmetrical development pattern. However, the human face does not display perfect symmetry. Asymmetry may be considered subclinical, also named relative symmetry or mild asymmetry, or may be moderate or severe, demanding orthodontic and or orthopedic intervention when it affects facial and smile esthetics.1–3 The prevalence of facial asymmetries reported in the literature varies between 11% and 37%.2–6 When evaluation is made through more strict or accurate diagnostic methods, the prevalence of asymmetry can approach or exceed 50%.7–10 In determining facial asymmetry, it is known that deviations in the mandible are the most striking characteristic of the disharmony, particularly the lateral displacement of the chin in relation to the midsagittal plane.2,7,11 Mandibular asymmetry (MA) is frequently found in subjects affected by trauma, syndromes, or other disorders of the craniofacial area.12 However, there is limited knowledge of factors associated with idiopathic

a Postdoctoral Fellow, Department of Orthodontics, Saint Louis University, St Louis, MO, USA; and Associate Professor, Department of Orthodontics, University of Southern Santa Catarina, Florianopolis, SC, Brazil. b Postdoctoral Fellow, Department of Orthodontics, University of Michigan, Ann Arbor, MI, USA. c Associate Professor, Department of Orthodontics, Lutheran University of Brazil, Canoas, RS, Brazil. d Clinical Associate Professor, Department of Orthodontics, Saint Louis University, St Louis, MO, USA. e Associate Professor, Department of Orthodontics, Saint Louis University, St Louis, MO, USA. Corresponding author: Dr Guilherme Thiesen, Rua Idalina ´ Pereira dos Santos 67, 1106, Agronomica, Florianopolis, SC 88025-260, Brazil (e-mail: [email protected])

Accepted: February 2018. Submitted: November 2017. Published Online: April 18, 2018 Ó 0000 by The EH Angle Education and Research Foundation, Inc. DOI: 10.2319/111517-785.1

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THIESEN, GRIBEL, FREITAS, OLIVER, KIM

Table 1. Landmarks and Reference Planes Used in the Study Landmark/Plane

Abbreviation

Anatomic porion Orbitale Anterior nasal spine Basion Sella Nasion Subspinale

Po Or ANS Ba S N A

Supramentale

B

Gnathion Pterygoid

Gn Pt

Frankfort plane

Frankfort

Midsagittal plane

MSP

asymmetries occurring without accompanying acquired disease or congenital alterations.1 Epidemiological data on these asymmetries are not abundant in the literature. Among the existing studies, most4–6 analyzed dentofacial deformities as a whole and cited MA among those. Few2,3,8,10 investigated MA specifically and evaluated associated factors with large samples. Moreover, those studies did not demonstrate how substantial the associations were. Therefore, this study aimed at estimating the prevalence of different intensities of MA in orthodontic and orthognathic surgery patients with complete dentitions. Multiple logistic regression was also used to determine demographic and skeletal factors associated with this disharmony. MATERIALS AND METHODS For this cross-sectional study, the sample was composed of cone-beam computed tomography (CBCT) images of 1178 individuals, using the database of a service center for dental diagnosis and planning (Compass3D, Belo Horizonte, MG, Brazil), which receives tomographic images from all over the country. The images were obtained from orthodontic and orthognathic surgery patients between 2011 and 2013. Information from the tomographic images was used exclusively for scientific purposes, fully preserving the anonymity of the patients. Institutional review board approval was obtained before the study was initiated (protocol number 771.293). Initially, a pilot study with 120 individuals who were not participating in the main study was conducted in order to obtain the proportion of MA in subjects with different sagittal jaw relationships. Epi Info version 7 software (CDC, Atlanta, Ga) was used, evaluating the Angle Orthodontist, Vol 00, No 00, 0000

Definition Most superior point of the external acoustic meatus Most inferior point of the infraorbital margin Point located at the tip of the anterior process of the maxilla Middle point on the anterior rim of the occipital foramen Point in the center of the sella turcica Most anterior and median point of the frontonasal suture Point located at the largest concavity of the anterior portion of the maxilla Point located at the largest concavity of the anterior portion of the mental symphysis Most anterior inferior point on the bony chin Most superior and posterior point in the upper contour of the pterygomaxillary fissure Plane passing through the right and left anatomic porion points and the left orbitale point (PoR, PoL - OrL) Plane that refers to the junction of nasion and basion points, perpendicular to the Frankfort plane

association between the exposure variables and MA. There was an expected prevalence of 40% of MA in unexposed subjects, using a 95% confidence interval and 80% statistical power. Assuming a proportion of unexposed (skeletal Class I) to exposed (skeletal Classes II and III) of 1:1 and a minimum prevalence ratio of 1.25, a sample size of 1178 individuals would be adequate. For inclusion in the sample, the following criteria were used: CBCT images requested because of clinical need or because conventional radiography could not meet clinical requirements, thereby conforming to the SEDENTEXCT project and the American Academy of Oral and Maxillofacial Radiology guidelines;13,14 patients 19 through 60 years of age; no missing teeth other than third molars; and images acquired using the same brand of CBCT machine (iCAT, Imaging Sciences International, Hatfield, Pa). Exclusion criteria were: prior history of facial fractures or facial surgery; degenerative disease involving the temporomandibular joint; or craniofacial anomalies. To perform the exams, the CBCT scanner was adjusted to operate under the following specifications: extended field of view (16 3 22 cm or 17 3 23 cm) 120KvP, 3-8mA, and 0.4mm3 voxel size. Patients were asked to occlude at maximum intercuspation and relax their lips. The DICOM files were imported into SimPlant Ortho Pro 2.0 software (Materialise Dental, Leuven, Belgium), which is capable of providing exact values for the measurements of choice. Landmarks were located using multiplanar reconstruction slices, and a measurement scale of 0.01 mm and 0.018 was used. The landmarks and reference planes used in this study are described in Table 1. The tomographic measurements evaluated are described in Table 2 and illustrated in Figure 1A,B,C.

MANDIBULAR ASYMMETRIES AND ASSOCIATED FACTORS Table 2.

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Tomographic Measurements Evaluated

Measurement

Definition

Variable

Gn-MSP ANB angle N-Ba.PtLeft-Gn angle N-S-Ba angle ANS-MSP

Distance from the gnathion to the midsagittal plane Angle formed by the intersection of the NA and NB lines Angle formed by the intersection of the NBa and PtLeftGn lines Angle formed by the intersection of the SN and SBa lines Distance from the anterior nasal spine to the midsagittal plane

Mandibular asymmetry Sagittal jaw relationship Vertical skeletal relationship Cranial base angle Maxillary asymmetry

The outcome was MA, which was later categorized as a qualitative polytomous ordinal variable (relative symmetry, moderate asymmetry, or severe asymmetry). The sample was divided into three groups on the basis of MA intensity by analyzing chin laterality2,7,11 independently if deviated to the left or right. Asymmetry was defined as the extent to which the patient’s gnathion was displaced from the midsagittal plane. Patients with displacements of 2 mm or less were defined as exhibiting relative symmetry.9,15 Patients whose gnathion was displaced by more than 2 mm and up to 4 mm were defined as exhibiting moderate asymmetry. Patients with gnathion displacement from the midsagittal plane greater than 4 mm were defined as exhibiting severe asymmetry.7,11,16 The exposure variables and their respective forms of analysis were: Demographic: Sex (male or female), Age 19 through 60 years of age (with subjects divided into two groups relative to the median age of 29 years as younger or older). Skeletal: Side of mandibular displacement determined by displacement of gnathion from the midsagittal plane (right or left), Sagittal jaw relationship determined by the ANB angle and classified as Class I (from 08 to 4.58), Class II (.4.58) or Class III (,08), as suggested by Tweed.17 Vertical skeletal relationship determined by the N-Ba PtLeft-Gn angle and classified as horizontal (.938), normal (from 878 to 938), or vertical (,878) as suggested by Ricketts.18 Cranial base angle

determined by the N-S-Ba angle as acute (,1278), normal (from 1278 to 1368) or obtuse (.1368) as ¨ 19 Maxillary asymmetry (absent or suggested by Bjork. present) determined by the distance from the anterior nasal spine to the midsagittal plane (when this distance exceeded 2 mm, the patients were defined as having maxillary asymmetry as suggested by Haraguchi et al.)7 Since tomographic measurements were made by three examiners, the method error was determined by the intraobserver and interobserver intraclass correlation coefficients (ICC). The three examiners analyzed 10% of the sample at two different times, with a twoweek interval. The intraobserver and interobserver ICC value was .0.90 for the evaluated measurements (considered highly reliable), except for the ANB angle which displayed an interobserver ICC of 0.89 (considered reliable). The results demonstrated good repeatability and reproducibility of the method. Statistical analyses were conducted using STATA version 13.0 (StataCorp, College Station, Tex). To verify the association between exposure variables and mandibular asymmetries, a bivariate analysis was initially conducted using the chi-square test (X2). Simple and adjusted ordinal logistic regression (partial proportional odds model) was then performed. This model was chosen because the outcome was polytomous and categorized ordinally. Only exposure variables with P , .20 in the bivariate analysis were entered into the multiple logistic regression analysis. The final model was used to estimate OR for those

Figure 1. Measurements used in the study for skeletal variables: (A) ANB Angle (sagittal jaw relationship); (B) Gn-MSP (mandibular asymmetry), ANS-MSP (maxillary asymmetry), and side of mandibular displacement; (C) N-Ba PtE-Gn angle (vertical skeletal relationship) and N-S-Ba angle (cranial base angle). Angle Orthodontist, Vol 00, No 0, 0000

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Table 3.

Characteristics of Sampled Individuals

Variables / Category Sex Male Female Age Younger Older Side of mandibular displacement Right Left Sagittal jaw relationship Class I Class II Class III Vertical skeletal relationship Horizontal Normal Vertical Cranial base angle Acute Normal Obtuse Maxillary asymmetry Absent Present

N (%) 402 (34.1) 776 (65.9) 589 (50.0) 589 (50.0) 498 (42.3) 680 (57.7) 496 (42.1) 411 (34.9) 271 (23.0)

DISCUSSION 281 (23.9) 516 (43.8) 381 (32.3) 371 (31.5) 655 (55.6) 152 (12.9) 1025 (87.0) 153 (13.0)

variables selected after adjustment and differences were classified as statistically significant for variables with P , .05 and a 95% confidence interval (95% CI). RESULTS The mean age of the subjects was 32.28 (SD ¼ 11.33). Displacement of gnathion in relation to the midsagittal plane was 2.51 mm (SD ¼ 2.69) in absolute terms, varying from 19.94 mm for the right side to 21.49 mm for the left side. Other characteristics of the exposure variables are shown in Table 3. Table 4 shows that the prevalence of relative mandibular symmetry, moderate asymmetry, and severe asymmetry on the total sample was 55.2% (95% CI 52.3–58.0), 27.2% (95% CI: 24.8–29.9), and 17.6% (95% CI: 15.5– 19.8), respectively. From the bivariate analysis (Table 4), the variables age (P ¼ .151), side of mandibular displacement (P ¼ .008), sagittal jaw relationship (P ¼ .074), and maxillary asymmetry (P , .001) were included in the regression model. In the adjusted regression model (Table 5), it was observed that mandibular asymmetries were independently associated only with the side of mandibular displacement (P ¼ .006) and maxillary asymmetry (P , .001). For the ordinal logistic regression analysis, both groups of mandibular asymmetries were compared to the relative symmetry group. When compared to subjects with symmetry, the odds of moderate MA were 1.5 times higher when there was a mandibular deviation to the left (OR ¼ 1.50; 95% CI: Angle Orthodontist, Vol 00, No 00, 0000

1.01–2.24) and 2.04 times higher when maxillary asymmetry was present (OR ¼ 2.04; 95% CI: 1.11– 3.76). The odds of severe MA were 2.09 times higher if there was mandibular deviation to the left (OR ¼ 2.09; 95% CI: 1.27–3.44) and 4.93 times higher when maxillary asymmetry was present (OR ¼ 4.93; 95% CI: 2.64–9.20) compared to subjects with mandibular symmetry. The model showed an adjusted coefficient of determination (R2) of 0.076 (Table 5), which means that only 7.6% of MA could be explained by the model of variables analyzed in this study.

Epidemiological studies are often highly clinically relevant since they enable professionals to know the frequency of disharmonies and also to identify specific groups of people who are prone to the alteration. This epidemiological study on non-syndromic and nonpathological mandibular asymmetries had two main objectives: to estimate the prevalence of different intensities of MA in orthodontic and orthognathic surgery patients and to investigate demographic and skeletal factors associated with these disharmonies. Combined with the use of regression analysis, some uncertainties surrounding MA may be better understood. Prevalence values of 55.2%, 27.2%, and 17.6% were observed for relative mandibular symmetry, moderate MA, and severe MA, respectively. Mandibular asymmetries were independently associated with the variables ‘‘side of mandibular deviation’’ and ‘‘maxillary asymmetry.’’ The methodology used to define the midsagittal plane in this study was previously validated by Damstra el al.20 Once this plane was determined, mandibular asymmetry was classified into three groups: relative mandibular symmetry, moderate MA, and severe MA. According to some scholars,7,11,16 the clinical expression of asymmetry only occurs when there is a skeletal deviation of at least 4 mm. Asymmetries below that can be verified but may not require comprehensive treatment. In other words, human sensitivity for perceiving facial imbalance increases when the skeletal deformation is close to or larger than 4 mm. However, the expression of asymmetry or its masking depends on individual characteristics such as the thickness of the soft tissue in the area. Because of that, some other authors consider there to be facial asymmetry in cases with skeletal deviations larger than 2 mm.7,9 Thus, this study evaluated asymmetry and divided it into three distinct categories. For statistical analysis of the data in this study, ordinal regression models were used. These models

MANDIBULAR ASYMMETRIES AND ASSOCIATED FACTORS Table 4.

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Bivariate Analysis of the Association Between Mandibular Asymmetries and the Exposure Variables, Using the X2 Test n (%)

Variables / Category

Relative Symmetry

Moderate Asymmetry

Severe Asymmetry

650 (55.2)

321 (27.2)

207 (17.6)

215 (53.5) 435 (56.1)

117 (29.1) 204 (26.3)

70 (17.4) 137 (17.6)

312 (52.9) 338 (57.4)

162 (27.5) 159 (27.0)

115 (19.6) 92 (15.6)

300 (60.2) 350 (51.5)

125 (25.1) 196 (28.8)

73 (14.7) 134 (19.7)

271 (54.6) 238 (57.9) 141 (52.0)

136 (27.4) 116 (28.2) 69 (25.5)

89 (18.0) 57 (13.9) 61 (22.5)

153 (54.5) 295 (57.2) 202 (53.0)

81 (28.8) 139 (26.9) 101 (26.5)

47 (16.7) 82 (15.9) 78 (20.5)

186 (50.1) 385 (58.8) 79 (52.0)

113 (30.5) 167 (25.5) 41 (26.9)

72 (19.4) 103 (15.7) 32 (21.1)

600 (58.5) 50 (32.7)

274 (26.7) 47 (30.7)

151 (14.7) 56 (36.6)

Total Sex Male Female Age Younger Older Side of mandibular displacement Right Left Sagittal jaw relationship Class I Class II Class III Vertical skeletal relationship Horizontal Normal Vertical Cranial base angle Acute Normal Obtuse Maxillary asymmetry Absent Present

P Value .578

.151

.008

.074

.428

.240

,.001

enable researchers to estimate the odds of occurrence of an adverse event, such as MA. In ordinal logistic regression, the OR can be interpreted as the number of times the odds of the outcome occurring increases when the exposure variable is modified in a unit/

category. Thus, the OR is used as a measure of association intensity.21 When compared to subjects with symmetry, the odds of moderate MA were 1.5 times higher when there was a lateral deviation to the left and approximately two times higher when maxillary

Table 5. Unadjusted and Adjusted Odds Ratio (OR) and 95% Confidence Intervals for Moderate and Severe Mandibular Asymmetries Among Adults According to Demographic and Biological Characteristics Unadjusted OR Moderate Asymmetry OR (95%CI) Age Younger Older

Adjusted OR

Severe Asymmetry p

1 0.90 0.442 (0.69–1.18) Side of mandibular displacement Right 1 Left 1.34 0.033* (1.02–1.76) Sagittal jaw relationship Class I 1 Class II 0.97 0.850 (0.71–1.31) Class III 0.97 0.889 (0.68–1.38) Maxillary asymmetry Absent 1 Present 2.05 0.037* (1.05–3.48)

OR (95%CI)

Moderate Asymmetry p

p Model

R2

OR (95%CI)

Severe Asymmetry p

OR (95%CI)

p

p Model

R2a

0.473 0.076 1 0.73 (0.54–1.01)

1 0.86 0.465 (0.58–1.28)

0.054

1 0.75 (0.46–1.22)

0.248

0.008* 0.010 1 1.57 (1.14–2.18)

0.006* 1 1 1.50 0.046* 2.09 (1.01–2.24) (1.27–3.44)

0.006*

0.004*

0.075 0.008 1 0.73 (0.50–1.06) 1.31 (0.90–1.93)

0.319 1 0.83 0.405 (0.54–1.28) 1.09 0.760 (0.62–1.94)

0.099 0.160

1 0.79 (0.46–1.35) 1.64 (0.86–3.13)

0.384 0.133

,0.001* 0.043 1 4.45 ,0.001* (2.36–7.69)

,0.001* 1 1 2.07 0.022* 4.93 ,0.001* (1.11–3.76) (2.64–9.20)

* P , .05; a adjusted. Angle Orthodontist, Vol 00, No 0, 0000

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asymmetry was present. The odds of severe MA was about two times higher when there was a lateral deviation to the left and approximately five times higher when maxillary asymmetry was present, compared to subjects with mandibular symmetry. Other studies also pointed out a relationship between the presence of MA and lateral deviation to the left,2,8 as well as the concomitant presence of maxillary asymmetry.7,15 However, those studies did not demonstrate how intense the association was. The higher frequency of deviation of gnathion to the left may be explained by the dominant growth potential of the right side of the face given the dominance of the right side when evaluating the dimensions of the skull and brain.7,12 Another possible mechanism causing this facial laterality could be imbalanced development of cells during embryogenesis since asymmetry exists in cell polarization and division.12 As for maxillary asymmetry, which was measured by the lateral deviation of anterior nasal spine (ANS), it has been reported that it is usually of a smaller magnitude than that of MA,2,7,11 suggesting that most maxillary asymmetries are secondary to asymmetric mandibular growth.1 It is important to mention that, in this study, maxillary asymmetry was evaluated by the lateral displacement of ANS to the midsagittal plane, as was also done by Haraguchi et al.7 However, since it is known that mandibular asymmetry is also related to vertical differences in maxillary heights16 (also described as maxillary cant), future studies should be designed to analyze this variable. The findings from this study demonstrated that there was no independent association between MA and sex, age, sagittal jaw relationship, vertical skeletal relationship, or cranial base angle in the evaluated subjects. Such results are consistent with most reports in the literature as to sex and age.8–10 However, there were some differences related to the other variables that were analyzed. Some authors found that facial asymmetry was equally distributed in skeletal Class I, II, and III,8 while others demonstrated asymmetry was more frequently associated with Class III,6,10,22 or less common in Class II.2 The current findings showed that severe MA was more frequent in skeletal Class III individuals, but moderate MA was more frequent in Class II individuals. However, these differences were not statistically significant. Regarding differences related to vertical skeletal pattern, Good et al.22 evaluated 66 orthodontic patients and suggested that MA was related to an increased lower anterior face height. Celik et al.23 evaluated condylar and ramal vertical asymmetry in 101 adult patients with different vertical growth patterns and concluded that the asymmetry index values were not Angle Orthodontist, Vol 00, No 00, 0000

THIESEN, GRIBEL, FREITAS, OLIVER, KIM

statistically different between the groups, similar to what was observed in the present study. Kim et al.15 observed a larger volume of the cranial base on the side contralateral to the mandibular deviation. However, studies performed by Kwon et al.24 and Baek et al.16 did not verify morphological differences in the cranial base between symmetric and asymmetric subjects. In evaluating the angle of the cranial base, the current study did not observe an association between this variable and mandibular asymmetry. In this study, the final regression model explained only 7.6% of the variance. Other variables that may have predictive value should be investigated in additional studies. A limitation of the study was that it was cross-sectional in design, and the temporal relationship between the outcome and predictors could not be defined. The cross-sectional design makes it difficult or impossible to discern the order of occurrence of events in time, which may lead to a so-called reverse causality bias.21 Additionally, mandibular functional shifts that could contribute a postural component to mandibular asymmetries were not analyzed. A large sample size and robust statistical testing were strengths of this study. The purpose was to give professionals a better understanding about the factors associated with mandibular asymmetries and the intensity of these associations. The results indicated that clinical investigation of skeletal mandibular asymmetries are necessary for orthodontic and orthognathic surgery patients, since their prevalence was found to be quite high. If misdiagnosed, asymmetries may lead to extended treatment time or compromised outcomes. These asymmetries happen independently of the individual’s sex, age, sagittal jaw relationship, vertical skeletal relationship, or cranial base angle. However, since the odds of mandibular asymmetries were higher when chin deviation was to the left, as well as when maxillary asymmetry was present, whenever patients present with those characteristics, the existence of mandibular asymmetry should be carefully considered. CONCLUSIONS 



The prevalence of mandibular asymmetry in adults was 44.8%, of which 27.2% was for moderate MA and 17.6% for severe MA. The odds of presenting with MA were significantly higher when the chin was deviated to the left or when maxillary asymmetry was present.

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14. American Academy of Oral and Maxillofacial Radiology. Clinical recommendations regarding use of cone beam computed tomography in orthodontic treatment. Oral Surg Oral Med Oral Pathol Oral Radiol. 2013;116:238–257. 15. Kim SJ, Lee KJ, Lee SH, Baik HS. Morphologic relationship between the cranial base and the mandible in patients with facial asymmetry and mandibular prognathism. Am J Orthod Dentofac Orthop. 2013;144:330–340. 16. Baek SH, Cho IS, Chang YI, Kim MJ. Skeletodental factors affecting chin point deviation in female patients with class III malocclusion and facial asymmetry: a three-dimensional analysis using computed tomography. Oral Surg, Oral Med Oral Pathol Oral Radiol Endod. 2007;104:628–639. 17. Tweed C. The Frankfort-Mandibular Incisor Angle (FMIA) in orthodontic diagnosis, treatment planning and prognosis. Angle Orthod. 1954;24:121–169. 18. Ricketts RM. A foundation for cephalometric communication. Am J Orthod. 1960;46:330–357. ¨ A. Cranial base development: A follow-up x-ray study 19. Bjork of the individual variation in growth occurring between the ages of 12 and 20 years and its relation to brain case and face development. Am J Orthod. 1955;41:198–225. 20. Damstra J, Fourie Z, De Wit M, Ren Y. A three-dimensional comparison of a morphometric and conventional cephalometric midsagittal planes for craniofacial asymmetry. Clin Oral Investig. 2012;16:285–294. 21. Pandis N. Biostatistics in Orthodontics: Design, Analysis, Reporting and Synthesis of Clinical Studies. Bern, Switzer¨ Bern; 2014. land: Zahnmedizinische Kliniken der Universitat 22. Good S, Edler R, Wertheim D, Greenhill D. A computerized photographic assessment of the relationship between skeletal discrepancy and mandibular outline asymmetry. Eur J Orthod. 2006;28:97–102. 23. Celik S, Celikoglu M, Buyuk SK, Sekerci AE. Mandibular vertical asymmetry in adult orthodontic patients with different vertical growth patterns: A cone beam computed tomography study. Angle Orthod. 2016;86:271–277. 24. Kwon TG, Park HS, Ryoo HM, Lee SH. A comparison of craniofacial morphology in patients with and without facial asymmetry–a three-dimensional analysis with computed tomography. Int J Oral Maxillofac Surg. 2006;35:43–48.

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