ORIGINAL ARTICLE
Cephalometric configuration of the occlusal plane in patients with anterior open bite Yoon Jeong Choi,a Dong Jae Kim,b Jaewook Nam,c Chooryung J. Chung,d and Kyung-Ho Kime Seoul and Suwon, Korea
Introduction: This study was performed to investigate the cephalometric configuration of the occlusal plane in patients with anterior open bite. Methods: Of 61 subjects with open bite (overbite $3.75 mm) who had been recruited consecutively from January 2006 to November 2013 and had no history of orthodontic treatment, 14 cephalometric landmarks indicating the incisal edge or the buccal or mesiobuccal cusp tips of each tooth were used for K-means clustering to classify the occlusal plane configuration. For the open-bite group and a control group with normal occlusion (n 5 38), dentoalveolar height, which is the perpendicular distance of each tooth to the palatal or mandibular plane, was compared among the clusters and between the 2 groups. Results: The open-bite subjects were divided into 2 clusters according to occlusal contact of the premolars: Y-form and V-form (with and without premolar contact, respectively). The normalized dentoalveolar heights of the 4 mandibular teeth (lateral incisor to second premolar) were significantly greater in the Y-form class than in the V-form class. The dentoalveolar heights of the 5 maxillary teeth (lateral incisor to first molar) were significantly greater in the open-bite group than in the control group. Conclusions: For anterior open-bite treatment, the cephalometric configuration of the occlusal plane should be considered based on the occlusal contacts of the premolars. (Am J Orthod Dentofacial Orthop 2016;149:391-400)
T
he treatment of anterior open bite (AOB) is challenging because of its high relapse rate.1-4 Although surgical and nonsurgical approaches have been proposed for adults, no consensus for the optimal treatment has been established yet.1 The treatment protocol should be selected in consideration of many factors, including skeletal and dentoalveolar features, esthetics, and patient's expectations.5-7 For a better understanding of AOB, several authors have investigated its cephalometric features and agreed a Assistant professor, Department of Orthodontics, Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea. b Postgraduate student, School of Chemical Engineering, Sungkyunkwan University, Suwon, Korea. c Assistant professor, School of Chemical Engineering, Sungkyunkwan University, Suwon, Korea. d Associate professor, Department of Orthodontics, Gangnam Severance Dental Hospital, Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea. e Professor and chair, Department of Orthodontics, Gangnam Severance Dental Hospital, Yonsei University, Seoul, Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by a faculty research grant of Yonsei University College of Dentistry (6-2012-0114). Address correspondence to: Kyung-Ho Kim, Department of Orthodontics, Gangnam Severance Dental Hospital, Yonsei University, 211 Eonju-ro, Gangnam-gu, Seoul 135-720, Korea; e-mail, [email protected]. Submitted, March 2015; revised and accepted, August 2015. 0889-5406/$36.00 Copyright Ó 2016 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2015.08.020
on some skeletal characteristics such as a decrease in the ratio of posterior to anterior facial height and an increase in lower anterior facial height, Y-axis, gonial angle, and mandibular plane angle.8-11 However, there have been some controversies regarding dentoalveolar characteristics such as the interincisal angle,8,9,12 dental heights,5-7,13 and occlusal plane angle. In particular, the occlusal plane angle was generally greater in the AOB group than in the normal occlusion group, but its definition was inconsistent in the studies. Tsang et al9 addressed 3 occlusal planes: the functional occlusal plane, drawn along the maximum intercuspation of the posterior teeth; the maxillary occlusal plane (MxOP); and the mandibular occlusal plane (MnOP). Taibah and Feteih8 used the MxOP and the MnOP only, whereas other authors did not clarify the definition of the occlusal plane.7,12,14 Some researchers have reported that the MxOP and MnOP should be considered separately in AOB patients because the measurement of the occlusal plane angle, by bisecting the AOB, may lead to the wrong conclusion that the AOB produces an increase in the occlusal plane angle.10,15,16 Hence, the MxOP and the MnOP angles were measured separately, as a line connecting the incisal edge of the central incisor and the mesiobuccal cusp tip of the first molar.8-10,15-17 However, the positions of other teeth composing the occlusal plane have been rarely considered, in spite of their clinical 391
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importance. The configuration of each occlusal plane can influence the treatment plan and posttreatment stability. For example, an AOB with 2 distinct occlusal planes can be corrected by orthognathic surgery with routine presurgical orthodontic treatment, segmental surgery, or intrusion of the occluding teeth, and each treatment modality has a different posttreatment stability. Previous studies have tried to distinguish skeletal open bite from dental open bite on a lateral cephalogram to understand the etiologic factors of this condition.14,16,18,19 A study suggested that a dental open bite occurs most often in children, and a skeletal open bite in adults16; another study reported that the 2 types of open bite could be distinguished by the growth pattern of the jaw.18 However, it has been difficult to make a clear distinction between the 2 types.20 Therefore, it would be better for clinicians to identify the cephalometric configurations rather than the etiologic factors of open bite. Because the treatment of AOB aims to change the MxOP and the MnOP, a better understanding of the cephalometric configuration of the occlusal plane is essential for correct diagnosis, proper treatment planning, and successful stability. However, there have been only a few studies on the configuration of the occlusal plane in patients with AOB. Therefore, this study was performed to investigate the cephalometric configuration of the occlusal plane in patients with AOB, to measure the height of each tooth from the palatal or mandibular plane, and to compare these heights with those of subjects with normal occlusion. MATERIAL AND METHODS
This study included an open-bite group (n 5 61; 16 men, 45 women; mean age, 25.4 years; range, 20.542.0 years) and a control group (n 5 38; 12 men, 26 women; mean age, 25.5 years; range, 20.4-37.8 years) (Table I). The 61 subjects in the open-bite group were selected from a total of 164 orthodontic patients who had visited the Gangnam Severance Dental Hospital in Seoul, Korea, between January 2006 and November 2013, had lateral cephalograms and impressions taken of both arches for the fabrication of dental casts, and had been diagnosed with AOB. The inclusion criteria were moderate-to-severe AOB ($3.75 mm),15 no missing teeth except for the third molars, age over 20 years, and mild facial asymmetry with less than 1 mm of occlusal plane canting and less than 2 mm of menton deviation. The exclusion criteria were history of orthodontic treatment, systemic disease, cleft lip or palate, and craniofacial syndromes. The open-bite group
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Table I. Demographic features of the subjects Age (y) Overbite* (mm) Overjet (mm) SNA ( ) SNB* ( ) ANB ( ) APDI ( ) ODI* ( ) Bj€ ork sum ( ) Gonial angle ( ) SN-MP ( ) PP-MP ( ) PFH/AFH U1-SN ( ) IMPA ( )
Open bite (n 5 61) Control (n 5 38) P value 25.36 6 3.27 25.50 6 6.04 0.922 5.40 6 1.56 2.80 6 0.70 0.000y 4.38 6 2.85 3.44 6 0.39 0.278 81.08 6 3.19 81.21 6 2.59 0.833 75.04 6 6.27 78.61 6 2.43 0.000y 5.42 6 2.48 2.60 6 0.94 0.000y 78.49 6 6.01 85.10 6 3.58 0.000y 66.53 6 7.38 71.37 6 3.71 0.000y 405.70 6 5.96 395.71 6 2.67 0.000y 126.95 6 7.46 121.14 6 4.73 0.000y 45.70 6 5.96 35.71 6 2.67 0.000y 35.64 6 5.99 25.52 6 3.54 0.000y 58.42 6 4.55 65.23 6 2.56 0.000y 106.98 6 7.14 106.79 6 6.97 0.895 93.19 6 7.66 94.08 6 5.93 0.542
SNA, Sella-nasion–A-point angle; SNB, sella-nasion–B-point angle; ANB, A-point–nasion–B-point angle; APDI, anteroposterior dysplasia indicator; ODI, overbite depth indicator; Bj€ork sum, sum of saddle angle, articular angle, and gonial angle; SN, sellanasion; MP, mandibular plane; PP, palatal plane; PFH, posterior facial height; AFH, anterior facial height; U1, maxillary central incisor; IMPA, mandibular incisor to mandibular plane angle. *Mann-Whitney U test was used because overbite, SNB, and ODI were not normally distributed. Other variables were analyzed with an independent t test; yP \0.001.
included patients with skeletal Class I (n 5 6), Class II (n 5 52), and Class III (n 5 3) malocclusions. The control group was carefully selected from the archives of the orthodontic department of the same hospital with Class I skeletal and dental relationships, a normodivergent facial profile, and less than 2 mm of arch length-tooth size discrepancy. The same inclusion criteria of the open-bite group were applied to the control group, including additionally 2 to 4 mm of overjet and overbite. This study was approved by the institutional review board of the Gangnam Severance Dental Hospital (32012-0116). Based on the lateral cephalograms, 19 landmarks were identified and digitized using an imagemeasuring program (Image-Pro PLUS, version 3.0; Media Cybernetics, Bethesda, Md). Fourteen landmarks indicated the incisal edges or the buccal and mesiobuccal cusp tips of each tooth, and 4 landmarks (anterior nasal spine, posterior nasal spine, lower gonion, and menton) composed 2 reference planes: the palatal plane, which connects the anterior and posterior nasal spines, and the mandibular plane, which connects lower gonion and menton (Fig 1, A). Nasion was also digitized to measure the anterior facial height that was used to normalize distances related to the teeth. Each landmark was coordinated, and linear and angular measurements were
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Fig 1. A, Graphic representation of the position of each tooth in the basal bone. Examples of 3 descriptor types considered in this study: B, F4, the perpendicular distance from the maxillary first premolar to a corresponding line constructed by 2 adjacent mandibular teeth; C, F12, the perpendicular distance from the mandibular second premolar to a corresponding line constructed by two adjacent maxillary teeth; D, F20, the angle between a line connecting the maxillary first and second molars and a line connecting the mandibular corresponding teeth.
performed using MATLAB software (MathWorks, Natick, Mass). Pattern recognition is a method that automatically detects regularities from given data.21 K-means clustering is one of such methods that split data into several groups based on their similarities.22 To measure the similarities, we defined features representing linear and angular relationships of the teeth. Here, 20 features (F1–F20) were selected that could be categorized into 3 types: the perpendicular distance from a given maxillary tooth to a corresponding line constructed by 2 adjacent mandibular teeth (F1–F7) (Fig 1, B); the perpendicular distance from a given mandibular tooth to a corresponding line constructed by 2 adjacent maxillary teeth (F8– F14) (Fig 1, C); and the angle between each maxillary tooth line and the corresponding mandibular tooth line (F15–F20) (Fig 1, D). The subscript number of each feature increases from the central incisor to the second molar. Figure 1 shows the position of each tooth in the basal bone and examples of 3 descriptor types. Features F1-F14 were normalized by the anterior facial height of each subject to compensate for their vertical differences and conduct fair comparisons.
Not all features are useful in cluster analysis. Therefore, feature selection is a crucial step in the analysis. In this study, the t test and U test could not be used because the distributions of features were neither normal nor similar to each other. To overcome this difficulty, we used the entropy-based feature ranking method.23 Entropy is a measure of the average amount of information in each sample drawn from a distribution. For example, if the removal of feature F1 leads to higher entropy than the removal of feature F2, then it is concluded that feature F1 is more important than feature F2. This method uses this removal process in series to select several high-ranking features. Table II shows the ranking of features used in this study. Details on how to determine the ranking are shown in the Appendix. To determine the optimal number of features and clusters for K-means clustering, we used 2 criteria: the Calinski-Harabasz criterion24 and the mean of silhouette values.25 A higher Calinski-Harabasz index indicates better-defined clusters,24 and the silhouette value shows how well the data lie within the clusters.25 We added high-ranking features one by one and checked the above criteria to determine the optimal number of features.
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Table II. Feature ranking with the entropy-based feature ranking method Ranking 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Variables F12 F5 F4 F11 F13 F6 F20 F14 F10 F9 F7 F8 F3 F1 F2 F18 F16 F19 F17 F15
Feature Perp distance of MnPM2 Perp distance of MxPM2 Perp distance of MxPM1 Perp distance of MnPM1 Perp distance of MnM1 Perp distance of MxM1 Angle between a line connecting MxM1 and MxM2 and a line connecting MnM1 and MnM2 Perp distance of MnM2 Perp distance of MnC Perp distance of MnI2 Perp distance of MxM2 Perp distance of MnI1 Perp distance of MxC Perp distance of MxI1 Perp distance of MxI2 Angle between a line connecting MxPM1 and MxPM2 and a line connecting MnPM1 and MnPM2 Angle between a line connecting MxI2 and MxC and a line connecting MnI2 and MnC Angle between a line connecting MxPM2 and MxM1 and a line connecting MnPM2 and MnM1 Angle between a line connecting MxC and MxPM1 and a line connecting MnC and MnPM1 Angle between a line connecting MxI1 and MxI2 and a line connecting MnI1 and MnI2
Entropy 529.18 528.98 528.77 528.71 528.64 528.39 528.17 528.00 527.90 527.78 527.75 527.66 527.59 527.56 527.48 526.94 526.55 526.34 526.23 525.98
Features F1-F14 were normalized by anterior facial height of each subject to compensate for their vertical differences and to conduct fair comparisons. Perp distance, Perpendicular distance from a given maxillary or mandibular tooth to a corresponding line constructed by 2 adjacent mandibular or maxillary teeth; Mx, maxillary; Mn, mandibular; I1 and I2, central and lateral incisors, respectively; C, canine; PM1 and PM2, first and second premolars, respectively; M1 and M2, first and second molars, respectively.
Based on the number of clusters and high-ranking features, an expert (Y.J.C.) with more than 10 years of experience classified the open-bite subjects using dental casts, and the results were compared with those from the cluster analysis. The dentoalveolar heights of each tooth, which were the perpendicular distances to the palatal and mandibular planes in the maxilla and the mandible, respectively, were calculated and compared between the open-bite and control groups using the Mann-Whitney U test. Based on the cluster analysis, the comparisons among subgroups in each cluster were also performed with the same test. A random selection of 10 lateral cephalograms from each group was digitized twice within 2 weeks by 1 examiner (Y.J.C.), and intraclass correlations were calculated. The correlations ranged from 97.3% to 99.5%; hence, the first reference points were used. RESULTS
The open-bite subjects were divided into 2 clusters using the top 3 features (Table III). Figure 2, A, shows the Calinski-Harabasz index values for the different clusters using the top 3 features, and Figure 2, B, shows the corresponding silhouette plot of the 2 clusters. The top 3 features were F12, F5, and F4, which indicated the perpendicular distances of the mandibular second premolar, the maxillary second premolar, and the maxillary
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Table III. Feature selection and quality of clustering
analysis Number of most important features 1 2 3* 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimum number of cluster (C-H criterion) 10 10 2* 2 2 2 10 10 10 10 10 9 10 10 10 10 10 2 3 2
Quality of cluster analysis (mean of silhouette values) 0.7515 0.6542 0.8653* 0.8409 0.8262 0.8149 0.7900 0.7900 0.7897 0.7895 0.7895 0.7997 0.7890 0.7887 0.7885 0.6190 0.5878 0.6021 0.4584 0.3692
C-H, Calinski-Harabasz. *Highest silhouette values.
first premolar to a corresponding line constructed by 2 adjacent teeth in the opposite dentition, respectively (Table II).
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Fig 2. A, Determination of the optimal numbers of clusters based on the Calinski-Harabasz criterion; B, the mean of silhouette values. Both the maximum Calinski-Harabasz value, marked as a red dot in A, and the silhouette values show that the optimal number of clusters is 2.
Figure 3, A, demonstrates the division of the 2 clusters based on the top 3 features, and Table IV shows the values of these features in each cluster. All values in cluster 1 were much higher than those in cluster 2, which were close to zero. This indicated that in cluster 1 the maxillary first and second premolars and the mandibular second premolar were out of occlusion; in cluster 2, the teeth had occlusal contacts with the opposite teeth. Figure 3, B and C, illustrates typical figures of each cluster. Based on these figures, we named clusters 1 and 2 the Y-form class and the V-form class, respectively. Figure 4, A and B, shows typical intraoral photographs of the Y-form and V-form classes, respectively, and Figure 4, C, depicts the top 3 features. Figure 3, D, shows the results of the expert's classification. The expert divided the occlusal planes of the open-bite subjects into the V-form and Y-form classes, according to the occlusal contacts of the premolars. The results of the expert's classification were the same as those from the cluster analysis. The dentoalveolar heights were not significantly different between the 2 clusters (P .0.05; Table V). However, after normalization, the parameters were significantly higher in the Y-form class than in the Vform class for the 4 mandibular teeth, lateral incisor to second premolar (P \0.05; Table VI). When the openbite group in total was compared with the control group, the 5 maxillary teeth, lateral incisor to first molar, in the open-bite group showed greater dentoalveolar heights than did those in the control group (P \0.05; Table V).
to obtain a successful treatment outcome and stability.19 This study demonstrates that the cephalometric configuration of the occlusal plane in patients with AOB is divided into 2 classes, according to the occlusal contact of the premolars, called the V-form and Y-form classes. To identify a similar pattern for the occlusal plane, we addressed linear measurements between the MxOP and the MnOP (F1–F14), which represented how the 2 occlusal planes diverged by showing the perpendicular distances of each tooth to the opposite dentition. Angular measurements (F15–F20) were also addressed to determine the curvature of the occlusal planes. Angular measurements were close to zero when the teeth were in occlusion, and the values increased when the teeth were out of occlusion. The values were constant if the 2 planes were straight lines, but the values increased gradually if the planes were curved. The top 3 features (F12, F5, and F4) were enough to divide the AOB subjects into 2 clusters; the angular measurements were not powerful enough to differentiate the subjects. These results indicate that the occlusal planes were not divided according to their curvature, but to interocclusal distances in the premolar area. Angular measurements were insignificant probably because the sagittal relationship—eg, Class II malocclusion—was not taken into account. To find a condition to separate the 2 classes, linear discriminate analysis was used. According to the analysis, a simple linear equation
DISCUSSION
was used as a criterion to distinguish the 2 classes: DðF12 ; F5 ; F4 Þ . 0 for the V-form class and DðF12 ; F5 ; F4 Þ \ 0 for the Y-form class. The oblique plane in the middle of Figure 3, A, stands for DðF12 ; F5 ; F4 Þ 5 0.
The treatment goal for AOB is to establish a functional occlusion by closing the open bite; this is necessarily accompanied by changes in the occlusal plane. Therefore, correct diagnosis of the occlusal plane is crucial
DðF12 ; F5 ; F4 Þ 51988:67 F12 126:77 F5 1272:19 F4 24:53
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Fig 3. Graphic representations of cluster division based on 3 selected features. A, The open-bite subjects were divided into 2 clusters based on K-means clustering; the equation obtained by linear discriminate analysis represents the plane that can divide the space into 2 clusters. B and C, Typical example figures of each cluster. D, Result of the expert's classification.
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Table IV. Top 3 ranked features of clusters 1 and 2 F12 F5 F4
Cluster 1 (n 5 19) 0.0186 6 0.0041 (2.44 6 0.68) 0.0133 6 0.0053 (1.78 6 0.87) 0.0217 6 0.0050 (2.86 6 0.77)
Cluster 2 (n 5 42) 0.0027 6 0.0019 (0.34 6 0.24) 0.0024 6 0.0018 (0.31 6 0.23) 0.0049 6 0.0049 (0.61 6 0.60)
All values are presented as means and standard deviations. Numbers in parenthesis are the values before normalization (mm). F12, Perpendicular distance from the mandibular second premolar to a corresponding line constructed by 2 adjacent maxillary teeth; F4 and F5, perpendicular distances from the maxillary first and second premolars to a corresponding line constructed by 2 adjacent mandibular teeth, respectively. The features were normalized by the anterior facial height of each subject to compensate for the vertical difference.
Occlusal contact of the premolars in the Y-form class may be a dental adaptation to increase the occlusal contacts because of the extrusive nature of the teeth.26 In particular, the mandibular teeth seemed to move for the adaptation. Normalized dentoalveolar heights support this assumption, showing higher values for the 4 mandibular teeth (lateral incisor to second premolar) in the Y-form class than in the V-form class (P \0.05; Table VI). Previous studies have also reported the important role of the mandibular teeth in AOB patients.5,15-17,27 With increasing severity of AOB, the MnOP becomes steeper because of downward growth of the mandible.15,16,27 In subjects having a skeletal vertical excess with an incisal overlap, significant elongation of the anterior teeth was noticed to compensate for the change, with the mandibular teeth playing an even more important role.5 Therefore, the following hypothesis can be proposed: when the severity of the AOB is increased or the patients with AOB are getting older, the occlusal plane can be classified into the Yform class rather than the V-form class. Because of the limited number of subjects in this study, we could not identify any significant differences between the 2 classes in terms of overbite and age (P .0.05). A future study with more AOB subjects is necessary to verify the hypothesis. The expert's classification confirmed the high accuracy of cluster analysis. These results showed that occlusal contact of the premolars is a good standard to distinguish the 2 classes clinically as well as radiographically. The identification of the cusp tips in a lateral cephalogram may be confusing because of superimposed bilateral structures. In addition, yawing of the entire arch or canting of the occlusal plane can make landmark identification difficult in a lateral cephalogram. We tried to decrease identification errors by
excluding subjects with facial asymmetry and confirmed the reliability of cluster analysis using dental casts. Further study of subjects with AOB and facial asymmetry using scans of dental casts is essential to gain a better understanding of the occlusal plane. Dentoalveolar heights before normalization indicate the absolute vertical height of each tooth, whereas heights after normalization indicate the relative vertical height of each tooth in the facial skeleton. We conducted the normalization procedure to illustrate the cephalometric configuration in subjects with AOB, excluding any potential bias derived from intersexual or individual differences in anterior facial height.28 The normalization procedure showed significant differences between the 2 classes for the 4 mandibular teeth, which were not significantly different before the normalization. As mentioned earlier, the mandibular lateral incisor, canine, first premolar, and second premolar may contribute to the cephalometric configuration of the Y-form class. A comparison of the total open-bite group with the control group showed that the 5 maxillary teeth, lateral incisor to first molar, in the open-bite group had greater dentoalveolar heights than did those in the control group. Increased molar height has been reported as a common finding in patients with AOB.5,6,13 This may be a cause of the open-bite condition,8 or on the contrary, the teeth may move to compensate for the downward growth of the mandible.5 Since the maxillary teeth move independently from the facial skeleton while the mandibular teeth act in a compensatory mechanism,7 the increased dentoalveolar heights of the maxillary first molar and premolars might be the most relevant etiologic factor for the open-bite condition in this study sample. A tongue with abnormal activity or abnormal size may also be a causative factor for the open bite, although it may have adapted to the problem.14,29 In open-bite patients, differential diagnosis in treatment planning is crucial for successful treatment and stability.19 The treatment method depends on several factors, such as incisor display, amount of open bite, smile arc, and vertical facial dimension.30 The classification of the occlusal plane can be a guideline for treatment planning and eventually can affect posttreatment stability. For example, nonsurgical correction of AOB involves either intrusion of the molars or extrusion of the incisors: in the case of the V-form, rotation of the occlusal plane by intrusion of several molars can easily resolve the open bite; however, for the Y-form, intrusion of the premolars and molars should be performed to correct the open bite. If extrusion of incisors is indicated, the Y-form class is easier to treat than the V-form class because relatively fewer teeth will be extruded. When surgical intervention is needed, leveling of the 2 occlusal
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Fig 4. Typical intraoral photographs showing: A, the Y-form class; B, the V-form class; C, the top 3 features, F12, F5, and F4, were enough to divide the subjects into 2 clusters. F12, F5, and F4 indicate the perpendicular distances of the mandibular second premolar, the maxillary second premolar, and the maxillary first premolar to a corresponding line constructed by 2 adjacent teeth in the opposite dentition, respectively. Table V. Dentoalveolar heights of each tooth in the open-bite and control groups (mm) Open bite
PP-U1 PP-U2 PP-U3 PP-U4 PP-U5 PP-U6 PP-U7 MP-L1 MP-L2 MP-L3 MP-L4 MP-L5 MP-L6 MP-L7
Cluster 1 (V-form) 30.78 6 3.87 30.52 6 3.77 30.03 6 3.63 29.04 6 3.49 27.84 6 3.19 26.21 6 3.36 23.17 6 3.38 42.66 6 5.12 41.73 6 4.93 40.51 6 4.65 38.92 6 4.64 36.91 6 4.85 35.30 6 5.03 32.58 6 5.36
P value* 0.657 0.538 0.668 0.907 0.518 0.379 0.518 1.000 0.932 0.570 0.233 0.362 0.691 0.882
Cluster 2 (Y-form) 30.06 6 2.79 29.86 6 2.79 29.61 6 2.75 28.99 6 2.71 27.36 6 2.78 25.24 6 3.05 22.30 6 3.70 42.30 6 4.86 41.52 6 4.81 40.76 6 4.71 39.48 6 4.44 37.31 6 4.28 34.88 6 4.34 31.59 6 4.24
Total 30.29 6 3.15 30.06 6 3.11 29.74 6 3.03 29.00 6 2.94 27.51 6 2.90 25.54 6 3.16 22.57 6 3.60 42.41 6 4.91 41.59 6 4.81 40.69 6 4.66 39.31 6 4.47 37.19 6 4.43 35.01 6 4.53 31.90 6 4.59
Control 29.43 6 2.68 28.51 6 2.50 27.86 6 2.44 27.01 6 2.24 25.89 6 2.24 24.11 6 2.04 21.41 6 2.23 41.32 6 3.36 40.62 6 3.22 40.59 6 3.25 38.89 6 3.26 36.64 6 2.90 34.60 6 3.02 32.30 6 2.89
P valuey 0.375 0.032§ 0.003§ 0.002§ 0.010z 0.018z 0.101 0.366 0.521 0.590 0.874 0.751 0.956 0.191
Dentoalveolar heights are presented as means and standard deviations. PP, Palatal plane; MP, mandibular plane; U1 to U7 and L1 to L7, maxillary and mandibular teeth from the central incisor to the second molar, respectively; PP-U1 and MP-L1, perpendicular distances of U1 and L1 to the PP and MP, respectively. *P values were obtained from Mann-Whitney U tests between clusters 1 and 2; yP values were obtained from the same test between the open-bite group in total and the control group; zP \0.05; §P \0.01.
planes by segmental surgery should be considered in a patient of the Y-form class. If a continuous archwire is used for leveling the 2 occlusal planes in the Y-form class, extrusion of the anterior teeth and a slight
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intrusion of the premolars would occur; this may influence the posttreatment stability of the AOB.1,31 However, because the clustering analysis in this study was performed with a limited number of subjects, and
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Table VI. Normalized dentoalveolar heights of each
tooth in the open-bite group PP-U1 PP-U2 PP-U3 PP-U4 PP-U5 PP-U6 PP-U7 MP-L1 MP-L2 MP-L3 MP-L4 MP-L5 MP-L6 MP-L7
Cluster 1 (V-form) 0.236 6 0.019 0.234 6 0.018 0.230 6 0.015 0.222 6 0.013 0.213 6 0.013 0.200 6 0.013 0.177 6 0.014 0.326 6 0.014 0.319 6 0.013 0.310 6 0.013 0.298 6 0.012 0.282 6 0.014 0.270 6 0.017 0.248 6 0.021
Cluster 2 (Y-form) 0.238 6 0.016 0.236 6 0.013 0.234 6 0.012 0.229 6 0.012 0.216 6 0.012 0.199 6 0.014 0.176 6 0.020 0.334 6 0.016 0.327 6 0.016 0.321 6 0.016 0.311 6 0.016 0.294 6 0.017 0.275 6 0.018 0.249 6 0.021
2. P value* 0.858 0.738 0.387 0.065 0.379 0.932 0.895 0.080 0.036y 0.006z 0.002z 0.018y 0.204 1.000
Dentoalveolar heights are presented as means and standard deviations. PP, Palatal plane; MP, mandibular plane; U1 to U7 and L1 to L7, maxillary and mandibular teeth from the central incisor to the second molar, respectively; PP-U1 and MP-L1, perpendicular distances of U1 and L1 to the PP and MP, respectively. *P value was obtained from the Mann-Whitney U test between clusters 1 and 2; yP \0.05; zP \0.01.
they were mostly patients with a skeletal Class II malocclusion as previously reported, a future study with more subjects should be considered.32,33
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CONCLUSIONS 13.
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3.
4.
The open-bite subjects were divided into 2 clusters, V-form class and Y-form class, according to the occlusal contacts of the premolars. Occlusal contacts of the premolars can be used as a good standard to distinguish the 2 classes clinically as well as radiographically. Occlusal contacts of the premolars in the Y-form class may be a dental adaptation to increase occlusal contact. Greater dentoalveolar heights of the maxillary teeth in the open-bite group compared with the control group indicate that the open-bite condition may be caused by overeruption of the maxillary molars.
14. 15.
16. 17. 18.
19. 20.
SUPPLEMENTARY DATA
Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ajodo.2015.08. 020. REFERENCES
21. 22. 23.
1. Greenlee GM, Huang GJ, Chen SS, Chen J, Koepsell T, Hujoel P. Stability of treatment for anterior open-bite malocclusion: a
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meta-analysis. Am J Orthod Dentofacial Orthop 2011;139: 154-69. Jensen U, Ruf S. Success rate of anterior open-bite orthodontic-orthognathic surgical treatment. Am J Orthod Dentofacial Orthop 2010;138:716-9. Baek MS, Choi YJ, Yu HS, Lee KJ, Kwak J, Park YC. Long-term stability of anterior open-bite treatment by intrusion of maxillary posterior teeth. Am J Orthod Dentofacial Orthop 2010;138: 396.e1-9:discussion, 396-8. Denison TF, Kokich VG, Shapiro PA. Stability of maxillary surgery in openbite versus nonopenbite malocclusions. Angle Orthod 1989;59:5-10. Kucera J, Marek I, Tycova H, Baccetti T. Molar height and dentoalveolar compensation in adult subjects with skeletal open bite. Angle Orthod 2011;81:564-9. Cangialosi TJ. Skeletal morphologic features of anterior open bite. Am J Orthod 1984;85:28-36. Kuitert R, Beckmann S, van Loenen M, Tuinzing B, Zentner A. Dentoalveolar compensation in subjects with vertical skeletal dysplasia. Am J Orthod Dentofacial Orthop 2006; 129:649-57. Taibah SM, Feteih RM. Cephalometric features of anterior open bite. World J Orthod 2007;8:145-52. Tsang WM, Cheung LK, Samman N. Cephalometric characteristics of anterior open bite in a southern Chinese population. Am J Orthod Dentofacial Orthop 1998;113:165-72. Ellis E 3rd, McNamara JA Jr, Lawrence TM. Components of adult Class II open-bite malocclusion. J Oral Maxillofac Surg 1985;43: 92-105. Jones OG. A cephalometric study of 32 North American black patients with anterior open bite. Am J Orthod Dentofacial Orthop 1989;95:289-96. Stuani AS, Stuani AS, Stuani MB, Saraiva Mda C, Matsumoto MA. Anterior open bite–cephalometric evaluation of the dental pattern. Braz Dent J 2006;17:68-70. Schendel SA, Eisenfeld J, Bell WH, Epker BN, Mishelevich DJ. The long face syndrome: vertical maxillary excess. Am J Orthod 1976; 70:398-408. Subtelny JD, Sakuda M. Open-bite: diagnosis and treatment. Am J Orthod 1964;50:337-58. Tsang WM, Cheung LK, Samman N. Cephalometric parameters affecting severity of anterior open bite. Int J Oral Maxillofac Surg 1997;26:321-6. Nahoum HI, Horowitz SL, Benedicto EA. Varieties of anterior open-bite. Am J Orthod 1972;61:486-92. Epker BN, Fish LC. The surgical-orthodontic correction of Class III skeletal open-bite. Am J Orthod 1978;73:601-18. Nielsen IL. Vertical malocclusions: etiology, development, diagnosis and some aspects of treatment. Angle Orthod 1991;61: 247-60. Jarabak JR. Open bite. skeletal morphology. Fortschr Kieferorthop 1983;44:122-33. Bock JJ, Bock F, Bohm B, Fuhrmann RA. Classification of anterior open bite using individualized cephalometry. J Orofac Orthop 2005;66:338-48. Bishop CM. Pattern recognition and machine learning. New York: Springer; 2006. Hartigan JA, Wong MA, Algorithm AS. 136: a k-means clustering algorithm. Applied Statistics 1979;28:100-8. Dash M, Liu H. Feature selection for clustering. In: Terano T, Liu H, Chen AL, editors. Knowledge discovery and data mining. Current issues and new applications. Berlin, Germany: Springer; 2000. p. 110-21.
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24. Cali nski T, Harabasz J. A dendrite method for cluster analysis. Commun Statistics 1974;3:1-27. 25. Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis. Hoboken, NJ: John Wiley & Sons; 2009. 26. Jager A. Histomorphometric study of age-related changes in remodelling activity of human desmodontal bone. J Anat 1996; 189(Pt 2):257-64. 27. Enunlu N. Palatal and mandibular plane variations in open bite cases with varying aetiology. Trans Eur Orthod Soc 1974;165-71. 28. Burstone CJ, James RB, Legan H, Murphy GA, Norton LA. Cephalometrics for orthognathic surgery. J Oral Surg 1978;36:269-77. 29. Gracco A, Perri A, Siviero L, Bonetti GA, Cocilovo F, Stellini E. Multidisciplinary correction of anterior open bite
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30.
31.
32.
33.
relapse and upper airway obstruction. Korean J Orthod 2015;45:47-56. Davidovitch M, Rebellato J. Two-couple orthodontic appliance systems utility arches: a two-couple intrusion arch. Semin Orthod 1995;1:25-30. Espeland L, Dowling PA, Mobarak KA, Stenvik A. Three-year stability of open-bite correction by 1-piece maxillary osteotomy. Am J Orthod Dentofacial Orthop 2008;134:60-6. Schudy FF. Vertical growth versus anteroposterior growth as related to function and treatment. Angle Orthod 1964;35: 36-50. Proffit WR, White PR, Sarver DM. Contemporary treatment of dentofacial deformity. St Louis: Mosby Elsevier; 2003.
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Cephalometric configuration of the occlusal plane in patients with anterior open bite Yoon Jeong Choi,a Dong Jae Kim,b Jaewook Nam,c Chooryung J. Chung,d and Kyung-Ho Kime Seoul and Suwon, Korea
Introduction: This study was performed to investigate the cephalometric configuration of the occlusal plane in patients with anterior open bite. Methods: Of 61 subjects with open bite (overbite $3.75 mm) who had been recruited consecutively from January 2006 to November 2013 and had no history of orthodontic treatment, 14 cephalometric landmarks indicating the incisal edge or the buccal or mesiobuccal cusp tips of each tooth were used for K-means clustering to classify the occlusal plane configuration. For the open-bite group and a control group with normal occlusion (n 5 38), dentoalveolar height, which is the perpendicular distance of each tooth to the palatal or mandibular plane, was compared among the clusters and between the 2 groups. Results: The open-bite subjects were divided into 2 clusters according to occlusal contact of the premolars: Y-form and V-form (with and without premolar contact, respectively). The normalized dentoalveolar heights of the 4 mandibular teeth (lateral incisor to second premolar) were significantly greater in the Y-form class than in the V-form class. The dentoalveolar heights of the 5 maxillary teeth (lateral incisor to first molar) were significantly greater in the open-bite group than in the control group. Conclusions: For anterior open-bite treatment, the cephalometric configuration of the occlusal plane should be considered based on the occlusal contacts of the premolars. (Am J Orthod Dentofacial Orthop 2016;149:391-400)
T
he treatment of anterior open bite (AOB) is challenging because of its high relapse rate.1-4 Although surgical and nonsurgical approaches have been proposed for adults, no consensus for the optimal treatment has been established yet.1 The treatment protocol should be selected in consideration of many factors, including skeletal and dentoalveolar features, esthetics, and patient's expectations.5-7 For a better understanding of AOB, several authors have investigated its cephalometric features and agreed a Assistant professor, Department of Orthodontics, Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea. b Postgraduate student, School of Chemical Engineering, Sungkyunkwan University, Suwon, Korea. c Assistant professor, School of Chemical Engineering, Sungkyunkwan University, Suwon, Korea. d Associate professor, Department of Orthodontics, Gangnam Severance Dental Hospital, Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea. e Professor and chair, Department of Orthodontics, Gangnam Severance Dental Hospital, Yonsei University, Seoul, Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by a faculty research grant of Yonsei University College of Dentistry (6-2012-0114). Address correspondence to: Kyung-Ho Kim, Department of Orthodontics, Gangnam Severance Dental Hospital, Yonsei University, 211 Eonju-ro, Gangnam-gu, Seoul 135-720, Korea; e-mail, [email protected]. Submitted, March 2015; revised and accepted, August 2015. 0889-5406/$36.00 Copyright Ó 2016 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2015.08.020
on some skeletal characteristics such as a decrease in the ratio of posterior to anterior facial height and an increase in lower anterior facial height, Y-axis, gonial angle, and mandibular plane angle.8-11 However, there have been some controversies regarding dentoalveolar characteristics such as the interincisal angle,8,9,12 dental heights,5-7,13 and occlusal plane angle. In particular, the occlusal plane angle was generally greater in the AOB group than in the normal occlusion group, but its definition was inconsistent in the studies. Tsang et al9 addressed 3 occlusal planes: the functional occlusal plane, drawn along the maximum intercuspation of the posterior teeth; the maxillary occlusal plane (MxOP); and the mandibular occlusal plane (MnOP). Taibah and Feteih8 used the MxOP and the MnOP only, whereas other authors did not clarify the definition of the occlusal plane.7,12,14 Some researchers have reported that the MxOP and MnOP should be considered separately in AOB patients because the measurement of the occlusal plane angle, by bisecting the AOB, may lead to the wrong conclusion that the AOB produces an increase in the occlusal plane angle.10,15,16 Hence, the MxOP and the MnOP angles were measured separately, as a line connecting the incisal edge of the central incisor and the mesiobuccal cusp tip of the first molar.8-10,15-17 However, the positions of other teeth composing the occlusal plane have been rarely considered, in spite of their clinical 391
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importance. The configuration of each occlusal plane can influence the treatment plan and posttreatment stability. For example, an AOB with 2 distinct occlusal planes can be corrected by orthognathic surgery with routine presurgical orthodontic treatment, segmental surgery, or intrusion of the occluding teeth, and each treatment modality has a different posttreatment stability. Previous studies have tried to distinguish skeletal open bite from dental open bite on a lateral cephalogram to understand the etiologic factors of this condition.14,16,18,19 A study suggested that a dental open bite occurs most often in children, and a skeletal open bite in adults16; another study reported that the 2 types of open bite could be distinguished by the growth pattern of the jaw.18 However, it has been difficult to make a clear distinction between the 2 types.20 Therefore, it would be better for clinicians to identify the cephalometric configurations rather than the etiologic factors of open bite. Because the treatment of AOB aims to change the MxOP and the MnOP, a better understanding of the cephalometric configuration of the occlusal plane is essential for correct diagnosis, proper treatment planning, and successful stability. However, there have been only a few studies on the configuration of the occlusal plane in patients with AOB. Therefore, this study was performed to investigate the cephalometric configuration of the occlusal plane in patients with AOB, to measure the height of each tooth from the palatal or mandibular plane, and to compare these heights with those of subjects with normal occlusion. MATERIAL AND METHODS
This study included an open-bite group (n 5 61; 16 men, 45 women; mean age, 25.4 years; range, 20.542.0 years) and a control group (n 5 38; 12 men, 26 women; mean age, 25.5 years; range, 20.4-37.8 years) (Table I). The 61 subjects in the open-bite group were selected from a total of 164 orthodontic patients who had visited the Gangnam Severance Dental Hospital in Seoul, Korea, between January 2006 and November 2013, had lateral cephalograms and impressions taken of both arches for the fabrication of dental casts, and had been diagnosed with AOB. The inclusion criteria were moderate-to-severe AOB ($3.75 mm),15 no missing teeth except for the third molars, age over 20 years, and mild facial asymmetry with less than 1 mm of occlusal plane canting and less than 2 mm of menton deviation. The exclusion criteria were history of orthodontic treatment, systemic disease, cleft lip or palate, and craniofacial syndromes. The open-bite group
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Table I. Demographic features of the subjects Age (y) Overbite* (mm) Overjet (mm) SNA ( ) SNB* ( ) ANB ( ) APDI ( ) ODI* ( ) Bj€ ork sum ( ) Gonial angle ( ) SN-MP ( ) PP-MP ( ) PFH/AFH U1-SN ( ) IMPA ( )
Open bite (n 5 61) Control (n 5 38) P value 25.36 6 3.27 25.50 6 6.04 0.922 5.40 6 1.56 2.80 6 0.70 0.000y 4.38 6 2.85 3.44 6 0.39 0.278 81.08 6 3.19 81.21 6 2.59 0.833 75.04 6 6.27 78.61 6 2.43 0.000y 5.42 6 2.48 2.60 6 0.94 0.000y 78.49 6 6.01 85.10 6 3.58 0.000y 66.53 6 7.38 71.37 6 3.71 0.000y 405.70 6 5.96 395.71 6 2.67 0.000y 126.95 6 7.46 121.14 6 4.73 0.000y 45.70 6 5.96 35.71 6 2.67 0.000y 35.64 6 5.99 25.52 6 3.54 0.000y 58.42 6 4.55 65.23 6 2.56 0.000y 106.98 6 7.14 106.79 6 6.97 0.895 93.19 6 7.66 94.08 6 5.93 0.542
SNA, Sella-nasion–A-point angle; SNB, sella-nasion–B-point angle; ANB, A-point–nasion–B-point angle; APDI, anteroposterior dysplasia indicator; ODI, overbite depth indicator; Bj€ork sum, sum of saddle angle, articular angle, and gonial angle; SN, sellanasion; MP, mandibular plane; PP, palatal plane; PFH, posterior facial height; AFH, anterior facial height; U1, maxillary central incisor; IMPA, mandibular incisor to mandibular plane angle. *Mann-Whitney U test was used because overbite, SNB, and ODI were not normally distributed. Other variables were analyzed with an independent t test; yP \0.001.
included patients with skeletal Class I (n 5 6), Class II (n 5 52), and Class III (n 5 3) malocclusions. The control group was carefully selected from the archives of the orthodontic department of the same hospital with Class I skeletal and dental relationships, a normodivergent facial profile, and less than 2 mm of arch length-tooth size discrepancy. The same inclusion criteria of the open-bite group were applied to the control group, including additionally 2 to 4 mm of overjet and overbite. This study was approved by the institutional review board of the Gangnam Severance Dental Hospital (32012-0116). Based on the lateral cephalograms, 19 landmarks were identified and digitized using an imagemeasuring program (Image-Pro PLUS, version 3.0; Media Cybernetics, Bethesda, Md). Fourteen landmarks indicated the incisal edges or the buccal and mesiobuccal cusp tips of each tooth, and 4 landmarks (anterior nasal spine, posterior nasal spine, lower gonion, and menton) composed 2 reference planes: the palatal plane, which connects the anterior and posterior nasal spines, and the mandibular plane, which connects lower gonion and menton (Fig 1, A). Nasion was also digitized to measure the anterior facial height that was used to normalize distances related to the teeth. Each landmark was coordinated, and linear and angular measurements were
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Fig 1. A, Graphic representation of the position of each tooth in the basal bone. Examples of 3 descriptor types considered in this study: B, F4, the perpendicular distance from the maxillary first premolar to a corresponding line constructed by 2 adjacent mandibular teeth; C, F12, the perpendicular distance from the mandibular second premolar to a corresponding line constructed by two adjacent maxillary teeth; D, F20, the angle between a line connecting the maxillary first and second molars and a line connecting the mandibular corresponding teeth.
performed using MATLAB software (MathWorks, Natick, Mass). Pattern recognition is a method that automatically detects regularities from given data.21 K-means clustering is one of such methods that split data into several groups based on their similarities.22 To measure the similarities, we defined features representing linear and angular relationships of the teeth. Here, 20 features (F1–F20) were selected that could be categorized into 3 types: the perpendicular distance from a given maxillary tooth to a corresponding line constructed by 2 adjacent mandibular teeth (F1–F7) (Fig 1, B); the perpendicular distance from a given mandibular tooth to a corresponding line constructed by 2 adjacent maxillary teeth (F8– F14) (Fig 1, C); and the angle between each maxillary tooth line and the corresponding mandibular tooth line (F15–F20) (Fig 1, D). The subscript number of each feature increases from the central incisor to the second molar. Figure 1 shows the position of each tooth in the basal bone and examples of 3 descriptor types. Features F1-F14 were normalized by the anterior facial height of each subject to compensate for their vertical differences and conduct fair comparisons.
Not all features are useful in cluster analysis. Therefore, feature selection is a crucial step in the analysis. In this study, the t test and U test could not be used because the distributions of features were neither normal nor similar to each other. To overcome this difficulty, we used the entropy-based feature ranking method.23 Entropy is a measure of the average amount of information in each sample drawn from a distribution. For example, if the removal of feature F1 leads to higher entropy than the removal of feature F2, then it is concluded that feature F1 is more important than feature F2. This method uses this removal process in series to select several high-ranking features. Table II shows the ranking of features used in this study. Details on how to determine the ranking are shown in the Appendix. To determine the optimal number of features and clusters for K-means clustering, we used 2 criteria: the Calinski-Harabasz criterion24 and the mean of silhouette values.25 A higher Calinski-Harabasz index indicates better-defined clusters,24 and the silhouette value shows how well the data lie within the clusters.25 We added high-ranking features one by one and checked the above criteria to determine the optimal number of features.
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Table II. Feature ranking with the entropy-based feature ranking method Ranking 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Variables F12 F5 F4 F11 F13 F6 F20 F14 F10 F9 F7 F8 F3 F1 F2 F18 F16 F19 F17 F15
Feature Perp distance of MnPM2 Perp distance of MxPM2 Perp distance of MxPM1 Perp distance of MnPM1 Perp distance of MnM1 Perp distance of MxM1 Angle between a line connecting MxM1 and MxM2 and a line connecting MnM1 and MnM2 Perp distance of MnM2 Perp distance of MnC Perp distance of MnI2 Perp distance of MxM2 Perp distance of MnI1 Perp distance of MxC Perp distance of MxI1 Perp distance of MxI2 Angle between a line connecting MxPM1 and MxPM2 and a line connecting MnPM1 and MnPM2 Angle between a line connecting MxI2 and MxC and a line connecting MnI2 and MnC Angle between a line connecting MxPM2 and MxM1 and a line connecting MnPM2 and MnM1 Angle between a line connecting MxC and MxPM1 and a line connecting MnC and MnPM1 Angle between a line connecting MxI1 and MxI2 and a line connecting MnI1 and MnI2
Entropy 529.18 528.98 528.77 528.71 528.64 528.39 528.17 528.00 527.90 527.78 527.75 527.66 527.59 527.56 527.48 526.94 526.55 526.34 526.23 525.98
Features F1-F14 were normalized by anterior facial height of each subject to compensate for their vertical differences and to conduct fair comparisons. Perp distance, Perpendicular distance from a given maxillary or mandibular tooth to a corresponding line constructed by 2 adjacent mandibular or maxillary teeth; Mx, maxillary; Mn, mandibular; I1 and I2, central and lateral incisors, respectively; C, canine; PM1 and PM2, first and second premolars, respectively; M1 and M2, first and second molars, respectively.
Based on the number of clusters and high-ranking features, an expert (Y.J.C.) with more than 10 years of experience classified the open-bite subjects using dental casts, and the results were compared with those from the cluster analysis. The dentoalveolar heights of each tooth, which were the perpendicular distances to the palatal and mandibular planes in the maxilla and the mandible, respectively, were calculated and compared between the open-bite and control groups using the Mann-Whitney U test. Based on the cluster analysis, the comparisons among subgroups in each cluster were also performed with the same test. A random selection of 10 lateral cephalograms from each group was digitized twice within 2 weeks by 1 examiner (Y.J.C.), and intraclass correlations were calculated. The correlations ranged from 97.3% to 99.5%; hence, the first reference points were used. RESULTS
The open-bite subjects were divided into 2 clusters using the top 3 features (Table III). Figure 2, A, shows the Calinski-Harabasz index values for the different clusters using the top 3 features, and Figure 2, B, shows the corresponding silhouette plot of the 2 clusters. The top 3 features were F12, F5, and F4, which indicated the perpendicular distances of the mandibular second premolar, the maxillary second premolar, and the maxillary
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Table III. Feature selection and quality of clustering
analysis Number of most important features 1 2 3* 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Optimum number of cluster (C-H criterion) 10 10 2* 2 2 2 10 10 10 10 10 9 10 10 10 10 10 2 3 2
Quality of cluster analysis (mean of silhouette values) 0.7515 0.6542 0.8653* 0.8409 0.8262 0.8149 0.7900 0.7900 0.7897 0.7895 0.7895 0.7997 0.7890 0.7887 0.7885 0.6190 0.5878 0.6021 0.4584 0.3692
C-H, Calinski-Harabasz. *Highest silhouette values.
first premolar to a corresponding line constructed by 2 adjacent teeth in the opposite dentition, respectively (Table II).
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Fig 2. A, Determination of the optimal numbers of clusters based on the Calinski-Harabasz criterion; B, the mean of silhouette values. Both the maximum Calinski-Harabasz value, marked as a red dot in A, and the silhouette values show that the optimal number of clusters is 2.
Figure 3, A, demonstrates the division of the 2 clusters based on the top 3 features, and Table IV shows the values of these features in each cluster. All values in cluster 1 were much higher than those in cluster 2, which were close to zero. This indicated that in cluster 1 the maxillary first and second premolars and the mandibular second premolar were out of occlusion; in cluster 2, the teeth had occlusal contacts with the opposite teeth. Figure 3, B and C, illustrates typical figures of each cluster. Based on these figures, we named clusters 1 and 2 the Y-form class and the V-form class, respectively. Figure 4, A and B, shows typical intraoral photographs of the Y-form and V-form classes, respectively, and Figure 4, C, depicts the top 3 features. Figure 3, D, shows the results of the expert's classification. The expert divided the occlusal planes of the open-bite subjects into the V-form and Y-form classes, according to the occlusal contacts of the premolars. The results of the expert's classification were the same as those from the cluster analysis. The dentoalveolar heights were not significantly different between the 2 clusters (P .0.05; Table V). However, after normalization, the parameters were significantly higher in the Y-form class than in the Vform class for the 4 mandibular teeth, lateral incisor to second premolar (P \0.05; Table VI). When the openbite group in total was compared with the control group, the 5 maxillary teeth, lateral incisor to first molar, in the open-bite group showed greater dentoalveolar heights than did those in the control group (P \0.05; Table V).
to obtain a successful treatment outcome and stability.19 This study demonstrates that the cephalometric configuration of the occlusal plane in patients with AOB is divided into 2 classes, according to the occlusal contact of the premolars, called the V-form and Y-form classes. To identify a similar pattern for the occlusal plane, we addressed linear measurements between the MxOP and the MnOP (F1–F14), which represented how the 2 occlusal planes diverged by showing the perpendicular distances of each tooth to the opposite dentition. Angular measurements (F15–F20) were also addressed to determine the curvature of the occlusal planes. Angular measurements were close to zero when the teeth were in occlusion, and the values increased when the teeth were out of occlusion. The values were constant if the 2 planes were straight lines, but the values increased gradually if the planes were curved. The top 3 features (F12, F5, and F4) were enough to divide the AOB subjects into 2 clusters; the angular measurements were not powerful enough to differentiate the subjects. These results indicate that the occlusal planes were not divided according to their curvature, but to interocclusal distances in the premolar area. Angular measurements were insignificant probably because the sagittal relationship—eg, Class II malocclusion—was not taken into account. To find a condition to separate the 2 classes, linear discriminate analysis was used. According to the analysis, a simple linear equation
DISCUSSION
was used as a criterion to distinguish the 2 classes: DðF12 ; F5 ; F4 Þ . 0 for the V-form class and DðF12 ; F5 ; F4 Þ \ 0 for the Y-form class. The oblique plane in the middle of Figure 3, A, stands for DðF12 ; F5 ; F4 Þ 5 0.
The treatment goal for AOB is to establish a functional occlusion by closing the open bite; this is necessarily accompanied by changes in the occlusal plane. Therefore, correct diagnosis of the occlusal plane is crucial
DðF12 ; F5 ; F4 Þ 51988:67 F12 126:77 F5 1272:19 F4 24:53
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Fig 3. Graphic representations of cluster division based on 3 selected features. A, The open-bite subjects were divided into 2 clusters based on K-means clustering; the equation obtained by linear discriminate analysis represents the plane that can divide the space into 2 clusters. B and C, Typical example figures of each cluster. D, Result of the expert's classification.
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Table IV. Top 3 ranked features of clusters 1 and 2 F12 F5 F4
Cluster 1 (n 5 19) 0.0186 6 0.0041 (2.44 6 0.68) 0.0133 6 0.0053 (1.78 6 0.87) 0.0217 6 0.0050 (2.86 6 0.77)
Cluster 2 (n 5 42) 0.0027 6 0.0019 (0.34 6 0.24) 0.0024 6 0.0018 (0.31 6 0.23) 0.0049 6 0.0049 (0.61 6 0.60)
All values are presented as means and standard deviations. Numbers in parenthesis are the values before normalization (mm). F12, Perpendicular distance from the mandibular second premolar to a corresponding line constructed by 2 adjacent maxillary teeth; F4 and F5, perpendicular distances from the maxillary first and second premolars to a corresponding line constructed by 2 adjacent mandibular teeth, respectively. The features were normalized by the anterior facial height of each subject to compensate for the vertical difference.
Occlusal contact of the premolars in the Y-form class may be a dental adaptation to increase the occlusal contacts because of the extrusive nature of the teeth.26 In particular, the mandibular teeth seemed to move for the adaptation. Normalized dentoalveolar heights support this assumption, showing higher values for the 4 mandibular teeth (lateral incisor to second premolar) in the Y-form class than in the V-form class (P \0.05; Table VI). Previous studies have also reported the important role of the mandibular teeth in AOB patients.5,15-17,27 With increasing severity of AOB, the MnOP becomes steeper because of downward growth of the mandible.15,16,27 In subjects having a skeletal vertical excess with an incisal overlap, significant elongation of the anterior teeth was noticed to compensate for the change, with the mandibular teeth playing an even more important role.5 Therefore, the following hypothesis can be proposed: when the severity of the AOB is increased or the patients with AOB are getting older, the occlusal plane can be classified into the Yform class rather than the V-form class. Because of the limited number of subjects in this study, we could not identify any significant differences between the 2 classes in terms of overbite and age (P .0.05). A future study with more AOB subjects is necessary to verify the hypothesis. The expert's classification confirmed the high accuracy of cluster analysis. These results showed that occlusal contact of the premolars is a good standard to distinguish the 2 classes clinically as well as radiographically. The identification of the cusp tips in a lateral cephalogram may be confusing because of superimposed bilateral structures. In addition, yawing of the entire arch or canting of the occlusal plane can make landmark identification difficult in a lateral cephalogram. We tried to decrease identification errors by
excluding subjects with facial asymmetry and confirmed the reliability of cluster analysis using dental casts. Further study of subjects with AOB and facial asymmetry using scans of dental casts is essential to gain a better understanding of the occlusal plane. Dentoalveolar heights before normalization indicate the absolute vertical height of each tooth, whereas heights after normalization indicate the relative vertical height of each tooth in the facial skeleton. We conducted the normalization procedure to illustrate the cephalometric configuration in subjects with AOB, excluding any potential bias derived from intersexual or individual differences in anterior facial height.28 The normalization procedure showed significant differences between the 2 classes for the 4 mandibular teeth, which were not significantly different before the normalization. As mentioned earlier, the mandibular lateral incisor, canine, first premolar, and second premolar may contribute to the cephalometric configuration of the Y-form class. A comparison of the total open-bite group with the control group showed that the 5 maxillary teeth, lateral incisor to first molar, in the open-bite group had greater dentoalveolar heights than did those in the control group. Increased molar height has been reported as a common finding in patients with AOB.5,6,13 This may be a cause of the open-bite condition,8 or on the contrary, the teeth may move to compensate for the downward growth of the mandible.5 Since the maxillary teeth move independently from the facial skeleton while the mandibular teeth act in a compensatory mechanism,7 the increased dentoalveolar heights of the maxillary first molar and premolars might be the most relevant etiologic factor for the open-bite condition in this study sample. A tongue with abnormal activity or abnormal size may also be a causative factor for the open bite, although it may have adapted to the problem.14,29 In open-bite patients, differential diagnosis in treatment planning is crucial for successful treatment and stability.19 The treatment method depends on several factors, such as incisor display, amount of open bite, smile arc, and vertical facial dimension.30 The classification of the occlusal plane can be a guideline for treatment planning and eventually can affect posttreatment stability. For example, nonsurgical correction of AOB involves either intrusion of the molars or extrusion of the incisors: in the case of the V-form, rotation of the occlusal plane by intrusion of several molars can easily resolve the open bite; however, for the Y-form, intrusion of the premolars and molars should be performed to correct the open bite. If extrusion of incisors is indicated, the Y-form class is easier to treat than the V-form class because relatively fewer teeth will be extruded. When surgical intervention is needed, leveling of the 2 occlusal
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Fig 4. Typical intraoral photographs showing: A, the Y-form class; B, the V-form class; C, the top 3 features, F12, F5, and F4, were enough to divide the subjects into 2 clusters. F12, F5, and F4 indicate the perpendicular distances of the mandibular second premolar, the maxillary second premolar, and the maxillary first premolar to a corresponding line constructed by 2 adjacent teeth in the opposite dentition, respectively. Table V. Dentoalveolar heights of each tooth in the open-bite and control groups (mm) Open bite
PP-U1 PP-U2 PP-U3 PP-U4 PP-U5 PP-U6 PP-U7 MP-L1 MP-L2 MP-L3 MP-L4 MP-L5 MP-L6 MP-L7
Cluster 1 (V-form) 30.78 6 3.87 30.52 6 3.77 30.03 6 3.63 29.04 6 3.49 27.84 6 3.19 26.21 6 3.36 23.17 6 3.38 42.66 6 5.12 41.73 6 4.93 40.51 6 4.65 38.92 6 4.64 36.91 6 4.85 35.30 6 5.03 32.58 6 5.36
P value* 0.657 0.538 0.668 0.907 0.518 0.379 0.518 1.000 0.932 0.570 0.233 0.362 0.691 0.882
Cluster 2 (Y-form) 30.06 6 2.79 29.86 6 2.79 29.61 6 2.75 28.99 6 2.71 27.36 6 2.78 25.24 6 3.05 22.30 6 3.70 42.30 6 4.86 41.52 6 4.81 40.76 6 4.71 39.48 6 4.44 37.31 6 4.28 34.88 6 4.34 31.59 6 4.24
Total 30.29 6 3.15 30.06 6 3.11 29.74 6 3.03 29.00 6 2.94 27.51 6 2.90 25.54 6 3.16 22.57 6 3.60 42.41 6 4.91 41.59 6 4.81 40.69 6 4.66 39.31 6 4.47 37.19 6 4.43 35.01 6 4.53 31.90 6 4.59
Control 29.43 6 2.68 28.51 6 2.50 27.86 6 2.44 27.01 6 2.24 25.89 6 2.24 24.11 6 2.04 21.41 6 2.23 41.32 6 3.36 40.62 6 3.22 40.59 6 3.25 38.89 6 3.26 36.64 6 2.90 34.60 6 3.02 32.30 6 2.89
P valuey 0.375 0.032§ 0.003§ 0.002§ 0.010z 0.018z 0.101 0.366 0.521 0.590 0.874 0.751 0.956 0.191
Dentoalveolar heights are presented as means and standard deviations. PP, Palatal plane; MP, mandibular plane; U1 to U7 and L1 to L7, maxillary and mandibular teeth from the central incisor to the second molar, respectively; PP-U1 and MP-L1, perpendicular distances of U1 and L1 to the PP and MP, respectively. *P values were obtained from Mann-Whitney U tests between clusters 1 and 2; yP values were obtained from the same test between the open-bite group in total and the control group; zP \0.05; §P \0.01.
planes by segmental surgery should be considered in a patient of the Y-form class. If a continuous archwire is used for leveling the 2 occlusal planes in the Y-form class, extrusion of the anterior teeth and a slight
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intrusion of the premolars would occur; this may influence the posttreatment stability of the AOB.1,31 However, because the clustering analysis in this study was performed with a limited number of subjects, and
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Table VI. Normalized dentoalveolar heights of each
tooth in the open-bite group PP-U1 PP-U2 PP-U3 PP-U4 PP-U5 PP-U6 PP-U7 MP-L1 MP-L2 MP-L3 MP-L4 MP-L5 MP-L6 MP-L7
Cluster 1 (V-form) 0.236 6 0.019 0.234 6 0.018 0.230 6 0.015 0.222 6 0.013 0.213 6 0.013 0.200 6 0.013 0.177 6 0.014 0.326 6 0.014 0.319 6 0.013 0.310 6 0.013 0.298 6 0.012 0.282 6 0.014 0.270 6 0.017 0.248 6 0.021
Cluster 2 (Y-form) 0.238 6 0.016 0.236 6 0.013 0.234 6 0.012 0.229 6 0.012 0.216 6 0.012 0.199 6 0.014 0.176 6 0.020 0.334 6 0.016 0.327 6 0.016 0.321 6 0.016 0.311 6 0.016 0.294 6 0.017 0.275 6 0.018 0.249 6 0.021
2. P value* 0.858 0.738 0.387 0.065 0.379 0.932 0.895 0.080 0.036y 0.006z 0.002z 0.018y 0.204 1.000
Dentoalveolar heights are presented as means and standard deviations. PP, Palatal plane; MP, mandibular plane; U1 to U7 and L1 to L7, maxillary and mandibular teeth from the central incisor to the second molar, respectively; PP-U1 and MP-L1, perpendicular distances of U1 and L1 to the PP and MP, respectively. *P value was obtained from the Mann-Whitney U test between clusters 1 and 2; yP \0.05; zP \0.01.
they were mostly patients with a skeletal Class II malocclusion as previously reported, a future study with more subjects should be considered.32,33
3.
4.
5.
6. 7.
8. 9.
10.
11.
12.
CONCLUSIONS 13.
1.
2.
3.
4.
The open-bite subjects were divided into 2 clusters, V-form class and Y-form class, according to the occlusal contacts of the premolars. Occlusal contacts of the premolars can be used as a good standard to distinguish the 2 classes clinically as well as radiographically. Occlusal contacts of the premolars in the Y-form class may be a dental adaptation to increase occlusal contact. Greater dentoalveolar heights of the maxillary teeth in the open-bite group compared with the control group indicate that the open-bite condition may be caused by overeruption of the maxillary molars.
14. 15.
16. 17. 18.
19. 20.
SUPPLEMENTARY DATA
Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ajodo.2015.08. 020. REFERENCES
21. 22. 23.
1. Greenlee GM, Huang GJ, Chen SS, Chen J, Koepsell T, Hujoel P. Stability of treatment for anterior open-bite malocclusion: a
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meta-analysis. Am J Orthod Dentofacial Orthop 2011;139: 154-69. Jensen U, Ruf S. Success rate of anterior open-bite orthodontic-orthognathic surgical treatment. Am J Orthod Dentofacial Orthop 2010;138:716-9. Baek MS, Choi YJ, Yu HS, Lee KJ, Kwak J, Park YC. Long-term stability of anterior open-bite treatment by intrusion of maxillary posterior teeth. Am J Orthod Dentofacial Orthop 2010;138: 396.e1-9:discussion, 396-8. Denison TF, Kokich VG, Shapiro PA. Stability of maxillary surgery in openbite versus nonopenbite malocclusions. Angle Orthod 1989;59:5-10. Kucera J, Marek I, Tycova H, Baccetti T. Molar height and dentoalveolar compensation in adult subjects with skeletal open bite. Angle Orthod 2011;81:564-9. Cangialosi TJ. Skeletal morphologic features of anterior open bite. Am J Orthod 1984;85:28-36. Kuitert R, Beckmann S, van Loenen M, Tuinzing B, Zentner A. Dentoalveolar compensation in subjects with vertical skeletal dysplasia. Am J Orthod Dentofacial Orthop 2006; 129:649-57. Taibah SM, Feteih RM. Cephalometric features of anterior open bite. World J Orthod 2007;8:145-52. Tsang WM, Cheung LK, Samman N. Cephalometric characteristics of anterior open bite in a southern Chinese population. Am J Orthod Dentofacial Orthop 1998;113:165-72. Ellis E 3rd, McNamara JA Jr, Lawrence TM. Components of adult Class II open-bite malocclusion. J Oral Maxillofac Surg 1985;43: 92-105. Jones OG. A cephalometric study of 32 North American black patients with anterior open bite. Am J Orthod Dentofacial Orthop 1989;95:289-96. Stuani AS, Stuani AS, Stuani MB, Saraiva Mda C, Matsumoto MA. Anterior open bite–cephalometric evaluation of the dental pattern. Braz Dent J 2006;17:68-70. Schendel SA, Eisenfeld J, Bell WH, Epker BN, Mishelevich DJ. The long face syndrome: vertical maxillary excess. Am J Orthod 1976; 70:398-408. Subtelny JD, Sakuda M. Open-bite: diagnosis and treatment. Am J Orthod 1964;50:337-58. Tsang WM, Cheung LK, Samman N. Cephalometric parameters affecting severity of anterior open bite. Int J Oral Maxillofac Surg 1997;26:321-6. Nahoum HI, Horowitz SL, Benedicto EA. Varieties of anterior open-bite. Am J Orthod 1972;61:486-92. Epker BN, Fish LC. The surgical-orthodontic correction of Class III skeletal open-bite. Am J Orthod 1978;73:601-18. Nielsen IL. Vertical malocclusions: etiology, development, diagnosis and some aspects of treatment. Angle Orthod 1991;61: 247-60. Jarabak JR. Open bite. skeletal morphology. Fortschr Kieferorthop 1983;44:122-33. Bock JJ, Bock F, Bohm B, Fuhrmann RA. Classification of anterior open bite using individualized cephalometry. J Orofac Orthop 2005;66:338-48. Bishop CM. Pattern recognition and machine learning. New York: Springer; 2006. Hartigan JA, Wong MA, Algorithm AS. 136: a k-means clustering algorithm. Applied Statistics 1979;28:100-8. Dash M, Liu H. Feature selection for clustering. In: Terano T, Liu H, Chen AL, editors. Knowledge discovery and data mining. Current issues and new applications. Berlin, Germany: Springer; 2000. p. 110-21.
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Choi et al
400
24. Cali nski T, Harabasz J. A dendrite method for cluster analysis. Commun Statistics 1974;3:1-27. 25. Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis. Hoboken, NJ: John Wiley & Sons; 2009. 26. Jager A. Histomorphometric study of age-related changes in remodelling activity of human desmodontal bone. J Anat 1996; 189(Pt 2):257-64. 27. Enunlu N. Palatal and mandibular plane variations in open bite cases with varying aetiology. Trans Eur Orthod Soc 1974;165-71. 28. Burstone CJ, James RB, Legan H, Murphy GA, Norton LA. Cephalometrics for orthognathic surgery. J Oral Surg 1978;36:269-77. 29. Gracco A, Perri A, Siviero L, Bonetti GA, Cocilovo F, Stellini E. Multidisciplinary correction of anterior open bite
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30.
31.
32.
33.
relapse and upper airway obstruction. Korean J Orthod 2015;45:47-56. Davidovitch M, Rebellato J. Two-couple orthodontic appliance systems utility arches: a two-couple intrusion arch. Semin Orthod 1995;1:25-30. Espeland L, Dowling PA, Mobarak KA, Stenvik A. Three-year stability of open-bite correction by 1-piece maxillary osteotomy. Am J Orthod Dentofacial Orthop 2008;134:60-6. Schudy FF. Vertical growth versus anteroposterior growth as related to function and treatment. Angle Orthod 1964;35: 36-50. Proffit WR, White PR, Sarver DM. Contemporary treatment of dentofacial deformity. St Louis: Mosby Elsevier; 2003.
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