ORIGINAL ARTICLE
Cranial-base morphology in adults with skeletal Class III malocclusion Seetala Sanggarnjanavanich,a Toshiko Sekiya,b Yoshiaki Nomura,c Takahiro Nakayama,d Nobuhiro Hanada,e and Yoshiki Nakamuraf Yokohama, Japan
Introduction: The objectives of this study were to clarify the characteristics of cranial-base morphology in adults with skeletal Class III malocclusion and investigate factors relating to the establishment of a skeletal Class III malocclusion. Methods: Initial lateral cephalograms of women were examined. Subjects with an ANB angle of 0 to 4 , normal overjet and overbite, and a Class I molar relationship were classified as Class I (n 5 86). Those with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, and a Class III molar relationship were the Class III group (n 5 86) in this study. Angular, linear, and coordinate measurements were made. Multivariate analysis of variance and the Student t test were used to analyze significant differences between the 2 groups. Discriminant analysis, logistic regression analysis, and decision analysis were used to identify which cranial-base and maxillomandibular variables influenced the establishment of a skeletal Class III malocclusion. Results: The Class III group had smaller values for NSBa, SeSBa, FH-SSe, and FH-SBa. Sphenoidale and basion were more inferior and anterior than those of the Class I group. There was no difference in the anterior and posterior cranial-base lengths between the groups. Greater mandibular length was the first major characteristic in the Class III group, followed by smaller values for SeSBa and NSBa. Conclusions: Cranial-base morphology in adults with a skeletal Class III malocclusion is different from that in a skeletal Class I malocclusion. Smaller cranial-base angles, steeper posterior cranial bases, more inferiorly positioned sphenoidale, and more anteriorly positioned basion are major characteristics of skeletal Class III malocclusions. These characteristics play important roles in the establishment of a skeletal Class III malocclusion. (Am J Orthod Dentofacial Orthop 2014;146:82-91)
A
skeletal Class III malocclusion results from morphologic or positional disharmony between the maxilla and the mandible during the growth period.1 In 1916, Young2 reported that the cranial-base morphology might be related to jaw prognathism. Since then, several studies have investigated the relationship between the cranial-base and maxillomandibular components.2-8 The cranial base includes both the anterior and posterior cranial bases. The anterior cranial base relates to
From the School of Dental Medicine, Tsurumi University, Yokohama, Japan. a Postgraduate student, Departments of Orthodontics and Translational Research. b Assistant professor, Department of Orthodontics. c Associate professor, Department of Translational Research. d Postgraduate student, Department of Orthodontics. e Professor and chairman, Department of Translational Research. f Professor and chairman, Department of Orthodontics. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Yoshiki Nakamura, Department of Orthodontics, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi Tsurumi-ku, Yokohama, Japan 230-8501; e-mail, [email protected]. Submitted, June 2013; revised and accepted, April 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.04.014
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the position of the maxilla,5 whereas the posterior cranial base relates to the positions of the glenoid fossa and the mandible.9-14 Recently, the correlations between the lateral basicranium and facial form, mandibular morphology and position, and malocclusion patterns have also been investigated.15-17 Bastir et al15 and Bastir and Rosas16 demonstrated that both the midline cranial base and the middle cranial fossa correlate with mandibular ramus morphology. One of the most commonly used cranial-base characteristics is the cranial-base angle from the flexion of the anterior and posterior cranial bases at sella turcica in the midsagittal plane. It has been considered that the cranial-base angle has an influence on the anteroposterior intermaxillary relationship and the type of malocclusion.5,6,11,18,19 Furthermore, the dimensions of the cranial base play an important role in determining the sagittal jaw relationship.6 A small cranial-base angle (NSBa)7,11,18-24 and a short cranial-base length (S-N)7,18,21-23,25 are major morphologic features of skeletal Class III patients. A deficiency of the cranial base that flattens during growth has been considered a factor associated with skeletal Class III malocclusion.26-28 However, recent
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studies have reported no correlation between the cranialbase angle and a skeletal Class III malocclusion.29,30 Since the evidence is still inconclusive, whether the cranial-base morphology in a skeletal Class III malocclusion differs from that of a skeletal Class I malocclusion and has a relationship to the establishment of a skeletal Class III malocclusion remains controversial. Furthermore, most previous researchers selected their subjects irrespective of sex and age. There have been few cranial-base studies in adults with a skeletal Class III malocclusion.24,25 The objectives of this study were to clarify the characteristics of cranial-base morphology in adults with a skeletal Class III malocclusion by comparing them with those with a skeletal Class I malocclusion, and to investigate factors related to the establishment of a Class III malocclusion. MATERIAL AND METHODS
Initial lateral cephalometric radiographs of 424 Japanese women, ages 16 to 35 years, from the Department of Orthodontics, Dental Hospital, of Tsurumi University in Yokohama, Japan, were examined in our study. The study protocol was approved by the institutional review board of the university. The image magnification of the cephalostat for this study was 10%, and all linear measurements were adjusted accordingly. All subjects were adults because all cephalograms showed stage 6 of cervical vertebral maturation, indicating that at least 2 years had passed after the pubertal growth peak.31,32 Subjects with an ANB angle from 0 to 4 with normal overjet and overbite, a Class I molar relationship, and a normal facial profile were classified as the Class I group, and those with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, a Class III molar relationship, and a concave facial profile were the Class III group. The exclusion criteria were cleft lip and palate, craniofacial syndrome, mandibular deviation more than 5 mm, remaining deciduous or missing teeth (except third molars), a previous history of orthodontic treatment, and poor-quality cephalograms. Consequently, 86 skeletal Class I and 86 Class III subjects met the inclusion criteria. The skeletal Class I and Class III subjects' ages ranged from 16.1 to 34.0 years (mean, 21.6 years; standard deviation [SD], 3.9) to 16.0 to 35.0 years (mean, 22.0 years; SD, 4.3), respectively. Each lateral cephalogram was traced on 0.003-in frosted acetate by 1 investigator (S.S.) and checked for accuracy by another investigator (T.S.). Cephalometric landmarks were identified, digitized, and analyzed with CephaloMetrics AtoZ software (version 9.5J; Yasunaga Computer Systems, Fukui, Japan). Definitions for these landmarks are given in Figure 1.
Fig 1. Coordinate axes and cephalometric landmarks: A, Point A, the deepest point on the midsagittal plane between supradentale and the anterior nasal spine; ANS, anterior nasal spine, the most anterior point on the maxilla at the level of the palate in the midsagittal plane; Ar, articulare, the point of intersection between the anterior surface of the sphenoid bone and the posterior contour of the mandibular ramus; B, Point B, the deepest point on the midsagittal plane between infradentale and pogonion; Ba, basion, the most posteroinferior point of the anterior margin of the foramen magnum in the midsagittal plane; Cd, condylion, the most posterior superior point on the condyle of the mandible; Gn, gnathion, the most downward and forward point on the symphysis at the intersection of the facial and mandibular planes; Go, gonion, the most posterior inferior point at the angle of the mandible; Me, menton, the most inferior midpoint of the symphysis; N, nasion, the most anterior point of the frontonasal suture in the midsagittal plane; Or, orbitale, the deepest point on the infraorbital margin; PNS, posterior nasal spine, the most posterior point on the palatine bone in the midsagittal plane; Po, porion, the most superior point of the external auditory meatus; Pog, pogonion, the most anterior midpoint of the symphysis; Ptm, pterygomaxillary fissure, the contour of the pterygomaxillary fissure formed anteriorly by the retromolar tuberosity of the maxilla and posteriorly by the anterior curve of the pterygoid process of the sphenoid bone; S, sella, the center of the hypophyseal fossa in the midsagittal plane; Se, sphenoidale, the deepest point of intersection between the greater wings of the sphenoid and the anterior cranial base.
The positions of the landmarks were recorded in Cartesian coordinates (x- and y-axes) with sella as the origin of the axes (x, y 5 0, 0). The horizontal reference plane (x-axis) was parallel to the Frankfort horizontal plane passing through sella. The vertical plane (y-axis) was
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set perpendicular to the horizontal plane. The anterior and inferior areas near sella were set to positive, whereas the posterior and superior areas near sella were set to negative. To test the error of point identification, the lateral cephalograms of 25 subjects were randomly selected, retraced, and redigitized 2 months after the initial analysis by the same investigator (S.S.). Errors in identifying and locating cephalometric landmarks were assessed by Dahlberg's formula (measurement error estimation), and the coefficient of reliability was calculated as follows. pP ffiffiffiffiffiffiffiffiffiffiffi d2 0 Dahlberg s formula5 2n where d is the mean difference between repeated measurements, and n is the number of measurements.33,34 Coefficient of reliability51
S2e S2t
where Se2 is the variance due to random error, and St2 is the total variance of the measurements.35 Dahlberg's errors were 0.17 to 0.50 , 0.14 to 0.39 mm, and 0.15 to 0.32 mm for angular, linear, and coordinated value measurements, respectively. The coefficient of reliability indicated that the observed values of the measured variables were between 0.925 and 0.999.
Fig 2. Maxillomandibular measurements:1, SNA; 2, SNB; 3, mandibular plane angle; 4, ramus inclination (90 , the angle between the Frankfort horizontal plane [FH] and the line tangent to the posterior border of the ramus and Ar); 5, gonial angle; 6, A0 -Ptm0 ; 7, anterior maxillary height, A Mx H (the distance from ANS to its perpendicular intersection on the horizontal plane); 8, posterior maxillary height; P Mx H (the distance from PNS to its perpendicular intersection on the horizontal plane); 9, Gn-Cd; 10, Pog-Go; 11, Cd-Go.
Statistical analysis
Angular, linear, and coordinate values measurements for groups of maxillomandibular variables and cranialbase variables were performed (Figs 2-4). Significant differences between the Class I and Class III groups in maxillomandibular and cranial-base variables were tested with the Hotelling T2 test (multivariate analysis of variance; MANOVA) as an initial exploratory test. When significance was found, the independent-sample Student t test was used to identify significant between-group differences for each cephalometric variable. Because of multiple testing, we adjusted the level of significance according to Holm's sequentially rejective multiple test procedure. Three statistical models—decision analysis by classification and regression trees,36,37 discriminant analysis by stepwise regression, and logistic regression analysis by forward selection—were performed to identify the variables in the cranial base, maxilla, and mandible that characterize skeletal Class I and Class III subjects. The independent variables were ramus inclination, mandibular plane angle, gonial angle, A0 -Ptm0 , A Mx H, P Mx H, Gn-Cd, Pog-Go, Cd-Go, NSBa, SeSBa, FH-SN, FH-SSe, FH-SBa, S-N, S-Se, N-Se, and S-Ba.
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Fig 3. Linear cranial-base measurements: 1, S-N; 2, S-Ba; 3, S-Se; 4, N-Se.
To compare the accuracy of the 3 statistical models, the cutoff values were obtained from the receiver operating characteristic curves, and classification accuracy was called the crude hit rate. It was calculated as follows. number of truepositives1truenegatives Crudehit rate5 totalnumber of subjects where true positives are subjects in both the actual and predicted Class I groups, and true negatives are subjects in both the actual and predicted Class III groups.38
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Fig 4. Angular cranial-base measurements: 1, NSBa; 2, SeSBa; 3, FH-SN; 4, FH-SBa; 5, FH-SSe. RESULTS
Dahlberg's errors for angular, linear, and coordinated value measurements were small and acceptable. Results from the reliability assessment showed high correlations with the measured variables. Normal distribution of all variables was confirmed by the Kolmogorov-Smirnov test. Parametric tests were performed. Means and SDs of the ANB angles in the skeletal Class I and Class III subjects were 2.52 6 0.99 and 3.70 6 1.83 , respectively. To determine whether there were differences between the 2 groups of subjects at the beginning of the study, the maxillomandibular and cranial-base variables grouped as a multivariate variable in each maxillomandibular and cranial-base group were analyzed by MANOVA. A statistically significant difference was found between the skeletal Class I and Class III subjects (P \0.0001 and P \0.0047, respectively). Since the MANOVA showed a significant difference, the Student t test was used to determine significant differences between the skeletal Class I and Class III subjects. Mandibular measurements showed significant differences between the Class I and Class III groups. The Class III group had significant anteriorly inclined rami and larger gonial angles. The anterior part of the mandible (Point B) was more anteriorly and inferiorly located. The posterior part of the mandible (articulare) was also more anteriorly located. Mandibular length (Gn-Cd), body length (Pog-Go), and ramus height (Cd-Go) were significantly larger than in the Class I group. However, the maxillary measurements had no significant differences in both position (Point A) and sizes (A0 -Ptm0 , A Mx H, and P Mx H) between the groups (Table I). Cranial-base measurements showed significant differences between the Class I and Class III groups. The cranial-base angle (NSBa) and the angle between the sphenoid and occipital bones (SeSBa) were significantly smaller in the Class III group. The angle of the sphenoid
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bone to the Frankfort horizontal plane (FH-SSe) and the vertical position of sphenoidale (Se[y]) in the Class III group were also significantly smaller and more inferiorly located. However, there was no significant difference between the groups in anterior cranial-base lengths (S-N, S-Se, and N-Se) (Table II). Posterior cranial-base measurements showed considerable differences between the Class I and Class III groups. The angle of the posterior cranial base to the Frankfort horizontal plane (FH-SBa) in the Class III group was significantly smaller than that in the Class I group. Furthermore, the horizontal position of basion (Ba[x]) in the Class III group was also significantly more anteriorly located. However, posterior cranial-base length (S-Ba) showed no difference between the groups (Table II). Decision analysis using cranial base, and maxillary and mandibular variables showed that the most important variable for the characterization between the skeletal Class I and Class III subjects was mandibular length (Gn-Cd), and the subsequent variables were SeSBa and NSBa. From the decision tree, 89.4% of the subjects with a Gn-Cd greater than 124.20 mm and SeSBa equal to or less than 136.81 were skeletal Class III subjects. Among them, those with gonial angles greater than 114.92 were also skeletal Class III subjects (92.2%). On the other hand, 50% of the subjects with SeSBa greater than 136.81 were skeletal Class I, even though their mandibular lengths were greater than 124.20 mm. Only 50% of the subjects with mandibular length and SeSBa greater than 124.20 mm and 136.81 , respectively, were skeletal Class III subjects. Among them, all subjects with a ramus inclination greater than 14.37 were also skeletal Class III subjects. On the other hand, 96.1% of the subjects with mandibular length equal to or less than 124.20 mm and NSBa greater than 131.04 were skeletal Class I (Fig 5). Discriminant and logistic regression analysis demonstrated that ramus inclination, A0 -Ptm0 , Gn-Cd, Pog-Go, N-Se, NSBa, FH-SBa, and P Mx H were the predictor variables characterizing the skeletal Class III subjects (Tables III and IV). Classification results of the 3 statistical models were evaluated by the crude hit rate, which means the proportion of correctly classified subjects. All models showed high values, but decision analysis had the highest (Table V). DISCUSSION
Even though there have been several studies on the relationship between the cranial base and malocclusion, their results are controversial.2-8 Most previous studies selected subjects without sex and age considerations.
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Table I. Maxillomandibular measurements of skeletal Class I and Class III subjects Class I subjects Cephalometric measurement SNA ( ) SNB ( ) Mandibular plane angle ( ) Ramus inclination ( ) Gonial angle ( ) A0 -Ptm0 (mm) A Mx H (mm) P Mx H (mm) Gn-Cd (mm) Pog-Go (mm) Cd-Go (mm) A(x) (mm) A(y) (mm) B(x) (mm) B(y) (mm) Ar(x) (mm) Ar(y) (mm)
Mean 80.29 77.76 28.53 4.88 123.41 47.17 46.12 45.06 121.65 79.11 60.98 67.25 52.24 62.28 94.91 16.94 31.95
SD 3.25 3.25 5.19 4.90 7.08 3.19 3.26 2.68 5.83 4.40 4.88 4.01 3.01 5.35 4.74 2.80 3.07
Class III subjects
Min 71.78 70.64 15.45 5.03 109.85 40.14 35.99 39.10 109.08 68.86 49.32 56.08 44.46 50.03 83.20 22.54 24.60
Max 87.89 84.60 43.24 15.24 140.89 56.33 52.76 51.37 134.54 90.00 73.77 75.79 57.82 73.35 107.68 9.47 40.92
Mean 80.49 84.18 27.69 10.03 127.72 46.34 47.14 45.84 131.27 83.98 64.14 66.21 53.36 72.22 97.78 14.54 31.33
SD 3.38 3.75 5.54 5.13 7.08 2.63 3.75 3.00 6.07 3.89 4.44 3.96 4.00 6.75 6.04 2.91 2.74
Min 71.75 74.65 13.17 0.22 115.71 40.08 39.22 38.69 119.13 72.34 53.99 55.02 44.43 56.51 85.06 20.86 24.71
Max 89.36 93.89 39.14 20.60 143.21 53.46 57.34 54.67 153.12 98.27 73.90 77.49 63.67 90.21 109.36 6.98 37.82
Significance 0.6918 \0.0001y 0.3064 \0.0001y \0.0001y 0.0619 0.0583 0.0757 \0.0001y \0.0001y \0.0001y 0.0902 0.0406 \0.0001y 0.0007* \0.0001y 0.1654
Hotelling T2 5 736.610; F 5 45.061; P \0.0001, significant. Min, Minimum; Max, maximum. *Significant at 5%; ysignificant at 1%.
Table II. Cranial-base measurements of skeletal Class I and Class III subjects Class I subjects Cephalometric measurement Cranial-base angle NSBa ( ) SeSBa ( ) Anterior cranial base FH-SN ( ) FH-SeS ( ) S-N (mm) S-Se (mm) N-Se (mm) Na(x) (mm) Na(y) (mm) Se(x) (mm) Se(y) (mm) Posterior cranial base FH-SBa ( ) S-Ba (mm) Ba(x) (mm) Ba(y) (mm)
Class III subjects
Mean
SD
Min
Max
Mean
SD
Min
Max
Significance
134.80 138.14
4.79 5.58
124.43 124.47
146.80 156.76
131.84 133.70
5.09 6.65
114.36 114.30
144.20 149.63
0.0001y \0.0001y
9.26 12.61 68.64 26.61 42.21 67.68 11.13 25.92 5.81
2.36 4.36 3.07 2.41 3.21 3.07 2.80 2.36 2.05
4.76 3.12 61.83 20.48 33.89 60.33 19.57 20.44 10.56
15.89 24.87 76.69 32.77 50.34 75.79 6.13 32.21 1.24
8.41 10.27 68.26 27.07 41.32 67.45 9.93 26.56 4.78
2.84 4.59 3.11 2.10 3.35 3.08 3.45 2.14 2.12
1.02 0.53 61.77 18.85 35.27 60.99 17.27 18.80 9.54
15.05 20.53 77.79 32.92 52.13 76.10 0.69 32.91 0.24
0.0343 0.0007* 0.4191 0.1842 0.0779 0.6256 0.0136 0.0622 0.0015*
125.54 47.07 27.26 38.24
3.79 3.29 3.28 3.12
117.25 38.22 37.51 29.50
134.96 57.51 20.64 47.60
123.43 46.81 25.72 38.96
4.23 2.66 3.04 3.12
113.34 41.73 33.54 30.18
133.51 53.99 18.16 48.07
0.0007* 0.5746 0.0016* 0.1327
Hotelling T2 5 38.25; F 5 2.344; P 5 0.0047, significant. Min, Minimum; Max, maximum. *Significant at 5%; ysignificant at 1%.
Therefore, their results could not be compared because of subject variations. Subjects of 1 sex provide more accurate linear measurements than do the previous studies that pooled the sexes. The average craniofacial complex is 5% to 9%
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larger in men than in women39; especially, skeletal Class III men have greater values for most linear measurements when compared with women.40 Therefore, we selected only female subjects to eliminate sex differences in the craniofacial components.
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Fig 5. Decision tree for characterizing skeletal Class I and Class III subjects by cranial-base and maxillomandibular variables; ramus inclination, mandibular plane angle, gonial angle, A0 -Ptm0 , A Mx H, P Mx H, Gn-Cd, Pog-Go, Cd-Go, NSBa, SeSBa, FH-SN, FH-SSe, FH-SBa, S-N, S-Se, N-Se, and S-Ba. I, Skeletal Class I subjects; III, skeletal Class III subjects.
Table III. Canonical discriminant function coefficients Ramus inclination A0 -Ptm0 Gn-Cd Pog-Go N-Se NSBa FH-SBa P Mx H (Intercept)
Unstandardized 0.143 0.199 0.074 0.188 0.109 0.206 0.178 0.157 0.537
Standardized 0.717 0.581 0.440 0.780 0.359 1.016 0.714 0.448
Wilks l 5 0.346; chi-square 5 176.278; P \0.001.
We aimed to investigate not only the characteristics of cranial-base morphology in skeletal Class III malocclusions, but also its relationship to the establishment of a skeletal Class III malocclusion. Cranial-base and maxillomandibular components were necessary to investigate the relationship between them. Thus, in subjects who have passed the pubertal growth peak it is necessary to observe the maxillomandibular components. Research on the morphologic maturation of the human skull has
Table IV. Logistic regression model 95% CI
Ramus inclination A0 -Ptm0 Gn-Cd Pog-Go N-Se P Mx H NSBa FH-SBa
Odds ratio 2.251 0.378 1.370 2.947 0.586 0.388 0.425 1.698
Upper 1.479 0.221 1.045 1.651 0.414 0.213 0.256 1.086
Lower 3.426 0.647 1.797 5.261 0.830 0.710 0.706 2.653
P \0.001 \0.001 0.023 \0.001 0.003 0.002 0.001 0.020
Likelihood ratio test.
demonstrated that both the maxilla and the mandible achieve adult size around age 16 years in girls.41 Subjects with large mandibular deviations were excluded because a large lateral mandibular deviation causes morphologic asymmetry in the mandible. Shorter ramus and mandibular body are often observed on the deviated side, which significantly affects the mandibular variables in this study.42-44
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Table V. Predictions by the 3 statistical models Predicted group
Decision analysis* Actual group Class I Class III Discriminant analysisy Actual group Class I Class III Logistic regression analysisz Actual group Class I Class III
Class I
Class III
79 (45.9%) 4 (2.3%)
7 (4.1%) 82 (47.7%)
77 (44.8%) 4 (2.3%)
9 (5.2%) 82 (47.7%)
80 (46.5%) 6 (3.5%)
6 (3.5%) 80 (46.5%)
*Crude hit rate 5 93.6%; ycrude hit rate 5 92.5%; zcrude hit rate 5 93.0%.
Both dental and skeletal criteria were used to select true skeletal Class I and Class III subjects. ANB angle less than 0 , Wits appraisal less than 0 mm, negative overjet, Class III molar relationship, and concave profile are generally used as inclusion criteria for skeletal Class III subjects.24,25,45-50 The conjunctive use of the ANB angle and the Wits appraisal is recommended to assess the anteroposterior intermaxillary relationship in subjects.51 The gold standard criteria for skeletal classification based on ANB angle, overjet, and molar relationship are also an established method.52 All subjects in our study were classified by ANB angle, Wits appraisal, overjet, molar relationship, and facial profile. The ANB norm for Japanese women is 0 to 4 in skeletal Class I and less than 0 in skeletal Class III subjects.53 Subjects with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, a Class III molar relationship, and a concave facial profile were selected as our Class III group to exclude skeletal Class III borderline subjects. Consequently, mean ANB angles of 3.70 in the Class III group and 2.52 in the Class I group indicated proper subject selection. Most of the skeletal Class III subjects had true skeletal Class III Japanese characteristics: mandibular prognathism with a normal maxillary position.54 The Frankfort horizontal plane was selected as our reference plane on the basis of its wide usage and relative acceptance in orthodontics.14,19,21,47,50,55-63 To compare our results with those from most previous studies that used the Frankfort horizontal plane as a craniofacial reference plane, we used this plane to reflect findings in anatomic structures. However, some studies reported variability in locating cephalometric points.64-66 Poor-quality radiographs, including ambiguous landmarks, were excluded from this study.
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Dahlberg's error was also performed to assess errors in identifying and locating cephalometric landmarks. Porion and orbitale identifications showed minimal errors to determine an accurate Frankfort horizontal plane. Consequently, this plane was reliable to use in this study. Sphenoidale (Se), the boundary between the sphenoid and ethmoid bones, was selected to examine the anterior cranial base.67 The area around sphenoidale influences maxillofacial morphology.68 Although S-N is commonly used in cranial-base studies, S-Se is also a main component factor of the anterior cranial base.57 In addition to the conventional variable FH-SN, FHSSe was measured to examine the inclination of the anterior cranial base. FH-SSe in the Class III group was significantly smaller than that in the Class I group, whereas there was no difference in FH-SN between the 2 groups. These findings suggest that the inclination of S-Se is an important anterior cranial-base characteristic that helps to distinguish skeletal Class III from Class I subjects. A flatter inclination of S-Se is related to the vertical deformation of the S-Se region in those with a skeletal Class III malocclusion.26-28 No difference between the Class I and Class III groups was found in anterior cranial-base length, and maxillary length, height, and position. Thus, our skeletal Class III subjects demonstrated a normal anterior cranial-base length with a normal maxillary position. This indicates that anterior cranial-base length is closely related to maxillary position.57 The posterior cranial-base inclination (FH-SBa) in the Class III group was significantly smaller than that in the Class I group, although there was no difference in the posterior cranial-base length between the groups. The angle of the posterior cranial-base inclination depends on the horizontal position of basion, indicating that it is located more anteriorly in the Class III group. Because of the close relationship between the positions of basion and articulare, the mandible is evidently located anteriorly in the Class III group; consequently, this worsens the intermaxillary relationship.69,70 Inferiorly positioned sphenoidale and anteriorly positioned basion are the anterior and posterior cranial-base characteristics in skeletal Class III malocclusions, respectively. Smaller NSBa and SeSBa values were reflected in the Class III group because of these landmark positions. Smaller cranial-base angles in the Class III group were related to deficient orthocephalization, implying insufficient horizontalization of the cranial-base angle in skeletal Class III malocclusions.26-28 Our results differed from those of previous studies. Anterior18,21,22,25 and posterior cranial-base lengths18 were shorter in those with a skeletal Class III malocclusion, and there was no difference in NSBa between the Class I
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and Class III groups.25,29,30 These differences might be due to the inclusion criteria for the subjects and the skeletal classifications. Most of the aforementioned studies selected prepubertal subjects and used only the Class III molar relationship to define their Class III subjects. Thus, in this study, we carefully selected subjects representing skeletal Class III malocclusions. The results of the Student t test clearly showed the differences in the morphology of the cranial base, maxilla, and mandible between the Class I and Class III groups. However, the variables of cranial base, maxilla, and mandible that contributed to the establishment of a skeletal Class III malocclusion were still unclear. Therefore, discriminant analysis, logistic regression analysis, and decision analysis were performed. Results from comparing the good decision counts among the 3 statistical models confirmed that all of them had high crude hit rates, which signifies highly correct classification rates. However, both the discriminant analysis and the logistic regression analysis selected the same predictor variables, whereas the decision analysis selected some different predictors. In general, regression models including discriminant analysis and logistic regression analysis do not consider the classifications of subgroups. In contrast, decision analysis automatically finds important variables in each subgroup. A classification and regression tree is a classification analysis displayed as a binary tree in which all subjects are split into 2 nodes representing each group. This function automatically determines whether to fit a regression or a classification tree. The most broadly used splitting criterion in a classification and regression tree is the Gini index (an impurity-based criterion) to find the best variable to separate the data into 2 parts with maximum homogeneity and repeat until all subjects in the data set are classified into a single category. The Gini index is used to measure the probability of misclassification of a set of subjects.36 This study is the first orthodontic research with decision analysis to examine the influence of the cranialbase and maxillomandibular variables on skeletal Class III malocclusions in a hierarchical way. This is the most suitable and an easy-to-use analysis for observing subjects in clinical diagnosis. It helps us to understand the relationship between individual variations in variables and the establishment of a skeletal Class III malocclusion. Mandibular morphology is the strongest contributor to skeletal Class III manifestation.55,71 The results of decision analysis demonstrated that in the Class III group, greater mandibular length was the first major characteristic, followed by smaller SeSBa and NSBa values. This suggests that the posterior cranial-base
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inclination influences the mandibular position and results in a skeletal Class III malocclusion. Interestingly, decision analysis demonstrated that 92.2% of the skeletal Class III subjects had greater mandibular lengths (.124.20 mm), smaller SeSBa values (#136.81 ), and larger gonial angles (.114.92 ), whereas 100% of the skeletal Class I subjects had shorter mandibular lengths (#124.20 mm), larger NSBa values (.131.04 ), greater maxillary lengths (.41.08 mm), and greater posterior maxillary heights (.38.90 mm). A smaller SeSBa was 1 characteristic of a skeletal Class III malocclusion. We recommend using SeSBa as an additional variable for NSBa in cranial-base morphologic studies because it was significantly different between the 2 groups and could help to distinguish skeletal Class III subjects from skeletal Class I subjects. Sphenoidale is located at the intersection of the greater wings of the sphenoid with the floor of the anterior cranial fossa.15 This point is a stable reference landmark obviously seen on the lateral cephalogram. Furthermore, nasion is not part of the cranial base. In the future, a longitudinal study is recommended to observe cranial-base morphology in growing subjects with skeletal Class III malocclusion. CONCLUSIONS
The cranial-base morphology in adults with a skeletal Class III malocclusion is different from that in a skeletal Class I malocclusion. Smaller cranial-base angles (NSBa and SeSBa), a steeper posterior cranial base (FH-SBa), more inferiorly positioned sphenoidale (Se[y]), and more anteriorly positioned basion (Ba[x]) are major characteristics of skeletal Class III malocclusions. The morphologic characteristics of the posterior cranial base cause the mandible to be located more anteriorly; consequently, this plays an important role in the establishment of a skeletal Class III malocclusion. REFERENCES 1. Proffit WR. The etiology of orthodontic problems. In: Proffit WR, Fields HW Jr., Sarver DM, editors. Contemporary orthodontics. 4th ed. St Louis: Mosby; 2007. p. 130-61. 2. Young M. A contribution to the study of the Scottish skull. Trans R Soc Edinb 1916;51:347-453. 3. Moss ML, Greenberg SN. Growth of the human skull base. Angle Orthod 1955;25:77-84. 4. Brodie AG. The behavior of the cranial base and its components as revealed by serial cephalometric roentgenograms. Angle Orthod 1955;25:148-60. 5. Scott JH. The cranial base. Am J Phys Anthropol 1958;16:319-48. 6. Hopkin GB, Houston WJ, James GA. The cranial base as an aetiological factor in malocclusion. Angle Orthod 1968;38:250-5. 7. Varjanne I, Koski K. Cranial base, sagittal jaw relationship and occlusion: a radiological-craniometric appraisal. Proc Finn Dent Soc 1982;78:179-83.
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8. Lewis AB, Roche AF, Wagner B. Pubertal spurts in cranial base and mandible comparisons within individuals. Angle Orthod 1985;55: 17-30. 9. Bj€ ork A. Cranial base development: a follow-up x-ray study on 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. 10. Droel R, Isaacson RJ. Some relationships between the glenoid fossa position and various skeletal discrepancies. Am J Orthod 1972;61: 65-78. 11. Kerr WJS, Adams CP. Cranial base and jaw relationship. Am J Phys Anthropol 1988;77:213-20. 12. Baccetti T, Antonini A, Franchi L, Tonti M, Tollaro I. Glenoid fossa position in different facial types: a cephalometric study. Br J Orthod 1997;24:55-9. 13. Sekiya T, Sasaki K, Nakamura Y, Kuwahara Y. Morphological differences in craniofacial complex between surgical case and nonsurgical case with skeletal Class III malocclusion in the pubertal growth. Orthod Waves-Jpn Ed 1999;58:233-41. 14. Innocenti C, Gluntini V, Defraia E, Baccetti T. Glenoid fossa position in Class III malocclusion associated with mandibular protrusion. Am J Orthod Dentofacial Orthop 2009;135:438-41. 15. Bastir M, Rosas A, Kuroe K. Petrosal orientation and mandibular ramus breadth: evidence for an integrated petroso-mandibular developmental unit. Am J Phys Anthropol 2004;123:340-50. 16. Bastir M, Rosas A. Hierarchical nature of morphological integration and modularity in the human posterior face. Am J Phys Anthropol 2005;128:26-34. 17. Gkantidis N, Halazonetis DJ. Morphological integration between the cranial base and the face in children and adults. J Anat 2011;218:426-38. 18. Dibbets JMH. Morphological associations between the Angle classes. Eur J Orthod 1996;18:111-8. 19. Reyes BC, Baccetti T, McNamara JA Jr. An estimate of craniofacial growth in Class III malocclusion. Angle Orthod 2006;76: 577-84. 20. Battagel JM. The aetiological factors in Class III malocclusion. Eur J Orthod 1993;15:347-70. 21. Mouakeh M. Cephalometric evaluation of craniofacial pattern of Syrian children with Class III malocclusion. Am J Orthod Dentofacial Orthop 2001;119:640-9. 22. Singh GD, McNamara JA Jr, Lozanoff S. Allometry of the cranial base in prepubertal Korean subjects with Class III malocclusions: finite element morphology. Angle Orthod 1999;69:507-14. 23. Chang HP, Chou TM. Cranial-base morphology in children with Class III malocclusion. Kaohsiung J Med Sci 2005;21:159-65. 24. Proff P, Will F, Bokan I, Fanghanel J, Gedrange T. Cranial base features in skeletal Class III patients. Angle Orthod 2008;78: 433-9. 25. Koodaryan R, Rafighi A, Hafezeqoran A. Components of adult Class III malocclusion in an Iranian population. J Dent Res Dent Clin Dent Prospect 2009;3:20-3. 26. Singh GD, McNamara JA Jr, Lozanoff S. Morphometry of the cranial base in subjects with Class III malocclusion. J Dent Res 1997;76:694-703. 27. Singh GD, McNamara JA Jr, Lozanoff S. Finite element analysis of the cranial base in subjects with Class III malocclusion. Br J Orthod 1997;24:103-12. 28. Singh GD, McNamara JA Jr, Lozanoff S. Thin-plate spline analysis of the cranial base in subjects with Class III malocclusion. Eur J Orthod 1997;19:341-53. 29. Guyer EC, Ellis EE, McNamara JA, Behrents RG. Components of Class III malocclusion in juveniles and adolescents. Angle Orthod 1986;56:7-30.
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30. Dhopatkar A, Bhatia S, Rock P. An investigation into the relationship between the cranial base angle and malocclusion. Angle Orthod 2002;72:456-63. 31. Baccetti T, Franchi L, McNamara JA Jr. The cervical vertebral maturation (CVM) method for the assessment of optimal treatment timing in dentofacial orthopedics. Semin Orthod 2005;11:119-29. 32. Baccetti T, Reyes BC, McNamara JA Jr. Gender differences in Class III malocclusion. Angle Orthod 2005;75:510-20. 33. Dahlberg G. Statistical methods for medical and biological students. London, United Kingdom: George Allen and Unwin Ltd; 1940. p. 40-9. 34. Kim HY. Statistical notes for clinical researchers: evaluation of measurement error 2: Dahlberg's error, Bland-Altman method, and kappa coefficient. Restor Dent Endod 2013;38:182-5. 35. Guilford JP, Fruchter B. Fundamental statistics in psychology and education. 6th ed. Auckland, New Zealand: McGraw-Hill International Book; 1984. p. 409-10. 36. Breiman L, Friedman JH, Olshen RA, Stone CJ. Classification and regression trees. Boca Raton, Fla: Chapman & Hall/CRC press; 1984. 37. Kohavi R, Quinlan JR. Data mining tasks and methods. In: _ Kl€osgen W, Zytkow JM, editors. Handbook of data mining and knowledge discovery. New York: Oxford Press; 2002. p. 267-75. 38. Fejerskov O, Kidd E. Dental caries: the disease and its clinical management. 2nd ed. Oxford, United Kingdom: John Wiley & Sons; 2008. p. 531. 39. Forsberg CM. Facial morphology and ageing: a longitudinal investigation of young adults. Eur J Orthod 1979;1:15-23. 40. Wei SHY. Craniofacial variations, sex differences and the nature of prognathism in Chinese subjects. Angle Orthod 1969;39:303-15. 41. Bastir M, Rosas A, Higgins PO. Craniofacial levels and the morphological maturation of the human skull. J Anat 2006;209:637-54. 42. 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;104:628-39. 43. Baek C, Paeng JY, Lee JS, Hong J. Morphologic evaluation and classification of facial asymmetry using 3-dimensional computed tomography. J Oral Maxillofac Surg 2012;70:1161-9. 44. 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 Dentofacial Orthop 2013;144:330-40. 45. Ishii N, Deguchi T, Hunt NP. Craniofacial differences between Japanese and British Caucasian females with a skeletal Class III malocclusion. Eur J Orthod 2002;24:493-9. 46. Bui C, King T, Proffit W, Bowers SF. Phenotypic characterization of Class III patients. Angle Orthod 2006;76:564-9. € O, € Kaya B. Changes in cranial base morphology in different 47. Polat O malocclusions. Orthod Craniofac Res 2007;10:216-21. 48. Kochel J, Emmerich S, Marcotty PM, Eisenhauer AS. New model for surgical and nonsurgical therapy in adults with Class III malocclusion. Am J Orthod Dentofacial Orthop 2011;139:e165-74. 49. Martin O, Muelas L, Vi~ nas MJ. Comparative study of nasopharyngeal soft-tissue characteristics in patients with Class III malocclusion. Am J Orthod Dentofacial Orthop 2011;139:242-51. 50. Uribe LMM, Vela KC, Kummet C, Dawson DV, Southard TE. Phenotypic diversity in white adults with moderate to severe Class III malocclusion. Am J Orthod Dentofacial Orthop 2013; 144:32-42. 51. Ishikawa H, Nakamura S, Iwasaki H, Kitazawa S. Seven parameters describing anteroposterior jaw relationships: postpubertal prediction accuracy and interchangeability. Am J Orthod Dentofacial Orthop 2000;117:714-20.
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52. Anderson G, Fields HW, Beck M, Chacon G, Vig KWL. Development of cephalometric norms using a unified facial and dental approach. Angle Orthod 2006;76:612-8. 53. Nagaoka K, Kuwahara Y. Normal standards for various roentgen cephalometric and cast model analyses in present day Japanese adults: part 1. J Jpn Orthod Soc 1993;52:467-80. 54. Hanada K, Sawa S, Ryokawa H, Watanabe K, Shimizu Y, Tomii M, et al. The surgical and orthodontic approach to the skeletal Class III malocclusions. J Jpn Orthod Soc 1975;34:96-115. 55. Sanborn RT. Differences between the facial skeletal patterns of Class III malocclusion and normal occlusion. Angle Orthod 1955; 25:208-22. 56. Leitao P, Nanda RS. Relationship of natural head position to craniofacial morphology. Am J Orthod Dentofacial Orthop 2000; 117:406-17. 57. Hayashi I. Morphological relationship between the cranial base and dentofacial complex obtained by reconstructive computer tomographic images. Eur J Orthod 2003;25:385-91. 58. Andria LM, Leite LP, Prevatte TM, King LB. Correlation of the cranial base angle and its components with other dental/skeletal variables and treatment time. Angle Orthod 2004;74: 361-6. 59. Kuroe K, Rosas A, Molleson T. Variation in the cranial base orientation and facial skeleton in dry skulls sampled from three major populations. Eur J Orthod 2004;26:201-7. 60. Halazonetis DJ. Morphometrics for cephalometric diagnosis. Am J Orthod Dentofacial Orthop 2004;125:571-81. 61. Ahn SJ, Baek SH, Kim TW, Nahm DS. Discrimination of internal derangement of temporomandibular joint by lateral cephalometric analysis. Am J Orthod Dentofacial Orthop 2006;130:331-9.
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62. Ogura M, Al-Kalaly A, Sakashita R, Kamegai T, Miyawaki S. Relationship between anteroposterior cranial vault deformation and mandibular morphology in a pre-Columbian population. Am J Orthod Dentofacial Orthop 2006;130:535-9. 63. Kim DK, Baek SH. Change in maxillary incisor inclination during surgical-orthodontic treatment of skeletal Class III malocclusion: comparison of extraction and nonextraction of the maxillary first premolars. Am J Orthod Dentofacial Orthop 2013;143:324-35. 64. Moorrees CFA. Normal variation and its bearing on the use of cephalometric radiographs in orthodontic diagnosis. Am J Orthod 1953;39:942-50. 65. Richardson A. An investigation into the reproducibility of some points, planes, and lines used in cephalometric analysis. Am J Orthod 1966;52:631-51. 66. Lundstr€om A, Lundstr€ om F. The Frankfort horizontal as a basis for cephalometric analysis. Am J Orthod Dentofacial Orthop 1995; 107:537-40. 67. Enlow DH, Kuroda T, Lewis AB. The morphological and morphogenetic basis for craniofacial form and pattern. Angle Orthod 1971;41:161-88. 68. Lozanoff S, Jureczek S, Feng T, Padwal R. Anterior cranial base morphology in mice with midfacial retrusion. Cleft Palate Craniofac J 1994;31:417-28. 69. Coben SE. The integration of facial skeletal variants: a serial cephalometric roentgenographic analysis of craniofacial form and growth. Am J Orthod 1955;41:407-34. 70. Seward S. Relation of basion to articulare. Angle Orthod 1981;51: 151-61. 71. Jacobson A. Mandibular prognathism. Am J Orthod 1974;66: 140-71.
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Cranial-base morphology in adults with skeletal Class III malocclusion Seetala Sanggarnjanavanich,a Toshiko Sekiya,b Yoshiaki Nomura,c Takahiro Nakayama,d Nobuhiro Hanada,e and Yoshiki Nakamuraf Yokohama, Japan
Introduction: The objectives of this study were to clarify the characteristics of cranial-base morphology in adults with skeletal Class III malocclusion and investigate factors relating to the establishment of a skeletal Class III malocclusion. Methods: Initial lateral cephalograms of women were examined. Subjects with an ANB angle of 0 to 4 , normal overjet and overbite, and a Class I molar relationship were classified as Class I (n 5 86). Those with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, and a Class III molar relationship were the Class III group (n 5 86) in this study. Angular, linear, and coordinate measurements were made. Multivariate analysis of variance and the Student t test were used to analyze significant differences between the 2 groups. Discriminant analysis, logistic regression analysis, and decision analysis were used to identify which cranial-base and maxillomandibular variables influenced the establishment of a skeletal Class III malocclusion. Results: The Class III group had smaller values for NSBa, SeSBa, FH-SSe, and FH-SBa. Sphenoidale and basion were more inferior and anterior than those of the Class I group. There was no difference in the anterior and posterior cranial-base lengths between the groups. Greater mandibular length was the first major characteristic in the Class III group, followed by smaller values for SeSBa and NSBa. Conclusions: Cranial-base morphology in adults with a skeletal Class III malocclusion is different from that in a skeletal Class I malocclusion. Smaller cranial-base angles, steeper posterior cranial bases, more inferiorly positioned sphenoidale, and more anteriorly positioned basion are major characteristics of skeletal Class III malocclusions. These characteristics play important roles in the establishment of a skeletal Class III malocclusion. (Am J Orthod Dentofacial Orthop 2014;146:82-91)
A
skeletal Class III malocclusion results from morphologic or positional disharmony between the maxilla and the mandible during the growth period.1 In 1916, Young2 reported that the cranial-base morphology might be related to jaw prognathism. Since then, several studies have investigated the relationship between the cranial-base and maxillomandibular components.2-8 The cranial base includes both the anterior and posterior cranial bases. The anterior cranial base relates to
From the School of Dental Medicine, Tsurumi University, Yokohama, Japan. a Postgraduate student, Departments of Orthodontics and Translational Research. b Assistant professor, Department of Orthodontics. c Associate professor, Department of Translational Research. d Postgraduate student, Department of Orthodontics. e Professor and chairman, Department of Translational Research. f Professor and chairman, Department of Orthodontics. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Yoshiki Nakamura, Department of Orthodontics, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi Tsurumi-ku, Yokohama, Japan 230-8501; e-mail, [email protected]. Submitted, June 2013; revised and accepted, April 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.04.014
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the position of the maxilla,5 whereas the posterior cranial base relates to the positions of the glenoid fossa and the mandible.9-14 Recently, the correlations between the lateral basicranium and facial form, mandibular morphology and position, and malocclusion patterns have also been investigated.15-17 Bastir et al15 and Bastir and Rosas16 demonstrated that both the midline cranial base and the middle cranial fossa correlate with mandibular ramus morphology. One of the most commonly used cranial-base characteristics is the cranial-base angle from the flexion of the anterior and posterior cranial bases at sella turcica in the midsagittal plane. It has been considered that the cranial-base angle has an influence on the anteroposterior intermaxillary relationship and the type of malocclusion.5,6,11,18,19 Furthermore, the dimensions of the cranial base play an important role in determining the sagittal jaw relationship.6 A small cranial-base angle (NSBa)7,11,18-24 and a short cranial-base length (S-N)7,18,21-23,25 are major morphologic features of skeletal Class III patients. A deficiency of the cranial base that flattens during growth has been considered a factor associated with skeletal Class III malocclusion.26-28 However, recent
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studies have reported no correlation between the cranialbase angle and a skeletal Class III malocclusion.29,30 Since the evidence is still inconclusive, whether the cranial-base morphology in a skeletal Class III malocclusion differs from that of a skeletal Class I malocclusion and has a relationship to the establishment of a skeletal Class III malocclusion remains controversial. Furthermore, most previous researchers selected their subjects irrespective of sex and age. There have been few cranial-base studies in adults with a skeletal Class III malocclusion.24,25 The objectives of this study were to clarify the characteristics of cranial-base morphology in adults with a skeletal Class III malocclusion by comparing them with those with a skeletal Class I malocclusion, and to investigate factors related to the establishment of a Class III malocclusion. MATERIAL AND METHODS
Initial lateral cephalometric radiographs of 424 Japanese women, ages 16 to 35 years, from the Department of Orthodontics, Dental Hospital, of Tsurumi University in Yokohama, Japan, were examined in our study. The study protocol was approved by the institutional review board of the university. The image magnification of the cephalostat for this study was 10%, and all linear measurements were adjusted accordingly. All subjects were adults because all cephalograms showed stage 6 of cervical vertebral maturation, indicating that at least 2 years had passed after the pubertal growth peak.31,32 Subjects with an ANB angle from 0 to 4 with normal overjet and overbite, a Class I molar relationship, and a normal facial profile were classified as the Class I group, and those with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, a Class III molar relationship, and a concave facial profile were the Class III group. The exclusion criteria were cleft lip and palate, craniofacial syndrome, mandibular deviation more than 5 mm, remaining deciduous or missing teeth (except third molars), a previous history of orthodontic treatment, and poor-quality cephalograms. Consequently, 86 skeletal Class I and 86 Class III subjects met the inclusion criteria. The skeletal Class I and Class III subjects' ages ranged from 16.1 to 34.0 years (mean, 21.6 years; standard deviation [SD], 3.9) to 16.0 to 35.0 years (mean, 22.0 years; SD, 4.3), respectively. Each lateral cephalogram was traced on 0.003-in frosted acetate by 1 investigator (S.S.) and checked for accuracy by another investigator (T.S.). Cephalometric landmarks were identified, digitized, and analyzed with CephaloMetrics AtoZ software (version 9.5J; Yasunaga Computer Systems, Fukui, Japan). Definitions for these landmarks are given in Figure 1.
Fig 1. Coordinate axes and cephalometric landmarks: A, Point A, the deepest point on the midsagittal plane between supradentale and the anterior nasal spine; ANS, anterior nasal spine, the most anterior point on the maxilla at the level of the palate in the midsagittal plane; Ar, articulare, the point of intersection between the anterior surface of the sphenoid bone and the posterior contour of the mandibular ramus; B, Point B, the deepest point on the midsagittal plane between infradentale and pogonion; Ba, basion, the most posteroinferior point of the anterior margin of the foramen magnum in the midsagittal plane; Cd, condylion, the most posterior superior point on the condyle of the mandible; Gn, gnathion, the most downward and forward point on the symphysis at the intersection of the facial and mandibular planes; Go, gonion, the most posterior inferior point at the angle of the mandible; Me, menton, the most inferior midpoint of the symphysis; N, nasion, the most anterior point of the frontonasal suture in the midsagittal plane; Or, orbitale, the deepest point on the infraorbital margin; PNS, posterior nasal spine, the most posterior point on the palatine bone in the midsagittal plane; Po, porion, the most superior point of the external auditory meatus; Pog, pogonion, the most anterior midpoint of the symphysis; Ptm, pterygomaxillary fissure, the contour of the pterygomaxillary fissure formed anteriorly by the retromolar tuberosity of the maxilla and posteriorly by the anterior curve of the pterygoid process of the sphenoid bone; S, sella, the center of the hypophyseal fossa in the midsagittal plane; Se, sphenoidale, the deepest point of intersection between the greater wings of the sphenoid and the anterior cranial base.
The positions of the landmarks were recorded in Cartesian coordinates (x- and y-axes) with sella as the origin of the axes (x, y 5 0, 0). The horizontal reference plane (x-axis) was parallel to the Frankfort horizontal plane passing through sella. The vertical plane (y-axis) was
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set perpendicular to the horizontal plane. The anterior and inferior areas near sella were set to positive, whereas the posterior and superior areas near sella were set to negative. To test the error of point identification, the lateral cephalograms of 25 subjects were randomly selected, retraced, and redigitized 2 months after the initial analysis by the same investigator (S.S.). Errors in identifying and locating cephalometric landmarks were assessed by Dahlberg's formula (measurement error estimation), and the coefficient of reliability was calculated as follows. pP ffiffiffiffiffiffiffiffiffiffiffi d2 0 Dahlberg s formula5 2n where d is the mean difference between repeated measurements, and n is the number of measurements.33,34 Coefficient of reliability51
S2e S2t
where Se2 is the variance due to random error, and St2 is the total variance of the measurements.35 Dahlberg's errors were 0.17 to 0.50 , 0.14 to 0.39 mm, and 0.15 to 0.32 mm for angular, linear, and coordinated value measurements, respectively. The coefficient of reliability indicated that the observed values of the measured variables were between 0.925 and 0.999.
Fig 2. Maxillomandibular measurements:1, SNA; 2, SNB; 3, mandibular plane angle; 4, ramus inclination (90 , the angle between the Frankfort horizontal plane [FH] and the line tangent to the posterior border of the ramus and Ar); 5, gonial angle; 6, A0 -Ptm0 ; 7, anterior maxillary height, A Mx H (the distance from ANS to its perpendicular intersection on the horizontal plane); 8, posterior maxillary height; P Mx H (the distance from PNS to its perpendicular intersection on the horizontal plane); 9, Gn-Cd; 10, Pog-Go; 11, Cd-Go.
Statistical analysis
Angular, linear, and coordinate values measurements for groups of maxillomandibular variables and cranialbase variables were performed (Figs 2-4). Significant differences between the Class I and Class III groups in maxillomandibular and cranial-base variables were tested with the Hotelling T2 test (multivariate analysis of variance; MANOVA) as an initial exploratory test. When significance was found, the independent-sample Student t test was used to identify significant between-group differences for each cephalometric variable. Because of multiple testing, we adjusted the level of significance according to Holm's sequentially rejective multiple test procedure. Three statistical models—decision analysis by classification and regression trees,36,37 discriminant analysis by stepwise regression, and logistic regression analysis by forward selection—were performed to identify the variables in the cranial base, maxilla, and mandible that characterize skeletal Class I and Class III subjects. The independent variables were ramus inclination, mandibular plane angle, gonial angle, A0 -Ptm0 , A Mx H, P Mx H, Gn-Cd, Pog-Go, Cd-Go, NSBa, SeSBa, FH-SN, FH-SSe, FH-SBa, S-N, S-Se, N-Se, and S-Ba.
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Fig 3. Linear cranial-base measurements: 1, S-N; 2, S-Ba; 3, S-Se; 4, N-Se.
To compare the accuracy of the 3 statistical models, the cutoff values were obtained from the receiver operating characteristic curves, and classification accuracy was called the crude hit rate. It was calculated as follows. number of truepositives1truenegatives Crudehit rate5 totalnumber of subjects where true positives are subjects in both the actual and predicted Class I groups, and true negatives are subjects in both the actual and predicted Class III groups.38
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Fig 4. Angular cranial-base measurements: 1, NSBa; 2, SeSBa; 3, FH-SN; 4, FH-SBa; 5, FH-SSe. RESULTS
Dahlberg's errors for angular, linear, and coordinated value measurements were small and acceptable. Results from the reliability assessment showed high correlations with the measured variables. Normal distribution of all variables was confirmed by the Kolmogorov-Smirnov test. Parametric tests were performed. Means and SDs of the ANB angles in the skeletal Class I and Class III subjects were 2.52 6 0.99 and 3.70 6 1.83 , respectively. To determine whether there were differences between the 2 groups of subjects at the beginning of the study, the maxillomandibular and cranial-base variables grouped as a multivariate variable in each maxillomandibular and cranial-base group were analyzed by MANOVA. A statistically significant difference was found between the skeletal Class I and Class III subjects (P \0.0001 and P \0.0047, respectively). Since the MANOVA showed a significant difference, the Student t test was used to determine significant differences between the skeletal Class I and Class III subjects. Mandibular measurements showed significant differences between the Class I and Class III groups. The Class III group had significant anteriorly inclined rami and larger gonial angles. The anterior part of the mandible (Point B) was more anteriorly and inferiorly located. The posterior part of the mandible (articulare) was also more anteriorly located. Mandibular length (Gn-Cd), body length (Pog-Go), and ramus height (Cd-Go) were significantly larger than in the Class I group. However, the maxillary measurements had no significant differences in both position (Point A) and sizes (A0 -Ptm0 , A Mx H, and P Mx H) between the groups (Table I). Cranial-base measurements showed significant differences between the Class I and Class III groups. The cranial-base angle (NSBa) and the angle between the sphenoid and occipital bones (SeSBa) were significantly smaller in the Class III group. The angle of the sphenoid
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bone to the Frankfort horizontal plane (FH-SSe) and the vertical position of sphenoidale (Se[y]) in the Class III group were also significantly smaller and more inferiorly located. However, there was no significant difference between the groups in anterior cranial-base lengths (S-N, S-Se, and N-Se) (Table II). Posterior cranial-base measurements showed considerable differences between the Class I and Class III groups. The angle of the posterior cranial base to the Frankfort horizontal plane (FH-SBa) in the Class III group was significantly smaller than that in the Class I group. Furthermore, the horizontal position of basion (Ba[x]) in the Class III group was also significantly more anteriorly located. However, posterior cranial-base length (S-Ba) showed no difference between the groups (Table II). Decision analysis using cranial base, and maxillary and mandibular variables showed that the most important variable for the characterization between the skeletal Class I and Class III subjects was mandibular length (Gn-Cd), and the subsequent variables were SeSBa and NSBa. From the decision tree, 89.4% of the subjects with a Gn-Cd greater than 124.20 mm and SeSBa equal to or less than 136.81 were skeletal Class III subjects. Among them, those with gonial angles greater than 114.92 were also skeletal Class III subjects (92.2%). On the other hand, 50% of the subjects with SeSBa greater than 136.81 were skeletal Class I, even though their mandibular lengths were greater than 124.20 mm. Only 50% of the subjects with mandibular length and SeSBa greater than 124.20 mm and 136.81 , respectively, were skeletal Class III subjects. Among them, all subjects with a ramus inclination greater than 14.37 were also skeletal Class III subjects. On the other hand, 96.1% of the subjects with mandibular length equal to or less than 124.20 mm and NSBa greater than 131.04 were skeletal Class I (Fig 5). Discriminant and logistic regression analysis demonstrated that ramus inclination, A0 -Ptm0 , Gn-Cd, Pog-Go, N-Se, NSBa, FH-SBa, and P Mx H were the predictor variables characterizing the skeletal Class III subjects (Tables III and IV). Classification results of the 3 statistical models were evaluated by the crude hit rate, which means the proportion of correctly classified subjects. All models showed high values, but decision analysis had the highest (Table V). DISCUSSION
Even though there have been several studies on the relationship between the cranial base and malocclusion, their results are controversial.2-8 Most previous studies selected subjects without sex and age considerations.
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Table I. Maxillomandibular measurements of skeletal Class I and Class III subjects Class I subjects Cephalometric measurement SNA ( ) SNB ( ) Mandibular plane angle ( ) Ramus inclination ( ) Gonial angle ( ) A0 -Ptm0 (mm) A Mx H (mm) P Mx H (mm) Gn-Cd (mm) Pog-Go (mm) Cd-Go (mm) A(x) (mm) A(y) (mm) B(x) (mm) B(y) (mm) Ar(x) (mm) Ar(y) (mm)
Mean 80.29 77.76 28.53 4.88 123.41 47.17 46.12 45.06 121.65 79.11 60.98 67.25 52.24 62.28 94.91 16.94 31.95
SD 3.25 3.25 5.19 4.90 7.08 3.19 3.26 2.68 5.83 4.40 4.88 4.01 3.01 5.35 4.74 2.80 3.07
Class III subjects
Min 71.78 70.64 15.45 5.03 109.85 40.14 35.99 39.10 109.08 68.86 49.32 56.08 44.46 50.03 83.20 22.54 24.60
Max 87.89 84.60 43.24 15.24 140.89 56.33 52.76 51.37 134.54 90.00 73.77 75.79 57.82 73.35 107.68 9.47 40.92
Mean 80.49 84.18 27.69 10.03 127.72 46.34 47.14 45.84 131.27 83.98 64.14 66.21 53.36 72.22 97.78 14.54 31.33
SD 3.38 3.75 5.54 5.13 7.08 2.63 3.75 3.00 6.07 3.89 4.44 3.96 4.00 6.75 6.04 2.91 2.74
Min 71.75 74.65 13.17 0.22 115.71 40.08 39.22 38.69 119.13 72.34 53.99 55.02 44.43 56.51 85.06 20.86 24.71
Max 89.36 93.89 39.14 20.60 143.21 53.46 57.34 54.67 153.12 98.27 73.90 77.49 63.67 90.21 109.36 6.98 37.82
Significance 0.6918 \0.0001y 0.3064 \0.0001y \0.0001y 0.0619 0.0583 0.0757 \0.0001y \0.0001y \0.0001y 0.0902 0.0406 \0.0001y 0.0007* \0.0001y 0.1654
Hotelling T2 5 736.610; F 5 45.061; P \0.0001, significant. Min, Minimum; Max, maximum. *Significant at 5%; ysignificant at 1%.
Table II. Cranial-base measurements of skeletal Class I and Class III subjects Class I subjects Cephalometric measurement Cranial-base angle NSBa ( ) SeSBa ( ) Anterior cranial base FH-SN ( ) FH-SeS ( ) S-N (mm) S-Se (mm) N-Se (mm) Na(x) (mm) Na(y) (mm) Se(x) (mm) Se(y) (mm) Posterior cranial base FH-SBa ( ) S-Ba (mm) Ba(x) (mm) Ba(y) (mm)
Class III subjects
Mean
SD
Min
Max
Mean
SD
Min
Max
Significance
134.80 138.14
4.79 5.58
124.43 124.47
146.80 156.76
131.84 133.70
5.09 6.65
114.36 114.30
144.20 149.63
0.0001y \0.0001y
9.26 12.61 68.64 26.61 42.21 67.68 11.13 25.92 5.81
2.36 4.36 3.07 2.41 3.21 3.07 2.80 2.36 2.05
4.76 3.12 61.83 20.48 33.89 60.33 19.57 20.44 10.56
15.89 24.87 76.69 32.77 50.34 75.79 6.13 32.21 1.24
8.41 10.27 68.26 27.07 41.32 67.45 9.93 26.56 4.78
2.84 4.59 3.11 2.10 3.35 3.08 3.45 2.14 2.12
1.02 0.53 61.77 18.85 35.27 60.99 17.27 18.80 9.54
15.05 20.53 77.79 32.92 52.13 76.10 0.69 32.91 0.24
0.0343 0.0007* 0.4191 0.1842 0.0779 0.6256 0.0136 0.0622 0.0015*
125.54 47.07 27.26 38.24
3.79 3.29 3.28 3.12
117.25 38.22 37.51 29.50
134.96 57.51 20.64 47.60
123.43 46.81 25.72 38.96
4.23 2.66 3.04 3.12
113.34 41.73 33.54 30.18
133.51 53.99 18.16 48.07
0.0007* 0.5746 0.0016* 0.1327
Hotelling T2 5 38.25; F 5 2.344; P 5 0.0047, significant. Min, Minimum; Max, maximum. *Significant at 5%; ysignificant at 1%.
Therefore, their results could not be compared because of subject variations. Subjects of 1 sex provide more accurate linear measurements than do the previous studies that pooled the sexes. The average craniofacial complex is 5% to 9%
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larger in men than in women39; especially, skeletal Class III men have greater values for most linear measurements when compared with women.40 Therefore, we selected only female subjects to eliminate sex differences in the craniofacial components.
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Fig 5. Decision tree for characterizing skeletal Class I and Class III subjects by cranial-base and maxillomandibular variables; ramus inclination, mandibular plane angle, gonial angle, A0 -Ptm0 , A Mx H, P Mx H, Gn-Cd, Pog-Go, Cd-Go, NSBa, SeSBa, FH-SN, FH-SSe, FH-SBa, S-N, S-Se, N-Se, and S-Ba. I, Skeletal Class I subjects; III, skeletal Class III subjects.
Table III. Canonical discriminant function coefficients Ramus inclination A0 -Ptm0 Gn-Cd Pog-Go N-Se NSBa FH-SBa P Mx H (Intercept)
Unstandardized 0.143 0.199 0.074 0.188 0.109 0.206 0.178 0.157 0.537
Standardized 0.717 0.581 0.440 0.780 0.359 1.016 0.714 0.448
Wilks l 5 0.346; chi-square 5 176.278; P \0.001.
We aimed to investigate not only the characteristics of cranial-base morphology in skeletal Class III malocclusions, but also its relationship to the establishment of a skeletal Class III malocclusion. Cranial-base and maxillomandibular components were necessary to investigate the relationship between them. Thus, in subjects who have passed the pubertal growth peak it is necessary to observe the maxillomandibular components. Research on the morphologic maturation of the human skull has
Table IV. Logistic regression model 95% CI
Ramus inclination A0 -Ptm0 Gn-Cd Pog-Go N-Se P Mx H NSBa FH-SBa
Odds ratio 2.251 0.378 1.370 2.947 0.586 0.388 0.425 1.698
Upper 1.479 0.221 1.045 1.651 0.414 0.213 0.256 1.086
Lower 3.426 0.647 1.797 5.261 0.830 0.710 0.706 2.653
P \0.001 \0.001 0.023 \0.001 0.003 0.002 0.001 0.020
Likelihood ratio test.
demonstrated that both the maxilla and the mandible achieve adult size around age 16 years in girls.41 Subjects with large mandibular deviations were excluded because a large lateral mandibular deviation causes morphologic asymmetry in the mandible. Shorter ramus and mandibular body are often observed on the deviated side, which significantly affects the mandibular variables in this study.42-44
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Table V. Predictions by the 3 statistical models Predicted group
Decision analysis* Actual group Class I Class III Discriminant analysisy Actual group Class I Class III Logistic regression analysisz Actual group Class I Class III
Class I
Class III
79 (45.9%) 4 (2.3%)
7 (4.1%) 82 (47.7%)
77 (44.8%) 4 (2.3%)
9 (5.2%) 82 (47.7%)
80 (46.5%) 6 (3.5%)
6 (3.5%) 80 (46.5%)
*Crude hit rate 5 93.6%; ycrude hit rate 5 92.5%; zcrude hit rate 5 93.0%.
Both dental and skeletal criteria were used to select true skeletal Class I and Class III subjects. ANB angle less than 0 , Wits appraisal less than 0 mm, negative overjet, Class III molar relationship, and concave profile are generally used as inclusion criteria for skeletal Class III subjects.24,25,45-50 The conjunctive use of the ANB angle and the Wits appraisal is recommended to assess the anteroposterior intermaxillary relationship in subjects.51 The gold standard criteria for skeletal classification based on ANB angle, overjet, and molar relationship are also an established method.52 All subjects in our study were classified by ANB angle, Wits appraisal, overjet, molar relationship, and facial profile. The ANB norm for Japanese women is 0 to 4 in skeletal Class I and less than 0 in skeletal Class III subjects.53 Subjects with an ANB angle less than 1 , a Wits appraisal less than 2 mm, a negative overjet, a Class III molar relationship, and a concave facial profile were selected as our Class III group to exclude skeletal Class III borderline subjects. Consequently, mean ANB angles of 3.70 in the Class III group and 2.52 in the Class I group indicated proper subject selection. Most of the skeletal Class III subjects had true skeletal Class III Japanese characteristics: mandibular prognathism with a normal maxillary position.54 The Frankfort horizontal plane was selected as our reference plane on the basis of its wide usage and relative acceptance in orthodontics.14,19,21,47,50,55-63 To compare our results with those from most previous studies that used the Frankfort horizontal plane as a craniofacial reference plane, we used this plane to reflect findings in anatomic structures. However, some studies reported variability in locating cephalometric points.64-66 Poor-quality radiographs, including ambiguous landmarks, were excluded from this study.
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Dahlberg's error was also performed to assess errors in identifying and locating cephalometric landmarks. Porion and orbitale identifications showed minimal errors to determine an accurate Frankfort horizontal plane. Consequently, this plane was reliable to use in this study. Sphenoidale (Se), the boundary between the sphenoid and ethmoid bones, was selected to examine the anterior cranial base.67 The area around sphenoidale influences maxillofacial morphology.68 Although S-N is commonly used in cranial-base studies, S-Se is also a main component factor of the anterior cranial base.57 In addition to the conventional variable FH-SN, FHSSe was measured to examine the inclination of the anterior cranial base. FH-SSe in the Class III group was significantly smaller than that in the Class I group, whereas there was no difference in FH-SN between the 2 groups. These findings suggest that the inclination of S-Se is an important anterior cranial-base characteristic that helps to distinguish skeletal Class III from Class I subjects. A flatter inclination of S-Se is related to the vertical deformation of the S-Se region in those with a skeletal Class III malocclusion.26-28 No difference between the Class I and Class III groups was found in anterior cranial-base length, and maxillary length, height, and position. Thus, our skeletal Class III subjects demonstrated a normal anterior cranial-base length with a normal maxillary position. This indicates that anterior cranial-base length is closely related to maxillary position.57 The posterior cranial-base inclination (FH-SBa) in the Class III group was significantly smaller than that in the Class I group, although there was no difference in the posterior cranial-base length between the groups. The angle of the posterior cranial-base inclination depends on the horizontal position of basion, indicating that it is located more anteriorly in the Class III group. Because of the close relationship between the positions of basion and articulare, the mandible is evidently located anteriorly in the Class III group; consequently, this worsens the intermaxillary relationship.69,70 Inferiorly positioned sphenoidale and anteriorly positioned basion are the anterior and posterior cranial-base characteristics in skeletal Class III malocclusions, respectively. Smaller NSBa and SeSBa values were reflected in the Class III group because of these landmark positions. Smaller cranial-base angles in the Class III group were related to deficient orthocephalization, implying insufficient horizontalization of the cranial-base angle in skeletal Class III malocclusions.26-28 Our results differed from those of previous studies. Anterior18,21,22,25 and posterior cranial-base lengths18 were shorter in those with a skeletal Class III malocclusion, and there was no difference in NSBa between the Class I
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and Class III groups.25,29,30 These differences might be due to the inclusion criteria for the subjects and the skeletal classifications. Most of the aforementioned studies selected prepubertal subjects and used only the Class III molar relationship to define their Class III subjects. Thus, in this study, we carefully selected subjects representing skeletal Class III malocclusions. The results of the Student t test clearly showed the differences in the morphology of the cranial base, maxilla, and mandible between the Class I and Class III groups. However, the variables of cranial base, maxilla, and mandible that contributed to the establishment of a skeletal Class III malocclusion were still unclear. Therefore, discriminant analysis, logistic regression analysis, and decision analysis were performed. Results from comparing the good decision counts among the 3 statistical models confirmed that all of them had high crude hit rates, which signifies highly correct classification rates. However, both the discriminant analysis and the logistic regression analysis selected the same predictor variables, whereas the decision analysis selected some different predictors. In general, regression models including discriminant analysis and logistic regression analysis do not consider the classifications of subgroups. In contrast, decision analysis automatically finds important variables in each subgroup. A classification and regression tree is a classification analysis displayed as a binary tree in which all subjects are split into 2 nodes representing each group. This function automatically determines whether to fit a regression or a classification tree. The most broadly used splitting criterion in a classification and regression tree is the Gini index (an impurity-based criterion) to find the best variable to separate the data into 2 parts with maximum homogeneity and repeat until all subjects in the data set are classified into a single category. The Gini index is used to measure the probability of misclassification of a set of subjects.36 This study is the first orthodontic research with decision analysis to examine the influence of the cranialbase and maxillomandibular variables on skeletal Class III malocclusions in a hierarchical way. This is the most suitable and an easy-to-use analysis for observing subjects in clinical diagnosis. It helps us to understand the relationship between individual variations in variables and the establishment of a skeletal Class III malocclusion. Mandibular morphology is the strongest contributor to skeletal Class III manifestation.55,71 The results of decision analysis demonstrated that in the Class III group, greater mandibular length was the first major characteristic, followed by smaller SeSBa and NSBa values. This suggests that the posterior cranial-base
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inclination influences the mandibular position and results in a skeletal Class III malocclusion. Interestingly, decision analysis demonstrated that 92.2% of the skeletal Class III subjects had greater mandibular lengths (.124.20 mm), smaller SeSBa values (#136.81 ), and larger gonial angles (.114.92 ), whereas 100% of the skeletal Class I subjects had shorter mandibular lengths (#124.20 mm), larger NSBa values (.131.04 ), greater maxillary lengths (.41.08 mm), and greater posterior maxillary heights (.38.90 mm). A smaller SeSBa was 1 characteristic of a skeletal Class III malocclusion. We recommend using SeSBa as an additional variable for NSBa in cranial-base morphologic studies because it was significantly different between the 2 groups and could help to distinguish skeletal Class III subjects from skeletal Class I subjects. Sphenoidale is located at the intersection of the greater wings of the sphenoid with the floor of the anterior cranial fossa.15 This point is a stable reference landmark obviously seen on the lateral cephalogram. Furthermore, nasion is not part of the cranial base. In the future, a longitudinal study is recommended to observe cranial-base morphology in growing subjects with skeletal Class III malocclusion. CONCLUSIONS
The cranial-base morphology in adults with a skeletal Class III malocclusion is different from that in a skeletal Class I malocclusion. Smaller cranial-base angles (NSBa and SeSBa), a steeper posterior cranial base (FH-SBa), more inferiorly positioned sphenoidale (Se[y]), and more anteriorly positioned basion (Ba[x]) are major characteristics of skeletal Class III malocclusions. The morphologic characteristics of the posterior cranial base cause the mandible to be located more anteriorly; consequently, this plays an important role in the establishment of a skeletal Class III malocclusion. REFERENCES 1. Proffit WR. The etiology of orthodontic problems. In: Proffit WR, Fields HW Jr., Sarver DM, editors. Contemporary orthodontics. 4th ed. St Louis: Mosby; 2007. p. 130-61. 2. Young M. A contribution to the study of the Scottish skull. Trans R Soc Edinb 1916;51:347-453. 3. Moss ML, Greenberg SN. Growth of the human skull base. Angle Orthod 1955;25:77-84. 4. Brodie AG. The behavior of the cranial base and its components as revealed by serial cephalometric roentgenograms. Angle Orthod 1955;25:148-60. 5. Scott JH. The cranial base. Am J Phys Anthropol 1958;16:319-48. 6. Hopkin GB, Houston WJ, James GA. The cranial base as an aetiological factor in malocclusion. Angle Orthod 1968;38:250-5. 7. Varjanne I, Koski K. Cranial base, sagittal jaw relationship and occlusion: a radiological-craniometric appraisal. Proc Finn Dent Soc 1982;78:179-83.
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American Journal of Orthodontics and Dentofacial Orthopedics
July 2014 Vol 146 Issue 1
