analisis de kim

Angle Orthodontist, Vol 75, No 3, 2005311

Original Article

Classification of the Skeletal Variation in Normal OcclusionJi-Young Kima; Shin-Jae Leeb; Tae-Woo Kimc; Dong-Seok Nahmd; Young-Il Changd

Abstract: The aims of this study were to classify normal occlusion samples into specific skeletal typesand to analyze the dentoalveolar compensation in a normal occlusion in order to provide the clinicallyapplicable differential diagnostic criteria for an individual malocclusion patient. Lateral cephalograms of294 normal occlusion samples, who were selected from 15,836 adults through a community dental healthsurvey, were measured. Using a principal component analysis, two factors representing the anteroposteriorand vertical skeletal relationships were extracted from 18 skeletal variables. Cluster analysis was then usedto classify the skeletal patterns into nine types. Nine types of polygonal charts with a profilogram werecreated. Discriminant analysis with a stepwise entry of variables was designed to identify several potentialvariables for skeletal typing, which could be linked with computerized cephalometric analysis for anindividual malocclusion patient. Discriminant analysis assigned 87.8% classification accuracy to the pre-dictive model. It was concluded that because the range of a normal occlusion includes quite diverseanteroposterior and vertical skeletal relationships, classifying the skeletal pattern and establishing an in-dividual dentoalveolar treatment objective might facilitate clinical practice. (Angle Orthod 2005;75:311–319.)

Key Words: Skeletal typing; Principal component analysis; Cluster analysis

INTRODUCTION

It has long been emphasized that a patient with a mal-occlusion should not be treated by standardized cephalo-metric analysis, but rather by the individual norm of ceph-alometric analysis.1–4 A relatively good occlusion with askeletal discrepancy is not uncommon, and a large variationin the skeletal relationship has been reported even in normalocclusion samples.1,2 This confirms that significant anatom-ical variations exist even within a so-called normal occlu-sion and to a greater degree in a malocclusion. Therefore,simple cephalometric analysis for a patient using the nu-merical standards derived from other persons with an av-erage skeletal relationship is unreasonable.

Many studies on the dentoalveolar compensatory mech-anism have been reported, and most of them have been in

a Former Graduate Student, Department of Orthodontics, Collegeof Dentistry, Seoul National University, Seoul, South Korea.

b Assistant Professor, Department of Orthodontics, College of Den-tistry, Seoul National University, Seoul, South Korea.

c Chairman, Associate Professor, Department of Orthodontics, Col-lege of Dentistry, Seoul National University, Seoul, South Korea.

d Professor, Department of Orthodontics, College of Dentistry,Seoul National University, Seoul, South Korea.

Corresponding author: Young-Il Chang, DDS, MSD, PhD, Depart-ment of Orthodontics, College of Dentistry, Seoul National Univer-sity, 28-22 Yunkeun-Dong, Chongro-Ku, Seoul 110-744, South Korea(e-mail: [email protected]).

Accepted: May 2004. Submitted: February 2004.q 2005 by The EH Angle Education and Research Foundation, Inc.

favor of a more individualized treatment approach accord-ing to the individual skeletal type.5–9 However, they sepa-rately analyzed the skeletal pattern either anteroposteriorlyor vertically. The terms retrognathic and prognathic are in-adequate for describing the facial types.6 The variations inthe vertical dimensions are also significant when identifyingfacial types. Therefore, it is important to define the multi-dimensional combinations in order to make a more accurateidentification of the facial types because the interrelation ofthe anteroposterior and vertical relationship is responsiblefor the various facial types.4,5,10 Considering both the an-teroposterior and vertical dimensions at the same timewould lead to a more precise diagnosis from which a morespecific treatment could be planned.

The nonnumerical, graphic evaluation of the facial formdeveloped by Fishman,2 cephalomorphic analysis, is be-lieved to be a sophisticated method in tailoring an individ-ualized clinical diagnosis and treatment plan. However,many cephalometric analyses are computer-based, printinganalysis reports with a ‘‘norm’’ and ‘‘variation.’’ In thiscircumstance, although the visual approach to classify theskeletal type gives a direct indication, a mathematical com-putation corresponds to the current computer-based envi-ronment more harmoniously. In this respect, digitizing thecephalometric tracing, immediate classification of the skel-etal pattern, and analysis of the dentoalveolar characteristicswith an individualized skeletal type would be more valuablethan just a simple ‘‘standardized’’ analysis.

The aim of this study was to classify normal occlusion

312 KIM, LEE, KIM, NAHM, CHANG


FIGURE 1. Anteroposterior (A, B) and vertical skeletal (C) measurements.

samples into specific skeletal types with the aid of mathe-matics. In addition, the dentoalveolar compensation mech-anism and the ranges of skeletal variations that could permitthe establishment of a normal occlusion are discussed. Dis-criminant analysis was also designed to provide a comput-erized classification method for an individual malocclusionpatient.

MATERIALS AND METHODS

Selection of normal occlusion samples

Two hundred ninety-four normal occlusion samples wereselected from 15,836 adults through a community dentalhealth survey in Seoul, South Korea. These subjects con-sisted of 177 male and 117 female individuals with a meanage of 20.2 years. The selection criteria of the normal oc-clusion samples were as follows:

1. Class I molar and canine relationship with normal oc-clusal interdigitation;

2. fully erupted permanent dentition except the third mo-lars;

3. normal overjet and overbite (2–4 mm);4. minimal crowding (less than three mm) and spacing

(less than one mm);5. no history of previous orthodontic or prosthodontic

treatment.

Cephalometric analysis

Complete orthodontic records were made, which includ-ed various radiographs, casts, and photographs. The lateralcephalograms were traced, digitized, and analyzed by Vi-sual C11 (Microsoft, Redmond, Wash) software that wasdesigned for this study. The cephalometric measurementsused were as follows.

Anteroposterior skeletal measurements. The anteropos-terior skeletal measurements are as follows (Figure 1A,B):

1. SN-AB, the angle between the SN plane and the ABplane;

2. FH-AB, the angle between the FH plane and the ABplane;

3. APDI, the anteroposterior dysplasia indicator, the sumof the FH plane to the facial plane angle, the FH planeto the palatal plane angle, and the AB line to the facialplane angle;

4. ANB, the angle between the NA line and the NB line;5. Wits appraisal, the distance between perpendiculars drawn

from point A and point B onto an occlusal plane;6. AF-BF, the distance between the perpendiculars drawn

from point A and point B onto the Frankfort horizontalplane;

7. AFB, the angle between the AF line and the BF line;8. AB plane angle, the angle between the AB plane and

the facial plane.

Vertical skeletal measurements. The vertical skeletalmeasurements are as follows (Figure 1C):

1. SN-MP, the angle between the SN plane and the man-dibular plane;

2. PMA, the angle between the palatal plane and the man-dibular plane;

3. ODI, overbite depth indicator, the sum of the AB to themandibular plane angle and the palatal plane angle;

4. FMA, the angle between the FH plane and the man-dibular plane;

5. AB-MP, the angle between the AB line and the man-dibular plane;

6. Bjork sum: the sum of the saddle angle, articular angle,and gonial angle;

7. Gonial angle, the angle formed by the mandibularplane and the line drawn from the articulare to the pos-terior-inferior border of the ramus;

8. APFHR, the anterior-posterior facial height ratio, theratio of the posterior facial height to the anterior facialheight;

9. ALFHR, the anterior-lower facial height ratio, the ratioof the anterior lower facial height to the anterior totalfacial height;

313CLASSIFICATION OF THE SKELETAL VARIATION


TABLE 1. Variability of Skeletal Measurements

Minimum Mean 6 SDMaxi-mum Range

FH-ABANBSN-ABAPDIWits appraisal

72.723.063.973.7

29.0

84.6 6 4.42.6 6 1.9

76.1 6 4.784.3 6 3.9

21.7 6 2.6

97.38.0

87.493.98.6

24.610.912.020.217.5

AF-BFAFBABPAPMASN-MP

26.224.3

212.211.716.8

4.3 6 3.63.0 6 2.4

24.3 6 2.623.6 6 4.531.8 6 5.2

14.09.34.7

35.245.3

20.313.616.923.528.4

FMAAB-MPODIBjork sum

9.055.450.9

376.8

23.3 6 4.772.1 6 4.371.8 6 5.4

391.8 6 5.2

34.885.387.3

405.3

25.829.836.428.4

Gonial angleAP FHRAL FHRY axis angle

94.258.750.953.1

117.1 6 5.968.8 6 4.755.6 6 1.761.4 6 2.9

135.484.160.270.8

41.225.49.3

17.6

FIGURE 2. Tree dendrogram of cluster analysis derived from 294lateral cephalograms.

10. y-axis angle, the angle between the FH plane and theS-Gn line.

Statistical analysis

Principal component analysis was used to summarize 18skeletal variables. The factor scores were calculated foreach individual, and these factor scores were then used asnew variables in the following cluster analysis.

The Ward method of hierarchical cluster analysis wasused to classify the skeletal pattern. The number of skeletalpatterns was decided by a dendrogram.

In subgrouping the samples, the skeletal types were ar-ranged into a contingency table with the x axis representingthe anteroposterior and the y axis representing the verticalskeletal relationship. Descriptive statistics including analy-sis of variance and post hoc test were used to characterizethe skeletal and dentoalveolar distinctions of each type. Tointerpret the dentoalveolar compensation mechanism, sev-eral variables indicating the position of the upper incisor,lower incisor, premolar, molar, and occlusal plane were an-alyzed. The correlation coefficient between the skeletal var-iables and the dentoalveolar variables was also calculated.Finally, discriminant analysis with stepwise entry of vari-ables was designed to facilitate the classification of an in-dividual malocclusion patient.

RESULTS

Initially, to test the reliability, 30 lateral cephalogramswere randomly selected, which were traced and digitizedagain on separate days two months after the initial tracing.The error in estimation ranged from 0.008 to 0.178 and thatof the linear measurements ranged from 0.00 to 0.12 mm.

Variability of skeletal relationship of normalocclusion samples

All the skeletal cephalometric measurements for normalocclusion samples showed a wide range of variation. Theanteroposterior skeletal measurement FH-AB angle rangedfrom 72.78 to 97.38 with a mean of 84.68 (Table 1).

Classification of normal occlusion

Two factors with an eigenvalue greater than 1.0 were ex-tracted after the principal component analysis. These twofactors could account for 83.7% of the normal samples onthe skeletal pattern, which were identified as the anteropos-terior and vertical variables. The anteroposterior variableswere mainly composed of FH-AB, ANB, SN-AB, APDI, andthe Wits appraisal. The vertical variables were mainly com-posed of PMA, SN-MP, FMA, AB-MP, and ODI.

Figure 2 shows the tree dendrogram obtained from clusteranalysis based on the two factor scores, which apparentlyexpresses nine skeletal patterns. As an analysis of the lineagein the dendrogram, Types 7 and 5, Types 4 and 1, Types 8and 9, and Types 2 and 3 were in close relationship witheach other. Type 6 was somewhat different from the othertypes.

These nine types were arranged into a three 3 three con-tingency table. This table represents a skeletal Class III ten-dency on the right part, a skeletal Class II tendency on theleft part, a hyperdivergent facial pattern on the upper part,and a hypodivergent facial pattern on the lower part. Thenomenclature selected for the skeletal types was parallel tothe skeletal characteristics of each facial type (Figure 3).

Pattern analysis and comparison of skeletal anddentoalveolar characteristics of the nine

skeletal types

Types 1, 3, 7, and 9 represented the extremes of thecharacteristic skeletal pattern that could form a normal oc-clusion. To observe a representative case of each type, aprofilogram, which was closest to the mean value of anyvariable of the type, was depicted. Figure 4 shows the su-perimposed profilograms for the cases that were presentedas a prototype.

The skeletal variables and several dentoalveolar mea-surements with the means and standard deviations for thenine different types were analyzed (Tables 2 and 3). Be-cause there were nine dependent variables for each pairwise



TABLE 2. Means and Standard Deviations for Skeletal Measurements of the Nine Types

Type 1 (n 5 52) Type 2 (n 5 48) Type 3 (n 5 8) Type 4 (n 5 19)

Anteroposterior skeletal measurements

FH-ABANBAPDISN-AB

80.8 6 2.54.2 6 2.1

81.1 6 2.772.0 6 2.4

84.7 6 2.12.5 6 1.2

83.7 6 2.275.2 6 2.2

90.8 6 2.020.8 6 1.490.1 6 1.782.1 6 2.1

77.6 6 1.95.0 6 1.0

78.6 6 2.268.3 6 2.0

Wits appraisalAF-BFAFBABPA

20.8 6 1.77.6 6 2.15.2 6 1.4

26.0 6 1.6

22.8 6 1.84.3 6 1.83.0 6 1.2

23.6 6 1.5

27.3 6 1.220.7 6 1.720.5 6 1.2

1.0 6 2.1

1.2 6 2.09.9 6 1.86.8 6 0.9

27.9 6 1.5

Vertical skeletal measurements

PMASN-MPFMAAB-MPODI

27.0 6 2.936.1 6 3.127.3 6 3.171.9 6 1.672.1 6 2.8

28.4 6 2.636.9 6 2.527.5 6 2.567.9 6 1.866.9 6 3.0

27.5 6 3.135.5 6 3.526.7 6 1.662.4 6 3.061.6 6 4.5

25.0 6 2.735.3 6 2.826.0 6 2.776.5 6 1.677.4 6 3.5

Bjork sumGonial angleAP FHRAL FHRY-axis angle

396.1 6 3.1120.4 6 5.065.7 6 2.755.8 6 1.563.7 6 2.5

396.9 6 2.5121.2 6 3.963.8 6 2.455.9 6 1.661.9 6 2.5

395.5 6 3.5121.9 6 5.865.3 6 2.956.9 6 1.761.5 6 1.1

395.3 6 2.8117.2 6 3.966.2 6 2.254.5 6 1.364.1 6 2.5

TABLE 3. Means and Standard Deviations for Dentoalveolar Measurements

Type 1 Type 2 Type 3 Type 4

Upper and lower incisor

U1 to SNU1 to FHU1 to PPL1 to SNL1 to FH

102.7 6 4.7111.5 6 4.6111.7 6 4.847.8 6 4.656.5 6 4.6

104.1 6 5.6113.5 6 4.9112.6 6 4.951.7 6 4.761.2 6 5.4

107.0 6 2.8115.7 6 4.1115.0 6 4.058.6 6 4.967.4 6 4.0

98.8 6 4.0108.1 6 3.0109.0 6 4.544.7 6 4.254.0 6 4.2

L1 to NBL1 to MPInterincisal angle

30.2 6 4.296.1 6 4.3

125.1 6 7.1

27.0 6 5.291.4 6 4.5

127.6 6 8.7

22.5 6 3.585.9 6 4.3

131.6 6 6.1

31.2 6 3.9100.1 6 4.4125.9 6 5.3

Premolar and molar

U4 to PPU5 to PPU6 to PPU7 to PP

88.5 6 3.285.3 6 4.080.6 6 4.573.2 6 6.3

89.4 6 3.585.6 6 3.981.2 6 4.872.9 6 6.7

92.0 6 3.887.3 6 5.181.9 6 5.374.3 6 5.4

88.3 6 4.384.3 6 2.979.4 6 4.571.5 6 6.6

L4 to MPL5 to MPL6 to MPL7 to MP

82.7 6 4.481.4 6 4.079.8 6 4.083.7 6 5.2

80.1 6 4.379.5 6 3.678.2 6 3.383.1 6 3.9

79.6 6 4.177.3 6 4.478.5 6 4.483.7 6 4.1

85.0 6 3.383.2 6 3.682.4 6 3.286.4 6 3.7

Occlusal plane

SN-OPFH-OPPP-OPMP-OPAB-OP

19.0 6 3.010.2 6 3.09.9 6 2.8

17.1 6 2.991.0 6 2.1

18.2 6 3.18.8 6 2.89.7 6 2.8

18.7 6 2.593.5 6 2.2

16.9 6 2.98.1 6 2.08.9 6 1.7

18.7 6 3.298.9 6 1.3

20.2 6 3.210.9 6 3.59.9 6 2.3

15.0 6 2.288.5 6 2.5

test, it was difficult to observe a regular sequence amongthese types. Therefore, correlation analysis provided aclearer and continuous insight into the relationship betweenthe skeletal variables and the dentoalveolar measurements.A strong positive correlation was found between the an-teroposterior relationship of the mandible and the inclina-tion of the upper and lower incisors. The angulation of the

upper premolar and molar showed a negative correlationwith the PMA. On the other hand, the angulation of thelower premolar and molar showed a positive correlationwith the AB-MP angle. The occlusal plane angle correlatedwith the anteroposterior skeletal relationship with a moreflattened occlusal plane for the Class III patterns. However,the interincisal angle did not show substantively significant



TABLE 2. Extended

Type 5 (n 5 41) Type 6 (n 5 75) Type 7 (n 5 7) Type 8 (n 5 26) Type 9 (n 5 18)

82.8 6 2.13.5 6 1.1

83.2 6 2.174.3 6 2.1

87.9 6 2.61.3 6 1.2

87.3 6 2.679.8 6 2.9

77.5 6 2.86.0 6 1.4

79.2 6 3.270.8 6 3.5

86.2 6 1.82.1 6 1.1

85.9 6 2.479.1 6 2.1

91.2 6 2.80.2 6 0.9

88.9 6 2.782.7 6 2.6

20.2 6 1.65.7 6 1.64.0 6 1.1

25.8 6 1.7

23.1 6 1.91.7 6 2.11.2 6 1.5

22.6 6 1.7

4.2 6 2.410.0 6 2.66.8 6 1.6

29.7 6 1.4

21.0 6 2.33.1 6 1.52.1 6 1.0

24.1 6 1.6

23.2 6 1.721.0 6 2.320.7 6 1.621.4 6 1.4

21.4 6 1.830.3 6 2.521.8 6 2.675.4 6 1.975.8 6 3.0

22.9 6 2.330.4 6 2.522.3 6 2.169.8 6 2.069.2 6 3.5

17.8 6 3.226.2 6 3.319.6 6 3.483.0 6 1.584.7 6 2.0

16.5 6 2.923.3 6 2.916.2 6 2.877.6 6 2.477.3 6 3.2

17.7 6 2.224.0 6 1.515.4 6 2.873.4 6 1.471.1 6 2.9

390.3 6 2.5115.4 6 4.870.3 6 2.655.1 6 2.061.6 6 1.8

390.4 6 2.5117.1 6 4.669.6 6 2.555.7 6 1.760.3 6 2.2

386.2 6 3.3111.8 6 5.573.8 6 3.353.9 6 1.462.2 6 1.7

383.3 6 2.9110.6 6 5.376.5 6 3.055.5 6 1.359.7 6 2.2

384.0 6 2.5110.5 6 5.675.4 6 2.456.0 6 1.657.7 6 2.9

TABLE 3. Extended

Type 5 Type 6 Type 7 Type 8 Type 9

104.4 6 4.9112.9 6 5.1113.3 6 4.850.5 6 5.559.0 6 5.3

107.8 6 5.5115.9 6 5.2115.3 6 4.756.5 6 5.064.6 6 4.9

101.2 6 4.3107.9 6 2.4109.6 6 3.750.5 6 4.857.2 6 5.5

108.9 6 5.3116.0 6 5.6115.7 6 5.956.1 6 5.563.2 6 5.1

108.4 6 4.8116.9 6 6.1114.6 6 6.561.9 6 6.370.5 6 5.9

29.1 6 4.799.2 6 5.4

126.1 6 8.5

25.2 6 4.693.1 6 4.6

128.7 6 7.6

29.4 6 4.8103.3 6 3.1129.3 6 6.7

26.2 6 5.2100.6 6 5.5127.2 6 9.3

21.1 6 4.694.1 6 4.6

133.6 6 8.7

91.1 6 3.987.3 6 4.183.2 6 4.676.4 6 6.0

91.5 6 3.688.7 6 3.684.6 6 3.677.2 6 5.8

91.7 6 2.988.6 6 3.185.0 6 4.478.2 6 5.1

93.1 6 3.989.2 6 4.586.5 6 4.879.8 6 6.6

93.0 6 4.089.6 6 3.884.6 6 4.478.4 6 6.9

85.5 6 4.284.3 6 3.882.9 6 3.587.0 6 4.9

81.7 6 3.781.1 6 4.180.6 6 3.984.5 6 4.5

88.0 6 2.786.7 6 1.984.0 6 2.588.8 6 2.5

88.8 6 3.887.3 6 3.586.2 6 4.688.8 6 5.2

85.1 6 3.784.5 6 3.283.6 6 3.889.4 6 4.4

15.9 6 3.17.4 6 2.97.0 6 2.9

14.4 6 2.790.2 6 2.1

14.1 6 3.26.0 6 3.06.6 6 2.4

16.3 6 2.693.9 6 2.3

14.0 6 3.17.3 6 0.95.6 6 2.4

12.2 6 3.284.8 6 2.8

12.1 6 3.15.0 6 2.95.3 6 2.4

11.2 6 3.491.2 6 2.9

11.4 6 4.22.9 6 4.05.2 6 3.5

12.5 6 2.794.1 6 2.2

correlation with the anteroposterior and vertical skeletalvariables (Table 4).

Stepwise variable selection and discriminantanalysis to determine each skeletal typing

The stepwise variable selection generated a four-variablemodel (AB-MP, SN-AB, PMA, and ANB) that produced

the most efficient separation between the nine types. Be-cause Wilks lambda was used as the entry criterion, thevariables that produced the smallest lambda for each stepwere selected.

There were four functions with nonzero eigenvalues. Inparticular, the first and second eigenvalues were more than100 times larger than the eigenvalue for the third and fourth



TABLE 4. Correlation Coefficient Between Several Skeletal Variables and Dentoalveolar Measurements

SN-AB ANB PMA AB-MP

Upper and lower incisor

U1 to SNU1 to FHU1 to PP

.615**

.479**

.328**

2.318**2.358**2.264**

2.164**2.119*2.259**

2.173**2.241**2.195**

L1 to SNL1 to FHL1 to NBL1 to MPInterincisal angle

.756**

.638**2.455**2.300**

.189**

2.551**2.588**

.583**

.390**2.230**

2.310**2.274**

.195**2.346**2.140**

2.178**2.234**

.192**

.674**2.025 NS

Premolar and molar

U4 to PPU5 to PPU6 to PPU7 to PP

.279**

.302**

.314**

.265**

2.229**2.232**2.194**2.108 NS

2.519**2.473**2.469**2.403**

.065 NS

.031 NS

.082 NS

.135*L4 to MPL5 to MPL6 to MPL7 to MP

2.084 NS2.033 NS

.052 NS

.035 NS

.137*

.121*

.032 NS2.029 NS

2.490**2.518**2.531**2.403**

.612**

.598**

.539**

.425**

Occlusal plane

SN-OPFH-OPPP-OP

2.733**2.575**2.380**

.304**

.378**

.255**

.390**

.359**

.636**

2.106 NS2.030 NS2.127*

* P , .05; ** P , .01; NS, not significant.

FIGURE 3. Classification diagram with frequency of each skeletaltype.

FIGURE 4. The superimposition of profilogram was done by super-imposing on the SN plane and registering on the Sella.

function, and only the first two functions were found to besignificant. A higher canonical correlation coefficient wasfound for the first two functions, which indicated that thereis a strong relationship between the types and the first twodiscriminant functions.

The standardized canonical discriminant function coef-ficient showed that the AB-MP (0.858) and SN-AB (0.714)exerted the highest contribution on the function 1 and 2,respectively. Fisher linear combination of the discriminat-ing variables, which maximizes the group differences whileminimizing the variation within the groups, was calculatedfor the computerized classification algorithm. The sum ofthe correct predictions resulted in an 87.8% accuracy.

DISCUSSION

The results confirmed that there was a wide range ofnormal variations not only in the skeletal relationship butalso in the dentoalveolar compensation within the normalocclusion samples. It was interesting that the skeletal pat-terns of the normal occlusion samples were similar to thoseof the malocclusion patients with skeletal imbalances. In-deed, this study was inspired by the research of Casko andSheperd.1 They reported that a naturally occurring ANBangle ranged from 23.0 to 8.0, which was identical to ourdata. Table 1, as compared with the that of Casko and She-



FIGURE 5. Polygonal charts that were produced by computerized cephalometric analysis combined with nine skeletal typings.

perd,1 showed a broader range in the skeletal variables,whereas it showed a less diverse range in the dentoalveolarmeasurements.

As a result of the principal component analysis, althoughthe ODI and AB-MP have been regarded as the verticalskeletal variables, they also are estimated to have an an-teroposterior component. This was inferred from the factthat the factor loading of the ODI was higher in antero-posterior factor than in vertical factor. Consequently, theODI decreased according to the anteroposterior relationshipin the same vertical skeletal pattern. These findings are con-sistent with the report by Yang et al,11 where the ODI de-creased with increases in the APDI in a normal overbitesample, which reflects the characteristics of the AB-MP.

The Class I skeletal pattern and the normodivergent pat-tern were the most frequent skeletal patterns among the threetypes of anteroposterior and vertical skeletal relationships.However, Type 6 had the largest number of members. UnlikeCaucasians, there is a higher prevalence (more than 20%) ofClass III malocclusion in Asians.12 Therefore, it appears thatour society will more easily accept the Class III tendencywith normodivergent skeletal pattern as ‘‘normal,’’ althoughit is difficult to generalize. Types 3 and 7 were the leastdominant types among the normal occlusion samples. On theother hand, it is known to be the predominant type in themalocclusion group.13 This suggests that a Class III hyper-divergent pattern and a Class II hypodivergent pattern aredifficult to constitute a normal occlusion.



The results of this study and the studies of the earlierauthors1,14–16 suggest that a proclined upper incisor was cor-related with a forward mandibular position and a retro-clined upper incisor with a backward mandibular position.A vertical skeletal pattern also correlated with the moreretroclined incisors to form a normal occlusion, which is awell-known phenomenon of the dentoalveolar compensa-tory mechanism. However, the interincisal angle showed arelatively narrow range and a poor correlation with the an-teroposterior or vertical skeletal variables. Therefore, therelatively inert feature of the interincisal angle suggestedthe importance of the incisal relationship to form a normalocclusion with an esthetic facial profile.

Both the anteroposterior and vertical positions of themandible influenced the upper premolar and molar axes tothe palatal plane angle. The lower premolar and molar axesto the mandibular plane angle were mainly influenced bythe vertical mandibular position. This observation pertainsto the research reported by Chang and Moon,17 who re-ported the relationship between the tooth axis and the ver-tical skeletal pattern. The variation in the occlusal planeangle was also notable, with the Class II patterns showinga steep occlusal plane and a Class III pattern showing a flatocclusal plane. This result is similar to the finding of Si-mons18 that a Class II molar relationship changes into aClass I molar relationship as the occlusal plane rotatesdownward-backward and the report of Jacobson19 that aClass III changes into a Class I as the occlusal plane rotatesupward-forward.

The main advantage of discriminant analysis was thecompatibility with computerized cephalometrics. The poly-gonal chart for each skeletal type, which is composed ofseveral skeletal and dentoalveolar measurements, could becreated using Excel VBA (Microsoft) (Figure 5) that islinked to the classification algorithm. Therefore, it is pos-sible to classify the individual malocclusion patients im-mediately after digitizing their cephalograms automatically.Initially, this computerized approach needs a mathematicalcomputation of the cephalometric variables. On a clinicalbasis, inclusion of fewer variables in the discriminant anal-ysis results in a greater possibility of application. By re-ducing the cephalometric variables and incorporating theminto a discriminating computation, this study attempted toidentify a more prospective method to distinguish the spe-cific skeletal type from an individual skeletal pattern.

The contribution of the individual variables to the dis-criminant function could be explained by the standardizedcanonical discriminant function coefficients. However, thesimilarity between a single variable and a discriminantfunction, namely, the structure coefficient, showed thatfunction 1 is closely related to AB-MP (0.975). The Bjorksum (0.744) was the most dominant variable on function 2.Therefore, function 1 could refer to the ODI dimension ifthe contribution of palatal plane angle is small. Function 2could be called the Bjork sum dimension. Therefore, the

most similar variables to the statistically significant two dis-criminant functions determine the skeletal morphology interms of a quadrangle, which is composed of four angularpoints, Sella, Gonion, and two points of contact formed bythe SN-AB and AB-MP.

The proportion of cases correctly classified indicates theaccuracy of this procedure and indirectly confirms the de-gree of group separation. Because there were nine types inthis study, the prior probability for these nine groups wasonly 11.1%. Therefore, the hit ratio of 87.8% is a consid-erable improvement, although it is far from perfect. Morefavorably, there were no misclassified cases in Types 1, 3,7, and 9, which represent the skeletal extremes.

The skeletal patterns are the relationships that we havevery little control of in orthodontic treatment except by theuse of surgical techniques. A differential diagnosis is oftendifficult in these cases that fall on the borderline betweena nonsurgical orthodontic correction and a surgical ortho-dontic treatment modality. Therefore, the ranges in skeletalvariation will provide an additional basis for the skeletalrelationships that can allow normal occlusions by a dentaladjustment.

Although this study investigated the dentoalveolar com-pensation according to the anteroposterior and vertical skel-etal relationships, more studies aimed at evaluating thetransverse skeletal relationship in the three-dimensionalplane are recommended. In addition, it will be necessary toincrease the number of samples and examine the sex dif-ferences to establish the concrete limitations of dentoalve-olar compensation as well as the appropriate diagnostic cri-teria for individual craniofacial relationship.

CONCLUSIONS

An assessment of the individual skeletal variability usingthe mean cephalometric measurements is unreasonable be-cause there is a wide range of normal variations in the skel-etal relationship that can form a normal occlusion. The in-dividual treatment goal for each specific skeletal type can beestablished if the characteristics of dentoalveolar compen-sation of the extreme skeletal types are carefully studied andthe dentoalveolar measurements are examined. In this aspect,a skeletal type classification linked with computerized ceph-alometric analysis will be useful in clinical practice.

ACKNOWLEDGMENT

This study was supported by a grant 03-2001-090 from the SeoulNational University Hospital Research Fund.

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