INTRODUCTION

Although a number of researchers have attempted to identify an arch form unique to a certain ethnic group, most of their studies compare average clinical arch forms derived from normal untreated samples1–5 or research arch forms established by measuring arch dimensions using the incisal edges and cusp tips as landmarks.6–15

From the standpoint of clinical orthodontics, however, not only does the determination of the patient's posttreatment arch form help meet esthetic requirements but it also is vital for long-term occlusal stability. Based on previous studies on relapse, it is generally agreed that postorthodontic occlusal stability is enhanced through maintenance of the original mandibular intercanine width and preservation of the original arch form.16–19

Little,20 based on more than 35 years of research, recommended as a clinical guideline that the patient's pretreatment arch form be used as a guide to posttreatment arch shape. The application of a single ideal arch form to every member of an ethnic group, despite individual variations, may adversely affect posttreatment occlusal stability.^4,21–23

Meanwhile, with the recent advancements in elastic wire materials and preadjusted appliance systems, preformed arch wires have been commercially available and frequently used, mainly in the leveling and alignment stage. However, their superelastic property makes customization of arch form and size difficult. Clinically, it seems more reasonable to have several types of preformed arch wires available and to select the shape that most closely matches the patient's pretreatment arch form according to his or her ethnicity and type of malocclusion.

This study was designed to clarify morphological differences between the Caucasian and Japanese clinical mandibular arches in Class I, Class II, and Class III malocclusions by measuring their arch dimensions. Furthermore, the subjects were regrouped into tapered, ovoid, and square arch forms to determine the frequency distribution of the 3 arch forms for comparison between the ethnic groups in each Angle classification.

MATERIALS AND METHODS

The Caucasian cases included pretreatment mandibular dental models of 60 Class I, 50 Class II, and 50 Class III cases from the University of Southern California, Department of Orthodontics, and a private practice in San Diego, Calif. The Japanese cases included 60 Class I, 50 Class II and 50, Class III cases from Tokyo Dental College, Department of Orthodontics (Table 1). All cases were subjected to the following inclusion criteria: (1) Class I, II, and III malocclusions of a dentoalveolar nature, (2) permanent dentitions with normal tooth size and shape, (3) a 3 mm or less arch length discrepancy, and (4) without restorations extending to contact areas, cusp tips, or incisal edges.

TABLE 1. Sample Characteristics

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The occlusal surfaces of the mandibular models were photocopied with a ruler included for magnification correction. The photocopied images were placed on a digitizer and the most facial portions of 13 proximal contact areas around the arch were digitized (Figure 1). These points are used to estimate corresponding bracket slot locations (clinical bracket point) for each tooth. The proximal contact between the 2 central incisors was used as the origin of the XY coordinate. The original XY coordinate on the digitizer was corrected for magnification and adjusted to establish a new X′Y′ coordinate in such a way that the mean inclination of straight lines connecting the right and left contact points between the first and second premolars and those between the second premolar and first molar became parallel to the original X axis. The perpendicular to a line connecting mesial and distal contact points of each tooth on the coordinate was drawn from the midpoint of the mesiodistal line for the incisors, canines, and premolars and from the mesial third of the line for the molars. The perpendicular was extended labially or buccally to locate a clinical bracket point for each tooth based on the mandibular tooth thickness data of Andrews.24

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The following 4 linear and 2 proportional measurements were taken (Figure 2):

• intercanine width: the distance between the canine clinical bracket points

• intermolar width: the distance between the first molar clinical bracket points

• canine depth: the shortest distance from a line connecting the canine clinical bracket points to the origin between the central incisors

• molar depth: the shortest distance from a line connecting the first molar clinical bracket points to the origin between the central incisors

• canine W/D ratio: the ratio of the intercanine width and the canine depth

• molar W/D ratio: the ratio of the intermolar width and the molar depth.

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In addition, 12 clinical bracket points per patient were printed at full size to select from square, ovoid, and tapered arch forms (OrthoForm, 3M Unitek, Calif) the arch form that best fit the 8 clinical bracket points from first premolar to first premolar (Figure 2).

The means and standard deviations were calculated for each sample. Ethnic differences in arch dimensions were analyzed by unpaired t-tests and differences in frequency distribution of the 3 arch forms were analyzed using the chi-square test. In addition, the subjects were regrouped into the 3 arch form samples to recalculate means and standard deviations for statistical analysis by unpaired t-tests. The levels of significance used were P < .01 (**) and P < .05 (*), where P ≥ .05 was considered not significant (NS).

The measurement error was assessed by statistically analyzing the difference between duplicate measurements taken at least 2 weeks apart on 24 casts selected at random. The measurement errors were generally small (less than 5% of the measured mean value) and within acceptable limits.

RESULTS

Table 2 depicts the arch dimension measurements and results of the t-test for the Caucasian and Japanese Class I, II, and III samples. The Caucasian group showed significantly smaller intercanine width, intermolar width, and molar W/D ratio in all 3 Angle classifications. In addition, the Caucasian group also showed a significantly smaller canine W/D ratio in Class I and Class II malocclusions and significantly larger canine and molar depths in Class I and Class III malocclusions than the Japanese group. When Class I, II, and III malocclusions were combined, statistically significant differences were observed in all the measured variables between the Caucasian and Japanese ethnic groups.

TABLE 2. Comparison of Variables Between Caucasian and Japanese for Class I, II, and III Samples^a

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Table 3 shows the frequency distributions of the 3 arch forms and the results of the chi-square test for the Caucasian and Japanese groups. In the Caucasian Class I sample, ovoid and tapered arch forms were almost equally distributed, accounting for more than 90% of the sample, while the square arch form was rarely seen. In contrast, a square arch form was observed in more than 50% of the Japanese Class I arches, with a combined frequency of square and ovoid arch forms exceeding 90%. Sixty percent of the Caucasian Class II arches displayed a tapered arch form, with most of the remainder showing an ovoid arch form. The frequency of the ovoid arch form among the Japanese Class II arches was over 50%, with square and tapered shapes accounting for approximately 25% each. In the Caucasian Class III sample, the 3 arch forms were almost evenly distributed, with square arch forms found at the highest frequency of over 40%. Almost all the Japanese Class III arches were of either square or ovoid shape, the former accounting for over 50%.

TABLE 3. Comparison of Frequency Distribution of Square, Ovoid, and Tapered Arch Forms Between Caucasian and Japanese^a

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All the Class I, II, and III samples demonstrated statistically significant differences in frequency distribution of the arch shapes between the 2 ethnic groups. When all 3 Angle classifications were combined, nearly 50% of the Caucasian patients exhibited a tapered arch form, with over 80% of them showing either tapered or ovoid arch form. Almost 90% of the Japanese cases demonstrated either square or ovoid arch forms, with both arch forms being almost equal in frequency.

Table 4 depicts the arch dimension measurements and results of t-test obtained by regrouping the subjects into square, ovoid, and tapered arch form samples. Both ethnic groups showed increasing intercanine width, intermolar width, canine W/D ratio, and molar W/D ratio and decreasing canine and molar depths as the mandibular arches changed in form from square to ovoid to tapered. Regardless of arch form, the Caucasian arches tended to be narrower and deeper than the Japanese arches while the canine W/D ratios of the 2 ethnic groups were almost equal. No statistically significant difference was observed in any of the variables measured.

TABLE 4. Comparison of Variables Between Caucasian and Japanese for Square, Ovoid, and Tapered Arch Form Groups^a

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DISCUSSION

In the present study, a clinical bracket point corresponding to a bracket slot point was mathematically estimated from the most facial portion of the proximal contact area for each tooth and used as a landmark for mandibular arch form assessment in Class I, Class II, and Class III malocclusions. Many of the conventional studies included normal untreated samples for determining arch form mathematically1–5 or for characterizing arch form through various measurements using the incisal edges and cusp tips as landmarks.6–15 While this methodology may suffice for anthropological arch form assessment and comparison among different ethnic groups, it may be inappropriate from the standpoint of posttreatment occlusal stability to clinically apply data obtained in these studies to edgewise orthodontic treatment of malocclusions. Not only did our results clarify ethnic differences in arch form between the Caucasian and Japanese but they also seem to offer a great clinical value for modern orthodontics with the frequent use of preformed superelastic arch wires.

Regardless of Angle classification, the Caucasians showed narrower arch forms than those of the Japanese, with approximately 1 mm less mean intercanine width and 1.5 mm less intermolar width. Differences among Angle classifications were observed in arch depth, however, with a statistically significant ethnic difference in canine depth in the Class I sample and in molar depth in the Class III sample.

There was no ethnic difference in the canine W/D ratio in the Class III sample nor in the anterior curvature. These results clearly indicate that Caucasians have narrower and deeper arch forms in both canine and molar regions than Japanese. Aoki et al6 reported similar findings. In their study, the transverse width of the canines and molars was greater for the Japanese than for the Caucasian, while the ratio of the antero-posterior length to the canine width was larger for the Japanese than for the Caucasian.

In general, the dolichocephalic head form is commonly seen among Caucasians, while Japanese are mostly brachycephalic.25 It is conceivable that the racial difference in head form is closely related to arch width and depth, as suggested previously.10,11 Although males have a larger arch size than females, it is generally agreed that there is no gender difference in arch form.7,8,26 For this reason and because of similar male-to-female ratios in both ethnic groups, no analysis was made of gender differences in arch form in this study.

Braun et al27 stated in their report on differences in arch dimensions between Angle classes that the Class II mandibular arches exhibited generalized reduced arch width and depth compared with the Class I arches and that the Class III mandibular arches had smaller arch depth and greater arch widths than the Class I arches. Our results showed that the Class I arches were deeper than the Class II arches, with little difference in arch width between the 2 in either ethnic group, and that Class II arches had the smallest canine and molar W/D ratios, followed by Class I arches and then by Class III arches. The minimal arch width difference observed between the Class I and Class II arches seems to be due to a more tapered anterior curvature of the Class II arches, causing the canines to be positioned more distally where the intercanine width is almost as wide as that of the Class I arches. The Class III arches were the widest and the shallowest. The present study was able to characterize differences in the morphology of mandibular arches by ethnicity and Angle classification through measurement of arch dimensions and comparison of the mean values.

However, the analysis of frequency distribution of the 3 arch forms in the Class I arches revealed the predominance of ovoid and tapered arch forms in the Caucasian population and of square and ovoid arch forms in the Japanese population. The frequency of narrower arch forms was higher in the Caucasian population. Felton et al22 reported that there was little difference between the arch forms of the Class I and Class II malocclusion groups. In the present study, however, the Class II arches in the Caucasian group were associated with a decreased frequency of ovoid arch form and an increased frequency of tapered arch form. The Japanese group showed increased frequencies of ovoid and tapered arch forms and a decreased frequency of square arch form, showing a tendency to shift to narrower arch forms in both ethnic groups.

For the Class III arches, on the other hand, the frequency of square arch form was the highest in both groups, followed by ovoid and then by tapered arch forms. The much smaller, though statistically significant, ethnic difference in frequency distribution of arch forms among the Class III arches seems to indicate less influence of ethnicity on Class III mandibular dentition. This can be explained by the common pathogenesis of Class III malocclusion and the resultant dental compensation by lingual tipping of the mandibular anterior teeth, causing the anterior part of the mandibular arch to flatten.

With all 3 Angle classifications combined, more than 80% of the Caucasian had ovoid and tapered arch forms and more than 80% of the Japanese had ovoid and square arch forms. Considering the difference in incidence of each type of malocclusion between the 2 ethnic groups,25 actual racial differences in frequency distribution of the arch forms may be even more pronounced than those found in this study. That is, the frequency of tapered arch form may further increase with a decreased frequency of square arch form in Caucasian patients while the opposite may be true for Japanese patients.

The comparison of arch dimensions by regrouping the subjects by arch form revealed no statistically significant difference in any of the measured variables between the 2 ethnic groups, though the Caucasians tended to have smaller intercanine widths and larger canine depths than the Japanese. However, the canine W/D ratios of the 2 ethnic groups were almost identical, indicating that anterior curvatures of their dental arches are also very similar. Our results showed that, despite differences in frequency distribution of the arch forms between the Caucasian and the Japanese, there was no racial difference within each arch form type.

CONCLUSION

Engel28 classified human arches into 9 shapes and Raberin et al4 into 5 shapes in an attempt to cope with the great variability in arch form encountered in clinical practice. In the present study, mandibular arches were classified into square, ovoid, and tapered arch forms in order to determine the frequency distribution of the 3 arch forms for each ethnic group. As a result, no statistically significant difference was found between the 2 ethnic groups within each arch form sample, suggesting that it may be acceptable to classify patients' dentitions into the 3 arch forms. Our results made it clear that there is no single arch form unique to any of the Angle classifications or ethnic groups and that it is the frequency of a particular arch form that varies between the ethnic groups or among Angle classifications. This study suggests the usefulness of determining each patient's arch form based on the pretreatment mandibular dental model in order to achieve posttreatment esthetics and occlusal stability.