INTRODUCTION

F Graf von Spee, who used skulls with abraded teeth to define a line of occlusion, first described the curve of Spee in 1890. That line lies on a cylinder that is tangent to the anterior border of the condyle, the occlusal surface of the second molar, and the incisal edges of the mandibular incisors. Spee located the center of this cylinder in the midorbital plane so that it had a radius of 6.5 to 7.0 cm.1 However, clinically the distal marginal ridges of the posterior teeth in the arch and the incisal edges of the central incisors determine the curve of Spee.2

The functional significance of the curvature has not been completely understood.3 However, it has been suggested that the curve of Spee has a biomechanical function during food processing by increasing the crush-shear ratio between the posterior teeth and the efficiency of occlusal forces during mastication.45

Recently, the curve of Spee and/or leveling of this curve has been related to incisor overbite,6–9 lower arch circumference,710–13 lower incisor proclination,1013–17 and craniofacial morphology.381819 A deep curve of Spee is usually associated with an increased overbite. Orthodontic correction of the overbite often involves leveling the curve of Spee by anterior intrusion, posterior extrusion, or a combination of these actions. The process of proclining the lower incisor has been used in some cases to decrease the relative vertical overlap of the lower incisors by the upper incisors.16

Leveling of the curve of Spee represents a routine procedure in orthodontic practice. Clinicians have been concerned for some time with the degree of reduction in arch circumference that accompanies leveling of the curve of Spee because they believe that this leads to incisor protrusion.20

On the other hand, Andrews21 stated that there is a natural tendency for the curve of Spee to deepen with time because the lower jaw's growth downward and forward sometimes is faster and continues longer than that of the upper jaw. This causes the lower anterior teeth, which are confined by the upper anterior teeth and lips, to be forced back and up, resulting in crowded lower anterior teeth and/ or a deeper overbite and deeper curve of Spee.

These findings suggested that the curve of Spee might be related to the position and inclination of the upper and lower incisors, lower arch crowding, overjet and overbite. Thus, the determination of this relationship may be useful to assess the feasibility of leveling the curve of Spee by orthodontic treatment. Therefore, this study aimed to:

• Examine differences in the position and inclination of the upper and lower incisors, overjet, overbite, and lower arch crowding in subjects with different depths of curve of Spee.

• Determine the relationships between the depth of curve of Spee and these variables.

MATERIALS AND METHODS

The material comprised pretreatment lateral cephalometric head films and dental casts from a sample of 137 adolescent subjects, 61 boys and 76 girls, aged 13 to 16 years. All the subjects were healthy with complete dentition, with no history of orthodontic treatment, with no severe craniofacial disorders, such as cleft palate, with no absent maxillary and mandibular permanent teeth, except for the third molars. The sample investigated consisted of a group with skeletal and dental Class I and slight Class II or Class III malocclusions (ANB angle between 1 and 5 degrees). Severe Class II and Class III malocclusions were not included.

The subjects were divided into three groups according to the depth of curve of Spee. The three Spee groups were classified as follows:

• Normal Spee group: the depth of curve of Spee was >2 mm but ≤4 mm;

• Flat Spee group: the depth of curve of Spee was ≤2 mm;

• Deep Spee group: the depth of the curve of Spee was >4 mm.

In this classification, the results of a preliminary study regarding the amount of curve of Spee in subjects with normal occlusion and acceptable facial profile were used.

The normal Spee group consisted of 20 boys and 33 girls, the flat Spee group 20 boys and 23 girls, and the deep Spee group 21 boys and 23 girls. The depth of curve of Spee was measured as the perpendicular distance between the deepest cusp tip and a flat plane that was laid on top of the mandibular dental cast, touching the incisal edges of the central incisors and the distal cusp tips of the most posterior teeth in the lower arch16 (Figure 1). The measurement was made on the right and left side of the dental arch, and the mean value of these two measurements was used as the depth of curve of Spee.

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The cephalometric radiographs were exposed using standard methods. A single investigator performed the cephalometric tracings on tracing paper. The cephalometric and dental cast measurements used in the study are described in Figures 2 and 3, respectively. Nine angular and six linear measurements were performed on lateral cephalometric head films. The measurements of the depth of curve of Spee, overjet, overbite, and anterior lower crowding were made on dental casts.

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RESULTS

The means and SDs of the chronological ages and the depth of curve of Spee for each group and the F values are presented in Table 1. No statistically significant differences between the chronological age among the Spee groups were found, whereas there were statistically significant differences in Spee measurements among the groups (P < .001).

TABLE 1. Sample Description and F Values Found By Analysis of Variance

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Descriptive statistics, including the mean and SD values, were determined for each Spee group and are shown in Table 2. The mean and SD values of the upper incisor–NA (mm) measurement were calculated separately for each sex because this measurement demonstrated significant sex differences.

TABLE 2. The Mean and Standard Deviation Values for Each Spee Groups and Sex^a

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The results of the analysis of variance are shown in Table 3. These results indicated that the overjet and overbite measurements were significantly different among the Spee groups. Upper incisor–NA distances demonstrated a significant sex difference. In addition, overbite showed significant interaction effects between sex and Spee groups.

TABLE 3. The Results of Analysis of Variance

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The results of the LSD post hoc test are shown in Table 4. According to these results, overjet showed significant differences between the normal and flat Spee groups and between the flat and deep Spee groups. However, overbite demonstrated significant differences between the normal and deep Spee groups and between the flat and deep Spee groups.

TABLE 4. The Results of the Least Significant Difference Test^a

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Pearson's correlation coefficients were calculated between the depth of curve of Spee and other variables (Table 5). The largest correlation coefficient was present between the depth of curve of Spee and overbite (mm, + .42). In addition, statistically significant correlations were found between the depth of curve of Spee and overjet (mm, + .30), lower incisor–NPg (mm, − .23), lower incisor–NB (mm, − .20), and lower incisor–NB (angle, −0.17) measurements.

TABLE 5. Correlation Coefficients Between the Depth of Curve of Spee and Other Variables

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The results of the multiple linear regression analysis are presented in Table 6. After the stepwise elimination, the overbite (mm) alone explained 17.3% of the total variance of the depth of curve of Spee. Age and all other variables showed no significant correlation with the amount of the curvature in the stepwise model. Therefore, these variables were excluded from the regression model. In the enter method, age and all other variables used in the study were included into the regression model. All of them explained only 28.7% of the total variance of the curve of Spee. Among the parameters tested in the enter method, only overbite (mm), lower incisor–NB (°), lower incisor–NPg (°), and lower incisor–NB (mm) correlated significantly with the depth of curve of Spee. These four variables explained only 22.6% of the total variance of the depth of curve of Spee. The depth of curve Spee was not significantly influenced by the age of the subjects investigated.

TABLE 6. The Results of Multiple Regression Analysis^a

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DISCUSSION

Although leveling the curve of Spee is an everyday occurrence in orthodontic practices, little research has been dedicated to the examination of the relationship between the depth of the curve of Spee and dentofacial structures. In the present study, therefore, the relationships between the depth of the curve of Spee and the positions of upper and lower incisors, overjet, overbite, and anterior lower crowding were investigated.

The data obtained in this study indicated that there were no significant differences in the positions and inclinations of the lower and upper incisors and anterior lower crowding among the subjects with different depths of curve of Spee. However, statistically significant differences in the overbite and overjet were found between different Spee groups. The statistically significant correlation coefficients between the depth of curve of Spee and overbite (+ .42) and overjet (+ .30) confirmed this result. The overjet and overbite measurements in the deep Spee group were significantly larger than in the normal and flat Spee groups. The most pronounced differences for overjet and overbite were found between the flat and deep Spee groups.

The results of multiple regression analysis suggested that overbite explained the variation of the depth of curve of Spee to the largest extent. The amount of overbite alone explained 17.3% of the total variance of the curve of Spee in the stepwise regression model. The position of the lower incisor (ie, lower incisor–NB and lower incisor–NPg angles and lower incisor–NB distance) also influenced the curve of Spee. However, the variance explained by these measurements was very limited, amounting for only about 5% of the total variance. In the enter regression model, overbite and these three measurements explained only 22.6% of the total variance of the curvature.

Balridge10 reported that decreasing the depth of curve of Spee leads to an increase in arch circumference and that often the lower incisors will be proclined in direct response to this increase. Braun and Hnat23 found an association between lower incisor proclination and reduction in lower intercanine width. However, other clinicians have attributed this incisor proclination to the treatment mechanics used for orthodontic treatment.

Woods15 showed that incisor flaring might be primarily related to the mechanics of leveling the curve of Spee and not necessarily because of the differential in arch circumference. Braun et al7 confirmed this in a study with computer-supported technology. AlQabandi et al16 reported that there is no significant correlation between reduction in the depth of curve of Spee and proclination of the lower incisor. However, they found lower incisor proclination significantly correlated with reduction in intercanine width and reduction of crowding. In the present study, the positions and inclinations of the upper and lower incisors and anterior lower crowding showed no statistically significant differences between Spee groups, whereas significant differences in the measurements of overjet and overbite were found between the groups. In addition, significant correlation coefficients were found between the depth of curve of Spee and overjet and overbite. Furthermore, some significant correlation coefficients were found between the depth of curve of Spee and position of lower incisors. However, the correlations were relatively low (Table 5).

It was interesting to observe the statistically significant changes in the overjet and overbite among the Spee groups without significant changes in the positions and axial inclinations of the upper and lower incisors. These findings support the results of Braun et al7 and Woods,17 who have shown that the reduction of the curve of Spee and overbite may be achieved without flaring of the incisors by using appropriate mechanics.

Trauten et al6 and Orthlieb8 reported that there was a negative curve of Spee in open-bite cases, whereas a deep curve of Spee in deep-bite cases was found. On the other hand, Farella et al3 found that the curve of Spee is more marked in short-face subjects and less marked in long-face subjects. Similarly, we found that the overbite in the deep Spee group was significantly larger than in the normal and flat Spee groups.

Dusek17 and Çelik19 concluded that there were significant correlations between the curve of Spee and the positions and inclinations of lower incisors. Dusek17 also found that the more protrusively the lower incisor is positioned, the less marked the depth of curve of Spee is. In our study, the positions and inclinations of lower and upper incisors showed no statistically significant differences among the Spee groups. However, there were some significant, but low, correlations between the depth of curve of Spee and the position of lower incisors.

CONCLUSIONS

Overall, the findings of the present study suggested that the positions and inclinations of the lower and upper incisors and anterior lower crowding were not affected by the variation of the depth of curve of Spee, whereas the amount of overjet and overbite was significantly influenced by the variation of the curve. The overjet and overbite in the deep Spee group were significantly larger than in the normal and flat Spee groups. The correlation coefficients obtained from the study confirmed these results. The largest correlation was found between the depth of curve of Spee and overbite. The overbite had a positive correlation with the depth of curve of Spee.

The multiple regression analysis showed that the curve of Spee was significantly influenced by the overbite. The overbite alone explained about 17% of the total variance of the curve of Spee in the stepwise regression model. The amount of the curvature was weakly influenced by the positions and inclinations of the lower and upper incisors and anterior lower crowding.

Only a minor part of the variance of the curve of Spee could be explained by the cephalometric variables describing incisor positions and chronological age. Most of the variation of the curve of Spee remains unexplained by these variables and is probably explained better by other factors.