INTRODUCTION

An understanding of craniofacial growth has been the fundamental basis of orthodontic practice.1 The introduction of the cephalogram2 in 1931 allowed longitudinal studies to be performed on living, growing individuals, and numerous subsequent studies have unveiled many features of complicated craniofacial complex growth.3,4 Establishing references and coordinate systems is of the utmost importance for comparative measurements of longitudinal changes in the face.5

Different anatomic reference systems have been proposed for conventional cephalometry. In fact, it can be stated that the world of orthodontics is now full of orientation and reference planes.6 The best-known of these are based on the Frankfort horizontal plane (FH) and the anterior cranial base (sella to nasion line [SN]). They are widely used despite their individual variability, and several researchers support the alternative use of natural head position based on the reproducibility of this method.7–10

Since the Frankfurt agreement concluded in Germany in 1884, the FH has been generally recognized as the reference plane for the skull and has proved, as such, to be of great value to orthodontists, too. This plane is defined by a line drawn from the lowest point on the inferior orbital margin (orbitale [Or]) to the most superior point of the outline of the external auditory meatus (porion [Po]), directly above its center. Its popular use is due to the belief that it may produce the most acceptable estimation of the true horizontal plane.11

The cranial base reference, SN, was initially mentioned by Renfroe,12 Bjork,13 and Ricketts.14 This line is not only reliable but also biologically meaningful, as it represents the anterior cranial base. Other authors stated that establishing the cranial base's role should be advanced in evaluating problems related to an inadequate relationship between the jaws and the dental arches.15–18

The literature suggests that the angle between these lines is relatively constant at 7°, and the true horizontal axis or constructed FH is obtained by tracing a line in a clockwise direction approximately 7° from SN.19–21 However, this constancy has not yet been sufficiently proven by reliable evidence. In addition, the angle between the FH and SN should remain constant during growth if this approximation is to be used safely in cephalometric analysis.

Until now, longitudinal changes in the angle between FH and SN in growing children have been the subject of few studies. The present study investigates this angle using longitudinal cephalometric data of normal children from 6 to 14 years of age. The aim of the present study was to evaluate the constancy of the relationship between the FH and SN during growth.

MATERIALS AND METHODS

The study subjects were selected from participants in the Korean Dental Growth Study,22,23 which took place from 1995 to 2003. A total of 407 subjects from northern Gyeonggi-do, Korea, participated in this study, and they were all healthy without systemic diseases or developmental anomalies. None had received any treatments interfering with growth, and all had no records of orthodontic treatment before or during the observation period. The parents/guardians of all subjects provided written, informed consent. We examined lateral cephalometric radiographs from 223 children who had full sets of data available (107 males and 116 females) and had been followed annually from 6 to 14 years of age, with the exception of their 10th year, when the study was temporarily suspended due to financial reasons. The Institutional Review Board for the Protection of Human Subjects reviewed and approved the research protocol (S-D2010013).

All radiographs were traced by a single observer in order to eliminate interexaminer variability and were analyzed using Vceph version 6.0 (Osstem, Seoul, Korea). Landmarks, reference planes, and measurements are shown in Figure 1. The following three measurements were taken from cephalometric radiographs of all children at all ages in order to investigate the growth changes occurring with regard to the relationship between FH and SN: 1) the angle between FH and SN (SNFH), 2) the closest distance from the FH to the nasion (NFH), and 3) the closest distance from the FH to the sella (SFH). The difference between the NFH and SFH (Δ) was also calculated. To test the reliability, 10 cephalometric radiographs were randomly selected, measured again, and compared using an intraclass correlation coefficient 1 month after the initial measurements.

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SPSS software (SPSS for Windows, version 12.0; SPSS Inc, Chicago, Ill) was used to calculate the means and standard deviations of all measurements, and independent t-tests were used to determine significant differences between genders according to age. Since the serial measurements were correlated for individual subjects, a mixed-effects regression model (MRM) analysis was performed using the language R.24 The analysis model for the data was written as y_ij  =  μ + β₁sex_i + β₂age_ij + β₃sex_i*age_ij + b_i1 + b_i2*age_ij + e_ij, where μ is the total mean, β₁ is the sex effect, β₂ is the age effect, β₃ is the interaction effect between sex and age, and b_i (i  =  1, 2, …, 223) is the random effect for an individual subject. Significance was set at the .05 level of confidence, but was also assessed at the .01 level of confidence.

RESULTS

Intra-examiner reliability coefficients ranged from .927 to .976. In terms of root mean square values, the random errors of estimation were less than 0.53 mm for linear measurements and 1.02° for angular measurements. None of the variables were significantly different between test and retest measurements.

Descriptive statistics and results of the comparison between sexes are shown in Table 1. The mean values of SNFH showed some fluctuations in both girls and boys according to age; however, the ranges were relatively small (9.26° to 9.74° in girls and 8.45° to 8.95° in boys) considering the size of the random error in measurements. The mean values of NFH and SFH gradually increased according to age, irrespective of sex. The values of Δ also tended to increase, except in 13- and 14-year-old boys (Figure 2). There were statistically significant differences in SNFH values between sexes at 6, 7, 8, 12, 13, and 14 years; in NFH values at 6, 9, 11, 12, 13, and 14 years of age; and in Δ at 8, 12, 13, and 14 years of age. There were statistically significant differences in SFH values in all ages throughout the investigation period (Table 1).

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Table 1. Descriptive Statistics of the Measured Variables According to Age and Sex^a

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MRM analysis revealed that the SNFH showed significant individual differences but did not differ significantly with respect to annual change or sex. In contrast, NFH, SFH, and Δ showed statistically significant differences within individuals as well as in the magnitude of annual changes. In addition, there was a significant interaction between age and sex with regard to SFH and Δ (Table 2). The individual random variability of the initial value was quite large compared with that of the annual increase (Table 3).

Table 2. Summary of Fixed Effects According to the Mixed-Effects Regression Model Analysis^a

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Table 3. Effect of Individual Random Variability From Age 6 Years to the Annual Increases Over Time^a

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DISCUSSION

In the present study, the constancy of the angle between FH and SN during growth was investigated using longitudinal cephalometric data. In a study of macerated skulls,21 it was reported that the angle increased from 5.2° at 2.5–5 years to 8.3° at 18–20 years. However, the nature of the study was not longitudinal, and the results should, therefore, be interpreted accordingly. On the other hand, several studies have indirectly provided the angle between the FH and SN in comparison with other reference planes, such as true vertical or true horizontal.11,25–29 The reported data ranged from 3.7° to 10.01°. The subjects of those investigations were mostly of European decent, with the exception of the study by Madsen et al.,30 whose subjects were from a variety of ethnic backgrounds.

In this regard, the universal use of 7° as a constant angle is hard to justify. The results of the present study support this conclusion in many respects. First, the average SNFH ranged from 9.04° to 9.31°, which is somewhat higher than 7°. However, this difference may also be the result of the subject population composition. Second, there were statistically significant differences between sexes, which may indicate that this angle has some degree of sexual dimorphism. Third and most important, the SNFH showed very large individual differences on MRM analysis.

On the other hand, the SNFH remained relatively constant, although some degree of fluctuation was detected during the observation period. The degree of change was minimal when considering measurement error. In addition, the annual changes in SNFH as a fixed effect showed no statistical significance, in contrast to the NFH, SFH, and Δ. The relatively small random variability in the annual increase in comparison to the initial SNFH was in line with these results. This finding can be interpreted to mean that a gradual increase or growth in NFH and SFH does occur, while SNFH does not change because of its particular spatial orientation. Greiner et al.21 suggested the cause of this constancy is the sagittal growth component between the porion and orbitale. The displacing effect of the spheno-occipital synchondrosis upon the anterior cranial base may be the cause of this sagittal growth.31

The dimensional measurements in this study suggested there might be sexual dimorphism in the relationship between the cranial base and porion and orbitale. First, the absolute dimensions of the average NFH and SFH were larger in boys than in girls. However, the difference, Δ, was larger in girls than in boys. Second, the SFH and Δ showed some difference between sexes, whereas the NFH showed a relatively similar increase in both sexes. In the SFH curves, the increment after age 11 was large in boys in comparison with girls. Therefore, the Δ begins to increase after this age. This interpretation is consistent with the results of MRM analysis. A statistically significant interaction between age and sex was observed as a fixed effect with regard to the SFH and Δ. In other words, annual increments differed between sexes. Unfortunately, cephalometric data were not available for the study subjects after age 14 years, which is the age at take-off or age at peak height velocity, especially in boys.

The results of the present study indicate there is a wide range of angles, although the relative constancy of the SNFH was verified. Well-planned longitudinal studies could provide further insight; however, gathering appropriate sample data is quite difficult. In order to better examine the sexual dimorphism and individual growth patterns in the general population, further studies should be performed with subjects classified in a more sophisticated fashion.

CONCLUSIONS

• The SNFH angle differed considerably among individuals, ranging from 1.82° to 16.59°.

• However, the value remained relatively constant in each individual during the observation period, from 6 to 14 years of age, despite the minute change.

• The NFH and SFH increased during the growth period, and there were statistically significant sexual differences in all the measurements at several ages.

• The annual change in the SFH and Δ showed sexual dimorphism.

• The SNFH angle seems stable over the period of the study, but, due to wide individual variation, use of the population average should be used with caution.