INTRODUCTION

Class II malocclusion is the most common orthodontic problem in the white Caucasian population.1 Traditionally, occlusal and craniofacial characteristics of growing subjects with Class II molar relationship have been studied in the sagittal and vertical plane.2–10 But Class II malocclusion is a complex clinical entity that entails a combination of different three-dimensional dental and skeletal components.

Interestingly, studies on the transverse relationship of the maxilla to the mandible in Class II subjects in the mixed dentition have been limited to the analysis of the arch widths measured on the dental casts. Fröhlich11 compared the intercanine and intermolar widths of the upper and lower arches of 51 children with Class II malocclusion with the data collected by Moorrees12 on children with normal occlusion. He found that the absolute arch widths of Class II children did not differ appreciably from those of children with normal occlusion.

On the other hand, Tollaro et al13 have shown that an underlying negative posterior transverse interarch discrepancy (PTID) (ie, a narrow maxillary arch when compared with the mandibular arch) exists in dental arches with Class II malocclusion (−3.4 mm on average) and seemingly normal buccal relationships. This underlying transverse discrepancy can be unmasked clinically by having the patient posture the mandible in an anterior position so that the canines are positioned in a Class I relationship.14

In 1997 Baccetti et al15 demonstrated that a negative PTID is recorded consistently in Class II subjects in the deciduous dentition and that the negative PTID is maintained or worsens in the transition to the mixed dentition. In a recent study Varrela16 confirmed that children with distal occlusion have narrower intermolar and intercanine distance from the age of 3 years when compared with normal subjects and that this difference increases with age. All these studies have been performed on dental casts, which allows for an evaluation of the width of the dental arches regardless of the transverse skeletal dimensions of both jaws. To our knowledge no data are available in the literature on the evaluation of transverse dentoskeletal characteristics of Class II subjects in the mixed dentition by analysis of posteroanterior (PA) cephalograms.

Conventional cephalometrics based on linear and angular measurements has shown an increasing number of limitations17 along with the proposal and implementation of new biometric analyses of landmark data (eg, elliptic Fourier analysis, finite element analysis, tensor and shape-coordinate analysis).18–24 Major advantages of these still evolving methods include the separate evaluation of shape (or shape change) and size, an optimal superimposition of landmarks for analysis of shape change in complex skeletal configurations without the use of conventional reference lines, and an explanation of the morphological changes by viewing them using transformation grids.

A recent morphometric approach to the comparison of configurations of landmarks in two or more specimens is known as thin-plate spline (TPS) analysis, developed by Bookstein.25 In TPS analysis the differences in the two configurations of landmarks are expressed as a continuous deformation by using regression functions in which homologous points are matched between forms to minimize the bending energy.26 Bending energy can be defined as the energy required to bend an infinitely thin metal plate over one set of landmarks so that the height over each landmark is equal to the coordinates of the homologous point in the other form. TPS analysis enables the construction of transformation grids that capture the shape differences and are available for visual interpretation. For a more detailed review of the theoretical bases, calculation procedures, assumptions, and limitations of TPS morphometrics, see Bookstein,25–29 Rohlf and Marcus,30 Rohlf et al,31 and Dryden and Mardia.32 In recent times TPS analysis has been gaining increasing importance in orthodontic literature for investigating modifications in shape related both to facial growth and to treatment.33–41

The aim of the present study was to evaluate the dentoskeletal features of subjects with Class II malocclusion in the mixed dentition by means of a morphometric analysis (TPS analysis) applied to PA cephalograms.

MATERIALS AND METHODS

A sample of 49 subjects (24 males, 25 females; mean age 7 years, 9 ± 5 months) was selected and classified as Class II Division 1 malocclusion group according to the following inclusionary criteria: bilateral Class II molar relationship in centric occlusion, bilateral Class II deciduous/permanent canine relationship in centric occlusion, and buccal inclination of upper incisors. As a control group 50 subjects (17 boys, 33 girls; mean age 8 years, 4 ± 3 months) with bilateral molar and deciduous/permanent canine Class I relationship in centric occlusion, and without anterior or lateral cross-bites, were selected. All subjects were taken from the files of the Department of Orthodontics, University of Florence before any orthodontic intervention. Subjects of both groups were in the mixed dentition, did not show missing teeth (due to aplasia, trauma, or deep caries), had no history of orthodontic treatment, and did not present with craniofacial syndromes.

PA cephalograms were of good quality for all the subjects in both groups. All cephalograms were taken with the Frankfurt plane parallel to the floor, with the head front and the nose tip in contact with the radiographic cassette. PA cephalograms were hand-traced with a 0.5-mm lead on a 0.003-mm matte acetate tracing paper. All tracings were performed by one investigator and were subsequently verified by another investigator. The traced PA cephalograms were analyzed using a digitizing tablet (Numonics, Landsdale, Pennsylvania) and a digitizing software (Viewbox ver. 2.6). All the cephalograms were converted to a 10% enlargement to standardize the magnification data. A description of the cephalometric landmarks used in this study is given in Figure 1.

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To analyze the combined error of landmark location and digitization, 25 randomly selected PA cephalograms were retraced and redigitized. The standard error deviation for each dimension was calculated from the double determinations using Dahlberg's formula.42 The mean value for the method error was 0.55 ± 0.23 mm.

In the present study the TPS program43 computed the orthogonal least-squares Procrustes average configuration of landmarks both in the Class II group and in the control group. Following this method every object's coordinates are translated, rotated, and scaled iteratively until the least-squared fit of all configurations cannot be improved any more.44 Therefore, all configurations are scaled to an equivalent size (centroid size = 1) and registered with respect to one another.

The average craniofacial configurations were subjected to TPS analysis to compare the differences in shape between the two groups. Statistical analysis of shape differences was performed by means of permutation tests with 1000 random permutations on Wilk's lambda statistics.43

RESULTS

TPS analysis applied to PA cephalograms revealed significant shape differences in the craniofacial configuration of subjects with Class II malocclusion when compared with subjects with normal occlusion in the mixed dentition (P < .0001) (Figure 2). Significant shape differences were localized in the maxillary region and in the nasal region. The greatest deformation could be described as a contraction of the maxilla at both the skeletal and the dental levels, ie, a bilateral compression in the horizontal plane at point Mx and at point Um bilaterally. The contraction on the transverse plane was associated with an extension of the maxilla in the vertical plane due to a downward displacement of point Mx bilaterally. A slight contraction of the base of the nose was also evident. No significant difference in shape could be detected in the orbital region and in the mandible when comparing Class II subjects with Class I controls, with the exception of a slight upward dislocation of point Me.

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DISCUSSION

Studies on transverse dimension in subjects with Class II malocclusion in the mixed dentition have been usually performed on dental casts measuring dental arch characteristics, regardless of the transverse skeletal dimensions of both jaws. Most authors agree that transverse interarch discrepancy due a narrow maxillary arch can be considered a typical feature of Class II malocclusion from the early developmental phases.13–16

Interestingly, no data are available on both dental and skeletal aspects of transverse dimension in Class II malocclusion using PA cephalograms. The aim of the present study was to evaluate the dentoskeletal features of Class II malocclusion in the transverse plane with the help of a morphometric analysis (TPS analysis) applied to PA cephalograms. Major advantages of TPS analysis applied to cephalometric landmark configurations with respect to both conventional cephalometrics and previous morphometric techniques (eg, shape-coordinate analysis) include (1) an optimal superimposition of landmarks for analysis of shape change in complex skeletal configurations without the use of any conventional reference line, and (2) a visual interpretation of the craniofacial shape differences independent of size variations using transformation grids.26

The results of the present study showed that subjects with Class II malocclusion exhibited significant shape differences in craniofacial configuration in the frontal plane when compared with subjects with normal occlusion; these differences mainly consisted of a contraction of the maxilla at both the skeletal and the dentoalveolar levels and a narrowing of the base of the nose. The reduction in skeletal width of the maxilla was associated with an increase in vertical height due to a downward displacement of point Mx bilaterally. No significant difference in shape could be detected in the mandible on the transverse plane when comparing Class II subjects with Class I controls.

The findings of the current study have obvious clinical implications. Because transverse deficiency in the maxilla at both the skeletal and the dentoalveolar levels appears to be a typical feature of Class II malocclusion in the mixed dentition phase, an initial goal of treatment might be early correction of the transverse occlusal relationships by rapid maxillary expansion (RME). Early treatment with RME is further supported by the findings of a recent investigation,38 which showed that patients treated before the pubertal growth spurt exhibit significant and more effective long-term changes at the skeletal level in both maxillary and circummaxillary structures. When RME treatment is performed after the pubertal peak, maxillary adaptations to expansion therapy shift from the skeletal level to the dentoalveolar level. In another study45 that analyzed by means of TPS analysis the long-term effects induced by RME, it was noted that RME is able to normalize the shape of the maxillary complex in subjects presenting with transverse deficiency of the maxilla during the early developmental phases. In particular, RME is able to induce transverse increments of the naso-maxillary complex, which remain stable in the long term.

It is not uncommon, from a clinical point of view, to observe a spontaneous correction of the Class II occlusal relationship in patients with mild to moderate Class II problems treated in the early mixed dentition with RME followed by a palatal stabilization plate, even though no definitive Class II therapy (eg, extra oral traction, functional jaw orthopedics) has been provided.14 McNamara and Brudon14 hypothesize that expansion of the maxillary dentition may create an “endogenous functional appliance” in that lingual cusps of the maxillary dental arch, overexpanded after RME relative to the mandibular dental arch, will encourage the growing patient to posture his or her jaw in a more protrusive position when establishing comfortable contact in centric occlusion, ultimately leading to a stable occlusal change.

If a spontaneous correction is not observed, and in patients with more severe skeletal and muscular problems, a functional jaw orthopedic appliance (eg, bionator, FR-2 of Fränkel, twin block) or extra oral traction can be used after an initial phase of expansion, during or slightly after the onset of the pubertal peak in growth velocity,46 to address the underlying anteroposterior skeletal discrepancy.

CONCLUSIONS

Subjects with Class II malocclusion in the mixed dentition present with significant shape differences in craniofacial configuration in the frontal plane when compared with subjects with normal occlusion. Shape variations in Class II subjects mainly consisted of a contraction of the maxilla at both the skeletal and the dentoalveolar levels and a narrowing of the base of the nose at the maxilla.