Effects of Early Activator Treatment in Patients with Class II Malocclusion Evaluated by Thin-Plate Spline Analysis

In the last few decades, many investigations have been carried out to evaluate the effects of activator therapy on dental and skeletal structures in patients with Class II malocclusion. In this context, one of the main questions has been whether the growth of the craniofacial skeleton, specifically the location and size of the mandible, can be influenced by orthodontic therapy during a comparatively short period of craniofacial development.1 

For a detailed review of the literature concerning therapeutic growth modifications in Class II malocclusions, the reader is referred to the surveys of Tulloch et al,2 Bishara and Ziaja,3 Aelbers and Dermaut,1 and Barton and Cook.4 Bishara and Ziaja3 concluded that there is still no consensus about the mechanisms involved here, especially the degree to which dento-alveolar or skeletal components can be influenced.

In nearly all existing cephalometric studies dealing with the mechanisms of Class II correction, angles, linear measurements, or ratios have been used to assess craniofacial changes. Moyers and Bookstein5 clearly expounded the fundamental limitations of this common cephalometric approach. As any measured angle is a function of 3 points of 2 coordinates each (in all, 6 degrees of freedom), growth movements of all 3 points can affect the change of an angle. Thus, interpretation with respect to the underlying growth processes is difficult since different patterns of deformation may result in similar angular changes.6 

In the subsequent years, novel morphometric approaches, such as tensor analysis, finite-element methods, and shape- coordinate techniques6–10 as well as the Euclidean distance matrix analysis,11 provided methodical progress in morphometrics. Nevertheless, tensor analysis and related techniques require, as a rule, an a priori construction of triangles on the basis of landmarks, which leads to considerable arbitrariness and impedes the recognition of global growth effects such as uniform shape changes.12,13 

In 1989, Bookstein14 introduced a new morphometric method for shape comparisons, namely the thin-plate spline analysis. The basic principle of this technique is modeling biological shape differences between 2 configurations of landmarks as a continuous deformation analogous to the bending of an infinitely thin metal plate.14 In the field of dentofacial orthopedics, this new morphometric approach has been gaining increasing importance. For instance, Pae et al15 used thin-plate spline analysis to investigate the shape characteristics of the face and tongue in obstructive sleep apnea. Singh et al16,17 examined the role of the cranial base and the morphological differences of mandibular shape in Class III malocclusions by means of thin-plate spline analysis. In addition, the characteristics of soft-tissue profiles in Class III patients were investigated using this morphometric approach.18,19 Baccetti et al20 also demonstrated the usefulness of thin-plate spline analysis in a longitudinal cephalometric comparison between a treated and an untreated Class III patient group.

The aim of this longitudinal cephalometric study was to evaluate dentofacial shape changes in Class II patients induced by early activator treatment. In addition, the potential of the new morphometric approach of thin-plate spline analysis was to be used to assess dental as well as skeletal craniofacial changes, particularly against the background that the mechanisms of correcting a Class II malocclusion and skeletal discrepancy are still controversial.

In this longitudinal cephalometric study, male patients with a skeletal Class II malrelationship and increased overjet who had been treated at the University of Heidelberg were compared with a group of untreated male subjects of the Belfast Growth Study.21 Both the treated patients and the untreated controls had to meet the following inclusion criteria:

1. ANB angle ≥ 5° in the initial lateral cephalogram,

2. overjet ≥ 5 mm in the initial lateral cephalogram,

3. first cephalogram taken at age 9.5 ± 1 years,

4. second cephalogram taken at age 11.5 ± 1 years,

5. time interval between the 2 cephalograms of 2 ± 1 years,

The activator group consisted of 20 patients who were treated without extraction of teeth with a modified Andresen–Häupl-type activator in the respective 2-year interval, as shown in Figure 1. The construction bite was taken with teeth in neutralocclusion and with an approximate vertical increase in the molar region of about 4–5 mm. Patients were excluded from the study if there was a hint of a repeated insufficient compliance during activator treatment, especially concerning the recommendation to wear the appliance about 14 hours a day.

Fifteen male untreated probands from the Belfast Growth Study, the material for which had been collected by Professor C. P. Adams at the Queens University of Belfast, served as a control group. The ages of the treated and untreated children when the lateral cephalograms were taken were, for the activator group, t₁ = 9.48 ± 0.69 years and t₂ = 11.68 ±0.46 years, and for the control group, t₁ = 9.50 ± 0.37 years and t_s = 11.32 ± 0.38 years.

For the cephalometric analysis, the landmarks shown in Figure 2 were identified. All the cephalograms had been traced first, and subsequently the coordinates of the landmarks were registered by means of a digitizing tablet (Calcomp). Replicate tracings of 10 lateral cephalograms were used for evaluating the measurement error according to Dahlberg's formula.22 The combined error of the method concerning landmark location and accuracy of measurement was calculated for the x-coordinate (parallel to sella-nasion line) and for the y-coordinate (vertical to sella-nasion line) of each of the 15 landmarks. No landmark displayed an error larger than 1 mm. The landmarks sella and gnathion showed the smallest errors, being within the range 0.2–0.3 mm both in the x and y directions. The landmarks upper incisor apex and lower incisor apex displayed the largest errors, being around 0.8 mm in either the x or y directions.

The coordinates of the landmarks provided the data base for the computation of the thin-plate splines and the conventional cephalometric analysis.

For a geometrical and graphical description of the shape changes occurring in the activator and the control groups, a thin-plate spline analysis12,14 was performed. Thin-plate spline analysis is an interpolation technique inspired by the theory of the bending of an infinitely thin metal plate. It mathematically realizes the idea that, when a metal plate is fixed at certain heights vertical to the plane, it tends toward a form of minimal energy, ie, the form of minimal curvature.

In the cephalometric context, changes between 2 configurations of landmarks can be depicted by a pair of splines, with one spline representing the change in the x-coordinate of each landmark and the other one the change in the y- coordinate.14 The combination of these 2 splines yields a transformation of the plane that maps each landmark of the initial configuration to the respective homologue landmark of the final configuration. In this way, biological shape change is modeled as a deformation and the spatial changes between the 2 sets of landmarks can be visualized by means of transformation grids.14 

The deformation between 2 sets of landmarks can be decomposed into an affine part and an affine-free part. The affine part corresponds to a tilting or lifting, not a bending of the metal plate, thus not affecting bending energy.14 

The nonaffine part describes the local deformations and can be decomposed into a series of progressively localized components.

The initial landmark configuration defines a series of n − 3 orthogonal functions, the so-called principal warps, where n is the number of landmarks. They are calculated from the eigenvectors of the bending energy matrix and describe the change of shape at different geometric scales.

The principal warps serve as a basis for the shape changes between the 2 landmark configurations. The nonaffine part of the deformation can be projected on the principal warps, and the resulting decomposition of shape change leads to the partial warps, which are again deformations in the plane. Hence, each partial warp is the contribution of the corresponding principal warp to the total spline. The coordinates in the basis of the principal warps are called partial-warp scores and are appropriate for a statistical testing of the shape changes between the 2 groups.23 

In this study, the thin-plate splines were calculated using the program tpspline.24 For both the activator and the control group at t₁ and t₂, a scaled (with the so-called centroid size12 as scaling factor) average configuration of landmarks was computed based on the generalized least-squares orthogonal Procrustes analysis.25 In the next step, the shape changes between t₁ and t₂ were displayed for both groups by means of thin-plate splines. For a description of the whole craniofacial shape changes, a set of 13 cephalometric landmarks (cf Figure 1) was used to show dental as well as skeletal shape changes (the landmarks pogonion and menton were omitted in the spline depiction due to the redundancy of data). In addition, a second spline based on the 7 landmarks nasion, sella, gonion, gnathion, articulare and anterior and posterior nasal spines was used to show up the skeletal shape changes in both groups without the depiction of any dental component.

In addition to the visual inspection of the shape changes in both groups by means of thin-plate splines, a multivariate statistical analysis based on the matrices of partial-warp scores23 was used to test for differences in the shape changes from t₁ to t₂ in both groups. On the basis of net Procrustes distance, a matched version of a permutation test24 was used for the comparison of the differences in the partial-warp scores representing the shape change (including the uniform term) in each group.

For better comparability with the results of former cephalometric studies, thin-plate spline analysis was supplemented by a conventional cephalometric analysis. The variables shown in Tables 1 and 2 were used. First, a comparison at baseline (t₁) was performed between both groups using Wilcoxon's rank sum test. A nonparametric test was used in order to perform conservative hypothesis testing. In a second step, the same procedure was used to test for statistical significance concerning the changes between the 2 groups.

The splines shown in Figure 3 visualize, both for the activator and the control group, the whole craniofacial shape changes between the average configurations at 9.5 and 11.5 years. In the activator group, a pronounced reduction of overjet is visualized by a horizontal compression of the grid between the edges of the upper and lower incisors (Figure 3a). In addition, the pattern of grid deformation points to a marked retrusion of the upper incisors as well as an additional protrusion of the lower incisors, thus suggesting a considerable dento-alveolar contribution to overjet correction. In Figure 3a, the retrusion of the upper incisors is suggestively visualized by means of the bending of the grid in the region of the upper incisor edges. In addition, an anteriorly directed stretching of the grid is visible in the mandibular region, which is also shown—more clearly—in the 7-landmark configuration (Figure 4a). In the activator group, the pattern of grid deformation points out comparatively slight shape changes in the vertical dimension in contrast with a marked antero-posterior compression or stretching.

By contrast, in the thin-plate spline analysis of the control group (Figure 3a), the grid lines deviate only marginally from straight lines, indicating merely slight local, nonaffine deformations especially affecting the region between the A point and the anterior nasal spine. The total spline is affected by a homogeneous shear rather than by pronounced localized shape changes (Figure 4a). In the multivariate statistical analysis, the shape changes based on the configuration of 13 landmarks differ significantly at P < .001.

In the spline depiction of the configuration of the 7 landmarks (Figure 4a,b), the differences concerning the mere skeletal reactions are visualized more distinctly since the rather strong tippings of the incisors, which markedly influence the grid transformation, are omitted. In the activator group (Figure 4a), an anteriorly directed bending of the grid lines can be seen in the intermaxillary region, which points to an intermaxillary positional change, particularly a slight advancement of the mandible. This pattern of shape change differs significantly at P < .001 from the control group (Figure 4b), where the shape changes are dominated by a uniform component rather than by more localized intermaxillary shape changes.

As a first step, the 2 groups were compared at baseline (9.5 years). Table 1 shows the results of the Wilcoxon's rank sum test. Statistically significant differences between the 2 groups were found in the extent of overjet and in the inclination of the upper incisors. At the beginning of treatment in the activator group, the upper incisors are more proclined and the overjet is significantly larger (mean 9.5 mm) than in the control group (mean 7.1 mm). No significant differences were found in the sagittal and vertical relationships (P > .05).

As a next step, it was tested whether the changes of the cephalometric variables in both groups differ significantly. Table 2 shows the results of Wilcoxon's rank sum test. In the activator group, a pronounced uprighting of the proclined incisors is evident, in contrast with the control group, where this effect is negligible. Moreover, the lower incisors procline more in the activator group than in the control group. Here, the strong grid deformations in the dento-alveolar area shown in the spline analysis correspond to the changes in the angular measurements. In this way, the conventional cephalometric analysis underlines the strong dento-alveolar component in overjet correction.

As far as the changes in sagittal relationships are concerned, an ANB reduction of 1.38° is found in the activator group, which differs significantly (P < .05) from the decrease of 0.54° in the control group. Similarly, the increase in the SNB angle is significantly larger (P < .001) in the activator group than in the control group. In the case of the SNA angle, the changes between the 2 groups do not differ significantly. Moreover, no significant differences were found between the 2 groups concerning vertical relationships. This corresponds to the observation that, in both groups, the grid lines in the respective spline transformations show next to no change in the vertical dimension.

In the present cephalometric study, a thin-plate spline analysis and a conventional cephalometric analysis were undertaken to visualize the dental and skeletal changes during activator treatment at an early stage of development, usually well before the pubertal growth spurt commenced. As Barton and Cook4 pointed out, functional appliances are becoming increasingly important in a 2-phase therapy concept for Class II malrelationships. After a period of correcting sagittal discrepancies with a functional appliance, the remaining treatment needs (eg, a further reduction of overjet or tooth alignment) are carried out by means of fixed appliances. Hence, it seemed clinically interesting to evaluate the effectiveness of activator treatment during the first phase of Class II therapy in the mixed dentition using extended morphometric methods.

In the interpretation of the results, ie, determining to what degree the changes observed can be attributed to treatment and not to growth processes, the small sample sizes, especially of the control group, and the retrospective study design must be taken into account. As Tulloch et al2 pointed out, in retrospective studies, the treatment group usually consists of patients who were considered to respond favorably to the treatment intended. This source of bias due to nonrandomized treatment assignment may introduce dissimilarities between the samples and, in addition, impair the comparability of studies of different investigators.2 

In the present study, the use of thin-plate spline analysis seemed to be valuable because the depiction of shape changes by transformation grids following the spirit of Thompson26 allows for a suggestive visualization of the underlying patterns of shape change. In addition, this morphometric technique makes possible a separation of size differences and uniform shape changes from those changes describing inhomogeneous nonaffine or local deformations.12,13 As Rohlf and Marcus13 pointed out, it must be stressed that the use of splines does not imply that biological tissues behave like metal sheets but that spline functions are able to depict the differences in 2 configurations of landmarks as a continuous deformation.

In the present study, the activator turned out to be a valuable tool for the reduction of overjet and, to a certain degree, for a moderation of sagittal discrepancies. The grid deformation of thin-plate spline analysis suggests a comparatively strong dento-alveolar component that is marked by a retroclination of the upper incisors and a moderate proclination of the lower incisors. However, the angular change of the lower incisor inclination compared with the untreated controls does not reach statistical significance. Both the spline analysis and the conventional cephalometric analysis point to an additional skeletal mechanism altering the relative mandibular-maxillary position, which is mainly characterized by a skeletal mandibular reaction during the 2-year interval.

Bishara and Ziaja3 summarized the results of numerous studies on different modes of Class II activator action, inferring that probably a combination of orthodontic (60– 70%) and orthopedic (30–40%) movements is responsible for treatment success—a conclusion that is roughly in keeping with the results of the morphometric approach in the present study. However, predicting individually the extent of a possible skeletal response to activator treatment is impeded by the wide dentofacial morphological variation within the Class II division 1 malocclusion. Those patients show their own unique individual growth patterns,27 which again results in a wide individual variation in treatment response.28 

Within the limits of this retrospective study, the following conclusions can be drawn:

1. Thin-plate spline analysis seems to provide a valuable supplement for conventional angular analyses because the complex patterns of shape change are visualized suggestively by means of grid deformations, thus opening up a wide field of possible applications in cephalometrics.

2. In male subjects exhibiting a Class II skeletal discrepancy, the Andresen–Häupl-type activator seems to be a suitable tool for overjet reduction and a moderation of sagittal discrepancies. Thin-plate spline analysis supports the hypothesis that dento-alveolar mechanisms seem to play an important role in this correction but also suggests a relative mandibulo-maxillary displacement, mainly a mandibular advancement. In future, additional studies with a prospective study design are called for, also with respect to the long-term stability of the dental and skeletal changes.

We wish to express our gratitude to Professor Fred L. Bookstein, University of Michigan, for his advice on statistical testing and related matters. In addition, we want to thank Professor Andrew Richardson, Professor Emeritus of the Queens University of Belfast, for permitting access to the material of the Belfast Growth Study.