Sample Selection

Functional Regulator of Fränkel (FR-2) sample

This group was comprised of 22 school children (11 boys and 11 girls) with an initial mean age of nine years and was treated at the orthodontic graduate program at Bauru Dental School, University of São Paulo. All patients presented with Class II, division 1 malocclusion with at least an end-to-end Class II molar relationship, minimal or no crowding and were treated for a mean period of 17 months (Table 1). Patients were instructed to wear the appliances four hours a day in the first week, eight hours a day in the second week, 12 hours a day in the third week, and 24 hours a day thereafter (with the exception of eating and playing certain sports) until the end of treatment. These 22 cases were a subsample of a larger parent sample of 50 cases. They represented the best results obtained in terms of occlusal relationship and compliance in wearing the appliance. The FR-2 appliances worn by patients were fabricated according to the principles of McNamara and Huge.29 On average, the FR-2 advanced the mandible forward 5 mm and opened the bite 5 mm from the intercuspal position. When the overjet was larger than 7 mm, the mandible was advanced gradually in 2–3 mm increments following Falck and Fränkel.30 Lateral cephalometric radiographs in habitual occlusion were taken initially and after 17 months of treatment. During this period no appliance was used other than the FR-2.

TABLE 1. Descriptive Statistics: Sample Description*

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Cephalometric analysis

The 88 lateral cephalograms were traced on acetate paper by one investigator (MRA) and verified by a second author (JFCH). Any disparities in landmark position were resolved by mutual agreement. All cephalograms were digitized (Houston Instruments DT-11 digitizer, Austin, Texas). The data were stored on a computer and analyzed with the Dentofacial Planner 7.0 (Dentofacial Planner Software Inc, Toronto, Canada), which corrected the 6% image magnification factor of the radiographs present in the control group and the initial experimental group. The radiographs of the experimental group after 17 months were exposed on a different X-ray machine having a magnification of 9.2%, which was also corrected.

Statistical analysis

All statistical analyses were performed with the aid of a commercial statistical package (SIGMA STAT^TM, Statistical Software for Windows, Version 1.0, SPSS Inc, Chicago, Ill). The main purpose of this study was to conduct between-group comparisons of the various skeletal and dentoalveolar changes occurring during treatment. Because the length of treatment varied between groups, a direct comparison of the cephalometric changes would be difficult to interpret. Thus, a patient treated for 18 months, for example, would be expected to grow more than a patient treated for 12 months, even if treated identically. Therefore, in order to conduct direct and meaningful comparisons, all cephalometric increments of the FR-2 group were adjusted to the time interval of the control sample, namely 13 months, according to the protocols of Toth and McNamara.17

Error of the Method

In order to assess the error of localizing the reference points and the digitizing procedure, 20 randomly selected tracings were retraced and remeasured by the same examiner (MRA) about one month after the initial data was recorded. The casual errors were assessed using Dahlberg's formula and systematic errors were ascertained using paired t-tests similar to the recommendations of Houston.31 The casual error of the method (Dahlberg formula) did not exceed 0.77 ° or 0.56 mm. Paired t-tests demonstrated statistically significant differences only in five measurements (SNB, SN-GoMe, IMPA, B-FHp, and S-Go) for systematic errors.

Descriptive Statistics

Means and standard deviations for the two groups isolated according to gender and then grouped together, were calculated for all cephalometric variables at T₁ and T₂. In addition, mean differences and standard deviations were determined, as well as mean differences and standard deviations calculated for the adjusted 13-month interval for both groups, as mentioned previously.

Inferential Statistics

Sexual dimorphism in the two groups was evaluated using paired t-tests. The starting forms of the two groups (T₁) were compared using a Student t-test (Table 2). Likewise the changes over the treatment/observation period were compared between the two groups using the same analysis (Table 3).

TABLE 2. Comparison of Starting Forms^a

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TABLE 3. Mean Changes (T₁ to T₂) Standardized to 13 Months^a

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Sexual Dimorphism

The results demonstrated that sexual dimorphism was not present at T₁ for both groups evaluated. Only one statistically significant difference was observed between boys and girls for Fränkel group with a linear measurement Co-A. Once this was determined, the two sexes were grouped and evaluated together.

Comparison of Starting Forms —T₁ (Table 2)

The equivalence of starting form was examined by comparing pretreatment cephalometric values between the groups (Table 2). In general, there was an equivalence of the initial cephalometric measures between both groups; however, in the control group, the maxilla and the upper incisors were more retruded than in the FR-2 group. Growth direction was predominantly vertical in both groups, while the palatal plane was rotated more clockwise in the control group.

Analysis of Treatment Effects

The average interval varied between the pretreatment and post-treatment cephalograms between the groups (13 months in the control group and 17 months in the FR-2 group). Statistical comparisons of the adjusted changes for the two groups are shown in Table 3.

Changes in the Mandibular Skeletal Component

Although the present samples are relatively small (N = 22), the efforts to minimize technical error conferred an ability to detect differences in the 1- to 2-mm range. As shown in Table 3, the linear measurements Go-Gn, Ar-Gn, and Co-Gn increased significantly more in the FR-2 group. These differences are significant both statistically and clinically. In the experimental group the Articulare-to-gnathion and condylion-to-gnathion length measures increased 3.1 mm and 3.9 mm, respectively, during a standardized 13-month period. Other authors1417–202527 have reported an effective increase in total mandibular length during FR-2 treatment of 1.8 mm,18 3.3 mm,20 3.6 mm,19 3.8 mm,25 4.0 mm,27 4.4 mm,14 and 4.6 mm17 per year. The variation among studies is probably related to differences in sampling criteria, methods used to measure mandibular growth, and differences in protocols (appliance design, starting age, and construction bite).20 The finding of an increase in mandibular length after functional appliance treatment is in agreement with the results of a number of investigations involving the FR-2 appliance,141719,202627 although others1525 did not report such increase. The finding of a small increase in the length from condylion to gnathion in the treated sample of Fränkel patients compared to the controls (only 0.7 mm) was somewhat surprising, but it is in agreement with McNamara et al,27 who found that there was less difference between treated and control individuals who underwent FR therapy at a younger age than those treated in the circumpubertal growth period. This increase in effective mandibular length should discriminate between ramus height and corpus length. No statistical difference was observed in the ramus height (Ar-Go) between the FR-2 and control groups. Mandibular body length (Go-Gn), however, seemed to contribute more to the effective mandibular length, consistent with other investigators.202636 However, it does not agree with McNamara et al,2728 who found no evidence of statistically significant increase in mandibular body length in patients treated with an FR-2.

Fränkel therapy did not produce statistically significant increases in the SNB angle compared to the control group. Others reported similar observations in patients treated with the same appliance.1518253337,38 It should be noted, however, that the SNB angle might increase or decrease depending on incisor position changes. Indeed, the proclination of the lower incisors observed in FR-2 treatment could be a factor that contributed to a negative interpretation of mandibular protrusion.

There was no evidence of a morphologic change in the mandible, as measured by the angle ArGoMe, between Fränkel and the control groups, according to the results of the current study. Schulhof and Engel26 also demonstrated that this mandibular morphology did not change.

Changes in Maxillomandibular Skeletal Relationship

The maxillomandibular relationship showed marked improvement in the experimental group compared to the control group (Table 3), with a statistically significant difference. Improvement in basal bone relations resulted from small changes in maxillary anterior growth and by the increase in anterior growth of the mandible in the Fränkel group. Similar findings were found with Bionator/Activator therapy by several authors3639–47 and also for the FR-2.17192025272848 Changes of the ANB angle in the treated group were a result of several small, but cumulative effects upon dentofacial structures associated with the normal craniofacial growth. These changes were not sufficient to correct or to improve the skeletal Class II relationship in the untreated group.

Vertical Component

Several authors111427284344 have reported that functional appliances do not change the craniofacial growth pattern, although facial height has been noted to increase.* Although a small increase in lower anterior facial height (ANS to menton) was observed in both groups, it might be stressed that there were no statistically significant differences between the control and FR-2 groups. This result is in agreement with the results published by Righellis14 and Nelson et al,49 who found no evidence of increased facial height during FR-2 treatment. This finding, however, is not supported by Toth and McNamara,17 who found a lower anterior facial height increase of 1.0 mm more in FR-2 patients than in untreated subjects. Posterior facial height (S-Go) increased similarly in both groups, showing no statistical significant difference.

As a result of the observed interplay of both the anterior and the posterior facial heights, the mandibular plane was not significantly affected. The equal increases in both anterior and posterior vertical facial dimensions resulted in maintenance of the mandibular plane angle (SNGoMe). Similar conclusions were reached by Toth and McNamara.17 This observation is probably related to the posterior bite-opening that occurred when the mandible was brought forward in the experimental group and the molars were encouraged to erupt. There was a greater tendency for a clockwise rotation of the palatal plane angle (SNPP) during Fränkel therapy compared to the control group, which experienced a counter-clockwise rotation.

Maxillomandibular Dentoalveolar Components

Many other investigators have shown that the Fränkel appliance, and almost all Functional appliances, produce lingual tipping of the upper incisors (−4.9°, Table 3).4045–4750–58 In the control group, the upper incisors remained stable (0.0°) relative to the palatal plane. This effect was expected since the FR-2 labial bow may come in contact with the incisors during sleeping hours causing them to retract.1131517–1925–28

In the control group, the lower incisors remained stable (0.5°) relative to the Nasion-B line. However, some proclination of the lower incisors was produced by FR-2 treatment (2.7°) relative to the same line. This effect is probably consequent to the resultant mesial force on the lower incisors induced by the protrusion of the mandible. This finding corroborates other studies for the Fränkel appliance1315181925–28 and contradicts the result published by Toth and McNamara,17 who found that FR-2 therapy generally produced dentoalveolar changes that were not statistically different from those that occur during normal growth. Indeed, Wieslander and Lagerström,39 and Bolmgren and Moshiri,50 all reported that the treatment with Activator appliance does not produce an alteration in the position on the lower incisors. Our study indicates that care should be taken when the FR-2 is used in patients with proclined mandibular incisors because this condition could become more pronounced.

In the untreated group, the upper first molars extruded 0.3 mm relative to palatal plane, which was not statistically different from the FR-2 group (0.4 mm). Toth and McNamara17 reported similar findings in which significant differences in the vertical eruption of the maxillary molars were not evident in comparison to controls or to patients treated with the FR-2 appliance of Fränkel.

The vertical eruption of the lower first molars (6-GoMe) was greater in the FR-2 group (1.1 mm) in comparison with controls (0.3 mm). This extrusive effect of the lower molars with the Fränkel appliance was usually seen by others investigators.1425272832

In the FR-2 group, the advancement of the mandible contributes to opening the bite in the posterior region. This allows a greater vertical increase of the lower posterior teeth, and helps correct the overbite, the Class II molar relationship and a deep curve of Spee. McNamara et al27 described this theory as the differential eruption principle of Harvold.