Subjects
Forty-eight patients with posterior crossbite were consecutively selected. The patients were treated at the Department of Orthodontics, University of Siena (Italy) and were selected according to the following criteria:
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Early or mid mixed dentition stage
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Cervical vertebral stage 1 through 3 (CVS methods 1–3) [13]
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Unilateral posterior crossbite
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Angle Class I or Class II malocclusion
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Underwent RPE banded (Haas type) therapy (RPE, treated group) or to be submitted to RPE banded (Haas type) therapy (control group)
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No subsequent comprehensive orthodontic treatment implemented in either the maxilla or the mandible
The exclusion criteria for selection were as follows:
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Angle Class III malocclusion
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Previous orthodontic treatment
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Hypodontia in any quadrant excluding third molars
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Hormonal imbalances
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TMJ signs and/or symptoms
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Craniofacial abnormalities (e.g., cleft lip and palate)
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Arthritis
The RPE group consisted of 18 girls and 15 boys; average age at T1 was 8.8 years (sd 1.1 years). The control group consisted of 8 girls and 7 boys; average age at T1 was 8.3 (sd 1.2 years). These patients were matched for age, sex, and skeletal maturity with the RPE groups but did not receive any orthodontic treatment, and their dental casts were taken a second time after approximately 12 months.
In the RPE group, the records included pre-treatment (T1, immediately before the cementation of the appliance) and post-treatment dental casts (T2, after the appliance was removed and replaced by a removal plate, 15 months interval on average).
All palatal expanders (tooth-tissue supported, Haas type) were manufactured, cemented, and activated according to the following protocol: at initial activation, the appliances received two quarter turns (0.4 mm). Thereafter, the appliance was activated one quarter turn in the morning and one quarter turn in the evening. The subjects were seen at weekly intervals for approximately 3 weeks. When the desired overcorrection for each patient was achieved, the appliance was stabilized. Expansion was considered adequate when the occlusal aspect of the maxillary lingual cusp of upper first molars contacted the occlusal aspect of the facial cusp of the mandibular lower first molars. The expander was in situ during the expansion and stabilization period for a mean time of 7 months (range 5–9 months). After the removal of the expander, a loose, removable acrylic plate was placed within 48 h. Generally, each patient wore the acrylic plate for a variable amount of time (minimum 8 h/day).
Cast analysis
The sample consisted of 96 cast models which were scanned by a 3SHAPE D640 SCANNER (3Shape, Copenhagen, DK) 3D digital model (*.stl) were thus obtained.
3D digital model processing and cast analysis were accomplished with a multi-step procedure. The first step consisted of landmark digitization on each model through VAM application version 2.8.3 (Canfield Scientific Inc., Fairfield-NJ, USA). The protocol developed by Huanca Ghislanzoni et al. [14] was followed. Dental landmarks were taken on screen on the scanned mandibular dental casts by the principal investigator (A.U.). When either the deciduous teeth were missing or the permanent teeth were not fully erupted, the measurements for that variable were eliminated. For each patient, a total of 15 mandibular landmarks were digitized (two landmarks each for the first molars, canines, and central incisors; plus 3 landmarks as reference plane). Two landmarks per teeth allowed to trace the facial axis of the clinical crown (FACC) of the first permanent molars, deciduous canines, and permanent central incisors, at T1 and at T2, respectively. Mandibular reference planes were computed between the incisive papilla and the intersections of lingual sulci of the first permanent molars with the gingival margin (Fig. 1a, b). Lingual measurements for mandibular intermolar width were obtained at the point of the intersection of the lingual groove with the cervical gingival margin, according to McDougall et al. [15] The occlusal intermolar width was measured as the distance between the mesiobuccal cusp tips of the first permanent molars bilaterally; the intercanine width was the distance between cusp tips bilaterally. Mandibular first molar, canine, and incisor angulations were calculated as the angle of projection of the FACC on the reference plane.
The whole set of landmarks was exported into a .txt file. The .txt file was imported into an Excel matrix, and x, y, and z coordinates were divided into three columns.
The 3D point set was re-orientated putting the reference lingual plane parallel to the X plane. Finally, the data set was analyzed with a custom excel procedure for 3D arch analysis. The process was repeated for each mandibular arch cast (Fig. 1a, b).
Method error
Intraclass correlation coefficients were calculated to compare within-subjects variability to between-subjects variability; all values were larger than 0.93. Standard deviations between repeated measurements were found to be in the range of 0.08 to 0.17 mm for linear measurements and in the range of 0.5° to 1.9° for angular measurements. Overall, the method error was considered negligible.
Statistical analysis
Descriptive statistics were computed for all analyzed variables: occlusal and lingual intermolar distances; intercanine distance; left and right molar, canine, and central incisor angulation values; and molar, canine, and incisors mean (right and left average angulation values).
Shapiro-Wilk’s test showed that data were normally distributed, and parametric statistics were applied. Patient (RPE group) data were compared with the data collected from the untreated group using Student’s t tests. Probabilities of less than 0.05 were accepted as significant in all statistical analyses. Sample size was calculated a priori to obtain a statistical power of the study greater than 0.85 at an alpha of 0.05, using the mean values and standard deviations of mandibular molar expansion after RPE therapy found by Lima et al. [7].
The effects size (ES) coefficient was also calculated [16]. The ES coefficient is the ratio of the difference between the recordings of two different groups (within the same recording condition) or two recording conditions (within the same group) divided by the within-subject standard deviation (sd), and it was calculated as follows:
$$ \mathrm{E}\mathrm{S}=\frac{m_{\mathrm{a}}-{m}_{\mathrm{b}}}{\surd \left[\left(\mathrm{s}{{\mathrm{d}}_{\mathrm{a}}}^2\mathrm{x}\kern0.5em {n}_{\mathrm{a}}+\mathrm{s}{{\mathrm{d}}_{\mathrm{b}}}^2\kern0.5em \mathrm{x}\kern0.5em {n}_{\mathrm{b}}\right)/\mathrm{s}{\mathrm{d}}_{\mathrm{a}}+\mathrm{s}{\mathrm{d}}_{\mathrm{b}}\right]} $$
where, m
a and m
b are the means for the generic group⁄recording conditions A and B; sda and sdb are the corresponding standard deviations; n
a and n
b are the corresponding sample sizes. For Cohen’s d, an effect size of 0.2 to 0.3 might be a “small” effect; around 0.5, a “medium” effect; and 0.8 to infinity, a “large” effect.
A linear regression model was employed to assess correlations between treatment duration (months of therapy, MOT) and mandibular dental angulation values.