Study Design and Data Recording

Before the investigation was begun, approval for this study design was received from the local Institutional Review Board, along with a signed informed consent from the parents of all subjects. A group of 26 healthy white children aged 5.3 ± 0.3 years (4.9–6.1 years) were randomly selected from a local kindergarten. The group consisted of 15 boys and 11 girls in primary dentition without malocclusion and having good general health with no nutritional problems. All subjects had no respiratory, deglutition, or masticatory problems and had undergone no previous or concomitant orthodontic treatments. Impressions of the dental arches were obtained at baseline and at 12, 18, and 30 months follow-up. Study casts were scanned at a distance of 60 cm with a Konica/Minolta Vivid 910 laser scanner (Konica/Minolta Holdings, Tokyo, Japan) using a lens with a focal distance of 25 mm. With this lens, the scanner has a reported accuracy of 0.22 mm.24

Each scan of the study cast was preprocessed to remove unwanted data. To measure palatal surface area and calculate palatal volume, the boundaries of the palate must be defined. The gingival plane and a distal plane were used as boundaries for the palate. The gingival plane was created by connecting the midpoints of the dentogingival junction of all primary teeth. The distal plane was created through two points at the distal surface of the second primary molar perpendicular to the gingival plane (Figure 1). Palatal surface area (Figure 1A) and palatal volume (Figure 1B) were then calculated.

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Sample Size Calculation and Method Error Analysis

A sample size of at least 21 subjects was set to detect an effect size coefficient of 0.830 for either palatal parameter (surface area and volume) between any two paired comparisons of values at 12, 18, and 30 months vs baseline values, with an alpha set at .01 and a power of 0.8.31 The effect size (ES) coefficient is the ratio of the difference between the recordings of two different time points (eg, 12 months vs baseline), divided by the within-subject standard deviation (SD). An effect size of at least 0.8 was considered a reliable index of a large effect,30 that is, clinically relevant growth as detected through current parameters. Method error for each palatal parameter was calculated using interclass correlation coefficients on a random sample of 10 replicate measurements, yielding values of at least 0.95.

Statistical Analysis

The Statistical Package for the Social Sciences (SPSS) software, version 13.0 (SPSS Inc, Chicago, Ill), and Comprehensive Meta-Analysis, version 2 (Biostat, Englewood, NJ), were used to perform the statistical analyses. After the normality of the data was tested with the Shapiro-Wilk test and Q-Q normality plots, and equality of variance among datasets was assessed with a Levene test, nonparametric methods were used for data analysis. Nevertheless, means ± SDs are reported for descriptive purposes. A Friedman test was used to assess the significance of the differences in both palatal parameters over time. A Bonferroni-corrected Wilcoxon test was used for pairwise comparisons.

Moreover, as indices of potential diagnostic accuracy of each palatal parameter, ES coefficients (as Hedges's g coefficients), along with the 95% confidence intervals (CIs), have been calculated at each time point, as previously described.30,32 In this regard, a threshold of 1.0 was used to assess potentially good diagnostic accuracy.33 P < .05 was used for rejection of the null hypothesis.

Changes in the Palatal Vault

In the present study, dimensional changes in the palatal vault at different dental stages were evaluated; 3D digital images of study casts showed a high degree of accuracy when different measurements were performed.26,34 In particular, growth of the maxillary bone was assessed by measuring palatal surface area and palatal volume at each time point; this has previously been demonstrated to be a valid tool for assessing skeletal changes in the maxillary bone before and after treatment.27,28,35

Of note, growth in length may be excluded in this study because the palatal vault was delimitated posteriorly by a plane passing through two points located at the distal aspects of the last erupted primary molars, even if first permanent molars were present in the oral cavity (Figure 1B). Nevertheless, an almost linear increase in palatal surface area was observed during the study, regardless of the dentition stage. However, the transition from primary to mixed dentition, with the permanent incisors erupting more labially, may have led to relocation of the boundaries of the palatal vault, influencing the size of the palatal surface area.

On the other hand, from 12 to 18 months follow-up, when all of the children had completed the transition to the early mixed dentition stage, a slight, although not significant, decrease in palatal volume was observed. Regardless of this slight decrease, maxillary growth in the transverse and vertical direction continued at almost the same rate throughout the observation period.

Although a longer period of follow-up on a larger group is needed to determine the ideal time to start orthopedic treatment36 in the maxillary bone, this study demonstrates that during the primary dentition stage, the transitional dentition stage, and the mixed dentition stage, growth of the maxillary bone was observed as in increase in palatal surface area and volume.

Diagnostic Accuracy of 3D Digital Images of Study Casts

A further goal of the present study was to estimate the diagnostic accuracy of measurements on 3D digital images of study casts as indicators of palatal growth in individual subjects. Indeed, any diagnostic tool has to provide measurement outcomes wherein the responses obtained can be considered accurate (ie, to have high sensitivity and specificity) in terms of the presence/absence of a given condition (eg, growth). In this regard, further difficulty in appraising palatal parameters resides in intragroup variability and the number of subjects examined, on which recorded variability also depends.

Therefore, a critical approach to assessing the relevance of measurements on 3D digital images of study casts as a diagnostic aid in orthodontics has to rely on the high accuracy of measurements, and the fact that measurements recorded at two time points (eg, baseline vs 12 months) have to show notable changes as compared with corresponding variances. Indeed, a low ratio would be responsible for low sensitivity and specificity, revealing poor diagnostic performance of a given tool. A statistical approach to quantifying this ratio (taking into account the sizes of study populations) is provided by calculation of the ES coefficient.30

The present appraisal through the ES coefficients demonstrates that palatal surface area would be more reliable than palatal volume in assessment of growth changes (Table 2). Moreover, evidence that both parameters would be capable of detecting palatal vault changes in a group of children (as shown by ES coefficients greater than 0.6) does not imply that a reliable assessment is provided on an individual basis. Therefore, only the ES coefficient for palatal surface area after 30 months reached the required threshold for this parameter (at least 1.0, considering also the full confidence interval) to reliably describe palatal growth modifications in individual subjects. Although both parameters may be successfully applied in detecting growth changes during research activity, from a clinical standpoint, palatal surface area should be preferred because it is a more reliable parameter, and follow-up activities should occur at least 30 months apart, at least in the age ranges included in the present study.