Morphologic changes of the palate after rapid maxillary expansion: A 3-dimensional computed tomography evaluation

Morphologic changes of the palate after rapid maxillary expansion: A 3-dimensional computed tomography evaluation

ORIGINAL ARTICLE Morphologic changes of the palate after rapid maxillary expansion: A 3-dimensional computed tomography evaluation Andriana Phatouros...

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ORIGINAL ARTICLE

Morphologic changes of the palate after rapid maxillary expansion: A 3-dimensional computed tomography evaluation Andriana Phatouros,a and Mithran S. Goonewardeneb Nedlands, Western Australia, Australia Introduction: The purpose of this retrospective study was to estimate the area change of the palate after rapid maxillary expansion (RME) in the early mixed dentition stage by using a 3-dimensional (3D) helical computed tomography (CT) scanning technique. In addition, linear changes in the maxillary arch were evaluated. Methods: The treated sample consisted of 43 children (mean age, 9 years 1 month) treated with a bonded RME appliance. The untreated control group consisted of 7 children (mean age, 9 years 3 months). Pretreatment and posttreatment dental casts were evaluated by using 3D helical CT scanning procedures. The Student t test was used to compare the linear, area, and angular differences between the treatment times. Results: RME produced clinically significant increases in interdental widths across the canines, the deciduous first molars, and the permanent first molars in the maxillary arch. Significant increases in cross-sectional area were observed across the permanent first molars (15.3 mm2). There was marked variability in the buccal tipping of the permanent first molars. Conclusions: Three-dimensional helical CT scanning is an accurate and cost-effective method of assessing dental cast morphologic changes. It can also provide fast and accurate data acquisition and subsequent analysis. (Am J Orthod Dentofacial Orthop 2008; 134:117-24)

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apid maxillary expansion (RME) appliances have been routinely used for management of transverse arch deficiencies. Since the popularization of the RME by Haas,1,2 Krebs,3,4 and Wertz,5 several modifications to the original design have been proposed. The occlusal bonded RME, described by Alpern and Yurosko6 and Sarver and Johnston,7 can be effective in correcting maxillary transverse deficiency, particularly in the mixed dentition. Posterior crossbite in the mixed dentition is a common malocclusion. Its prevalence varies widely from 4%8 to 23%,9 and most posterior crossbites are unilateral and most often functional. RME is effective in correcting maxillary transverse deficiency, thereby correcting posterior crossbites by increasing intermolar width. Many studies have evaluated the effects of RME appliances both skeletally and dentally, by using various techniques ranging from From the Department of Orthodontics, Dental School, University of Western Australia, Nedlands, Western Australia, Australia. a Former resident. b Program director. Reprint requests to: Mithran S. Goonewardene, Department of Orthodontics, Dental School, University of Western Australia, 17 Monash Ave, Nedlands, 6907, Western Australia, Australia; e-mail, [email protected] Submitted, September 2004; revised and accepted, May 2007. 0889-5406/$34.00 Copyright © 2008 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2007.05.015

manual measurement of dental casts10-15 to plane film radiographic techniques with lateral cephalograms5,7,13,16 and posteroanterior cephalograms.14,16-18 Ladner and Muhl,12 using dental casts, measured linear changes indirectly after maxillary arch expansion in adolescents. They used a symmetrograph (previously described by Lebret15) to measure palatal width changes and a palatal depth gauge to report on palatal depth changes. More sophisticated techniques for evaluation of morphological changes in the dentofacial complex have been developed, including digital probes as in the reflex microscope,19 the perceptor,20 and the optocom.21 However, these techniques have not been used to report on the effect on the maxillary arch after RME. More recently, the introduction of the surface laser scanning of plaster casts has made it possible to capture accurate 3D models of plaster casts and make accurate 3D measurements.22-25 Oliveira et al25 described the method as accurate, less time-consuming, and relatively inexpensive, when they demonstrated morphologic changes of the maxilla after RME treatment in adolescents. Geran et al26 used a digital imaging system (Bioscan OPTIMAS Imaging System) to measure dental casts after maxillary expansion in the early mixed dentition. Three-dimensional helical computed tomography 117

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(CT) technology is an alternative method for producing 3D images. It is a noninvasive and time-efficient method. There is also the recent development of 3D digital imaging by merging CT scanning of the craniofacial region with laser scanning of dental plaster casts27 and the development of 3D cone-beam CT models.28-30 These have not been fully used in the evaluation of orthodontic treatment outcomes. The purpose of this study was to use a 3D method to evaluate the morphologic changes of the palate after RME and to compare them with use of the digital calipers. Three-dimensional helical CT technology was selected to estimate the area change of the palate and the standard linear changes observed in the maxillary arch after RME treatment. The objectives were to (1) compare the accuracy of the linear measures of the 3D images to the gold standard of digital caliper measuring, and (2) determine whether area changes after RME treatment can be predicted by pretreatment parameters. MATERIAL AND METHODS

The subjects comprised 43 children (23 girls, 20 boys; mean age, 9 years 1 month) treated with a bonded RME appliance and 7 children (4 girls, 3 boy; mean age, 9 years 3 months) who received no treatment. These groups were not subdivided by sex because there are no reported sexual differences for transverse dentofacial variables in this age group.31 In the RME group, 22 children had posterior crossbite (18 unilateral, 4 bilateral). Crossbite was defined as involving at least 1 tooth in the arch. Twenty-one children had some maxillary constriction (dental compensation for a transverse discrepancy), without posterior crossbite. The subjects in the control group had some maxillary arch constriction, with 2 subjects having posterior unilateral crossbite. Each patient in the RME group was treated with a Hyrax bonded expansion appliance. This consisted of a midpalatal jackscrew placed as close to the roof of the palate as possible without impinging on the palatal soft tissue.16 Four rigid steel wires radiating outward from the jackscrew were soldered to wire loops placed over the occlusal surfaces. The acrylic portion covered the occlusal surfaces and extended over one third of the surfaces lingually and buccally of the maxillary deciduous first and second molars and the permanent first molars. The parents were instructed to activate the expansion appliance for a full turn, twice a day (2 mm a day) for the first 3 days and then daily for a full turn (1 mm a day) for the next 7 days. Activation then continued twice a week until the buccal segments were overcorrected by half a cusp in the transverse dimension.16

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Fig 1. Occlusal view of volume-rendered image of CT scanned plaster casts and multi-planar reconstructed 2D image with a cross-sectional slice across the permanent first molars.

This final activation period averaged 9 weeks (range, 6-12 weeks). A stabilization period followed with the appliance left in place for a mean period of 13 weeks (range, 8-17 weeks). Thus, average treatment time was 22 weeks. Dental casts of the treatment group subjects were obtained from alginate impressions before expansion (T1) and again 2 or 3 days after appliance removal to allow settling of any gingival edema (T2). The dental casts of the 7 untreated subjects were collected for evaluation. The control sample matched the treated sample as to mean age at T1 (9 years 3 months) and mean duration of observation period (25 weeks). There was no need to duplicate the dental casts because the scanning procedure was noninvasive. Reference markers were constructed by using the radiopaque properties of gutta percha. Spheres of gutta percha (1 mm) were placed at the junction of the lingual groove with the gingival margin for the permanent first molar, the most lingual points at the gingival margin of the deciduous first molar, and the canine. The maxillary dental casts were scanned in a 16-slice CT scanner (Toshiba Aquilion 16, Tustin, Calif). Six sets of pretreatment and posttreatment dental casts were scanned simultaneously. The scanned plaster casts (initial data set) were reconstructed into volumerendered images (Fig 1); this is specific to the modality of CT scanning. The volume-rendered images then produced 2-dimensional (2D) images by multi-planar reconstructions (Fig 1). The radiopacities depict the gutta percha spheres. Digitization of the landmarks was achieved by using both the volume-rendered images and the 2D images. The variables were computed with an Advantage Windows work station (version AW 4.0,

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Fig 4. Palatal depth measurements.

Fig 2. Dental width measurements. Fig 5. Cross-sectional area measurement.

Fig 3. Palatal width measurements.

General Electric, Medical Systems, Fairfield, Conn) software, which was also specific to the CT scanning technique used in medicine and dentistry. The CT scanned images were used to measure the following: (1) intermolar width (IMW), the cross-sectional distance across the most buccogingival point of the gutta percha markers (Fig 2); (2) interdeciduous molar width (IDMW), the cross-sectional distance across the most buccogingival point of the gutta percha markers (Fig 2); (3) intercanine width (ICW), the cross-sectional distance across the most buccogingival point of the gutta percha markers (Fig 2); (4) palatal width 1 (PW1), the cross-sectional distance across the constructed line one third of the distance from the palatal floor to the IMW line at right angles to the palatal depth line (Fig 3); (5) palatal width 2 (PW2), cross-sectional distance across the constructed line two thirds from the palatal floor to the IMW line at right angles to the palatal depth line (Fig 3); (6) palatal depth (PD), the line measured from the

perpendicular midpoint of the IMW (MPD) to the palatal floor and the perpendicular midpoint of the interdeciduous molar width (DMPD) to the palatal floor (Fig 4); (7) the cross-sectional palatal area, the area encompassing the palate up to the IMW at the first deciduous molar (DMArea) and the first permanent molar (MArea) (Fig 5); (8) arch length (AL), a line perpendicular to the IMW line of the first permanent molar to the center point of the maxillary central incisors (Fig 6); and (9) molar tipping, the intersection of lines marked tangentially to the occlusal plane of the first permanent molar (MA) (Fig 7). The dental casts were used to directly measure the following with digital calipers: (1) IMW, cross-sectional distance across the junction of the lingual groove with the gingival margin for the first permanent molars (Fig 2); (2) IDMW, cross-sectional distance across the most lingual point at the gingival margin of the deciduous first molars (Fig 2); and (3) ICW, cross-sectional distance across the most lingual point at the gingival margin of the deciduous canines (Fig 2). RESULTS

Linear measurements were subjected to method error analysis. Linear measurements from the CT models were compared with the linear measurements from the digital calipers. Estimation of the method error was achieved by

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Table I.

Estimation of method error for difference between 3D CT method and digital caliper method of measuring Linear changes (mm)

Variable

Mean difference

Confidence interval

P value

0.24 0.07 0.7

⫺0.007-0.487 ⫺0.243 0.425-0.924

0.056 0.64 ⬍0.001

IMW IDMW ICW

Fig 6. Arch length measurement.

Fig 7. Angular measurements.

calculating a confidence interval for the difference between the 3D CT and the caliper methods of measuring, testing for significance at a P value of ⬍0.001. The results of the method error analysis indicated no systematic differences for IMW of the deciduous and permanent first molars, but there was statistical significance with the deciduous canine width (Table I). Paired t tests were used to examine the differences between pretreatment and posttreatment expansion changes, testing for significance at a P value of ⬍0.001. Linear measures in the RME group were smaller before expansion when compared with the control group. However, these were not statistically smaller: IMW across the permanent first molar, PD at the deciduous first molar, AL, and PW2 (Table II). The cross-sectional area measurement across the permanent first molar and the deciduous first molar were both statistically significantly smaller for the

RME group when compared with control group. There were also no significant differences in the maxillary permanent first molar angulations in the RME group when compared with the control group and in the AL values (Table II). Treatment with RME produced significantly greater increases in all width variables for maxillary arch width when compared with the control group (Table III). In the RME group, the expansion amounts averaged 4.8 mm at the permanent first molars, 5.0 mm at the deciduous first molars, and 3.9 mm at the canines. In the control group, the expansion amounts averaged 0.2 mm at the permanent molars, ⫺0.2 mm at the deciduous molars, and ⫺0.5 mm at the canines (Table III, Fig 8). Treatment changes in the RME group produced increases in the cross-sectional area across both permanent and deciduous molars, but they were not statistically significant increases when compared with the control group. The cross-sectional area increases in the RME group at the permanent first molars and deciduous first molars averaged 15.3 mm2 (P ⬍0.0001) and 15.8 mm2 (P ⬍0.0014), respectively; the cross-sectional area increases in the control group were 7.1 and 9.1 mm2, respectively. The values are summarized in Table III and diagrammatically shown in Figure 9. Postexpansion changes in the angulations of the maxillary first molars showed a mean permanent molar change of 3.6° of buccal tipping (SD, 5.3°) in the RME group and 1.6° (SD, 8.5°) of uprighting in the control group. DISCUSSION

RME treatment is a common procedure to manage maxillary transverse arch deficiencies. These clinical data demonstrated that treatment of maxillary constriction in the early mixed dentition with a bonded appliance is generally successful, producing significant change in the transverse width dimensions when compared with the control group. The sample was not

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Table II.

Comparison of RME group vs control group at T1 RME group

IMW IDMW ICW PW1 PW2 MPD DMPD MArea DMArea AL MA

mm mm mm mm mm mm mm mm2 mm2 mm °

Control group

Mean

SD

SE

Mean

SD

SE

t value

P value

Significance

33.5 25.7 24.4 17.1 24.8 10.7 9.9 221.1 140.2 33.0 154.1

2.4 2.3 1.9 2.2 2.2 1.8 1.4 41.1 25.1 1.8 8.3

0.4 0.4 0.4 0.3 0.3 0.3 0.3 6.3 4.8 0.3 1.3

35.1 28.5 27.2 19.4 26.6 12.4 10.9 265.3 168.6 33.5 153.6

3.2 2.1 2.5 3.0 2.9 2.4 0.9 65.9 26.5 1.5 4.3

1.2 0.8 0.9 1.1 1.1 0.9 0.4 24.9 10.0 0.6 1.6

1.5 2.8 3.3 2.4 1.8 2.1 1.6 2.4 2.6 0.6 ⫺0.2

0.14 0.008 0.03 0.019 0.067 0.04 0.1 0.02 0.01 0.52 0.8

NS †

* * NS * NS * * NS NS

NS, Not significant; *P ⬍0.05; † P ⬍0.01. Table III.

Comparison of RME group vs control group at T2 RME group

IMW IDMW ICW PW1 PW2 MPD DMPD MArea DMArea AL MA

mm mm mm mm mm mm mm mm2 mm2 mm °

Control group

Mean

SD

Mean

SD

t value

P value

Significance

4.8 5.0 3.9 0.8 1.6 0.09 0.15 15.3 15.8 ⫺0.4 ⫺3.6

1.3 1.0 0.9 0.8 0.9 0.5 1.0 17.3 23.0 0.9 5.3

0.2 ⫺0.2 ⫺0.5 1.3 0.9 0.7 0.2 7.1 9.1 0.07 1.6

0.6 0.7 1.2 1.2 0.6 2.1 0.8 11.4 13.8 0.9 8.5

⫺9.29 ⫺12.64 ⫺10.23 1.4 ⫺2.0 1.77 0.22 ⫺1.19 ⫺0.73 1.3 2.2

0.000 0.000 0.000 0.17 ⫺0.05 0.82 0.82 0.24 0.47 0.19 0.035

† † †

NS * NS NS NS NS NS *

NS, Not significant; *P ⬍0.05; † P ⬍0.001.

subdivided by sex because there are no reported sexual differences for transverse dentofacial variables in this age group.31 The IMW measurement is frequently used to assess the outcome of maxillary expansion. In this study, the permanent IMW increase during the treatment period was 4.8 mm. Sandikçiog˘lu and Hazar,32 using a banded RME appliance, and da Silva Filho et al,17 using a modified Haas appliance, both treated maxillary arch constrictions in the early mixed dentition (8-9 years of age). They reported changes across the permanent first molars of 5.5 and 5.46 mm, respectively, similar to our study. Sandikçiog˘lu and Hazar32 measured the linear changes directly on dental casts, and da Silva Filho et al17 measured the linear changes using a posteroanterior cephalogram. More recently, Geran et al,26 who measured dental casts using a digital imaging system,

reported an increase of 3.4 mm across the permanent first molars with a bonded RME appliance in the early mixed dentition (8 years 10 months). Sandikçiog˘lu and Hazar32 measured the changes across the deciduous first molars as 6.0 mm. This study recorded a deciduous IMW increase of 5.0 mm, whereas 2.8 mm was recorded in the study of Geran et al.26 The ICW increase was comparable in this study (3.9 mm) with the results of Sandikçiog˘lu and Hazar,32 who reported an increase of 3.3 mm, and also with the study of Geran et al26 (2.7 mm). A greater increase in ICW is expected after RME. Wertz5 reported that opening the midpalatal suture is greater in the anterior than posterior region. In this study, the canine was not part of the anchorage unit and thus not expected to have a great increase.32 Perhaps the perioral soft tissues play a role in not allowing a greater increase in the ICW.

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Table IV. Net changes in RME group compared with control group Permanent first molar

RME (n ⫽ 43) T1-T2 Control (n ⫽ 7) T1-T2 Net changes T1-T2

Fig 8. Box plot of mean linear changes after RME treatment.

Fig 9. Box plot of the mean area changes after RME treatment.

Minimal changes were seen in the control group; they could be due to growth and development during the observation period (25 weeks). These changes were also seen in the study of Erdinç et al33: a maxillary IMW change of 0.4 mm and an ICW change of 0.7 mm after 0.7 years in children with an average age of 9.4 years. Erdinç et al33 used digital calipers and directly recorded the changes on the dental casts. At T2, the increase in maxillary IMW for the RME group was 4.8 mm, which was 4.6 mm greater than in the control group (Table IV). The deciduous first molar width increase was 5.0 mm in the RME group, 5.2 mm larger than in the control group. Increased width was also seen in the deciduous canine measurement in the RME group, 4.4 mm larger than in the control group at

Deciduous first molar

Deciduous canine

Width

Area

Width

Area

Width

4.8

15.3

5.0

15.8

3.9

0.2

7.1

⫺0.2

9.1

⫺0.5

4.6

8.2

5.2

6.7

4.4

T2. These net increases were expected in the RME group during expansion. The net changes in area of the RME group at T2 are also large when compared with the control group. The net changes in area were 8.2 mm across the permanent first molars and 6.7 mm across the deciduous first molars. When examining the differences of palatal width at different levels of the first permanent molar, it appeared that RME treatment produces greater changes at the IMW as well as two thirds up from the PW2 than in the control group. This would be an expected finding when considering the shape of the palatal vault. In this study, the AL changes in both groups were small (⫺0.43 and 0.07 mm). These small changes were similar to the study of Adkins et al,10 who measured the linear changes from photographs of the dental casts in adolescent patients. Thus, these differences would be more a result of growth and development than treatment effects. PD after RME treatment is expected to reduce by the lowering of the palatal shelves of the maxilla during RME.1 We recorded a small increase in PD (0.09 mm, SD, 0.55 mm) at the permanent first molar level. Similar small changes were seen at the deciduous molar level (0.15 mm). However, they were not statistically different when compared with the control group. Ladner and Muhl,12 using the PD gauge, reported a PD increase of 2.3 mm (⫾ 1.6 mm). An explanation of this increase in PD might be due to an increase in dentoalveolar height during dental eruption. However, the length of treatment time in the study of Ladner and Muhl12 would account for this marked increase, because the subjects completed full fixed appliance therapy and were adolescents at the start of treatment. The PD in this study was measured from the perpendicular midpoint of the IMW to the palatal floor and not from the median palatal raphe. There is some asymmetry of palatal widths as seen by Tsai and Tan.34 They concluded that, in a group of 4 to 5 year olds, the

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left side of the palate was statistically significantly larger than the right side for both sexes; however, the median palatal raphe was used as a reference. They also reported their findings using measurements from photographs of the distal surface of the dental casts. A goal of this study was to determine the crosssectional area changes from RME. The RME group at the beginning of treatment had a statistically smaller cross-sectional area at both permanent and deciduous molars than did the control group. After RME treatment, the area change across the first permanent molar increased on average by 15.3 mm2 (P ⬍0.0001). Although the area change across the deciduous first molars was great (15.8 mm2), it was not statistically significant. The area changes across the permanent first molars (7.14 mm2) and the deciduous first molars (9.14 mm2) in the control group were smaller when compared with the RME group but not statistically significant. The net changes in area of the RME group, at the end of expansion, were large when compared with the control group. The net changes in area were 8.2 mm across the permanent first molars and 6.7 mm across the deciduous first molars (Table IV). This marked increase in net area change might suggest that expansion of the constricted maxillary arch produces marked increases in area of the palate. However, there was marked variation in area change from a large decrease posttreatment to a large increase. It can be assumed that the marked increase in area in the RME group reflects the changes in IMW as a result of the midpalatal suture opening in conjunction with alveolar arch tipping and buccal tipping of molars but not by the PD changes. Larger samples for the RME and the control groups could confirm this. After RME treatment, the permanent first molars in the RME group showed large variations in buccal tipping, so that some teeth had little or no buccal tipping, and others had buccal tipping up to 19°. Wertz5 showed RME to be associated with various degrees of dental tipping; even if there are no angular changes of the teeth in each maxillary buccal segment, the outward tilting of the alveolar processes would still result in the appearance of tipped teeth. This could explain why there was an average of 1.6° of uprighting of the permanent first molar in the control group. There were also small increases in IMW, IPMW, PW1, and PW2 that could reflect minimal outward tilting of the alveolar processes in the control group. CONCLUSIONS

Data acquisition of the palate after RME treatment with 3D helical CT scanning technology obtained the following conclusions.

1. There were clinically significant increases in interdental widths across the canines, the deciduous first molars, and the permanent first molars. 2. There was a significant increase in cross-sectional area across the permanent first molars but not across the deciduous first molars. There was variability in the amounts of change. 3. There was marked variability in the buccal tipping of the permanent first molars regardless of occlusal coverage with acrylic. 4. Assessing morphologic changes of the palate after RME treatment in the early mixed dentition with helical 3D CT scanning is effective and time efficient. There is no need to duplicate dental casts, and up to 6 dental casts can be scanned at 1 time. The linear measurements from this method are comparable to those of digital calipers. Thus, 3D helical CT scanning can provide fast and accurate data acquisition and subsequent analysis. 5. Perhaps analyzing treatment outcomes of RME therapy by using 3D digital imaging with laser scanning, CT helical scanning,27 or 3D cone-beam CT28-30 could provide additional information of the 3D volumetric changes of the palate after RME treatment or identify treatment predictors. REFERENCES 1. Haas A. Rapid expansion of the maxillary dental arch and nasal cavity by opening the midpalatal suture. Angle Orthod 1961;31: 73-90. 2. Haas A. The treatment of maxillary deficiency by opening the midpalatal suture. Angle Orthod 1965;35:200-17. 3. Krebs A. Expansion of the midpalatal suture studied by means of metallic implants. Acta Odontol Scand 1959;17:491-501. 4. Krebs A. Rapid expansion of midpalatal suture by fixed appliance: an implant study over a 7 year period. Trans Eur Orthod Soc 1964:141-2. 5. Wertz R. Skeletal and dental changes accompanying rapid midpalatal suture opening. Am J Orthod 1970;58:41-64. 6. Alpern MC, Yurosko JJ. Rapid palatal expansion in adults with and without surgery. Angle Orthod 1987;57:245-63. 7. Sarver DM, Johnston MW. Skeletal changes in vertical and anterior displacement of the maxilla with bonded rapid palatal expansion appliances. Am J Orthod Dentofacial Orthop 1989;95:462-6. 8. Thilander B, Pena L, Infante C, Parada S, de Mayorga C. Prevalence of malocclusion and orthodontic treatment needs in children and adolescents in Bogota, Colombia. An epidemiological study related to different stages of dental development. Eur J Orthod 2001;23:153-67. 9. Kurol J, Bergland L. Longitudinal study and cost-benefit analysis of the effect of early treatment of posterior cross-bites in the primary dentition. Eur J Orthod 1992;14:173-9. 10. Adkins MD, Nanda RS, Currier GF. Arch perimeter changes on rapid palatal expansion. Am J Orthod Dentofacial Orthop 1990; 97:194-9. 11. Akkaya S, Lorenzon S, Ucem TT. Comparison of dental arch and arch perimeter changes between bonded rapid and slow maxillary expansion procedures. Eur J Orthod 1998;20:255-61.

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24. Kusnoto B, Evans CA. Reliability of a 3D surface laser scanner for orthodontic applications. Am J Orthod Dentofacial Orthop 2002;122:342-8. 25. Oliviera NL, Da Silveira AC, Kusnoto B, Viana G. Threedimensional assessment of morphologic changes of the maxilla: a comparison of 2 kinds of palatal expanders. Am J Orthod Dentofacial Orthop 2004;126:354-62. 26. Geran RG, McNamara JA Jr, Baccetti T, Franchi L, Shapiro LM. A prospective long-term study on the effects of rapid maxillary expansion in the early mixed dentition. Am J Orthod Dentofacial Orthop 2006;129:631-40. 27. Macchi A, Carrafiello G, Cacciafesta V, Norcini A Threedimensional digital modeling and setup. Am J Orthod Dentofacial Orthop 2006;129:605-10. 28. Cevidanes LH, Styner MA, Proffit WR. Image analysis and superimposition of 3-dimensional cone-beam computed tomography models. Am J Orthod Dentofacial Orthop 2006;129:611-8. 29. Halazonetis D. From 2-dimensional cephalograms to 3-dimensional computed tomography scans. Am J Orthod Dentofacial Orthop 2005;127:627-37. 30. Hatcher DC, Aboudara CL. Diagnosis goes digital. Am J Orthod Dentofacial Orthop 2004;125:512-5. 31. Athanasiou AE, Droschl H, Bosch C. Data and patterns of transverse dentofacial structure of 6- to 15-year-old children: a posteroanterior cephalometric study. Am J Orthod Dentofacial Orthop 1992;101:465-71. 32. Sandikcioglu M, Hazar S. Skeletal and dental changes after maxillary expansions in the mixed dentition. Am J Orthod Dentofacial Orthop 1997;111:321-7. 33. Erdinc AE, Uger T, Erbay E. A comparison of different treatment techniques for posterior crossbite in the mixed dentition. Am J Orthod Dentofacial Orthop 1999;116:287-300. 34. Tsai H, Tan CT. Morphology of the palatal vault of primary dentitions in transverse view. Angle Orthod 2004;74:774-9.