Anthropol. Anz. 72/2 (2015), pp. 223–234 J. Biol. Clinic. Anthropol. published online 23 January 2015; published in print May 2015
Article
Evaluation of arch form between Vietnamese and North American Caucasians using 3-dimensional virtual models Vu Thi Thu Trang1, Jae Hyun Park2, Mohamed Bayome3, Shruti Shastry4, Alex Mellion5, and Yoon-Ah Kook6 1 Former graduate student, Graduate School, The Catholic University of Korea, Seoul, Korea kook190 [email protected] 2 Associate professor and chair, Postgraduate Orthodontic Program, Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ, USA, and Adjunct Professor, Graduate School of Dentistry, Kyung Hee University, Seoul, South Korea 3 Research assistant professor, Department of Orthodontics, The Catholic University of Korea, Seoul, Korea, and visiting professor, Department of Postgraduate Studies, the Universidad Autonoma del Paraguay, Asuncion, Paraguay 4 Former Postgraduate Resident, Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ, USA 5 Former Postgraduate Resident, Department of Orthodontics, Center for Advanced Dental Education, Saint Louis University, Saint Louis, MO, USA 6 Professor, Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, Seoul, Korea
With 5 figures and 3 tables
Summary: The purpose of this study was to investigate the three-dimensional (3D) morphologic differences in the mandibular arch of Vietnamese and North American White subjects. The sample included 113 Vietnamese subjects (41 Class I, 37 Class II and 35 Class III) and 96 White subjects (29 Class I, 30 Class II and 37 Class III). The samples were regrouped according to arch form types (tapered, ovoid, and square) to compare the frequency distribution of the three arch forms between ethnic groups in each angle classification. The facial axis point of each tooth was digitized on 3D virtual models. Four linear and two ratio variables were measured. In comparing arch dimensions, the intercanine and intermolar widths were wider in Vietnamese than in Whites (p < 0.001, p = 0.042, respectively). In the White group, there was even frequency distribution of the three arch forms. However, in the Vietnamese group, the square arch form was the most frequent followed by tapered and ovoid arch forms. The arch forms of Whites were narrower than Vietnamese. In North American Whites, the distribution of the arch form types showed similar frequency. In Vietnamese, the square arch form was more frequent. Key words: arch form, arch dimension, ethnic group, Vietnamese, North American Whites.
Introduction Arch form is considered an important element for functional and esthetic purposes 쏘 2015 E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, Germany DOI: 10.1127/anthranz/2015/0395 eschweizerbart_XXX
www.schweizerbart.de 0003-5548/15/0395 $ 3.25
224
Vu Thi Thu Trang et al.
and essential aspect in studying differences among ethnic groups, growth patterns and development. Although previous studies have evaluated arch forms, most of this research based its landmark selection on cusp tips, incisal edges, and cervical margins (Collins & Harris 1998, de la Cruz et al. 1995, DeKock 1972, Felton et al. 1987). Unfortunately, these landmarks may not be appropriate representations of clinical bracket points due to inherent limitations of the two-dimensional (2D) method for finding the labial and buccal landmarks. With the rapidly expanding three-dimensional (3D) imaging technology, the accuracy and versatility of the virtual models have been confirmed in several studies (Kusnoto & Evans 2002, Sohmura et al. 2000). Nonetheless, few studies using this technology have evaluated the arch form and dimensions (Bayome et al. 2011a, Kim et al. 2011, Slaj et al. 2011, Thiruvenkatachari et al. 2009). Camporesi et al. (2006) evaluated the average dental arch form through 3D derived facial axis (FA) points that are more relevant to clinical practice. Also, Bayome et al. (2011a) suggested a new classification of arch form based on the FA points. The arch dimensions of several ethnic groups have been evaluated (Bayome et al. 2011b, Brown et al. 1987, Burris & Harris 2000, Collins & Harris 1998, Gafni et al. 2011, Kasai et al. 1997, Kook et al. 2004, Koyoumdjisky-Kaye et al. 1976, Nojima et al. 2001, Nummikoski et al. 1988, Othman et al. 2012, Schaefer et al. 2006). The dimensions and distribution of the arch forms of Caucasian subjects were found to be different than those of other ethnic groups (Bayome et al. 2011b, Brown et al. 1987, Collins & Harris 1998, Gafni et al. 2011, Kook et al. 2004, Nojima et al. 2001), but the arch form of the Vietnamese population which originates from a homogeneous ethnic background in southeast Asia has not yet been assessed. In addition, no arch form evaluation via FA points has been reported using 3D virtual models for better accuracy. Therefore, the objective of this study was to identify the mandibular dental arch dimensions and arch form distribution within a sample of the Vietnamese population and to compare these values to the North American White population using 3D virtual models.
Material and methods The North American White sample included 96 mandibular casts (29 Class I, 30 Class II and 37 Class III); 44 male and 52 female subjects with mean age of 17.87 ± 6.72 years which were collected from the Department of Orthodontics, Arizona School of Dentistry & Oral Health, A.T. Still University and from Saint Louis University. The Vietnamese sample included 113 mandibular casts (41 Class I, 37 Class II and 35 Class III); 45 male and 68 female subjects with mean age of 22.22 ± 2.97 years which were collected from the Department of Orthodontic at Faculty of Odontostomatology, Medicine Hanoi University, and private clinics in Hanoi and Hochiminh City. The study was approved by the institutional review board of The Catholic University of Korea (KIRB-003 907-001). Inclusion criteria were having full permanent dentition excluding third molars, no supernumerary teeth, normal tooth size and shape, and arch-length discrepancy less than 3 mm. Exclusion criteria were having previous orthodontic treatment or restorations extending to contact areas, incisal edges (cusp tips), facial surfaces, or cervical areas. The mandibular Vietnamese models were scanned with a 3D laser scanner (KOD-300, Orapix, Seoul, Korea) at 20 μm unit resolution. Virtual models were viewed and digitized
eschweizerbart_XXX
3-dimensional virtual models of differences in the mandibular arch
225
using Rapidform 2006 software (INUS Technology, Seoul, Korea). North American White models were scanned with an iOC 3D scanner (Cadent, Inc., Align technology, Inc., San Jose, CA), then viewed and digitized using OrthoCAD software (Cadent, Computer Aided Dentistry, Fairview, NJ) (Fig. 1). All digitization was made by one investigator (V.T.) to eliminate interoperator variability. The transverse direction was represented by the X-axis; the antero-posterior direction, the Y-axis; and the plane perpendicular to the X- and Y-planes, the Z-axis. The contact point between the mandibular central incisors was set as the origin of the X-, Y- and Z-axes. The original X-axis was adjusted so that it was parallel to the mean inclination of line A (straight line connecting the right and left contact points between the rst and second premolars) and line B (straight line connecting the right and left contact points between the second premolars and the first molars) (Fig. 2). FA points (Andrews 1972) were digitized on each tooth from the right to left mandibular first molar on each virtual model to represent the dental arch forms (Fig. 3). The following 4 linear measurements and 2 ratio variables were taken: (1) intercanine width: the distance between the canines’ FA points (2) intermolar width: the distance between the first molars’ FA points (3) intercanine depth: the shortest distance from a line connecting the canines’ FA points to the origin point between the central incisors (4) intermolar depth: the shortest distance from a line connecting the first molars’ FA points to the origin point between the central incisors (5) canine width/depth (W/D) ratio: the ratio of intercanine width to intercanine depth (6) molar W/D ratio: the ratio of intermolar width to intermolar depth. The x and y coordinates for the FA points of each case were entered into mathematical software (MATLAB 7.5 (R2007b), MathWorks, Natick, MA) to draw the best-fitting curve that represented each arch. Because the polynomial function has been reported to be one of the best mathematical representations of the dental arch, several polynomial functions were applied, and the fourth degree [f (x) = ax4 + bx3 + cx2 +dx + e] was selected, since it most accurately represented the arch form and produced the smoothest curves with no wave-like properties. The curves were printed in a 1:1 scale and superimposed over tapered, ovoid, and
Fig. 1. Digitized mandibular cast. A, Facial axis (FA) point on central incisor; B, FA point on 1st molar.
eschweizerbart_XXX
226
Vu Thi Thu Trang et al.
Fig. 2. 3D virtual model reorientation method. X-axis was adjusted so that it becomes parallel to the mean inclination (C) of line A (straight line connecting the right and left contact points between the first and second premolars) and line B (straight line connecting the right and left contact points between the second premolars and the first molars).
Fig. 3. Arch form dimensions. (A) intermolar width; (B) intermolar depth; (C) intercanine width; (D) intercanine depth; red dots represent FA points; blue dot represents the origin point.
eschweizerbart_XXX
3-dimensional virtual models of differences in the mandibular arch
227
square arch-form clear templates (Orthoform, 3M Unitek, Monrovia, CA) at the center of the curvature of the best-fitting curve. The subjects were grouped according to arch form types (tapered, ovoid, and square). To evaluate reliability, 30 randomly selected casts were redigitized by the same operator. The differences between the two measurements were evaluated using the intraclass correlation coefficient (ICC) and the result showed good reliability (ICC > 0.98). Also, the measurement error was calculated according to Dahlberg formula d i2 i 1 2 N n
and was found to be 0.3 mm. To evaluate the differences between the two software programs, 10 Vietnamese casts were rescanned then digitized by OrthoCAD. The reliability of the measurements obtained from the two software programs were assessed by ICC and all variables showed ICC > 0.95.
Statistical analysis The frequency distribution of the Angle classifications of each arch form was compared between the 2 ethnic groups using a Chi-square test. Multivariate analysis of covariance (MANCOVA) was performed to compare adjusted means of arch dimensions between the two ethnic groups by Angle Class and arch form separately. Age, gender and arch form or Angle Class, respectively were used as covariates to compensate for their effect of the comparison. MANCOVA was also applied to compare gender and Angle classification differences within both White and Vietnamese samples, independently. All analyses were tested at the significance level of .05.
Results Table 1 demonstrates the comparison of arch dimensions between the North American White and Vietnamese groups and Angle classification. In the MANCOVA, ethnic group, Angle classification and arch form showed main significant effects (p = 0.013, p = 0.01, and p < 0.001, respectively). The intercanine width was significantly wider in the Vietnamese population than with the Whites (p < 0.001). Also, it was wider in Class III than in Class II (p = 0.004). Table 2 depicts the comparison of arch dimensions between the 2 ethnic groups after being regrouped according to the arch form type. Ethnic group, arch form and gender showed main significant effects (p = 0.005, p < 0.001, and p = 0.047, respectively). The intercanine and intermolar widths were significantly different according to ethnic group (p < 0.001, p = 0.042, respectively) as well as arch form (p < 0.001). Table 3 demonstrates the frequency distribution of the arch form types within White and Vietnamese populations. The distribution of the arch form types in the White population was significantly different than that of the Vietnamese (p < 0.001). The three arch forms were of similar percentages in the White group, but the square arch form was by far the most frequent in the Vietnamese group (63.7 %). Figure 4 shows that the distribution of the arch forms within Class III cases was not significantly different between the Whites (Tapered, 19 %; Ovoid, 32 %; Square,
eschweizerbart_XXX
0.293 0.227 0.459 0.363 0.818 0.031
28.61 4.045 50.31 25.54 7.906 1.976
28.46 4.561 51.11 26.07 6.992 1.972
Mean
0.307 0.238 0.481 0.38 0.857 0.032
SE
29.44 3.82 51.64 25.44 8.582 2.039
Mean 0.263 0.204 0.412 0.326 0.735 0.027
SE
SE
0.118 29.773 0.245 0.016 4.424 0.19 0.124 51.961 0.384 0.238 26.037 0.303 0.019 7.285 0.684 0.155 2.007 0.026
pMean value* 29.37 4.596 51.74 26.2 6.635 1.982
Mean 0.26 0.201 0.408 0.322 0.726 0.027
SE 30.18 4.381 51.63 26.38 8.574 1.966
Mean 0.276 0.214 0.433 0.342 0.771 0.029
SE
Cl I (n = 41) Cl II (n = 37) Cl III (n = 35)
Vietnamese (n = 113) pvalue!
Multiple comparison
0.041 < 0.001 0.004 Cl III > Cl II 0.582 0.093 0.068 0.961 0.055 0.488 0.283 0.092 0.579 0.626 0.637 0.068 0.297 0.687 0.680
ppvalue* value†
Multivariate analysis of covariance. Comparison of adjusted means for age, gender and arch form. *Level of significance of the comparison of arch dimensions within each ethnic group. † Level of significance of the comparison of arch dimensions according to ethnic groups. ! Level of significance of the comparison of arch dimensions according to Angle classification groups. ICW, Intercanine width; ICD, intercanine depth; IMW, intermolar width; IMD, intermolar depth; CWD, canine width/depth ratio; MWD, molar width/depth ratio.
ICW ICD IMW IMD CWD MWD
SE
Mean
Cl I (n = 29) Cl II (n = 30) Cl III (n = 37)
North American White (n = 96)
Table 1. Comparison of arch dimensions according to ethnic groups and Angle classification.
228 Vu Thi Thu Trang et al.
eschweizerbart_XXX
0.27 0.21 0.43 0.34 0.76 0.03
ICW 27.86 ICD 4.28 IMW 48.48 IMD 25.65 CWD 7.25 MWD 1.90
28.70 4.31 50.76 25.98 7.11 1.97
Mean
0.32 0.25 0.50 0.39 0.88 0.03
SE
Ovoid (O) (n = 26)
29.54 3.96 52.37 25.48 8.50 2.06
Mean 29.24 4.72 50.02 25.94 6.68 1.94
0.41 0.32 0.63 0.50 1.13 0.04
SE
Tapered (T) (n = 15) pMean value*
0.27 0.001 0.21 0.51 0.42 < 0.001 0.33 0.541 0.75 0.047 0.03 0.001
SE
Square (S) (n = 37)
29.78 4.74 51.01 26.65 6.61 1.92
Mean 0.31 0.24 0.49 0.38 0.87 0.03
SE
Ovoid (O) (n = 26)
30.07 4.26 53.07 26.09 8.20 2.04
Mean
ppvalue* value†
pvalue!
0.19 0.125 < 0.001 < 0.001 T
Article
Evaluation of arch form between Vietnamese and North American Caucasians using 3-dimensional virtual models Vu Thi Thu Trang1, Jae Hyun Park2, Mohamed Bayome3, Shruti Shastry4, Alex Mellion5, and Yoon-Ah Kook6 1 Former graduate student, Graduate School, The Catholic University of Korea, Seoul, Korea kook190 [email protected] 2 Associate professor and chair, Postgraduate Orthodontic Program, Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ, USA, and Adjunct Professor, Graduate School of Dentistry, Kyung Hee University, Seoul, South Korea 3 Research assistant professor, Department of Orthodontics, The Catholic University of Korea, Seoul, Korea, and visiting professor, Department of Postgraduate Studies, the Universidad Autonoma del Paraguay, Asuncion, Paraguay 4 Former Postgraduate Resident, Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ, USA 5 Former Postgraduate Resident, Department of Orthodontics, Center for Advanced Dental Education, Saint Louis University, Saint Louis, MO, USA 6 Professor, Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, Seoul, Korea
With 5 figures and 3 tables
Summary: The purpose of this study was to investigate the three-dimensional (3D) morphologic differences in the mandibular arch of Vietnamese and North American White subjects. The sample included 113 Vietnamese subjects (41 Class I, 37 Class II and 35 Class III) and 96 White subjects (29 Class I, 30 Class II and 37 Class III). The samples were regrouped according to arch form types (tapered, ovoid, and square) to compare the frequency distribution of the three arch forms between ethnic groups in each angle classification. The facial axis point of each tooth was digitized on 3D virtual models. Four linear and two ratio variables were measured. In comparing arch dimensions, the intercanine and intermolar widths were wider in Vietnamese than in Whites (p < 0.001, p = 0.042, respectively). In the White group, there was even frequency distribution of the three arch forms. However, in the Vietnamese group, the square arch form was the most frequent followed by tapered and ovoid arch forms. The arch forms of Whites were narrower than Vietnamese. In North American Whites, the distribution of the arch form types showed similar frequency. In Vietnamese, the square arch form was more frequent. Key words: arch form, arch dimension, ethnic group, Vietnamese, North American Whites.
Introduction Arch form is considered an important element for functional and esthetic purposes 쏘 2015 E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, Germany DOI: 10.1127/anthranz/2015/0395 eschweizerbart_XXX
www.schweizerbart.de 0003-5548/15/0395 $ 3.25
224
Vu Thi Thu Trang et al.
and essential aspect in studying differences among ethnic groups, growth patterns and development. Although previous studies have evaluated arch forms, most of this research based its landmark selection on cusp tips, incisal edges, and cervical margins (Collins & Harris 1998, de la Cruz et al. 1995, DeKock 1972, Felton et al. 1987). Unfortunately, these landmarks may not be appropriate representations of clinical bracket points due to inherent limitations of the two-dimensional (2D) method for finding the labial and buccal landmarks. With the rapidly expanding three-dimensional (3D) imaging technology, the accuracy and versatility of the virtual models have been confirmed in several studies (Kusnoto & Evans 2002, Sohmura et al. 2000). Nonetheless, few studies using this technology have evaluated the arch form and dimensions (Bayome et al. 2011a, Kim et al. 2011, Slaj et al. 2011, Thiruvenkatachari et al. 2009). Camporesi et al. (2006) evaluated the average dental arch form through 3D derived facial axis (FA) points that are more relevant to clinical practice. Also, Bayome et al. (2011a) suggested a new classification of arch form based on the FA points. The arch dimensions of several ethnic groups have been evaluated (Bayome et al. 2011b, Brown et al. 1987, Burris & Harris 2000, Collins & Harris 1998, Gafni et al. 2011, Kasai et al. 1997, Kook et al. 2004, Koyoumdjisky-Kaye et al. 1976, Nojima et al. 2001, Nummikoski et al. 1988, Othman et al. 2012, Schaefer et al. 2006). The dimensions and distribution of the arch forms of Caucasian subjects were found to be different than those of other ethnic groups (Bayome et al. 2011b, Brown et al. 1987, Collins & Harris 1998, Gafni et al. 2011, Kook et al. 2004, Nojima et al. 2001), but the arch form of the Vietnamese population which originates from a homogeneous ethnic background in southeast Asia has not yet been assessed. In addition, no arch form evaluation via FA points has been reported using 3D virtual models for better accuracy. Therefore, the objective of this study was to identify the mandibular dental arch dimensions and arch form distribution within a sample of the Vietnamese population and to compare these values to the North American White population using 3D virtual models.
Material and methods The North American White sample included 96 mandibular casts (29 Class I, 30 Class II and 37 Class III); 44 male and 52 female subjects with mean age of 17.87 ± 6.72 years which were collected from the Department of Orthodontics, Arizona School of Dentistry & Oral Health, A.T. Still University and from Saint Louis University. The Vietnamese sample included 113 mandibular casts (41 Class I, 37 Class II and 35 Class III); 45 male and 68 female subjects with mean age of 22.22 ± 2.97 years which were collected from the Department of Orthodontic at Faculty of Odontostomatology, Medicine Hanoi University, and private clinics in Hanoi and Hochiminh City. The study was approved by the institutional review board of The Catholic University of Korea (KIRB-003 907-001). Inclusion criteria were having full permanent dentition excluding third molars, no supernumerary teeth, normal tooth size and shape, and arch-length discrepancy less than 3 mm. Exclusion criteria were having previous orthodontic treatment or restorations extending to contact areas, incisal edges (cusp tips), facial surfaces, or cervical areas. The mandibular Vietnamese models were scanned with a 3D laser scanner (KOD-300, Orapix, Seoul, Korea) at 20 μm unit resolution. Virtual models were viewed and digitized
eschweizerbart_XXX
3-dimensional virtual models of differences in the mandibular arch
225
using Rapidform 2006 software (INUS Technology, Seoul, Korea). North American White models were scanned with an iOC 3D scanner (Cadent, Inc., Align technology, Inc., San Jose, CA), then viewed and digitized using OrthoCAD software (Cadent, Computer Aided Dentistry, Fairview, NJ) (Fig. 1). All digitization was made by one investigator (V.T.) to eliminate interoperator variability. The transverse direction was represented by the X-axis; the antero-posterior direction, the Y-axis; and the plane perpendicular to the X- and Y-planes, the Z-axis. The contact point between the mandibular central incisors was set as the origin of the X-, Y- and Z-axes. The original X-axis was adjusted so that it was parallel to the mean inclination of line A (straight line connecting the right and left contact points between the rst and second premolars) and line B (straight line connecting the right and left contact points between the second premolars and the first molars) (Fig. 2). FA points (Andrews 1972) were digitized on each tooth from the right to left mandibular first molar on each virtual model to represent the dental arch forms (Fig. 3). The following 4 linear measurements and 2 ratio variables were taken: (1) intercanine width: the distance between the canines’ FA points (2) intermolar width: the distance between the first molars’ FA points (3) intercanine depth: the shortest distance from a line connecting the canines’ FA points to the origin point between the central incisors (4) intermolar depth: the shortest distance from a line connecting the first molars’ FA points to the origin point between the central incisors (5) canine width/depth (W/D) ratio: the ratio of intercanine width to intercanine depth (6) molar W/D ratio: the ratio of intermolar width to intermolar depth. The x and y coordinates for the FA points of each case were entered into mathematical software (MATLAB 7.5 (R2007b), MathWorks, Natick, MA) to draw the best-fitting curve that represented each arch. Because the polynomial function has been reported to be one of the best mathematical representations of the dental arch, several polynomial functions were applied, and the fourth degree [f (x) = ax4 + bx3 + cx2 +dx + e] was selected, since it most accurately represented the arch form and produced the smoothest curves with no wave-like properties. The curves were printed in a 1:1 scale and superimposed over tapered, ovoid, and
Fig. 1. Digitized mandibular cast. A, Facial axis (FA) point on central incisor; B, FA point on 1st molar.
eschweizerbart_XXX
226
Vu Thi Thu Trang et al.
Fig. 2. 3D virtual model reorientation method. X-axis was adjusted so that it becomes parallel to the mean inclination (C) of line A (straight line connecting the right and left contact points between the first and second premolars) and line B (straight line connecting the right and left contact points between the second premolars and the first molars).
Fig. 3. Arch form dimensions. (A) intermolar width; (B) intermolar depth; (C) intercanine width; (D) intercanine depth; red dots represent FA points; blue dot represents the origin point.
eschweizerbart_XXX
3-dimensional virtual models of differences in the mandibular arch
227
square arch-form clear templates (Orthoform, 3M Unitek, Monrovia, CA) at the center of the curvature of the best-fitting curve. The subjects were grouped according to arch form types (tapered, ovoid, and square). To evaluate reliability, 30 randomly selected casts were redigitized by the same operator. The differences between the two measurements were evaluated using the intraclass correlation coefficient (ICC) and the result showed good reliability (ICC > 0.98). Also, the measurement error was calculated according to Dahlberg formula d i2 i 1 2 N n
and was found to be 0.3 mm. To evaluate the differences between the two software programs, 10 Vietnamese casts were rescanned then digitized by OrthoCAD. The reliability of the measurements obtained from the two software programs were assessed by ICC and all variables showed ICC > 0.95.
Statistical analysis The frequency distribution of the Angle classifications of each arch form was compared between the 2 ethnic groups using a Chi-square test. Multivariate analysis of covariance (MANCOVA) was performed to compare adjusted means of arch dimensions between the two ethnic groups by Angle Class and arch form separately. Age, gender and arch form or Angle Class, respectively were used as covariates to compensate for their effect of the comparison. MANCOVA was also applied to compare gender and Angle classification differences within both White and Vietnamese samples, independently. All analyses were tested at the significance level of .05.
Results Table 1 demonstrates the comparison of arch dimensions between the North American White and Vietnamese groups and Angle classification. In the MANCOVA, ethnic group, Angle classification and arch form showed main significant effects (p = 0.013, p = 0.01, and p < 0.001, respectively). The intercanine width was significantly wider in the Vietnamese population than with the Whites (p < 0.001). Also, it was wider in Class III than in Class II (p = 0.004). Table 2 depicts the comparison of arch dimensions between the 2 ethnic groups after being regrouped according to the arch form type. Ethnic group, arch form and gender showed main significant effects (p = 0.005, p < 0.001, and p = 0.047, respectively). The intercanine and intermolar widths were significantly different according to ethnic group (p < 0.001, p = 0.042, respectively) as well as arch form (p < 0.001). Table 3 demonstrates the frequency distribution of the arch form types within White and Vietnamese populations. The distribution of the arch form types in the White population was significantly different than that of the Vietnamese (p < 0.001). The three arch forms were of similar percentages in the White group, but the square arch form was by far the most frequent in the Vietnamese group (63.7 %). Figure 4 shows that the distribution of the arch forms within Class III cases was not significantly different between the Whites (Tapered, 19 %; Ovoid, 32 %; Square,
eschweizerbart_XXX
0.293 0.227 0.459 0.363 0.818 0.031
28.61 4.045 50.31 25.54 7.906 1.976
28.46 4.561 51.11 26.07 6.992 1.972
Mean
0.307 0.238 0.481 0.38 0.857 0.032
SE
29.44 3.82 51.64 25.44 8.582 2.039
Mean 0.263 0.204 0.412 0.326 0.735 0.027
SE
SE
0.118 29.773 0.245 0.016 4.424 0.19 0.124 51.961 0.384 0.238 26.037 0.303 0.019 7.285 0.684 0.155 2.007 0.026
pMean value* 29.37 4.596 51.74 26.2 6.635 1.982
Mean 0.26 0.201 0.408 0.322 0.726 0.027
SE 30.18 4.381 51.63 26.38 8.574 1.966
Mean 0.276 0.214 0.433 0.342 0.771 0.029
SE
Cl I (n = 41) Cl II (n = 37) Cl III (n = 35)
Vietnamese (n = 113) pvalue!
Multiple comparison
0.041 < 0.001 0.004 Cl III > Cl II 0.582 0.093 0.068 0.961 0.055 0.488 0.283 0.092 0.579 0.626 0.637 0.068 0.297 0.687 0.680
ppvalue* value†
Multivariate analysis of covariance. Comparison of adjusted means for age, gender and arch form. *Level of significance of the comparison of arch dimensions within each ethnic group. † Level of significance of the comparison of arch dimensions according to ethnic groups. ! Level of significance of the comparison of arch dimensions according to Angle classification groups. ICW, Intercanine width; ICD, intercanine depth; IMW, intermolar width; IMD, intermolar depth; CWD, canine width/depth ratio; MWD, molar width/depth ratio.
ICW ICD IMW IMD CWD MWD
SE
Mean
Cl I (n = 29) Cl II (n = 30) Cl III (n = 37)
North American White (n = 96)
Table 1. Comparison of arch dimensions according to ethnic groups and Angle classification.
228 Vu Thi Thu Trang et al.
eschweizerbart_XXX
0.27 0.21 0.43 0.34 0.76 0.03
ICW 27.86 ICD 4.28 IMW 48.48 IMD 25.65 CWD 7.25 MWD 1.90
28.70 4.31 50.76 25.98 7.11 1.97
Mean
0.32 0.25 0.50 0.39 0.88 0.03
SE
Ovoid (O) (n = 26)
29.54 3.96 52.37 25.48 8.50 2.06
Mean 29.24 4.72 50.02 25.94 6.68 1.94
0.41 0.32 0.63 0.50 1.13 0.04
SE
Tapered (T) (n = 15) pMean value*
0.27 0.001 0.21 0.51 0.42 < 0.001 0.33 0.541 0.75 0.047 0.03 0.001
SE
Square (S) (n = 37)
29.78 4.74 51.01 26.65 6.61 1.92
Mean 0.31 0.24 0.49 0.38 0.87 0.03
SE
Ovoid (O) (n = 26)
30.07 4.26 53.07 26.09 8.20 2.04
Mean
ppvalue* value†
pvalue!
0.19 0.125 < 0.001 < 0.001 T
