- Email: [email protected]
A new way of analyzing occlusion 3 dimensionally
TECHNO BYTES
A new way of analyzing occlusion 3 dimensionally Haruaki Hayasaki,a Renato Parsekian Martins,b Luiz Gonzaga Gandini Jr,c Issei Saitoh,d and Kazuaki Nonakae Fukuoka, Japan, and Araraquara, Brazil This article introduces a new method for 3-dimensional dental cast analysis, by using a mechanical 3-dimensional digitizer, MicroScribe 3DX (Immersion, San Jose, Calif), and TIGARO software (not yet released, but available from the author at [email protected]). By digitizing points on the model, multiple measurements can be made, including tooth dimensions; arch length, width, and perimeter; curve of Spee; overjet and overbite; and anteroposterior discrepancy. The bias of the system can be evaluated by comparing the distance between 2 points as determined by the new system and as measured with digital calipers. Fifteen pairs of models were measured digitally and manually, and the bias was evaluated by comparing the variances of both methods and checking for the type of error obtained by each method. No systematic errors were found. The results showed that the method is accurate, and it can be applied to both clinical practice and research. (Am J Orthod Dentofacial Orthop 2005;128:128-32)
A
number of articles have been published reporting data obtained from dental casts.1-20 Three-dimensional (3D) model analysis has been carried out with simple observation,21 calipers,4,11,17,22 calipers in conjunction with protractors and rulers,1,23 digital calipers,10,19,20,22 computer analysis with punch cards,7 computers and digitized photocopies of casts,8,13,14 video cameras,22 scanners,15 devices used for precision production,6,12 electromagnetic 3D digitizers,9,24 scanner-based 3D digitizers (as done by OrthoCAD),17,20,22 laser-based scanners,18 and mechanical 3D digitizers,2 as used in this study. One limitation of digital, 3D cast analysis is the difficulty of taking interarch measurements; it is sometimes impossible to do so without damaging the model. MicroScribe 3DX (Immersion, San Jose, Calif), is a mechanical 3D digitizing system that captures the physical properties of 3D objects and translates them into digital 3D models. The data (3-plane coordinates) are registered in an Excel (Microsoft, Redmond, Wash) a
Assistant professor, Pediatric Dental Clinic, Kyushu University Hospital, Fukuoka, Japan. b PhD student, Orthodontic Department, Araraquara Dental School, University of the State of São Paulo, Brazil. c Assistant professor, Orthodontic Department, Araraquara Dental School, University of the State of São Paulo, Brazil. d Research assistant, Pediatric Dental Clinic, Kyushu University Hospital, Fukuoka, Japan. e Professor and chairman, Department of Pediatric Dentistry, Kyushu University, Fukuoka, Japan. Reprint requests to: Dr Renato Parsekian Martins, Instituto de Ortodontia, Prof Dr Joel Claudio da Rosa Martins, Rua Carlos Gomes, 2158, 14801-340 Araraquara, São Paulo, Brazil; e-mail, [email protected]. Submitted and accepted, July 2004. 0889-5406/$30.00 Copyright © 2005 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2004.07.039
128
table, and another software program is needed to work with the data. We used TIGARO software (not yet released, but available from the author at hayasaki@ dent.kyushu-u.ac.jp). This software makes mathematical calculations that relate the maxillary arch to the mandibular arch by means of the 3 base points that are each digitized 3 times. From that relationship, it is possible to make measurements between the arches in all 3 planes of space. Interarch distances can be measured with the models occluded without damaging them. Although some research has already been done with this technique,25 more work is needed to assess the bias of the method and to determine how the method compares with traditional methods. The aims of this article are to introduce TIGARO software for cast analysis (to be used with data collected systematically by a mechanical 3D digitizer) and to evaluate bias in relation to the measurements obtained with digital calipers. The program
Among the measurements TIGARO can calculate are (1) intercanine, interpremolar, and intermolar distances; (2) arch perimeter and length; (3) arch shape; (4) thickness of the teeth in the middle third; (5) depth of the curve of Spee; (6) tooth angulation and inclination; (7) cusp height; (8) crown height; (9) overjet and overbite; (10) angulations and distances between maxillary and mandibular planes of occlusion; (11) curves of Wilson and Monson; (12) midline deviation; (13) differences in incisal level of incisors; and (14) accom-
Hayasaki et al 129
American Journal of Orthodontics and Dentofacial Orthopedics Volume 128, Number 1
Fig 1. Points marked on models to be digitized systematically.
Fig 2. A, MicroScribe 3DX; B, maxillary model fixed and ready to be digitized; C, models occluded for digitization.
modation of the maxillary second premolar between the mandibular second premolar and the first molar (distance of class). The program works in 3 phases. First, the upper model is digitized, then the lower model, and, finally, the upper model data are related to the lower by means of the base points. To collect the required data, the model is first digitized with the MicroScribe device. After checking the model for imperfections, 133 points on the upper cast and 129 on the lower are marked with a 0.3-mm mechanical pencil (Fig 1). The points must be at
specific positions; the most important points are on the base of the upper model. The points are then systematically digitized with a MicroScribe 3D digitizer (Fig 2, A), and the data are registered in an Excel table. Fixed to a table with a vise (Fig 2, B), the upper cast is digitized first. After the data have been saved, the lower model can be fixed to the table, and the upper model can be occluded to it (Fig 2, C). Three base points are digitized again the same way, and then the remaining points of the lower model are digitized and saved. By correlating the 3D positions of the 3 base
130 Hayasaki et al
American Journal of Orthodontics and Dentofacial Orthopedics July 2005
coefficient of the line (I) to the y-axis of the plane, 1 is the slope of the line (I), and ε is the error. If 0 ⫽ 0 and if 1 ⫽ 1, then D2 ⫽ D1. The error can be systematic or systematic and random; if the values of ε are adjusted to the normal distribution of probability with average 0, it will be considered only random. RESULTS
The data in Table I show that: ●
Fig 3. Regression line for type of error obtained by digital vs caliper measurements. ●
points, the software can provide interarch measurements. Raphe points are included for several reasons. These points are used to generate an anteroposterior (Z) axis along the midpalatal suture, which is needed for referencing measurements made by the program. Points 11 (incisal papillae), 12 (first transverse palatal ruga), and 13 (third transverse palatal ruga) are needed in case the program is used for longitudinal studies, because these areas are considered stable and suitable for superimposition.26,27
●
The data in Table II relate to ε identification in the model (I). It shows that: ● ●
MATERIAL AND METHODS
Fifteen cast models with normal occlusion were selected randomly from the archives of the Orthodontic Department of the Araraquara Dental School. The models were digitized twice by the same operator (R.P.M.), with 7 days between digitizations. To assess the bias of this method in measuring distances 3-dimensionally, we compared the measurements obtained by TIGARO with measurements taken with a digital caliper. The measurement selected was the distance between a point in the middle of the crown of the maxillary first molar and a like point on the mandibular first molar. The variances of both methods were compared and checked for the type of error obtained by each method. A linear regression model was applied (Fig 3), in which a line was adjusted by the formula D2 ⫽ 0 ⫹ 1 ⫻ D1 ⫹ ε (I), where D2 is the measurement obtained by the program (3D), D1 is the measurement obtained by the digital caliper, 0 is the intercept
The intercept coefficient (0) was 0 and the slope coefficient (1) was 1, because the observed values for the Student t test (t0) were not significant, resulting in P ⬎ .05 for each. The data generated by the program (D2) was statistically equal to the data obtained with the calipers (D1). So it can be said that the error (ε) of the model (I) was not systematic. The points in the Cartesian plane were adjusted to the regression model, because the values observed in the statistic (F0) associated with each measurement were significant (P ⬍ .05 was obtained). The determination coefficients (R2) associated were relevant, because it was verified that the model explained at least 74% of the variation of the obtained data in the D2 digitization, related to that obtained in the D1 measurement.
●
The ε average was 0, so the error was not systematic. The data of the ε are adjusted to the normal theoretical model of probability. In fact, for a group of data to be adjusted to the normal distribution, it would be necessary for the asymmetry coefficient to be 0 and the kurtosis coefficient to be 3. This is what occurred with our results, since (1) the asymmetry coefficient is 0, because the value of t0 was not significant (P ⬎ .05); also (2) the kurtosis coefficient minus 3 is 0, because the respective value of t0 was not significant (P ⬎ .05). The ε in the model (I) was only casual, because it was normally distributed with an average of 0, and variance or precision given in the second column.
In general, the results show that there is no statistical difference between the 2 methods for the test measurement (middle of the crown of the maxillary first molar to a like point on the mandibular first molar). Because the regression line statistically intercepts the y-axis at 0 and the slope of the line is 1, the systematic error is nonexistent, and the random error is normally distributed.
Hayasaki et al 131
American Journal of Orthodontics and Dentofacial Orthopedics Volume 128, Number 1
Table I.
Estimates, standard errors for 0 and 1 coefficients, values of t0, F0, R2, and P SE
t0
P⬍
F0
P⬍
R2 (%)
0.893 0.161
0.194 (ns) 0.193 (ns)
.194 .196
40.178 (s)
.001
74.4
Estimates 0 ⫽ 0.174 1 ⫽ 1.031
s, Significant; ns ⫽ not significant. Table II.
Average, variance, coefficients of asymmetry, and kurtosis for residual error ε
Average
Variance
Asymmetry
t0
P⬍
Kurtosis
t0
P⬍
0.092
⫺0.117
⫺0.207 (ns)
.839
⫺0.396
⫺0.363 (ns)
.722
0.0000
ns ⫽ Not significant.
DISCUSSION
The use of 3D scanning to produce virtual models can be an efficient method of obtaining measurements.17,20,22 However, the method is not without problems. First, most models collected so far are physical casts; converting them to digital records would take much time and money. Second, the cost of producing digital models is still relatively high, and only a few businesses provide this service. Third, because most of these businesses are in the United States, importation and customs taxes could discourage foreign investigators from using the service. For these reasons, we chose to use a mechanical 3D digitizer, the MicroScribe 3DX; it is relatively inexpensive compared with 3D scanners (about $3500 US) and relatively easy to work with. It takes about 5 minutes to digitize a pair of models. The easiest way to use this digitizer is to register the data in a Microsoft Excel spreadsheet; a mathematical formula or program is needed to further process the data. However, investigators using this device have reported only intra-arch measurements, never interarch.2,28 A recent master’s thesis analyzing normal occlusion in Brazilians reported linear values, such as the one examined in this study, of high reliability.25 CONCLUSIONS
Calculating 3D measurements with this new method of analyzing cast models is statistically equal to taking measurements with a digital caliper, thus it can be used for research and clinical practice. We thank Professor Ary Dias Mendes for his help with biostatistics. References 1. Andrews LF. Straight wire: the concept and appliance. San Diego: L. A. Wells; 1989. p. 23-35.
2. Ashmore JL. A 3-dimensional analysis of molar movement during headgear treatment. Am J Orthod Dentofacial Orthop 2001;121:18-30. 3. Bell A, Ayoub AF, Siebert P. Assessment of the accuracy of a three-dimensional imaging system for archiving dental study models. J Orthod 2003;30:219-23. 4. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod 1958; 28:113-30. 5. Burstone CJ. Diagnosis and treatment planning. Semin Orthod 1998;4:153-64. 6. Braun S, Hnat WP, Johnson BE. The curve of Spee revisited. Am J Orthod Dentofacial Orthop 1996;110:206-10. 7. Currier JH. A computerized geometric analysis of human dental arch form. Am J Orthod Dentofacial Orthop 1996;56:164-79. 8. Felton JM, Sinclair PM, Jones DL, Alexander RG. A computerized analysis of the shape and stability of mandibular arch form. Am J Orthod Dentofacial Orthop 1987;92:478-83. 9. Ferrario VF, Sforza C, Poggio CE, Serrao G, Colombo A. Three-dimensional dental arch curvature in adolescents and adults. Am J Orthod Dentofacial Orthop 1999;115:401-5. 10. Harris EF. A longitudinal study of arch size and form in untreated adults. Am J Orthod Dentofacial Orthop 1997;111: 419-27. 11. Little RM. The irregularity index: a quantitative score of mandibular anterior alignment. Am J Orthod 1975;68:554-63. 12. Nie Q, Lin J. Comparison of intermaxillary tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1999;116:539-44. 13. Nojima K, McLaughlin RP, Isshiki Y, Sinclair PM. A comparative study of Caucasian and Japanese mandibular clinical arch forms. Angle Orthod 2001;71:195-200. 14. Noroozi H, Hosseinzadeh Nik T, Saeeda R. The dental arch form revisited. Angle Orthod 2001;71:386-9. 15. Parkinson CE, Buschang PH, Behrents RG, Throckmorton GS, English JD. A new method of evaluating posterior occlusion and its relation to posttreatment occlusal changes. Am J Orthod Dentofacial Orthop 2001;120:503-12. 16. Raberin M, Laumon B, Martin JL, Brunner F. Dimensions and form of dental arches in subjects with normal occlusions. Am J Orthod Dentofacial Orthop 1993;104:67-72. 17. Santoro M, Galkin S, Teredesai M, Nicolay OF, Cangialosi TJ. Comparison of measurements made on digital and plaster models. Am J Orthod Dentofacial Orthop 2003;124:101-5. 18. Sohmura T, Kojima T, Wakabayashi K, Takahashi J. Use of an ultrahigh-speed laser scanner for constructing three-dimen-
132 Hayasaki et al
19.
20.
21. 22.
23. 24.
sional shapes of dentition and occlusion. J Prosthet Dent 2000;84:345-52. Warren JJ, Bishara SE. Comparison of dental arch measurements in the primary dentition between contemporary and historic samples. Am J Orthod Dentofacial Orthop 2001;119:211-5. Zilberman O, Huggare JÅV, Parikakis KA. Evaluation of the validity of tooth size and arch width measurements using conventional and three-dimensional virtual orthodontic models. Angle Orthod 2003;73:301-6. Angle EH. Classification of malocclusion. Dent Cosmos 1889; 41:248-64. Tomassetti JJ, Taloumis LJ, Denny JM, Fischer JR. A comparison of 3 computerized Bolton tooth-size analyses with a commonly used method. Angle Orthod 2001;71:351-7. Andrews LF. The six keys to a normal occlusion. Am J Orthod 1972;62:296-309. Ferrario VF, Sforza C, Colombo A, Ciusa V, Serrao G. Threedimensional inclination of the dental axes in healthy permanent
American Journal of Orthodontics and Dentofacial Orthopedics July 2005
25.
26.
27. 28.
dentitions: a cross-sectional study in a normal population. Angle Orthod 2001;71:257-64. Martins RP. Análise tridimensional da oclusão normal na população brance brasileira (Tridimensional study of normal occlusion in white Brazilians) [thesis]. Araraquara, Brazil: Faculdade de Odontologia de Araraquara, Universidade Estadual Paulista; 2004. Almeida MA, Phillips C, Kula K, Tulloch C. Stability of the palatal rugae as landmarks for analysis of dental casts. Angle Orthod 1995;65:43-8. van der Linden FPGM. Changes in the position of posterior teeth in relation to ruga points. Am J Orthod 1978;74:142-61. Dinelli TCS. Mudanças dimensionais dos arcos dentários em crianças entre 3 e 6 anos de idade (Dimensional dental arch changes in children from 3 to 6 years old). [thesis]. Araraquara, Brazil: Faculdade de Odontologia de Araraquara, Universidade Estadual Paulista; 2002.
A new way of analyzing occlusion 3 dimensionally Haruaki Hayasaki,a Renato Parsekian Martins,b Luiz Gonzaga Gandini Jr,c Issei Saitoh,d and Kazuaki Nonakae Fukuoka, Japan, and Araraquara, Brazil This article introduces a new method for 3-dimensional dental cast analysis, by using a mechanical 3-dimensional digitizer, MicroScribe 3DX (Immersion, San Jose, Calif), and TIGARO software (not yet released, but available from the author at [email protected]). By digitizing points on the model, multiple measurements can be made, including tooth dimensions; arch length, width, and perimeter; curve of Spee; overjet and overbite; and anteroposterior discrepancy. The bias of the system can be evaluated by comparing the distance between 2 points as determined by the new system and as measured with digital calipers. Fifteen pairs of models were measured digitally and manually, and the bias was evaluated by comparing the variances of both methods and checking for the type of error obtained by each method. No systematic errors were found. The results showed that the method is accurate, and it can be applied to both clinical practice and research. (Am J Orthod Dentofacial Orthop 2005;128:128-32)
A
number of articles have been published reporting data obtained from dental casts.1-20 Three-dimensional (3D) model analysis has been carried out with simple observation,21 calipers,4,11,17,22 calipers in conjunction with protractors and rulers,1,23 digital calipers,10,19,20,22 computer analysis with punch cards,7 computers and digitized photocopies of casts,8,13,14 video cameras,22 scanners,15 devices used for precision production,6,12 electromagnetic 3D digitizers,9,24 scanner-based 3D digitizers (as done by OrthoCAD),17,20,22 laser-based scanners,18 and mechanical 3D digitizers,2 as used in this study. One limitation of digital, 3D cast analysis is the difficulty of taking interarch measurements; it is sometimes impossible to do so without damaging the model. MicroScribe 3DX (Immersion, San Jose, Calif), is a mechanical 3D digitizing system that captures the physical properties of 3D objects and translates them into digital 3D models. The data (3-plane coordinates) are registered in an Excel (Microsoft, Redmond, Wash) a
Assistant professor, Pediatric Dental Clinic, Kyushu University Hospital, Fukuoka, Japan. b PhD student, Orthodontic Department, Araraquara Dental School, University of the State of São Paulo, Brazil. c Assistant professor, Orthodontic Department, Araraquara Dental School, University of the State of São Paulo, Brazil. d Research assistant, Pediatric Dental Clinic, Kyushu University Hospital, Fukuoka, Japan. e Professor and chairman, Department of Pediatric Dentistry, Kyushu University, Fukuoka, Japan. Reprint requests to: Dr Renato Parsekian Martins, Instituto de Ortodontia, Prof Dr Joel Claudio da Rosa Martins, Rua Carlos Gomes, 2158, 14801-340 Araraquara, São Paulo, Brazil; e-mail, [email protected]. Submitted and accepted, July 2004. 0889-5406/$30.00 Copyright © 2005 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2004.07.039
128
table, and another software program is needed to work with the data. We used TIGARO software (not yet released, but available from the author at hayasaki@ dent.kyushu-u.ac.jp). This software makes mathematical calculations that relate the maxillary arch to the mandibular arch by means of the 3 base points that are each digitized 3 times. From that relationship, it is possible to make measurements between the arches in all 3 planes of space. Interarch distances can be measured with the models occluded without damaging them. Although some research has already been done with this technique,25 more work is needed to assess the bias of the method and to determine how the method compares with traditional methods. The aims of this article are to introduce TIGARO software for cast analysis (to be used with data collected systematically by a mechanical 3D digitizer) and to evaluate bias in relation to the measurements obtained with digital calipers. The program
Among the measurements TIGARO can calculate are (1) intercanine, interpremolar, and intermolar distances; (2) arch perimeter and length; (3) arch shape; (4) thickness of the teeth in the middle third; (5) depth of the curve of Spee; (6) tooth angulation and inclination; (7) cusp height; (8) crown height; (9) overjet and overbite; (10) angulations and distances between maxillary and mandibular planes of occlusion; (11) curves of Wilson and Monson; (12) midline deviation; (13) differences in incisal level of incisors; and (14) accom-
Hayasaki et al 129
American Journal of Orthodontics and Dentofacial Orthopedics Volume 128, Number 1
Fig 1. Points marked on models to be digitized systematically.
Fig 2. A, MicroScribe 3DX; B, maxillary model fixed and ready to be digitized; C, models occluded for digitization.
modation of the maxillary second premolar between the mandibular second premolar and the first molar (distance of class). The program works in 3 phases. First, the upper model is digitized, then the lower model, and, finally, the upper model data are related to the lower by means of the base points. To collect the required data, the model is first digitized with the MicroScribe device. After checking the model for imperfections, 133 points on the upper cast and 129 on the lower are marked with a 0.3-mm mechanical pencil (Fig 1). The points must be at
specific positions; the most important points are on the base of the upper model. The points are then systematically digitized with a MicroScribe 3D digitizer (Fig 2, A), and the data are registered in an Excel table. Fixed to a table with a vise (Fig 2, B), the upper cast is digitized first. After the data have been saved, the lower model can be fixed to the table, and the upper model can be occluded to it (Fig 2, C). Three base points are digitized again the same way, and then the remaining points of the lower model are digitized and saved. By correlating the 3D positions of the 3 base
130 Hayasaki et al
American Journal of Orthodontics and Dentofacial Orthopedics July 2005
coefficient of the line (I) to the y-axis of the plane, 1 is the slope of the line (I), and ε is the error. If 0 ⫽ 0 and if 1 ⫽ 1, then D2 ⫽ D1. The error can be systematic or systematic and random; if the values of ε are adjusted to the normal distribution of probability with average 0, it will be considered only random. RESULTS
The data in Table I show that: ●
Fig 3. Regression line for type of error obtained by digital vs caliper measurements. ●
points, the software can provide interarch measurements. Raphe points are included for several reasons. These points are used to generate an anteroposterior (Z) axis along the midpalatal suture, which is needed for referencing measurements made by the program. Points 11 (incisal papillae), 12 (first transverse palatal ruga), and 13 (third transverse palatal ruga) are needed in case the program is used for longitudinal studies, because these areas are considered stable and suitable for superimposition.26,27
●
The data in Table II relate to ε identification in the model (I). It shows that: ● ●
MATERIAL AND METHODS
Fifteen cast models with normal occlusion were selected randomly from the archives of the Orthodontic Department of the Araraquara Dental School. The models were digitized twice by the same operator (R.P.M.), with 7 days between digitizations. To assess the bias of this method in measuring distances 3-dimensionally, we compared the measurements obtained by TIGARO with measurements taken with a digital caliper. The measurement selected was the distance between a point in the middle of the crown of the maxillary first molar and a like point on the mandibular first molar. The variances of both methods were compared and checked for the type of error obtained by each method. A linear regression model was applied (Fig 3), in which a line was adjusted by the formula D2 ⫽ 0 ⫹ 1 ⫻ D1 ⫹ ε (I), where D2 is the measurement obtained by the program (3D), D1 is the measurement obtained by the digital caliper, 0 is the intercept
The intercept coefficient (0) was 0 and the slope coefficient (1) was 1, because the observed values for the Student t test (t0) were not significant, resulting in P ⬎ .05 for each. The data generated by the program (D2) was statistically equal to the data obtained with the calipers (D1). So it can be said that the error (ε) of the model (I) was not systematic. The points in the Cartesian plane were adjusted to the regression model, because the values observed in the statistic (F0) associated with each measurement were significant (P ⬍ .05 was obtained). The determination coefficients (R2) associated were relevant, because it was verified that the model explained at least 74% of the variation of the obtained data in the D2 digitization, related to that obtained in the D1 measurement.
●
The ε average was 0, so the error was not systematic. The data of the ε are adjusted to the normal theoretical model of probability. In fact, for a group of data to be adjusted to the normal distribution, it would be necessary for the asymmetry coefficient to be 0 and the kurtosis coefficient to be 3. This is what occurred with our results, since (1) the asymmetry coefficient is 0, because the value of t0 was not significant (P ⬎ .05); also (2) the kurtosis coefficient minus 3 is 0, because the respective value of t0 was not significant (P ⬎ .05). The ε in the model (I) was only casual, because it was normally distributed with an average of 0, and variance or precision given in the second column.
In general, the results show that there is no statistical difference between the 2 methods for the test measurement (middle of the crown of the maxillary first molar to a like point on the mandibular first molar). Because the regression line statistically intercepts the y-axis at 0 and the slope of the line is 1, the systematic error is nonexistent, and the random error is normally distributed.
Hayasaki et al 131
American Journal of Orthodontics and Dentofacial Orthopedics Volume 128, Number 1
Table I.
Estimates, standard errors for 0 and 1 coefficients, values of t0, F0, R2, and P SE
t0
P⬍
F0
P⬍
R2 (%)
0.893 0.161
0.194 (ns) 0.193 (ns)
.194 .196
40.178 (s)
.001
74.4
Estimates 0 ⫽ 0.174 1 ⫽ 1.031
s, Significant; ns ⫽ not significant. Table II.
Average, variance, coefficients of asymmetry, and kurtosis for residual error ε
Average
Variance
Asymmetry
t0
P⬍
Kurtosis
t0
P⬍
0.092
⫺0.117
⫺0.207 (ns)
.839
⫺0.396
⫺0.363 (ns)
.722
0.0000
ns ⫽ Not significant.
DISCUSSION
The use of 3D scanning to produce virtual models can be an efficient method of obtaining measurements.17,20,22 However, the method is not without problems. First, most models collected so far are physical casts; converting them to digital records would take much time and money. Second, the cost of producing digital models is still relatively high, and only a few businesses provide this service. Third, because most of these businesses are in the United States, importation and customs taxes could discourage foreign investigators from using the service. For these reasons, we chose to use a mechanical 3D digitizer, the MicroScribe 3DX; it is relatively inexpensive compared with 3D scanners (about $3500 US) and relatively easy to work with. It takes about 5 minutes to digitize a pair of models. The easiest way to use this digitizer is to register the data in a Microsoft Excel spreadsheet; a mathematical formula or program is needed to further process the data. However, investigators using this device have reported only intra-arch measurements, never interarch.2,28 A recent master’s thesis analyzing normal occlusion in Brazilians reported linear values, such as the one examined in this study, of high reliability.25 CONCLUSIONS
Calculating 3D measurements with this new method of analyzing cast models is statistically equal to taking measurements with a digital caliper, thus it can be used for research and clinical practice. We thank Professor Ary Dias Mendes for his help with biostatistics. References 1. Andrews LF. Straight wire: the concept and appliance. San Diego: L. A. Wells; 1989. p. 23-35.
2. Ashmore JL. A 3-dimensional analysis of molar movement during headgear treatment. Am J Orthod Dentofacial Orthop 2001;121:18-30. 3. Bell A, Ayoub AF, Siebert P. Assessment of the accuracy of a three-dimensional imaging system for archiving dental study models. J Orthod 2003;30:219-23. 4. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod 1958; 28:113-30. 5. Burstone CJ. Diagnosis and treatment planning. Semin Orthod 1998;4:153-64. 6. Braun S, Hnat WP, Johnson BE. The curve of Spee revisited. Am J Orthod Dentofacial Orthop 1996;110:206-10. 7. Currier JH. A computerized geometric analysis of human dental arch form. Am J Orthod Dentofacial Orthop 1996;56:164-79. 8. Felton JM, Sinclair PM, Jones DL, Alexander RG. A computerized analysis of the shape and stability of mandibular arch form. Am J Orthod Dentofacial Orthop 1987;92:478-83. 9. Ferrario VF, Sforza C, Poggio CE, Serrao G, Colombo A. Three-dimensional dental arch curvature in adolescents and adults. Am J Orthod Dentofacial Orthop 1999;115:401-5. 10. Harris EF. A longitudinal study of arch size and form in untreated adults. Am J Orthod Dentofacial Orthop 1997;111: 419-27. 11. Little RM. The irregularity index: a quantitative score of mandibular anterior alignment. Am J Orthod 1975;68:554-63. 12. Nie Q, Lin J. Comparison of intermaxillary tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1999;116:539-44. 13. Nojima K, McLaughlin RP, Isshiki Y, Sinclair PM. A comparative study of Caucasian and Japanese mandibular clinical arch forms. Angle Orthod 2001;71:195-200. 14. Noroozi H, Hosseinzadeh Nik T, Saeeda R. The dental arch form revisited. Angle Orthod 2001;71:386-9. 15. Parkinson CE, Buschang PH, Behrents RG, Throckmorton GS, English JD. A new method of evaluating posterior occlusion and its relation to posttreatment occlusal changes. Am J Orthod Dentofacial Orthop 2001;120:503-12. 16. Raberin M, Laumon B, Martin JL, Brunner F. Dimensions and form of dental arches in subjects with normal occlusions. Am J Orthod Dentofacial Orthop 1993;104:67-72. 17. Santoro M, Galkin S, Teredesai M, Nicolay OF, Cangialosi TJ. Comparison of measurements made on digital and plaster models. Am J Orthod Dentofacial Orthop 2003;124:101-5. 18. Sohmura T, Kojima T, Wakabayashi K, Takahashi J. Use of an ultrahigh-speed laser scanner for constructing three-dimen-
132 Hayasaki et al
19.
20.
21. 22.
23. 24.
sional shapes of dentition and occlusion. J Prosthet Dent 2000;84:345-52. Warren JJ, Bishara SE. Comparison of dental arch measurements in the primary dentition between contemporary and historic samples. Am J Orthod Dentofacial Orthop 2001;119:211-5. Zilberman O, Huggare JÅV, Parikakis KA. Evaluation of the validity of tooth size and arch width measurements using conventional and three-dimensional virtual orthodontic models. Angle Orthod 2003;73:301-6. Angle EH. Classification of malocclusion. Dent Cosmos 1889; 41:248-64. Tomassetti JJ, Taloumis LJ, Denny JM, Fischer JR. A comparison of 3 computerized Bolton tooth-size analyses with a commonly used method. Angle Orthod 2001;71:351-7. Andrews LF. The six keys to a normal occlusion. Am J Orthod 1972;62:296-309. Ferrario VF, Sforza C, Colombo A, Ciusa V, Serrao G. Threedimensional inclination of the dental axes in healthy permanent
American Journal of Orthodontics and Dentofacial Orthopedics July 2005
25.
26.
27. 28.
dentitions: a cross-sectional study in a normal population. Angle Orthod 2001;71:257-64. Martins RP. Análise tridimensional da oclusão normal na população brance brasileira (Tridimensional study of normal occlusion in white Brazilians) [thesis]. Araraquara, Brazil: Faculdade de Odontologia de Araraquara, Universidade Estadual Paulista; 2004. Almeida MA, Phillips C, Kula K, Tulloch C. Stability of the palatal rugae as landmarks for analysis of dental casts. Angle Orthod 1995;65:43-8. van der Linden FPGM. Changes in the position of posterior teeth in relation to ruga points. Am J Orthod 1978;74:142-61. Dinelli TCS. Mudanças dimensionais dos arcos dentários em crianças entre 3 e 6 anos de idade (Dimensional dental arch changes in children from 3 to 6 years old). [thesis]. Araraquara, Brazil: Faculdade de Odontologia de Araraquara, Universidade Estadual Paulista; 2002.