ORIGINAL ARTICLE
Effect of bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics: A 3-dimensional finite element study Jun-ya Tominaga,a Hiroya Ozaki,b Pao-Chang Chiang,b Mayumi Sumi,b Motohiro Tanaka,c Yoshiyuki Koga,d Christoph Bourauel,e and Noriaki Yoshidaf Nagasaki, Japan, and Bonn, Germany
Introduction: It has been found that controlled movement of the anterior teeth can be obtained by attaching a certain length of power arm onto an archwire in sliding mechanics. However, the impact of the archwire/bracket play on anterior tooth movement has not been clarified. The purpose of this study was to compare the effect of the power arm on anterior tooth movements with different dimensions of bracket slots and archwires. Methods: A 3-dimensional finite element method was used to simulate en-masse anterior tooth retraction in sliding mechanics. Displacements of the maxillary central incisor and the archwire deformation were calculated when applying retraction forces from different lengths of power arms. Results: When a 0.017 3 0.022-in archwire was engaged into the 0.018-in slot bracket, bodily movement of the incisor was obtained with 9.1-mm length of the power arm. When a 0.022-in slot system was coupled with a 0.019 3 0.025-in archwire, bodily movement was observed with a power arm length of 11.6 mm. Conclusions: Archwire/bracket play has a remarkable impact on anterior tooth movement. An effective torque application to the anterior teeth becomes clinically difficult in sliding mechanics combined with power arms when the archwire/bracket play is large. (Am J Orthod Dentofacial Orthop 2014;146:166-74)
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he demand for speedy, effective, and accurate orthodontic treatment systems has increased to shorten the treatment period.1-6 Accordingly, the
a Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan; research fellow, Department of Oral Technology, School of Dentistry, University of Bonn, Bonn, Germany. b Postgraduate student, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. c Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. d Senior assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. e Cendres+Metaux endowed professor and chair, Department of Oral Technology, School of Dentistry, University of Bonn, Bonn, Germany. f Professor and chair, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Noriaki Yoshida, Department of Orthodontics and Dentofacial Orthopedics, Nagasaki University Graduate School of Biomedical Sciences, 1-7-1 Sakamoto, Nagasaki 852-8588, Japan; e-mail, nori@ nagasaki-u.ac.jp. Submitted, September 2013; revised and accepted, April 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.04.016
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use of implant anchorage in sliding mechanics has become more common all around the world. In addition to this system, sliding mechanics with the combined use of power arms has gradually been applied for obtaining controlled anterior tooth movements during space closure (Fig 1). That is, the desired type of anterior tooth movement, such as lingual crown tipping, bodily movement, or lingual root tipping, can be easily achieved by attaching various lengths of power arms onto an archwire in sliding mechanics.7-14 Several studies have been carried out to investigate various biomechanical factors affecting tooth movement in sliding mechanics, such as the flexural rigidity of the archwire, friction, and height of the retraction force.8,12–16 However, optimal loading conditions for controlled movement of anterior teeth in sliding mechanics combined with power arms are not fully understood. A few attempts with the finite element (FE) method have been reported on tooth displacement when a single canine retraction or an en-masse retraction is performed in sliding mechanics.17-19 In those studies, spring elements are used between a tooth and an archwire instead of friction between the surface of a bracket slot and an archwire. Therefore, the mechanical
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Fig 1. Intraoral picture of the en-masse maxillary anterior tooth retraction in sliding mechanics combined with power arms and skeletal anchorages.
condition is not sufficiently accurate to approximate an actual clinical situation. To our knowledge, there are only 2 studies that simulate en-masse retraction when brackets were modeled and a coefficient of friction was given to the interface between bracket slots and an archwire including contact-sliding problems.20,21 It was found that the anterior tooth movement varied depending on the amount of archwire/bracket play. However, the effect of play on anterior tooth movement has not been fully understood; clinicians must consider this in an actual clinical situation for any treatment step in sliding mechanics. The purpose of this study was to clarify the effect of the bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics by means of a 3-dimensional (3D) FE model. MATERIAL AND METHODS
The construction method of the 3D FE model has been described previously.20 Computed tomography images of the 14 maxillary teeth, taken with a multi-image cone-beam computed tomography scanner (3DX; J. Morita, Kyoto, Japan), were saved as DICOM data and exported to 3D image processing and editing software (Mimics 10.02; Materialize Software, Leuven, Belgium). The 3D solid model was created and converted to a 3D FE model using FE analysis preprocess and postprocess software (Patran 2008r1; MSC Software, Los Angeles, Calif). Each 3D FE model for the periodontal ligament (PDL), alveolar bone, bracket, archwire, and power arm was separately constructed using the same software. The PDL had a uniform thickness of 0.2 mm.22-24 The bracket height of the maxillary central incisor was placed according to a prescription, which was 4.5 mm in height from the incisal edge of the tooth.25,26 Two 3D solid models were constructed. One had the combination of brackets with a 0.018 3 0.025-in slot
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and a 0.017 3 0.022-in stainless steel archwire, and the other had 0.022 3 0.028-in slot brackets and a 0.019 3 0.025-in archwire. Based on these 3D solid models, an FE mesh was created to make a node-tonode connection between tooth, PDL, and alveolar bone. An FE mesh of the archwire was created separately from the bracket to allow the archwire to slide through the bracket slots. The 3D FE model consisted of 423,772 isoparametric tetrahedral solid elements (10 noded) and 83,790 nodes, or 432,356 elements and 85,957 nodes (Fig 2). The material parameters used in this study are represented in the Table.23,24 To simplify the model and reduce the time for analysis, the same properties were given to the archwires, power arms, and brackets. Other structures such as teeth, alveolar bone, and PDL were modeled as homogenous and isotropic for the same reason. Assuming that the case model was diagnosed as maxillary protrusion, bilateral maxillary first premolar extractions were indicated. The model included 12 teeth, and 2 skeletal anchorages (miniscrews or miniplate implants) were inserted at both sides of the buccal region between the second premolar and the first molar. Two power arms were attached onto an archwire bilaterally at the segment between the lateral incisor and the canine, and these lengths were changed from 0 to 12 mm with 0.1-mm intervals from the bracket slot level (Fig 3). The horizontal retraction force of 1.5 N was applied from the implant anchorage to the power arm on both sides. The model was restrained in 6 of freedom at the bottom of the alveolar bone. The coefficient of friction between the bracket slots and the archwire was assumed to be 0.2.27-29 A cross-sectional view indicating the boundary between the bracket and the archwire is shown in Figure 4. The archwire was horizontally positioned to contact the bottom surface of the bracket slots and vertically in the middle of the bracket. Under these conditions, 3D FE analysis was performed using a 3D FE program (Marc; MSC Software). We analyzed how the archwire was deformed and, consequently, how the maxillary central incisor moved. Then we compared the results obtained with the 0.017 3 0.022-in stainless steel archwire in the 0.018-in slot and the 0.019 3 0.025-in archwire in the 0.022-in slot. RESULTS
The relationship between the degree of labiolingual tipping of the maxillary central incisor and the height of retraction force on the power arm is shown in Figure 5. If the 0.017 3 0.022-in stainless steel archwire was engaged into the 0.018-in slot brackets as shown by a solid line in Figure 5, lingual crown tipping of the
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Fig 2. Three-dimensional FE model of the maxillary dentition, including the PDL, alveolar bone, brackets, and archwire.
Table. Material parameters of tooth, PDL, alveolar
bone, archwire, power arm, and bracket Material Tooth PDL Alveolar bone Archwire/power arm/bracket
Young's modulus (MPa) 20000 0.05 2000 200000
Poisson's ratio 0.30 0.30 0.30 0.30
maxillary central incisor was observed when the retraction force was applied at 0 mm, which corresponds to the bracket slot level. The direction of tooth rotation changed from lingual crown tipping to lingual root tipping as the level of the retraction force on the power arm was moved apically from the bracket slot level. At the height of 9.1 mm, no rotation was observed; ie, bodily movement occurred. Lingual root tipping of the incisor was produced when the retraction force was set above 9.1 mm. When the 0.022-in slot bracket system was combined with the 0.019 3 0.025-in archwire, bodily movement of the incisor was achieved at the height level of the retraction force of 11.6 mm as shown by a dotted line in Figure 5, although the rotational endency was the same as the 0.018-in slot system. Figure 6 shows the loading conditions under which controlled anterior tooth movements, such as controlled lingual root tipping, bodily movement, and controlled lingual crown tipping, can be achieved. Controlled lingual root tipping is defined
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as the type of tooth movement in which the tooth tips around its incisal edge as the center of rotation. On the other hand, controlled lingual crown tipping indicates the movement in which the tooth tips around its root apex as the center of rotation. If the 0.017 3 0.022-in archwire was used in a 0.018in slot, controlled lingual root tipping was carried out at the height of the retraction force of 9.5 mm, which was 2.3 mm higher than the level of the center of resistance. At a height of 9.1 mm, bodily movement was achieved. Controlled lingual crown tipping was observed at the 8.3-mm height of retraction force level (Fig 6, A). When the 0.019 3 0.025-in archwire was used in the 0.022-in slot, controlled lingual root tipping was obtained at the height of 13.0 mm. Bodily movement was produced at an 11.6-mm height of retraction force. Controlled lingual crown tipping occurred at a level of 10.3-mm height (Fig 6, B). The deformation of the archwire and the resultant displacement of the maxillary central incisor and first molar after the application of retraction force at the level of 12 mm are shown in Figure 7. For a better understanding of the deformation of the archwire and the tooth displacement, these displacements were magnified 50 times, and the displacements of the central incisor were focused on. The tooth and the archwire in blue show the initial positions. When the 0.017 3 0.022-in archwire was used in the 0.018-in slot, the anterior segment of the archwire was deformed upward. The root of the maxillary central
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Fig 3. Illustration of the experimental conditions of anterior tooth retraction with the combinations of various lengths of power arms and skeletal anchorage in sliding mechanics.
Fig 4. Cross-sectional view of the archwire/bracket interface in the FE model.
incisor was moved lingually, and the crown was moved labially (Fig 7, A). The labiolingual tipping was 0.17 (lingual root tipping). When the 0.019 3 0.025-in archwire was used in the 0.022-in slot, the incisor showed almost bodily movement with less lingual root tipping of 0.02 , although the tendency of archwire deformation was similar to that of the 0.018-in slot coupled with the 0.017 3 0.022-in archwire (Fig 7, B).
DISCUSSION
We found that the dimension of the play between the bracket slot and the archwire has a significant impact on anterior tooth movement when the retraction force was applied to a power arm in sliding mechanics. Even if the same height of the horizontal retraction force was applied, there were great discrepancies in the types of anterior tooth movement between the 2 combinations
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Fig. 5. Degree of the labiolingual tipping of the maxillary central incisor subjected to the various heights of retraction force on the power arm. Positive signs indicate lingual crown tipping, whereas negative signs indicate lingual root tipping.
of bracket slot size and archwire size. When the height level of the force was increased, this discrepancy was also increased (Fig 5). Although controlled tooth movement from lingual crown tipping to lingual root tipping can be easily achieved with a 0.017 3 0.022-in archwire in a 0.018-in slot, lingual root tipping can hardly be generated with power arms shorter than 10 mm if a 0.019 3 0.025-in archwire is used in a 0.022-in slot. This might be due to the difference in the play between brackets and archwires. From a biomechanical point of view, it has been stated that the type of tooth movement, such as lingual crown tipping, bodily movement, or lingual root tipping, is determined by the relationship between a line of action of a force and the location of the center of resistance of a tooth, and a single force passing through the center of resistance causes bodily tooth movement.7,30,31 However, as shown in Figure 6, the tooth movements analyzed in this study did not agree with that concept based on the biomechanical principles. Since the location of the center of resistance of the maxillary central incisor in the FE model, which we used, was determined to be at the level of 7.2 mm apically from the bracket slot, bodily movement of the incisor was expected to be produced at the height of 7.2 mm of retraction force. Nevertheless, FE analysis showed that bodily movement of the incisor occurred at the height of 9.1 mm, which is 1.9 mm apical to the level of the center of resistance with
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a 0.017 3 0.022-in archwire in a 0.018-in slot (Fig 6, A). On the other hand, bodily movement occurs at the level of 11.6 mm, which is 4.4 mm apical to the position of the center of resistance with a 0.019 3 0.025-in archwire in a 0.022-in slot (Fig 6, B). Those results indicate that the concepts based on theoretical considerations cannot be simply applied to multibracket appliances. When a 0.017 3 0.022-in archwire is used in a 0.018in slot, longer power arms than the perpendicular distance from the bracket level to the center of resistance are required to achieve controlled movement of the anterior teeth, including controlled lingual root tipping, bodily movement, and controlled lingual crown tipping (Fig 6, A). If a 0.019 3 0.025-in archwire is engaged into a 0.022-in slot, much longer power arms are required to produce any anterior tooth movement (Fig 6, B). As mentioned in the previous articles, when long power arms were used, a substantial amount of bending moment is generated at the portion of the archwire where the power arms were attached as a cantilever effect.20,21 As a result, the anterior segment of the archwire was raised upward, causing lingual root tipping with a full-sized 0.018 3 0.025-in archwire. Although in this study we found similar results for the phenomenon of the cantilever effect, bodily movement or lingual root tipping seems to be difficult to obtain with the 0.022-in slot system compared with the 0.018-in slot system in sliding mechanics with the combined use of power arms. Since the torsion of the archwire within a bracket slot and its general deformation were considered to have major impacts on tooth movement, displacements of the archwire and the resultant tooth displacement were analyzed when 0.017 3 0.022-in and 0.019 3 0.025-in archwires are used (Fig 7). The anterior segment of the archwire is subjected to torsion caused by the power arms. When a 0.017 3 0.022-in archwire is used in a 0.018-in slot, the torque is likely to be practically transmitted to the bracket on the incisor. Moreover, a smaller play between the brackets and the archwire might contribute to a more efficient torque application. Thus, lingual root tipping can be clinically achieved with power arms in the 0.018-in slot (Fig 7, A). Contrary to this, the torsion of the archwire is less likely to be transmitted effectively to the incisor because of the greater play between the brackets and the archwire, thereby causing less lingual root tipping in the 0.022-in slot (Fig 7, B). To compare the interaction of an archwire with brackets on the incisor in the 0.018-in slot with that in the 0.022-in slot and elucidate the mechanism of generation of lingual root torque, the sagittal crosssectional view at the mesial surface of the maxillary central incisor bracket was constructed before and after
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Fig 6. Loading conditions when controlled movements of a maxillary central incisor are obtained: A, 0.017 3 0.022-in archwire in 0.018-in slot; B, 0.019 3 0.025-in archwire in 0.022-in slot. CRe, Center of resistance; CRo, center of rotation.
Fig 7. Displacement of the maxillary central incisor and the deformation of the archwire on the application of retraction force at the height of 12 mm. For a better understanding of the displacement of the tooth and deformation of the archwire, these movements are magnified 50 times. Initial positions of the tooth and archwire are indicated by blue lines. A, 0.017 3 0.022-in archwire in 0.018-in slot; B, 0.019 3 0.025-in archwire in 0.022-in slot.
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Fig 8. Sagittal cross-section at the mesial surface of the maxillary central incisor bracket before exerting retraction force (left) and after the application of the force at the height of 12 mm (right): 0.017 3 0.022-in archwire in 0.018-in slot (top) and 0.019 3 0.025-in archwire in 0.022-in slot (bottom).
the application of the orthodontic force at the level of 12 mm (Fig 8). When an archwire is twisted by a bending moment of the power arms, the diagonally opposite corners of the archwire contact the surface of the bracket slot. Then a pair of normal forces, called lingual root tipping moments, is generated. That is, torque acting on the anterior tooth becomes applicable with a combination of a 0.017 3 0.022-in archwire and 0.018-in slot brackets with smaller archwire/bracket clearances (Fig 8, top). However, a normal force in the downward direction is not produced at this crosssectional view when a 0.019 3 0.025-in archwire was used in the 0.022-in slot, which has a larger play (Fig 8, bottom). Although the horizontal dimension of the play in the 0.018-in slot system is the same as that in the 0.022-in slot, the vertical dimension of the play in the 0.022-in slot is 3 times as large as that in the 0.018-in slot (Fig 8). This indicates that play in the vertical dimension has a greater impact on the movements of the anterior teeth than in the horizontal dimension. It is considered that the greater the play between the archwire and the bracket, the weaker the normal forces. As a result, less lingual root tipping moment is transmitted to the incisor in the 0.022-in slot system. Therefore, it becomes more difficult to prescribe an optimal power arm length for achieving the
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desired type of anterior tooth movement if there is a large archwire/bracket clearance. As mentioned above, the dimension of the play is the most influential factor in determining the type of anterior tooth movement in sliding mechanics combined with power arms. Thus, the conventional biomechanical principles of tooth movement in orthodontics cannot be directly applied in actual clinical situations. Although a comprehension of the relationship between a line of action of a retraction force and the position of the center of resistance of a tooth is an important key to an estimation of how the tooth will move, the effect of the archwire deflection within the bracket slot and its general deformation on the force system acting on a tooth should also be considered (Figs 7 and 8). Although applying a retraction force on the power arm modifies the type of anterior tooth movement in sliding mechanics in a simple way, quite long power arms of 10 to 13 mm are required to achieve controlled movement of the anterior teeth in the 0.022-in slot system. Particularly, controlled lingual root tipping is only obtained with power arms of 13 mm; this is too long to be applied in a clinical situation. In this case, the use of high-torque brackets on the anterior teeth seems recommendable to optimize torque application.
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Even if the 0.018-in slot system is coupled with a 0.017 3 0.022-in archwire, power arms longer than 9 mm are required for obtaining bodily movement or lingual root tipping. Therefore, the clinical application of power arms combined with sliding mechanics is difficult in some patients whose gingivobuccal fold is shallow. Also, it is necessary to give full consideration to anatomic parameters that vary between patients to precisely predict the tooth movements during the orthodontic treatment. Especially, an estimation of the center of resistance position is of utmost clinical importance because the required length of the power arm producing a certain type of tooth movement is closely related to the location of the center of resistance. The height of the retraction force relative to the level of the center of resistance is more critical than the length of the power arm, which by itself has no consequence. For example, power arms 1.1 mm longer than the perpendicular distance from the bracket level to the center of resistance are indicated for achieving controlled lingual crown tipping in the 0.018-in slot system (Fig 6). A clinical study is needed to confirm these conclusions from this FE investigation; it should consider not only the relationship between the line of action of a retraction force and the location of the center of resistance of a tooth, but also the effect of the archwire deformation including the torsion within the different dimensions of bracket slots and archwires. This will be a great help in establishing an optimal treatment plan and achieving speedy, effective, and accurate orthodontic tooth movement. CONCLUSIONS
Controlled anterior tooth movement can be achieved in sliding mechanics with the combined use of power arms as long as the archwire/bracket clearance is small. The dimension of the play that is determined by the combination of the bracket slot size and the archwire size has a great impact on the control of the anterior tooth movement. The greater the archwire/bracket play becomes, the more difficult it is to apply an effective torque to the anterior teeth. Optimal power-arm length must be longer than the perpendicular distance from the bracket level to the center of resistance of the anterior tooth to obtain any type of anterior tooth movement. Particularly with a large archwire/bracket play, much longer power arms are necessary to apply an effective torque. Therefore, a clinical application of power arms combined with sliding mechanics becomes more difficult for patients with a limited depth of the gingivobuccal fold.
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Effect of bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics: A 3-dimensional finite element study Jun-ya Tominaga,a Hiroya Ozaki,b Pao-Chang Chiang,b Mayumi Sumi,b Motohiro Tanaka,c Yoshiyuki Koga,d Christoph Bourauel,e and Noriaki Yoshidaf Nagasaki, Japan, and Bonn, Germany
Introduction: It has been found that controlled movement of the anterior teeth can be obtained by attaching a certain length of power arm onto an archwire in sliding mechanics. However, the impact of the archwire/bracket play on anterior tooth movement has not been clarified. The purpose of this study was to compare the effect of the power arm on anterior tooth movements with different dimensions of bracket slots and archwires. Methods: A 3-dimensional finite element method was used to simulate en-masse anterior tooth retraction in sliding mechanics. Displacements of the maxillary central incisor and the archwire deformation were calculated when applying retraction forces from different lengths of power arms. Results: When a 0.017 3 0.022-in archwire was engaged into the 0.018-in slot bracket, bodily movement of the incisor was obtained with 9.1-mm length of the power arm. When a 0.022-in slot system was coupled with a 0.019 3 0.025-in archwire, bodily movement was observed with a power arm length of 11.6 mm. Conclusions: Archwire/bracket play has a remarkable impact on anterior tooth movement. An effective torque application to the anterior teeth becomes clinically difficult in sliding mechanics combined with power arms when the archwire/bracket play is large. (Am J Orthod Dentofacial Orthop 2014;146:166-74)
T
he demand for speedy, effective, and accurate orthodontic treatment systems has increased to shorten the treatment period.1-6 Accordingly, the
a Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan; research fellow, Department of Oral Technology, School of Dentistry, University of Bonn, Bonn, Germany. b Postgraduate student, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. c Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. d Senior assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. e Cendres+Metaux endowed professor and chair, Department of Oral Technology, School of Dentistry, University of Bonn, Bonn, Germany. f Professor and chair, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Biomedical Sciences, Nagasaki University, Nagasaki, Japan. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Noriaki Yoshida, Department of Orthodontics and Dentofacial Orthopedics, Nagasaki University Graduate School of Biomedical Sciences, 1-7-1 Sakamoto, Nagasaki 852-8588, Japan; e-mail, nori@ nagasaki-u.ac.jp. Submitted, September 2013; revised and accepted, April 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.04.016
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use of implant anchorage in sliding mechanics has become more common all around the world. In addition to this system, sliding mechanics with the combined use of power arms has gradually been applied for obtaining controlled anterior tooth movements during space closure (Fig 1). That is, the desired type of anterior tooth movement, such as lingual crown tipping, bodily movement, or lingual root tipping, can be easily achieved by attaching various lengths of power arms onto an archwire in sliding mechanics.7-14 Several studies have been carried out to investigate various biomechanical factors affecting tooth movement in sliding mechanics, such as the flexural rigidity of the archwire, friction, and height of the retraction force.8,12–16 However, optimal loading conditions for controlled movement of anterior teeth in sliding mechanics combined with power arms are not fully understood. A few attempts with the finite element (FE) method have been reported on tooth displacement when a single canine retraction or an en-masse retraction is performed in sliding mechanics.17-19 In those studies, spring elements are used between a tooth and an archwire instead of friction between the surface of a bracket slot and an archwire. Therefore, the mechanical
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Fig 1. Intraoral picture of the en-masse maxillary anterior tooth retraction in sliding mechanics combined with power arms and skeletal anchorages.
condition is not sufficiently accurate to approximate an actual clinical situation. To our knowledge, there are only 2 studies that simulate en-masse retraction when brackets were modeled and a coefficient of friction was given to the interface between bracket slots and an archwire including contact-sliding problems.20,21 It was found that the anterior tooth movement varied depending on the amount of archwire/bracket play. However, the effect of play on anterior tooth movement has not been fully understood; clinicians must consider this in an actual clinical situation for any treatment step in sliding mechanics. The purpose of this study was to clarify the effect of the bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics by means of a 3-dimensional (3D) FE model. MATERIAL AND METHODS
The construction method of the 3D FE model has been described previously.20 Computed tomography images of the 14 maxillary teeth, taken with a multi-image cone-beam computed tomography scanner (3DX; J. Morita, Kyoto, Japan), were saved as DICOM data and exported to 3D image processing and editing software (Mimics 10.02; Materialize Software, Leuven, Belgium). The 3D solid model was created and converted to a 3D FE model using FE analysis preprocess and postprocess software (Patran 2008r1; MSC Software, Los Angeles, Calif). Each 3D FE model for the periodontal ligament (PDL), alveolar bone, bracket, archwire, and power arm was separately constructed using the same software. The PDL had a uniform thickness of 0.2 mm.22-24 The bracket height of the maxillary central incisor was placed according to a prescription, which was 4.5 mm in height from the incisal edge of the tooth.25,26 Two 3D solid models were constructed. One had the combination of brackets with a 0.018 3 0.025-in slot
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and a 0.017 3 0.022-in stainless steel archwire, and the other had 0.022 3 0.028-in slot brackets and a 0.019 3 0.025-in archwire. Based on these 3D solid models, an FE mesh was created to make a node-tonode connection between tooth, PDL, and alveolar bone. An FE mesh of the archwire was created separately from the bracket to allow the archwire to slide through the bracket slots. The 3D FE model consisted of 423,772 isoparametric tetrahedral solid elements (10 noded) and 83,790 nodes, or 432,356 elements and 85,957 nodes (Fig 2). The material parameters used in this study are represented in the Table.23,24 To simplify the model and reduce the time for analysis, the same properties were given to the archwires, power arms, and brackets. Other structures such as teeth, alveolar bone, and PDL were modeled as homogenous and isotropic for the same reason. Assuming that the case model was diagnosed as maxillary protrusion, bilateral maxillary first premolar extractions were indicated. The model included 12 teeth, and 2 skeletal anchorages (miniscrews or miniplate implants) were inserted at both sides of the buccal region between the second premolar and the first molar. Two power arms were attached onto an archwire bilaterally at the segment between the lateral incisor and the canine, and these lengths were changed from 0 to 12 mm with 0.1-mm intervals from the bracket slot level (Fig 3). The horizontal retraction force of 1.5 N was applied from the implant anchorage to the power arm on both sides. The model was restrained in 6 of freedom at the bottom of the alveolar bone. The coefficient of friction between the bracket slots and the archwire was assumed to be 0.2.27-29 A cross-sectional view indicating the boundary between the bracket and the archwire is shown in Figure 4. The archwire was horizontally positioned to contact the bottom surface of the bracket slots and vertically in the middle of the bracket. Under these conditions, 3D FE analysis was performed using a 3D FE program (Marc; MSC Software). We analyzed how the archwire was deformed and, consequently, how the maxillary central incisor moved. Then we compared the results obtained with the 0.017 3 0.022-in stainless steel archwire in the 0.018-in slot and the 0.019 3 0.025-in archwire in the 0.022-in slot. RESULTS
The relationship between the degree of labiolingual tipping of the maxillary central incisor and the height of retraction force on the power arm is shown in Figure 5. If the 0.017 3 0.022-in stainless steel archwire was engaged into the 0.018-in slot brackets as shown by a solid line in Figure 5, lingual crown tipping of the
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Fig 2. Three-dimensional FE model of the maxillary dentition, including the PDL, alveolar bone, brackets, and archwire.
Table. Material parameters of tooth, PDL, alveolar
bone, archwire, power arm, and bracket Material Tooth PDL Alveolar bone Archwire/power arm/bracket
Young's modulus (MPa) 20000 0.05 2000 200000
Poisson's ratio 0.30 0.30 0.30 0.30
maxillary central incisor was observed when the retraction force was applied at 0 mm, which corresponds to the bracket slot level. The direction of tooth rotation changed from lingual crown tipping to lingual root tipping as the level of the retraction force on the power arm was moved apically from the bracket slot level. At the height of 9.1 mm, no rotation was observed; ie, bodily movement occurred. Lingual root tipping of the incisor was produced when the retraction force was set above 9.1 mm. When the 0.022-in slot bracket system was combined with the 0.019 3 0.025-in archwire, bodily movement of the incisor was achieved at the height level of the retraction force of 11.6 mm as shown by a dotted line in Figure 5, although the rotational endency was the same as the 0.018-in slot system. Figure 6 shows the loading conditions under which controlled anterior tooth movements, such as controlled lingual root tipping, bodily movement, and controlled lingual crown tipping, can be achieved. Controlled lingual root tipping is defined
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as the type of tooth movement in which the tooth tips around its incisal edge as the center of rotation. On the other hand, controlled lingual crown tipping indicates the movement in which the tooth tips around its root apex as the center of rotation. If the 0.017 3 0.022-in archwire was used in a 0.018in slot, controlled lingual root tipping was carried out at the height of the retraction force of 9.5 mm, which was 2.3 mm higher than the level of the center of resistance. At a height of 9.1 mm, bodily movement was achieved. Controlled lingual crown tipping was observed at the 8.3-mm height of retraction force level (Fig 6, A). When the 0.019 3 0.025-in archwire was used in the 0.022-in slot, controlled lingual root tipping was obtained at the height of 13.0 mm. Bodily movement was produced at an 11.6-mm height of retraction force. Controlled lingual crown tipping occurred at a level of 10.3-mm height (Fig 6, B). The deformation of the archwire and the resultant displacement of the maxillary central incisor and first molar after the application of retraction force at the level of 12 mm are shown in Figure 7. For a better understanding of the deformation of the archwire and the tooth displacement, these displacements were magnified 50 times, and the displacements of the central incisor were focused on. The tooth and the archwire in blue show the initial positions. When the 0.017 3 0.022-in archwire was used in the 0.018-in slot, the anterior segment of the archwire was deformed upward. The root of the maxillary central
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Fig 3. Illustration of the experimental conditions of anterior tooth retraction with the combinations of various lengths of power arms and skeletal anchorage in sliding mechanics.
Fig 4. Cross-sectional view of the archwire/bracket interface in the FE model.
incisor was moved lingually, and the crown was moved labially (Fig 7, A). The labiolingual tipping was 0.17 (lingual root tipping). When the 0.019 3 0.025-in archwire was used in the 0.022-in slot, the incisor showed almost bodily movement with less lingual root tipping of 0.02 , although the tendency of archwire deformation was similar to that of the 0.018-in slot coupled with the 0.017 3 0.022-in archwire (Fig 7, B).
DISCUSSION
We found that the dimension of the play between the bracket slot and the archwire has a significant impact on anterior tooth movement when the retraction force was applied to a power arm in sliding mechanics. Even if the same height of the horizontal retraction force was applied, there were great discrepancies in the types of anterior tooth movement between the 2 combinations
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Fig. 5. Degree of the labiolingual tipping of the maxillary central incisor subjected to the various heights of retraction force on the power arm. Positive signs indicate lingual crown tipping, whereas negative signs indicate lingual root tipping.
of bracket slot size and archwire size. When the height level of the force was increased, this discrepancy was also increased (Fig 5). Although controlled tooth movement from lingual crown tipping to lingual root tipping can be easily achieved with a 0.017 3 0.022-in archwire in a 0.018-in slot, lingual root tipping can hardly be generated with power arms shorter than 10 mm if a 0.019 3 0.025-in archwire is used in a 0.022-in slot. This might be due to the difference in the play between brackets and archwires. From a biomechanical point of view, it has been stated that the type of tooth movement, such as lingual crown tipping, bodily movement, or lingual root tipping, is determined by the relationship between a line of action of a force and the location of the center of resistance of a tooth, and a single force passing through the center of resistance causes bodily tooth movement.7,30,31 However, as shown in Figure 6, the tooth movements analyzed in this study did not agree with that concept based on the biomechanical principles. Since the location of the center of resistance of the maxillary central incisor in the FE model, which we used, was determined to be at the level of 7.2 mm apically from the bracket slot, bodily movement of the incisor was expected to be produced at the height of 7.2 mm of retraction force. Nevertheless, FE analysis showed that bodily movement of the incisor occurred at the height of 9.1 mm, which is 1.9 mm apical to the level of the center of resistance with
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a 0.017 3 0.022-in archwire in a 0.018-in slot (Fig 6, A). On the other hand, bodily movement occurs at the level of 11.6 mm, which is 4.4 mm apical to the position of the center of resistance with a 0.019 3 0.025-in archwire in a 0.022-in slot (Fig 6, B). Those results indicate that the concepts based on theoretical considerations cannot be simply applied to multibracket appliances. When a 0.017 3 0.022-in archwire is used in a 0.018in slot, longer power arms than the perpendicular distance from the bracket level to the center of resistance are required to achieve controlled movement of the anterior teeth, including controlled lingual root tipping, bodily movement, and controlled lingual crown tipping (Fig 6, A). If a 0.019 3 0.025-in archwire is engaged into a 0.022-in slot, much longer power arms are required to produce any anterior tooth movement (Fig 6, B). As mentioned in the previous articles, when long power arms were used, a substantial amount of bending moment is generated at the portion of the archwire where the power arms were attached as a cantilever effect.20,21 As a result, the anterior segment of the archwire was raised upward, causing lingual root tipping with a full-sized 0.018 3 0.025-in archwire. Although in this study we found similar results for the phenomenon of the cantilever effect, bodily movement or lingual root tipping seems to be difficult to obtain with the 0.022-in slot system compared with the 0.018-in slot system in sliding mechanics with the combined use of power arms. Since the torsion of the archwire within a bracket slot and its general deformation were considered to have major impacts on tooth movement, displacements of the archwire and the resultant tooth displacement were analyzed when 0.017 3 0.022-in and 0.019 3 0.025-in archwires are used (Fig 7). The anterior segment of the archwire is subjected to torsion caused by the power arms. When a 0.017 3 0.022-in archwire is used in a 0.018-in slot, the torque is likely to be practically transmitted to the bracket on the incisor. Moreover, a smaller play between the brackets and the archwire might contribute to a more efficient torque application. Thus, lingual root tipping can be clinically achieved with power arms in the 0.018-in slot (Fig 7, A). Contrary to this, the torsion of the archwire is less likely to be transmitted effectively to the incisor because of the greater play between the brackets and the archwire, thereby causing less lingual root tipping in the 0.022-in slot (Fig 7, B). To compare the interaction of an archwire with brackets on the incisor in the 0.018-in slot with that in the 0.022-in slot and elucidate the mechanism of generation of lingual root torque, the sagittal crosssectional view at the mesial surface of the maxillary central incisor bracket was constructed before and after
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Fig 6. Loading conditions when controlled movements of a maxillary central incisor are obtained: A, 0.017 3 0.022-in archwire in 0.018-in slot; B, 0.019 3 0.025-in archwire in 0.022-in slot. CRe, Center of resistance; CRo, center of rotation.
Fig 7. Displacement of the maxillary central incisor and the deformation of the archwire on the application of retraction force at the height of 12 mm. For a better understanding of the displacement of the tooth and deformation of the archwire, these movements are magnified 50 times. Initial positions of the tooth and archwire are indicated by blue lines. A, 0.017 3 0.022-in archwire in 0.018-in slot; B, 0.019 3 0.025-in archwire in 0.022-in slot.
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Fig 8. Sagittal cross-section at the mesial surface of the maxillary central incisor bracket before exerting retraction force (left) and after the application of the force at the height of 12 mm (right): 0.017 3 0.022-in archwire in 0.018-in slot (top) and 0.019 3 0.025-in archwire in 0.022-in slot (bottom).
the application of the orthodontic force at the level of 12 mm (Fig 8). When an archwire is twisted by a bending moment of the power arms, the diagonally opposite corners of the archwire contact the surface of the bracket slot. Then a pair of normal forces, called lingual root tipping moments, is generated. That is, torque acting on the anterior tooth becomes applicable with a combination of a 0.017 3 0.022-in archwire and 0.018-in slot brackets with smaller archwire/bracket clearances (Fig 8, top). However, a normal force in the downward direction is not produced at this crosssectional view when a 0.019 3 0.025-in archwire was used in the 0.022-in slot, which has a larger play (Fig 8, bottom). Although the horizontal dimension of the play in the 0.018-in slot system is the same as that in the 0.022-in slot, the vertical dimension of the play in the 0.022-in slot is 3 times as large as that in the 0.018-in slot (Fig 8). This indicates that play in the vertical dimension has a greater impact on the movements of the anterior teeth than in the horizontal dimension. It is considered that the greater the play between the archwire and the bracket, the weaker the normal forces. As a result, less lingual root tipping moment is transmitted to the incisor in the 0.022-in slot system. Therefore, it becomes more difficult to prescribe an optimal power arm length for achieving the
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desired type of anterior tooth movement if there is a large archwire/bracket clearance. As mentioned above, the dimension of the play is the most influential factor in determining the type of anterior tooth movement in sliding mechanics combined with power arms. Thus, the conventional biomechanical principles of tooth movement in orthodontics cannot be directly applied in actual clinical situations. Although a comprehension of the relationship between a line of action of a retraction force and the position of the center of resistance of a tooth is an important key to an estimation of how the tooth will move, the effect of the archwire deflection within the bracket slot and its general deformation on the force system acting on a tooth should also be considered (Figs 7 and 8). Although applying a retraction force on the power arm modifies the type of anterior tooth movement in sliding mechanics in a simple way, quite long power arms of 10 to 13 mm are required to achieve controlled movement of the anterior teeth in the 0.022-in slot system. Particularly, controlled lingual root tipping is only obtained with power arms of 13 mm; this is too long to be applied in a clinical situation. In this case, the use of high-torque brackets on the anterior teeth seems recommendable to optimize torque application.
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Even if the 0.018-in slot system is coupled with a 0.017 3 0.022-in archwire, power arms longer than 9 mm are required for obtaining bodily movement or lingual root tipping. Therefore, the clinical application of power arms combined with sliding mechanics is difficult in some patients whose gingivobuccal fold is shallow. Also, it is necessary to give full consideration to anatomic parameters that vary between patients to precisely predict the tooth movements during the orthodontic treatment. Especially, an estimation of the center of resistance position is of utmost clinical importance because the required length of the power arm producing a certain type of tooth movement is closely related to the location of the center of resistance. The height of the retraction force relative to the level of the center of resistance is more critical than the length of the power arm, which by itself has no consequence. For example, power arms 1.1 mm longer than the perpendicular distance from the bracket level to the center of resistance are indicated for achieving controlled lingual crown tipping in the 0.018-in slot system (Fig 6). A clinical study is needed to confirm these conclusions from this FE investigation; it should consider not only the relationship between the line of action of a retraction force and the location of the center of resistance of a tooth, but also the effect of the archwire deformation including the torsion within the different dimensions of bracket slots and archwires. This will be a great help in establishing an optimal treatment plan and achieving speedy, effective, and accurate orthodontic tooth movement. CONCLUSIONS
Controlled anterior tooth movement can be achieved in sliding mechanics with the combined use of power arms as long as the archwire/bracket clearance is small. The dimension of the play that is determined by the combination of the bracket slot size and the archwire size has a great impact on the control of the anterior tooth movement. The greater the archwire/bracket play becomes, the more difficult it is to apply an effective torque to the anterior teeth. Optimal power-arm length must be longer than the perpendicular distance from the bracket level to the center of resistance of the anterior tooth to obtain any type of anterior tooth movement. Particularly with a large archwire/bracket play, much longer power arms are necessary to apply an effective torque. Therefore, a clinical application of power arms combined with sliding mechanics becomes more difficult for patients with a limited depth of the gingivobuccal fold.
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