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Original Article

Korean J Orthod 2023; 53(6): 420-430   https://doi.org/10.4041/kjod23.035

First Published Date September 14, 2023, Publication Date November 25, 2023

Copyright © The Korean Association of Orthodontists.

Biomechanical analysis for different mandibular total distalization methods with clear aligners: A finite element study

Sewoong Oha , Youn-Kyung Choib, Sung-Hun Kima, Ching-Chang Koc, Ki Beom Kimd, Yong-Il Kima,e

aDepartment of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Yangsan, Korea
bDepartment of Orthodontics, Pusan National University Hospital, Busan, Korea
cDivision of Orthodontics, College of Dentistry, The Ohio State University, Columbus, OH, USA
dDepartment of Orthodontics, Saint Louis University, Saint Louis, Mo, USA
eDental and Life Science Institute, School of Dentistry, Pusan National University, Yangsan, Korea

Correspondence to:Yong-Il Kim.
Professor, Department of Orthodontics, School of Dentistry, Pusan National University, 20 Geumo-ro, Mulgeum-eup, Yangsan 50612, Korea.
Tel +82-55-360-5163 e-mail kimyongil@pusan.ac.kr

How to cite this article: Oh S, Choi YK, Kim SH, Ko CC, Kim KB, Kim YI. Biomechanical analysis for different mandibular total distalization methods with clear aligners: A finite element study. Korean J Orthod 2023;53(6):420-430. https://doi.org/10.4041/kjod23.035

Received: February 14, 2023; Revised: September 8, 2023; Accepted: September 14, 2023

Abstract

Objective: The purpose of this finite element method (FEM) study was to analyze the biomechanical differences and tooth displacement patterns according to the traction direction, methods, and sites for total distalization of the mandibular dentition using clear aligner treatment (CAT). Methods: A finite element analysis was performed on four FEM models using different traction methods (via a precision cut hook or button) and traction sites (mandibular canine or first premolar). A distalization force of 1.5 N was applied to the traction site by changing the direction from –30 to +30° to the occlusal plane. The initial tooth displacement and von Mises stress on the clear aligners were analyzed. Results: All CAT-based total distalization groups showed an overall trend of clockwise or counterclockwise rotation of the occlusal plane as the force direction varied. Mesiodistal tipping of individual teeth was more prominent than that of bodily movements. The initial displacement pattern of the mandibular teeth was more predominant based on the traction site than on the traction method. The elastic deformation of clear aligners is attributed to unintentional lingual tipping or extrusion of the mandibular anterior teeth. Conclusions: The initial tooth displacement can vary according to different distalization strategies for CAT-based total distalization. Discreet application and biomechanical understanding of traction sites and directions are necessary for appropriate mandibular total distalization.

Keywords: Finite element method, Clear aligner, Distalization

INTRODUCTION

Skeletal Class III malocclusion arises from maxillary undergrowth, mandibular overgrowth, or a combination of the two. The main features of skeletal Class III malocclusion are anterior crossbite, concave facial profile due to midface deficiency, and mandibular prognathism. Various treatment methods for Class III malocclusion are available, ranging from growth modification and camouflage treatment to orthognathic surgery, which places clinicians at a crossroads. However, growth modification has temporal constraints and its outcome is difficult to predict, and orthognathic surgery is invasive and expensive despite its high predictability.1

Camouflage treatment can be a reasonable choice in adult patients presenting with mild to moderate skeletal deformities.2 Camouflage treatment manages skeletal Class III malocclusion via retraction of the mandibular anterior teeth, protraction of the maxillary anterior teeth, and mandibular posterior rotation.3 Notably, it causes a satisfactory outcome in patients with a short face when clockwise mandibular rotation is allowed.

In addition, temporary anchorage devices (TADs) have extended the scope of Class III camouflage treatment via total distalization of the entire mandibular dentition.4,5 The total distalization using TADs is exceptionally advantageous in allowing strategic treatment according to clinical situations because it is not dependent on patient compliance or the implantation site, and the direction and point of action of the force can be selected.4,6

Based on these advantages, numerous cases and biomechanical analyses have been reported for Class III camouflage treatment using TADs and total mandibular distalization. Roberts et al.7 reported that infrazygomatic crest or mandibular buccal shelf TADs might be used to achieve a Class I molar relationship with simultaneous counterclockwise rotation of the mandibular dentition and reduction in facial height. Chae et al.8 compared the distalization force in various directions to expand the biomechanical understanding of total distalization in a conventional bracket-wire system.

Recently, the scope of clear aligners has steadily widened in clinical practice owing to their esthetic benefits, negligible discomfort, and convenient oral hygiene management.9,10 In addition to camouflage treatment for Class III malocclusion with enamel stripping in the mandibular dentition,11 Ojima reported the possibility of treatment using sequential distalization of the molar through the TADs.12 Rota et al.13 reported that sequential distalization using clear aligners allowed the mandibular second molar to distalize by 2.47 mm, and the first molar by 1.16 mm. However, the majority of reports on camouflage treatment using clear aligners have focused on Class II malocclusion, with a lack of studies on Class III malocclusion.

In particular, clear aligners involve the force and moment generated due to the morphological mismatch of the aligners and teeth, which makes it difficult to predict the treatment outcome.14 In contrast to the conventional bracket-wire system, tooth movement using clear aligners does not have specific points of action, as it occurs solely based on surface contact. Thus, the effects of the attachment and morphological properties of clear aligners and teeth are significant, leading to highly complex aspects of predicting tooth movement.15 To solve the biomechanical problem of such complex factors, the finite element method (FEM) has been applied in various ways. An accurate understanding of tooth displacement patterns via FEM-based biomechanical analysis would provide valuable information for extending the scope of clear aligner treatment (CAT) to include skeletal Class III malocclusion and the distalization of mandibular molar teeth.

This study aimed to present a biomechanical analysis of camouflage treatment for Class III malocclusion using CAT. An FEM-based analysis was performed to compare the displacement tendency and biomechanical system based on the traction method (precision cut hook or button on the canine), site (mandibular canine or mandibular first premolar), and direction of the distalization force.

MATERIALS AND METHODS

This was an in vitro study, and ethical approval was not required.

Model construction

From the cone-beam computed tomography data (Pax-Zenith 3D; Vatech Co., Seoul, Korea) of an individual with normal occlusion, the mandible with teeth was segmented using a 3D-slicer. To model the periodontal ligament (PDL), a PDL space with a uniform thickness of 0.25 mm surrounding the roots was maintained. The clear aligners were modeled to have a thickness of 0.5 mm, while all the marginal and interdental parts were shaped to be circular to prevent sharp edges.

Four FEM models were constructed using a CAD program (ANSYS Inc., Canonsburg, PA, USA) to compare the differences in displacement patterns according to the traction methods and sites. A rectangular attachment of 3 mm height, 2 mm width, and 1 mm thickness was applied on the tooth at the traction site to prevent tooth rotation and loss of clear aligners due to the traction force. The four FEM models in the analysis were: (1) Group C1, distalization with a button on the canine; (2) Group C2, distalization with a precision cut hook on the canine; (3) Group P1, distalization with a button on the first premolar; and (4) Group P2, distalization with a precision cut hook on the first premolar (Figure 1). Based on the presumption of left-to-right symmetry, only the right side was analyzed in all 4 models.

Figure 1. Four finite element method models. A, Group C1: distalization with a button on canine; B, Group C2: distalization with a precision cut hook on canine; C, Group P1: distalization with a button on first premolar; D, Group P2: distalization with a precision cut hook on first premolar.

Finite element analysis

According to a previous study reporting the lack of significant differences in the overall pattern of tooth movement, even when using the linear elastic modulus in PDL modeling, the jawbone, dentition, PDL, attachments, and buttons were all presumed to be homogenous and exhibit a linear isotropic elastic behavior.16-21 The material properties of each structure are depicted in Table 1. The material properties of composite attachments were obtained from the manufacturer (3M, St. Paul, MN, USA).

Table 1 . Material properties of each structure

StructureYoung’s modulus (MPa)Poisson’s
ratio
Mandible1613,7000.30
Periodontal ligament160.450.67
Dentition17,1819,6000.30
Clear aligner17,185280.36
Composite attachment1912,5000.36
Button20200,0000.30


To maintain the boundary conditions in the FEM model, frictionless contact was applied between the teeth and aligner and between adjacent teeth, and bonded contact was applied between the jawbone and PDL and between the PDL and tooth. All the elements were linear. For the mesh size, the following conditions were set after the convergence study based on the displacement of the canine for Groups C1 and C2 and the first premolar for Groups P1 and P2 (Table 2).

Table 2 . Element and node number of 4 finite element models

GroupElement numberNode number
Group C13,333,574643,775
Group C22,978,423578,884
Group P13,257,487627,886
Group P23,628,755712,577


To compare the effects according to the traction direction, 1.5 N of distalization force was applied on a button or a precision cut hook on the sagittal plane in line with the occlusal plane in the following directions: –30°, –20°, –10°, 0°, +10°, +20°, and +30°. The line of action of the force from the occlusal plane was set at a point 1 mm lateral to the gingiva (Figure 2).

Figure 2. Direction and magnitude of the distalization force. A, lateral and B, occlusal view.

Data analysis

After FEM analysis, the translation and rotation of the mandibular central incisor, canine, first premolar, and first molar were analyzed using MATLAB (version 2020b; MathWorks Inc., Natick, MA, USA) and were based on the center of the clinical crown. The directions of the translational motion were mediolateral, anteroposterior, and apicocoronal. Lateral, anterior, and coronal directions were considered positive. Buccolingual, mesiodistal, and occlusal rotations were evaluated based on the longitudinal axis of the tooth, and buccal tipping, mesial tilting, and mesial-in rotation were defined as positive. Furthermore, to examine the changes in the clear aligners according to the distalization force, the displacement and von Mises stress of the clear aligners were analyzed.

RESULTS

Tooth displacement tendency

Except for the –30° traction in Group C2, all groups showed lingual tipping and extrusion of the mandibular anterior teeth irrespective of the direction of force. The level of lingual tipping or extrusion of the anterior mandibular teeth varied more markedly according to the traction site (canine vs. first premolar) than the traction method (button vs. precision cut hook). In the case of traction at the first premolar sites, as in Groups P1 and P2, the level of lingual tipping or extrusion of the mandibular anterior teeth was more predominant, irrespective of the traction method, which concurrently led to a higher level of crown displacement in the posterior direction. However, in the case of traction at the canine sites, as in Groups C1 and C2, considerable variations were observed for lingual tipping or extrusion of the mandibular anterior teeth with respect to traction direction, whereas traction at the first premolar sites showed few variations according to traction direction (Figures 3 and 4).

Figure 3. Displacement pattern of dentition. A, B, Displacement (μm) of the dentition for +30°and –30° traction in Group C1, respectively. C, D, Displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.

Figure 4. Pattern of tooth movement at the mandibular central incisor. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

The displacement pattern in the mandibular canines was more predominant according to the traction site than the traction method. Traction at canine sites, as in Groups C1 and C2, indicated a substantial impact on the level of intrusion or extrusion of mandibular canines according to the traction direction; intrusion occurred at –30° and –20° traction, whereas extrusion occurred in all other cases. Traction at the first premolar sites, as in Groups P1 and P2, also indicated an impact on the level of intrusion or extrusion of the mandibular canines according to the traction force direction, although the degree of impact was comparatively lower. The distal tipping of the canine was shown to be greater in the traction at the premolar than at the canine sites, which was due to the anti-tipping effect of the attachment on the canine. In addition, the level of lingual tipping of the canine increased as the traction force direction shifted from –30° to +30° (Figures 3 and 5).

Figure 5. Pattern of tooth movement at the mandibular canine. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

The displacement pattern in the mandibular first premolars was more predominant according to the traction site than the traction method. This pattern was similar to that observed for canine traction. The level of distal tipping of the first premolar was more significant in traction at the canine sites than at the first premolar sites, which is due to a reason similar to the aforementioned canine movement pattern: the anti-tipping effect of attachment to the premolar. In the first premolars, –30° traction led to buccal tipping and +30° traction led to lingual tipping (Figures 3 and 6).

Figure 6. Pattern of tooth movement at mandibular first premolar. A, Crown-centered medio- distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

For mandibular first molars, between-group variations were observed according to the traction site. Traction at the first premolars gave rise to a low level of lingual tipping on the mandibular first molars as the force direction was shifted from –30° to +30°, which might be due to deformation of clear aligners or lingual tipping at the mandibular first premolar affecting the traction force. In contrast, traction at the canines had a weak impact on the buccolingual tipping of the mandibular first molars according to the force direction. No variation was observed in the mesial tipping of the mandibular first molars according to the traction site. While mesial tipping occurred in all traction directions, a high level of mesiodistal tipping was detected as the traction direction shifted from –30° to +30° (Figures 3 and 7).

Figure 7. Pattern of tooth movement at mandibular first molar. A, Crown-centered medio distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

Analyses of displacement and stress for clear aligners

The clear aligners exhibited a posterosuperior rotation pattern with an increase in the superior direction of the distalization force. In contrast, as a –30° posteroinferior distalization force was applied, deformation occurred at the anterior of the traction site of action in lieu of en masse rotation of the entire dentition. In the case of posterosuperior traction, predominant changes in the clear aligners were observed on the buccal side of the first molar, and the use of a precision cut hook resulted in a greater level of change (Figure 8).

Figure 8. Total displacement pattern of aligners. A, B, Total displacement (μm) of the dentition for +30° and –30° traction in Group C1, respectively. C, D, Total displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Total displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Total displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.

For the von Mises stress of clear aligners, the distalization force induced concentrated stress on the adjacent tooth at the traction sites. The use of a precision cut hook focused on the stress on the hook. As in Groups P1 and P2, traction at the first premolar sites led to concentrated stress in the interdental space between the canine and the first premolar. The –30° traction in Group P2 caused the highest von Mises stress in the interdental space between the canine and first premolar across all experimental groups (Figure 9).

Figure 9. Elastic strain (mm/mm) of clear aligners. A, B, For +30° and –30° traction in Group C1, respectively. C, D, For +30° and –30° traction in Group C2, respectively. E, F, For +30° and –30° traction in Group P1, respectively. G, H, For +30° and –30° traction in Group P2, respectively.

DISCUSSION

Tooth movement caused by distalization of the mandibular dentition can be modulated mainly through angulation of the distalization force in a conventional bracket-wire system. The distalization force on the posterior occlusal side, as in an infrazygomatic crest screw, shows a greater moment for rotation of the mandibular occlusal plane owing to a greater distance from the center of resistance. In contrast, traction towards the mandibular buccal shelf screw shows a lower level of rotation of the occlusal plane due to a shorter distance from the center of resistance.7 Chae et al.8 reported that the relationship between the center of resistance of the mandibular dentition and the distalization force direction was the most critical predictor of tooth movement. The authors also reported that the variation in archwire elasticity could be another determinant of tooth movement.8 Notably, as previously described, the magnitude of the moment on the archwire increases with superior distalization force, with a higher level of lingual tipping in the anterior dentition.8

In the CAT-based Class II camouflage treatment, the precision cut hook is mainly applied to the maxillary canines and mandibular molars to distalize the maxillary dentition and protract the mandibular dentition through Class II elastics, or to reinforce anchorage in the sequential distalization of maxillary molars. On the other hand, button cut-outs are used for Class II malocclusion with lingually tipped anterior teeth to separate the retraction sites and aligners to prevent additional lingual tipping of the anterior teeth during retraction of the anterior teeth.22 In addition, if the clinical crown is too short or if a strong force is present on the precision cut hook, clear aligners may be displaced from the dentition to cause inappropriate tooth movements; in such cases, button cut-outs and buttons attached to the teeth are recommended.23

This biomechanical strategy may be used in the camouflage treatment of Class III malocclusions. When applying the distalization force, the precision cut hook may be applied in cases where the level of dentoalveolar compensation is low (i.e., the level of lingual tipping of the mandibular anterior teeth is small), whereas button cut-outs may be applied in cases with excessive compensation of the mandibular anterior teeth for separation from the traction force, which may interfere with labial tipping. Additionally, care should be taken when selecting the force direction, when it is necessary to adjust the occlusal plane, or when applying vertical adjustments.

Furthermore, the traction points of total distalization may have a significant effect on the entire biomechanical system. Considering the traction points, traction at the mandibular first premolar rather than the mandibular canine may induce a lower level of moment in the mandibular dentition, irrespective of the retraction force direction, owing to the shorter distance between the center of resistance and the line of action of the force in the mandibular dentition, resulting in a lower level of rotation in the mandibular dentition according to the force direction. With additional consideration of the damping effects on clear aligners, traction at the mandibular first premolar, which is farther from the mandibular anterior teeth, is conjectured to allow more effective suppression of lingual tipping of the mandibular anterior teeth.24 However, no reports have been made on these assumptions.

For the conventional bracket-wire system, applying the retractive force to the anterior dentition causes an overall en masse-like tooth movement following the changes in the occlusal plane with little impact on individual tooth movement because of the gap between the bracket and wire.25 For clear aligners, however, mesiodistal tipping of individual teeth was predominant rather than bodily movement. This is because, while the wire in the bracket-wire system ensures sufficiently high elasticity, the elasticity from clear aligners is not sufficient for generating adequate counter momentum.26 Thus, it is presumed that the attachments are essential to cause counter momentum.

The FEM analysis results showed that in contrast to the prediction of a more potent suppression of lingual tipping of the mandibular anterior teeth via traction at the mandibular first premolar, higher levels of extrusion and lingual tipping of the mandibular anterior teeth were observed for traction at the mandibular first premolar than at the mandibular canine. In addition, while the trend of gradual lingual tipping increased with the retractive force directed posterosuperiorly at the mandibular canine, a higher level of lingual tipping and extrusion of the mandibular incisors was observed at the mandibular first premolar traction, regardless of the force direction or traction method. This was in contrast to lingual tipping with extrusion of the mandibular anterior teeth upon distalization force occlusal to the center of resistance, and labial tipping with intrusion upon retraction force inferior to the center of resistance in the bracket-wire system.8

This result may be attributed to the lingual tipping of canine and low elastic modulus in clear aligners, leading to elastic deformation. A comparison of the strain in this study showed that the traction at the mandibular first premolar focused on the strain between the mandibular first premolar and canine sites (Figure 9). This may indicate that rather than en masse movement of the entire dentition, tooth movement occurred independently of the respective deformations (Figure 10). Hence, with intrusion at the mandibular first premolar, extrusion occurred at the mandibular first molar as well as lingual tipping and extrusion of the mandibular anterior teeth. Lingual tipping of the mandibular anterior teeth in traction at the mandibular first premolar, regardless of the force direction, occurs because of the additional lingual tipping of the mandibular anterior teeth owing to the clear aligner deformations caused by the downward force.

Figure 10. Force diagram showing aligner deformation during distal retraction with a precision cut hook. A, The force system with –30° posteroinferior distalization force on a precision cut hook (black dot: center of resistance of mandibular dentition, red arrow: distalization force). B, Equivalent force system assuming CA as an ideal rigid body. Rotation occurred following the translation in the whole. C, Mesiodistal tipping of individual tooth rather than bodily movement occurred with lingual tipping and extrusion of the anterior teeth due to the deformation as the aligner is an elastic body (black dashed arrow: deformation of CA due to distalization force, black lined arrow: lingual tipping of the anterior teeth).
CA, clear aligner.

Elastic modulus is a critical physical property indicating the magnitude of the orthodontic force of thermoforming materials.23 Upadhyay et al.27 pointed out that clear aligners are prone to deformations even at little force due to their low elastic modulus (40–50 times lower than the NiTi wire), with a viscoelastic nature which causes permanent deformations due to low resiliency. Therefore, the sequential distalization of molar teeth to apply a lower level of retractive force may be more appropriate than the total distalization to prevent the aligner deformation. It may also be wise to consider applying bite ramps to the maxillary anterior teeth or providing additional labial tipping torque and intrusive forces to the mandibular anterior teeth via TADs, as well as using a thicker sheet. In addition, selecting the mandibular canine, rather than the mandibular first premolar, as the traction site may be more appropriate when applying a posteroinferior retraction force.

In contrast to the prediction that using buttons would reduce lingual tipping of the mandibular anterior teeth,22 the level of lingual tipping of the mandibular anterior teeth did not vary significantly according to the retraction method (precision cut hook vs. button). However, the use of buttons led to rotations of the teeth below the button, resulting in extrusion of the mandibular anterior and adjacent teeth. Therefore, it is likely more advantageous to apply a direct retraction force to clear aligners through a precision cut hook instead of applying a retractive force to an individual tooth with buttons, if a suitable attachment can be applied.

This study had some limitations. The material properties and structures applied in modeling the mandibular dentition may not completely incorporate the biological diversity across individual patients in clinical practice. Moreover, clear aligners in a clinical setting may display a significantly reduced orthodontic force owing to plasticization caused by factors such as water absorption. Thus, future studies should conduct FEM analyses that consider the time-dependent physical properties of clear aligners.

CONCLUSIONS

In this study, the displacement tendency of total mandibular distalization with clear aligners according to the retraction direction, traction points, and traction methods was analyzed using FEM. Biomechanical systems were also compared.

For distalization with clear aligners, lingual inclination of the mandibular anterior teeth and buccolingual and mesiodistal inclinations of the canines, premolars, and molars occurred and varied depending on the traction direction. Rotation of the entire dentition occurred, but tipping of the individual teeth was more prominent.

For total distalization with clear aligners, the variations in tooth movement according to the traction method, such as the use of a precision cut hook or lingual button, were insignificant in the presence of attachment at the point of action of the force.

Differences in the lingual inclination of the mandibular anterior teeth were observed depending on the traction site. Specifically, when traction force was applied to the mandibular first premolars, significant lingual inclination and extrusion of the mandibular anterior teeth occurred, regardless of the traction direction and method, with the deformation of the clear aligner.

FUNDING

This research was funded by the National Research Foundation of Korea (NRF) grant funded by the Korean government (2021R1A2C1003240).

AUTHOR CONTRIBUTIONS

Conceptualization: SO, YIK. Methodology: SO, YKC. Project administration: YIK. Software: SO. Supervision: CCK, KBK, SHK. Validation: YKC, CCK, KBK, SHK. Visualization: SO. Writing–original draft: SO, YKC, CCK, KBK, SHK. YIK. Writing–review & editing: SO, YKC, CCK, KBK, SHK, YIK.

CONFLICTS OF INTEREST

No potential conflict of interest relevant to this article was reported.

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  20. Kawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics. Prog Orthod 2019;20:3. https://doi.org/10.1186/s40510-018-0255-8
    Pubmed KoreaMed CrossRef
  21. Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res 2005;84:428-33. https://doi.org/10.1177/154405910508400506
    Pubmed CrossRef
  22. Tai S. Clear aligner technique. Batavia: Quintessence; 2018. https://www.amazon.com/Clear-Aligner-Technique-Sandra-Tai/dp/0867157771
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  23. Eliades T, Athanasiou AE. Orthodontic aligner treatment. New York: Thieme; 2021. https://shop.thieme.com/Orthodontic-Aligner-Treatment/9783132411487
    CrossRef
  24. Chan E, Darendeliler MA. The Invisalign&reg appliance today: a thinking person's orthodontic appliance. Semin Orthod 2017;23:12-64. https://doi.org/10.1053/j.sodo.2016.10.003
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  25. Kawamura J, Park JH, Kojima Y, Tamaya N, Kook YA, Kyung HM, et al. Biomechanical analysis for total mesialization of the maxillary dentition: a finite element study. Am J Orthod Dentofacial Orthop 2021;159:790-8. https://doi.org/10.1016/j.ajodo.2020.02.021
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  26. Brezniak N. The clear plastic appliance: a biomechanical point of view. Angle Orthod 2008;78:381-2. https://pubmed.ncbi.nlm.nih.gov/18251593/
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  27. Upadhyay M, Shah R, Peterson D, Asaki T, Yadav S, Agarwal S. Force system generated by elastic archwires with vertical V bends: a three-dimensional analysis. Eur J Orthod 2017;39:202-8. https://doi.org/10.1093/ejo/cjw044
    Pubmed KoreaMed CrossRef

Article

Original Article

Korean J Orthod 2023; 53(6): 420-430   https://doi.org/10.4041/kjod23.035

First Published Date September 14, 2023, Publication Date November 25, 2023

Copyright © The Korean Association of Orthodontists.

Biomechanical analysis for different mandibular total distalization methods with clear aligners: A finite element study

Sewoong Oha , Youn-Kyung Choib, Sung-Hun Kima, Ching-Chang Koc, Ki Beom Kimd, Yong-Il Kima,e

aDepartment of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Yangsan, Korea
bDepartment of Orthodontics, Pusan National University Hospital, Busan, Korea
cDivision of Orthodontics, College of Dentistry, The Ohio State University, Columbus, OH, USA
dDepartment of Orthodontics, Saint Louis University, Saint Louis, Mo, USA
eDental and Life Science Institute, School of Dentistry, Pusan National University, Yangsan, Korea

Correspondence to:Yong-Il Kim.
Professor, Department of Orthodontics, School of Dentistry, Pusan National University, 20 Geumo-ro, Mulgeum-eup, Yangsan 50612, Korea.
Tel +82-55-360-5163 e-mail kimyongil@pusan.ac.kr

How to cite this article: Oh S, Choi YK, Kim SH, Ko CC, Kim KB, Kim YI. Biomechanical analysis for different mandibular total distalization methods with clear aligners: A finite element study. Korean J Orthod 2023;53(6):420-430. https://doi.org/10.4041/kjod23.035

Received: February 14, 2023; Revised: September 8, 2023; Accepted: September 14, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Objective: The purpose of this finite element method (FEM) study was to analyze the biomechanical differences and tooth displacement patterns according to the traction direction, methods, and sites for total distalization of the mandibular dentition using clear aligner treatment (CAT). Methods: A finite element analysis was performed on four FEM models using different traction methods (via a precision cut hook or button) and traction sites (mandibular canine or first premolar). A distalization force of 1.5 N was applied to the traction site by changing the direction from –30 to +30° to the occlusal plane. The initial tooth displacement and von Mises stress on the clear aligners were analyzed. Results: All CAT-based total distalization groups showed an overall trend of clockwise or counterclockwise rotation of the occlusal plane as the force direction varied. Mesiodistal tipping of individual teeth was more prominent than that of bodily movements. The initial displacement pattern of the mandibular teeth was more predominant based on the traction site than on the traction method. The elastic deformation of clear aligners is attributed to unintentional lingual tipping or extrusion of the mandibular anterior teeth. Conclusions: The initial tooth displacement can vary according to different distalization strategies for CAT-based total distalization. Discreet application and biomechanical understanding of traction sites and directions are necessary for appropriate mandibular total distalization.

Keywords: Finite element method, Clear aligner, Distalization

INTRODUCTION

Skeletal Class III malocclusion arises from maxillary undergrowth, mandibular overgrowth, or a combination of the two. The main features of skeletal Class III malocclusion are anterior crossbite, concave facial profile due to midface deficiency, and mandibular prognathism. Various treatment methods for Class III malocclusion are available, ranging from growth modification and camouflage treatment to orthognathic surgery, which places clinicians at a crossroads. However, growth modification has temporal constraints and its outcome is difficult to predict, and orthognathic surgery is invasive and expensive despite its high predictability.1

Camouflage treatment can be a reasonable choice in adult patients presenting with mild to moderate skeletal deformities.2 Camouflage treatment manages skeletal Class III malocclusion via retraction of the mandibular anterior teeth, protraction of the maxillary anterior teeth, and mandibular posterior rotation.3 Notably, it causes a satisfactory outcome in patients with a short face when clockwise mandibular rotation is allowed.

In addition, temporary anchorage devices (TADs) have extended the scope of Class III camouflage treatment via total distalization of the entire mandibular dentition.4,5 The total distalization using TADs is exceptionally advantageous in allowing strategic treatment according to clinical situations because it is not dependent on patient compliance or the implantation site, and the direction and point of action of the force can be selected.4,6

Based on these advantages, numerous cases and biomechanical analyses have been reported for Class III camouflage treatment using TADs and total mandibular distalization. Roberts et al.7 reported that infrazygomatic crest or mandibular buccal shelf TADs might be used to achieve a Class I molar relationship with simultaneous counterclockwise rotation of the mandibular dentition and reduction in facial height. Chae et al.8 compared the distalization force in various directions to expand the biomechanical understanding of total distalization in a conventional bracket-wire system.

Recently, the scope of clear aligners has steadily widened in clinical practice owing to their esthetic benefits, negligible discomfort, and convenient oral hygiene management.9,10 In addition to camouflage treatment for Class III malocclusion with enamel stripping in the mandibular dentition,11 Ojima reported the possibility of treatment using sequential distalization of the molar through the TADs.12 Rota et al.13 reported that sequential distalization using clear aligners allowed the mandibular second molar to distalize by 2.47 mm, and the first molar by 1.16 mm. However, the majority of reports on camouflage treatment using clear aligners have focused on Class II malocclusion, with a lack of studies on Class III malocclusion.

In particular, clear aligners involve the force and moment generated due to the morphological mismatch of the aligners and teeth, which makes it difficult to predict the treatment outcome.14 In contrast to the conventional bracket-wire system, tooth movement using clear aligners does not have specific points of action, as it occurs solely based on surface contact. Thus, the effects of the attachment and morphological properties of clear aligners and teeth are significant, leading to highly complex aspects of predicting tooth movement.15 To solve the biomechanical problem of such complex factors, the finite element method (FEM) has been applied in various ways. An accurate understanding of tooth displacement patterns via FEM-based biomechanical analysis would provide valuable information for extending the scope of clear aligner treatment (CAT) to include skeletal Class III malocclusion and the distalization of mandibular molar teeth.

This study aimed to present a biomechanical analysis of camouflage treatment for Class III malocclusion using CAT. An FEM-based analysis was performed to compare the displacement tendency and biomechanical system based on the traction method (precision cut hook or button on the canine), site (mandibular canine or mandibular first premolar), and direction of the distalization force.

MATERIALS AND METHODS

This was an in vitro study, and ethical approval was not required.

Model construction

From the cone-beam computed tomography data (Pax-Zenith 3D; Vatech Co., Seoul, Korea) of an individual with normal occlusion, the mandible with teeth was segmented using a 3D-slicer. To model the periodontal ligament (PDL), a PDL space with a uniform thickness of 0.25 mm surrounding the roots was maintained. The clear aligners were modeled to have a thickness of 0.5 mm, while all the marginal and interdental parts were shaped to be circular to prevent sharp edges.

Four FEM models were constructed using a CAD program (ANSYS Inc., Canonsburg, PA, USA) to compare the differences in displacement patterns according to the traction methods and sites. A rectangular attachment of 3 mm height, 2 mm width, and 1 mm thickness was applied on the tooth at the traction site to prevent tooth rotation and loss of clear aligners due to the traction force. The four FEM models in the analysis were: (1) Group C1, distalization with a button on the canine; (2) Group C2, distalization with a precision cut hook on the canine; (3) Group P1, distalization with a button on the first premolar; and (4) Group P2, distalization with a precision cut hook on the first premolar (Figure 1). Based on the presumption of left-to-right symmetry, only the right side was analyzed in all 4 models.

Figure 1. Four finite element method models. A, Group C1: distalization with a button on canine; B, Group C2: distalization with a precision cut hook on canine; C, Group P1: distalization with a button on first premolar; D, Group P2: distalization with a precision cut hook on first premolar.

Finite element analysis

According to a previous study reporting the lack of significant differences in the overall pattern of tooth movement, even when using the linear elastic modulus in PDL modeling, the jawbone, dentition, PDL, attachments, and buttons were all presumed to be homogenous and exhibit a linear isotropic elastic behavior.16-21 The material properties of each structure are depicted in Table 1. The material properties of composite attachments were obtained from the manufacturer (3M, St. Paul, MN, USA).

Table 1 . Material properties of each structure.

StructureYoung’s modulus (MPa)Poisson’s
ratio
Mandible1613,7000.30
Periodontal ligament160.450.67
Dentition17,1819,6000.30
Clear aligner17,185280.36
Composite attachment1912,5000.36
Button20200,0000.30


To maintain the boundary conditions in the FEM model, frictionless contact was applied between the teeth and aligner and between adjacent teeth, and bonded contact was applied between the jawbone and PDL and between the PDL and tooth. All the elements were linear. For the mesh size, the following conditions were set after the convergence study based on the displacement of the canine for Groups C1 and C2 and the first premolar for Groups P1 and P2 (Table 2).

Table 2 . Element and node number of 4 finite element models.

GroupElement numberNode number
Group C13,333,574643,775
Group C22,978,423578,884
Group P13,257,487627,886
Group P23,628,755712,577


To compare the effects according to the traction direction, 1.5 N of distalization force was applied on a button or a precision cut hook on the sagittal plane in line with the occlusal plane in the following directions: –30°, –20°, –10°, 0°, +10°, +20°, and +30°. The line of action of the force from the occlusal plane was set at a point 1 mm lateral to the gingiva (Figure 2).

Figure 2. Direction and magnitude of the distalization force. A, lateral and B, occlusal view.

Data analysis

After FEM analysis, the translation and rotation of the mandibular central incisor, canine, first premolar, and first molar were analyzed using MATLAB (version 2020b; MathWorks Inc., Natick, MA, USA) and were based on the center of the clinical crown. The directions of the translational motion were mediolateral, anteroposterior, and apicocoronal. Lateral, anterior, and coronal directions were considered positive. Buccolingual, mesiodistal, and occlusal rotations were evaluated based on the longitudinal axis of the tooth, and buccal tipping, mesial tilting, and mesial-in rotation were defined as positive. Furthermore, to examine the changes in the clear aligners according to the distalization force, the displacement and von Mises stress of the clear aligners were analyzed.

RESULTS

Tooth displacement tendency

Except for the –30° traction in Group C2, all groups showed lingual tipping and extrusion of the mandibular anterior teeth irrespective of the direction of force. The level of lingual tipping or extrusion of the anterior mandibular teeth varied more markedly according to the traction site (canine vs. first premolar) than the traction method (button vs. precision cut hook). In the case of traction at the first premolar sites, as in Groups P1 and P2, the level of lingual tipping or extrusion of the mandibular anterior teeth was more predominant, irrespective of the traction method, which concurrently led to a higher level of crown displacement in the posterior direction. However, in the case of traction at the canine sites, as in Groups C1 and C2, considerable variations were observed for lingual tipping or extrusion of the mandibular anterior teeth with respect to traction direction, whereas traction at the first premolar sites showed few variations according to traction direction (Figures 3 and 4).

Figure 3. Displacement pattern of dentition. A, B, Displacement (μm) of the dentition for +30°and –30° traction in Group C1, respectively. C, D, Displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.

Figure 4. Pattern of tooth movement at the mandibular central incisor. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

The displacement pattern in the mandibular canines was more predominant according to the traction site than the traction method. Traction at canine sites, as in Groups C1 and C2, indicated a substantial impact on the level of intrusion or extrusion of mandibular canines according to the traction direction; intrusion occurred at –30° and –20° traction, whereas extrusion occurred in all other cases. Traction at the first premolar sites, as in Groups P1 and P2, also indicated an impact on the level of intrusion or extrusion of the mandibular canines according to the traction force direction, although the degree of impact was comparatively lower. The distal tipping of the canine was shown to be greater in the traction at the premolar than at the canine sites, which was due to the anti-tipping effect of the attachment on the canine. In addition, the level of lingual tipping of the canine increased as the traction force direction shifted from –30° to +30° (Figures 3 and 5).

Figure 5. Pattern of tooth movement at the mandibular canine. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

The displacement pattern in the mandibular first premolars was more predominant according to the traction site than the traction method. This pattern was similar to that observed for canine traction. The level of distal tipping of the first premolar was more significant in traction at the canine sites than at the first premolar sites, which is due to a reason similar to the aforementioned canine movement pattern: the anti-tipping effect of attachment to the premolar. In the first premolars, –30° traction led to buccal tipping and +30° traction led to lingual tipping (Figures 3 and 6).

Figure 6. Pattern of tooth movement at mandibular first premolar. A, Crown-centered medio- distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

For mandibular first molars, between-group variations were observed according to the traction site. Traction at the first premolars gave rise to a low level of lingual tipping on the mandibular first molars as the force direction was shifted from –30° to +30°, which might be due to deformation of clear aligners or lingual tipping at the mandibular first premolar affecting the traction force. In contrast, traction at the canines had a weak impact on the buccolingual tipping of the mandibular first molars according to the force direction. No variation was observed in the mesial tipping of the mandibular first molars according to the traction site. While mesial tipping occurred in all traction directions, a high level of mesiodistal tipping was detected as the traction direction shifted from –30° to +30° (Figures 3 and 7).

Figure 7. Pattern of tooth movement at mandibular first molar. A, Crown-centered medio distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).

Analyses of displacement and stress for clear aligners

The clear aligners exhibited a posterosuperior rotation pattern with an increase in the superior direction of the distalization force. In contrast, as a –30° posteroinferior distalization force was applied, deformation occurred at the anterior of the traction site of action in lieu of en masse rotation of the entire dentition. In the case of posterosuperior traction, predominant changes in the clear aligners were observed on the buccal side of the first molar, and the use of a precision cut hook resulted in a greater level of change (Figure 8).

Figure 8. Total displacement pattern of aligners. A, B, Total displacement (μm) of the dentition for +30° and –30° traction in Group C1, respectively. C, D, Total displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Total displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Total displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.

For the von Mises stress of clear aligners, the distalization force induced concentrated stress on the adjacent tooth at the traction sites. The use of a precision cut hook focused on the stress on the hook. As in Groups P1 and P2, traction at the first premolar sites led to concentrated stress in the interdental space between the canine and the first premolar. The –30° traction in Group P2 caused the highest von Mises stress in the interdental space between the canine and first premolar across all experimental groups (Figure 9).

Figure 9. Elastic strain (mm/mm) of clear aligners. A, B, For +30° and –30° traction in Group C1, respectively. C, D, For +30° and –30° traction in Group C2, respectively. E, F, For +30° and –30° traction in Group P1, respectively. G, H, For +30° and –30° traction in Group P2, respectively.

DISCUSSION

Tooth movement caused by distalization of the mandibular dentition can be modulated mainly through angulation of the distalization force in a conventional bracket-wire system. The distalization force on the posterior occlusal side, as in an infrazygomatic crest screw, shows a greater moment for rotation of the mandibular occlusal plane owing to a greater distance from the center of resistance. In contrast, traction towards the mandibular buccal shelf screw shows a lower level of rotation of the occlusal plane due to a shorter distance from the center of resistance.7 Chae et al.8 reported that the relationship between the center of resistance of the mandibular dentition and the distalization force direction was the most critical predictor of tooth movement. The authors also reported that the variation in archwire elasticity could be another determinant of tooth movement.8 Notably, as previously described, the magnitude of the moment on the archwire increases with superior distalization force, with a higher level of lingual tipping in the anterior dentition.8

In the CAT-based Class II camouflage treatment, the precision cut hook is mainly applied to the maxillary canines and mandibular molars to distalize the maxillary dentition and protract the mandibular dentition through Class II elastics, or to reinforce anchorage in the sequential distalization of maxillary molars. On the other hand, button cut-outs are used for Class II malocclusion with lingually tipped anterior teeth to separate the retraction sites and aligners to prevent additional lingual tipping of the anterior teeth during retraction of the anterior teeth.22 In addition, if the clinical crown is too short or if a strong force is present on the precision cut hook, clear aligners may be displaced from the dentition to cause inappropriate tooth movements; in such cases, button cut-outs and buttons attached to the teeth are recommended.23

This biomechanical strategy may be used in the camouflage treatment of Class III malocclusions. When applying the distalization force, the precision cut hook may be applied in cases where the level of dentoalveolar compensation is low (i.e., the level of lingual tipping of the mandibular anterior teeth is small), whereas button cut-outs may be applied in cases with excessive compensation of the mandibular anterior teeth for separation from the traction force, which may interfere with labial tipping. Additionally, care should be taken when selecting the force direction, when it is necessary to adjust the occlusal plane, or when applying vertical adjustments.

Furthermore, the traction points of total distalization may have a significant effect on the entire biomechanical system. Considering the traction points, traction at the mandibular first premolar rather than the mandibular canine may induce a lower level of moment in the mandibular dentition, irrespective of the retraction force direction, owing to the shorter distance between the center of resistance and the line of action of the force in the mandibular dentition, resulting in a lower level of rotation in the mandibular dentition according to the force direction. With additional consideration of the damping effects on clear aligners, traction at the mandibular first premolar, which is farther from the mandibular anterior teeth, is conjectured to allow more effective suppression of lingual tipping of the mandibular anterior teeth.24 However, no reports have been made on these assumptions.

For the conventional bracket-wire system, applying the retractive force to the anterior dentition causes an overall en masse-like tooth movement following the changes in the occlusal plane with little impact on individual tooth movement because of the gap between the bracket and wire.25 For clear aligners, however, mesiodistal tipping of individual teeth was predominant rather than bodily movement. This is because, while the wire in the bracket-wire system ensures sufficiently high elasticity, the elasticity from clear aligners is not sufficient for generating adequate counter momentum.26 Thus, it is presumed that the attachments are essential to cause counter momentum.

The FEM analysis results showed that in contrast to the prediction of a more potent suppression of lingual tipping of the mandibular anterior teeth via traction at the mandibular first premolar, higher levels of extrusion and lingual tipping of the mandibular anterior teeth were observed for traction at the mandibular first premolar than at the mandibular canine. In addition, while the trend of gradual lingual tipping increased with the retractive force directed posterosuperiorly at the mandibular canine, a higher level of lingual tipping and extrusion of the mandibular incisors was observed at the mandibular first premolar traction, regardless of the force direction or traction method. This was in contrast to lingual tipping with extrusion of the mandibular anterior teeth upon distalization force occlusal to the center of resistance, and labial tipping with intrusion upon retraction force inferior to the center of resistance in the bracket-wire system.8

This result may be attributed to the lingual tipping of canine and low elastic modulus in clear aligners, leading to elastic deformation. A comparison of the strain in this study showed that the traction at the mandibular first premolar focused on the strain between the mandibular first premolar and canine sites (Figure 9). This may indicate that rather than en masse movement of the entire dentition, tooth movement occurred independently of the respective deformations (Figure 10). Hence, with intrusion at the mandibular first premolar, extrusion occurred at the mandibular first molar as well as lingual tipping and extrusion of the mandibular anterior teeth. Lingual tipping of the mandibular anterior teeth in traction at the mandibular first premolar, regardless of the force direction, occurs because of the additional lingual tipping of the mandibular anterior teeth owing to the clear aligner deformations caused by the downward force.

Figure 10. Force diagram showing aligner deformation during distal retraction with a precision cut hook. A, The force system with –30° posteroinferior distalization force on a precision cut hook (black dot: center of resistance of mandibular dentition, red arrow: distalization force). B, Equivalent force system assuming CA as an ideal rigid body. Rotation occurred following the translation in the whole. C, Mesiodistal tipping of individual tooth rather than bodily movement occurred with lingual tipping and extrusion of the anterior teeth due to the deformation as the aligner is an elastic body (black dashed arrow: deformation of CA due to distalization force, black lined arrow: lingual tipping of the anterior teeth).
CA, clear aligner.

Elastic modulus is a critical physical property indicating the magnitude of the orthodontic force of thermoforming materials.23 Upadhyay et al.27 pointed out that clear aligners are prone to deformations even at little force due to their low elastic modulus (40–50 times lower than the NiTi wire), with a viscoelastic nature which causes permanent deformations due to low resiliency. Therefore, the sequential distalization of molar teeth to apply a lower level of retractive force may be more appropriate than the total distalization to prevent the aligner deformation. It may also be wise to consider applying bite ramps to the maxillary anterior teeth or providing additional labial tipping torque and intrusive forces to the mandibular anterior teeth via TADs, as well as using a thicker sheet. In addition, selecting the mandibular canine, rather than the mandibular first premolar, as the traction site may be more appropriate when applying a posteroinferior retraction force.

In contrast to the prediction that using buttons would reduce lingual tipping of the mandibular anterior teeth,22 the level of lingual tipping of the mandibular anterior teeth did not vary significantly according to the retraction method (precision cut hook vs. button). However, the use of buttons led to rotations of the teeth below the button, resulting in extrusion of the mandibular anterior and adjacent teeth. Therefore, it is likely more advantageous to apply a direct retraction force to clear aligners through a precision cut hook instead of applying a retractive force to an individual tooth with buttons, if a suitable attachment can be applied.

This study had some limitations. The material properties and structures applied in modeling the mandibular dentition may not completely incorporate the biological diversity across individual patients in clinical practice. Moreover, clear aligners in a clinical setting may display a significantly reduced orthodontic force owing to plasticization caused by factors such as water absorption. Thus, future studies should conduct FEM analyses that consider the time-dependent physical properties of clear aligners.

CONCLUSIONS

In this study, the displacement tendency of total mandibular distalization with clear aligners according to the retraction direction, traction points, and traction methods was analyzed using FEM. Biomechanical systems were also compared.

For distalization with clear aligners, lingual inclination of the mandibular anterior teeth and buccolingual and mesiodistal inclinations of the canines, premolars, and molars occurred and varied depending on the traction direction. Rotation of the entire dentition occurred, but tipping of the individual teeth was more prominent.

For total distalization with clear aligners, the variations in tooth movement according to the traction method, such as the use of a precision cut hook or lingual button, were insignificant in the presence of attachment at the point of action of the force.

Differences in the lingual inclination of the mandibular anterior teeth were observed depending on the traction site. Specifically, when traction force was applied to the mandibular first premolars, significant lingual inclination and extrusion of the mandibular anterior teeth occurred, regardless of the traction direction and method, with the deformation of the clear aligner.

FUNDING

This research was funded by the National Research Foundation of Korea (NRF) grant funded by the Korean government (2021R1A2C1003240).

AUTHOR CONTRIBUTIONS

Conceptualization: SO, YIK. Methodology: SO, YKC. Project administration: YIK. Software: SO. Supervision: CCK, KBK, SHK. Validation: YKC, CCK, KBK, SHK. Visualization: SO. Writing–original draft: SO, YKC, CCK, KBK, SHK. YIK. Writing–review & editing: SO, YKC, CCK, KBK, SHK, YIK.

CONFLICTS OF INTEREST

No potential conflict of interest relevant to this article was reported.

Fig 1.

Figure 1.Four finite element method models. A, Group C1: distalization with a button on canine; B, Group C2: distalization with a precision cut hook on canine; C, Group P1: distalization with a button on first premolar; D, Group P2: distalization with a precision cut hook on first premolar.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 2.

Figure 2.Direction and magnitude of the distalization force. A, lateral and B, occlusal view.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 3.

Figure 3.Displacement pattern of dentition. A, B, Displacement (μm) of the dentition for +30°and –30° traction in Group C1, respectively. C, D, Displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 4.

Figure 4.Pattern of tooth movement at the mandibular central incisor. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 5.

Figure 5.Pattern of tooth movement at the mandibular canine. A, Crown-centered medio-distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 6.

Figure 6.Pattern of tooth movement at mandibular first premolar. A, Crown-centered medio- distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 7.

Figure 7.Pattern of tooth movement at mandibular first molar. A, Crown-centered medio distal displacement (μm); B, crown-centered bucco-lingual displacement (μm); C, crown-centered apico-coronal displacement (μm); D, buccolingual inclination change (°); E, mesiodistal inclination change (°); F, occlusal rotation (°).
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 8.

Figure 8.Total displacement pattern of aligners. A, B, Total displacement (μm) of the dentition for +30° and –30° traction in Group C1, respectively. C, D, Total displacement (μm) of the dentition for +30° and –30° traction in Group C2, respectively. E, F, Total displacement (μm) of the dentition for +30° and –30° traction in Group P1, respectively. G, H, Total displacement (μm) of the dentition for +30° and –30° traction in Group P2, respectively.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 9.

Figure 9.Elastic strain (mm/mm) of clear aligners. A, B, For +30° and –30° traction in Group C1, respectively. C, D, For +30° and –30° traction in Group C2, respectively. E, F, For +30° and –30° traction in Group P1, respectively. G, H, For +30° and –30° traction in Group P2, respectively.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Fig 10.

Figure 10.Force diagram showing aligner deformation during distal retraction with a precision cut hook. A, The force system with –30° posteroinferior distalization force on a precision cut hook (black dot: center of resistance of mandibular dentition, red arrow: distalization force). B, Equivalent force system assuming CA as an ideal rigid body. Rotation occurred following the translation in the whole. C, Mesiodistal tipping of individual tooth rather than bodily movement occurred with lingual tipping and extrusion of the anterior teeth due to the deformation as the aligner is an elastic body (black dashed arrow: deformation of CA due to distalization force, black lined arrow: lingual tipping of the anterior teeth).
CA, clear aligner.
Korean Journal of Orthodontics 2023; 53: 420-430https://doi.org/10.4041/kjod23.035

Table 1 . Material properties of each structure.

StructureYoung’s modulus (MPa)Poisson’s
ratio
Mandible1613,7000.30
Periodontal ligament160.450.67
Dentition17,1819,6000.30
Clear aligner17,185280.36
Composite attachment1912,5000.36
Button20200,0000.30

Table 2 . Element and node number of 4 finite element models.

GroupElement numberNode number
Group C13,333,574643,775
Group C22,978,423578,884
Group P13,257,487627,886
Group P23,628,755712,577

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