Effects of clear aligner edentulous space design on distal canine movement: An iterative finite element analysis in cases involving extraction

Seung Eun Baek; Kiyean Kim; Youn-Kyung Choi; Sung-Hun Kim; Seong-Sik Kim; Ki Beom Kim; Yong-Il Kim

doi:10.4041/kjod24.286

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Baek, Kim, Choi, Kim, Kim, Kim, and Kim: Effects of clear aligner edentulous space design on distal canine movement: An iterative finite element analysis in cases involving extraction

Original Article

Korean J Orthod 2025;55(3):193-201.

Published online: 4 April 2025

DOI: https://doi.org/10.4041/kjod24.286

Effects of clear aligner edentulous space design on distal canine movement: An iterative finite element analysis in cases involving extraction

Seung Eun Baek^a

, Kiyean Kim^b,

, Youn-Kyung Choi^a,^b

, Sung-Hun Kim^a,^b

, Seong-Sik Kim^a

, Ki Beom Kim^c

, Yong-Il Kim^a,^b,

^aDepartment of Orthodontics, Dental Research Institute, School of Dentistry, Pusan National University, Yangsan, Korea

^bDental and Life Science Institute, School of Dentistry, Pusan National University, Yangsan, Korea

^cDepartment of Orthodontics, Saint Louis University, Saint Louis, MO, USA

Corresponding author: 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

Corresponding author: Kiyean Kim., Post-doc Researcher, Dental and Life Science Institute, School of Dentistry, Pusan National University, 20 Geumo-ro, Mulgeum-eup, Yangsan 50612, Korea., Tel +82-55-360-5164 e-mail kiyean.kim990@gmail.com

How to cite this article: Baek SE, Kim K, Choi YK, Kim SH, Kim SS, Kim KB, Kim YI. Effects of clear aligner edentulous space design on distal canine movement: An iterative finite element analysis in cases involving extraction. Korean J Orthod 2025;55(3):-201. https://doi.org/10.4041/kjod24.286

Received 10 December 2024 Revised 16 January 2025 Accepted 23 February 2025

(open-access):

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

Using finite element method (FEM) analysis of a clear aligner (CA), this study aimed to investigate the effects of varying the edentulous space on canine distal bodily movement during space closure following maxillary first premolar extraction.

Methods

FEM analysis was used to simulate distal canine bodily movement following maxillary first premolar extraction using CAs. Four CA designs for edentulous spaces were compared no-pontic, full-pontic, half-pontic, and beam. Three-dimensional models of the tooth components and CA were created. The target was set at a 0.25-mm distal canine movement. Long-term tooth movement was simulated using an iterative calculation method.

Results

All the groups initially showed crown displacement, distal tipping, and distal rotation. Over time, the movement patterns differed in relation to the design. The no-pontic design exhibited the greatest displacement and tipping. The beam design exhibited the largest initial displacement but showed the lowest displacement and tipping thereafter. Full- and half-pontic designs yielded intermediate results. Significant force reduction was observed immediately after CA application, and was followed by a gradual decrease. The mean tooth-movement achievement rate was approximately 76.7%.

Conclusions

The edentulous space design of the CA substantially affected tooth-movement behavior. An iterative simulation is necessary to evaluate long-term tooth-movement patterns. The beam design demonstrated optimal suitability for bodily movement with minimal tipping. For optimal results, additional setup or overcorrection may be necessary.

Keywords: Finite element method, Extraction space, Clear aligner design

INTRODUCTION

Clear aligners (CAs) were initially limited in scope and were primarily used in cases involving simple tooth movements.¹ To expand their clinical applicability, extensive research was conducted on the mechanisms underlying tooth movement during CA treatment.^2-4 These biomechanical studies have increased the reliability of CA treatments and broadened their range of applications.⁵ Consequently, CAs have been successfully used in tooth extraction cases, an area initially considered a contraindication to this treatment modality. This expansion into more complex orthodontic scenarios is supported by ongoing research and clinical advancements.⁶

In orthodontic treatment involving premolar extraction, space closure often leads to undesirable outcomes, commonly known as the “roller-coaster effect.” This phenomenon involves insufficient posterior movement of the anterior teeth, which causes distal tilting. Simultaneously, anchorage loss in the posterior teeth leads to mesial tilting.⁷ Extensive studies have been conducted to mitigate these adverse effects.^8-10 A comprehensive understanding of biomechanics is crucial for achieving proper tooth movement during orthodontic treatment with CAs. This will enable orthodontists to achieve predictable, safe, and stable outcomes. However, the sequential nature of CA treatment, wherein aligners are replaced in stages and tooth contact relationships constantly evolve during treatment, poses challenges in predicting the precise locations of aligner actions and forces/moments. To address these complexities, many researchers have used the finite element method (FEM), which has become a valuable tool for examining and verifying CA biomechanics. This approach enables detailed analysis of the stress distributions and deformations within complex geometries.^7,8,10

Despite the widespread use of CAs in orthodontic treatment, a comprehensive solution for managing tooth migration into edentulous spaces remains elusive. Achieving bodily movement in these spaces remains challenging. Despite prior studies on attachments and CA structures, refining the CA design is crucial for minimizing adverse effects during distal bodily movements of the canines in cases involving first premolar extraction. In particular, research on the effects of the CA design on canine distal bodily movements during extraction space closure is limited.

FEM is an invaluable tool for understanding the biomechanics of tooth movement in complex intraoral environments such as extraction spaces. In this study, we utilized FEM to investigate how the design of the edentulous space on CAs influences the canine distal bodily movement during space closure following maxillary first premolar extraction.

MATERIALS AND METHODS

Model construction

Imaging data of the maxillary structure were acquired using cone-beam computed tomography (PaX-Zenith 3D, Vatech Co., Seoul, Korea) to create a three-dimensional (3D) model. Subsequently, 3D models of the maxillary dentition and maxilla were segmented from the acquired computed tomography data using the 3D Slicer open-source software. The 3D model included the alveolar bone, dentition, and periodontal ligament (PDL), and the teeth were repositioned for a normal bite. SOLIDWORKS (Dassault Systèmes, Vélizy-Villacoublay, France) was used for the PDL and CA modeling processes. A 0.25-mm-thick PDL was created on the outer side of the root surface, and a 0.5-mm-thick CA was modeled from the outer surface of the tooth crown according to the design of each experimental group. All margins and interdental areas were circularized to avoid stress concentration. A horizontal rectangular attachment was modeled and applied to the maxillary tooth to accurately assess its movement in the maxillary tooth. The attachment had a height of 2 mm, width of 3 mm, and thickness of 1 mm. This helped simulate the interaction between the CA and teeth more precisely (Figure 1).

For computational efficiency, only the right half of the maxillary dentition was modeled, assuming anatomical symmetry. The experimental design compared four variations of the CA design in the edentulous space to simulate the maxillary canine posterior bodily movement into the edentulous space after extraction of the maxillary first premolars. To achieve this, we constructed four types of FEM models (Figure 2).

(1) Group 1: the extraction space was in an edentulous state (no-pontic design).

(2) Group 2: the extraction space was in the premolar pontic state (full-pontic design).

(3) Group 3: the extraction space was in half of the premolar pontic state (half-pontic design).

(4) Group 4: the extraction space was in the beam state (beam design).

The teeth, maxilla, attachments, and CAs were modeled as homogeneous linearly elastic materials.^4,11,12 The PDLs were modeled as linear elastic materials based on previous studies showing that linear nonlinear elastic properties did not significantly affect long-term orthodontic behavior.¹³ The material properties of the attachments were set on the basis of data provided by the manufacturer (Table 1). Finite element modeling and analysis were performed using FEM software and ANSYS 2024R (ANSYS Inc., Canonsburg, PA, USA). The interfacial conditions were set to be frictionless between the tooth and aligner and between adjacent teeth. Bonded contacts were assumed between the alveolar bone and PDL and between the PDL and tooth. For mesh generation, the optimal size was determined by considering the characteristics of each structure. The mesh size was determined by balancing the accuracy of the analysis with the computational efficiency; the detailed mesh sizes for each structure are listed in Table 2. In this study, a global coordinate system was used to define the orientations along the x-, y-, and z-axes (Figure 1).

Simulation of tooth movement using the clear aligner

Because the elastic moduli of the tooth and alveolar bone are significantly larger than those of the PDL and CAs, under this assumption, the nodes of the alveolar socket (i.e., the nodes on the outer surface of the PDL) were defined as rigid surfaces that move with tooth movement. The movement of the tooth and PDL due to the alveolar bone remodeling that occurs during tooth movement was simulated using FEM. The outer surface of the PDL coinciding with the alveolar bone socket was displaced by calculating the initial displacement caused by elastic deformation of the PDL. The simulations were performed using the method described by Yokoi et al.¹³

RESULTS

Analysis of displacement and rotation

The initial CA fitting (Stage 1) revealed the distinct influence of the aligner design on maxillary canine displacement (Figure 3), distal tipping (Figure 4), and rotational movement (Figure 5). The no-pontic design (Group 1) exhibited minimal canine movement, with a crown displacement of 0.15851 mm, distal tipping of 0.6397°, and distal rotation of 0.0931°.

The full-pontic design (Group 2) showed a crown displacement of 0.158 mm, which was comparable to that of the no-pontic design. However, the full-pontic design demonstrated increased distal tipping (0.6469°) and decreased rotation (0.0799°) in comparison with the corresponding values in Group 1. The half-pontic design (Group 3) showed a slightly higher crown displacement (0.15961 mm) than those in the no-pontic and full-pontic designs. It exhibited the highest distal tipping (0.6515°) and moderate rotation (0.0836°) among Groups 1, 2, and 3. The beam design (Group 4) yielded the highest crown displacement (0.16456 mm) among all the designs. It also showed the most significant distal tipping (0.6759°), but it showed the least rotational movement (0.0763°).

To address long-term tooth movement following application of CAs with each design, the biomechanical behavior was simulated for up to 50 iterations (Figure 6). Each design exhibited distinct patterns of long-term tooth movement (Figure 3), tipping effects (Figure 4), and rotation (Figure 5).

No-pontic design (Group 1): after 50 stages, crown displacement increased to 0.21137 mm, distal tipping increased to 0.7781°, and distal rotation decreased to 0.0118°. This indicates a reduction in occlusal plane rotation over time but a continued increase in distal tipping.

Full-pontic design (Group 2): after 50 stages, the crown displacement increased to 0.1864 mm, the distal tipping increased to 0.6713°, and the distal rotation was effectively minimized to 0.0005°.

Half-pontic design (Group 3): by Stage 50, the crown displacement reached 0.18497 mm, which is slightly lower than that of the full-pontic design. Distal tipping remained lower than that in the full-pontic design at 0.6573°, but distal rotation was higher at 0.0013°.

Beam design (Group 4): by Stage 50, this design showed the lowest crown displacement (0.18465 mm) among all designs. Distal tipping was reduced to 0.6283° and distal rotation remained low at 0.0043°, demonstrating significant tooth movement while maintaining excellent control over distal tipping and rotation.

Analysis of force and moment

All CA designs exhibited significant force reduction between Stages 1 and 2 (Figure 7). For instance, the force decreased from 23.916 to 5.3294 N for the beam design, and from 23.021 to 5.1648 N for the no-pontic design. From Stages 3 to 50, a gradual decrease in force was observed across all designs (Figure 7). Notably, the beam design consistently maintained higher force levels than other designs throughout the simulations. At Stage 50, the beam design sustained a force of 0.8831 N, whereas the other designs, particularly the no-pontic design, exhibited relatively lower forces. All CA designs showed a dramatic decrease in the moment between Stages 1 and 2 (Figure 8). For example, the moment decreased from 0.02942 to 0.02227 Nm for the beam design and from 0.02971 to 0.02116 Nm for the no-pontic design. Following the initial sharp decrease, a gradual reduction in the moment was observed across all designs for the remaining stages (Figure 8). The beam design consistently exhibited the highest moment across all stages, whereas the no-pontic design consistently exhibited the lowest moment. At Stage 50, the beam design maintained a moment of 0.01006 Nm, compared to 0.00742 Nm for the no-pontic design.

DISCUSSION

Tooth movement in CAs is characterized by long-term, gradual, and continuous processes. Accurately analyzing this complex, ongoing tooth movement requires approaches similar to the iterative computational method introduced by Kojima et al.¹⁴ In this study, we applied an iterative computational simulation method to conduct biomechanical analysis of the long-term tooth-movement behavior of the maxillary canine. This approach enabled more accurate modeling of continuous tooth movement during CA treatment. Moreover, this evaluation extended beyond the scope of an initial displacement analysis.

In this study, we simulated a 0.25-mm distal bodily movement of the tooth using four distinct CA designs in the edentulous space: no-pontic (Group 1), full-pontic (Group 2), half-pontic (Group 3), and beam (Group 4). Our results revealed that while all groups exhibited distal tipping, the pattern of tooth movement varied significantly among the groups. In the early stages (immediately after application), tipping was the most pronounced in Group 4, followed by Groups 3, 2, and 1. However, this order was inverted in the final stage (after the iterative simulation). Group 1, with structurally weaker CAs in the edentulous space, exhibited continuous tipping with a decreasing moment in comparison with the other groups, resulting in maximum displacement and tipping. In contrast, Group 4 initially showed the most tipping but ultimately exhibited the least tipping. This group consistently produced larger moments than the other groups from the outset, leading to a gradual reduction in distal tipping over time. Groups 2, 3, and 4 demonstrated similar patterns of reduced distal tipping over time, unlike Group 1. In these groups, the elastic force of the aligner generated a moment in the tipped tooth, which improved its inclination. However, in Group 1, the moment was insufficient to correct the tilt, resulting in progressive tipping. This difference in moment actions distinguished Groups 2, 3, and 4 from Group 1.

Our findings differ from those reported by Jiang et al.,¹⁵ who observed mesial tipping and intrusion of the canine during en masse retraction (0.25-mm bodily movement) of the maxillary anterior teeth in premolar extraction cases. This discrepancy could be primarily attributed to the following factors.

(1) Movement pattern: our study focused solely on the posterior movement of the canines, whereas Jiang et al.¹⁵ examined the mass retraction of both canines and incisors.

(2) Simulation method: Jiang et al.¹⁵ simulated only initial displacement, in contrast to our iterative calculation approach that modeled long-term tooth movement.

Interestingly, Zhang et al.¹⁶ reported canine distal inclination and protrusion during en masse retraction as a result of iterative calculations in a case of premolar extraction. These comparisons underscore the importance of iterative simulations for accurately modeling long-term orthodontic tooth movement. Such simulations are critical for understanding the effects of the mechanical loads imposed by CAs. Studies employing initial displacement analysis differ significantly from those that use iterative calculations. Our findings emphasize the necessity of iterative methods to understand tooth movement mechanics during CA treatment.

Mao et al.¹⁷ reported that in CA treatment for premolar extraction space closure, a higher edentulous space height on the CA led to increased tipping, whereas a lower height resulted in less tipping. They attributed this to the ability of the lower-height designs to apply a force closer to the center of resistance of the canine. Based on their findings, Group 1, which had the lowest edentulous space height, was expected to exhibit the least tipping. However, our results showed the opposite, with Group 1 experiencing the greatest tipping. In contrast, Groups 2 (full-pontic) and 3 (half-pontic), with higher edentulous space heights, demonstrated less tipping than Group 1. This contradictory finding suggests that tooth-movement behavior is not solely determined by the height of the edentulous space, but is also significantly influenced by its shape. A key distinction between our study and that of Mao et al.¹⁷ is the design approach. Mao et al.¹⁷ varied only the height of the central part of the edentulous space while maintaining consistent contact with the distal surface of the canine. In contrast, our study employed different shapes for each group, resulting in varying canine coverage. This fundamental difference in design limited the scope for direct comparisons between the two studies. Interestingly, Group 4 (beam structure) demonstrated the most desirable distal bodily movement with minimal tipping and rotation. This occurred despite a higher edentulous space height than that used in the study by Mao et al.¹⁷ This outcome contrasts with the conclusion reported by Mao et al.,¹⁷ who observed that a higher edentulous space height leads to more difficult tooth-movement control. Although the CA designs differed between the two studies, our findings underscore a crucial point: both the height and shape of the CA in the edentulous space can significantly influence tooth-movement patterns.

Our study revealed distinct displacement patterns across the four CA designs. Initially, all groups showed increased displacement. However, Groups 2, 3, and 4 subsequently exhibited a decrease in displacement up to Stage 50, whereas Group 1 maintained constant displacement throughout. Consequently, Group 1 exhibited the largest overall displacement. Among Groups 2, 3, and 4, which shared similar displacement tendencies, Group 4 initially displayed the highest displacement. Interestingly, this pattern was reversed as the simulation progressed, with Group 4 ultimately showing the least displacement at Stage 50. These findings contrast with those reported by Mao et al.,¹⁷ who observed that a higher edentulous space in CAs led to increased stress resistance, reduced root control, and greater displacement. They suggested that CA bending in the edentulous space generates stress. This stress is greater in designs with more edentulous spaces, reduced root control, and increased displacement. In our study, Groups 2 and 3 showed the highest edentulous space heights. However, contrary to the expectations based on the findings reported by Mao et al.,¹⁷ these groups did not show the largest displacements. Instead, groups 4 and 1 exhibited the highest displacements in the initial and final stages, respectively. Notably, Group 1 had the lowest edentulous space height, but it ultimately showed the largest displacement, contradicting previous findings. Thus, while tooth displacement is a crucial consideration, the extent of crown coverage by the CA also plays a significant role in efficient root movement. Therefore, when planning effective root movements, multiple aspects of CA design beyond the height of the edentulous space require consideration.

Our study revealed that distal rotation occurred in all four groups as the canines moved into the edentulous space, with the degree of rotation progressively decreasing over time. Notably, Group 4 (beam design) exhibited the least initial rotation, but ended up with the second-highest rotation at the final stage. The beam design of Group 4 featured a solid interior structure that exhibited relatively little deformation upon CA application. This resulted in less initial rotational variation in the canine in comparison with those in Groups 1, 2, and 3. We postulated that the edentulous space design of Group 4 influenced the CA strain, which in turn affected the rotational changes in the tooth through the elastic energy generated by the deformed CA.

Our findings are in contrast with those obtained by Mao et al.,¹⁷ who reported that a higher edentulous space height leads to greater stress concentration on the lingual margin, resulting in increased rotation. In our study, Groups 2 and 3, which had the highest edentulous space height, showed less rotation than Group 1, which had the lowest height. When comparing Groups 2, 3, and 4, Group 4 initially displayed the least rotation owing to its lower height. However, at Stage 50, its rotation exceeded those of Groups 2 and 3. This pattern aligns with the findings obtained by Mao et al.¹⁷ for the initial CA applications. However, it diverges from the findings obtained when long-term tooth movement is analyzed through iterative calculations.¹⁷ Interestingly, we also noted a difference in rotation between Groups 2 and 3, both of which showed low levels of rotation. These groups shared the same edentulous space heights. However, this difference suggests that the buccolingual width significantly influences tooth rotation.

In the initial stage, Group 4 showed the highest achievement rate of 65.8%. Groups 3, 1, and 2 showed achievement rates of 63.8%, 63.4%, and 63.2%, respectively. The differences among Groups 1, 2, and 3 were not significant. The average initial movement across all groups was 0.16 mm, with a 64.0% achievement rate. By the final stage (Stage 50), the displacement achievement rates had increased for all groups. However, their relative performances shifted notably. Group 1 showed the highest rate (84.5%), followed by Groups 2, 3, and 4 (74.6%, 74.0%, and 73.9%, respectively). All four CA designs exhibited similar long-term movement patterns: an increase in crown displacement and tipping, accompanied by a decrease in rotation from Stage 1 to Stage 50. A significant force reduction occurred between Stages 1 and 2 after CA placement. The force gradually decreased as tooth movement progressed. Notably, although our iterative simulation did not directly correspond to the real-time progression, it effectively revealed the long-term patterns of tooth movement.

In our study, we simulated a 0.25-mm distal bodily movement of the maxillary canine, achieving an average movement of approximately 0.19 mm, corresponding to an average achievement rate of 76.7%. This rate surpasses that reported in clinical studies of CAs. For instance, Migliorati et al.¹⁸ found an achievement rate of approximately 65% for torque control in the maxillary canines, whereas Castroflorio et al.¹⁹ reported an achievement rate of approximately 60% for linear mesiodistal movement of maxillary canines. The higher achievement rate in our simulation in comparison with those reported in clinical studies can be attributed to several factors. Our study calculated the tooth movement to the target position using a single aligner. In contrast, clinical treatment typically involves multiple alignment changes. Moreover, clinical outcomes are influenced by patient-specific factors such as treatment direction and individual tooth-movement conditions. However, these factors were not accounted for in our simulations. Because of these complexities, achieving the level of movement observed in our simulation may be challenging in real-world clinical scenarios. However, the insights gained from our study on maxillary canine bodily movements can inform future clinical research and practice. Treatment plans based on our findings can enhance the biomechanical understanding of posterior tooth movement and improve treatment planning for maxillary canines.

CONCLUSIONS

Movement following CA application was the most active in the initial phase after application, and was followed by gradual relaxation. Importantly, tooth-movement patterns may vary significantly after repeated calculations, highlighting the need for this approach.

• The no-pontic design resulted in the greatest displacement but also maximized tipping and rotation.

• The beam design proved to be the most suitable for bodily movement, exhibiting the least tipping.

• With a target tooth movement of 0.25 mm, an average achievement rate of 76.7% was observed.

Thus, additional setup or overcorrection may be necessary when planning tooth movement to achieve the desired clinical outcomes.

Notes

AUTHOR CONTRIBUTIONS

Conceptualization: SEB, KK, YIK. Formal analysis: SEB, KK, YIK. Investigation: SEB, KK, YIK. Methodology: KK, YIK. Software: KK. Validation: YKC, SHK, SSK, KBK. Writing–original draft: All authors. Writing–review & editing: All authors.

CONFLICTS OF INTEREST

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

FUNDING

This study was supported by Busan-Gyeongnam-Ulsan branch of Korean Association of Orthodontists.

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Figure 1

All components of the finite element method model with the coordinate system.

Figure 2

Four designs of the clear aligner finite element method model. A, Group 1: No-pontic design; B, Group 2: Full-pontic design; C, Group 3: Half-pontic design; D, Group 4: Beam design.