Clear aligners have gained worldwide popularity as orthodontic appliances1,2 initially introduced as an esthetic alternative to fixed appliances correcting mild and moderate crowding.3,4 Clinicians and patients favor these appliances due to the reduced chair time, user-friendliness, minimal discomfort, and convenience during nutrition and oral hygiene maintenance.5,6 However, aligners also have certain limitations, such as difficulties in achieving root parallelism, correcting rotations, controlling extrusions, limited interocclusal correction, movements beyond the orthodontist's control, and higher associated costs.7 With growing interest from both the clinicians and the patients, aligner technology has improved in design, material, and biomechanics, and the predictability of more complex tooth movements such as diastema closure, intrusion, extrusion, and labialization.8,9

Torque is the force that allows an orthodontist to control the axial inclination of the tooth, ensuring an esthetic finish. When torque movements are not well understood and managed, the treatment process becomes more challenging, leading to less desirable outcomes.10 The first crucial step in repositioning palatally located teeth involves creating a sufficient arch space, followed by achieving the desired incisor inclination through appropriate orthodontic mechanics. With advancements in clear-aligner technology, the use of attachments has become essential for facilitating complex tooth movements. Studies have shown that attachment designs and other auxiliary elements are necessary to establish an adequate force system.11 Nucera et al.1 recommend the use of attachments, power ridges, and proper anchorage planning to achieve anterior root torque with clear aligners. Moreover, the specific placement of the composite attachments plays a key role in influencing the direction and magnitude of force.4

Finite element analysis (FEA) has become a valuable tool in dentistry due to its ability to assess the mechanical behavior of biomaterials and various tissues that are challenging to evaluate in vivo. FEA simplifies the physiological responses of the dentoalveolar complex to orthodontic forces, providing quantitative data12 and offering valuable insights into the biomechanical and physiological effects within tissues such as the periodontal ligament (PDL) and alveolar bone in a non-invasive manner.13 Previous studies have employed FEA to investigate tooth movements during clear aligner therapy. Gomez et al.14 highlighted the importance of attachments for achieving parallel tooth movements. Kim et al.15 evaluated the optimal attachment positions during mandibular canine distalization, revealing that lingual attachments were more effective for torque control and that cylindrical attachments played a significant role in stress distribution. Another study on maxillary incisor retraction demonstrated that when the intrusion was involved, additional lingual root torque occurred, underscoring the intricate nature of tooth movement with clear aligners.16

The aim of our study was to evaluate the effect of different attachment positions and clear aligners on torque control using FEA during the labialization of palatally positioned maxillary lateral incisors.

The organization of the three-dimensional mesh structure, its transformation into a mathematically compatible solid mesh, the development of three-dimensional FEA models, and the finite element stress analysis were performed using HP workstations equipped with INTEL Xeon E-2286 processors (Intel, Santa Clara, CA, USA) operating at 2.40 GHz and 64 GB ECC memory. In this study, high-resolution tomography data provided by the Visible Human Project (VHP) were utilized. The VHP is a project developed by the National Library of Medicine with the aim of modeling and visualizing human anatomy in three dimensions. The dataset includes digitized image sets of male and female individuals, featuring scans with millimetric precision.

Cone-beam computed tomography (CBCT) data from an adult female patient with no craniofacial anomalies, skeletal malocclusion, prior orthodontic treatment, and maintained periodontal health were obtained from the archives of Tinus Technologies (Ankara, Türkiye). CBCT data were reconstructed with a slice thickness of 0.1 mm. The resulting tomographic images in DICOM format were then imported into 3D-Slicer software (Ultimaker BV, Geldermalsen, Netherlands). These images were segmented based on the Hounsfield values to create a three-dimensional model, which was subsequently exported in standard triangle language (STL) format.

The STL model was imported into the ANSYS SpaceClaim software (ANSYS Inc., Canonsburg, PA, USA) to create maxillary cortical bone and tooth geometry models. The inner surface of the three-dimensional maxillary cortical bone, with an adjusted thickness of 2 mm, served as a reference for generating the trabecular bone. PDLs with a thickness of 0.25 mm were modeled based on the outer surface of the teeth.17 The relationship between the root of the lateral incisor and the alveolar bone is shown in Figure 1. All models were accurately positioned in space, and the entire modeling process was conducted using the same software. Clear aligner and attachment models were designed using the dimensions provided by the Orthero product catalog (Seffaf Aparey Ortodonti ve Elektronik San. Tic. AŞ., Istanbul, Türkiye). The clear aligners were set to a thickness of 0.625 mm, and the attachments measured 3 mm × 2 mm × 1 mm (width × depth × height). We assigned the linear material properties of all components, with mechanical properties listed in Table 1, based on values from previous studies.14,18,19

Figure 1. Mathematical model showing anatomical structures and clear aligner. A, A section of an existing model;
B, Maxillary tissues created based on patient data, and clear aligner; C, Methematical model.

Table 1 . Material properties of the components in the study.

Component	Elastic modulus (MPa)	Poisson ratio
Trabecular bone14,18,19	1,370	0.30
Cortical bone14,18,19	13,700	0.30
Tooth14,18,19	19,600	0.30
Periodontal ligament14,18,19	0.67	0.45
Composite attachment14,18,19	12,500	0.36
Clear aligner18,19	528	0.36

To perform the analyses, mathematical models prepared using ANSYS Workbench software (ANSYS Inc.) were transferred to the LS-DYNA program (Livermore Software Technology Corporation, Livermore, CA, USA). The mathematical model obtained by dividing the geometric model into simple and small parts is shown in Figure 2.

Figure 2. Models prepared for different study protocols. A, Group 1 (no attachment); B, Group 2 (gingivally positioned labial attachment); C, Group 3 (mid-crown labial attachment); D, Group 4 (incisally positioned labial attachment); E, Group 5 (palatal attachment); F, Group 6 (combined attachments).

Study design

In this study, a total of five different experimental models were generated, with the first group serving as the control model without attachments. The designs of all the models are shown in Figure 3. Labially positioned attachments in the study models were placed using a gingival bevel, while palatally positioned attachments were placed using an occlusal bevel.

Figure 3. Boundary conditions.

• Group 1:

  Attachment-free group

• Group 2:

  Group with the attachment placed labially in a gingival position

• Group 3:

  Group with the attachment placed labially in mid-crown

• Group 4:

  Group with the attachment placed labially in an incisal position

• Group 5:

  Group with the attachment placed palatally

• Group 6:

  Group with combined attachments placed both labially and palatally in the incisal position

Loading and boundary conditions

In this study, a reverse activation force of 0.25 mm was applied to the lateral incisor in the direction opposite to labialization. The forces exerted by the aligner on each tooth were determined based on this activation force and then applied to the model in the direction of labialization. This force application model was used for all models, resulting in five non-linear analyses.

To prevent any movement along all three axes, all degrees of freedom were fixed at the nodal points in the upper region of the cortical and trabecular bones. Additionally, boundary conditions were implemented to ensure symmetry across the Y-Z plane, with the X-axis perpendicular to it (Figure 4).

Figure 4. Displacement pattern of the lateral incisor with the activation of the 0.625 mm thick clear aligner (material). A, Group 1 (no attachment); B, Group 2 (gingivally positioned labial attachment); C, Group 3 (mid-crown labial attachment); D, Group 4 (incisally positioned labial attachment); E, Group 5 (palatal attachment); F, Group 6 (combined attachments).

Integration of systems and connection status of components

To analyze the mathematical models and obtain precise results, it is essential to establish surface relationships between the components within the analysis software. Non-linear frictional contacts with a coefficient of friction set to 0.2 were defined for the interfaces between the clear aligner and the tooth, as well as between the clear aligner and the attachment.

Bonded-type contact definitions were applied to the contact regions involving tooth-PDL, tooth attachment, and cortical and trabecular bone-PDL interactions. This approach assumes that the components move in a complete correlation during motion.

We conducted stress distribution and displacement analyses for all models considered in this study. The lateral incisor is situated within the curved region of the dental arch. In the global coordinate system, from an occlusal view, the X axis represents the left-to-right plane, whereas the Y axis represents the front-to-back plane. Labialization is achieved through a combination of negative movements along both the X- and Y-axes.

Displacement of lateral ıncisor in X and Y axes

In all models, the incisal edge of the lateral incisor displayed uncontrolled labial tipping accompanied by palatal movement of the root apex. Moving from the incisal edge towards the cervical region on the labial surface of the lateral incisor, the degree of labial tipping gradually decreased. The magnitudes of the apex and crown displacements along the X- and Y-axes are shown in Figure 4 and Table 2.

Table 2 . Displacement amounts of the upper lateral incisor (mm).

Direction	Location	Group 1	Group 2	Group 3	Group 4	Group 5	Group 6
X	Apex	0.03958	0.03862	0.03778	0.03759	0.03889	0.03640
	Crown	–0.1267	–0.1250	–0.1219	–0.1205	–0.1257	–0.1172
Y	Apex	0.04015	0.04017	0.03997	0.03852	0.04047	0.03832
	Crown	–0.1277	–0.1251	–0.1242	–0.1233	–0.1267	–0.1215

X, mesial/distal movement; Y, labial/palatal movement; Apex, the tip of the lateral incisor root; Crown, the incisal edge of the lateral incisor..

Among the groups, Group 6, with combined attachments, exhibited the smallest displacement of the apex along the X-axis (0.03640 mm). In contrast, the root apex experienced the greatest displacement along the X-axis in attachment-free Group 1 (0.03958 mm).

For the lateral incisor crown, the greatest displacement in the X-axis was observed in the attachment-free Group 1 (–0.1267 mm), while the least displacement was observed in Group 6 with combined attachments (–0.1172 mm).

On the Y-axis, the apex of the lateral incisor exhibited the highest displacement in Group 5 with palatal attachment (0.04047 mm), whereas the least displacement was observed in Group 6 with combined attachments (0.03832 mm).

With respect to the crown of the lateral incisor in the Y-axis, the greatest displacement was found in attachment-free Group 1 (–0.1277 mm), while the least displacement was observed in Group 6 with the combined attachments (–0.1215 mm).

Clear aligner deformation

When assessing all the models, clear aligner deformation was primarily concentrated at the incisal edge of the lateral incisor and progressively reduced toward the cervical region. Additionally, deformation in the clear aligner gradually diminished from the lateral incisors to the posterior teeth. Detailed data regarding the aligner deformation are shown in Table 3 and Figure 5.

Figure 5. Clear aligner deformation values. A, Group 1 (no attachment); B, Group 2 (gingivally positioned labial attachment); C, Group 3 (mid-crown labial attachment); D, Group 4 (incisally positioned labial attachment); E, Group 5 (palatal attachment); F, Group 6 (combined attachments).

Table 3 . Clear aligner deformation and minimum-maximum deformation locations.

Group	Maximum deformation (mm)	Location of maximum deformation	Minimum deformation (mm)	Location of minimum deformation
Group 1	0.2933	Incisal edge of the lateral incisor	0.1391	Cervical third of the lateral incisor
Group 2	0.3021	Incisal edge of the lateral incisor	0.1439	Cervical third of the lateral incisor
Group 3	0.2878	Incisal edge of the lateral incisor	0.1372	Cervical third of the lateral incisor
Group 4	0.2849	Incisal edge of the lateral incisor	0.1363	Cervical third of the lateral incisor
Group 5	0.2971	Incisal edge of the lateral incisor	0.1420	Cervical third of the lateral incisor
Group 6	0.2809	Incisal edge of the lateral incisor	0.1249	Cervical third of the lateral incisor

The maximum deformation in the clear aligner occurred at the incisal edge of the lateral incisor in Group 2, with a gingivally positioned labial attachment (0.3021 mm). The minimum deformation was observed at the cervical third of the lateral incisor in Group 6 with combined attachments (0.1249 mm).

Comparison of periodontal ligament stress values

In all the models, the highest Von Mises stress values were observed in the tissues surrounding the lateral incisor. The maximum Von Mises stress within the PDL was recorded in Group 5 with a palatal attachment (0.2265 MPa), while the lowest Von Mises stress was noted in Group 3 with mid-crown attachment (0.000448 MPa). Detailed stress distributions for all groups are presented in Table 4 and Figure 6.

Figure 6. Von Mises stress values in periodontal ligament at 0.25 mm activation of the clear aligner. A, Group 1 (no attachment); B, Group 2 (gingivally positioned labial attachment); C, Group 3 (mid-crown labial attachment); D, Group 4 (incisally positioned labial attachment); E, Group 5 (palatal attachment); F, Group 6 (combined attachments).

Table 4 . Von Mises stress values and distribution on the lateral incisor.

Group	Maximum value (MPa)	Maximum value location	Minimum value (MPa)	Minimum value location
Group 1	0.2207	Cervical line of the palatal surface	0.004025	Middle third of the labial and palatal surfaces
Group 2	0.2138	Cervical line of the palatal surface	0.001736	Middle third of the labial and palatal surfaces
Group 3	0.2018	Cervical line of the palatal surface	0.000448	Middle third of the labial and palatal surfaces
Group 4	0.1987	Cervical line of the palatal surface	0.002366	Middle third of the labial and palatal surfaces
Group 5	0.2265	Cervical line of the palatal surface	0.000761	Middle third of the labial and palatal surfaces
Group 6	0.1968	Cervical line of the palatal surface	0.001391	Middle third of the labial and palatal surfaces

The highest stress values were consistently observed at the cervical line of the lateral incisor, with stress more pronounced presence on the palatal surface than on the labial side. Conversely, the region with the least Von Mises stress was the middle third of the lateral incisor root on both the palatal and labial surfaces.

Clear aligners, which have gained popularity for their aesthetic and comfortable nature, were initially used for cases with minimal misalignment and relapse.20 However, advancements in material technology and auxiliary components now allow their application to more complex cases. Despite these improvements, the mechanism of tooth movement with clear aligners and the specific mechanical properties required to achieve desired tooth movement remains unclear. Although tipping movements are among the most predictable, torque movement has been reported to be less predictable.21 Therefore, this study aimed to comparatively evaluate the effect of different attachment positions on torque control during the labialization of palatally positioned maxillary lateral incisors using FEA.

The biomechanical behavior of clear aligners, which were developed as an alternative to fixed orthodontic appliances, is more complex than that of traditional fixed orthodontic systems. This complexity arises from the fact that the exact points of force application for clear aligners are not fully known.22 To optimize control over tooth movement, the use of attachments, interproximal reduction, and adjustment in activation force is recommended.23 Simon et al.11 suggested that 42% of torque control and intrusion for incisors can be achieved with clear aligners, advocating for the overcorrection of these movements during planning. Supporting tooth movement with horizontal ellipsoid attachments or a power ridge is also recommended. D'Antò et al.24 reported that only 35% of the expected torque movement was achieved for the central incisors and canines. Predicting torque movement in clear aligner, which depends on factors such as tooth morphology, aligner material, and the planned magnitude of tooth movement.25

FEA is a highly successful method for quantitatively assessing the physiological response of adjacent dental tissues such as the PDL and alveolar bone. It is frequently used to evaluate orthodontic tooth movement with both fixed and clear aligners. In the present study, the effect of attachment position on torque control during the labialization of a palatally positioned maxillary lateral incisor was investigated during clear aligner treatment. A global coordinate system was used to assess tooth movement, with the vector sum of the tooth movements within this system serving to evaluate the crown and root movement. The pattern of clear aligners directly reflects the manner in which force is applied, and applying force from different points can influence the findings.26,27 Therefore, the force required for lateral incisor movement was initially evaluated, followed by the application of forces in the opposite direction to achieve labialization with the aligner.

Attachments enhance the effectiveness of orthodontic treatment using clear aligners and contribute to the success of various tooth movements. In this study, we examined labial attachments positioned at three different vertical levels: palatal attachments and a combination of labial and palatal attachments. Previous studies have reported that beveled-design attachments provide greater retention and are advantageous for controlling root movement.14,28 Jones et al.29 found that a gingivally beveled horizontal attachment positioned centrally was the most retentive placement and recommended it for tooth movements requiring retention. Another study noted that conventional attachments with at least one beveled edge were beneficial for both tooth movement and anchorage, recommending placement in the palatal region of anterior teeth for therapeutic and aesthetic reasons.30 Therefore, in this study, all attachments were preferred to have a beveled design and were applied to both the labial and palatal sides.

In all models, uncontrolled tipping occurred, wherein the incisal edge of the crown moved labially, and the root apex moved palatally, resulting in unsuccessful torque control. This observation aligns with the findings of Ahmed et al.,31 who investigated similar tooth movement, specifically maxillary incisor retrusion, using clear aligners. Similarly, the least amount of tooth movement was observed when attachments were placed both labially and palatally; however, the vertical position of the rectangular attachments remained unchanged. It is believed that the greater thickness of the clear aligners produced through the thermoforming process in the incisal region creates more rigidity during tooth movement, thus providing better movement control.32 Therefore, in the current study, a combination of incisally positioned labial and palatal attachments was additionally assessed to improve torque control. Another study demonstrated that combined attachments in clear aligner treatments for extraction cases provided bodily control during tooth movement.33 Crown movement was greatest in the attachment-free model in both axes; root movement occurred in the attachment-free group on the X-axis and in the palatal group on the Y-axis. In another study, tooth movement along the Y-axis was evaluated, and it was found that root movement was greatest in the attachment-free group, whereas crown movement was observed in the palatal attachment model.31 This difference may be attributed to the occlusal bevel attachment design preferred in our study and the variation in the direction of the applied force.

In the current study, the highest clear aligner deformation was observed in the lateral incisor and incisal third, where tooth movement was the most intense. Consistent with our findings, another study found that the highest clear aligner deformation occurred in the tooth undergoing movement, with no significant difference observed between attachment and attachment-free models.34 In our study, the highest deformation was observed in the model with gingivally positioned labial attachment, while the least deformation was noted in the combined attachments model. These results suggest that reducing the tipping movement and positioning the attachment closer to the area of the greatest movement intensity can reduce aligner deformation.

Clear aligners facilitate tooth movement by applying push forces to the teeth. Due to their material properties, they exert less force than traditional fixed appliances. However, the irregular structure of teeth causes uneven distribution of stress across tooth surfaces. In one study, the highest Von Mises stress values were observed in the tooth undergoing movement and in its surrounding areas, while stress levels decreased.35 This finding suggests that the structure of clear aligners, which covers the entire dentition, provides anchorage to the targeted area of movement. In the lateral incisor, PDL stress was highest on both surfaces, especially in the palatal and cervical regions. Similarly, Ahmed et al.31 reported that stress occurred on both the labial and palatal surfaces, with concentration in the cervical region. In the present study, the lowest stress was observed in the middle third of the root. It is postulated that this occurs because the middle third of the root of the lateral incisor functions as the center of rotation during labialization, resulting in decreased stress in this area due to reduced movement.

In this study, we investigated the biomechanics of clear aligners during labialization of the lateral incisor and the impact of different attachment positions on tooth movement. While the mechanism of clear aligners is informative and has been elucidated, our FEA has certain limitations. In clinical applications, there may be some imperfections in both impression-taking as well as in the production and application of clear aligners. However, in this study, these potential imperfections were not considered during the evaluation. Additionally, factors such as aligner thickness, material, attachment design, lateral incisor anatomy and position, and patient compliance were assessed under standardized assumptions. Another limitation of this FEA study is that it evaluated the effect of a single aligner with a movement of 0.25 mm. Changes in attachment design and location may be necessary to accommodate different tooth movements in the later stages of clear alignment treatment. The placement of palatal attachments has some limitations. The anatomical complexity of the palatal surface can complicate precise attachment placement, leading to variations in force application and potentially inconsistent treatment outcomes. Additionally, the palatal position may cause discomfort to patients, potentially affecting their compliance with prescribed aligners. Beyond clinical effectiveness, patients’ perspectives and comfort are critical, as these factors significantly influence overall treatment satisfaction and adherence. Achieving successful and aesthetically pleasing results within a brief timeframe can enhance patient satisfaction in clinical applications. While we believe that the results of our current study will contribute to aligner treatment planning, further investigation is essential to recognize the need for further investigation. Future research should examine each of these parameters individually and support our findings using clinical data.

1. Utilizing attachments enables more precise control of tooth movement.

2. Labial attachments exhibited less tipping compared to palatal attachments when considering the attachment position.

3. Positioning the combined labial attachment closer to the incisal edge, along with the palatal attachment, minimizes tipping.

4. Increased crown movement of the lateral tooth correlated with a higher stress level in the PDL.

We are grateful for the assistance of Orthero and Tinus Technologies in providing technical guidance.

Conceptualization: NK. Data curation: SG. Investigation: SG. Methodology: NK. Project administration: NK, ÖPÖ. Resources: SG. Supervision: NK. Visualization: NK. Writing–original draft: NK, IO. Writing–review & editing: NK, IO, ÖPÖ.

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

None to declare.