The effectiveness of the attachment position in rotated premolar in clear aligner treatment: a finite element study

Abstract

Background

The purpose of the study was to evaluate the impact of different placements of vertical rectangular and bevelled vertical rectangular attachments on the correction of rotated premolars with clear aligners using finite element analysis.

Methods

A three-dimensional finite element model was constructed that included mandibular teeth, periodontal ligament structures and attachments. Rotational correction without attachments were compared to rotational control with two different attachments. Seven different scenarios were created with these attachments positioned on the buccal, lingual and both buccal and lingual surfaces. For all scenarios, 1.2^o of aligner activation was applied. The amount of tooth displacement, stress distributions in the periodontal ligament and clear aligner deformation were analyzed.

Results

It was observed that the models with attachments demonstrated superior efficacy in rotation correction compared to those without attachments. The tooth demonstrated a clockwise movement in all models. While the highest Pmax (0.1150 MPa), Pmin (-0.1299 MPa) and Von Mises values in the periodontal ligament (0.05279 MPa) were measured in Model 7, the lowest Pmax (0.02461 MPa), Pmin (-0.02992 MPa) and Von Mises (0.01097 MPa) values were measured in Model 1. Among all attachment configurations, the bevelled vertical rectangular attachment positioned both buccally and lingually exhibited the highest levels of displacement (35 μm), stress on the periodontal ligament (0.05279 MPa), and deformation of the clear aligner (88.97 μm).

Conclusions

The utilisation of an attachment for the purpose of rotation correction was found to be more effective. The results obtained with the two different attachment types were found to be similar. The addition of a bevel to the attachment and its positioning buccally and lingually resulted in an increase in the amount of movement in the tooth, the deformation of the clear aligner, and the stress experienced by the periodontal ligament.

Background

Clear aligners apply pressure on tooth surfaces to facilitate movement; however, for certain complex movements, attachments are necessary to enhance aligner grip, redirect forces, and improve treatment predictability [1]. As highlighted by Nucera et al. [2], a crucial aspect of orthodontic aligners that affects the transfer of force from the aligner to the tooth is the incorporation of auxiliary elements, including attachments. The geometric properties and positioning of these elements play a significant role in load transfer and, as a result, tooth movement.

The effectiveness of clear aligner treatment in correcting malocclusions can also be affected by the shape of the teeth, as the geometric relationship between the teeth and the aligners plays a role. Current research indicates that premolar derotation has the lowest predictability and accuracy using aligners [3, 4], partly due to the absence of interproximal undercuts, leading to potential slipping during derotation. This results in a loss of tracking between the aligner and the tooth, limiting rotational efficiency [5–7].

Research has explored the use of vertical rectangular attachments to enhance rotational control. Cortona et al. [7] found that buccal attachments significantly improved rotation efficiency, while Ferlias et al. [8] reported that attachments with larger surface areas were particularly effective. However, most studies have only evaluated a single attachment type or placement, leaving a gap in understanding how different attachment designs and positions influence treatment outcomes [7–9]. Thus, a comprehensive comparison of these factors in clear aligner treatments remains absent from the literature.

Another approach to optimizing attachment efficiency is bevelling the edges of rectangular attachments, which can improve aligner fit and force application [9, 10]. Bevelled attachments create a flat surface that enhances aligner adaptation, reducing unwanted movement and improving rotation control [11, 12]. While some studies report no significant improvement with bevelling [8], others suggest that bevelled attachments provide greater rotational correction [9, 10].

Finite element analysis (FEA) provides a validated numerical approach for evaluating orthodontic force application by simulating stress distribution and tooth movement in a controlled environment [13, 14].

FEA has been extensively applied in molar distalization, incisor intrusion, and space closure studies [15–20], yet research on attachment efficiency in premolar derotation remains limited [7, 10]. Additionally, while numerous studies focus on tooth displacement and stress distribution in the periodontal ligament (PDL) [7, 9, 10, 21], fewer have examined aligner deformation during rotation correction [7, 17, 22]. Thus, this study also assesses the deformation of clear aligners during the correction of premolar rotation.

This study aims to evaluate and compare the effects of vertical rectangular and bevelled vertical rectangular attachments placed on the buccal, lingual, and both buccal and lingual surfaces during the derotation of premolars using FEA. The findings will help determine the optimal attachment shape and placement for improving rotational efficiency in clear aligner therapy.

Methods

This thesis study was approved by the institutional review board of Yeditepe University, Istanbul, Turkey (approval date and number: 08.12.2023 and E.83321821-805.02.03-307). The 3D CAD model used in this study was generated based on intraoral scan data from an actual patient, ensuring that the anatomical features and dimensions accurately reflect real clinical conditions. Ethical approval was obtained due to the utilization of real patient-derived data for model generation. The study was carried out in collaboration with the Yeditepe University Faculty of Dentistry and Tinus Technologies.

A three-dimensional CAD model of the mandibular arch was created using ANSYS SpaceClaim software (Version 22.0, Canonsburg, PA, USA) as given in Fig. 1. This model includes the mandibular teeth from the right second molar to the left second molar, with the right second premolar rotated 30° mesially, as well as vertical rectangular and bevelled vertical rectangular attachments, clear aligners, and PDL structures. Following the CAD design, all components were imported into ANSYS Workbench software (Version 22.0, Canonsburg, PA, USA), and the finite element (FE) models were analyzed using the LS-DYNA solver (LSTC, Livermore, CA, USA).

Fig. 1.

A finite element model

The teeth were modeled based on the Wheeler atlas data [23]. The PDL were modelled by taking the outer surface of the teeth as a reference and offset 0.25 mm outwards.

The attachments were designed with dimensions of 3 mm in length, 2 mm in width, and 1 mm in thickness, while the plastic aligner thickness was set at 0.5 mm according to the positioned attachments. The aligner thickness was set at 0.5 mm to reflect the commonly used thermoformed aligners in clinical orthodontic applications. The bevelled attachments positioned on the buccal surfaces are designed to be mesially inclined, whereas those placed on the lingual surfaces are inclined distally.

3D coordinate system and definition of boundary conditions

The X-direction shows the movements in the bucco-lingual direction for premolar teeth. The Y direction indicates movements in the mesiodistal direction. The Z direction indicates movements in the occlusogingival direction (intrusion-extrusion). The “+” direction shown in the figure defines lingual movement on the x-axis, distal movement on the y-axis and occlusal movement on the z-axis. The “-” direction defines buccal movement on the x-axis, mesial movement on the y-axis and gingival movement on the z-axis.

The models were fixed by restricting all degrees of freedom from the nodal points in the posterior region of the bone to prevent movement in all three axes. Boundary conditions were applied to all parts of the model to be symmetrical about the Y-Z plane perpendicular to the X axis.

Material properties and force loading

The linear material properties, with the modulus of elasticity and Poisson’s ratio specified in Table 1 [7, 10, 24, 25]. All materials in the models such as teeth, attachments, and aligners were considered homogeneous and isotropic, and PDL was considered linear isotropic material [7, 26].

Table 1.

Material properties

Material	Elastic Modulus [MPa]	Poisson’s Ratio [v]
Cortical Bone	13,700	0.30
Trabecular Bone	1370	0.30
Tooth	19,600	0.30
PDL	0.67	0.45
Attachment	12,500	0.36
Aligner	528	0.36

MPa: Megapascal

The mesh sizes of the components were set at range from 0.5 mm to 0.1 mm, depending on the model’s region of interest (ROI). Inferior part of the mandible was meshed with coarse mesh (0.5 mm); on the other hand ROI of the system, such as teeth, aligner, attachements and PDL, were meshed with finer mesh structure (0.1 mm).

In order to accurately represent structures with varying density values across different regions, a mesh system composed of nodal elements and nodes was employed, as detailed in Table 2. Given the complexity of both the bone structure and other components, it was essential to model them using 3D solid elements.

Table 2.

Number of nodes and elements of the models

Model	Total # of Nodes	Total # of Elements
Model 1	325702	1183683
Model 2	332405	1204658
Model 3	333147	1208979
Model 4	336449	1221063
Model 5	326080	1183645
Model 6	326103	1185249
Model 7	333982	1210554

*#: Number

For all models, a non-linear frictional contact with a coefficient of µ = 0.2 was established at the interfaces between the aligner and the teeth, as well as between the aligner and the attachments [26, 27]. A “bonded” contact was applied to the other interacting components, based on the assumption that these parts move together as a single unit during movement.

Seven models were created, each featuring different combinations of attachments on the rotated right second premolar:

• Model 1: No attachments.

• Model 2: Vertical rectangular attachment on the buccal surface.

• Model 3: Vertical rectangular attachment on the lingual surface.

• Model 4: Vertical rectangular attachment on both buccal and lingual surfaces.

• Model 5: Bevelled vertical rectangular attachment on the buccal surface.

• Model 6: Bevelled vertical rectangular attachment on the lingual surface.

• Model 7: Bevelled vertical rectangular attachment on both buccal and lingual surfaces.

In all models, a 1.2° rotational aligner activation force was applied from the active surfaces of the clear aligner to the second premolar.

Analyzed outcomes included

• Amount of displacement of tooth (Total and x, y, z axis).

• Stress on the PDL (Pmax, Pmin, Von Mises).

• Aligner deformation.

FEA can determine Von Mises stresses, principal stresses, and displacement values. Principal stresses are normal stresses that act perpendicular to the surface and result in zero shear stresses on all planes. The maximum principal stress (Pmax) is positive and represents the highest tensile stress, whereas the minimum principal stress (Pmin) is negative and indicates the greatest compressive stress. While Von Mises is superior in showing the distribution and intensity of stresses, principal stresses show the character of the stress and in which region it is effective.

Von Mises stress was calculated to evaluate stress distribution within the PDL and clear aligner structure. This stress measure was chosen as it provides a reliable indication of material deformation and structural integrity under applied forces. The highest stress concentrations were recorded in regions with direct force application, particularly around the attachment sites and rotated premolar [28].

Aligner deformation was analyzed by extracting nodal displacement values from the aligner’s surface mesh. Maximum deformation occurred in regions with direct contact, particularly at attachment interfaces and the rotated premolar, where force concentration was greatest. The deformation was quantified based on relative nodal displacement, allowing for an assessment of strain distribution and material response to rotational forces, which may influence treatment efficiency and aligner fit.

Statistical analysis

In FE studies, the validation of results obtained through FE simulations is sufficient, reducing the necessity for experimental readings. Therefore, statistical analysis was not deemed necessary [29].

Results

During lower right premolar derotation, total displacement of the tooth and the displacements in the transversal (x), sagittal (y) and vertical (z) directions, stress values and displacements in the aligner deformation were evaluated. The maximum and minimum principal stresses (Pmax and Pmin) and the Von Mises values are defined in MPa, while the displacement amounts are defined in micrometres (µm). While data for deformation and stress are reported in Tables 3, 4 and 5; total displacement amounts, Von Mises stress and aligner deformation in Figs. 2, 3, 4, 5, 6, 7, 8 and 9.

Table 3.

Total and x, y, z axis displacement amounts of tooth in rotation

Model	Total Displacement (µm)	X Axis Displacement (µm)	Y Axis Displacement (µm)	Z Axis Displacement (µm)
Model 1	8.114	7.182	6.448	-1.145
Model 2	16.17	11.52	12.48	-1.298
Model 3	11.12	10.51	9.518	-1.378
Model 4	27.82	21.40	21.89	-2.327
Model 5	21.78	16.82	17.59	-1.998
Model 6	19.05	16.44	15.94	-1.920
Model 7	35	28	28.48	-3.281

Table 4.

Stress values of PDL (MPa)

Model	Pmax	Pmin	Von Misses
Model 1	0.02461	-0.02992	0.01097
Model 2	0.05112	-0.05727	0.02323
Model 3	0.04472	-0.05183	0.01881
Model 4	0.08887	-0.1008	0.04092
Model 5	0.06159	-0.06962	0.03243
Model 6	0.05549	-0.06329	0.02926
Model 7	0.1150	-0.1299	0.05279

Table 5.

Amount of deformation of clear aligner

Model	Aligner deformation (µm)
Model 1	16.55
Model 2	20.87
Model 3	19.64
Model 4	76.64
Model 5	47.76
Model 6	26.49
Model 7	88.97

Fig. 2.

Total displacement amounts of 2nd premolar

Fig. 3.

Displacement amounts of 2nd premolar in x axis

Fig. 4.

Displacement amounts of 2nd premolar in y axis

Fig. 5.

Displacement amounts of 2nd premolar in z axis

Fig. 6.

Von Mises stress distributions of 2nd premolar

Fig. 7.

Pmax stress distributions of 2nd premolar

Fig. 8.

Pmin stress distributions of 2nd premolar

Fig. 9.

Aligner deformation of 2nd premolar

When the models are evaluated in terms of displacement amounts, it is observed that these numbers are relatively low and exhibit minimal variation among all models (Table 3). The rotated premolar performed a lingual movement in the x direction and distal movement in the y direction in all models. The maximum total displacement of the premolar was 35 μm in Model 7 and the minimum displacement was 8.114 μm in Model 1.

The highest Von Mises stress and Pmax (Tensile stress) stress distribution in the PDL was concentrated at the mesio-buccal gingival area in all models. The highest Pmin (Compressive stress) stress distribution in the PDL was concentrated at the lingual area in all models. In the aligner activation applied for premolar rotation, the highest Pmax (0.1150 MPa), Pmin (-0.1299 MPa) and Von Mises values in PDL (0.05279 MPa) were measured in Model 7 and the lowest Pmax (0.02461 MPa), Pmin (-0.02992 MPa) and Von Mises (0.01097 MPa) values were measured in Model 1 (Table 4).

When evaluating the maximum aligner deformation, it was found in the buccal surface of 2nd premolar in non-attachment model. In models with attachments, the highest amount of deformation was observed on the mesial and angled surface of the buccal attachment in Models 2, 4, 5 and 7, while the highest amount of deformation was observed on the distal and angled surface of the lingual attachment in Models 3, 4, 6 and 7. The amount of deformation decreases from red to blue. More deformation is observed in and around the attachment area where activation is applied. The posterior region exhibited greater deformation than the anterior region (Fig. 9). The highest deformation of the clear aligner was measured as 88.97 μm in Model 7 and the lowest deformation was measured as 16.55 μm in Model 1 (Table 5). It was observed that as the amount of tooth movement obtained with the models created in this study increased, the aligner deformation also increased.

Discussion

In the present study, FEA was used to assess the displacements of the tooth in the transverse, sagittal, and vertical directions, as well as the Pmax, Pmin, and Von Mises stress values in the PDL and the deformation of the clear aligner. This evaluation aimed to determine the effectiveness of rotating the mandibular second premolars using various attachments placed at different locations. All attachment combinations were effective in the correction of premolar rotation and showed similar results.

Most studies in the literature indicate that correcting the rotation of conical-shaped teeth with clear aligners is one of the most challenging orthodontic movements due to their lack of interproximal undercuts, which reduces aligner grip and force application efficiency [3, 6, 30]. While attachments and elastics are commonly used to improve aligner retention and force transmission, their effectiveness is highly dependent on their design, placement, and interaction with aligner thickness [31]. However, Kravitz et al. [5] reported that vertical ellipsoid-shaped attachments did not significantly improve canine rotation when placed centrally on the labial surface, suggesting that not all attachment shapes provide the same biomechanical advantage. In contrast, our study demonstrated that the presence of attachments significantly enhanced rotational displacement compared to simulations without attachments, which aligns with previous findings [1, 31].

The second premolar was selected for this study due to its clinical significance, anatomical characteristics, and the biomechanical challenges associated with its rotation. Compared to other teeth, its rounded shape makes it more prone to rotational relapse and difficult to control with clear aligners. Research suggests that premolar derotation is less predictable than incisor and molar movements due to reduced interproximal undercuts, which limit controlled force application [5, 12]. Additionally, while first premolars offer greater anchorage potential, second premolars are more susceptible to uncontrolled rotations, necessitating additional anchorage strategies such as optimized attachments [3, 8]. Studies also indicate that conical-shaped teeth, including premolars, lack surfaces perpendicular to rotational forces, further complicating movement [5]. Moreover, in vitro findings show that mandibular premolars experience less displacement and tension in the periodontal ligament compared to incisors during rotation [21]. Considering these biomechanical limitations and previous research, including Cortona et al. [7], the mandibular right second premolar was chosen for this study.

Some researchers have proposed using both buccal and lingual attachments to create a force pair for derotating conical-shaped teeth [32, 33]. In the current study, the greatest movement was observed with a bevelled vertical rectangular attachment placed on both the buccal and lingual surfaces (35 μm), followed by a vertical rectangular attachment positioned similarly (27.82 μm). These results can be explained by the larger active surface area of bevelled attachments, which increases mechanical interlocking between the aligner and the tooth. Furthermore, our findings indicated that buccal attachments provided greater rotational displacement than lingual attachments, likely due to the anatomical differences in force application and aligner fit on the buccal and lingual surfaces. Regardless of the type of attachment, the study found that models with only buccal attachments exhibited more displacement compared to models with only lingual attachments. Consistent with these findings, Ferlias et al. [8] reported that the aligner’s grip was more effective on the buccal surface than on the lingual surface due to the tooth’s anatomy.

The positioning of attachments also influenced vertical forces, leading to unintended intrusion in all models. Prior studies by Cortona et al. [7] and Ferlias et al. [8] observed a movement in the distal and lingual direction when force was applied to the rotated tooth. Similar to these studies, the displacement was found in the lingual and distal directions in all models. Researchers found that the positioning of the attachment caused the intrusion of the teeth in all models, although this was found to be at a minimal level [7, 8]. Similarly, in the present study, an intrusive effect was observed in all models which can be attributed to the mechanical properties of the aligner, attachment placement, and force distribution. The aligner’s flexural behavior generates a slight vertical compressive force upon activation, while the attachments alter the force vectors, introducing a vertical component to the applied force. Additionally, the aligner material distributes forces across multiple planes, contributing to unintended intrusive movement. These findings align with previous studies indicating that attachment geometry and aligner stiffness can influence vertical tooth displacement [24].

Bevelled attachments provide a more stable contact surface, improving mechanical engagement between the aligner and the tooth [11]. Kim et al. [9] and Biao et al. [10] found that bevelled attachments generate more controlled rotational forces compared to standard vertical rectangular attachments, a trend that was also evident in our study. The bevelled vertical rectangular attachment produced slightly greater displacement than the standard vertical rectangular attachment, which can be explained by its increased active mesial surface area and improved aligner adaptation.

The 0.5 mm aligner thickness was selected due to its prevalence in clinical practice and ability to deliver predictable forces while maintaining flexibility for effective tooth movement. Aligner thickness directly impacts force transmission, with thinner aligners exerting lower forces and thicker aligners increasing stress on the PDL [8, 24, 34, 35]. Recent research highlights that thickness variations significantly influence stress distribution, aligner fit, and retention [24, 36, 37], while attachments further modify force application [3]. While this study used a standard 0.5 mm aligner, future research should investigate different thicknesses and attachment variations to enhance biomechanical efficiency and treatment predictability.

To effectively move teeth, it is crucial to apply the optimal amount of force to stimulate a maximum cellular response without harming the surrounding tissues. The researchers found that increasing the force activation led to higher stress levels within the periodontal tissues. Generally, an activation of 1.2^o seemed to generate force levels on the PDL that align with the ‘optimal force paradigm’ in the biology of tooth movement [38, 39]. In terms of PDL stress, all simulations produced similar results. The highest stress values were found in the mesio-buccal cervical area of the premolar in the model with a bevelled rectangular attachment placed on both the buccal and lingual surfaces, due to the tooth’s movement in the distal and lingual directions. It can be said that stress in the PDL increases with the amount of tooth movement, depending on the type and positioning of the attachment. Consistent with the current study, other researchers have observed that greater stress accumulates in models with attachments, with higher Von Mises stress seen in the PDL around the tooth’s cervical region [7, 10].

Regarding aligner deformation, the results were similar between the models. The greatest deformation was observed at the corner surfaces of the attachment in the model featuring a bevelled vertical rectangular attachment on both the buccal and lingual sides of the rotated tooth. It can be said that the angled edges of the corner surfaces of the attachments concentrated the deformation in these areas. The least deformation in the clear aligner was found in the model without any attachments. It was observed that as the amount of tooth movement obtained with the models created in the present study increased, the clear aligner deformation also increased. Consistent with the present study, Cortona et al. [7] evaluated clear aligner deformation during premolar rotation correction with and without attachments. They found similar results between the two groups, with the deformation zone in the clear aligner mainly located in the area of the tooth where movement was desired.

In clinical practice, excessive aligner deformation may lead to loss of tracking, reducing the aligner’s ability to effectively control tooth movement. Studies suggest that when plastic deformation occurs beyond the aligner’s elastic threshold, treatment accuracy declines, necessitating overcorrection, refinement aligners, or optimized attachment positioning to mitigate these effects. The findings of the present study highlight the importance of considering aligner flexibility and force distribution when designing treatment plans to minimize unintended deformations.

The FEA method enables the assessment of findings based on changes that occur at the initial application of force or within a very short time. In this study, only one clear aligner was evaluated, whereas multiple clear aligners are typically used in orthodontic treatments. Tooth movement is influenced by the processes of bone apposition and resorption, which cannot be accurately simulated with FEA. As this is an in vitro FEA study on a single patient-derived CAD model, certain biological and environmental factors present in the oral cavity could not be incorporated into the simulation. Key limitations include the lack of moisture, body temperature, salivary buffering effects, and opposing occlusal interferences, all of which influence the real-world biomechanics of clear aligner treatment. Additionally, FEA does not account for bone remodeling, PDL adaptation, or cellular responses to orthodontic forces, which play a crucial role in tooth movement [24]. Therefore, while FEA provides valuable biomechanical insights, these results should be interpreted with caution and validated through incorporating multiple patient models and comprehensive clinical studies. Moreover, the study could be enhanced by exploring other factors, such as varying bevel angles or conducting repeated simulations.

Conclusions

• Attachments significantly aid in controlling tooth rotation.

• The greatest derotation (35 μm) occurred in the model with both buccal and lingual bevelled vertical attachments, while the least derotation (8.114 μm) was noted in the model without attachments.

• Vertical rectangular and bevelled vertical rectangular attachments exhibited similar outcomes, with the bevelled attachment on the both buccal and lingual surfaces enhancing three-dimensional movement, increasing deformation in the clear aligner, and raising stress on the periodontal ligament.

• Placing the attachment on the both buccal and lingual surfaces proved more beneficial for displacement than merely changing attachment types.

• Displacement was consistent across all models, with the gingival (z) direction showing less displacement compared to the transverse (x) and sagittal (y) directions.

• The highest Pmax (tensile stress) was observed mesiobuccally, while the highest Pmin (compressive stress) and Von Mises stress values were also highest mesiobuccally across all models.

• Deformation of the clear aligner was similar among models, increasing proportionally with the amount of movement.

• Future research incorporating multiple subject models or clinical validation is needed to further generalize these findings.

Abbreviations

FEA

Finite element analysis

PDL

Periodontal ligament

ROI

Region of interest

Pmax

The maximum principal stress

Pmin

The minimum principal stress

FE

Finite element

µm

Micrometres

Author contributions

E.T.: Conceptualization, Software, Data curation, Formal analysis, Visualization, Investigation, Writing- Original draft preparation. M.N.E.: Conceptualization, Methodology, Formal analysis, Validation, Writing-Reviewing and Editing.

Funding

No funding. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

The data supporting the study can be obtained directly from the authors.

Declarations

Ethics approval and consent to participate

Ethics approval was obtained from Ethical Committee of Yeditepe University (approval date and number: 08/12/23- E.83321821-805.02.03-307) and was conducted in accordance and informed consent was acquired from each subject before entering the study. Authors reporting experiments on humans and/or the use of human tissue samples must confirm that all experiments were performed in accordance with relevant guidelines and regulations.

Consent for publication

Not applicable.

Generative AI and AI-assisted technologies in the writing process

None.

Competing interests

The authors declare no competing interests.