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ORIGINAL RESEARCH |
https://doi.org/10.5005/jp-journals-10062-0200 |
Clear Aligner Orthodontic Therapy of Rotated Mandibular Incisors: A Finite Element Study
1,2,4–6Department of Orthodontics and Dentofacial Orthopedics, Sudha Rustagi College of Dental Sciences, Faridabad, Harayana, Uttar Pradesh, India
3Private Practitioner, Ghaziabad, Uttar Pradesh, India
Corresponding Author: Varun Goyal, Department of Orthodontics and Dentofacial Orthopedics, Sudha Rustagi College of Dental Sciences, Faridabad, Harayana, Uttar Pradesh, India, Phone: +91 7838683317, e-mail: varungoyalortho@gmail.com
How to cite this article: Aggarwal R, Singh G, Sharma S, et al. Clear Aligner Orthodontic Therapy of Rotated Mandibular Incisors: A Finite Element Study. J Oral Health Comm Dent 2024;18(3):116–125.
Source of support: Nil
Conflict of interest: None
Received on: 19 January 2025; Accepted on: 17 February 2025; Published on: 20 March 2025
ABSTRACT
Introduction: As a discrete and patient-friendly substitute for conventional fixed orthodontic appliances, clear aligner therapy has become increasingly popular. Using finite element analysis (FEA), this study assesses how well different composite attachments work to achieve rotational mobility of the mandibular lateral incisors. Orthodontic treatment has been transformed by Align Technology's Invisalign™ system and CAD/CAM technology, but rotational movements are still difficult, particularly for cylindrical and small teeth.
Material and methods: The alveolar bone, aligner systems, and periodontal ligament (PDL) were all included in the three-dimensional (3D) finite element model of the mandibular arch. Teeth with T-shaped composite attachments, half-ellipsoids, horizontal rectangles, and no attachments had their rotational forces examined. Forces were calibrated using strain gauge systems, and computer models examined stress distribution and displacement in teeth, aligners, and surrounding tissues. Importantly, while prior studies predominantly focused on larger teeth like canines and premolars, this investigation uniquely assessed the effects on smaller mandibular incisors, where maintaining structural integrity poses additional challenges. These findings provide valuable insights for clinicians in choosing appropriate instrumentation techniques for minimally invasive endodontic treatment.
Results: Results indicated that composite attachments significantly enhanced rotational movement compared to aligners without attachments. Among the attachment designs, the horizontal rectangular attachment yielded the highest rotational efficacy, followed by the T-shaped attachment. Stress patterns showed concentration in the labioincisal and cervical regions, with stress values remaining within physiological limits, suggesting no harm to periodontal structures. The aligner with T-shaped attachments exhibited the least distortion, improving its functional efficiency.
Keywords: Attachments, Clear aligner, Finite element analysis, Rotations.
INTRODUCTION
As a cosmetic substitute for permanent labial braces, Align Technology (Santa Clara, Calif.) unveiled the InvisalignTM line of detachable polyurethane aligners. Due to its discrete appearance and improved patient comfort over traditional orthodontic treatments, the InvisalignTM system, i.e. aligners, which uses CAD/CAM stereolithographic technology to build customized systems, has now achieved broad acceptance, especially among adult patients.1
This method of treatment is not a wholly novel idea in dentistry. Dr. H.D. Kesling initially suggested using a clear, vacuum-formed device called a “Tooth Positioning Appliance” to fix teeth for small tooth movement without the need of a band, bracket, or wires.2 Even yet, it was an extremely time-consuming procedure that required hand repositioning of teeth that had been reset in wax, especially for the repair of more complicated malocclusions. Until all of the teeth were in alignment, a clear vacuum-formed retainer was created for each tooth.
Complete derotation of the canine teeth and premolars was shown to be more challenging to accomplish, according to Kravitz’s research. To aid with the rotational movement, Align Technology Inc. suggests the use of resin attachments, interproximal reduction, thermopliers, overcorrection and auxiliaries.1 Nonetheless, within the constraints of the aligner material, the clinician still has the duty to identify problematic movement and recommend the appropriate course of action.
An efficient method for analyzing stress and strain in biological systems is the finite element method (FEM), which was first presented as one of the numerical studies. Finite element method represents a noninvasive, accurate method that provides quantitative and detailed data regarding the physiological responses occurring in tissues such as the periodontal ligament (PDL) and the alveolar bone, according to many authors. Finite element method is a commonly utilized engineering method for medical applications that computes the stress and deformation created on a geometric solid subjected to external forces.3
With FEM, different force systems can be applied analytically in any direction and at any place, and their distribution can be quantitatively evaluated. This instrument was therefore selected for the current investigation.
The overall approach and treatment plan for using clear aligners to correct tooth rotations is highly inconsistent. Clear aligners have already been the subject of numerous studies on the rotation of round teeth (premolar) and cylindrical teeth (canine) however, little study has been done specifically on the influence of various attachment shapes on small teeth (mandibular incisor).4,5 Given the foregoing, the next goal is to assess, using FEM, how various attachments affect the orthodontic rotations that the mandibular incisors may achieve.
MATERIALS AND METHODS
The load input determination process involved using ArchformTM software version 1.9.4, a 3D printer, 3D resin models, 0.75 mm thick thermoplastic aligner material, a base for the model fixture, an LCD display, a Spark Fun Load Cell Amplifier-Hx711, a load cell with six strain gauges and a chip-programmed controller (Figs 1 to 6).
Fig. 1: 3D resin model
Fig. 2: Aligner
Fig. 3: LCD display
Fig. 4: Fixture of model
Fig. 5: Load cell amplifier
Fig. 6: Load cell
The study utilized an Intel Core i3 processor, 4–8 GB of RAM, and a 1TB hard disk. The software used will be CAD modeling software Inventor® and Fusion® 360 from Autodesk, meshing software Hypermesh® from Altair Engineering Inc., and FEA software Ansys® version 19.2 for rotational movements analysis.
Numerical mathematical modeling of the teeth and the parts of the device to determine the ideal tooth movements can provide a better understanding of the precise amount of rotational movement attained by various attachments.
The concept of finite element analysis involves breaking a huge body up into smaller components, or elements, and connecting them at predetermined locations, or nodes. The nodal variables, known as degrees of freedom, are used to approximate element behavior. When assembling elements, loads and boundary conditions are carefully taken into account. A finite number of equations are produced as a result. The approximate solution to the geometrical structural problem is represented by these equations. Even so, a two-dimensional (2-D) model can be used to accomplish this practical approach.
The 2-D model may be oversimplified to depict a particular scenario and does not accurately replicate the in vivo condition in many respects. For this reason, a three-dimensional (3-D) model was created.
Force Calculation for the Study
The study involved designing aligners with a 2° rotation in the mandibular lateral incisor using Arch-form software version 1.9.4, which were then converted into resin models using a 3D printer. Matching thermoplastic aligners were produced using 0.75 mm thick Duran thermoplastic sheet and thermoforming technologies. The measuring apparatus consisted of a jaw fixture, load cell, and load cell amplifier with an LCD display.
The device’s sensitivity was tested using preset weights, revealing an accuracy of up to 1 g (0.001N). The composite material was interfaced with the load cell pin sensor, calibrated, and rebuilt using aligner number 1, and an aligner with activation was positioned to verify applied forces. The force required to rotate the tooth was found to be about 60 g when using an aligner with a 2° movement built in (Figs 7 and 8).
Fig. 7: Customized strain gauge set up on model
Fig. 8: Aligner with 2° rotation incorporated
Construction of 3D Model (CAD Modeling)
A 3D model of the mandibular arch was created using CAD software, including an aligner, rotated lateral incisors, and the PDL. The model’s lateral incisors were rotated 30°, and the PDL was modeled based on root geometry. Teeth were created using optimal anatomy and proportions. Aligners were created using tooth crown shapes and attachments.
The first model had built-in rotations in both left and right lateral incisors, with the right having a half-ellipsoid attachment and the left having no attachment (Fig. 9). In the 2nd model, the left lateral incisor had a T-shaped attachment, and the right had a horizontal rectangular attachment (Fig. 10).
Fig. 9: Model with half-ellipsoid attachment
Fig. 10: Model with horizontal rectangular attachment and T-shaped attachment
Material Property Data Representation
Teeth, PDL, alveolar bone, composite attachment, aligner were considered as isoparametric and homogeneous. The different structures involved in this study have a specific material property. The details of the materials are mentioned below (Table 1).
| Components | Young’s modulus (MPa) | Poisson’s ratio |
|---|---|---|
| Tooth | 1.98 × 104 | 0.3 |
| Compact bone | 1.37 × 104 | 0.3 |
| Cancellous bone | 1.37 × 103 | 0.3 |
| PDL | 0.667 | 0.45 |
| Composite attachment | 12.5 × 103 | 0.36 |
| Aligner | 528 | 0.36 |
Preprocessing (Meshing)
A 3D finite element model of bones was created using a computer, simplifying the mandible’s geometry into teeth, PDL, and alveolar bone. The model was created by modeling cortical and cancellous bone components separately, each with unique physical characteristics. The aligner and composite attachment were then assembled, considering the material characteristics of each component.
After that, the complete assembly was exported for ANSYSTM 19.2 analysis. Surface and line data from a geometric model were transformed into a finite element model, which has four nodes and a finite number of elements (type: First-order tetra) (Figs 11 and 12). Meshing is the term for this technique, which was carried out with Hypermesh® software (Hyperworks).
Figs 11A to D: Meshing (Model 1): (A) Labial view; (B) Angled view; (C) Lateral view; (D) Occlusal view
Figs 12A to D: Meshing (Model 2): (A) Labial view; (B) Angled view; (C) Lateral view; (D) Occlusal view
Contact Conditions
ANSYS® 19.2 created a stiff union condition without relative displacement for ligament-bone, tooth-ligament, and tooth-attachment interfaces, and a Coulomb friction condition in contact interfaces between the aligner and tooth crown surface and attachments, based on a friction coefficient of 0.2, similar to an in vitro wear test.
Defining the Boundary Condition
Boundary conditions were established to emulate the model’s constraints and prevent free movement. Nodes connected to the bone’s exterior surface were fastened in all directions. Free axial rotational movement of mandibular incisors was permitted due to restricted base and arrest of superior bone surface for all six degrees of freedom (Figs 13 and 14).
Fig. 13: Loading and boundary conditions (Model 1)
Fig. 14: Loading and boundary conditions (Model 2)
Application of Forces
The study used a modified strain gauge to calculate the force for rotation in various tooth models, including those without an attachment, half-ellipsoid attachment, 3 mm horizontal rectangular attachment, and T-shaped attachment. The force was calculated to be around 60 gm, and a 3-D force system was created for each tooth by applying a few 60 gm forces to each lateral incisor in a clockwise and anticlockwise motion on the right and left sides in the horizontal plane
Finite Element Solution
ANSYS 19.2 software was utilized for analysis and computation of movement patterns, stresses on aligners, PDL, cancellous, and cortical bones. Factors examined included tooth displacement pattern and magnitude, and stress distribution on alveolar bone, aligner, and PDL.
RESULTS
Amount of Rotation
The study found significant rotational movement in the distobuccal direction using various attachment methods. The table summarizes the rotation achieved with the necessary force in different models, including mandible and mandibular dentition with thermoplastic aligners, without attachment, half-ellipsoid attachment, horizontal rectangular attachment, and T-shaped attachment (Tables 2 and 3).
| Type of attachment | Maximum | Minimum |
|---|---|---|
| No ATT | 3.97 × 10–5 | 2.76 × 10–6 |
| Half-ellipsoid ATT | 5.14 × 10–5 | 3.23 × 10–6 |
| Horizontal ATT | 7.95 × 10–5 | 6.3 × 10–6 |
| T-shaped ATT | 7.77 × 10–5 | 6.04 × 10–6 |
| Type of attachment | Maximum | Minimum |
|---|---|---|
| No ATT | 1.29 × 10–4 | 1.53 × 10–6 |
| Half-ellipsoid ATT | 1.10 × 10–4 | 1.53 × 10–6 |
| Horizontal ATT | 8.79 × 10–5 | 5.16 × 10–6 |
| T-shaped ATT | 8.55 × 10–5 | 5.16 × 10–6 |
The study found that the 3 mm horizontal ATT in distobuccal direction was most effective for maximum rotational movement, followed by T-shaped ATT. The tooth with no attachment area showed the least movement. Displacement was observed on the tooth’s mesio-occlusal surface with horizontal and T-shaped ATT. The tooth with half-ellipsoid ATT showed maximum movement on the disto-occlusal face (Fig. 15). T-shaped ATT showed the least aligner distortion, while the tooth without ATT showed the most (Fig. 16). Therefore, the overall efficacy of the composite attachment was seen over rotational movement with no attachment areas.
Figs 15A to D: Tooth displacement: (A) Horizontal ATT; (B) T-shaped ATT; (C) Ellipsoid ATT; (D) No ATT
Figs 16A and B: Aligner deformation: (A) Model 1; (B) Model 2
Stress Distribution
The study found that the labial surface of a tooth had the highest overall equivalent stress, corresponding to the tooth displacement trend. The tooth with horizontal attachment (ATT) had the highest stress, while the tooth without attachment had the lowest (Table 4). In model number 1, the right lateral incisor’s mesiolingual surface had the highest von Mises stress, followed by the left lateral incisor. The right incisor’s labioincisal region and the left lateral incisor’s mesiolingual surface showed the highest stresses in model number 2 (Figs 17 and 18).
| Type of attachment | Maximum stress | Minimum stress |
|---|---|---|
| No ATT | 0.06610 | 1.31 × 10–4 |
| Half-ellipsoid ATT | 0.10333 | 1.50 × 10–4 |
| Horizontal ATT | 0.21505 | 2.6 × 10–4 |
| T-shaped ATT | 0.19083 | 3.0 × 10–4 |
Figs 17A and B: Overall stresses: (A) Model 1; (B) Model 2
Figs 18A to D: Overall stress pattern: (A) Horizontal ATT; (B) T-shaped ATT; (C) Ellipsoid ATT; (D) No ATT
Aligner Stress
The attachment interface region on the tooth’s labioincisal surface showed the highest aligner stress. The tooth with no composite attachment on the labial surface showed the highest values, followed by the tooth with half-ellipsoid ATT, the T-shaped tooth, and the tooth with horizontal ATT, which showed the lowest values (Table 5; Fig. 19).
| Type of attachment | Maximum stress | Minimum stress |
|---|---|---|
| No ATT | 0.0852 | 3.70 × 10–7 |
| Half-ellipsoid ATT | 0.0495 | 3.70 × 10–7 |
| Horizontal ATT | 0.0208 | 5.05 × 10–8 |
| T-shaped ATT | 0.0230 | 5.05 × 10–8 |
Figs 19A and B: Aligner stresses: (A) Model 1; (B) Model 2
Periodontal Stress
Periodontal ligament stresses were mainly concentrated in the cervical area on the labial and distal surfaces of the teeth. A lower number of stresses was also seen around the PDL of central incisors. The minimum number of stresses was seen in areas other than incisors (Table 6). The study found that teeth with T-shaped ATT had higher PDL strains, while half-ellipsoid ATT had the lowest stress. The tooth’s distal and cervicobuccal surfaces absorbed more stress (Fig. 20). The stress values were within the physiological range, indicating clear aligners don’t harm PDL.
| Type of attachment | Maximum stress | Minimum stress |
|---|---|---|
| No ATT | 1.95 × 10–7 | 2.18 × 10–8 |
| Half-ellipsoid ATT | 1.77 × 10–7 | 2.18 × 10–8 |
| Horizontal ATT | 6.72 × 10–6 | 1.59 × 10–6 |
| T-shaped ATT | 1.43 × 10–5 | 1.59 × 10–6 |
Figs 20A and B: PDL stresses: (A) Model 1; (B) Model 2
Alveolar Bone Stress
The study found that the T-shaped ATT produced the highest strains, followed by the horizontal ATT. The half-ellipsoid ATT produced the lowest stresses, and no ATT in the cancellous bone. Stresses were observed on the labial surface of the four incisors’ alveolar bones, dispersed uniformly throughout the cancellous bone’s labial cortex (Fig. 21). The cervical region had the highest stress concentration, decreasing as the study approached the apical region.
Figs 21A and B: Cancellous bone stresses: (A) Model 1; (B) Model 2
In contrast, the cervical region of the tooth had more concentrated cortical bone stresses (Fig. 22). Compared to the central incisors, the lateral incisors showed more stress. Compared to cancellous bone stresses, cortical bone stresses were comparatively higher (Tables 7 and 8).
Figs 22A and B: Cortical bone stresses: (A) Model 1; (B) Model 2
| Type of attachment | Maximum stress | Minimum stress |
|---|---|---|
| No ATT | 0.43 × 10–2 | 0.49 × 10–3 |
| Half-ellipsoid ATT | 0.41 × 10–2 | 0.49 × 10–3 |
| Horizontal ATT | 0.91 × 10–2 | 1.29 × 10–3 |
| T-shaped ATT | 1.15 × 10–2 | 1.29 × 10–3 |
| Type of attachment | Maximum stress | Minimum stress |
|---|---|---|
| No ATT | 0.92 × 10–2 | 0.10 × 10–2 |
| Half-ellipsoid ATT | 0.79 × 10–2 | 0.10 × 10–2 |
| Horizontal ATT | 3.68 × 10–2 | 0.47 × 10–2 |
| T-shaped ATT | 4.28 × 10–2 | 0.47 × 10–2 |
DISCUSSION
The orthodontic market is rapidly expanding, with clear aligner therapy being a popular choice for adults. The Invisalign™ system was used to treat 31% of adult orthodontic cases in 2013. Despite the desire for treatment, adults often refuse it due to aesthetic requirements. This is due to the primary advantage of clear aligners over conventional fixed appliances.1
A study by Rosvall et al.6 found that 62% of adult patients would refuse orthodontic treatment with a fixed appliance, despite wanting malocclusion rectified. Ceramic appliances were preferred over self-ligating brackets, while lingual appliances and clear aligners were preferred for esthetics. Adults were willing to spend more for transparent aligners than conventional metal bracket treatment.
A finite element model is a research tool that simplifies the geometric shape of a sample and idealizes its mechanical properties. Its effectiveness depends on its ability to accurately depict the simulated object’s mechanical characteristics and the realism of the simulations. It is considered a reliable method for comparing finite element model outcomes with real-world clinical scenarios, provided the simulation estimation results align with detailed clinical mechanical effects.7,8
The finite element method was used in an in vivo study to evaluate the biomechanics of clear aligner therapy. The study involved simulating the mandibular jaw with rotated lateral incisors and constructing solid models of dentition, PDL, alveolar bone, and clear aligners. The finite element methodology was used to compare displacement patterns and stress distribution with different attachment designs and no attachment in generating rotational movement.
Research on clear aligners has been limited to finite element models, with most studies focusing on one tooth or part of the dental arch. This study aims to investigate the impact of the entire mandibular arch on the surrounding periodontium, as previous studies have shown that the extension of the FE model affects the biomechanical response.
Clear thermoformed plastic aligners are more accurate and effective than traditional fixed appliances due to their coverage of the entire dentition during tooth movement. However, more study is needed to understand the biomechanics behind clear aligner therapy, despite their lower effectiveness in achieving rotational movement.
The orthodontics industry is rapidly expanding clear aligner therapy, but there is limited knowledge about its limitations, indications, and mode of action. Few randomized clinical trials exist, and most data is based on case reports and clinical opinions. This study aims to understand how attachments affect movement to improve the effectiveness of clear aligner therapy.
This study aimed to regulate tiny tooth rotation in clear aligners after extrusion.4,9 It assessed the impact of attachment forms on mandibular lateral incisors’ rotational motion. Kravitz’s et al.5 2008 strategies, overcorrection, composite attachments, and interproximal reduction were used to enhance the effectiveness of rotational movement in aligners.
Orthodontists often find using clear aligners to rotate round teeth challenging and unpredictable. To achieve consistent results, physicians use auxiliaries, overcorrection, attachments, and interproximal reduction. However, research on rotation correction with clear aligner force mechanisms is limited due to ambiguous information about the forces required. A strain gauge system was created to measure orthodontic forces in vitro.
The study used a 0° and 2° of rotational movement to create a model-aligner contact. Undercuts caused pressure buildup, resulting in a force of 0.5 gm/3 mm. The force measured in the aligner with two degrees of movement was around 60 gm/3 mm, consistent with previous research.10,11 The force measured by a strain gauge was used to analyze displacement and stress patterns with clear aligners.
The initial aligner systems relied solely on the aligner, without any auxiliary components. As technology advanced, second-generation manufacturers introduced attachments to improve tooth mobility. The third generation introduced force delivery mechanisms, pressure points, and precise attachments, with software automatically positioning them for extrusions, derotations, and root movements.12
The study suggests that aligners and composite attachments can regulate the rotation of mandibular incisor teeth. According to Garino et al.’s13 study, composite attachments enhance the expression of recommended tooth movement. The current study found higher rotation in groups with attachments compared to simulations without attachments. Attachments expand the surface area of contact between teeth and the clear plastic aligner (CPA), enhancing the efficiency of intended tooth movement.
Kravitz et al.9 found that every aligner activation and attachment combination leads to efficient tooth movement. They proposed using interproximal reduction and vertical-ellipsoid attachments to facilitate canine tooth rotational movement. They found that teeth with attachments had better outcomes. The study used various attachments, including horizontal ATT, T-shaped ATT, and half-ellipsoid ATT, to simulate intended tooth movements.
The study reveals that additional attachments were created to enhance the retention of the clear aligner, thereby facilitating more effective tooth movement, as they often interact with undercuts and irregularities.14
The labioincisal surface near the attachment interface area is more susceptible to clear aligner stress, indicating potential injury. Periodontal ligament stresses are concentrated on the tooth’s distal and cervicobuccal surfaces. The tooth with a T-shaped ATT has the highest PDL stresses, while the half-ellipsoid ATT has the lowest stressors, confirming similar stress patterns in clear aligners.
The study found that rotation in attachment-containing groups was more effective than in attachment-free simulations, indicating the use of composite attachments, specifically T-shaped ATT and 3mm horizontal ATT, in enhancing rotational movements during clear aligner therapy.
The study found stress patterns in the aligner, PDL cancellous bone, and cortical bone, with aligner stress primarily located near the tooth’s incisal region. Periodontal ligament strains were not harmful, indicating that composite attachments effectively induce rotational movement during clear aligner therapy.
Limitations
Clear aligner research uses functional element methods (FEM) to analyze force systems in orthodontic equipment. However, in vitro and in vivo studies may yield different results. Mechanical characteristics of aligners are influenced by factors like polymer composition, friction, thermoplastic properties, thermoforming processes, and appliance insertion and removal. Unfortunately, Clear Aligner cannot be studied in FEM studies due to trademark restrictions and a lack of commercially available factors.
Orthodontic FEM investigations often approximate the material properties of biologic components, particularly PDL, which is a significant limitation. Despite growing scientific knowledge, modeling PDL characteristics is still crucial for evaluating FEM findings. The simulation’s data primarily examines stress and displacement patterns during initial tooth movement, which is a dynamic process involving changes in tissues’ mechanical response and force system. Future research should consider the dynamic nature of tooth movement and experimental tests to confirm the accuracy of the current finite element model.
CONCLUSION
The finite element analysis reveals that the anticipated orthodontic tooth movement is influenced by the form and location of composite attachments. Half-ellipsoid ATT, T-shaped ATT, and horizontal ATT are effective for tooth rotation. There are notable differences between teeth with ATT and those without, and no discernible variations between T-shaped and horizontal ATT. Newly created composite attachments, like half-ellipsoid and T-shaped ATT, are effective in retaining the clear aligner and achieving necessary tooth movement.
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