Introduction
The aims and objectives of this study were to evaluate the von Mises stress and principal stress distribution and displacement of anterior teeth in a lingual orthodontics system along the periodontal ligament and alveolar bone by various combinations of mini-implants and lever arm during en-masse retraction. Four 3-dimensional finite element (FE) models of the bilateral maxillary first premolar extraction cases were constructed.
Methods
Lingual brackets were (0.018-in slots) positioned over the center of the clinical crown. In all 4 models, 150 g of retraction force was applied with the help of a nickel-titanium closed coil spring with different combinations of mini-implants and lever arm on each side. FE analysis was then performed to evaluate stress distribution, principal stress, von Mises stress, and displacement of the anterior teeth using ANSYS software (version 12.1; Ansys, Canonsburg, Pa). The FE study was enough to validate the analysis results obtained by software tools with FE simulation instead of experimental readings. Thus, statistical analysis was not required.
Results
In this study, maximum tensile stresses were observed in the periodontal ligament at the mesial cervical region of the canine with values of 1.84 MPa, 2.02 MPa, 1.88 MPa, and 2.08 MPa for models 1-4, respectively. Maximum von Mises stress in alveolar bone was 8.05 MPa, 8.23 MPa, 8.19 MPa, and 8.37 MPa for models 1-4, respectively, which was within the optimum limit (135 MPa). Variable amounts of displacements like lingual crown tipping, lingual root tipping, and extrusion were observed in all the models. The 15-mm long lever arm models (models 2 and 4) showed a more controlled crown (0.015 mm) and root movement (0.004 mm) compared with 12-mm long lever arm models (models 1 and 3).
Conclusions
In lingual orthodontics, controlled root movement increased as we increased the length of the lever arm. It was also concluded that the amount of increased controlled tipping found with the placement of the mini-implant was toward the palatal slope.
Highlights
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Stress distribution and anterior tooth displacement were studied in lingual orthodontics.
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Mini-implants and lever arms in various lengths were used for en-masse retraction.
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Controlled root movement increased as the length of the lever arm increased.
Lingual orthodontics (LiO) is preferred by many patients undergoing orthodontic treatment because of the esthetic demand it meets as compared with labial orthodontics (LaO). However, maintaining incisor torque during retraction is more difficult in LiO compared with LaO. Therefore, it is necessary to have a proper understanding and complete knowledge of the biomechanical differences between LiO and LaO for controlling torque. Liang et al concluded that force of the same magnitude produced translation movement of the maxillary incisor in labial orthodontics but lingual crown tipping of the same teeth in lingual orthodontics. This result indicates that loss of torque control of the maxillary incisors during retraction in extraction patients is more in lingual orthodontic treatment.
For achieving translation movement of anterior teeth during en-masse retraction, force must pass through the center of resistance (Cres). In LiO, it is quite difficult to achieve bodily movement because of the bracket position in relation to Cres, palatal contour, and point of the force application. The introduction of mini-implants and lever arm systems helps to solve this problem. Various implant placement sites on the palate and different lever arm lengths develop a straight line of force application, which pass near Cres. Bohara et al reported that to achieve bodily movement of anterior teeth, the force should be directed through the center of resistance of anterior teeth and also by altering the occlusogingival placement of mini-implants and the length of anterior retraction hook. Hong et al concluded that mini-implant in conjunction with lever arm could control the line of force nearer to Cres of anterior teeth.
Park et al reported that increasing intrusive force in anterior teeth makes torque control more difficult. Therefore, the best way is to apply force as near to Cres as possible. Placement of long lever arm may be prevented by the depth of the vestibule in LaO. However, placement in the lingual system is always possible because of the depth of palate. They also concluded that lever arm mechanics makes it possible to achieve torque control during retraction in LiO. Jang et al stated that the splinted lever arm reduced the lingual tipping and buccal displacement of canines, including anterior 4 incisors at lever arm length of 16.85 mm (palatal miniscrew) and 19.01 mm (midpalatal screw). Increasing the wire stiffness resulted in a decreased buccal displacement of canines. Mo et al in a finite element method (FEM) study, observed that increasing the vertical height of the lever arm resulted in tooth movement from uncontrolled tipping to the occurrence of root retraction.
Stress-induced in the periodontal structure is the activating factor for biologic changes; therefore, it is essential to analyze the stress level in the periodontal structure during various tooth movements. Because of the complexity of the tissue structures and analysis of stress, available information regarding the stresses that are induced in the periodontal structure is scarce. , FEM is a powerful tool in which the shape of complex geometric objects and their physical properties are computer-generated. Physical interactions of various components of the model can then be calculated in terms of stress and strain. With the help of FEM, we can analyze stress in nonliving as well as living structures. In FEM, by changing different computer simulation parameters, various 3-dimensional (3D) computer models can be mimicked in various combinations. With the help of FEM, qualitative and quantitative primary responses can be calculated on the alveolar bone, periodontal ligament (PDL), and teeth. Therefore, we can understand the biomechanics involved in the retraction of anterior segments better in LiO. Hence, the present FEM study aimed to analyze the principal and von Mises stress distribution as well as the displacement of anterior teeth in a lingual orthodontics system for effective en-masse retraction using lever arm and mini-implants.
Material and methods
Four 3D finite element (FE) models of the bilateral maxillary first premolar extraction cases were made ( Fig 1 ). All 4 models consisted of 12 teeth with their PDL, alveolar bone, lingual brackets, archwire, lever arm, and mini-implants constructed. The stresses produced onto the PDL and alveolar bone were determined upon applying retraction forces using a nickel-titanium (NiTi) closed coil spring on the maxillary anterior with the help of various combinations of mini-implants and lever arms.
Steps involved in the FE model preparation are (1) construction of the geometric model of the maxillary dentition with its periodontal structures (PDL, alveolar bone), (2) conversion of the geometric models to a FE model, (3) incorporation of the material properties of the tooth structure and periodontium, (4) defining boundary condition, (5) loading configuration, and (6) translation of results and interpretation.
Methodology
The computed tomography scan (Siemens, digital imaging and communications in medicine [DICOM], Syngo CT 2006 C2 format; cross-sections of 0.25 mm) images of maxilla and maxillary dentition were taken in the axial plane and saved as digital imaging and communications in medicine format. These data were exported to 3D image processing and editing software—Mimics (version 8.11; Materialise NV, Leuven, Belgium)—and, with the help of RapidForm 2004 software (3D Systems, Rock Hill, SC), a geometric model was constructed consisting of only surface data. Lingual brackets (slot size, 0.018-in; 7th generation; Ormco, Orange, Calif), segmented archwire (0.016 × 0.022-in stainless steel), titanium mini-implants (2 × 7 mm; SK Surgical, Mumbai, India), NiTi closed coil springs and lever arms (12 mm and 15 mm) were virtually modeled using a reverse engineering technique ( Fig 2 ).
The mesh of the PDL was considered to have a uniform thickness of 0.25 mm, according to Coolidge’s study. Three-dimensional surface to surface sliding contacts with 0.1 coefficient of friction used between bracket and wire. The contact and friction condition between the archwire and bracket was linear. Models were simulated at a 0.016 × 0.022-in stainless steel archwire stage; therefore, the contact condition between teeth and brackets was closely attached. In models 1 and 2, the implant was placed at the midpalatal suture, between the first and second molar region. In models 3 and 4, the implant was placed 5 mm away from the midpalatal suture between the first and second molar region. A 2 mm long implant with the head exposed in the palatal provides a straight line of force through the lever arm to the teeth.
Geometric models were imported to HyperMesh software (version 11.0; Altair Engineering, Troy, Mich), and all the individual parts, like the bone, teeth, PDL, brackets, wire, and mini-implants were assembled. HyperMesh software used a meshing process to convert the geometric models into FE models.
The FE model is representative of geometry in terms of the finite number of elements and nodes. This process is called discretization . These elements are interconnected at joints, which are called nodes or nodal points, whereas the corner nodes are called primary external nodes. The additional nodes that occur on the sides of the element are called secondary external nodes. The secondary nodes have fewer displacements than the corner nodes. For the maxilla, a 4-noded tetrahedral shape was selected as the FE. This element is more suitable for meshing irregular geometries ( Table I ).
| Model | Total no. of nodes | Total no. of elements |
|---|---|---|
| Model 1 | 86,841 | 406,925 |
| Model 2 | 86,841 | 406,948 |
| Model 3 | 89,496 | 422,763 |
| Model 4 | 89,496 | 422,763 |
Four models were formed along with details regarding lever arm position, , lever arm length, mini-implant size, mini-implant position, , archwire dimension, and applied force ( Table II ; Fig 1 ).
| Parameters | Model 1 | Model 2 | Model 3 | Model 4 |
|---|---|---|---|---|
| Lever arm position | Between central incisor and lateral incisor | Between central incisor and lateral incisor | Between lateral incisor and canine | Between lateral incisor and canine |
| Lever arm length, mm | 12 | 15 | 12 | 15 |
| Mini-implant size, mm | 2 × 7 | 2 × 7 | 2 × 7 | 2 × 7 |
| Mini-implant position | Midpalatal suture between first and second molar | Midpalatal suture between first and second molar | 5 mm from the midpalatal suture toward the palatal slope | 5 mm from the midpalatal suture toward the palatal slope |
| Archwire dimension | 0.016 × 0.022-in stainless steel | 0.016 × 0.022-in stainless steel | 0.016 × 0.022-in stainless steel | 0.016 × 0.022-in stainless steel |
| Force, g per side | 150 | 150 | 150 | 150 |
The geometric system was coordinated. The y-axis was the midsagittal line of the dental arch on the occlusal view; the z-axis was perpendicular to the y-axis in the occlusogingival direction. Experimentally determined material properties of teeth, PDL, and alveolar bone were used in this study ( Table III ). All materials employed for the FE model study were taken to be isotropic, homogenous, and linearly elastic.
| Serial no. | Material | Young modulus, MPa | Poisson ratio |
|---|---|---|---|
| 1 | Hard bone | 13,700 | 0.38 |
| 2 | Soft bone | 1370 | 0.38 |
| 3 | PDL | 0.068 | 0.49 |
| 4 | Teeth | 20,000 | 0.30 |
| 5 | Titanium implants | 110,000 | 0.30 |
| 6 | Stainless steel wire | 200,000 | 0.30 |
| 7 | NiTi close coil | 75,000 | 0.33 |
| 8 | Bracket | 214,000 | 0.30 |
The boundary condition of these FE models needs to be defined so that all movements of the model are restrained to prevent the model from body motion while the load is acting. For the above models, the fixed boundary condition was maintained at the base of the maxilla and was constrained in all models.
The loading configuration was designed to mimic the retraction type of orthodontic tooth movement applied to the maxillary anterior using NiTi closed coil springs and mini-implants. In all 4 models, 150 g of retraction force was applied bilaterally from the mini-implants onto the segmented archwire of the anterior segment with lever arms. FE models were imported into ANSYS software (version 12.1; Ansys, Canonsburg, Pa) for analyzing the displacement and stress distribution.
Color coding for stress and displacement was used in the FEM study. Blue indicates the minimum stress or displacement, and red indicates the maximum; the remaining shades represent variations of stress from minimum to maximum ( Fig 3 ).
