Introduction
Torque applied on anterior teeth is vital for root positioning and stability. The aim of this study was to evaluate the detailed slot wall deformation in stainless steel (SS) and titanium (Ti) edgewise brackets during palatal root torque using finite element analysis.
Methods
A finite element model was developed from a maxillary central incisor SS bracket (0.022 in). The generated torque values from an SS rectangular archwire (0.019 × 0.025 in) while twisting from 5° to 40° were obtained experimentally by a spine tester, and the calculated torque force was applied in the bracket slot. The deformations of the slot walls in both SS and Ti brackets were measured at various locations.
Results
There were gradual increases in the deformations of both bracket slot walls from the bottom to top locations. In the SS bracket slot for the 40° twist, the deformations were 9.28, 36.8, and 44.8 μm in the bottom, middle, and top slot wall locations, respectively. Similarly, in the Ti bracket slot for the 40° twist, the deformations were 39.2, 62.4, and 76.2 μm in the bottom, middle, and top slot wall locations, respectively. The elastic limits were reached at 28° for SS and at 37° for Ti.
Conclusions
Both SS and Ti bracket slots underwent deformation during torque application. There are variations in the deformations at different locations in the slot walls and between the materials.
Graphical abstract
Highlights
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Archwire-generated torque was obtained for the first time in the torque application.
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Stainless steel and titanium brackets commonly used by clinicians were analyzed.
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Detailed slot deformation was evaluated by FEA simulating the clinical situation.
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Both elastic and plastic deformations were evaluated.
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The FE results were validated analytically and both found similar.
Orthodontic brackets transfer the forces from the archwire to the teeth to enable tooth movement. Final root positioning of the teeth is vital for long-term stability, function, and esthetics and is usually done by torquing. Incisor torque is necessary for proper interincisal angle and overjet, and optimal posterior tooth occlusion. To achieve these, palatal root movement of the maxillary anterior teeth is commonly carried out in the finishing rectangular archwires by torquing the necessary archwire segments. Clinically, torque is the moment generated by a twisted orthodontic archwire inside the bracket slot. During this force transfer mechanism, because of the archwire contact on the slot walls, there might be deformation of the bracket slot. The clinically required torque is determined according to tooth inclination, slot-wire play, and bracket material. Gioka and Eliades proposed that a high-torque prescription should be selected to account for the lack of full expression of the prescribed torque that occurs clinically. McKnight et al suggested that full thickness stainless steel (SS) rectangular wires should be avoided with SS brackets, to prevent larger deformation of the brackets by overloading. Many factors affect the prescribed torque, and as the main torquing force is transferred to the bracket slot walls from the torqued archwire, we believe that the direct deformation of the bracket slot might be an important parameter in torque dissipation.
There were many experimental studies available to predict the behavior of conventional, preadjusted, and self-ligated orthodontic brackets of metallic, ceramic, and polycarbonate materials for applied torque. Few experimental studies on elastic and plastic deformation of orthodontic bracket tie wings using the digital image correlation technique are available. Major et al studied the deformation and warping of bracket slots in self-ligating brackets to an applied torque. These experiments need extensive instrumentation, are time-consuming, and are challenging to do the microscale measurements.
Clinicians like to have the visual display of deformation in the bracket slot. The finite element (FE) method is an approximation technique used to model the physics of complex problems. FE studies were recommended to quantify and evaluate the effects of torsional forces applied to achieve tooth movement. Huang et al studied the torque angle/torque moment capabilities of conventional and self-ligated brackets using the FE method but did not investigate deformation of the bracket slot. Because the torquing forces are exerted inside the bracket slot, it is necessary to study the deformation inside the slot—ie, in the slot wall regions. Detailed bracket slot wall deformation by FE analysis due to torque is not available in the literature. So, we planned to study the bracket slot wall deformation at different locations during torque. To our knowledge, this is the first study wherein the applied torque forces in the bracket slot were calculated from the archwire-generated torque. Thus, the aim of this study was to evaluate the torque-relevant deformation at different locations of SS and titanium (Ti) bracket slot walls in an FE model.
Material and methods
A conventional edgewise maxillary right central incisor SS bracket (Ormco, Glendora, Calif) with a 0.022 × 0.028-in slot was used in this study. The profile points of the SS bracket were captured using optical profile projector (ph 3515F; Mitutoyo , Takatsu-ku, Kawasaki, Kanagawa, Japan) under 10-times magnification. The obtained profile points of the bracket were imported to a drafting package (AutoCAD 2016; Autodesk, San Rafael, Calif), and its dimensions were measured. A 3-dimensional bracket model was constructed with the measured dimensions using modeling software (CATIA, version 5; Dassault Systèmes, Vélizy-Villacoublay, France). This study was designed to evaluate the torque deformation at different locations of SS and Ti bracket slot walls in an FE model. The FE model was generated with software (HyperMesh, version 13.0; Altair Engineering, Troy, Mich).
The bracket model was meshed with 472556 isoparametric 4-noded tetrahedral solid elements with 118045 nodes ( Fig 1 ). We used a tetrahedral element which is similar to the hexahedral element in precision and time of use of the central processing unit. The meshed model was imported to FE analysis software (R14.5; Ansys, Canonsburg, Pa). The material properties were considered to be homogenous and isotropic as shown in Table I .
| Material | Young’s modulus (MPa) | Poisson’s ratio | Yield strength (MPa) | Tangent modulus (MPa) |
|---|---|---|---|---|
| SS | 200000 | 0.30 | 241 | 2000 |
| Ti | 114000 | 0.31 | 795 | 1140 |
The bilinear isotropic hardening model was used in this analysis. In a bilinear isotropic hardening model, bilinear denotes that the stress-strain curve requires 2 inputs such as the yield strength and the tangent modulus of the material. Isotropic hardening means that the yield surface expands uniformly in all directions including the plasticity. Tangent modulus quantifies the “softening” or “hardening” of a material that occurs when it begins to yield. In this study, the tangent modulus was calculated from Young’s modulus for both SS and Ti.
An 8-mm length of 0.019 × 0.025-in SS wire was used, since this is the archwire length clinically engaged in a central incisor bracket mesiodistally. The wire segment was fixed in a customized jig attached to the jaws of the spine tester (370.72; MTS Systems, Eden Prairie, Minn). The wire segment was twisted from 5° to 40° in increments of 5° to reflect the clinical situation, and the generated torque (T) values were recorded from the spine tester. Figure 2 shows the spine tester machine and the customized jig used for archwire torquing. The archwire contact points in the gingival and incisal slot walls during torquing from 5° to 40° twists were identified graphically by rotating the archwire inside the bracket slot ( Fig 3 ) using a drafting package (AutoCAD 2016). These contact points were used to calculate the couple distance (D) for each angle of twist (distance between the 2 contact points of archwires inside the bracket slot). The applied torque force (F) in the bracket slot was calculated using the formula T = F × D. The generated torque, couple distance, and applied torque forces obtained for the angles of twist from 0° to 40° with 5° intervals are presented in Table II .
| Angle of twist (°) | Generated torque (Nmm) |
Couple distance (mm) |
Applied torque force (N) |
|---|---|---|---|
| 5 | 4 | 0.56 | 7.14 |
| 10 | 6 | 0.48 | 12.5 |
| 15 | 7.5 | 0.40 | 18.7 |
| 20 | 11.5 | 0.32 | 35.93 |
| 25 | 17 | 0.26 | 65.38 |
| 30 | 22 | 0.22 | 100 |
| 35 | 28 | 0.14 | 200 |
| 40 | 28.5 | 0.10 | 285 |
When a torqued archwire is inserted in the bracket slot, the archwire is in contact with the bracket slot walls at certain locations. In our study, the couple was applied in a palatal root torque fashion in the SS bracket slot. The same bracket profile was used for the Ti bracket analysis. In the boundary conditions of the FE model, all nodes in the base of the bracket were arrested in all degrees of freedom. In the constructed FE model, the nodal points at the top, middle, and bottom locations in the slot wall were identified. After the torque application, the deformations of the identified nodal points were measured in micrometers with the Ansys R14.5 software. The nodal deformations were measured at the top, middle, and bottom locations (0.71, 0.355, and 0.05 mm, respectively, from the slot base) in both the mesial (mesiogingival and mesioincisal) and distal (distogingival and distoincisal) slot walls of the bracket model as shown in Figure 4 . Figure 5 shows the boundary and loading conditions during torque.
Results
The deformation in both SS and Ti bracket slot walls at angles of twist from 5° to 40° in increments of 5° were recorded as shown in Table III .
| Angle of twist (°) | Bracket slot deformation (μm) | |||||
|---|---|---|---|---|---|---|
| SS | Ti | |||||
| Top | Middle | Bottom | Top | Middle | Bottom | |
| 5 | 0.3 | 0.1 | 0 | 0.7 | 0.3 | 0 |
| 10 | 0.6 | 0.4 | 0 | 1.2 | 0.7 | 0.1 |
| 15 | 0.9 | 0.6 | 0.06 | 1.8 | 1.1 | 0.2 |
| 20 | 2.0 | 1.3 | 0.1 | 3.6 | 2.2 | 0.4 |
| 25 | 3.7 | 2.4 | 0.3 | 6.7 | 4.4 | 0.8 |
| 30 | 5.6 | 3.8 | 0.7 | 10.2 | 7.1 | 1.3 |
| 35 | 13.4 | 9.3 | 4.6 | 32.3 | 26.5 | 8.4 |
| 40 | 44.8 | 36.8 | 9.28 | 76.2 | 62.4 | 39.2 |
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