Comparative finite element analysis of bracket deformation in tie wings and slot region during simulated torque

Introduction

Torque in orthodontics is the activation of the archwire for the third-order movement of teeth. During this force transfer mechanism from the twisted archwire, the bracket is prone to deformation. This study aimed to compare the deformation in tie wings and the slot region of the bracket during torque using finite element analysis.

Methods

Three-dimensionally modeled 0.017 × 0.025-in and 0.019 × 0.025-in stainless steel (SS) and titanium molybdenum alloy archwires were assembled in 0.018-in and 0.022-in solid modeled SS edgewise brackets, respectively. The finite element model of the bracket-archwire combinations was developed with contact boundary conditions. The deformation between tie wings and the slot was analyzed for various angles of twist.

Results

For SS archwires at 30° angle of twist, the tie wings deformation in 0.018-in and 0.022-in brackets were 48.67 μm and 34.87 μm, respectively. The slot deformations of 0.018-in and 0.022-in brackets were 66.33 μm and 45.69 μm, respectively. Similarly, the amount of deformation in the bracket—titanium molybdenum alloy archwire combinations were also presented.

Conclusions

The slot deformation was more than the tie wings deformation as the slot walls bear the immediate torque force. Thus, orthodontic researchers should know that the torque-relevant bracket deformation should ideally be evaluated in the slot region rather than the tie wings.

Graphical abstract

Highlights

  • Bracket slot and tie wings deformation during torque were compared.

  • Deformation was present in the slot and tie wings in 0.018-in and 0.022-in stainless steel brackets.

  • Slot deformation was always higher than the tie wings deformation.

  • Torque-relevant bracket deformation is better assessed by slot deformation.

The orthodontic bracket is an important component of a fixed appliance that transfers the forces from the archwire to the tooth. One of the highest forces acting on the brackets is during the torque application. During this torque transfer mechanism, the bracket is vulnerable to elastic or plastic deformation. Such deformation is an important parameter for torque loss and thus a delay in tooth positioning. Various methods of torque-relevant bracket deformation have been evaluated and reported in the literature as follows. Mcknight et al experimentally evaluated the bracket slot distortion because of various torque forces in stainless steel (SS), polycarbonate, and ceramic brackets and showed that elastic to plastic deformation was found in SS and polycarbonate brackets and no distortion in ceramic brackets. Major et al analyzed the slot changes because of torque in self-ligating brackets by a single-lens reflex digital camera attached to a microscope and found both elastic and plastic deformation in various brands of brackets.

Fischer-brandies et al experimentally evaluated the effect of torque from 3 sizes of SS archwires in a 0.018-in slot bracket and reported notching and bending of the slot flanks. Daratsianos et al studied the torque play and slot size changes in the lingual brackets with titanium molybdenum alloy (TMA) and SS archwires. In many studies, the torque-induced deformation was experimentally analyzed using digital image correlations (DIC) considering the tie wing surfaces. Finite element (FE) methods were used to analyze the proximal side slot wall deformation by applying archwire torque as a couple without using archwires. ,

Although the slot wall and tie wings are adjacent regions in a miniature-sized bracket, the real archwire torque is applied on the slot wall region, whereas the tie wings are away from the torque application area. Thus, it is important to understand whether it is advantageous to evaluate the torque-relevant bracket deformation in the slot wall or tie wings region. Unfortunately, more published work has evaluated the tie wings region. This stimulated us to compare and quantify the deformation between these regions so that clinicians and clinician-researchers can assess the torque loss better. Thus, this study aimed to compare the deformation in the slot and tie wings region of the bracket during varying degrees of torque using FE analysis in the commonly used bracket-archwire combinations.

Material and methods

The profile projector (ph 3500; Mitutoyo, Kawasaki, Japan) with 10× magnification and 1 μm resolution was used to measure the dimensions of maxillary central incisor standard edgewise SS 0.018 × 0.025-in and 0.022 × 0.025-in brackets (Leone SpA, Quaracchi, Italy). The solid modeling software SolidWorks 2018 (Dassault Systèmes, Vélizy-Villacoublay, France) was used to construct the solid model of the brackets. SolidWorks 2018 was used to develop the 3-dimensional model of rectangular SS archwires of sizes 0.017 × 0.025-in and 0.019 × 0.025-in (G&H Orthodontics, Franklin, Ind). The 0.017 × 0.025-in and 0.019 × 0.025-in archwires were assembled in 0.018-in and 0.022-in slots, respectively. No ligatures were used in the FE model because the archwire was assembled inside the bracket slot with contact on slot wall surfaces.

The meshing of the bracket-archwire assemblies was done using HyperMesh software (HyperMesh 10.0; Altair Engineering, Milwaukee, Wis) with 0.05 mm pentahedral and hexahedral elements for better accuracy. Because of the miniature-sized curvatures in the bracket’s geometry, it could not perform convergence testing with different element sizes. The solid 45 and solid 185 elements were used for archwires and brackets, respectively. The Ansys Workbench (R18.1; Ansys, Canonsburg, Pa) was used for the analysis and measurement of deformation in the slot and tie wings region.

The surface to surface contact with program-controlled formulation was used to connect the slot wall and bracket surfaces. A friction coefficient value of 0.13 was used in the contact surfaces. There were no constraints in the archwire for translational and rotational movements, and all degrees of freedom in the bracket’s base were arrested. Both ends of the archwire were twisted in a palatal root torque fashion from zero to 30° in increments of 5°. The linear, elastic, and isotropic properties with Poisson’s ratio of 0.29 and Young’s modulus of 200000 MPa were set for SS bracket-archwire assembly. For TMA wire, Young’s modulus was 81000 MPa, and Poisson’s ratio was set as 0.31. ,

The nodal points marked in the FE model for deformation measurements in the slot and tie wings region are illustrated in Figure 1 . Tie wings deformation was measured between the marked nodal points (tie wing distogingival [TDG]-tie wing disto-occlusal [TDO] and tie wing mesiogingival [TMG]-tie wing mesio-occlusal [TMO]) in the center of the labial side of both the distal and mesial tie wings, as commonly used in the literature. Similarly, the slot deformation was measured between the marked nodal points (slot distogingival [SDG]-slot disto-occlusal [SDO] and slot mesio-gingival [SMG]-slot mesio-occlusal [SMO]) located in the top edge of the proximal sides of the slot wall. The initial (pretorque) distances between the points, TDG-TDO and TMG-TMO on the tie wings, were 1.7 mm and 1.8 mm in 0.018-in and 0.022-in brackets, respectively. Similarly, between the points, SDG-SDO and SMG-SMO were 0.457 mm and 0.558 mm in 0.018-in and 0.022-in brackets, respectively. The archwire play and torque were measured in both bracket-archwire combinations. The deformation between the tie wings (TDG-TDO and TMG-TMO) and the slot walls (SDG-SDO and SMG-SMO) were measured before and after every 5° angle of twist in the archwire.

Fig 1
Line diagram showing the bracket orientation and palatal root torque ( curved arrows ) and the marked points.

Results

The archwire play of 0.017 × 0.025-in archwire in 0.018-in slot and 0.019 × 0.025-in archwire in 0.022-in slot were 8° and 11°, respectively. For SS wires at 30° angle of twist in 0.017 × 0.025-in archwire in 0.018-in slot and 0.019 × 0.025-in archwire in 0.022-in slot, the generated torque was 51 Nmm and 39 Nmm, respectively. For 30° angle of twist in 0.017 × 0.025-in archwire in 0.018-in slot and 0.019 × 0.025-in archwire in 0.022-in slot, the deformation of tie wings between points TDG-TDO and TMG-TMO was 48.67 μm and 34.87 μm, respectively. Similarly, the slot deformations in 0.017 × 0.025-in archwire in 0.018-in slot and 0.019 × 0.025-in archwire in 0.022-in slot between points SDG-SDO and SMG-SMO were 66.33 μm and 45.69 μm as presented in Table I . For TMA wires at 30° angle of twist in 0.017 × 0.025-in archwire in 0.018-in slot and 0.019 × 0.025-in archwire in 0.022-in slot, the generated torque was 33 Nmm and 27 Nmm, respectively. The slot and tie wing deformation between the points in bracket-TMA archwire combinations are presented in Table II .

Table I
Deformation of tie wings and slot in 0.018-in and 0.022-in brackets with SS archwires
Archwire size 0.017 × 0.025-in 0.019 × 0.025-in 0.017 × 0.025-in 0.019 × 0.025-in
Bracket size 0.018 × 0.025-in 0.022 × 0.025-in 0.018 × 0.025-in 0.022″ × 0.025-in

Angle of twist (°) Tie wings deformation (μm) Slot deformation (μm)
TDG-TDO TMG-TMO TDG-TDO TMG-TMO SDG-SDO SMG-SMO SDG-SDO SMG-SMO
5 0 0 0 0 0 0 0 0
10 2.34 2.34 0 0 5.22 5.22 0 0
15 14.83 14.83 9.52 9.52 19.81 19.81 15.42 15.42
20 26.39 26.39 18.12 18.12 36.42 36.42 24.71 24.71
25 38.18 38.18 26.41 26.41 51.37 51.37 34.21 34.21
30 48.67 48.67 34.87 34.87 66.33 66.33 45.69 45.69
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Oct 30, 2021 | Posted by in Orthodontics | Comments Off on Comparative finite element analysis of bracket deformation in tie wings and slot region during simulated torque
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