Summary
Introduction:
Biomechanical analysis of orthodontic tooth movement is complex, as many different tissues and appliance components are involved. The aim of this finite element study was to assess the relative effect of material alteration of the various components of the orthodontic appliance on the biomechanical behaviour of tooth movement.
Methods:
A three-dimensional finite element solid model was constructed. The model consisted of a canine, a first, and a second premolar, including the surrounding tooth-supporting structures and fixed appliances. The materials of the orthodontic appliances were alternated between: (1) composite resin or resin-modified glass ionomer cement for the adhesive, (2) steel, titanium, ceramic, or plastic for the bracket, and (3) β-titanium or steel for the wire. After vertical activation of the first premolar by 0.5mm in occlusal direction, stress and strain calculations were performed at the periodontal ligament and the orthodontic appliance.
Results:
The finite element analysis indicated that strains developed at the periodontal ligament were mainly influenced by the orthodontic wire (up to +63 per cent), followed by the bracket (up to +44 per cent) and the adhesive (up to +4 per cent). As far as developed stresses at the orthodontic appliance are concerned, wire material had the greatest influence (up to +155 per cent), followed by bracket material (up to +148 per cent) and adhesive material (up to +8 per cent).
Limitations:
The results of this in silico study need to be validated by in vivo studies before they can be extrapolated to clinical practice.
Conclusion:
According to the results of this finite element study, all components of the orthodontic fixed appliance, including wire, bracket, and adhesive, seem to influence, to some extent, the biomechanics of tooth movement.
Introduction
Orthodontic tooth movement is based on the ability of surrounding bone and periodontal ligament (PDL) to react to a mechanical stimulus with remodelling processes. Application of an orthodontic force system to a tooth causes displacement, stresses, and strains in the structures involved (1–2), while mechanotransductory processes are translated to cell-to-cell signalling (3). There has been evidence of a direct or indirect correlation of the calculated stress/strain values in the PDL with the distributions of osteoclasts in the alveolar bone and PDL of rats or monkeys (2, 4, 5). As force magnitude plays a pivotal role in determining whether physiologic remodelling phenomena or necrotizing phenomena take place in the PDL, quantification of strains developed in the ligament and alveolar bone can provide indications of favourable or unfavourable tooth movement (6). The magnitude of generated strains varies inversely with the area in which the load is applied (7, 8) and with the type of accompanying remodelling.
In recent years, the increased esthetic demands of patients who seek orthodontic treatment have led to the development of various esthetic materials, including orthodontic brackets. The two primary types of esthetic brackets are ceramic and plastic brackets (9, 10). Unlike metallic brackets, ceramic brackets have high brittleness and increased susceptibility to fracture and thus are more prone to complications for the orthodontist (11, 12), while also causing more damage to the enamel during debonding than metallic brackets (13). The main disadvantages of plastic brackets on the other side are reduced torque transmission, colour changes, morphological disturbances, and structural or hardness derangements (14–16). Moreover, the clinical efficiency of ceramic and plastic brackets might be considerably reduced during treatment due to intraoral aging (10, 17).
The biomechanical behaviour of the bracket is important to the orthodontist, as the risk of bracket wing fracture is increased with esthetic brackets (10, 17), which leads to increased chair time, patient discomfort, and potential aspiration of the wing fragment. This is attributed to the almost non-existing plastic deformation of ceramic brackets and their significantly lower fracture strength compared to metallic brackets. Additionally, the developed stresses in the bracket and its distribution to the underlying adhesive–bracket interface might lead to crack initiation and propagation and subsequent debonding of the bracket (18, 19). The elastic properties of the bracket and the adhesive have been associated with differences in the corresponding bond strength (20). Finally, development of excessive stresses in the wire might lead to permanent deformation, which can hamper tooth movement.
The relative influence of the various materials of orthodontic appliances on the resulting tooth movement has not been adequately studied. Two recent systematic reviews of clinical trials in humans indicated that there is limited evidence regarding both bracket material and wire material (21, 22). This lies in part in the complexity of the biomechanical behaviour of the complex between dental tissues and the orthodontic fixed appliances, as many tissues or materials with different properties are involved, including bone, PDL, tooth structures, adhesive, bracket, and wire.
The finite element (FE) method has been suggested as a solution for complex biomechanical questions and has been applied in several cases in orthodontics (23, 24) in order to assess the centre of resistance (25–27), various biomechanical aspects of tooth movement (28, 29), different bracket (30, 31), anchorage (32–35) or surgical 36, 37) treatment modalities, debonding (38–40, 41), and retention procedures (42). The reliability of FE analyses is dependent not only on the loading configuration, but also on the geometry of the structure and the material properties (23, 43). Experimental validation studies of the FE analyses (38) are also encouraged, whenever possible.
The primary objective of the present in silico study was to assess the influence of material variations on the strains induced at the PDL. The secondary objective was to assess the effect of material variation on the stresses developed at the orthodontic bracket.
Materials and methods
A three-dimensional (3D) solid model was constructed including a lower right canine, first premolar and second premolar, with the corresponding PDLs and alveoli. All separate PDLs had a uniform thickness of 0.2mm and all separate cortical bone layers had a uniform thickness of 0.5mm. A partial orthodontic fixed appliance was constructed with adhesive layers (mean thickness 0.2mm) and brackets on each of the three teeth, while a round 0.41mm (0.016 inch) wire was inserted into all bracket slots and ligated with two ligatures. For all teeth the same bracket was used, based on computer-aided design and computer-aided manufacturing (CAD/CAM) data from the discovery® (Dentaurum, Ispringen, Germany) brackets, provided by the manufacturer, with a slot size of 0.46×0.64mm (0.018×0.025 inch) and placed in the middle of the buccal side of the clinical crown (Figures 1 and 2).
Figure 1.
The constructed model with its components, including cortical bone layer, periodontal ligament, tooth, adhesive layer, bracket, wire, and ligatures.
Figure 2.
Details of each tooth modelled together with the components of the fixed appliance.
Based on these 3D solid models, an FE mesh was created to make a node-to-node connection between bracket, adhesive, tooth, PDL, and alveolar bone. An FE mesh of the wire was created separately from the bracket to allow the wire to slide through the bracket slots. A free mobility of the wire within the bracket slot was given by performing contact analyses based on the Coulomb friction model in the FE program used (MSC.Marc/Mentat v. 2010, MSC Software Corp., Santa Ana, California, USA). This means that the wire is not deformed until it comes into contact with the slot walls and thus the wire mobility was restricted by the slot walls and the ligature, respectively. A frictional coefficient between the bracket and the wire of 0.1 was used. The 3D FE model consisted of 624 118 isoparametric tetrahedral solid elements (four-noded) and 756 067 nodes (Figures 1–3).
Figure 3.
Details of the modelled bracket, wire, and ligatures.
The material properties used in this study were based on previously published studies (Table 1). All materials were considered to be homogenous and isotropic apart from the PDL, which was modelled as bilinear elastic (E 1 = 0.05MPa; E 2 = 0.20MPa; ε 12 = 7 per cent) (26). According to the objectives of this study, the following material parameters were used for the adhesive layer, the bracket, and the wire in order to assess the effect of this variation on the developed stresses and strains: (1) adhesive: composite resin or resin-modified glass ionomer cement, (2) bracket: stainless steel, titanium alloy, ceramic or plastic (polycarbonate), and (3) wire: stainless steel or β-titanium alloy (β-Ti). A total of 11 different models were generated with random variation of these materials. In five additional generated models, no computational convergence could be achieved, due to their complexity and the models were dropped from the analysis.
Table 1.
Material properties used in this study. RMGI, resin-modified glass ionomer cement; β-Ti, β-titanium alloy.
| Material | Young’s modulus (MPa) | Poisson’s ratio |
|---|---|---|
| Bone (29) | 2000 | 0.30 |
| Periodontal ligament (26) | Bilinear: 0.05/0.20 Ultimate strain Ε 12: 7.0% |
0.30 |
| Tooth (29) | 20 000 | 0.30 |
| Adhesive—composite resin (44) | 8823 | 0.25 |
| Adhesive—RMGI (40, 41) | 7600 | 0.30 |
| Bracket—stainless steel (30) | 200 000 | 0.30 |
| Bracket—titanium (45) | 114 000 | 0.30 |
| Bracket—ceramic (46) | 379 000 | 0.29 |
| Bracket—plastic (10) | 2200 | 0.30 |
| Elastic ligature (31) | 100 | 0.30 |
| Wire—stainless steel (30) | 200 000 | 0.30 |
| Wire—β-Ti (47) | 65 000 | 0.30 |
The simulation was designed to reflect the clinical situation of a deformed wire acting on a first premolar extruded by 0.5mm. By a preliminary FE simulation, the wire was inserted in the aligned slots of the three brackets and passively secured with the ligatures. In order to simulate the activated wire, the alveolus of the first premolar was deflected by 0.5mm in occlusal direction perpendicular to the tooth axis, while the other two alveoli were held (movement restriction of outer bone surface) and the ligatures were activated. After the middle tooth’s deflection was achieved, all three alveoli were held (movement restriction of outer bone surface), in order for the deformed wire to act on the middle tooth. The induced total equivalent strains in the PDL and the induced stresses (Von Mises stresses) in the bracket and wire of the first premolar were measured at the end of the 0.5mm deflection phase. Mean stresses/strains across models according to the various material parameters were calculated and analysed descriptively. All simulations of tooth movement were performed with the above-mentioned FE software. Models were created on a Dell Precision T5500 workstation (Dell, Frankfurt, Germany) and transferred to a 30-processor Dell server cluster to be solved, which took an average of 38–109 hours per individual simulation.
Results
The raw data of the 11 simulated models finally included are reported in Supplementary Table 1 and summarized as means across models in Tables 2–4. Characteristic examples of the developed strains in the PDL, the developed stresses in the bracket, and the developed stresses in the wire are illustrated in Figures 4–7, respectively. Developed strains in the PDL were uniformly distributed at the apical regions, where mainly vertical tooth displacement took place. On the contrary, strains at the buccal wall of the PDL were considerably higher than strains at the lingual wall of the PDL, as the tooth deflected in bucco-lingual direction lead by the archwire (Figures 4 and 5). Developed stresses at the bracket were mainly concentrated at the base of the bracket wing, close to its intersection with the bracket base, where the wire came into close contact with the bracket (Figure 6). Finally, developed stresses were uniformly distributed in the middle part of the wire and were transmitted to the bracket through small contact areas between bracket and wire (Figure 7).
Table 2.
Obtained strains in the PDL according to the various material properties. Ref, reference; RMGI, resin-modified glass ionomer cement; β-Ti, β-titanium alloy.
| Factor | Material | Mean strain | Strain change | Strain change % |
|---|---|---|---|---|
| Adhesive material | Composite resin | 0.164 | Ref | Ref |
| RMGI | 0.170 | +0.006 | +4% | |
| Bracket material | Ceramic | 0.133 | Ref | Ref |
| Stainless steel | 0.178 | +0.045 | +34% | |
| Titanium | 0.191 | +0.058 | +44% | |
| Plastic | 0.191 | +0.058 | +44% | |
| Wire material | β-Ti | 0.136 | Ref | Ref |
| Stainless steel | 0.221 | +0.085 | +63% |
Table 4.
Obtained stresses (MPa) in the wire according to the various material properties. Ref, reference; RMGI, resin-modified glass ionomer cement; β-Ti, β-titanium alloy.
| Factor | Material | Wire | ||
|---|---|---|---|---|
| Mean stress | Stress change | Stress change % | ||
| Adhesive material | Composite resin | 101.3 | Ref | Ref |
| RMGI | 108.1 | +6.8 | +7% | |
| Bracket material | Titanium | 60.8 | Ref | Ref |
| Stainless steel | 69.0 | +8.2 | +14% | |
| Ceramic | 119.3 | +58.5 | +96% | |
| Plastic | 137.3 | +76.5 | +126% | |
| Wire material | β-Ti | 66.8 | Ref | Ref |
| Stainless steel | 170.1 | +103.3 | +155% | |
Figure 4.
Example showing the distribution of total equivalent strains in the periodontal ligament from buccal view.
Figure 7.
Example showing the distribution of von Mises stresses in the wire.
Figure 5.
Example showing the distribution of total equivalent strains in the periodontal ligament from occlusal view.
Figure 6.
Example showing the distribution of von Mises stresses in the bracket.
The differences of the calculated strains at the PDL level are shown in Table 2. As can be seen, the greatest influence on strains was found for the wire material with a mean variation of 63 per cent. Variation of the bracket material on the other hand led to variations up to 44 per cent according to the material. Finally, variation of the adhesive material had a minimal effect on the developed strains (4 per cent).
The changes in the calculated stresses at the bracket level are shown in Table 3. The same tendency was shown, with the wire material exerting the highest influence (up to 152 per cent), followed by the bracket material (up to 148 per cent) and by the adhesive material (up to 8 per cent). The same observation was made for the stresses at the wire level, where the wire material exerted the highest influence (up to 155 per cent), followed by the bracket material (up to 126 per cent) and by the adhesive material (up to 7 per cent).
Table 3.
Obtained stresses (MPa) in the bracket and wire according to the various material properties. Ref, reference; RMGI, resin-modified glass ionomer cement; β-Ti, β-titanium alloy.
| Factor | Material | Bracket | ||
|---|---|---|---|---|
| Mean stress | Stress change | Stress change % | ||
| Adhesive material | Composite resin | 27.3 | Ref | Ref |
| RMGI | 29.4 | +2.1 | +8% | |
| Bracket material | Ceramic | 14.7 | Ref | Ref |
| Plastic | 25.0 | +10.3 | +70% | |
| Stainless steel | 30.6 | +15.9 | +108% | |
| Titanium | 36.5 | +21.8 | +148% | |
| Wire material | β-Ti | 18.2 | Ref | Ref |
| Stainless steel | 45.9 | +27.7 | +152% | |
Discussion
In this study, the relative contribution of the adhesive, bracket, and wire materials to the developed stresses and strains in the PDL, the bracket, and the wire was investigated in silico. It was observed that the strains induced at the PDL level were affected mainly by the wire, followed by the bracket and finally, minimally, by the used adhesive. The same observation was made for the developed stresses at the bracket or the wire level.
The FE method enables us to answer complex biomechanical questions in the field of orthodontics via simulation; moreover, it enables investigators to predict the behaviour of biological structures in many specific situations. In the specific example of this in silico study, the deformed wire acted on the bracket of the middle tooth, and through it, to its PDL, deforming it and inducing strains. The strains in the PDL were mainly concentrated at the buccal wall and the apical surface of the PDL, as the tooth intruded and tilted buccally, when the deformed wire was left to act. However, any solutions obtained via FE simulation will be numerical approximations. Although these numerical data are difficult to be replicated in clinical settings, they can nevertheless contribute useful information to clinical investigations.
The variation of the used materials had a profound effect on the developed strains in the PDL. This effect was more profound for the bracket and wire materials, but was also marginally existent for the adhesive material. It is therefore important to take this factor into account when making clinical decisions in orthodontics, as the developed strains in the PDL are directly associated with the biological processes of tooth movement (2, 4, 5). There is some evidence that, unlike light forces, heavy forces might cause necrosis (hyalinization) of the PDL, undermining bone resorption, and play a role in root resorption (48, 49).
Material variations of the adhesive, bracket, or wire influenced the developed stresses at the fixed appliance (bracket and wire), with the effect being stronger for the last two. This might have an influence on the fracture rate of the bracket wings or on the bond failure between bracket and adhesive. Comparing this study with similar work is limited, due to the absence of the latter. The influence of changes in the adhesive’s Young’s modulus on the developed stresses in the bracket was likewise found to be minimal in a previous study (50). In another simplified FE study, the effect of bracket material variation on the resulting stresses in the bracket was found to be limited (46). However, modelling and activation conditions differed from the present study and no direct comparison is possible. Finally, the stresses developed at the wire were influenced by the material variation of both the wire and the bracket as well. This should also be taken into account, for choosing the material of the fixed appliance, as the excessive stresses developed in the wire might lead to its permanent plastic deformation.
There are additional factors that might influence the biomechanical behaviour of fixed appliances. Ghosh et al., (51) investigated various designs of ceramic brackets and reported significant variation in the stresses in the bracket according to the bracket design, with uneven stress distributions with increased stresses at the edges of brackets with sharp lines and angles. Moreover, significant differences in the tie-wing tensile fracture strength of semi-twin and true-twin brackets have been reported (52). The former perform better, as the bulk piece of ceramic that connects the mesial and the distal wings has a cross-stabilizing effect. Additionally, Gkantidis et al., (10) reported that ceramic brackets present irregularities in the inner slot surface, which increase pressure expressed by the wire and lead to attrition, something that was not modelled in the present study. Likewise, all brackets modelled consisted from a single material phase and no different materials were used for the tie-wings and base of the bracket, as is sometimes done for metallic brackets (53).
Strengths
The strengths of this study include the bilinear modelling of the PDL, which is more accurate than the usually used simplified linear modelling of the PDL (54, 55). All material properties used were based on previous studies. To reduce the systematic error, no absolute values were considered to draw the conclusion, only the differences between the simulations. Since all simulations were affected by the simplification effects to the same extent, the analysis of the differences resulted in an additional increase of validity.
Limitations
The limitations of this study include the existing play between the bracket and wire of the simulated model, which could influence the results (28). However, this was the same for all tested models. On the other hand, a heavier or a rectangular wire would not make sense, as the stainless steel was amongst the tested wire materials and stainless steel rectangular wires are not widely used for initial alignment. To reduce the number of equations to be solved, the teeth were not differentiated into enamel, dentine, pulp, and cementum but were provided uniformly with the elasticity parameters of dentine. In view of the minor forces applied, the influence of this simplification is negligible because no substantial deformation of the dental hard tissue was to be expected. For the same reason, the bone was not differentiated into cancellous and cortical bone (56, 57). Finally, superelastic nickel titanium wires could not be modelled for this experiment, despite their wide clinical usefulness (58), as they caused computational problems, due to the heavy data load.
Conclusions
According to this in silico study, the following conclusions can be drawn:
The magnitude of the strains in the PDL was found to be dependent on the wire, bracket, and adhesive materials. The largest influence was noted for the wire material, followed by the bracket material.
Likewise, the wire, bracket, and adhesive materials had a direct influence on the severity of stresses developed at the bracket. Again, the largest influence was noted for the wire material, followed by the bracket and the adhesive materials.
As a result, the biomechanical behaviour of the orthodontic appliances should also be taken into account in clinical decision-making together with esthetic reasons and patient preferences. However, clinical studies need to be performed to verify these findings.
Supplementary material
Supplementary material is available at European Journal of Orthodontics online.
Funding
SNP was funded by the Clinical Research Unit (KFO208/TP09; German Research Foundation and Medical Faculty, University of Bonn, Bonn, Germany).
Acknowledgment
We thank the company Dentaurum (Ispringen, Germany) for providing the CAD/CAM models of the bracket.
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