|Year : 2017 | Volume
| Issue : 2 | Page : 183-189
A comparative evaluation of different compensating curves and power arm length during retraction of maxillary anterior teeth: A finite element study
Dhvani Sumatichandra Doshi, Tejashri Mirji Pradhan
Department of Orthodontics, KLE's VKIDS, Belgaum, Karnataka, India
|Date of Web Publication||30-May-2017|
Dhvani Sumatichandra Doshi
601, Meeras Apartment, 51 TPS Road, Borivali-W, Mumbai - 400 092, Maharashtra
Source of Support: None, Conflict of Interest: None
Introduction: The strategic design of an appliance for anterior retraction by using orthodontic mini-implant anchorage and sliding mechanics must take into account the height of the power arm and compensating curve in archwire. This study was conducted to analyze the change in maxillary anterior teeth displacement and stress distribution using different compensating curves in the arch wire and varying power arm length in first premolar extraction case during sliding mechanics.
Materials and Methods: 6 geometric models were created using ANSYS software. This geometric model was converted into a finite element model with the help of software HYPERMESH 11.0. Bilaterally mini-implants were placed in the bone between the roots of maxillary second premolar and first molar. Power arms were placed at two heights – 3 mm and 5.5mm. Compensatory curves were placed in the archwire (0, 3mm or 5mm) and a force of 150 gms was applied using NiTi coil springs bilaterally. Stresses in bone and tooth displacements were analyzed.
Results: There was more bodily movement of the teeth using the longer power arms. Incorporating a compensatory curve further helped to reduce tipping. The tooth that showed most bodily movement was the lateral incisor followed by central incisor and least by the canine. There was increased intrusion of the incisors and extrusion of canine with increase in power arm height.
Conclusion: Increase in power arm height causes an increased intrusive tendency and increased bodily movement during en masse retraction of anterior teeth using mini- implant anchorage. Incorporation of a 5mm compensatory curve further helps reduce the tipping tendency of the anterior teeth.
Keywords: Anterior retraction, compensatory curve, finite element analysis, mini-implants
|How to cite this article:|
Doshi DS, Pradhan TM. A comparative evaluation of different compensating curves and power arm length during retraction of maxillary anterior teeth: A finite element study. Indian J Health Sci Biomed Res 2017;10:183-9
|How to cite this URL:|
Doshi DS, Pradhan TM. A comparative evaluation of different compensating curves and power arm length during retraction of maxillary anterior teeth: A finite element study. Indian J Health Sci Biomed Res [serial online] 2017 [cited 2019 Jul 17];10:183-9. Available from: http://www.ijournalhs.org/text.asp?2017/10/2/183/207254
| Introduction|| |
Many strategies for anchorage control have been developed over the years that have made it possible to prevent undesirable tooth movement in all three planes of space. In recent years, titanium mini-implants have gained immense popularity among orthodontic practitioners. They can be used in cases with a high anchorage requirement, cases with insufficient teeth for the application of conventional anchorage, cases where the forces on the reactive unit would generate adverse side effects, and in some cases, as an alternative to orthognathic surgery. Advantages include ease of insertion and removal of the screws, immediate/early loading, low cost, and adequate anchorage support for orthodontic tooth movement. In addition, these screws only partially osseointegrate, resulting in stability during treatment but still allowing for easy removal after completion of treatment. Potential complications with miniscrews in orthodontics are soft tissue irritation at the site of insertion, risk of infection, and premature loosening of the screw.
If screws are placed in movable mucosa, soft tissue irritation may occur. If screws are placed in attached mucosa, it is less likely that irritation will be a complication. Inability to place the mini-implant higher in the movable mucosa necessitates modifications in the retraction assembly. The use of a rigid rectangular wire with a power arm placed near the center of resistance (Cres) of the anterior teeth enables one to achieve more predictable space closure. By varying the height of the power arm, it is possible to vary the line of action of the force bringing it closer to or away from the Cres. However, increasing the power arm height too much can cause irritation and discomfort to the patient. To overcome this limitation of the power arm, compensatory curves (CCs) can be placed in the archwire to encourage intrusion of anteriors during retraction and afford more control over the tooth movement. However, the optimal conditions for achieving the desired type of tooth movement are still unknown. Furthermore, it is prudent to remember that application of these forces may lead to the development of stress regions around the mini-implant which may lead to failure.
It has long been recognized that both the mini-implant and bone should be stressed within a certain range for physiological homeostasis. This mechanical stress in turn causes strain in the bone tissue. The upper limit of the bones' equilibrium is roughly 1000–1500 μ Strain (20 MPa). Bone formation is the initial response above this limit. Additional strain, however, leads to microfissures and microfractures in the bone tissue, which, at roughly 3000 μ Strain (60 MPa), surpasses ongoing repair processes leading to bone resorption and is likely to cause a microfracture of the bone trabecula and may ultimately lead to the failure of the mini-implant. Using the finite element analysis (FEA), it is possible to apply an external load and study the tooth movements and stress distributions in the dentoalveolar complex.
Very little data are available in the literature depicting the tooth movement and stress distribution in the bone surrounding mini-implants during en masse retraction of upper anterior teeth with a CC incorporated into the wire. The aim of this study was to analyze the change in maxillary anterior teeth displacement and stress distribution in bone using different compensating curves in the archwire and varying power arm length in first premolar extraction case during sliding mechanics.
| Materials and Methods|| |
FEM uses a complex system of points (nodes) and elements, which make a grid called as mesh. This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions.
In this study, the geometric models of whole maxillary dentition (except first premolars and third molars bilaterally) were constructed using the dimensions and morphology found in Wheeler's text book  using ANSYS software. Next, the periodontal ligament with the cortical and cancellous bone was constructed around it. Separate models were constructed for mini-implants of 1.3 mm diameter and 9 mm length  and 0.019 × 0.025”stainless steel wire, brackets, and molar tubes. Bilaterally mini-implants were placed in the bone between the roots of maxillary second premolar and first molar at a height of 3 mm from the alveolar crest. Power arms were placed at two heights which are commonly used –3 mm (models A, B, and C) and 5.5 mm (models D, E, and F). In models A and D, no CCs were placed, i.e., zero CC. In models B and C, CCs of 3 mm and in models E and F, CCs of 5 mm were incorporated.
This geometric model was converted into a finite element model with the help of software HYPERMESH 11.0 (Altair Engineering, Troy, Michigan, United States). The different structures involved in this study include alveolar bone, periodontal ligament, teeth, nickel-titanium (NiTi) coil spring, stainless steel archwire and power arm, and titanium mini-implant. Each structure has a specific material property. Some of the material properties used in this study were derived from a study by Chang et al., and the properties for NiTi coil spring and titanium implant was taken from a study by Jasmine et al. These material properties were the average values reported in the literature [Table 1]. In this study, all the tissues were assumed to be isotropic and elastic.
The boundary conditions were defined, and after this step, the final FEM models were ready to be analyzed. Constant retraction forces were applied in each model, i.e., 150 g bilaterally from miniscrew to hook power arm placed between the lateral incisor and canine. Stresses in the bone surrounding the mini-implant and tooth displacement were calculated and presented as different colors. Each color represents a different stress level. Red color column of the spectrum indicated maximum stress and blue represented the lowest level of stress and likewise for displacement.
| Results|| |
Displacement was measured along Y and Z axes. The Y axis represents movement in a sagittal direction where a +ve sign indicated lingual movement & a −ve sign indicated labial movement. The Z axis represents movements in a vertical direction where a +ve sign indicated an extrusive movement and a −ve sign indicated an intrusive movement.
Displacement along Y axis
In the models with 3 mm power arm height, it was seen that all three teeth tipped lingually. Of the three teeth, the lateral incisor showed a more bodily movement followed by the central incisor whereas the canine showed a more controlled tipping.
In the models with 3 mm power arm, a more bodily tooth movement was observed with the central incisor and canine with a zero CC, followed by the 5 mm CC and least with the 3 mm CC. For the lateral incisor, a more bodily tooth movement was observed with 5 mm CC, followed by the 3 mm CC and least with the zero CC.
In the models with the 5.5 mm power arm height also, it was observed that all three teeth tipped lingually, and the lateral incisor showed a more bodily movement followed by the central incisor whereas the canine showed a more controlled tipping.
However, a more bodily movement was seen with the canine and lateral incisor with the 5 mm CC, followed by the 3 mm CC and least with the zero CC. For the central incisor, the bodily movement was highest for the zero CC group closely followed by both the 3 mm and 5 mm CC.
On comparing the displacement between the 3 mm and 5.5 mm power arm height, overall it was seen that a more bodily movement was seen with the 5.5 mm power arm as compared to the 3 mm power arm for all the three teeth [Table 2] and [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6].
|Table 2: Displacement in mm of crown and root tips of central incisor, lateral incisor and canine along Y axis|
Click here to view
Displacement along Z axis
In the model with 3 mm power arm and zero CC, there was extrusion of central incisor and canine whereas intrusion of lateral incisor was observed. As a CC of 3 mm was added, there was a change in the extrusive tendency of central incisor to an intrusive tendency, a slight increase in the intrusive tendency of lateral incisor, and a slight reduction in the extrusive tendency of canine. However, there was not much change in the vertical movements when the CC was increased from 3 mm to 5 mm.
In the model with 5.5 mm power arm and zero CC, there was extrusion of central incisor and canine and intrusion of lateral incisor. As a CC of 3 mm was added, here also, there was a change in the extrusive tendency of central incisor to an intrusive tendency, an increase in the intrusive tendency of lateral incisor, and a reduction in the extrusive tendency of canine. However, here also there was not much change in the vertical movements when the CC was increased to 5 mm.
With increase in height of the power arm, the extrusion of central incisor was reduced and intrusion increased. The overall vertical movements of lateral incisor and canine were more with the 5.5 mm power arm [Table 3] and [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6].
|Table 3: Displacement in mm of crown tips of central incisor, lateral incisor & canine along Z axis|
Click here to view
Stress pattern in bone
For the 3 mm postantium (PA) length, maximum stress was observed in the bone surrounding the mini-implant with the zero CC model, followed by the 5 mm CC and least with the 3 mm CC. For the 5.5 mm PA length, maximum stress was observed in the bone surrounding the mini-implant with the 5 mm CC model, followed by the 3 mm CC and least with the zero CC. Overall the stresses were more with the 5.5 mm power arm than with the 3 mm power arm [Table 4].
| Discussion|| |
The FEA can provide the orthodontist with an understanding of the physiologic reactions of teeth and their surrounding structures to external loading, namely, the orthodontic force.
Jafari et al have pointed out the advantages of FEM.
- It is a noninvasive technique
- The actual amount of stress experienced at any given point can be theoretically measured
- The tooth, alveolar bone, periodontal ligament, and craniofacial bones can be simulated, and the material properties of these structures can be assigned to the nearest one that possibly can simulate the oral environment in vitro
- The displacement of the tooth can be visualized graphically
- The point of application, magnitude, and direction of a force may easily be varied to simulate the clinical situation
- Reproducibility does not affect the physical properties of the involved material
- The study can be repeated as many times as the operator wishes.
Although finite element method is a useful technique, it has certain limitations. This technique is based on several assumptions which were made in the development of the model for this study. All the models were assumed to be homogeneous and isotropic and to have linear elasticity. However, the material properties and the geometry of the model change from one person to another. This makes the problem even more complex. These are inherent limitations of this technique.
Chaimanee et al. have shown that for all skeletal patterns, the safest zone in the inter-radicular space of the posterior maxilla is the space between the second premolar and the first molar, and available inter-radicular space >3 mm was found only at 9- and 11-mm depths from the alveolar crest between the first molar and second premolars, an area likely to be covered by movable mucosa. Lim et al. have advised that mini-implants for orthodontic anchorage may be placed anywhere within the zone of attached gingiva up to 6 mm apical to the alveolar crest with adequate inter-radicular space. The height of attached gingiva was found to be less in the maxillary posterior region as compared to the anterior region. As it is advisable to place the mini-implants in areas of attached gingiva, in this study, the mini-implant was placed at a height of 3 mm from the alveolar crest between the roots of the upper first molar and second premolar.
The line of action of the force is the line joining the mini-implant and the power arm. Due to the anatomical limits of the inter-radicular bone and the soft tissue covering the bone, the possibilities of changing the mini-implant placement height to vary the line of action of force according to the tooth movement we desire are limited. We can, however, vary the power arm height to get the desired direction of force. Hence, in this study, two different power arm heights were compared to find the power arm height which best allows pure translation of the teeth being retracted. However, it may not always be possible to alter the power arm height due to lack of vestibular depth in some cases.
Another method that can be taken to overcome this limitation is incorporation of a CC in the archwire. Controlling vertical movements during retraction can be challenging. McLaughlin et al. have recommended placing bite-opening curves in the archwire during leveling for overbite control. Introducing a curve such that the archwire lies gingivally in the anterior region before engaging may encourage intrusion of anterior teeth during retraction.
Kojima et al. found in their study that in cases of the low position miniscrew (4 mm), when lengthening the power arm from 1 mm to 4 mm, rotation of the entire dentition decreased with decrease in distance of line of force to Cres of anteriors. Tominaga et al. found that a power arm of height 4-5 mm led to controlled tipping and increasing the height to 5.5 mm led to more bodily movement. In our study as well, it was observed that increase in power arm height led to a decreased tipping and a more bodily movement of all six anterior teeth. As the power arm height is increased, the point of force application moves nearer to the Cres of the six anterior teeth leading to decreased tipping tendency. This is also in agreement with Ashekar et al. who found reduced palatal tipping when mini-implant was placed at 6 mm from archwire and retraction hook height was increased from 0 to 5 mm.
In our study, the tendency of bodily movement was more for the lateral incisor followed by the central incisor and least for canine. This maybe because the lateral incisor is smallest in length and the force vector would be nearer to the Cres of this tooth as compared to the other two teeth. On the other hand, the canine has the longest root and the force vector is farthest from its Cres causing the tipping effect.
With an increase in power arm height, there was increase in intrusion of the incisors and extrusion of canine. This maybe because of archwire deformation that takes place when a force is applied to the power arm. Tominaga et al. stated that with increase in power arm height, there is an increased archwire deformation which takes place at the power arm archwire junction. This may lead to an upward deflection of the archwire mesial to the power arm and downward deflection distal to the power arm causing intrusion of incisors and extrusion of canine with increase in power arm height. This was in agreement with the findings of Deng et al. who found the extrusion tendency of central incisors reduced and the intrusion tendency increased with increase in power arm height from 2 mm to 4 mm with miniscrew placed at 4 mm from alveolar crest. This may be of significant importance in cases of deep bite where control of vertical tooth movement is required. Ashekar et al., on the other hand, found an intrusive effect when shorter power arms (0 mm) and higher mini-implants (10 mm) were used.
It was observed that with increase in CC, there was a decreased tendency of teeth to tip which was in agreement with Sung et al. who in their study comparing the effect of CCs on lingual and labial archwires found an anti-tip action of the CC on canine retraction. In our study, it was seen that the anti-tip action was more pronounced when a longer power arm was used. Hence, increase in power arm height with a CC in the archwire can be measures to decrease tipping and increase bodily movement during retraction.
When considering the Z axis, there was an extrusive effect seen on central incisors and canines and an intrusive effect on the lateral incisors when no CC was present in the archwire. However, incorporation of a CC changed the extrusive tendency of central incisor to an intrusive tendency, increased the intrusive tendency of lateral incisor, and reduced the extrusive tendency of canine.
Mini-implant failure is a common problem encountered in clinical situations. This has been attributed to infection as well as biomechanical factors such as insertion angle, structure of mini-implant, and the loading conditions.,, With respect to stress distribution, an increase in power arm height did seem to cause an increase in stress levels in the bone. However, all stress levels found in this study were well below the yield stress of bone (200 MPa) and also below the upper limit of the range of physiological homeostasis of bone (60 MPa) as given by Sivamurthy and Sundari. This indicates that the bone has sufficient strength to withstand the orthodontic loading.
| Conclusions|| |
The following conclusions were drawn after performing the study and by careful interpretation of results:
- Increase in power arm height causes a decrease in the tipping tendency and increased bodily movement during en masse retraction of anterior teeth using mini-implant anchorage
- Increase in power arm height also reduces the extrusive tendency and increases the intrusive tendency of the incisors during retraction which can be helpful in deep bite cases requiring vertical control
- Incorporation of a 5-mm CC along with increased power arm height further helps reduce the tipping tendency of the anterior teeth
- Though stresses generated increased with increase in power arm height and CC, they were low enough for the bone to withstand the orthodontic loading.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2], [Table 3], [Table 4]