|Year : 2017 | Volume
| Issue : 3 | Page : 152-159
Stress distribution and displacement of maxillary anterior teeth during en-masse intrusion and retraction: A FEM study
Parag Bohara1, Mukesh Kumar2, Hemant Sharma2, Poonam K Jayprakash3, Vivek Misra4, Khumanthem Savana5
1 Consultanat Orthodontist, Department of Orthodontics and Dentofacial Orthopedics, Teerthanker Mahaveer Dental College and Research Centre, Moradabad, Uttar Pradesh, India
2 Prof., Department of Orthodontics and Dentofacial Orthopedics, Teerthanker Mahaveer Dental College and Research Centre, Moradabad, Uttar Pradesh, India
3 Ex Reader, Department of Orthodontics and Dentofacial Orthopedics, Teerthanker Mahaveer Dental College and Research Centre, Moradabad, Uttar Pradesh, India
4 Ex Senior Lecturer, Department of Orthodontics and Dentofacial Orthopedics, Teerthanker Mahaveer Dental College and Research Centre, Moradabad, Uttar Pradesh, India
5 Consultant Orthodontist, Department of Orthodontics and Dentofacial Orthopedics, Teerthanker Mahaveer Dental College and Research Centre, Moradabad, Uttar Pradesh, India
|Date of Submission||14-Oct-2016|
|Date of Acceptance||09-May-2017|
|Date of Web Publication||17-Jul-2017|
Consultant Orthodontist, Jalgaon, Maharashtra
Source of Support: None, Conflict of Interest: None
Background: Space closure by en masse intrusion and retraction in orthodontics is of particular interest. Aim: The aim of this study was to evaluate the stress distribution and displacement of maxillary anterior teeth. Materials and Methods: Four different finite element models of maxillary arch were constructed to understand the nature of stresses and displacement patterns of anterior teeth during en masse intrusion and retraction on force application with different combinations of mini-implants and retraction hooks. Results: In this study, tensile stresses were seen in the cervical region and various movements of teeth such as lingual crown tipping, bodily movement, lingual root tipping, intrusion, and extrusion were observed. Conclusion: Nature of stresses changes from tensile to compressive from cervical area to apical area. Various tooth displacements suggest that different combinations of mini-implants and retraction hooks affect the direction of the tooth movement.
Keywords: Anterior teeth retraction, displacement, stress distribution, three-dimensional finite element
|How to cite this article:|
Bohara P, Kumar M, Sharma H, Jayprakash PK, Misra V, Savana K. Stress distribution and displacement of maxillary anterior teeth during en-masse intrusion and retraction: A FEM study. J Indian Orthod Soc 2017;51:152-9
|How to cite this URL:|
Bohara P, Kumar M, Sharma H, Jayprakash PK, Misra V, Savana K. Stress distribution and displacement of maxillary anterior teeth during en-masse intrusion and retraction: A FEM study. J Indian Orthod Soc [serial online] 2017 [cited 2019 May 25];51:152-9. Available from: http://www.jios.in/text.asp?2017/51/3/152/210906
| Introduction|| |
Malocclusion can occur in three planes of space, i.e., sagittal, transverse, and vertical plane. Extraction space closure is particularly interesting aspect of orthodontic treatment with respect to the principles of biomechanics due to the large movement of distances involved. As Newton's third law, for every action, there is equal and opposite reaction. Similarly, during space closure when forces are applied, there are favorable as well as unfavorable movements occur on the teeth. The actions and reactions of the forces and moments must, therefore, be studied so as to reduce empiricism in the orthodontic treatment.
Anchorage has significant consideration for orthodontists and is one of the important components in treatment planning. Clinically, in many of the cases, it is required to achieve absolute anchorage for retraction of anterior teeth or protraction of posterior teeth. Such anchorage can be provided extraorally with headgear or intraorally using adjacent teeth or dental implants. Orthodontic mini-implants (OMIs) have modernized orthodontic anchorage and biomechanics by making anchorage perfectly stable. Mini-implants have become popular and expanded the horizons of orthodontic treatment because of their biocompatibility, small size, and placement versatility. Mini-implants can provide good anchorage for anterior teeth retraction as well as for intrusion and can be placed in most desired locations. The demand for speedy and efficient orthodontic treatment has been increasing in recent years. Control of anterior teeth movement is essential for an orthodontist to execute an individualized treatment plan. Thus, straight wire appliances are extensively used for orthodontic space closure with en masse retraction of anterior teeth using a sliding mechanism. Solutions for managing force systems to achieve en masse retraction of anterior teeth is of considerable interest because lingual crown tipping of anterior teeth is still inevitable with a routine sliding mechanism even though rectangular stainless steel archwire is used. In sliding mechanics, retraction forces can be transferred to any height level on a retraction hook to move the tooth in a preprogrammed direction, such as controlled crown-lingual tipping, bodily translation movement, and controlled crown-labial movement. It has been reported that the bodily movement of the anterior teeth can be achieved by directing the force through the center of resistance of anterior teeth, by altering the occlusal–gingival location of mini-implants and the length of the anterior retraction hook (ARH)., To examine the biometric phenomena, both physiologically and histologically are very important in orthodontic process. Thus, biomechanical analysis for the applied orthodontic tools should be carried out before the procedure. The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. It is a powerful technique in dental biomechanics, as it is superior in the calculation of stress and strain of various complex structure., Evaluation of the stress distributions and three-dimensional (3D) displacements with an irregular geometry and physical properties is possible with the FEM.
Thus, the aim of the present FEM was to evaluate the stress response in the periodontal ligament (PDL) and alveolar bone and study the displacement of the maxillary anterior teeth during en masse intrusion and retraction with various combinations of mini-implants and retraction hooks.
| Materials and Methods|| |
In the present study, four 3D finite element models of the bilateral maxillary first premolar extraction case consisting of 12 teeth with its PDL, alveolar bone, brackets, archwire, retraction hooks, and mini-implants were constructed. Moreover, the stresses produced onto the PDL and alveolar bone were determined and tooth movements were also determined on applying the intrusive and retraction forces using nickel-titanium (NiTi) closed coil springs on the maxillary anteriors with the help of various combinations of mini-implants and retraction hooks.
- In the first model, mini-implants were placed bilaterally 6 mm from the cementoenamel junction between second premolar and first molar on buccal surface. Retraction hook of 6 mm in height in gingival direction were placed on the archwire between lateral incisor and canine bilaterally. A net force of 150 g was applied through NiTi closed coil springs on both sides. For this model, total number of nodes and elements were 98972 and 335781 [Figure 1]a
- In the second model, along with the configuration of the first model, another mini-implant was placed between central incisors and intrusive force of 60 g was applied through NiTi closed coil spring on the archwire between central incisors as midline traction. For this model, total number of nodes and elements were 93622 and 313944 [Figure 1]b
- In the third model, mini-implants were placed bilaterally 6 mm from the cementoenamel junction between second premolar and first molar on buccal surface. Retraction hook of 2 mm in height in incisal direction were placed on the archwire between lateral incisor and canine bilaterally. A net force of 150 g was applied through NiTi closed coil springs on both sides. For this model, total number of nodes and elements were 98972 and 335781 [Figure 1]c
- In the fourth model, along with the configuration of the third model, another mini-implant was placed between central incisors and intrusive force of 60 g was applied through NiTi closed coil spring on the archwire between central incisors as midline traction. For this model, total number of nodes and elements were 93622 and 313944 [Figure 1]d.
Steps involved in the finite element model preparation:
- Construction of the geometric model of the maxillary dentition with its periodontal structures (PDL, alveolar bone)
- Conversion of the geometric models to a finite element model
- Incorporation of material properties of tooth structure and periodontium
- Defining boundary condition
- Loading configuration
- Translation of results and interpretation
Construction of the geometric model of the maxillary dentition with its periodontal structures (periodontal ligament, alveolar bone)
In this study, the geometry of 3D finite element model of the maxilla and their periodontal structures, i.e., PDL, alveolar bone were constructed from a computed tomography scan image of a skull. These data were exported to 3D image processing and editing software-MIMICS (version 8.11) (Materialise NV, Materialise's Interactive Medical Image Control System). With the help of RapidForm2004 software, geometric model was constructed consisting of only surface data. Brackets (PEA MBT 0.022”), archwire (0.019 × 0.025” SS), titanium mini-implants (1.3 mm × 7 mm), closed coil springs, and retraction hooks (6 mm and 2 mm) were virtually modeled using reverse engineering technique.
Conversion of the geometric models to a finite element model
With the help of HYPERMESH (Altair Engineering, version 11.0) software, the geometric models were converted into finite element models. The finite element model is the representative of geometry in terms of finite number of elements and nodes. This process is called “discretization.” In this study, to model the irregular geometry of the teeth for maxilla, 4-noded tetrahedral shape was selected as the finite element.
In this study, the geometric system was coordinated. The X-axis was in the centrifugal (mesiodistal) direction. The Y-axis was the midsagittal (labiolingual) line of the dental arch on the occlusal view; the Z-axis was perpendicular to the Y-axis in occlusogingival direction.
Incorporation of material properties of tooth structure and periodontium
The material properties of teeth, PDL, and alveolar bone used were the average values reported in literature. All materials employed for the finite element model study were taken to be isotropic, homogenous, and linearly elastic [Table 1].
Defining boundary condition
Postfinite element model construction, the boundary condition of these models needs to be defined so that all movements of the model are restrained. Such a restraining is necessary so as to prevent the model from any type of body motion while the load is acting. In this study, the fixed boundary condition was maintained at the base of the maxilla and was constrained in all directions [Figure 1]a,[Figure 1]b,[Figure 1]c,[Figure 1]d.
In all the four models, 150 g retraction and intrusion force were applied bilaterally from mini-implants located between second premolar and first molar onto the retraction hooks attached between lateral incisor and canine using closed coil spring. While, in the second and fourth model along with the 150 g of force which was used in the first and third model, additional 60g of intrusive force was applied from the midline implant onto the archwire between two central incisors using closed coil spring.
Translation of results and interpretation
Finite element model consisting of nodes and elements of the teeth, periodontium, brackets, archwire, retraction hooks, mini-implants, NiTi closed coil springs were then imported into ANSYS (12.1 version, ANSYS, Inc) software for analyzing the displacement and stress distribution.
| Results|| |
The constructed models along with the load application were imported into ANSYS (version 12.1) software for analyzing the displacement and stress distribution corresponding to the force application. The results obtained consisted of the maximum von Mises stress concentration, stress distribution in the alveolar bone, PDL [Table 2], and initial displacement of each individual anterior tooth in all the three X-, Y-, and Z-axes [Table 3].
|Table 2: Von Mises stress observed in hard bone, soft bone, and periodontal ligament for all the four models (values expressed in MPa)|
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|Table 3: Displacement of teeth of right quadrant in X‑, Y‑, and Z‑axes for all the four models (all values expressed in mm)|
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von Mises stress and stress distribution in PDL are shown in [Figure 2]a,[Figure 2]b,[Figure 2]c,[Figure 2]d.
|Figure 2: (a‑d) Maximum stress and nature of stress observed in periodontal ligament|
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Displacement of central incisor, lateral incisor, and canine in X-axis, Y-axis, and Z-axis for Models 1, 2, 3, and 4 are shown in [Figure 3],[Figure 4],[Figure 5],[Figure 6],[Figure 7],[Figure 8].
|Figure 3: Displacement of central incisor in all the four models along the X‑axis (transverse) and Z‑axis (vertical)|
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|Figure 4: Displacement of lateral incisor in all the four models along the X‑axis (transverse) and Z‑axis (vertical)|
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|Figure 5: Displacement of canine in all the four models along the X‑axis (transverse) and Z‑axis (vertical)|
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|Figure 6: Displacement of central incisor in all the four models along the Y‑axis (sagittal)|
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|Figure 7: Displacement of lateral incisor in all the four models along the Y‑axis (sagittal)|
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|Figure 8: Displacement of canine in all the four models along the Y‑axis (sagittal)|
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| Discussion|| |
Orthodontic tooth movement is primarily a periodontal phenomenon where a bony response is mediated by the PDL corresponding to a prolonged pressure exerted on the teeth. On force application to a tooth initial displacement is produced, and then, orthodontic tooth movement starts. Thus, it is of utmost importance to study the forces applied on teeth and stresses produced in PDL at initial movement. Orthodontic tooth movement might not start if the amount of these forces and stresses are not suitable to produce bone remodeling. If torque is not controlled during the retraction of the teeth, the inclination of incisors will be reduced and the amount of retraction will be increased. In sliding mechanics, the tendency toward lingual crown or lingual root movement of the anterior teeth will be determined by the direction of the retraction force and notably by the rotational effects derived from the relation of the line of action of the retraction force relative to the center of resistance. To achieve bodily displacement of anterior teeth during retraction, clinician should exert force passing through the center of resistance of the anterior segment or a horizontal force combined with the proper moment, which produces homogeneous stress distribution in the periodontium.
Thus, the aim of this study was to evaluate the stress distribution along the PDL and alveolar bone by various combinations of mini-implants and retraction hooks during en masse intrusion and retraction of anterior teeth by FEM.
FEM is a commonly applied experimental research technique which enables us to study the effects of geometrical and material variations under load and internal mechanical process. The analysis shows areas of internal stress concentration, and consequently, predictions can be made of possible failure. In the last decade, the application of FEM has revolutionized dental biomedical research due to advantages of the method such as the actual physical properties of the materials involved can be simulated. Furthermore, reproducibility does not affect the physical properties involved and close resemblance to natural conditions.
The von Mises stress values for the bone in all the four models are far below than the ultimate tensile strength of alveolar bone of 135 MPa. Furthermore, Sugiura et al. had suggested that the critical threshold for bone resorption should be approximately 50 MPa. Also the von Mises stress values for the PDL in all the four models are below than the ultimate tensile strength of the PDL of 2.4 MPa. Thus, the alveolar bone and PDL in all the four models were safe during en masse intrusion and retraction of anterior teeth.
In all the four models, maximum stress in PDL was found in the cervical area. Moreover, the nature of stress changes from tensile to compressive from cervical area to root apex. This is in accordance with the findings of Zhang et al. and Sung et al., In the study done by Zhang et al., also, the pattern of stress changes from tensile in the cervical area to compressive toward root apex. Sung et al. also found highest tensile stress distribution at the labiocervical third of the canine.
Displacement along the X-axis
In this study, in Model 1 and Model 2 where height of retraction hook is 6 mm, distal crown movement of lateral incisor was seen while canine crown moved lingually and canine root moved buccally. In Model 3 and Model 4 where height of retraction hook is 2 mm incisally, lateral incisor crown tipped distally while canine showed buccal crown movement. Along the X-axis, the different tipping trend of the lateral incisor and canine may result from the transverse moment force of retraction force. This outward force moment passed through the hook to the archwire and produced opposing archwire deformation at lateral incisor and canine. Torque produced at lateral incisor made its crown tipped distally. In Model 1 and Model 2, retraction force is near the center of resistance; thus, torque at canine caused its root to tip buccally and crown to tip lingually. While in Model 3 and Model 4, retraction force is away from the center of resistance; thus, torque at canine caused its crown to tip buccally.
Displacement along the Y-axis
Along the Y-axis, in Model 1, central incisor showed almost bodily movement while in Model 3, it showed lingual crown tipping. This observation is consistent with the studies done by Tominaga et al., Zhang et al., and Sung et al. While the study done by Ashekar et al. shows lingual tipping of central incisor when force applied at 0 mm, 5 mm, and 8 mm of ARH from low, medium, and high traction OMI. In this study, in Model 3, when force was applied onto the retraction hook of 2 mm placed incisally, more of lingual crown tipping occurred than in Model 1 where force is applied at the retraction hook of 6 mm. It suggests that the force in Model 1 is passing near the center of resistance where in Model 3, the force is passing away from the center of resistance. Force vector has two components, horizontal and vertical. Horizontal component of force is responsible for retraction while vertical component of force is responsible for extrusion. In Model 3, vertical component of force vector is more and horizontal component of force vector is less than in Model 1; thus, more amount of extrusion with lingual crown tipping of central incisor is seen in Model 3.
Placing a mini-implant between two central incisors in the midline helps apply additional vertical component of intrusion forces and a direct effect on the central incisors is expected. In this study, only 60 g of force was applied from central mini-implant which causes lingual root torquing of central incisors in Model 2; while in Model 4, bodily movement of central incisors was seen. Increase in the intrusive vertical component of force occurs due to additional central mini-implant. In both the Models 2 and 4, horizontal component of force remains same as in Models 1 and 3, respectively, but the vertical component of force increases due to central mini-implant and thus preventing the extrusion and lingual crown tipping of the central incisors. According to Tominaga et al., lingual crown tipping of maxillary incisors was observed when retraction force was at 0 mm (bracket slot level). The direction of tooth rotation was changed from lingual crown tipping to lingual root tipping on increasing the height of the retraction hook. According to Ashekar et al., labial tipping of incisors did not occurred in high mini-implant condition also. Thus, to maintain or gain the torque, it is beneficial to place the central midline mini-implant as placed in Model 2 and Model 4 in this study.
Lateral incisors in Model 1 and 2 showed almost near bodily movement which is similar to the study of Zhang et al. In Model 3 and 4, lateral incisors showed lingual crown tipping. As the force applied onto the incisal retraction, hook of 2 mm is away from the center of resistance, more of lingual crown tipping of incisors will occur. In a study done by Ashekar et al., lateral incisor showed bodily movement only at 5 mm of ARH with medium traction OMI and at 8 mm of ARH from high OMI. In Model 2, lateral incisor showed the bodily movement while central incisor showed the lingual root tipping this difference is due to the force is applied from the central midline mini-implant on lateral incisor is far from the central incisor. Similarly, in Model 4, central incisor showed bodily movement while lateral incisor showed the lingual crown tipping. According to traditional orthodontic biomechanics, maxillary anterior teeth should generate lingual crown tipping movements. Results of study done by Tominaga et al. showed that rectangular archwire maintained the inclination of the incisors to a certain degree, compared with round wire. Differences between movements of central and lateral incisors were due to the archwire torsion between them. Thus, archwire used for retraction should be rigid enough to maintain the arch form and the relative position of each tooth.
Canines showed distal tipping in all the four models. The distal crown tipping of canine is more when retraction hook was placed 2 mm incisally than to the 6 mm gingival retraction hook as the force is passing away from the center of resistance. On placing midline mini-implant between central incisors, as in Model 2 and Model 4, the control on distal tipping of canine was not much as compared to central and lateral incisors because the force applied from the central mini-implant is far from the canine and thus have less effect on the movements of the canines. Such tipping movement of the canine can be due to torque loss because of archwire torsion as stated by Zhang et al. In addition, the canine at the back of this segment bared most of the palinal retraction force. Torque transmitted to maxillary canines could be insufficient to counteract the trend of distal crown tipping.
Displacement along the Z-axis
In this study, central and lateral incisors in Models 1, 3, and 4 showed extrusion of crowns while Model 2 with the midline mini-implant showed intrusion. This extrusion was slight and was limited to mostly crowns. Studies of Sung et al., Zhang et al., and Ashekar et al. showed intrusion of central incisors. Such difference in the vertical movement of the central incisor could be due to the height of the retraction force and amount of lingual crown tipping of central incisors. As in a study done, intrusion of the incisors was seen when force was applied at 0 mm of ARH from medium and high traction OMI and 5 mm of ARH from high traction OMI . However, placing mini-implants apically at higher levels possess difficulties and limitations. Furthermore, in other studies, controlled crown lingual tipping of central incisors was seen while in this study, more bodily movement of the central incisors is seen. In Model 2, slight intrusion of crown of the central and lateral incisor was seen which was due to the midline mini-implant force. Although midline mini-implant placed in Model 4, still extrusion of central and lateral incisors was seen in Model 4 due to retraction force acting at a larger distance from the center of resistance increasing the moment arm. Although initial displacements of each tooth may vary, their long-term vertical movements will be concordant and are dependent on the relationship between the retraction force direction and the center of resistance.
Limitations of the finite element study
Analytical results of FEM are highly dependent on the models developed; therefore, they have to be constructed to be equivalent to real objects in various aspects. The results of this study were obtained from simulated models, from which biologic variabilities may occur. Similar to previous studies, the PDL was modeled as a layer of uniform thickness and was treated as linear elastic and isotropic even though the PDL exhibits anisotropy and nonlinear viscoelastic behavior because of tissue fluid. There is no reliable and adequate data that pertain to anisotropic and nonlinear properties of the PDL. Another limitation of this study is the inability to directly predict long-term tooth movement quantitatively through simulation. Finite element model can only calculate initial tooth displacement and stress distribution after force application. The biological and time-dependent reaction is still unpredictable and requires more clinical evidence.
| Conclusion|| |
The nature of stress distribution in PDL changes from being tensile around the cervical region to compressive toward the root apex of the lateral incisors and canines. The teeth showed almost bodily movement and controlled lingual crown tipping when the gingival retraction hook of 6 mm was used. It suggests that the retraction force is passing near the center of resistance. On placing incisal retraction hook of 2 mm, more amount of lingual crown tipping occurred suggesting that retraction force is passing away from the center of resistance. On application of 60 g of vertical intrusive force from the midline implant between central incisors, lingual root displacement, control on lingual crown displacement, and intrusion can be obtained. And thus, Model 2 simulation can be considered as more reliable to obtain the controlled intrusion and retraction of the maxillary anterior teeth.
With the help of this study, the biomechanics for the bodily displacement, lingual crown tipping, labial crown diplacement, intrusion and extrusion of anterior teeth can be determined and managed.
The length of power arm could be considered the main influencing factor in determining the degree and course of movement of anterior teeth during sliding mechanics retraction. Thus, the retraction hook height could be the most easily modifiable clinical factor in determining and achieving the most desirable direction of anterior teeth displacement during intrusion and retraction of anterior teeth. This leads to a very important clinical clue. The clinical application of these findings relates to the chair-side simple estimation of the location of the center of resistance and height of retraction force on power arm in relation to preprogrammed tooth movement.
Finite element studies have provided the orthodontist with new concepts on the behavior of the oral and dental tissues in response to the forces. Although it is not possible to simulate the in vivo conditions' tissue fluids, cells, blood, and blood pressures, results obtained of finite element studies have been found to be highly reliable.
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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], [Figure 7], [Figure 8]
[Table 1], [Table 2], [Table 3]