|Year : 2016 | Volume
| Issue : 1 | Page : 34-43
A finite element analysis of initial stresses and displacements in the tooth and the periodontium in periodontally compromised simulations: Labial versus lingual force application
Jayam Bharath Kumar1, Gudimetla Jaisekhar Reddy2, Moturi Sridhar3, T Jayasimha Reddy4, Pyata Jaipal Reddy5, Sadam Srinivasa Rao6
1 Department of Orthodontics and Dentofacial Orthopedics, Dr. Syamala Reddy Dental College and Hospital, Bangalore, Karnataka, India
2 Department of Oral and Maxillofacial Surgery, Dr. Syamala Reddy Dental College and Hospital, Bangalore, Karnataka, India
3 Department of Conservative Dentistry and Endodontics, Jaipur Dental College, Jaipur, Rajasthan, India
4 Department of Prosthodontics, Al Badar Dental College, Bidar, Karnataka, India
5 Department of Orthodontics and Dentofacial Orthopedics, S.V. Institute of Dental Sciences, Mahabubnagar, Telangana, India
6 Department of Oral and Maxillofacial Surgery, Army College of Dental Sciences, Secunderabad, Andhra Pradesh, India
|Date of Web Publication||18-Mar-2016|
Jayam Bharath Kumar
Department of Orthodontics and Dentofacial Orthopedics, Dr. Syamala Reddy Dental College and Hospital, Bangalore, Karnataka
Source of Support: None, Conflict of Interest: None
Introduction: Orthodontics a unique branch in dentistry is inter-related with biology, mathematics and engineering sciences. Biomechanics is fundamental to the practice of orthodontics. Stresses generated at any point during orthodontic treatment are critical in remodeling of bone and type of tooth movement.
Aims and Objectives: The aim of the following study is to determine the initial stresses produced in the tooth, periodontal ligament (PDL) and bone when force is applied on the tooth for intrusion and tipping on labial and lingual sides in the presence of varying alveolar bone heights.
Materials and Methods: A geometric model generated using AutoCAD (Autodesk, Inc.). Six three-dimensional finite element models of a maxillary central incisor were designed with PDL and varying alveolar bone heights after applying the boundary conditions of the model, force was applied on the tooth.
Results: Results were obtained with color coded three-dimensional fringe patterns.
Conclusion: Alveolar bone loss causes an increase in the maximum initial stresses relative to the bone heights.
Keywords: Adult orthodontics, alveolar bone loss and orthodontics, finite element analysis
|How to cite this article:|
Kumar JB, Reddy GJ, Sridhar M, Reddy T J, Reddy PJ, Rao SS. A finite element analysis of initial stresses and displacements in the tooth and the periodontium in periodontally compromised simulations: Labial versus lingual force application. J NTR Univ Health Sci 2016;5:34-43
|How to cite this URL:|
Kumar JB, Reddy GJ, Sridhar M, Reddy T J, Reddy PJ, Rao SS. A finite element analysis of initial stresses and displacements in the tooth and the periodontium in periodontally compromised simulations: Labial versus lingual force application. J NTR Univ Health Sci [serial online] 2016 [cited 2020 Mar 31];5:34-43. Available from: http://www.jdrntruhs.org/text.asp?2016/5/1/34/178976
| Introduction|| |
Orthodontics a unique branch in dentistry is inter-related with biology, mathematics and engineering sciences. While orthodontic mechanics refers to the effect of force on teeth, periodontal ligament (PDL) and bone, the principles of orthodontic mechanics are based on dogmas of engineering principles. The orthodontist should therefore have a sound knowledge of bioengineering principles for an efficient and effective management in orthodontic practice.
The application of mechanical forces to produce orthodontic tooth movement carries with it some calculated risks particularly in adult patients where periodontal compromise is a most common feature. The resulting increase in the crown-to-root ratio contributes to the major risk of further bone loss and root resorption in an already periodontally compromised condition particularly with intrusion and controlled tipping tooth movements. The magnitude and point of force application relevant to adult orthodontics should therefore be carefully calibrated.
The percentage of adults seeking orthodontic treatment has increased significantly in the recent decades and the major challenge in adult orthodontics is to perform an efficient controlled tooth movement because of an increased crown-to-root ratio.
The study of orthodontic biomechanics requires the understanding of the nature of induced stress and strain to the periodontium. The effect of force application on periodontal tissue remodeling has been a subject of extensive research in orthodontics. Dental movements have been widely studied from many points of view namely, histological, histochemical, physiological, and biomechanical in both man and in an experimental animal. In-vitro simulations by photoelastic stress analysis, mathematical models and laser holography have also been attempted. All these methods have shortcomings in their analysis and studies. To overcome these problems finite element method (FEM) is being used in the more recent studies to evaluate the displacements, initial stresses and strains in the periodontium.
The PDL, tooth and alveolar bone all being deformable entities under a load, the patterns of initial stress distribution in them may be influenced by anatomic variables such as morphometrics and mechanical properties of each tissue. Stress in the PDL being the initiating factor in orthodontic tooth movement, a range of stresses is transmitted to the alveolar bone through the PDL. It is therefore essential to treat these tissues as a continuous unit for a quantitative assessment.
The FEM provides the orthodontist with quantitative data that can extend the understanding of the physiologic reactions that occur in-vitro. Such numerical techniques may yield an improved understanding of the reactions and interactions of individual tissues.
In the present study, FEM is being used to study the effect of force on periodontally compromised simulations, in-vitro. The FEM affords a method to accurately analyze the interaction between surrounding tissues and to numerically evaluate and visualize the stress and strain perceived by the various tissues in-vitro.
| Aims and Objectives|| |
The aims and objectives of this study are to determine the initial stresses produced in the tooth, PDL and bone when one Newton of force is applied on the tooth for intrusion and tipping on labial and lingual sides in the presence of varying alveolar bone heights. The study also determines the initial displacement of tooth in the PDL when force is applied on the tooth for intrusion and tipping separately.
| Materials and Methods|| |
A geometric model was generated using AutoCAD (Autodesk, Inc.) (computer aided designing) software [Figure 1]. Six three-dimensional finite element models of a maxillary central incisor were designed with PDL and varying alveolar bone heights of 12, 11, 9.5, 7, 5.5 and, 4 mm [Figure 2] [Figure 3] [Figure 4] [Figure 5]. Each model was morphometrically designed according to the textbook of "Ash's (Wheelers)  dental anatomy." Young's modulus and Poisson's ratio of tooth, PDL and bone were given to the software. (Young's modulus for tooth, PDL, and bone are 20,300, 0.667, and 13,700, whereas Poisson's ratio is 0.3, 0.49, and 0.38 N/mm 2 respectively). To evaluate forces at the nodes a numbering system identifying each nodal point with co-ordinates of each nodal point were noted with specified boundary constrains [Table 1]. After the data was specified, the displacements and the initial stresses were calculated using the ANSYS-7.1 (Ansys, Inc.) software.
|Figure 4: Three-dimensional picture of tooth, periodontal ligament and bone|
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|Figure 5: Three-dimensional pictures of the tooth with different bone heights|
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Magnitude of the force at all stages of the study was 1 N. Labial side force was applied on the center of the crown at 5.5 mm apical to the incisal edge, 16 mm from the root apex, on the long axis of the tooth. Lingual side force was applied at the center of the crown mesiodistally and 7 mm apical to the incisal edge, 14.5 mm from the root apex. Tipping force was applied in labiolingual direction and intrusive force in apical direction.
The three-dimensional model was oriented in such a way that mesiodistal planes were represented by X-axis, the vertical plane was represented by the Y-axis and labiolingual plane was represented by the Z-axis. Software specifications: Microsoft Windows (Microsoft), AutoCAD (Autodesk, Inc.), FEA software (LS-DYNA, USA), ANSYS-7.1 (Ansys, Inc.). After applying the boundary conditions of the model, force was applied on the tooth. Results were obtained with color coded three-dimensional fringe patterns [Figure 6] [Figure 7] [Figure 8] [Figure 9].
|Figure 6: Intrusion — labial side force application — stresses on the tooth|
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|Figure 7: Intrusion — labial side force application — stresses on the periodontal ligament|
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|Figure 8: Tipping — labial side force application — stresses on the tooth|
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|Figure 9: Tipping — labial side force application — stress on the periodontal ligament|
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| Results|| |
When 1 N of intrusion and tipping forces were applied on labial side of the tooth separately, stresses produced on the tooth, PDL and bone are shown in [Table 2].
|Table 2: Different bone heights and intial stress produced on tooth, periodontal ligament and bone for intrusion and tipping forces applied on labial side|
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When 1 N of intrusion and tipping forces were applied on the lingual side of the tooth separately, stresses produced on the tooth, PDL and bone are shown in [Table 3].
|Table 3: Different bone heights and initial stress produced on tooth, periodontal ligament and bone for intrusion and tipping forces applied on lingual side|
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Initial displacements of the tooth are mentioned in [Table 4] when 1 N of force was applied on the tooth labially and lingually separately.
On labial side in both intrusive and tipping forces the PDL perceived more stresses than the tooth and bone. In 4 mm bone height, stresses were 6 times greater for intrusive force and 5 times greater for tipping force when compared with 12 mm bone height. For intrusive force stresses increased apically, whereas stresses decreased apically for tipping force in the PDL.
|Table 4: Different bone heights and initial displacements of tooth when 1 n force Applied on tooth|
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On the lingual side in both intrusive and tipping forces PDL perceived more stresses than the tooth and bone, but in 4 mm bone height for tipping force tooth and bone perceived more stresses than PDL. In 4 mm bone height stresses were 2.4 times greater for intrusive force and 5 times greater for tipping force when compared to 12 mm bone height. For intrusive force stresses increased apically whereas stresses decreased apically for tipping force in the PDL.
| Discussion|| |
The present study highlights a method for in-vitro quantification of initial stresses and displacement perceived by tooth and periodontium during orthodontic tooth movement. The effect of labial versus lingual surface for force application in a simulated periodontally compromised situation is also evaluated.
Periodontal compromise, a major challenge in adult orthodontics, the varying bone levels and its implications from the point of view of change in the center of resistance has been assessed in the earlier studies.  Melsen  suggested applying a mild intrusive force in the treatment of adult patients with reduced bone height. On the other hand, some authors have reported an increased risk of root resorption in adult patients when large orthodontic forces are applied to produce continuous bodily (Thailander, 1985) and intrusive movement.  Maxillary  and mandibular incisors  have been shown to be more frequently involved than other teeth in apical root resorption. Lu et al.  have demonstrated higher activity of resorption in the apical root region than in the inter-radicular area. The occurrence of apical root resorption cannot be predicted on the basis of the morphology of the facial and dentoalveolar structures.  Cobo et al.  used FEM to determine the stress that appears in tooth, periodontal membrane (PDM) and alveolar bone when a labiolingual force of 100 g is applied in a labiolingual direction in a midpoint of the crown of lower canine, and its changes depending on the degree of loss of the supporting bone. They observed that, after applying the labiolingual force in the canine, a progressive increase in the stress of the labial and lingual zones of the tooth, PDM and alveolar bone, when the alveolar bone was reducing. In an article in 1996, Costopoulos and Nanda  have shown that it is impossible to correlate the amount of root resorption with the degree of intrusion. Resorption has been reported  to be less frequent and less severe in endodontically treated incisors than in vital teeth.  Andersen et al.  conducted a FEM study to obtain stress profiles for various force systems-as tipping, translation and root movement. They reported that there was a marked variation in the stress distribution from the cervix to apex when tipping forces were applied. Bodily tooth movement almost produced uniform stress distribution, and root movement produced stress patterns opposite to those observed during tipping.
In orthodontics, the study of initial stress concentration in the PDL is important because the ligament acts as a mediator for the tooth movement and any alteration from the optimal force produces adverse effects on the tooth and periodontium such as apical root resorption and alveolar bone loss. Orthodontic root resorption is frequently preceded by hyalinization of the PDL.  Kurol and Owman-Moll  have shown hyalinized areas opposite an intact root surface or close to an area of root resorption. An optimal force intends to induce a maximal cellular response and to establish stability of the tissue. An unfavorable force does not result in a precise biologic response and may initiate adverse tissue reactions. Middleton et al.  used FEM study to evaluate stresses and strains within the PDL and surrounding bone consequent to orthodontic loading of a tooth. These results suggested that the remodeling process may be controlled by PDL rather than the bone. During the initial force application, compression in limited areas in PDL frequently impedes vascular circulation and cell differentiation causing degradation of cells and vascular structures rather than proliferation and differentiation. The tissue change during this period is called hyalinization. The process of hyalinization is dependent on the local morphology of the compressed area, the magnitude of the applied force on the tooth and the duration of this force.
The most frequent complication preventing rapid tooth movement occurs when the applied force compresses the tooth against the alveolar bone that the PDL responds with local degeneration and sterile necrosis instead of cells that would have been able to perform the necessary reconstruction. This situation may lead to permanent damage on the involved tooth and its periodontium. 
Intrusive movement of the tooth produces maximum stresses at apical region of the PDL. When these stresses are beyond the optimal stresses, extensive hyalinization occurs in the PDL at the root apex which may cause apical root resorption. 
Tipping, the simplest form of tooth movement tends to concentrate stresses in limited areas of PDL. Its greatest effects were seen slightly below the alveolar crest. Owing to the development of a fulcrum, the portion of the root apical to this fulcrum moves in the opposite direction to that of the crown. The compressive stresses generated at the root apex can cause extensive hyalinization and therefore increase the risk for apical root resorption.  Because of the increased stress concentration at the cervical level bone loss at the alveolar crest also takes place.
The FEM has been used extensively for biomechanical investigations in dentistry, especially in orthodontics. The three-dimensional FEM model is a useful tool to simulate and analyze the stresses that occur in and around a tooth in response to an applied force.  The FEM is a numerical method of engineering mechanics, where the structure to be investigated is discretized into a certain finite number of elements. The mechanical behavior of each element is described by a set of differential equations that can be solved with the aid of a computer program. Based on the material parameters and force applied, it is possible to determine the mechanical stresses and strains as well as displacements of the individual components of the model. The flexibility of the FEM in modifying geometry allowed the simulation of various amounts of bone loss. The greatest strength of the FEM model is that it can be magnified nearly infinitely both in terms of the actual volumetric construction itself and the mathematical variability of its material parameters.
Since the analyzed results were dependent on the model used and related directly to the input data, the model was examined repeatedly for geometric and mechanical equivalences. As is usually the case with finite element analysis, boundary conditions of the model were established at the peripheral region of the bone to eliminate unreasonable motion of the whole model. Boundary condition restricts the stresses in the periodontium to that particular area of the FEM model; whereas in the biological system stresses transmit to the surrounding bones through the trajectories of the maxilla and mandible. Therefore, the stress concentrations were more in the FEM model compared to the biological system for the same magnitude of the force. This study demonstrated that the FEM provides a solid, workable foundation for modeling the system.
The results of the present study showed a significant increase in the initial stress concentration and displacement in the PDL due to an increased crown-to-root ratio. Because of the reduced bone support and PDL area, the same magnitude of load on the crown caused more stresses and displacements in the PDL of compromised models rather than the normal models as given below.
When force is applied on the labial side for intrusion the initial stresses perceived by the tooth, PDL and bone were gradually increased when bone heights were reduced from 12 to 4 mm. The PDL received the maximum initial stresses and increased apically and was compressive in nature at apical level.
In 4 mm bone height stresses perceived by PDL were 6 times greater for intrusive force when compared to 12 mm bone height for the same magnitude of the force. Stresses were increased in the PDL when bone heights were reduced, but there was minimal increase in the stress values from 12 to 9.5 mm bone heights and stresses were significantly increased from 7 to 5.5 mm and from 5.5 to 4 mm bone heights. The findings imply that, in severe bone loss conditions intrusion requires careful control of force magnitude that will produce light force and minimal stress. Because, the stresses are concentrated in a small area at the root apex, increased stress may induce more hyalinization and apical root resorption, further damaging the periodontium. , Geramy  used FEM to find out initial stresses produced in the PDM by orthodontic loads in the presence of varying bone loss. The results revealed that alveolar bone loss caused increased stress production under the same load compared with healthy bone support.
When force is applied on the labial side for tipping initial stresses was maximum at the cervical level. In 4 mm bone height initial stresses were 5 times greater when compared to 12 mm bone height in the PDL. Stresses were increased in the PDL when bone heights were reduced, but there is no significant change in the stresses for 12 mm, 11 mm, 9.5 mm and the stresses were almost double when bone height reduced from 9.5 to 7 mm, 7 to 5.5 mm and 5.5 to 4 mm bone heights.
Bone received less stress compared to the tooth and PDL and were not distributed uniformly.
When force was applied on the lingual side results showed the same pattern as labial side force application, but stresses produced were less compared to labial side force application.
When force was applied on the lingual side for intrusion in 4 mm bone height, PDL perceived more compressive stresses at apical level, although less compared to when the same load was applied labially. In 4 mm bone height stresses at the PDL were 2.4 times greater for intrusive force when compared to 12 mm bone height. Stresses were increased in the PDL when bone heights were reduced, but there is no significant change in the stresses for 12 mm, 11 mm, 9.5 mm and the stresses were significantly increased from 9.5 to 7 mm, 7 to 5.5 mm and reached the highest levels for 4 mm bone height [Table 5].
|Table 5: Comparison of stress on tooth, periodontal ligament and bone for 12 mm and 4 mm bone height for intrusion and tipping force|
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When force was applied on the lingual side for tipping in 4 mm bone height, PDL and bone perceived excessive compressive stresses which probably highlight the extent of injury that all the tissues could be subjected to in a periodontally compromised situation. In 4 mm bone height stresses were 5 times greater for tipping force when compared to 12 mm bone height in the PDL. Stresses were increased in the PDL when bone heights were reduced, but there is no significant change in the stresses for 12 mm, 11 mm, 9.5 mm and the stresses were almost double when bone height reduced from 9.5 to 7 mm, 7 to 5.5 mm and reached highest levels for 4 mm bone height implying the need to reduce force levels in periodontally compromised situations.
A comparison of forces applied on labial and lingual side, reveal that the stresses in the PDL were reduced with lingual force application compared to labial force application, significantly more for intrusion and less for tipping, implying the need for a lingual point of force application when intrusion is necessary. In lingual orthodontics, the bracket position and application of force are closer to the center of resistance of the tooth than is found with labial bracket placement.  An important clinical implication of the lingual bracket position is that the intrusive force vector is directed through the center of resistance of the tooth. As mentioned in the earlier studies center of resistance for maxillary incisors is placed on the lingual side. ,, Tanne et al. (1998)  used FEM to investigate the stress levels induced in periodontal tissue by orthodontic forces. Studies revealed that during tipping movement stresses nonuniformly varied with a large difference from the cervix to the apex of the root.
In orthodontics, the nature of initial tooth displacement is also of great interest in terms of an optimal force application and subsequent tooth movement. Patterns of initial tooth displacement of a tooth may be influenced by such anatomic variables as dimensions of the tooth and alveolar bone, widths of the PDL space and the attributed mechanical properties of the periodontium.
Tanne et al. (1987)  investigated the nature of initial tooth displacements associated with varying root lengths and alveolar bone heights with FEM and the results revealed that moment to force ratio values at the bracket level for translation of a tooth decreased with shorter root length and increased with lower alveolar bone height.
The present study was also intended to investigate the nature of initial tooth displacements associated with varying alveolar bone heights. In both intrusive and tipping movements' initial displacement of tooth within the PDL gradually increased in response to the reduced bone heights. In 4 mm bone height when force is applied on the labial side initial displacement was almost 4 times greater for intrusive force and 3 times greater for tipping force when compared to 12 mm bone height. For the same bone height when force is applied on the lingual side initial displacement was almost 4 times greater for intrusive and tipping forces when compared with 12 mm bone height implying that orthodontic forces must be kept low for optimal tooth movement.
The results of the present study have been in consonance with other studies. Geramy (2000)  concluded that for tipping forces highest stresses were found in the cervical level. Stress concentrations were the highest in sub-apical level for intrusive force. He also concluded that the alveolar bone resorption caused an increase in the maximum principal stresses. In an article in 1994, Wilson et al.  constructed a three-dimensional finite element model of maxillary canine and studied the stresses in the PDL when 1 N of intrusive and extrusive forces was applied on the tooth. They noticed that stresses were compressive entirely for intrusive forces and entirely tensile for extrusive forces. They demonstrated that the highest stresses are developed within the PDL in the area closest to the point of force application, while on the opposite side of the tooth model, this stress drops to a very low level. In 2001 Rudolph et al.  showed that stresses were concentrated at alveolar crest for tipping movement and at the root apex for the intrusive and extrusive movements.
However, the differences in the absolute values in the results obtained between the present study and those of the other previous studies could be due to the following reasons - assumptions of physical properties of the tooth and periodontium, differences in morphometrics of the tooth and PDL dimensions, the software used for the analysis and the number of nodes and elements used in the study.
The limitations of the present study however, are as with any in-vitro study, with a few inadequacies. The FEM, though the closest simulation method possible, is only a theoretical representation of a biological system. The differences in mechanical properties between juvenile and adult periodontium also needs to be considered for further FEM studies in adult orthodontics.
The present study mainly concentrated on initial stresses and initial displacements on periodontally compromised conditions. Further studies are required to evaluate the optimum orthodontic force for intrusion and tipping movements in periodontally compromised conditions. Furthermore, the root resorption and alveolar bone loss patterns need to be studied with further definition of the FEM model.
| Conclusion|| |
The conclusions of this study are as follows:
- Alveolar bone loss caused an increase in the maximum initial stresses relative to the bone heights
- When the tipping force was applied on the model the highest level of stresses were found at the cervical level
- An intrusive force causes a highest stress concentration at the apical level when the force applied on labial as well as lingual side
- Stresses were significantly less for the lingual side force application compared to the labial side for intrusion. Therefore, lingual point of force application is suitable when intrusion is necessary in case of periodontally compromised conditions
- Tipping force also produced less stresses when force was applied on the lingual side compared to labial side force application
- When the tipping and intrusive force applied on the tooth initial tooth displacements increased with the reducing bone heights.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]