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Table of Contents   
ORIGINAL RESEARCH  
Year : 2012  |  Volume : 23  |  Issue : 2  |  Page : 213-220
Apical stress distribution on maxillary central incisor during various orthodontic tooth movements by varying cemental and two different periodontal ligament thicknesses: A FEM study


1 Department of Orthodontics and Dentofacial Orthopedics, Thai Moogambigai Dental College and Hospital, Chennai, India
2 Department of Orthodontics and Dentofacial Orthopedics, Meenakshi Ammal Dental College and Hospital, Chennai, India

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Date of Submission08-Apr-2011
Date of Decision15-Jul-2011
Date of Acceptance13-Feb-2012
Date of Web Publication3-Sep-2012
 

   Abstract 

Context: During fixed orthodontic therapy, when the stress levels in the periodontal ligament (PDL) exceedsan optimum level, it could lead to root resorption.
Aims: To determine an apical stress incident on the maxillary central incisor during tooth movement with varying cemental and periodontal ligament thickness by Finite Element Method (FEM) modeling.
Settings and Design: A three dimensional finite element model of a maxillary central incisor along with enamel, dentin, cementum, PDL and alveolar bone was recreated using EZIDCOM and AUTOCAD software. ALTAIR Hyper mesh 7.0 version was used to create the Finite Element meshwork of the tooth. This virtual model was transferred to Finite Element Analysis software, ANSYS where different tooth movements were performed.
Materials and Methods: Cemental thickness at the root apex was varied from 200 μm to 1000 μm in increments of 200 μm. PDL thickness was varied as 0.24 mm and 0.15 mm. Intrusive, Extrusive, Rotation and Tipping forces were delivered to determine an apical stress for each set of parameters.
Results: Results indicated that an apical stress induced in the cementum and PDL, increased with an increase in cementum and PDL thickness respectively. Apical stress induced in the cementum remained the same or decreased with an increase in the PDL thickness. Apical stress induced in the PDL decreased with an increase in the cementum thickness.
Conclusion: The study concluded that the clinical delivery of an orthodontic forces will cause stress in the cementum and PDL. Hence, it is necessary to limit the orthodontic force to prevent root resorption.

Keywords: Cemental stress, FEM, finite element analysis, PDL stress, root resorption

How to cite this article:
Vikram N R, Senthil Kumar K S, Nagachandran K S, Hashir Y M. Apical stress distribution on maxillary central incisor during various orthodontic tooth movements by varying cemental and two different periodontal ligament thicknesses: A FEM study. Indian J Dent Res 2012;23:213-20

How to cite this URL:
Vikram N R, Senthil Kumar K S, Nagachandran K S, Hashir Y M. Apical stress distribution on maxillary central incisor during various orthodontic tooth movements by varying cemental and two different periodontal ligament thicknesses: A FEM study. Indian J Dent Res [serial online] 2012 [cited 2021 Oct 19];23:213-20. Available from: https://www.ijdr.in/text.asp?2012/23/2/213/100429

   Introduction Top


Orthodontic tooth movement is primarily a periodontal ligament (PDL) phenomenon. It is a bony response being mediated by the PDL when prolonged pressure is applied to the tooth. Various experimental techniques like animal experiments, [1] histological methods, [2],[3] strain gauge techniques, [4],[5] photo elastic methods [6] have been used to analyze the effects of orthodontic forces on teeth and the periodontal tissues. Finite element method has been used in engineering principles since its introduction by Farah in 1973. [7] Studies have included multi-rooted teeth [8],[9] along with an alveolar bone for stress analysis and they have concluded FEM to be a valuable non-invasive tool for analyzing the mechanical stress distribution within the periodontium during orthodontic force application. In recent years, researchers have recreated 3-D FE models of teeth and supporting tissues. [10],[11],[12] Different types of orthodontic tooth movements may produce different mechanical stresses at varying locations along the root. To plan for an efficient tooth movement, the clinician must understand the nature of the force being applied and the stress distribution in and around the investing tissues. [13],[14],[15],[16] The magnitude of applied forces should be well within the optimum levels as described by earlier investigators. [17]

Root resorption has been extensively researched and authors have reported that it could occur if orthodontic forces exceeds the capillary blood pressure (0.0020 to 0.0047 MPa). [5],[18] Maxillary central incisor was chosen in this study because during treatment, they are subjected to orthodontic forces for a prolonged period. [19],[20] More recently, studies have been conducted to correlate the stress distribution during orthodontic tooth movement and its relation to the root resorption. Shaw & Sameshima [21] determined the relationship between the thickness of cementum and magnitude of stress at root apex and concluded that the mechanical stress was found to increase at the root apex with an increase in the thickness of an apical cementum.

The objectives of this study were to determine an apical stress distribution in the maxillary central incisor during Intrusion, Extrusion, Tipping and Rotation tooth movements using three dimensional finite element modeling.

And also to evaluate the,

  • PDL stress distribution with varying cementum thickness
  • Periodontal ligament stress distribution with varying periodontal ligament thickness
  • Cementum stress distribution with varying cementum thickness
  • Cementum stress distribution with varying periodontal ligament thickness in all the four types of tooth movement.

   Materials and Methods Top


This study was conducted using three dimensional finite element analyzes to evaluate an apical stress distribution on a maxillary central incisor with various cementum thicknesses at root apex on application of various orthodontic tooth movements for two different periodontal ligament thicknesses.

Material Properties

Basically, four parameters will influence the predictive accuracy of a mechanical FE model.

  • Geometric details of an object to be modeled.
  • Choice of an element type
  • Material properties
  • Boundary conditions.
Computer softwares used are:

  • EZIDICOM AUTOCAD PRO/ENGINEER WILDFIRE 2.0 version
  • ALTAIR Hyper mesh 7.0 version
  • ANSYS 10.0 version.
The study was carried out in 4 steps

First, finite element model of an ideal central incisor with layer separating enamel, dentin, pulp & cementum including PDL & an alveolar bone was prepared [Figure 1].
Figure 1: 3D Finite element model of tooth

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Next, the PDL thickness was varied as 0.15 mm & 0.24 mm to simulate an adult and an adolescent PDL.

Third step was to prepare five models with varying thickness of cementum at an apex from 200 μm to 1000 μm adding in increments of 200 μm for both, 0.15 mm & 0.24 mm PDL thickness.

Finally, standard intrusion, extrusion, tipping & rotation forces as recommended were applied on the mesh of the central incisor model.

Material properties

Material properties were assigned to the various structures such as an alveolar bone, enamel, dentin, cementum, pulp, PDL in the finite element model. The material properties assigned in this study conform to data available from previous studies [22],[23] [Table 1].
Table 1: Youngs modulus and poissions ratio of the tooth

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Analytical considerations

FE model was then imported into the ANSYS version 10.0 software and parameters of Young's modulus and Poisson's ratio for tooth and periodontal ligament were established. Analysis was done with 10 models and each had been given 4 types of movement - intrusion, extrusion, tipping, and rotation and a non-linear stress analysis was carried out.

Interpretation of stress from FEM pictures

The stress generated in FEM pictures were represented by various - colors ranging from blue to red. The color coding was dependent on the force magnitude applied. Maximum stress areas are marked as (MX); and minimum stress areas are marked as (MN). However, the values for maximum and minimum stress areas will differ. For example, for intrusion, in 0.15 mm PDL with cementum thickness of 200 μm, the red area represents a stress of 0.445 E-4 whereas in the 0.24 mm PDL model with same cementum thickness, the red area represents a stress of 0.470 E-4 [Figure 2].
Figure 2: Tooth movements with finite element method

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However, in clinical situation, the stresses applied through the bracket to the tooth structure will be dissipated to the supporting structures like cementum, PDL and an alveolar bone. It is apparently difficult to mimic the same condition in the FEA study and the limitations should be considered.


   Results Top


Maximum PDL stress was seen when an extrusive force was applied for a cemental thickness of 200 μm and PDL thickness of 0.24 mm. Maximum cemental stress was observed when a tipping force was applied for a cemental thickness of 1000 μm and PDL thickness of 0.24 mm. The Results are shown in [Table 2] for PDL stress and [Table 3] for cemental stress.
Table 2: Periodontal ligament stress (Mpa)

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Table 3: Cementum stress values (Mpa)

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Periodontal stress

Extrusion

  • With 0.15 mm PDL thickness, the highest PDL stress (0.648 E-08 MPa) was seen in 400 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest PDL stress (1.00 E-08 MPa) was seen in 200 μm cementum thickness.
  • Generally, in extrusion, highest PDL stress was seen in 200 μm cemental thickness of 0.24 mm PDL thickness.
Intrusion

  • With 0.15 mm PDL thickness, the highest PDL stress (0.185 E-08 MPa) was seen in 400 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest PDL stress (0.286 E-08 MPa) was seen in 200 μm cementum thickness.
  • Generally, in intrusion, highest PDL stress was seen in 200 μm cemental thickness of 0.24 mm PDL thickness.
Rotation

  • With 0.15 mm PDL thickness, the highest PDL stress (0.779 E-08 MPa) was seen in 200 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest PDL stress (0.739 E-08 MPa) was seen in 1000 μm cementum thickness.
  • Generally, in rotation, highest PDL stress was seen in 200 μm cemental thickness of 0.15 mm PDL thickness.
Tipping

  • With 0.15 mm PDL thickness, the highest PDL stress (1.98 E-08 MPa) was seen in 200 μm 400 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest PDL stress (2.63 E- 08 MPa) was seen in 200 μm cementum thickness.
  • Generally, in tipping, highest PDL stress was seen in 200 μm cemental thickness of 0.15 mm PDL thickness.
Cemental stress

Extrusion

  • With 0.15 mm PDL thickness, the highest cemental stress (2.37 E-04 MPa) was seen in 1000 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest cemental stress (2.63 E-04 MPa) was seen in 1000 μm cementum thickness.
  • Generally, in extrusion, highest cemental stress was seen in 1000 μm cemental thickness of 0.24 mm PDL thickness.
Intrusion

  • With 0.15 mm PDL thickness, the highest cemental stress (0.677 E-04MPa) was seen in 1000 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest cemental stress (0.751 E-04 MPa) was seen in 1000 μm cementum thickness.
  • Generally, in intrusion, highest cemental stress was seen in 1000 μm cemental thickness of 0.24 mm PDL thickness.
Rotation

  • With 0.15 mm PDL thickness, the highest cemental stress (2.36 E-04 MPa) was seen in 200 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest cemental stress (2.29 E-04 MPa) was seen in 1000 μm cementum thickness.
  • Generally, in rotation, highest cemental stress was seen in 200 μm cemental thickness of 0.15 mm PDL thickness.
Tipping

  • With 0.15 mm PDL thickness, the highest cemental stress (4.82 E-04 MPa) was seen in 1000 μm cementum thickness.
  • With 0.24 mm PDL thickness, the highest cemental stress (5.05 E-04 MPa) was seen in 1000 μm cementum thickness.
  • Generally, in tipping, highest cemental stress was seen in 1000 μm cemental thickness of 0.24 mm PDL thickness.

   Discussion Top


The periodontal ligament (PDL) experiences relatively high stress on an application of orthodontic forces during tooth movement. [7],[24] Experimental techniques have their limitations in measuring these internal stress levels of the PDL. Strain gauge techniques may be useful in measuring tooth displacement however, they cannot be directly placed in the PDL without causing tissue damage. [25] The photo elastic techniques also have their limitations in determining the stress due to the crudeness of modeling and an interpretation. [6] However, FEM makes it possible to analytically apply various force systems at any point and in any direction. Hence, in this study, we created a FEM model for analyzing stress distributions within the periodontium during various tooth movements. The accuracy of computer models however depends on assigned constitutive properties and results are based on the nature of modeling systems. For this reason, the procedure of modeling is of paramount importance.

Maxillary central incisor was chosen because during orthodontic treatment, they are usually subjected to orthodontic forces for prolonged periods; and also owing to the fact that most studies stated that an apical root resorption occurs mainly in the anterior teeth with the maxillary teeth being more severely affected than the mandibular teeth. [19],[20] Thus in this study, three dimensional finite element model of a maxillary central incisor was created. Jones et al, [7] developed a three dimensional FE model of a central incisor using 15,000 four noded tetrahedral elements. This element was chosen by the author since it was thought to be good at meshing arbitrary geometries. In order to simulate the exact nature of tooth periodontium (PDL, cementum) and achieve accurate results, we improved the 3D FE model by using a range of 126,375 to 133,441 four noded linear tetrahedral type elements for enamel, dentin, cementum and an alveolar bone. Also PDL model was refined by using around 7000 shell elements. As the study concentrated on the stress distribution in an apical region, we recreated the maxillary central incisor model to represent the exact geometry of the root apex with normal morphology along with the PDL. Although the mechanical behavior of the PDL is understood to be non-linearly elastic, [26],[27] many investigators have assigned linear mechanical properties because of the lack of scientific quantitative data. [28] This dearth of information may be a possible source of error in computer simulations involving an orthodontic tooth movement. [24],[28],[29]

Investigators have suggested that PDL is a biological tissue with viscoelastic property and should not be considered as an engineering material. [30] However, all the previous studies have taken PDL into consideration. Furthermore, the cellular elements and tissue fluids could influence the property behavior of the biologic tissue. [31] In the present study, we created a 3D FE model of a maxillary central incisor along with PDL using non-linear mechanical properties. Young's modulus and Poisson's ratio for the models were assigned based on the data from earlier studies. [22] Keeping in mind the limitations of this study, we altered only the thickness of the PDL without altering the values for Young's modulus and Poisson's ratio. Coolidge [32] concluded that an apical periodontal ligament thickness varies between 0.24 mm and 0.15 mm between 11 years and 67 years respectively. Biological reactions of the PDL are determined primarily by the stress-strain levels induced by an applied orthodontic load and thus evaluation of PDL stress distribution helps us in understanding the mechanism of tooth movement. [33] Tanne and Jones, [13] using 3D FE model, evaluated the biomechanical response of the tooth and peridontium to orthodontic forces in an adolescent and adult subjects and concluded that adult PDL experienced almost an equivalent or an increased stress levels than young PDL. It was this that prompted us to look into the differences in stress distribution in the PDL of adults and adolescents. Therefore, in our model, we included two different PDL thicknesses of 0.24 mm and 0.15 mm simulating an adolescent and an adult PDL respectively. The study revealed that for tooth movements such as intrusion, tipping and extrusion, bigger stress was distributed in an adolescent PDL model than an adult PDL. During rotation, bigger stress was distributed in an adult PDL than an adolescent PDL. Overall, results showed that the stress induced in the PDL increased with an increase in the PDL thickness. These results differed from those of Tanne et al.[13] In general, the stress in the periodontal ligament was found to be maximum or minimum towards the mid root, when intrusive and extrusive force of 10 grams and 35 grams respectively were applied. In case of tipping movement of 35 grams, the maximum stress was seen at an apex tip and minimum tip near the apex. The maximum and minimum PDL stress was towards an apical region in case of tooth rotation movement when 35 grams force is applied.

Depending upon the force magnitude, the stress distribution in the FE model was represented by color coding ranging from red to blue with areas of maximum stress showing up as red; and blue areas showing areas of minimal stress. However, the values for the maximum and the minimum stress areas will differ in each figure. An influence of cementum thickness variation in PDL stress distribution during various tooth movements was also evaluated and it was found that increasing the cementum thickness decreased the stress distribution in the PDL for almost all types of tooth movement. The probable reason for this might be assumed that, as the cementum thickness increases the stress applied has to cross the entire thickness of cementum and then over to the PDL; by which time most of the stress has been distributed within the cementum itself. Moreover, in an FEM study, the magnitude of stress distributed in a model is the cumulative stress that is applied over a period of time; and Von Mises stress explains the combined stress values within the PDL.

During orthodontic tooth movement, root resorption is the pathological phenomenon that is constantly occurring on the surface of the cementum. In order to correlate the root resorption and the force magnitude during various tooth movements, the stress distribution within the cementum should be considered rather than the stress within the PDL. Schroeder, [34] in his histological evaluation found that an apical cementum thickness varies from 100 to 1000 μm. Hence, in our FEM model, we evaluated the stress distribution in an apical cementum by varying its thickness from 200 μm to 1000 μm with increments of 200 μm thickness during various orthodontic tooth movements. The results showed that maximum stress was observed in tipping tooth movement with highest cementum thickness (1000 μm). Overall results showed that, as the cementum thickness increases, the stress induced in the cementum also increases. This is in an agreement with the findings of Shaw and Sameshima et al.[21] Clinically, this stress distribution can be correlated with that in adult patients with increased cemental thickness; the susceptibility of root resorption is more. [20],[35] The influence of PDL thickness and variation in cementum stress distribution was also evaluated. It was found that increasing the PDL thickness, the cementum stress is almost equivalent or decreased. In nature as age advances, the cementum thickness increases and as compensation, the PDL thickness decreases to maintain the vertical tooth dimension. To logically interpret the FEM results with natural compensation, we compared the cementum stress values of 0.24 μm PDL thicknesses with minimum cemental thickness and that of 0.15 μm PDL thickness with maximum cemental thickness for various tooth movement and that is how we derived that the stress induced in the cementum decreased as with an increase in the PDL thickness.

When a tooth is intruded, the force is concentrated over a small area at an apex and for that reason, extremely light forces are needed to produce an appropriate pressure with the PDL during an intrusion. For an intrusion andextrusion, most of the previous investigators [4],[10],[23] evaluated the stress distribution in periodontium using same force values which was higher than optimal force values. In this study, we used the optimum force of 10 grams for an intrusion of single rooted tooth and interestingly we found that the cemental stress distribution pattern was maximum towards the mid root region and minimum towards the apex in all cementum thicknesses; and in both, 0.15 mm and 0.24 mm PDL thickness. We also used an optimum force of 35 grams for an extrusion and found that the cemental stress distribution pattern was maximum towards the mid- root region and minimal towards the apex for all cementum thicknesses; and in both, 0.15 mm and 0.24 mm PDL thickness. This stress distribution pattern was similar to that of an intrusion but only the magnitude differed which was higher for an extrusion. One possible reason for this could be that in an extrusion and intrusion, when the force is applied, the stress gets dissipated in an alveolar crest area and mid root area before it reaches an apex. Hence, significant stress is not observed in the apical regions. During tipping tooth movement, maximum stress areas are seen near the root apex and alveolar crest region. In our study for tipping tooth movement, we used an optimum force of 35 grams and found that the stress distribution in the cementum with thickness from 200 μm to 600 μm was concentrated maximum towards the mid root region and minimum at root tip; and in both, 0.15 mm and 0.24 mm PDL thicknesses. Interestingly, when the cementum thickness is increased to 800 μm and 1000 μm, the maximum stress is concentrated towards the root apex rather than the mid root region for both, 0.15 mm and 0.24 mm PDL thicknesses.

Although, theoretically we could not explain the reason for increased stress at the apex with increased cemental thickness, clinically as orthodontists, we should bear this in mind and avoid jiggling forces since the root tip is more susceptible to the resorption rather than the cervical portions of the root. For rotation tooth movement, we used the optimum force of 35 grams (couple force) for rotation of single rooted teeth and found the cementum stress distribution pattern in 200 μm to 1000 μm cementum thicknesses of both, 0.15 mm and 0.24 mm PDL thickness; the maximum and minimum stress was towards the mid root.

Earlier studies have shown that maxillary incisors are most susceptible to root resorption than any other teeth in the arches, in particularly the maxillary lateral incisors. The probable reason may be due to smaller root surface area than other teeth. [36],[37] Oppenheim [38] suggested that the morphology of the roots of the incisors was main catalyst in the root resorption. Mirabella found that the dilacerated teeth had the most root resorption than any other shaped teeth such as bottled or pointed shaped and it is mostly seen in maxillary incisors. [15],[19],[39] According to Poolthong, [40] the cementum covering an apical third of a root has lower value of hardness and elastic modulus than cementum covering the middle and cervical third of the root. This result was confirmed from the investigations done by Malek et al; [31] and they suggested that the hardness value of the cementum is related to its mineral content. The mineral content of the cementum might influence the resistance or susceptibility to the root resorption. [2],[41] Rex et al, [42] studied the Ca, P, F concentrations in the cervical, middle and apical third of the roots and found that an apical cementum is less mineralized than the cementum of the cervical and middle thirds of the root and hence an apical third is more susceptible to the root resorption. Moreover, authors have found that an apical third cemental resorption may also be due to the factors like fewer sharpey's fibres, greater blood supply which helps in formation of clast cells, higher metabolism in an adjacent PDL and the cementum structure similar to an alveolar bone. [43] Hohmann et al, [9] conducted a FEM study to evaluate the relationship between the root resorption and hydrostatic pressure of PDL. He found that the regions that showed increased hydrostatic pressure correlated with the locations of root resorption and concluded that if hydrostatic pressure exceeds typical human capillary blood pressure in the PDL, the risk of the root resorption increases. In this study we attempted to correlate the amount of stress distribution in the cementum to the susceptibility of root resorption. We found that the Von Mises stress (hydrostatic pressure) seen at the root apex was very much less than the normal capillary blood pressure of 0.0020 to 0.0047 MPa [9] when recommended optimal orthodontic forces were used.

Limitations and futurology of this study

There are insufficient data available regarding the material properties of PDL since it is not considered as an engineering material. Further studies should explain the exact material nature of PDL and cementum. The orientation of PDL fibres and its attachment to the tooth cementum and alveolar bone in young and adult individuals should also be included in the finite element model since in nature, PDL acts as a cushion to resist forces.

In clinical situation, the bracket slot, arch wire, the resin-tooth and resin bracket interface could also influence the distribution of stress within the periodontal tissues when orthodontic forces are applied. All these factors should be included in future studies of FEM to simulate the nearest possible clinical condition and elucidate the stress pattern during orthodontic tooth movement.

The future improvements in software and updated versions could help in refinement of meshing process and creating a more accurate 3D FE model.


   Conclusion Top


A three dimensional FEM model of a maxillary central incisor was created and non-linear stress analysis was carried out for 4 different types of tooth movement - intrusion, extrusion, tipping, and rotation movements with varying thickness of cementum & periodontal ligament.

From the results of our study, we concluded that for almost all types of tooth movement:

  • The apical stress induced in the cementum increases with an increase in cementum thickness.
  • The stress induced in the cementum is equivalent or decreased with an increase in PDL thickness.
  • The stress induced in the PDL increased with an increase in PDL thickness.
  • The stress induced in the PDL decreased with an increase in cementum thickness.
Clinically, this stress distribution can be taken to mean that in adult patients with increased cemental thickness at the root apex, the susceptibility to root resorption is greater and care should be exercised so as to use optimum orthodontic force levels for tooth movement.

 
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Correspondence Address:
N Raj Vikram
Department of Orthodontics and Dentofacial Orthopedics, Thai Moogambigai Dental College and Hospital, Chennai
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/0970-9290.100429

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