Journal of Pharmacy And Bioallied Sciences
Journal of Pharmacy And Bioallied Sciences Login  | Users Online: 2998  Print this pageEmail this pageSmall font sizeDefault font sizeIncrease font size 
    Home | About us | Editorial board | Search | Ahead of print | Current Issue | Past Issues | Instructions | Online submission




 
 Table of Contents  
DENTAL SCIENCE - REVIEW ARTICLE
Year : 2015  |  Volume : 7  |  Issue : 6  |  Page : 443-450  

Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures


1 Department of Orthodontics and Dentofacial Orthopaedics, The Oxford Dental College and Hospital, Bommanahalli, Bangalore, India
2 D.A.P.M.R.V. Dental College and Hospital, Bangalore, India
3 Noble Medical College Teaching Hospital and Research Centre, Kanchanbari, Biratnagar, Nepal

Date of Submission28-Apr-2015
Date of Decision28-Apr-2015
Date of Acceptance22-May-2015
Date of Web Publication1-Sep-2015

Correspondence Address:
Dr. M Sameena Begum
Department of Orthodontics and Dentofacial Orthopaedics, The Oxford Dental College and Hospital, Bommanahalli, Bangalore
India
Login to access the Email id

Source of Support: None, Conflict of Interest: None


DOI: 10.4103/0975-7406.163496

Rights and Permissions
   Abstract 

The finite element method (FEM) is a powerful computational tool for solving stress-strain problems; its ability to handle material inhomogeneity and complex shapes makes the FEM, the most suitable method for the analysis of internal stress levels in the tooth, periodontium, and alveolar bone. This article intends to explain the steps involved in the generation of a three-dimensional finite element model of tooth, periodontal ligament (PDL) and alveolar bone, as the procedure of modeling is most important because the result is based on the nature of the modeling systems. Finite element analysis offers a means of determining strain-stress levels in the tooth, ligament, and bone structures for a broad range of orthodontic loading scenarios without producing tissue damage.

Keywords: Finite element model, orthodontic forces, stress and strain


How to cite this article:
Begum M S, Dinesh M R, Tan KF, Jairaj V, Md Khalid K, Singh VP. Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures. J Pharm Bioall Sci 2015;7, Suppl S2:443-50

How to cite this URL:
Begum M S, Dinesh M R, Tan KF, Jairaj V, Md Khalid K, Singh VP. Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures. J Pharm Bioall Sci [serial online] 2015 [cited 2019 Aug 17];7, Suppl S2:443-50. Available from: http://www.jpbsonline.org/text.asp?2015/7/6/443/163496

Finite element models have their current origin and real use in mechanical engineering analysis and design. [1] It is as indispensable to an engineer who designs an airplane frame, as is a pair of arch wires to an orthodontist. The finite element method (FEM) has been successfully applied to the mechanical study of stress and strain in the field of engineering. It is a method for numerical analysis based on material properties. [2]

The FEM was introduced into dental biomechanical research in 1973 [3] and since then has been applied to analyze the stress and strain fields in the alveolar support structures. [4]

Finite element modeling is the representation of geometry in terms of a finite number of elements and their connection points known as nodes. These are the building blocks of numerical representation of the model. The "elements" present are of the finite number as opposed to a theoretical model with complete continuity. The object of interest has to be broken up into a "meshwork" that consists of a number of nodes on and in the object. These nodes or points are then connected to form a system of elements. For a two-dimensional example, if the brick wall is the network, the bricks are the elements and the four corners where the bricks meet each other are the "nodes". By knowing the mechanical properties of the object, such as modulus of elasticity and Poisson's ratio, one can determine how much distortion each part of the cube undergoes when other part is moved by a force. [2]


   Review of Literature on the Finite Element Method Top


In the general field of medicine, FEM has been applied mainly to orthopedic research [5],[6],[7],[8],[9],[10] in which the mechanical responses of bony structures relative to external forces were studied. Furthermore, some research [11],[12],[13] has been carried out in order to investigate the soft-tissue and skeletal responses to mechanical forces.

The applications of the FEM in dentistry have been found in studies by Thresher and Saito, [14] Knoell, [15] Tanne and Sakuda, [16] Atmaram and Mohammed, [17] Cook et al.[18] Tanne, [19] Rubin et al., [20] Moss et al., [21] and Miyasaka et al.[22] However, the application of this theory is relatively new in orthodontic research.

It has been shown in previous studies [16],[17],[18],[19],[20] that the FEM can be applicable to the problem of the strain-stress levels induced in internal structures. This method also has the potential for equivalent mathematic modeling of a real object of complicated shape and different materials. Thus, FEM offers an ideal method for accurate modeling of the tooth-periodontium system with its complicated three-dimensional geometry.

Experimental techniques are limited in measuring the internal stress levels of the PDL. Strain gauge techniques [23],[24] may be useful in measuring tooth displacement; however, they cannot be directly placed in the PDL without producing tissue damage. The photoelastic techniques [25] are also limited in determining the internal stress levels because of the crudeness of modeling and interpretation.

The force systems that are used on an orthodontic patient can be complicated. The FEM makes it possible to apply analytically various force systems at any point and in any direction. Experimental techniques on patients or animals are usually limited in applying known complex force systems.

It is very important to keep in mind that the FEM will give the results based on the nature of the modeling systems and, for that reason, the procedure for modeling is most important.


   Steps Involved in the Generation of Finite Element Model Top


  • Construction of a geometric model
  • Conversion of the geometric model to a finite element model
  • Material property data representation
  • Defining the boundary condition
  • Loading configuration
  • Solving the system of linear algebraic equation
  • Interpretation of the results.


Construction of a geometric model

The purpose of the geometric modeling phase is to represent a geometry in terms of points (grids), lines, surfaces (patches) and volume (hyper patches). In this study, the analytical model of maxillary first molar was developed according to dimensions and morphology found in a standard textbook of dental anatomy, physiology, and occlusion by Wheeler's. The buccal aspect of maxillary first molar is constructed using key points, which are identified from Wheeler's textbook. The key points are represented at different co-ordinate positions. The following key points mentioned below were plotted on the grids on the work plane to build the buccal surface of the maxillary first molar [Table 1]. The scale of the grid in the work plane measured 1 mm in X-axis and 1 mm in Y-axis.(K is the command to build key point, syntax of k command k, n, x, y, z where n is key point number, x is the x-coordinate, y is the y-coordinate, Z is the Z-coordinate) [Figure 1], [Figure 2], [Figure 3], [Figure 4] and [Figure 5].
Figure 1: Key point representation of the buccal aspect of maxillary first molar

Click here to view
Figure 2: Key point representation of the mesial aspect of maxillary first molar

Click here to view
Figure 3: Key point representation of the distal aspect of maxillary first molar

Click here to view
Figure 4: Key point representation of the palatal aspect of maxillary first molar

Click here to view
Figure 5: Key point representation of the occlusal aspect of maxillary first molar

Click here to view
Table 1: The keypoints of the buccal aspect of maxillary first molar

Click here to view


PREP7 (Activation of preprocessor)

The key points positions of the buccal aspect are joint to form lines. [Figure 6], [Figure 7], [Figure 8], [Figure 9], and [Figure 10] The key points numbering used for the built up is shown below; (BSPLINE - boundary smooth plane line) [Table 2].
Figure 6: Line point representation of the buccal aspect of maxillary first molar

Click here to view
Figure 7: Line point representation of the mesial aspect of maxillary first molar

Click here to view
Figure 8: Line point representation of the distal aspect of maxillary first molar

Click here to view
Figure 9: Line point representation of the palatal aspect of maxillary first molar

Click here to view
Figure 10: Line point representation of the occlusal aspect of maxillary first molar.

Click here to view
Table 2: BSPLINE used to join keypoints

Click here to view


The key points positions of the buccal aspect are joint to form lines and from lines to areas. The area plot of buccal aspect is built using ANSYS preprocessor [Figure 11], [Figure 12], [Figure 13], [Figure 14] and [Figure 15].
Figure 11: Area representation of the buccal aspect of maxillary first molar

Click here to view
Figure 12: Area representation of the mesial aspect of maxillary first molar

Click here to view
Figure 13: Area representation of the distal aspect of maxillary first molar

Click here to view
Figure 14: Area representation of the palatal aspect of maxillary first molar

Click here to view
Figure 15: Area representation of the occlusal aspect of maxillary first molar

Click here to view


All the aspects of the maxillary first molar are built up in the similar manner, extruded and Boolean operations are carried out to form three-dimensional geometric model [Figure 16].
Figure 16: Oblique view of the geometric model of the maxillary first molar

Click here to view


Individual models of enamel, dentin, periodontal ligament (PDL) and bone structure are built up [Figure 17], [Figure 18], [Figure 19] and [Figure 20].
Figure 17: The geometric model of dentin

Click here to view
Figure 18: The geometric model of dentin

Click here to view
Figure 19: The geometric model of periodontal ligament

Click here to view
Figure 20: The geometric model of alveolar bone

Click here to view


The coordinates defining the shape of the PDL was simulated as a 0.20 mm thick ring around the model of the tooth and bone. The software used for the geometric modelling was [Figure 21].
Figure 21: The geometric model comprises of tooth, periodontal ligament and alveolar bone

Click here to view


Conversion of geometric model to finite element model

Individual models of enamel, dentin, PDL and bone structure are converted to finite element models using [Figure 22], [Figure 23], [Figure 24] and [Figure 25] hypermesh 7.0.
Figure 22: The geometric model of enamel was converted into the three-dimension finite element

Click here to view
Figure 23: The geometric model of dentin was converted into the three-dimension finite element

Click here to view
Figure 24: The geometric model of periodontal ligament was converted into the three-dimension finite element

Click here to view
Figure 25: The geometric model of alveolar bone was converted the three-dimension finite element

Click here to view


The geometric models were converted into the finite element models using hypermesh 7.0 [Figure 26].
Figure 26: The geometric model was converted into the three-dimensional finite element model

Click here to view


The finite element model generation was achieved with the help of ANSYS 10 software. The element shape which was described in the model was a solid with a 4 noded tetra hedra (solid45) with 3 degrees of freedom (translations in the nodal x, y, and z directions). These elements were connected to adjacent elements with the help of nodes. The more the number of nodes and elements, greater will be the accuracy of the result. Hence, finite element model was constructed, which approximately consisted of 1, 69,036 elements and 29,518 nodes.

Material property data representation

The different structures in the finite element models are enamel, dentin, PDL, alveolar bone. Each structure is then assigned a specific material property. [26] These material properties were the average values reported in the literature. Each material is defined to be homogenous and isotropic [5] [Table 3].
Table 3: Material parameters used in the finite element model

Click here to view


Defining the boundary condition

The boundary condition, in the finite element models were defined at all the peripheral nodes of the bone with 0° of movement in all directions (the nodes of the base of the models were fixed to prevent free body displacement of the model). The final model was confirmatory from an engineering point of view for this study. It is very important to keep in mind that the finite element model will give the results based on the nature of the modeling system and for that reason, the procedure for modeling is most important.

Application of forces

Once the models were constructed, a force is applied.

Solving the system of linear algebraic equations

The sequential application of the above steps leads to a system of algebraic equations where the nodal displacements are unknown. These equations are solved by the frontal solver technique present in the ANSYS software (version 11.0, ANSYS, Canonsburg, Pennsylvania, US, 1970).


   Conclusion Top


Over the last few decades, numerical methods have been extensively used to calculate the stress and strain fields in the periodontium and the FEM has frequently been the method of choice. The FEM provides the orthodontist with quantitative data that can extend the understanding of the physiologic reactions that take place. In particular, such numerical techniques may yield an improved understanding of the reactions and interactions of individual tissues. Such detailed information on stresses and strains in tissues is difficult to obtain accurately by any other experimental techniques because of the interaction of the surrounding tissues, which may then distort the data obtained for any individual material response. By applying new techniques such as FEM can theoretically predict the stress and strain fields in the tooth, PDL and bone structures.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

 
   References Top

1.
Rudolph DJ, Willes PM, Sameshima GT. A finite element model of apical force distribution from orthodontic tooth movement. Angle Orthod 2001;71:127-31.  Back to cited text no. 1
    
2.
Shaw AM, Sameshima GT, Vu HV. Mechanical stress generated by orthodontic forces on apical root cementum: A finite element model. Orthod Craniofac Res 2004;7:98-107.  Back to cited text no. 2
    
3.
Farah JW, Craig RG, Sikarskie DL. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech 1973;6:511-20.  Back to cited text no. 3
[PUBMED]    
4.
Cobo J, Sicilia A, Argüelles J, Suárez D, Vijande M. Initial stress induced in periodontal tissue with diverse degrees of bone loss by an orthodontic force: Tridimensional analysis by means of the finite element method. Am J Orthod Dentofacial Orthop 1993;104:448-54.  Back to cited text no. 4
    
5.
Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 1987;20:1135-50.  Back to cited text no. 5
    
6.
Hakim NS, King AI. A three dimensional finite element dynamic response analysis of a vertebra with experimental verification. J Biomech 1979;12:277-92.  Back to cited text no. 6
[PUBMED]    
7.
Hayes WC, Swenson LW Jr, Schurman DJ. Axisymmetric finite element analysis of the lateral tibial plateau. J Biomech 1978;11:21-33.  Back to cited text no. 7
[PUBMED]    
8.
Khalil TB, Hubbard RP. Parametric study of head response by finite element modeling. J Biomech 1977;10:119-32.  Back to cited text no. 8
[PUBMED]    
9.
McPherson GK, Kriewall TJ. Fetal head molding: An investigation utilizing a finite element model of the fetal parietal bone. J Biomech 1980;13:17-26.  Back to cited text no. 9
[PUBMED]    
10.
Orr TE, Carter DR. Stress analyses of joint arthroplasty in the proximal humerus. J Orthop Res 1985;3:360-71.  Back to cited text no. 10
[PUBMED]    
11.
Pao YC, Chevalier PA, Rodarte JR, Harris LD. Finite-element analysis of the strain variations in excised lobe of canine lung. J Biomech 1978;11:91-100.  Back to cited text no. 11
[PUBMED]    
12.
Dale PJ, Matthews FL, Schroter RC. Finite element analysis of lung alveolus. J Biomech 1980;13:865-73.  Back to cited text no. 12
[PUBMED]    
13.
Simon BR, Kobayashi AS, Wiederhielm CA, Strandness DE. Deformation of the arterial vasa vasorum at normal and hypertensive arterial pressure. J Biomech 1973;6:349-59.  Back to cited text no. 13
[PUBMED]    
14.
Thresher RW, Saito GE. The stress analysis of human teeth. J Biomech 1973;6:443-9.  Back to cited text no. 14
[PUBMED]    
15.
Knoell AC. A mathematical model of an in vitro human mandible. J Biomech 1977;10:159-66.  Back to cited text no. 15
[PUBMED]    
16.
Tanne K, Sakuda M. A dynamic analysis of stress in the tooth and its supporting structures: The use of the finite element method as numerical analysis (author's transl). Nihon Kyosei Shika Gakkai Zasshi 1979;38:372-82.  Back to cited text no. 16
[PUBMED]    
17.
Atmaram GH, Mohammed H. Estimation of physiologic stresses with a natural tooth considering fibrous PDL structure. J Dent Res 1981;60:873-7.  Back to cited text no. 17
[PUBMED]    
18.
Cook SD, Weinstein AM, Klawitter JJ. A three-dimensional finite element analysis of a porous rooted Co-Cr-Mo alloy dental implant. J Dent Res 1982;61:25-9.  Back to cited text no. 18
[PUBMED]    
19.
Tanne K. Stress induced in the periodontal tissue at the initial phase of the application of various types of orthodontic force: Three-dimensional analysis by means of the finite element method. J Osaka Univ Dent Soc 1983;28:209-61.  Back to cited text no. 19
    
20.
Rubin C, Krishnamurphy N, Capilouto E, Yi H. Stress analysis of the human tooth using a three-dimensional finite element method. J Dent Res 1983;62:82-6.  Back to cited text no. 20
    
21.
Moss ML, Skalak R, Patel H, Sen K, Moss-Salentijn L, Shinozuka M, et al. Finite element method modeling of craniofacial growth. Am J Orthod 1985;87:453-72.  Back to cited text no. 21
[PUBMED]    
22.
Miyasaka J, Tanne K, Tsutsumi S, Sakuda M. Finite element analysis for the biomechanical effects of orthopedic forces on the craniofacial skeleton: Construction of the three-dimensional finite element model of the craniofacial skeleton. J Osaka Univ Dent Soc 1986;31:393-402.  Back to cited text no. 22
    
23.
Nakanishi Y. Effects of headgear traction on the human facial skeleton: A study with strain gauges. J Osaka Dent Univ 1973;7:7-30.  Back to cited text no. 23
    
24.
Tanne K, Miyasaka J, Yamagata Y, Sakuda M, Burstone CJ. Biomechanical changes in the craniofacial skeleton by the rapid expansion appliance. J Osaka Univ Dent Soc 1985;30:345-56.  Back to cited text no. 24
    
25.
Caputo AA, Chaconas SJ, Hayashi RK. Photoelastic visualization of orthodontic forces during canine retraction. Am J Orthod 1974;65:250-9.  Back to cited text no. 25
[PUBMED]    
26.
Hart RT. Quantitative response of bone to mechanical stress.[Dissertation.] Cleveland, Ohio: Department of Mechanical and Aerospace Engineering, Case Western Reserve University; 1983.  Back to cited text no. 26
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17], [Figure 18], [Figure 19], [Figure 20], [Figure 21], [Figure 22], [Figure 23], [Figure 24], [Figure 25], [Figure 26]
 
 
    Tables

  [Table 1], [Table 2], [Table 3]


This article has been cited by
1 Finite element analysis on tooth and periodontal stress under simulated occlusal loads
H. Zhang,J.-W. Cui,X. L. Lu,M.-Q. Wang
Journal of Oral Rehabilitation. 2017;
[Pubmed] | [DOI]



 

Top
 
 
  Search
 
    Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
 Related articles
    Access Statistics
    Email Alert *
    Add to My List *
* Registration required (free)  

 
  In this article
    Abstract
    Review of Litera...
    Steps Involved i...
   Conclusion
    References
    Article Figures
    Article Tables

 Article Access Statistics
    Viewed1266    
    Printed22    
    Emailed0    
    PDF Downloaded54    
    Comments [Add]    
    Cited by others 1    

Recommend this journal