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 Table of Contents  
ORIGINAL ARTICLE
Year : 2015  |  Volume : 49  |  Issue : 1  |  Page : 15-18

A comparative study of forces in labial and lingual orthodontics using finite element method


1 Professor, Department of Orthodontics and Dentofacial Orthopedics, Yenepoya Dental College, Yenepoya University, Mangalore, India
2 Professor, Department of Oral Medicine and Radiology, Yenepoya Dental College, Yenepoya University, Mangalore, India
3 Professor, Department of Aeronautical and Automobile Engineering, Manipal Institute of Technology, Manipal University, Manipal, Karnataka, India
4 Assistant Professor, Department of Orthodontics and Dentofacial Orthopedics, Yenepoya Dental College, Yenepoya University, Mangalore, India

Date of Submission24-Sep-2014
Date of Acceptance08-Apr-2015
Date of Web Publication12-Jun-2015

Correspondence Address:
Rohan Mascarenhas
Department of Orthodontics and Dentofacial Orthopedics, Yenepoya Dental College, Yenepoya University, Mangalore, Karnataka
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/0301-5742.158628

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  Abstract 

Background: Orthodontic treatment requires optimum force to achieve desirable tooth movement with minimal damage to the root, periodontal ligament (PDL), and alveolar bone. Hence, quantifying the magnitude and direction of force is very important for orthodontic treatment. Both labial orthodontics (LaO) and lingual orthodontics (LiO) are used for orthodontic tooth movements, which differ considerably in their biomechanics. Although these differences have been explained, force magnitude need to be evaluated. Aims: 1. To evaluate the differences in biomechanics of tipping movement in LaO and LiO using finite element method (FEM). 2. To quantify the reduced amount of force in LiO as compared LaO in tipping. Study Settings: It is a computational tool where three-dimensional (3D) FEM models of upper incisor is simulated in order to map and compare the stress produced by tipping movement performed with lingual and LaO. Materials and Methods: A 3D FEM model of the maxillary right central incisor was made from a geometric model. A 50 g tipping force was applied on a labial side. The principal stress patterns in the PDL for orthodontic tooth movement were recorded. When 50 g of tipping force was applied from a lingual side, higher stress values were observed. The forces on the lingual side were reduced to 45 g, 40 g, 35 g, 34 g, 33.5 g, and 33 g to check the maximum stress pattern on PDL. Results: A 50 g tipping force applied on the labial side will bring about 0.0252 N/mm 2 maximum principal stress. When the same amount of force applied on the lingual side will bring about 0.0375 N/mm 2 maximum principal stress. A 33.6-g force applied on the lingual side will bring about 0.0252 N/mm 2 maximum principal stress which is similar to 50 g of force applied on the lingual side. Conclusion: A palatally directed tipping force of 33.6 g in LiO was sufficient for orthodontic tooth movement. Tipping in LiO required 32.8% less force when compared to LaO.

Keywords: Biomechanics, finite element method, labial orthodontics, lingual orthodontics, periodontal ligament, principal stress, tipping


How to cite this article:
Mascarenhas R, Chatra L, Shenoy S, Husain A, Mathew JM, Parveen S. A comparative study of forces in labial and lingual orthodontics using finite element method. J Indian Orthod Soc 2015;49:15-8

How to cite this URL:
Mascarenhas R, Chatra L, Shenoy S, Husain A, Mathew JM, Parveen S. A comparative study of forces in labial and lingual orthodontics using finite element method. J Indian Orthod Soc [serial online] 2015 [cited 2019 May 25];49:15-8. Available from: http://www.jios.in/text.asp?2015/49/1/15/158628


  Introduction Top


Orthodontic treatment requires optimum force to bring about maximum tooth movement with minimal damage to the root, periodontal ligament (PDL), and alveolar bone. Hence, the quantification and direction of force is very important during orthodontic treatment. This force brings about changes in the PDL which in turn initiates orthodontic tooth movement. Therefore, the stressed state of the PDL needs to be studied in order to understand the effect of different forces. [1],[2],[3],[4],[5],[6],[7],[8],[9],[10]

Finite element method (FEM) is a mathematical method in which the shape of complex geometric objects and their physical properties are computer-constructed. Physical interactions of the various components of the model can then be calculated in terms of stress and strain, a detailed information which is difficult to obtain by any other experimental or analytical means due to the interaction of anatomical structures with the surrounding tissue.

Labial Orthodontics (LaO) and lingual Orthodontics (LiO) are used for similar tooth movements, but they differ considerably in their biomechanics. [11],[12],[13],[14],[15],[16],[17] Several methods can be used to evaluate the differences and the most suited method is the FEM or finite element analysis (FEA). This study evaluated the differences in the biomechanics of tipping movement in labial and LiO using FEM/FEA.


  Materials and Methods Top


The analytical model was developed from sequential computed tomography scan images, taken at 1 mm intervals of a skull of a young adult male after obtaining the patient consent and ethical clearance. The scanned images were used to create a geometric model using MIMICS( Materialise Interactive Medical Image Control System ) software -version 14.0, Materialise NV, Belgium.

In this study, the maxillary right central incisor tooth was used. The images obtained from MIMICS were in STL format. These images were imported to CATIA V5 R20 (Computer-Aided Three-Dimensional Interactive Application) by Dassault Systθmes' 3D for 3D modeling and simulation software, where it was meshed to get a solid model.This geometric model was imported to ANSYS software to get the finite element model. ANSYS Mechanical software is a comprehensive FEA analysis tool for structural analysis and provides a complete set of elements behavior, material models and equation solvers for a wide range of mechanical design problems.

Material properties were assigned for different structures such as bone, teeth, and PDL. The material properties used in this study were from experimental data of previous studies [Table 1]. [2],[6],[17],[18] The model was restrained at the superior border of the maxilla in order to avoid any motion against the loads imposed on the dentoalveolar structures.
Table 1: Material Properties


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Application of forces

Tipping force of 50 g was applied on the labial and lingual surfaces of the maxillary right central incisor 4 mm from the incisal edge [Figure 1]. [19],[20] In this study, the maxillary right central incisor was used for the FEA as it best represents tipping movement.
Figure 1: Stress patterns with tipping movement

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Both the stress patterns indicated tipping but with different stress values. The stress pattern in the PDL with 50-g force on the labial side was considered to be the desired stress pattern. However, when the same amount of force was applied on the lingual side, higher stress values were observed.

The force applied on the lingual side of the tooth was iterated, and reduced to 45 g [Table 2]. After achieving the solution, the stress values were compared with the stresses generated when 50 g of force was applied on the labial side. It was noticed that the stresses generated with the 45 g of force on the lingual side was still higher than the stress values generated in the PDL when 50 g of force was applied on the labial side.
Table 2: Maximum Principal Stress- PDL (when tipping force applied in labial and lingual orthodontics)


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This process of iteration or reduction of forces on the lingual side was further continued wherein 40 g, 35 g, 34 g, 33 g, 33.5 g were applied. 33.5 g showed very similar stress values. When the force on the lingual side was further iterated (increased) to 33.6 g, similar stress patterns and values were seen in the PDL as when 50-g force was applied on the labial side. Maximum principal stresses of PDL were studied.

Analysis of stress

Following stress patterns indicate tipping movement:

Labial side will display area of compression (blue) at apical half and area of tension (red) at cervical half [Figure 1].

Lingual side will display area of tension (red) at apical half and area of compression (blue) at cervical half [Figure 1].


  Results Top


Tipping force of 50 g was applied on the labial and lingual surfaces of the maxillary right central incisor 4 mm from the incisal edge [Figure 2] and [Figure 3]. The stress patterns indicated tipping but with different stress values. The stress pattern in the PDL with 50-g force on the labial side was considered to be the desired stress pattern but for the same amount of force on the lingual side, higher stress values were observed [Table 2].
Figure 2: (a-d) Maximum and minimum principal stress-labial and lingual view 50 g of force (labial orthodontics)

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Figure 3: (a-d) Maximum and minimum principal stress-labial and lingual view 50 g of force (lingual orthodontics)

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The force on the lingual side was iterated to 33.6 g [Figure 3]. This gave similar stress patterns and values in the PDL as when 50-g forces were applied on the labial side. The maximum and minimum principal stresses in the PDL were studied, and their values were recorded. The results are given below.

Labial orthodontics at 50 g

A 50-g force was applied on the labial side. The maximum and minimum principal stresses in the PDL were studied, and their values were recorded [Figure 2]a-d].

Lingual orthodontics at 50 g force

A 50-g force was applied on the lingual side. The maximum principal stresses in the PDL were studied and their values were recorded [Figure 3]a-d].

Lingual orthodontics at 33.6 g force

33.6-g force was applied on the lingual side. The maximum and minimum principal stresses in the PDL were studied and their values were recorded [Figure 4]a-d].
Figure 4: (a-d) Maximum and minimum principal stress-labial and lingual view 33.6 g of force (lingual orthodontics)

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  Discussion Top


Lingual orthodontics have developed rapidly in recent years, making proper understanding of the biomechanics involved very important. The biomechanics involved in LiO is different from LaO. Several methods can be used to study these differences and the most suited method is the FEM/FEA. In this study, three-dimensional (3D) FEA is used to evaluate the effect of labial and lingual forces on maxillary central incisor in tipping. FEM has the ability to study the simulation of different tooth movements. Tipping is the simplest form of orthodontic tooth movement produced when a single force is applied on a tooth making it the most suitable movement to study the difference between labial and LiO.

For better orthodontic results, it is essential to understand the differences in the biomechanical aspects between labial and LiO. Since the force application for labial and LiO is different, the biomechanics have to be understood and suitably modified.

Proffit pointed out that stress in the PDL is the first and key biomechanical phenomenon of tooth movement. Therefore in this study, we focused on the changes in the PDL and studied the maximum principal stresses in PDL. [1],[2],[3],[4],[5],[6],[7],[8],[9],[10]

In this study, a tipping force of 50 g was applied labially on the maxillary central incisor 4 mm from the incisal edge. This force was directed horizontally to the tooth. Maximum and minimum principal stresses in the PDL were studied and their values were recorded. To replicate similar stress patterns on the application of force lingually, the forces were iterated and stresses were recorded. A palatally directed tipping force of 33.6 g in LiO was sufficient. This demonstrates that lesser force (67.2% of labial force) is required for LiO when compared to LaO.

When a tipping force is applied on a crown of a tooth, the PDL is compressed near the apical half of the labial side and at the cervical half of the palatal side, tension is seen at the apical half of the lingual side and at the cervical half of the labial side [Figure 1]. During tipping movement, stresses varied non-uniformly with a large difference from the cervical half to the apical half of the tooth. In the present study, similar stress patterns were observed and it clearly shows that the force required is 32.8% lesser in LiO as compared to LaO.

A similar study [17] was conducted to compare the biomechanical response of upper incisors to labial and lingual force applications. A 3D finite element model was developed to analyze tooth displacement and stress distribution in the PDL. Lingually and apically directed forces of 1 N were applied at one point on the labial and at three points on the lingual surface of the crown. Tooth displacement and stress distribution resulting from lingual force applications were compared with those from the labial side. Lingual horizontal forces produced similar patterns of tooth displacement and stress distribution, irrespective of the point of application (labial-lingual) 2. Apically directed vertical forces applied at the lingual points produced more uniform tooth displacements and stress distributions, although the force applied on the lingual side close to the cementoenamel junction, which happened to be most distant from the tooth's long axis, generated a pattern of movement somewhat different from the remaining two lingual force applications. The present results suggest the crucial role of the positional relation between the long axis of the tooth, respectively the center of resistance, and the point of force application. They also deduced that the lingual force application may produce more optimal tooth movement and subsequent stress distributions in the PDL.

Theoretically retraction forces used in the lingual technique is three-fold lower than that with labial technique. [18] Controlling the position of anterior teeth is difficult in LiO, due to the variability in the morphology of the palatal surface of the anterior teeth, the reduced distance between the point of force application to the center of resistance of the tooth, the small interbracket distance, influencing arch wire rigidity, and friction. [20]


  Conclusion Top


Understanding and applying basic biomechanical principles in treatment improves the efficacy of an appliance system, simplifies the treatment, improves force delivery, and helps in achieving more predictable tooth movement with minimum side effects. Reduction in lingual forces as compared to labial forces were quantified and found to be 32.8% lesser in LiO.

 
  References Top

1.
McGuinness N, Wilson AN, Jones M, Middleton J, Robertson NR. Stresses induced by edgewise appliances in the periodontal ligament - A finite element study. Angle Orthod 1992;62:15-22.  Back to cited text no. 1
    
2.
Tanne K, Sakuda M, Burstone CJ. Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofacial Orthop 1987;92:499-505.  Back to cited text no. 2
    
3.
Tanne K, Koenig HA, Burstone CJ, Sakuda M. Effect of moment to force ratios on stress patterns and levels in the PDL. J Osaka Univ Dent Sch 1989;29:9-16.  Back to cited text no. 3
    
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.
Tanne K, Yoshida S, Kawata T, Sasaki A, Knox J, Jones ML. An evaluation of the biomechanical response of the tooth and periodontium to orthodontic forces in adolescent and adult subjects. Br J Orthod 1998;25:109-15.  Back to cited text no. 5
    
6.
Jeon PD, Turley PK, Moon HB, Ting K. Analysis of stress in the periodontium of the maxillary first molar with a three-dimensional finite element model. Am J Orthod Dentofacial Orthop 1999;115:267-74.  Back to cited text no. 6
    
7.
Qian H, Chen J, Katona TR. The influence of PDL principal fibers in a 3-dimensional analysis of orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2001;120:272-9.  Back to cited text no. 7
    
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Geramy A. Initial stress produced in the periodontal membrane by orthodontic loads in the presence of varying loss of alveolar bone: A three-dimensional finite element analysis. Eur J Orthod 2002;24:21-33.  Back to cited text no. 8
    
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Toms SR, Eberhardt AW. A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading. Am J Orthod Dentofacial Orthop 2003;123:657-65.  Back to cited text no. 9
    
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Mestrovic S, Slaj M, Miksic M. Finite element method stress analysis caused by orthodontic forces. Acta Stomatol Croat 2002;36:175-8.  Back to cited text no. 10
    
11.
Scuzzo G, Takemoto K. Biomechmaics and comparative biomechanics. In: Invisible Orthodontics - Current Concepts and Solutions in Lingual Orthodontics. 1 st ed. Germany: Quintessenz Verlags-GmbH; 2003. p. 55-6.  Back to cited text no. 11
    
12.
Geron S, Romano R, Brosh T. Vertical forces in labial and lingual orthodontics applied on maxillary incisors - A theoretical approach. Angle Orthod 2004;74:195-201.  Back to cited text no. 12
    
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Proffit WR. Mechanical principles in orthodontic force control. In: Contemporary Orthodontics. 5 th ed.  St.Louis, Missouri: Mosby Publication; 2013.  Back to cited text no. 13
    
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Romano R. Lingual Orthodontics. 1 st ed.  Hamilton, London: B.C. Decker Inc.; 1998.  Back to cited text no. 14
    
15.
Tanne K, Lu YC, Sakuda M. Biomechanical responses of tooth to orthodontic forces applied at the lingual bracket positions. J Osaka Univ Dent Sch 1992;32:6-13.  Back to cited text no. 15
    
16.
Sung SJ, Baik HS, Moon YS, Yu HS, Cho YS. A comparative evaluation of different compensating curves in the lingual and labial techniques using 3D FEM. Am J Orthod Dentofacial Orthop 2003;123:441-50.  Back to cited text no. 16
    
17.
Jost-Brinkmann PG, Tanne K, Sakuda M, Miethke RR. A FEM study for the biomechanical comparison of labial and palatal force application on the upper incisors. Finite element method. Fortschr Kieferorthop 1993;54:76-82.  Back to cited text no. 17
    
18.
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. 18
    
19.
Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426-31.  Back to cited text no. 19
    
20.
Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofacial Orthop 1991;100:66-71.  Back to cited text no. 20
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4]
 
 
    Tables

  [Table 1], [Table 2]


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