Finite element analysis of effectiveness of lever arm in lingual sliding mechanics

Kyeong-Hee Kim; Kee-Joon Lee; Jung-Yul Cha; Young-Chel Park

doi:10.4041/kjod.2011.41.5.324

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Kim, Lee, Cha, and Park: Finite element analysis of effectiveness of lever arm in lingual sliding mechanics

Original Article

Korean Journal of Orthodontics 2011; 41(5): 324-336.

Published online: 31 October 2011

DOI: https://doi.org/10.4041/kjod.2011.41.5.324

Finite element analysis of effectiveness of lever arm in lingual sliding mechanics

Kyeong-Hee Kim, DDS, MS^a, Kee-Joon Lee, DDS, MSD, PhD^b, Jung-Yul Cha, DDS, MSD, PhD^c, Young-Chel Park, DDS, MSD, PhD^d

^aPrivate Practice, Korea.

^bAssociate Professor, Department of Orthodontics, College of Dentistry, Yonsei University, Korea.

^cAssistant Professor, Department of Orthodontics, College of Dentistry, Yonsei University, Korea.

^dProfessor, Department of Orthodontics, College of Dentistry, Yonsei University, Korea.

Corresponding author: Young-Chel Park. Department of Orthodontics, College of Dentistry, Yonsei University, 250 Seongsanno, Seodaemun-gu, Seoul 120-752, Korea. +82 2 2228 3103; ypark@yuhs.ac.

Received 24 November 2010 Revised 10 May 2011 Accepted 13 May 2011

Abstract

Objective

The aim of this study was to conduct three-dimensional finite element analysis of individual tooth displacement and stress distribution when a posterior retraction force of 200 g was applied at different positions of the retraction hook on the transpalatal arch (TPA) of a molar, and over different lengths of the lever arm on the maxillary anterior teeth in lingual orthodontics.

Methods

A three-dimensional finite element model, including the entire upper dentition, periodontal ligaments, and alveolar bones, was constructed on the basis of a sample (Nissan Dental Product, Kyoto, Japan) survey of Asian adults. Individual movement of the incisal edge and root apex was estimated along the x-, y-, and z-coordinates to analyze tooth displacement and von Mises stress distribution.

Results

When the length of the lever arm was 15 mm and 20 mm, the incisal edge and root apex of the anterior teeth was displaced lingually, with a maximum lingual displacement at the lever arm length of 20 mm. When the posterior retraction hook was on the root apex, the molars showed distal displacement. When the length of the lever arm was 20 mm, anterior extrusion was reduced and the crown of the canine displaced toward the buccal side, in which case, the retraction hook was on the edge, rather than at the center, of the TPA.

Conclusions

The results of the analysis showed that when 6 anterior teeth were retracted posteriorly, lateral displacement of the canine and lingual displacement of the incisal edge and root apex of the anterior teeth occur without the extrusion of the anterior segment when the length of the lever arm is longer, and the posterior retraction hook is in the midpalatal area.

Keywords: Lingual orthodontics, Sliding mechanics, Lever arm, Finite element analysis

Figures and Tables

Fig. 1

A, Three-dimensional finite element model for upper teeth, periodontal ligaments and alveolar bones; B, experimental groups are divided into three groups depending on the position of retraction: position of retraction arm in the first group is placed at the bracket of the 2nd molar, at the furcation of the 2nd molar in the second group and at the root apex of the 2nd molar in the third group; C, the coordinate system is composed of X-axis, Y-axis and Z-axis. The origin of coordinate axes is the middle point of the incisal surface which connects with the upper right and left incisors. X-axis is the bucco-palatal direction (lingual (+), buccal (-)); Y-axis is the antero-posterior direction (anterior (+), posterior (-)); Z-axis is the superior-inferior direction (superior (+), inferior direction (-)). CEJ, Cemento enamel junction.

Fig. 2

Contour plot of frontal displacement at each condition. A, Length of lever arm is 0 mm and position of retraction hook is at the bracket of the 2nd molar; B, length of lever arm is 20 mm and position of retraction hook is at the bracket of the 2nd molar; C, length of lever arm is 0 mm and position of retraction hook is at the furcation of the 2nd molar; D, length of lever arm is 20 mm and position of retraction hook is at the furcation of the 2nd molar; E, length of lever arm is 0 mm and position of retraction hook is at the root apex of the 2nd molar; F, length of lever arm is 20 mm and position of retraction hook is at the root apex of the 2nd molar.

Fig. 3

Contour plot of vertical displacement at each condition. A, Length of lever arm is 0 mm and position of retraction hook is at the bracket of the 2nd molar; B, length of lever arm is 20 mm and position of retraction hook is at the bracket of the 2nd molar; C, length of lever arm is 0 mm and position of retraction hook is at the furcation of the 2nd molar; D, length of lever arm is 20 mm and position of retraction hook is at the furcation of the 2nd molar; E, length of lever arm is 0 mm and position of retraction hook is at the root apex of the 2nd molar; F, length of lever arm is 20 mm and position of retraction hook is at the root apex of the 2nd molar.

Fig. 4

Contour plot of lateral displacement at each condition. A, Length of lever arm is 0 mm and position of retraction hook is at the bracket of the 2nd molar; B, length of lever arm is 20 mm and position of retraction hook is at the bracket of the 2nd molar; C, length of lever arm is 0 mm and position of retraction hook is at the furcation of the 2nd molar; D, length of lever arm is 20 mm and position of retraction hook is at the furcation of the 2nd molar; E, length of lever arm is 0 mm and position of retraction hook is at the root apex of the 2nd molar; F, length of lever arm is 20 mm and position of retraction hook is at the root apex of the 2nd molar.

Fig. 5

Comparison of the position of lever arm and CR of anterior teeth from other studies35: (blue) kjod-41-324-i005

- study by Jeong et al35 showing center of resistance of six anterior teeth; (green) kjod-41-324-i006

- study by Vanden Bulcke et al31 showing center of resistance of four anterior teeth; (purple) kjod-41-324-i007

- study by Vanden Bulcke et al31 showing center of resistance of six anterior teeth. CR, Center of resistance; CEJ, cemento enamel junction.

Table 1

Material properties

Table 2

Amount of frontal displacement along the Y-axis for each group

Group 1, Retraction arm was positioned at the level of the 2nd molar bracket; Group 2, retraction arm was positioned at the furcation level of 2nd molar; Group 3, retraction arm was positioned at the root apex of 2nd molar; CI, central incisors; LI, lateral incisors; C, canine; PM, premolars; M, molars.

Table 3

Amount of vertical displacement along Z-axis for each group

Table 4

Amount of lateral displacement along X-axis for each group

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