Three dimensional finite element analysis of continuous and segmented arches with use of orthodontic miniscrews

Eon-Hwa Lee; Hyung-Seog Yu; Kee-Joon Lee; Young-Chel Park

doi:10.4041/kjod.2011.41.4.237

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Lee, Yu, Lee, and Park: Three dimensional finite element analysis of continuous and segmented arches with use of orthodontic miniscrews

Original Article

Korean J Orthod 2011;41(4):237-254.

Published online: 21 January 2011

DOI: https://doi.org/10.4041/kjod.2011.41.4.237

Three dimensional finite element analysis of continuous and segmented arches with use of orthodontic miniscrews

Eon-Hwa Lee^a,^b, Hyung-Seog Yu^c, Kee-Joon Lee^d, Young-Chel Park^c

DDS, MSD

DDS, MSD, PhD

^aMedical Professor, Department of Dentistry, College of Medicine, Inha University.

^bGraduate Student, Department of Orthodontics, College of Dentisrty, Yonsei University.

^cProfessor, Department of Orthodontics, College of Dentisrty, Yonsei University.

^dAssociate Professor, Department of Orthodontics, College of Dentisrty, Yonsei University.

Corresponding author: Young-Chel Park. Department of Orthodontics, College of Dentistry, Yonsei University, 250 Seongsanno, Seodaemun-gu, Seoul 120-752, Korea. *Supported by the grant of Craniofacial Deformity Research Institute at College of Dentistry, Yonsei University. ＋82 2 2228-3101; e-mail, ypark@yuhs.ac.

Received 7 March 201122 June 2011 Accepted 24 June 2011

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Objective

The purpose of this study was to compare the displacement patterns shown by finite element analysis when the maxillary anterior segment was retracted from different orthodontic miniscrew positions and different lengths of lever arms in lingual continuous and segmented arch techniques.

Methods

A three dimensional model was produced, the translation of teeth in both models was measured and individual displacement was calculated.

Results

When traction was carried out from miniscrews in the palatal slope, lingual tipping of crowns and extrusion of the maxillary anterior segment were found in both continuous and segmented arches as the lever arms were made shorter. With miniscrews in the midpalatal suture area, the displacement patterns were similar to the palatal slope, but bodily movement of the upper incisors was observed in both continuous and segmented arches with the lever arm at 20 mm. When lever arms were longer, there was less extrusion of the incisors and more buccal displacement of the canines. Such displacement was shown less in the continuous arch than the segmented arch. The second premolar showed crown mesial tipping and intrusion, and the molars showed distal tipping in the continuous arch. The posterior segment was displaced three dimensionally in the segmented arch, but the amount of displacement was less than the continuous arch.

Conclusions

It is recommended that lever arms of 20 mm in length be used for bodily movement of the anterior segment. Use of continuous or segmented arches affect the displacement patterns and induce differences in the amount of displacement.

Keywords: Finite element analysis, Lever arm, Continuous arch, Segmented arch

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Fig 1.

A Occlusal view of experimental groups. a, Continuous arch with lever arms and miniscrews in the palatal slope (condition 1A, lever arm length 0 mm; condition 2A, lever arm length 10 mm; condition 3A, lever arm length 20 mm); b, segmented arch with lever arms and miniscrews in the palatal slope (condition 1B, lever arm length 0 mm; condition 2B, lever arm length 10 mm; condition 3B, lever arm length 20 mm); c, continuous arch with lever arms and miniscrew in the midpalatal suture area (condition 1C, lever arm length 0 mm; condition 2C, lever arm length 10 mm; condition 3C, lever arm length 20 mm); d, segmented arch with lever arms and miniscrew in the midpalatal suture area (condition 1D, lever arm length 0 mm; condition 2D, lever arm length 10 mm; condition 3D, lever arm length 20 mm). B, Lateral view of experimental groups. a, Continuous arch with lever arms and miniscrews in the palatal slope; b, segmented arch with lever arms and miniscrews in the palatal slope; c, continuous arch with lever arms and miniscrew in the midpalatal suture area; d, segmented arch with lever arms and miniscrew in the midpalatal suture area. C, The coordinate system (X, medio-lateral direction (＋), medial (－), lateral; Y, anterio-posterior direction (＋), anterior (－), posterior; Z, superio-inferior direction (＋), superior (－), inferior.

Fig 2.

Contour plot of antero-posterior displacement of the continuous and segmented arches with miniscrews in the palatal slope. Condition 1A, Lever arm length of 0 mm with continuous arch; condition 2A, lever arm length of 10 mm with continuous arch; condition 3A, lever arm length of 20 mm with continuous arch; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch.

Fig 3.

Contour plot of antero-posterior displacement of continuous and segmented arches with miniscrew in the mid-palatal suture area. Condition 1A, Lever arm length of 0 mm with continuous arch; condition 2A, lever arm length of 10 mm with continuous arch; condition 3A, lever arm length of 20 mm with continuous arch; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch.

Fig 4.

Contour plot of vertical displacement of the continuous and segmented arches with miniscrews in the palatal slope. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch.

Fig 5.

Contour plot of vertical displacement of continuous and segmented arches with miniscrew in the midpalatal suture area. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch.

Fig 6.

Contour plot of lateral displacement of continuous and segmented arches with miniscrews in the palatal slope. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch.

Fig 7.

Contour plot of lateral displacement of continuous and segmented arches with miniscrew in the midpalatal suture area. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch.

Fig 8.

Deformation of main arch wire (meshed, before deformation; colored, after deformation; 1, central incisor; 2, lateral incisor; 3, canine).

Table 1.

Material properties

	Young’s modulus (g/mm²)	Poisson’s ratio
Periodontal ligament	5.0E＋00	0.49
Alveolar bone	2.0E＋05	0.30
Teeth	2.0E＋06	0.30
Stainless steel	2.0E＋07	0.30

Table 2.

Amount of tooth displacement for the continuous arch with miniscrews in the palatal slope (mm)

	X axis	Condition 1A	Condition 2A	Condition 3A
C.I	Cusp tip	8.53E-02	1.28E-01	1.59E-01
	Apex	-2.68E-02	-3.66E-02	-4.11E-02
L.I	Cusp tip	6.37E-02	8.97E-02	1.05E-01
	Apex	-2.02E-02	-4.53E-02	-6.06E-02
C	Cusp tip	3.13E-02	-2.43E-02	-8.86E-02
	Apex	-9.30E-03	8.39E-03	2.43E-02
PM2	Cusp tip	1.43E-02	-3.72E-02	-8.25E-02
	Apex	-7.64E-03	1.43E-02	3.46E-02
Ml	Cusp tip	6.17E-03	-1.73E-02	-4.23E-02
	Apex	-2.49E-03	6.51E-03	1.60E-02
M2	Cusp tip	2.07E-03	-8.67E-03	-2.12E-02
	Apex	-8.85E-04	3.27E-03	8.06E-03
	Y axis	Condition 1A	Condition 2A	Condition 3A
C.I	Cusp tip	-1.40E-01	-1.24E-01	-8.38E-02
	Apex	3.20E-02	9.63E-03	-2.22E-02
L.I	Cusp tip	-1.23E-01	-7.46E-02	-5.04E-03
	Apex	4.51E-02	3.08E-02	8.79E-04
C	Cusp tip	-1.20E-01	-2.68E-02	6.59E-02
	Apex	3.58E-02	1.86E-03	-2.47E-02
PM2	Cusp tip	1.47E-02	2.58E-03	3.09E-03
	Apex	-7.94E-03	-7.09E-03	-9.27E-03
M1	Cusp tip	1.47E-03	-4.34E-03	-1.17E-02
	Apex	-1.39E-03	5.26E-03	1.28E-02
M2	Cusp tip	-1.44E-04	-6.51E-03	-1.90E-02
	Apex	-4.43E-04	3.38E-03	8.95E-03
	Z axis	Condition 1A	Condition 2A	Condition 3A
C.I	Cusp tip	-7.72E-02	-4.91E-02	-3.18E-03
	Apex	5.51E-02	5.85E-02	5.44E-02
L.I	Cusp tip	-7.10E-02	-5.08E-02	-1.33E-02
	Apex	3.67E-02	3.07E-02	1.78E-02
C	Cusp tip	-4.12E-02	-9.18E-03	1.83E-02
	Apex	3.85E-02	-5.19E-03	-5.16E-02
PM2	Cusp tip	3.49E-03	1.36E-02	2.33E-02
	Apex	3.71E-03	2.16E-04	-5.07E-03
M1	Cusp tip	-6.33E-04	2.66E-04	-3.95E-04
	Apex	1.59E-03	-5.10E-03	-1.31E-02
M2	Cusp tip	-4.96E-05	-9.72E-04	-3.06E-03
	Apex	9.14E-04	-1.68E-04	9.35E-04

C.I, Central incisorå L.I, lateral incisorå C, canineå PM2, second premolarå Ml, first molarå M2, second molarå condition 1A, lever arm length of 0 mm with continuous archå condition 2A, lever arm length of 10 mm with continuous archå condition 3A, lever arm length of 20 mm with continuous arch.

Table 3.

Amount of tooth displacement for the segmented arch with miniscrews in the palatal slope (mm)

	X axis	Condition 1B	Condition 2B	Condition 3B
C.I	Cusp tip	8.32E-02	1.37E-01	1.81E-01
	Apex	-2.61E-02	-3.90E-02	-4.88E-02
L.I	Cusp tip	6.29E-02	9.19E-02	1.14E-01
	Apex	-1.97E-02	-4.43E-02	-6.62E-02
C	Cusp tip	3.20E-02	-3.35E-02	-1.03E-01
	Apex	-8.68E-03	6.56E-03	2.28E-02
PM2	Cusp tip	5.21E-06	-1.34E-05	-3.28E-05
	Apex	-1.52E-05	-1.96E-05	-2.23E-05
M1	Cusp tip	-1.52E-05	-2.53E-05	-3.37E-05
	Apex	-7.39E-06	-6.97E-06	-5.67E-06
M2	Cusp tip	-1.23E-05	-1.82E-05	-2.28E-05
	Apex	-1.93E-06	1.79E-06	5.77E-06
	Y axis	Condition 1B	Condition 2B	Condition 3B
C.I	Cusp tip	-1.45E-01	-1.33E-01	-1.03E-01
	Apex	3.41E-02	9.72E-03	-1.92E-02
L.I	Cusp tip	-1.30E-01	-7.54E-02	-4.51E-03
	Apex	4.77E-02	2.96E-02	5.15E-03
C	Cusp tip	-1.30E-01	-4.62E-03	1.36E-01
	Apex	4.01E-02	-6.23E-04	-4.57E-02
PM2	Cusp tip	-2.23E-05	-1.18E-05	1.38E-06
	Apex	-5.63E-05	-3.60E-05	-8.95E-06
M1	Cusp tip	-3.13E-05	-1.85E-05	-1.91E-06
	Apex	-2.05E-05	-1.08E-05	1.38E-06
M2	Cusp tip	-3.33E-05	-2.01E-05	-2.94E-06
	Apex	-8.87E-06	-4.39E-06	1.17E-06
	Z axis	Condition 1B	Condition 2B	Condition 3B
C.I	Cusp tip	-8.04E-02	-5.55E-02	-2.04E-02
	Apex	5.69E-02	5.97E-02	5.56E-02
L.I	Cusp tip	-7.33E-02	-5.31E-02	-2.35E-02
	Apex	3.96E-02	2.83E-02	1.21E-02
C	Cusp tip	-4.18E-02	3.31E-03	5.31E-02
	Apex	4.38E-02	-5.53E-03	-6.04E-02
PM2	Cusp tip	-3.39E-06	1.10E-06	6.01E-06
	Apex	-5.78E-06	-2.45E-06	1.58E-06
M1	Cusp tip	-5.02E-06	-1.42E-07	5.36E-06
	Apex	-3.58E-06	-4.15E-06	-4.29E-06
M2	Cusp tip	1.71E-06	2.97E-06	4.03E-06
	Apex	1.10E-05	3.85E-06	-4.63E-06

C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, first molar; M2, second molar; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch.

Table 4.

Amount of tooth displacement for the continuous arch with miniscrew in the midpalatal suture area (mm)

	X axis	Condition 1C	Condition 2C	Condition 3C
C.I	Cusp tip	6.10E-02	8.66E-02	1.16E-01
	Apex	-1.82E-02	-2.30E-02	-2.62E-02
L.I	Cusp tip	5.27E-02	6.47E-02	7.36E-02
	Apex	-1.48E-02	-2.51E-02	-3.04E-02
C	Cusp tip	3.54E-02	-7.89E-03	-8.04E-02
	Apex	-9.68E-03	9.16E-03	3.47E-02
PM2	Cusp tip	1.96E-02	-2.08E-02	-7.28E-02
	Apex	-9.44E-03	7.25E-03	3.02E-02
M1	Cusp tip	8.13E-03	-8.69E-03	-3.67E-02
	Apex	-3.30E-03	3.24E-03	1.38E-02
M2	Cusp tip	3.11E-03	-4.11E-03	-1.82E-02
	Apex	-1.30E-03	1.54E-03	6.96E-03
	Y axis	Condition 1C	Condition2C	Condition3C
C.I	Cusp tip	-1.10E-01	-9.98E-02	-6.66E-02
	Apex	2.53E-02	8.38E-03	-2.47E-02
L.I	Cusp tip	-1.10E-01	-7.57E-02	-7.70E-03
	Apex	3.85E-02	2.43E-02	-1.15E-02
C	Cusp tip	-1.18E-01	-4.41E-02	5.73E-02
	Apex	3.20E-02	9.06E-04	-3.46E-02
PM2	Cusp tip	1.72E-02	3.10E-03	4.84E-03
	Apex	-8.04E-03	-6.22E-03	-1.01E-02
M1	Cusp tip	1.35E-03	-1.59E-03	-9.75E-03
	Apex	-1.69E-03	2.51E-03	1.09E-02
M2	Cusp tip	-3.72E-04	-2.64E-03	-1.61E-02
	Apex	-5.95E-04	1.55E-03	7.68E-03
	Z axis	Condition 1C	Condition 2C	Condition 3C
C.I	Cusp tip	-5.61E-02	-3.76E-02	3.89E-03
	Apex	4.76E-02	4.81E-02	4.35E-02
L.I	Cusp tip	-5.73E-02	-4.00E-02	4.82E-04
	Apex	3.69E-02	3.08E-02	1.58E-02
C	Cusp tip	-3.74E-02	-5.14E-03	3.55E-02
	Apex	4.06E-02	1.02E-02	-3.55E-02
PM2	Cusp tip	2.46E-03	9.97E-03	2.25E-02
	Apex	3.72E-03	1.86E-03	-3.28E-03
M1	Cusp tip	-1.17E-03	5.49E-04	-1.33E-04
	Apex	2.06E-03	-2.43E-03	-1.14E-02
M2	Cusp tip	-1.99E-04	-4.83E-04	-2.66E-03
	Apex	1.36E-03	-3.66E-04	6.28E-04

C.I, Central incisorå L.I, lateral incisorå C, canineå PM2, second premolarå M1, first molarå M2, second molarå condition 1C, lever arm length of 0 mm with continuous archå condition 2C, lever arm legnth of 10 mm with continuous archå condition 3C, lever arm length of 20 mm with continuous arch.

Table 5.

Amount of tooth displacement for the segmented arch with miniscrew in the midpalatal suture area (mm)

	X axis	Condition 1D	Condition 2D	Condition 3D
C.I	Cusp tip	5.76E-02	9.05E-02	1.38E-01
	Apex	-1.70E-02	-2.37E-02	-3.42E-02
L.I	Cusp tip	5.17E-02	6.50E-02	7.80E-02
	Apex	-1.48E-02	-2.26E-02	-3.20E-02
C	Cusp tip	3.75E-02	-1.46E-02	-9.65E-02
	Apex	-8.75E-03	7.68E-03	3.35E-02
PM2	Cusp tip	8.81E-06	-5.20E-06	-2.69E-05
	Apex	-1.11E-05	-1.51E-05	-2.01E-05
M1	Cusp tip	-9.76E-06	-1.85E-05	-3.06E-05
	Apex	-6.03E-06	-6.09E-06	-5.63E-06
M2	Cusp tip	-8.47E-06	-1.39E-05	-2.13E-05
	Apex	-2.47E-06	1.51E-07	4.29E-06
	Y axis	Condition 1D	Condition 2D	Condition 3D
C.I	Cusp tip	-1.14E-01	-1.06E-01	-8.21E-02
	Apex	2.69E-02	7.96E-03	-2.15E-02
L.I	Cusp tip	-1.18E-01	-7.72E-02	-6.07E-03
	Apex	4.22E-02	2.23E-02	-1.18E-02
C	Cusp tip	-1.29E-01	-3.63E-02	1.14E-01
	Apex	3.62E-02	3.16E-03	-4.95E-02
PM2	Cusp tip	-2.06E-05	-1.33E-05	-7.29E-07
	Apex	-5.04E-05	-3.75E-05	-1.40E-05
M1	Cusp tip	-2.84E-05	-1.98E-05	-4.60E-06
	Apex	-1.89E-05	-1.24E-05	-1.06E-06
M2	Cusp tip	-3.01E-05	-2.13E-05	-5.62E-06
	Apex	-8.26E-06	-5.36E-06	-3.22E-07
	Z axis	Condition 1D	Condition 2D	Condition 3D
C.I	Cusp tip	-5.82E-02	-4.10E-02	-1.12E-02
	Apex	4.93E-02	4.92E-02	4.40E-02
L.I	Cusp tip	-6.01E-02	-4.04E-02	-5.09E-03
	Apex	4.03E-02	2.98E-02	1.02E-02
C	Cusp tip	-3.94E-02	7.87E-04	6.50E-02
	Apex	4.59E-02	1.23E-02	-4.14E-02
PM2	Cusp tip	-3.92E-06	-5.39E-07	4.89E-06
	Apex	-5.59E-06	-3.27E-06	6.98E-07
M1	Cusp tip	-5.32E-06	-1.72E-06	4.15E-06
	Apex	-2.85E-06	-3.48E-06	-4.18E-06
M2	Cusp tip	1.01E-06	2.10E-06	3.63E-06
	Apex	1.05E-05	5.38E-06	-3.26E-06

C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, irst molar; M2, second molar; condition 1D, lever arm legnth of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch.

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