Korean J Orthod.  2009 Apr;39(2):83-94. 10.4041/kjod.2009.39.2.83.

Finite-element investigation of the center of resistance of the maxillary dentition

• Jeong GM
• Sung SJ
• Lee KJ
• Chun YS
• Mo SS

• KMID: 1975813
• DOI: http://doi.org/10.4041/kjod.2009.39.2.83

Abstract

OBJECTIVE
The aim of this study was to investigate the 3-dimensional position of the center of resistance of the 4 maxillary anterior teeth, 6 maxillary anterior teeth, and the full maxillary dentition using 3-dimensional finite element analysis. METHODS: Finite element models included the whole upper dentition, periodontal ligament, and alveolar bone. The crowns of the teeth in each group were fixed with buccal and lingual arch wires and lingual splint wires to minimize individual tooth movement and to evenly disperse the forces to the teeth. A force of 100 g or 200 g was applied to the wire beam extended from the incisal edge of the upper central incisor, and displacement of teeth was evaluated. The center of resistance was defined as the point where the applied force induced parallel movement. RESULTS: The results of study showed that the center of resistance of the 4 maxillary anterior teeth group, the 6 maxillary anterior teeth group, and the full maxillary dentition group were at 13.5 mm apical and 12.0 mm posterior, 13.5 mm apical and 14.0 mm posterior, and 11.0 mm apical and 26.5 mm posterior to the incisal edge of the upper central incisor, respectively. CONCLUSIONS: It is thought that the results from this finite element models will improve the efficiency of orthodontic treatment.

Keyword

Finite element analysis; Center of resistance; Maxillary 4 anterior teeth group; Maxillary 6 anterior teeth group; Full maxillary dentition group

MeSH Terms

Crowns
Dentition
Displacement (Psychology)
Finite Element Analysis
Incisor
Periodontal Ligament
Splints
Tooth
Tooth Movement

Figure

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  Fig 1 Three-dimensional finite element mesh of tooth-periodontal ligament (PDL)-alveolar bone of the maxillary dentition. A and B, Frontal and lateral views of upper dentition and PDL; C and D, frontal and lateral views of tooth-PDL-alveolar bone.

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  Fig 2 Schematic representation of the coordinate system.

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  Fig 3 Finite element models of the teeth group. A, Four anterior teeth; B, six anterior teeth; C, full maxillary dentition. Blue wires on the buccal and lingual surface of the teeth are rigid and have no play with brackets, so the movement of the individual tooth is limited. Black wires cross-link left and right teeth, designed to distribute the applied force evenly on the dentition. D, vertical and horizontal force application.

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  Fig 4 The sum of horizontal displacement (Δy) of four anterior teeth. A, Six anterior teeth; B, full maxillary dentition; C, varying on the position of force on the Z-axis.

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  Fig 5 Contour plot of the full maxillary dentition according to the direction of horizontal retraction force. Original model (white mesh) and deformed model (color) in which the horizontal (Δy) displacement of teeth was magnified 500 times were superimposed. See the color scale bar for exact finite element analysis of analyzed horizontal teeth displacement. A, The line of force passing (z = 11 mm) through CR causes parallel tooth movement; B, the line of force passing (z = 0 mm) below CR causes counter-clockwise rotation of occlusal plane; C, the line of force passing (z = 16 mm) above CR causes clockwise rotation of the occlusal plane.

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  Fig 6 Standard deviation of vertical displacement (Δz) of four anterior teeth. A, Six anterior teeth; B, full maxillary dentition; C, varying on the position of force on the Y-axis.

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  Fig 7 The contour plot of the full maxillary dentition according to the direction of vertical intrusion force. Original model (white mesh) and deformed model (color) in which the vertical (Δz) displacement of teeth was magnified 500 times were superimposed. See the color scale bar for exact finite element analysis of analyzed vertical teeth displacement. A, The line of force passing (y = -26.5 mm) through CR causes intrusion; B, the line of force passing (y = -17 mm) anteriorly to CR causes clockwise rotation of occlusal plane; C, the line of force passing (y = -35 mm) posteriorly to CR causes counter-clockwise rotation of the occlusal plane.

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  Fig 8 Position of the center of resistance. A, The center of resistance of four anterior teeth; B, the center of resistance of six anterior teeth; C, the center of resistance of the maxillary dentition.

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  Fig 9 Comparison of the position of the center of resistance from other studies. A, 4 anterior teeth: present study (black dot); Vanden Bulcke et al11 (yellow); Pedersen et al6 (blue); Matsui et al12 (red); B, 6 anterior teeth: present study (black); Vanden Bulcke et al11 (yellow); Pedersen et al6 (blue); Choy et al7 (green); C, full maxillary dentition: present study (black); Billiet et al8 (violet).

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