Korean J Orthod.  2009 Oct;39(5):278-288.

Finite-element analysis of the shift in center of resistance of the maxillary dentition in relation to alveolar bone loss

• Sung SJ
• Kim IT
• Kook YA
• Chun YS
• Kim SH
• Mo SS

Abstract

OBJECTIVE
The aim of this study was to investigate the changes in the center of resistance of the maxillary teeth in relation to alveolar bone loss.
METHODS
A finite element model, which included the upper dentition and periodontal ligament, was designed according to the amount of bone loss (0 mm, 2 mm, 4 mm). The teeth in each group were fixed with buccal and lingual arch wires and splint wires. Retraction and intrusion forces of 200 g for 4 and 6 anterior teeth groups and 400 g for the full dentition group were applied.
RESULTS
The centers of resistance were at 13.5 mm, 14.5 mm, 15 mm apical and 12 mm, 12 mm, 12.5 mm posterior in the 4 incisor group; 13.5 mm, 14.5 mm, 15 mm apical and 14 mm, 14 mm, 14.5 mm posterior in the 6 anterior teeth group; and 11 mm, 13 mm, 14.5 mm apical and 26.5 mm, 27 mm, 25.5 mm posterior in the full dentition group respectively according to 0 mm, 2 mm, 4 mm bone loss.
CONCLUSIONS
The center of resistance shifted apically and posteriorly as alveolar bone loss increased in 4 and 6 anterior teeth groups. However, in the full dentition group, the center of resistance shifted apically and anteriorly in the 4 mm bone loss model.

Keyword

Finite element analysis; Center of resistance; Alveolar bone loss; Maxillary full dentition

MeSH Terms

Alveolar Bone Loss
Dentition
Finite Element Analysis
Incisor
Periodontal Ligament
Splints
Tooth

Figure

• 

  Fig. 1 3-Dimensional finite element mesh of tooth-periodontal ligament (PDL)-alveolar bone of the maxillary dentition. A, Lateral view of maxillary dentition; B, C and D, lateral views of tooth-PDL-alveolar bone model with 0 mm, 2 mm and 4 mm alveolar bone loss respectively.

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  Fig. 2 Finite element models of tooth groups. A, Four anterior teeth; B, six anterior teeth; C, maxillary full dentition. Blue wires on the buccal and palatal surface of the teeth are assumed as rigid body and have no play with brackets, so the movement of individual tooth is limited. Black wires crossing each left and right tooth are designed to distribute the applied force evenly on the dentition; D, vertical and horizontal force application.

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  Fig. 3 Schematic drawings of the coordinate system.

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  Fig. 4 The vertical position of center of resistance. A, Four anterior teeth: center of resistance (CR) are the points on the Z axis where each bone loss line crosses the sum of displacement (Δy) = 0 line, which are 13.5 mm, 14.5 mm and 15 mm for 0 mm, 2 mm, and 4 mm bone loss respectively; B, six anterior teeth: CR are the points on the Z axis where each bone loss line crosses the sum of displacement (Δy) = 0 line, which are 13.5 mm, 14.5 mm and 15.5 mm for 0 mm, 2 mm, and 4 mm bone loss respectively; C, maxillary full dentition: CR are the points on the Z axis where each bone loss line crosses the sum of displacement (Δy) = 0 line, which are 11 mm, 13 mm and 14.5 mm for 0 mm, 2 mm, and 4 mm bone loss respectively.

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  Fig. 5 The horizontal position of center of resistance. A, Four anterior teeth: CR are the points on the Y axis where each bone loss line crosses (or is closest to) the standard deviation of displacement (Δz) = 0 line, which are -12 mm, -12 mm and -12.5 mm for 0 mm, 2 mm, and 4 mm bone loss respectively; B, six anterior teeth: CR are the points on the Y axis where each bone loss line crosses (or is closest to) the standard deviation of displacement (Δz) = 0 line, which are -14 mm, -14 mm and -14.5 mm for 0 mm, 2 mm, and 4 mm bone loss respectively; C, maxillary full dentition: CR are the points on the Y axis where each bone loss line crosses (or is closest to) the standard deviation of displacement (Δz) = 0 line, which are -26.5 mm, -27 mm and -25.5 mm for 0 mm, 2 mm, and 4 mm bone loss respectively.

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  Fig. 6 The vertical and horizontal position of the center of resistance. Round, rectangular, triangle dots indicate the center of resistance of four incisors, six anterior teeth, and maxillary full dentition respectively, and black, blue and green colors represent 0 mm, 2 mm, 4 mm alveolar bone loss respectively.

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