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

Sang-Jin Sung; In-Tai Kim; Yoon-Ah Kook; Youn-Sic Chun; Seong-Hun Kim; Sung-Seo Mo

doi:10.4041/kjod.2009.39.5.278

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Sung, Kim, Kook, Chun, Kim, and Mo: Finite-element analysis of the shift in center of resistance of the maxillary dentition in relation to alveolar bone loss

Original Article

Korean Journal of Orthodontics

Korean Journal of Orthodontics 2009; 39(5): 278-288.

Published online: 31 October 2009

DOI: https://doi.org/10.4041/kjod.2009.39.5.278

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

Sang-Jin Sung, DDS, MSD, PhD^a, In-Tai Kim, DMD, MSD^b, Yoon-Ah Kook, DDS, MSD, PhD^c, Youn-Sic Chun, DDS, MSD, PhD^d, Seong-Hun Kim, DMD, MSD, PhD^e, Sung-Seo Mo, DDS, MSD, PhD^f

^aAssociate Professor, Department of Orthodontics, University of Ulsan College of Medicine, Asan Medical Center, Korea.

^bPostgraduate Student, Graduate School of Clinical Dental Science, The Catholic University of Korea, Korea.

^cProfessor, Division of Orthodontics, Department of Dentistry, College of Medicine, The Catholic University of Korea, Seoul St. Mary's Hospital, Korea.

^dProfessor, Division of Orthodontics, Department of Dentistry, School of Medicine, Ewha Womans University, Korea.

^eAssistant Professor, Division of Orthodontics, Department of Dentistry, College of Medicine, The Catholic University of Korea, Uijongbu St. Mary's Hospital, Korea.

^fAssistant Professor, Division of Orthodontics, Department of Dentistry, College of Medicine, The Catholic University of Korea, St. Mary's Hospital, Korea.

Corresponding author: Sung-Seo Mo. Department of Orthodontics, The Catholic University of Korea College of Medicine, St. Mary's Hospital, #62, Yeouido-dong, Youngdeungpo-gu, Seoul 150-713, Korea. +82 2 3779 1316; dmoss1@hanmail.net

Received 22 July 2009 Revised 27 August 2009 Accepted 29 August 2009

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.

Keywords: Finite element analysis, Center of resistance, Alveolar bone loss, Maxillary full dentition

Figures and Tables

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.

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.

Fig. 3

Schematic drawings of the coordinate system.

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.

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.

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.

Table 1

Mechanical properties of each material

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