Korean J Orthod.  2012 Aug;42(4):159-168. 10.4041/kjod.2012.42.4.159.

Three-dimensional finite element analysis of the deformation of the human mandible: a preliminary study from the perspective of orthodontic mini-implant stability

  • 1Division of Orthodontics, Department of Dentistry, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Korea. ssjmail@amc.seoul.kr
  • 2Division of Prosthodontics, Department of Dentistry, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Korea.
  • 3Department of Orthodontics, College of Dentistry, Yonsei University, Seoul, Korea.


The aims of this study were to investigate mandibular deformation under clenching and to estimate its effect on the stability of orthodontic mini-implants (OMI).
Three finite element models were constructed using computed tomography (CT) images of 3 adults with different mandibular plane angles (A, low; B, average; and C, high). An OMI was placed between #45 and #46 in each model. Mandibular deformation under premolar and molar clenching was simulated. Comparisons were made between peri-orthodontic mini-implant compressive strain (POMI-CSTN) under clenching and orthodontic traction forces (150 g and 200 g).
Three models with different mandibular plane angles demonstrated different functional deformation characteristics. The compressive strains around the OMI were distributed mesiodistally rather than occlusogingivally. In model A, the maximum POMI-CSTN under clenching was observed at the mesial aspect of #46 (1,401.75 microstrain [microE]), and similar maximum POMI-CSTN was observed under a traction force of 150 g (1,415 microE).
The maximum POMI-CSTN developed by clenching failed to exceed the normally allowed compressive cortical bone strains; however, additional orthodontic traction force to the OMI may increase POMI-CSTN to compromise OMI stability.


Orthodontic mini-implant; Stability; Neuromuscular force; Anatomy; Finite element method

MeSH Terms

Finite Element Analysis
Sprains and Strains


  • Figure 1 Segmentation and 3-dimensional surface generation with Bionix program (A) and finite element model construction using Hypermesh program (B).

  • Figure 2 The 3 finite element models. A, Model A (low angle); B, model B (average angle); C, model C (high angle).

  • Figure 3 The position and insertion angulation of the OMI in the FE model, and schematic modeling of the temporomandibular joint. A, Buccal view; B, occlusal view; C, cross-sectional view of #45 and #46; D, cross-sectional view of the right temporomandibular joint.

  • Figure 4 The cylindrical coordinate system for the application of orthotropic material properties. A, The cross-section of the mandibular body was selected at half its height. B, Five ellipses were drawn that best fit the right and left sections. The 5 centers of the ellipses and the 5 ratios between the lengths of the semimajor axes and the semiminor axes were calculated. Solid arrows indicate the material x-axis (x'). Dotted arrows indicate the material y-axis (y').

  • Figure 5 Four jaw-closing muscles and their lines of action. A, M: masseter muscle, T: temporal muscle; B, MT: medial pterygoid muscle, LT: lateral pterygoid muscle; C, boundary conditions for the clenching simulation.

  • Figure 6 Twenty-four reference nodes of the cortical bone. Reference node 1 is at the most occlusal direction.

  • Figure 7 The deformed shape (colored) with the undeformed model (white) after simulated molar clenching with orthotropic material properties (100× magnification). A, Model A; B, model B; C, model C.

  • Figure 8 Comparison of the strain distribution of the mandible under clenching in 3 models. A, Compressive strain; B, tensile strain. Unit: microstrain (µE).

  • Figure 9 Comparison of the peri-orthodontic mini-implant compressive strain using a polar line chart. Red dotted line-model A (isotropic); red solid line-model A (orthotropic); blue dotted line-model B (isotropic); blue solid line-model B (orthotropic); green dotted line-model A (isotropic); green solid line-model A (orthotropic). Unit: microstrain (µE).

  • Figure 10 Comparison of peri-orthodontic mini-implant compressive strain with a contour plot in model. A, During clenching; B, under a traction force of 150 g. Unit: microstrain (µE).


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