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The effectiveness of element downsizing on finite element
domains of infinite/finite element analysis in an implant-bonesystem
Jianping Geng, BDS, DrPH, MScD,a Xuanxiang Ma, DDS, PhD,b Gui-Rong Liu,PhD,c and Lung-an Ying, PhDdabChina Medical University Huayu Hospital, Shaoxing, P. R. China, Fourth Military Medical
cUniversity, Xi’an, P. R. China, Faculty of Engineering, National University of Singapore,dSingapore, and School of Mathematical Science, Peking University, Beijing, P. R. China
Purpose: The aim of this study is to investigate the effectiveness of element downsizing on finite element(FE) domains of infinite/finite element (IE/FE) analysis in an implant-bone system.
Materials and Methods: A 2-dimentional implant-bone system was studied by FE analysis and IE/FE
analysis respectively. Different element sizes of 3.0, 2.0, 1.0, and 0.5 mm were applied in FE domains
respectively.
Results: In IE/FE analysis, element size of 2.0 mm is suggested to be effective. While, in FE analysis, thatis 0.5 mm.
Conclusion: Larger element size can be applied in IE/FE analysis than that in FE analysis only.
(Int Chin J Dent 2004; 4: 63-66.)
Clinical Significance: IE/FE analysis will be a more effective method than FE analysis in dental
biomechanical study.
Key Words: element analysis, element size, implant, infinite element analysis.

Introduction
In 1977, Weinstein1 was the first to use finite element (FE) analysis in implant dentistry. Subsequently,
FE analysis was rapidly applied in many other aspects of implant dentistry. Vertical and transverse loads
from mastication induce axial forces and bending moments and result in stress gradients in the implant aswell as in the bone. A key factor for the success or failure of a dental implant is the manner in whichstresses are transferred to the surrounding bone. Load transfer from implants to surrounding bone depends
on the type of loading, the bone-implant interface, the length and diameter of the implants, the shape andcharacteristics of the implant surface, the prosthesis type and the quantity and quality of the surrounding
bone. FE analysis allows researchers to predict stress distribution in the contact area of the implants withcortical bone and around the apex of the implants in trabecular bone.
Infinite element (IE) analysis is a combination of an infinite partition technique and finite element
analysis.2 The first paper on this combination was by Thatcher.2 Infinite element analysis, as its nameindicates, can divide the domain into infinitely many pieces, causes more accuracy in computation of local
domains, especially stress concentration domains.3
For a given problem, if it is sufficient to use FE analysis, then, the conventional approach was used.
Otherwise, infinite element analysis was used to get higher precise.

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differently. To complex problems, infinite element analysis is only used in stress concentration domains
and finite element analysis is still used in other domains. That is infinite/finite element (IE/FE) analysis.
As Sato et al.4 mentioned, the element sizes were important for the validity of FE analysis. This study isto investigate the proper element size in IE/FE analysis in an implant-bone system and compare with that inFE analysis only.

Materials and Methods
Huang et al.5 modeled an endodontic endosseous implant in trabecular bone. The 2-dimentional dental
implant system was constructed based on a geometric and radiographic analysis of a section of incisionresidual root with endodontic endosseous implant in place. A vertical 100 N loading was applied at the topof implant. The elastic properties of responding materials in the model were shown in Table 1.
Table 1. Material parameters used in the implant-bone system.
Material

Elastic modulus (Pa)

Implant pure Ti
DentinPeriodontal membrane
Cortical bone
Trabecular bone

117x103
1.86x1046.9
1.34x104
1.37x103

Poisson’s Ratio
0.30
0.31
0.45
0.30
0.31

Author, Year
Ronald, 1995
Reinhardt, 1984
Farah, 1989
Cook, 1982
Borchers, 1983

Reference number
678910For FE analysis, four different element sizes of 3.0, 2.0, 1.0, and 0.5 mm were conducted in theimplant-bone system. These were termed models F30, F20, F10, and F05. The FE analysis was taken
under the software of Super-SAP5 (1991, Algorithm Corp., Pittsburgh, PA, USA).
For IE/FE analysis, four different element sizes of 3.0, 2.0, 1.0, and 0.5 mm were also conducted in theimplant-bone system except IE domains. Here, IE domains are the stress concentration domains aroundright-hand apical foramen of Huang's model. These were termed models I/F30, I/F20, I/F10, and I/F05.
Dirichlet-Neumann method was applied to conjunct IE and FE domains. The varies of displacements in theboundary was treated as the target function and the similar boundary condition was obtained by iterative
computation of the displacements outputted by FE analysis and the stresses outputted by IE analysis.

Results
Some key nodes in the implant model were calculated. Values of displacement induced with thedownsizing element at the nodes near stress concentration point. Displacement in the model F10, I/F30
was higher than that in the model F05, I/F20. However, there was no clear difference of displacement
values among the model F05, I/F20, I/F10, I/F05 (Fig. 1).

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Displacement (*e-3 mm)

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0-0.5

1234-1FEM models
IEM/FEM models

-1.5
-2
-2.5
05

102030Fig. 1. Values of displacement at one of respective notes in IE/FE and FE models.

Discussion
The maximum stress and responding displacement are at the node of stress concentration point.
Therefore, some key nodes near stress concentration point were selected to measure the effectiveness ofdownsizing element.

That is because mechanical quantities vary violently at these points and moresignificant changes could be found with downsizing element.
IE/FE analysis is a new method in calculation mechanics. It is the combination of IE analysis and FEanalysis. Effectiveness of downsizing element showed that it is significant from 3.0 to 2.0 in IE/FEanalysis, while, from 1.0 to 0.5 in FE analysis. That means the proper element size is recommended to be
2.0 mm in IE/FE analysis while less 0.5 mm in FE analysis. Larger element size will save computer
memory and calculation time. Therefore, IE/FE analysis is a more effective method in dental implantbiomechanical study.

References
1. Weinstein AM, Klawitter JJ, Anand SC, Schuessler R. Stress analysis of porous rooted dental implants. Implantologist
1977; 1: 104-9.
2. Ying LA. Infinite element methods. Beijing: Peking University Press; 1995.
3. Ying LA. The infinite similar element method for calculating stress intensity factors. Scientia Sinica 1978; 21: 19-43.
4. Sato Y, Wadamoto M, Tsuga K, Teixeira ER. The effectiveness of element downsizing on a three-dimensional finiteelement model of bone trabeculae in implant biomechanics. J Oral Rehabil 1999; 26: 288-91.
5. Huang H, Ma XX, Zhang SF. A mechanical model of endodontic endosseous implant. J Practical Stomatol 1996; 12:119-21.
6. Ronald LS, Svenn EB. Nonlinear contact analysis of preload in dental implant screws. Int J Oral Maxillofac Implants
1995; 10: 295-302.
7. Reinhardt RA, Pao YC, Krejci RF. Periodontal ligament stresses in the initiation of occlusal traumatism. J Periodontal
Res 1984; 19: 238-46.
8. Farah JW, Craig RG, Meroueh KA. Finite element analysis of three- and four-unit bridges. J Oral Rehabil 1989; 16:603-11.
9. Cook SD, Klawitter JJ, Weinstein AM. A model for the implant-bone interface characteristics of porous dental implants.
J Dent Res 1982; 61: 1006-9.
10. Borchers L, Reichart P. Three-dimensional stress distribution around a dental implant at different stages of interface
development. J Dent Res 1983; 62:155-9.

Acknowledgment
This study is partly supported by the National Natural Science Foundation (P. R. China, No.39570769).

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Reprint request to:
Dr. Xuanxiang Ma
Department of Prosthodontics, School of Stomatology, Fourth Military Medical University
7 Kangfu Road, Xi’an, 710032, P. R. China
TEL: +86-29-83376126
Received June 11, 2004. Revised July 13, 2004. Accepted August 15, 2004.
Copyright ©2004 by the Editorial Council of the International Chinese Journal of Dentistry.

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