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Research Papers

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone

[+] Author and Article Information
Yun-feng Liu

Key Laboratory of E&M,
Ministry of Education and Zhejiang Province,
Zhejiang University of Technology,
Hangzhou 310014, China
e-mail: liuyf76@126.com

Ying-ying Fan

Key Laboratory of E&M,
Ministry of Education and Zhejiang Province,
Zhejiang University of Technology,
Hangzhou 310014, China

Hui-yue Dong

Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310007, China

Jian-xing Zhang

Department of Stomatology,
Zhejiang Provincial People's Hospital,
Hangzhou 310014, China

1Corresponding author.

Manuscript received March 14, 2017; final manuscript received August 10, 2017; published online September 28, 2017. Assoc. Editor: Michael Detamore.

J Biomech Eng 139(12), 121006 (Sep 28, 2017) (11 pages) Paper No: BIO-17-1108; doi: 10.1115/1.4037633 History: Received March 14, 2017; Revised August 10, 2017

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

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Figures

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Fig. 1

Diagrams of triangular mesh and parametric surface: (a) triangular mesh and (b) parametric surface

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Fig. 2

Procedures involved in FEM modeling. The two solutions are based on both the CT images and the triangular mesh model.

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Fig. 3

Three-dimensional model of mandible reconstructed from CT images. The mandible was separated from whole tissues by extracting regions of interest: (a) coronal plane, (b) transverse plane, (c) sagittal plane, and (d) 3D view.

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Fig. 4

Volume mesh created from triangular mesh: the hollow of the surface model with the triangular mesh is filled with the volume mesh, but the internal structure of the bone marrow cavities remain hollow, thereby representing the actual structure of bone geometry: (a) triangular mesh model including 147,506 triangles, from the cut model certain internal structures can be seen and (b) tetrahedron mesh model including 419,296 elements, where the hollow model is filled by volume elements

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Fig. 5

Fixation of a customized plate was designed using triangular mesh model in 3-matic. There are many limitations in relation to the fixation holes, so a guide curve and a bent plate with two holes at two end sides need to be created directly; the other holes can then be designed based on a sketch, and extruded and merged with the bent plate using the unite operation: (a) guide curve designed on triangular mesh, (b) plate designed along the guide curve and bent with mesh surface, and (c) screw hole created by extruding a sketch and then uniting with plate.

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Fig. 6

Material properties of jaw bone divided into nine groups and shown using different colors, where each color with different grayscale represents a different density and Young's modulus. Young's modulus of bone is within 14.295 GPa, and the larger values are assigned to the teeth.

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Fig. 7

Parametric surface model creation: (a) curvature estimated based on triangular mesh (147,518 triangles) to create feature curves and separate initial patches using different colors (or different grayscale), (b) based on these feature curves, more patches created automatically on the triangular mesh for surface fitting (4876 patches), (c) patches were revised manually to obtain high quality for fitting (2183), (d) for each patch, interpolation grids created for fitting, which will determine the control points of each parametric surface, (e) surface model created by fitting of triangular mesh, and (f) parametric surface model compared to original triangular mesh model and deviation obtained

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Fig. 8

Finite element method mesh based on solid model: (a) seed points inserted into borders of each surface patch to create tetrahedral elements (approximate global size 2 mm) and (b) tetrahedral elements created from parametric surfaces (totally 24,633 elements)

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Fig. 9

Constraints and loading for numerical simulation. Muscles mimicked by springs, two condyles fixed on six degrees-of-freedom, and 500 N bite force loaded on left first molar.

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Fig. 10

Results based on triangular mesh FEM model: (a) von Mises stress distribution, (b) strain distribution, and (c) displacement distribution

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Fig. 11

Results based on parametric surface FEM model: (a) von Mises stress distribution in original model, where two singular areas exist (marked 1 and 2) causing stress concentration, (b) enlargement of singular area 1, (c) enlargement of singular area 2, where the stress peak decreased when singular area 1 was removed, (d) correct von Mises stress distribution of bone when two singular areas were removed from the whole model, (e) strain distribution, and (f) displacement distribution

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