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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Hammoudeh, J. A. , Howell, L. K. , Boutros, S. , Scott, M. A. , and Urata, M. M. , 2015, “ Current Status of Surgical Planning for Orthognathic Surgery: Traditional Methods Versus 3D Surgical Planning,” Plast. Reconstr. Surg. Global Open, 3(2), p. e307. [CrossRef]
Pujol, S. , Baldwin, M. , Nassiri, J. , Kikinis, R. , and Shaffer, K. , 2016, “ Using 3D Modeling Techniques to Enhance Teaching of Difficult Anatomical Concepts,” Acad. Radiol., 23(4), pp. 507–516. [CrossRef] [PubMed]
Jimenez-Delgado, J. J. , Paulano-Godino, F. , PulidoRam-Ramirez, R. , and Jimenez-Perez, J. R. , 2016, “ Computer Assisted Preoperative Planning of Bone Fracture Reduction: Simulation Techniques and New Trends,” Med. Image Anal., 30(5), pp. 30–45. [CrossRef] [PubMed]
Wang, M. J. , Li, H. L. , Si, J. W. , Wang, X. D. , Shen, S. G. F. , and Yu, H. B. , 2016, “ The Application of Digital Model Surgery in the Treatment of Dento-Maxillofacial Deformities,” Int. J. Clin. Exp. Med., 9(2), pp. 1808–1814.
Adolphs, N. , Liu, W. , Keeve, E. , and Hoffmeister, B. , 2013, “ Craniomaxillofacial Surgery Planning Based on 3D Models Derived From Cone-Beam CT Data,” Comput. Aided Surg., 18(5–6), pp. 101–108. [CrossRef] [PubMed]
Liu, Y. F. , Liao, W. Q. , Jin, G. S. , Yang, Q. M. , and Peng, W. , 2014, “ Additive Manufacturing and Digital Design Assisted Precise Apicoectomy: A Case Study,” Rapid Prototyping J., 20(1), pp. 33–40. [CrossRef]
Liu, Y.-F. , Xu, L.-W. , Zhu, H.-Y. , and Liu, S. S.-Y. , 2014, “ Technical Procedures for Template-Guided Surgery for Mandibular Reconstruction Based on Digital Design and Manufacturing,” Biomed. Eng. Online, 13, p. 63. [CrossRef] [PubMed]
Hart, R. T. , Hennebel, V. V. , Thongpreda, N. , Van Buskira, W. C. , and Anderson, R. C. , 1992, “ Modeling the Biomechanics of the Mandible: A Three-Dimensional Finite Element Study,” J. Biomech., 25(3), pp. 261–286. [CrossRef] [PubMed]
Vollmer, D. , Meyer, U. , Joos, U. , Vegh, A. , and Piffko, J. , 2000, “ Experimental and Finite Element Study of a Human Manbile,” J. Cranio-Maxillofac. Surg., 28(2), pp. 91–96. [CrossRef]
Singh, P. , Wang, C. , Ajmera, D. H. , Xiao, S. S. , Song, J. , and Ling, Z. , 2016, “ Biomechanical Effects of Novel Osteotomy Approaches on Mandibular Expansion: A Three-Dimensional Finite Element Analysis,” J. Oral Maxillofac. Surg., 74(8), pp. 1658.e1–1658.e15. [CrossRef]
Hylander, W. , 1984, “ Stress and Strain in the Mandible Symphysis of Primates: A Test of Competing Hypotheses,” Am. J. Phys. Anthropol., 64(1), pp. 1–46. [CrossRef] [PubMed]
Groning, F. , Liu, J. , Fagan, M. J. , and O'Higgins, P. , 2009, “ Validating a Voxel-Based Finite Element Model of a Human Mandible Using Digital Speckle Pattern Interferometry,” J. Biomech., 42(9), pp. 1224–1229. [CrossRef] [PubMed]
Liao, S. H. , Tong, R. F. , and Dong, J. X. , 2007, “ Anisotropic Finite Element Modeling for Patient-Specific Mandible,” Comput. Methods Programs Biomed., 88(3), pp. 197–209. [CrossRef] [PubMed]
de Zee, M. , Dalstra, M. , Cattaneo, P. M. , Rasmussen, J. , Svensson, P. , and Melsen, B. , 2007, “ Validation of a Musculo-Skeletal Model of the Mandible and Its Application to Mandibular Distraction Osteogenesis,” J.Biomech., 40(6), pp. 1192–1201. [CrossRef] [PubMed]
Shah, J. J. , and Mantyla, M. , 1995, Parametric and Feature-Based CAD/CAM Concepts, Techniques, Applications, Wiley, Chichester, UK.
Chaudhary, N. , Lovald, S. T. , Wagner, J. , Khraishi, T. , and Baack, B. , 2008, “ Experimental and Numerical Modeling of Screws Used for Rigid Internal Fixation of Mandibular Fractures,” Model. Simul. Eng., 2008(3), p. 628120.
Kan, B. , Coskunses, F. M. , Mutlu, I. , Ugur, L. , and Meral, D. G. , 2015, “ Effects of Inter-Implant Distance and Implant Length on the Response to Frontal Traumatic Force of Two Anterior Implants in an Atrophic Mandible: Three-Dimensional Finite Element Analysis,” Int. J. Oral Maxillofac. Surg., 44(7), pp. 908–913. [CrossRef] [PubMed]
Davis, M. L. , Vavalle, N. A. , Stitzel, J. D. , and Gayzik, F. S. , 2015, “ A Technique for Developing CAD Geometry of Long Bones Using Clinical CT Data,” Med. Eng. Phys., 37(11), pp. 1116–1123. [CrossRef] [PubMed]
Bujtar, P. , Sandor, G. K. B. , Bojtos, A. , Szucs, A. , and Barabas, J. , 2010, “ Finite Element Analysis of the Human Mandible at 3 Different Stages of Life,” Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endodontol., 110(3), pp. 301–309. [CrossRef]
Szucs, A. , Bujtar, P. , Sandor, G. K. B. , and Barabas, J. , 2010, “ Finite Element Analysis of the Human Mandible to Assess the Effect of Removing an Impacted Third Molar,” J. Can. Dent.Assoc., 76(a72), pp. 1–7.
Lin, D. , Li, Q. , Li, W. , Duckmanton, N. , and Swain, M. , 2010, “ Mandibular Bone Remodeling Induced by Dental Implant,” J. Biomech., 43(2), pp. 287–293. [CrossRef] [PubMed]
Morvan, J. M. , and Thibert, B. , 2002, “ Smooth Surface and Triangular Mesh: Comparison of the Area, the Normals and the Unfolding,” Seventh ACM Symposium of Solid Modeling and Applications (SMA), Saarbrücken, Germany, June 17–21, pp. 147–158.
Attene, M. , Falcidieno, B. , Spagnuolo, M. , and Wyvill, G. , 2003, “ A Mapping-Independent Primitive for the Triangulation of Parametric Surfaces,” Gr. Models, 65(5), pp. 260–273. [CrossRef]
Farin, G. , 2002, Curves and Surfaces for CAGD, 5th ed., Morgan Kaufmann Publishers, San Francisco, CA.
Ko, K. H. , 2003, “ Algorithms for Three-Dimensional Free-Form Object Matching,” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Piegl, L. , and Tille, W. , 1995, The NURBS Book, Springer-Verlag, Berlin. [CrossRef]
Rice, J. C. , 1988, “ On the Dependence of the Elasticity and Strength of Cancellous Bone on the Apparent Density,” J. Biomech., 21(2), pp. 155–168. [CrossRef] [PubMed]
Rho, J. Y. , Hobatho, M. C. , and Ashman, R. B. , 1995, “ Relations of Mechanical Properties to Density and CT Numbers in Human Bone,” Med. Eng. Phys., 17(5), pp. 347–355. [CrossRef] [PubMed]
Bezerra, T. P. , Silva, F. , Scarparo, H. C. , Costa, F. W. , and Studart-Soares, E. C. , 2013, “ Do Erupted Third Molars Weaken the Mandibular Angle After Trauma to the Chin Region? A 3D Finite Element Study,” Int. J. Oral. Maxillofac. Surg., 42(4), pp. 474–480. [CrossRef] [PubMed]
Antic, S. , Vukicevic, A. M. , Milasinovic, M. , Savejic, I. , Jovicic, G. , Filipovic, N. , Rakocevic, Z. , and Djuric, M. , 2015, “ Impact of the Lower Third Molar Presence and Position on the Fragility of Mandibular Angle and Condyle: A Three-dimensional Finite Element Study,” J. Cranio-Maxillofac. Surg., 43(6), pp. 870–878. [CrossRef]
Nalla, R. K. , Kinney, J. H. , and Ritchie, R. O. , 2003, “ Mechanistic Fracture Criteria for the Failure of Human Cortical Bone,” Nat. Mater., 2(3), pp. 164–168. [CrossRef] [PubMed]
Evans, G. F. , 1976, “ Mechanical Properties and Histology of Cortical Bone From Younger and Older Men,” Anat. Rec., 185(1), pp. 1–11. [CrossRef] [PubMed]
de Mello Santos, L. S. , Rossi, A. C. , Freire, A. R. , Matoso, R. I. , Caria, P. H. F. , and Prado, F. B. , 2015, “ Finite-Element Analysis of 3 Situations of Trauma in the Human Edentulous Mandible,” J. Oral Maxillofac. Surg., 73(4), pp. 683–691. [CrossRef] [PubMed]
Provatidis, C. , Georgiopoulos, B. , Kotinas, A. , and McDonald, J. P. , 2007, “ On the FEM Modeling of Craniofacial Changes During Rapid Maxillary Expansion,” Med. Eng. Phys., 29(5), pp. 566–579. [CrossRef] [PubMed]
Ainsworth, M. , and Oden, J. T. , 1997, “ A Posteriori Error Estimation in Finite Element Analysis,” Comput. Methods Appl. Mech. Eng., 142(1–2), pp. 1–88. [CrossRef]
Magne, P. , 2007, “ Efficient 3D Finite Element Analysis of Dental Restorative Procedures Using Micro-CT Data,” Dent. Mater., 23(5), pp. 539–548. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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)

Grahic Jump Location
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.

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In