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Technical Briefs

Accuracy of Individual Trabecula Segmentation Based Plate and Rod Finite Element Models in Idealized Trabecular Bone Microstructure

[+] Author and Article Information
Hong Wang

Department of Engineering Mechanics,
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, PRC
e-mail: wanghong06@mails.tsinghua.edu.cn

X. Sherry Liu

McKay Orthopaedic Research Laboratory,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: xiaoweil@mail.med.upenn.edu

Bin Zhou

e-mail: bz2159@columbia.edu

Ji Wang

e-mail: jw2857@columbia.edu
Bone Bioengineering Laboratory,
Department of Biomedical Engineering,
Columbia University,
New York, NY 10027

Baohua Ji

Biomechanics and Biomaterials Laboratory,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, PRC
e-mail: bhji@bit.edu.cn

Yonggang Huang

Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: y-huang@northwestern.edu

Keh-Chih Hwang

Department of Engineering Mechanics,
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, PRC
e-mail: huangkz@mail.tsinghua.edu.cn

X. Edward Guo

Bone Bioengineering Laboratory,
Department of Biomedical Engineering,
Columbia University,
New York, NY 10027
e-mail: ed.guo@columbia.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received September 5, 2012; final manuscript received January 14, 2013; accepted manuscript posted March 16, 2013; published online April 5, 2013. Assoc. Editor: Yener N. Yeni.

J Biomech Eng 135(4), 044502 (Apr 05, 2013) (5 pages) Paper No: BIO-12-1393; doi: 10.1115/1.4023983 History: Received September 05, 2012; Revised January 14, 2013

Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

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Figures

Grahic Jump Location
Fig. 1

Schematics of the experimental design for a comparison of the voxel-based FE model and the PR model for (a) plate-rod, and (b) rod-rod structures. The generation of the PR model and the voxel model were illustrated only in a unit cell.

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Fig. 2

Stress–strain curves under a uniaxial compression test of the idealized (a) plate-rod structure, and (b) rod-rod structure with varying trabecular thicknesses: 80, 160, 240, and 320 μm (voxel size: 20 μm)

Grahic Jump Location
Fig. 3

Linear correlation of the normalized Young's modulus E*/Es between the PR and voxel models for the idealized (a) plate-rod structure, and (b) rod-rod structure; correlation of normalized yield strength σy*/Es between the PR and voxel models for the idealized (c) plate-rod structure, and (d) rod-rod structure

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