TECHNICAL PAPERS: Bone/Orthopedics

Comparison of the Linear Finite Element Prediction of Deformation and Strain of Human Cancellous Bone to 3D Digital Volume Correlation Measurements

[+] Author and Article Information
R. Zauel, Y. N. Yeni, X. N. Dong

Bone and Joint Center,  Department of Orthopaedic Surgery, Henry Ford Health System, Detroit, MI 48202

B. K. Bay

 Oregon State University, Corvallis, OR 97331

D. P. Fyhrie1

Bone and Joint Center,  Department of Orthopaedic Surgery, Henry Ford Health System, Detroit, MI 48202


Corresponding author: Director of Research, Lawrence J. Ellison Musculoskeletal Research Center, University of California, Davis, 4635 Second Avenue, Room 2000, Sacramento, CA 95817; phone: (916)734-5079.

J Biomech Eng 128(1), 1-6 (Jul 21, 2005) (6 pages) doi:10.1115/1.2146001 History: Received November 03, 2003; Revised July 21, 2005

The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Flowchart for the project

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Figure 2

Prediction of FEM vertical deformation by DVC for femoral sample

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Figure 3

Prediction of FEM vertical strain by DVC for femoral sample

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Figure 4

Comparison of vertical displacement magnitude from DVC (left), averaged FEM (center), and actual FEM (right) for a coronal section through the femoral specimen. Colors represent displacement magnitude as presented in the key. The displacements are clearly similar and the averaged FEM displacements are comparable to those of the original FEM prediction. This shows both how the DVC and averaged FEM measures are similar and also that the averaging of the FEM was not so aggressive as to destroy its original character.

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Figure 5

Comparison of vertical strain (εzz) from DVC (left), strain calculatded from averaged FEM displacement (center), and actual FEM (right) for a coronal section through the femoral specimen. Colors represent strain presented in the key. The similarities between these strain panels are less than those for the displacement (Fig. 4).

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Figure 6

Average of the vertical strain (εzz) from the right panel of Fig. 5. These results, directly averaged from the FEM calculation of strain, are distinct from strain calculated from averaged FEM or from DVC measured displacements. Causes of the differences are discussed in the body of the text.



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