Shear stress distribution in the trabeculae of human vertebral bone

Fyhrie, D. P.; Hoshaw, S. J.; Hamid, M. S.; Hou, F. J.

Affiliations

¹Bone and Joint Center, Henry Ford Hospital, 2799 W. Grand Blvd., Detroit, MI

²Epidemiology and Biometrics, Dow Corning Corporation, P. O. Box 994, Mail #C1270 Midland, MI

³General Motors North America, Mid-Lux Car Group VSAS, Mail Code: 480-210-152, 30001 Van Dyke, Warren, MI

⁴Oil Technology Services, Inc., 3726 Dacoma, Houston, TX

Abstract and keywords

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r²) > 0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r²=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r²=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV=A+B exp(−x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

Keywords: Cancellous bone; stress; strain; strength; adaptation

Links

DOI: 10.1114/1.1318928

PubMed: 11144980

WoS: 000165632900004

History

Received: 1999-09-21

Accepted: 2000-08-28

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Cited By (18)

Year	Entry
2003	Yeni YN, Hou FJ, Ciarelli T, Vashishth D, Fyhrie DP. Trabecular shear stresses predict in vivo linear microcrack density but not diffuse damage in human vertebral cancellous bone. Ann Biomed Eng. June 2003;31(6):726-732.
2007	Kim D-G, Hunt CA, Zauel R, Fyhrie DP, Yeni YN. The effect of regional variations of the trabecular bone properties on the compressive strength of human vertebral bodies. Ann Biomed Eng. November 2007;35(11):1907-1913.
2004	Yeni YN, Dong XN, Fyhrie DP, Les CM. The dependence between the strength and stiffness of cancellous and cortical bone tissue for tension and compression: extension of a unifying principle. Bio-med Mater Eng. 2004;14(3):303-310.
2003	Ciarelli TE, Fyhrie DP, Parfitt AM. Effects of vertebral bone fragility and bone formation rate on the mineralization levels of cancellous bone from white females. Bone. March 2003;32(3):311-315.
2008	Yeni YN, Zelman EA, Divine GW, Kim D-G, Fyhrie DP. Trabecular shear stress amplification and variability in human vertebral cancellous bone: relationship with age, gender, spine level and trabecular architecture. Bone. March 2008;42(3):591-596.
2001	Yeni YN, Fyhrie DP. Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions. J Biomech. December 2001;34(12):1649-1654.
2005	Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech. 2005;38(4):707-716.
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2005	Yeni YN, Christopherson GT, Dong XN, Kim D-G, Fyhrie DP. Effect of microcomputed tomography voxel size on the finite element model accuracy for human cancellous bone. J Biomech Eng. February 2005;127(1):1-8.
2006	Zauel R, Yeni YN, Bay BK, Dong XN, Fyhrie DP. Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J Biomech Eng. February 2006;128(1):1-6.
2019	Emami AJ, Toupadakis CA, Telek SM, Fyhrie DP, Yellowley CE, Christiansen BA. Age dependence of systemic bone loss and recovery following femur fracture in mice. J Bone Miner Res. January 2019;34(1):157-170.
2005	Kaminsky J, Rodt T, Gharabaghi A, Forster J, Brand G, Samii M. A universal algorithm for an improved finite element mesh generation: mesh quality assessment in comparison to former automated mesh-generators and an analytic model. Med Eng Phys. 2005;27(5):383-394.
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2014	Carretta R. Post-Yield Mechanics and Material Composition of Single Trabeculae: A Combined Experimental and Modelling Approach [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2014.
2006	Nagaraja S. Microstructural Stresses and Strains Associated With Trabecular Bone Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; December 2006.
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2019	Emami AJ. Systemic Bone Loss After Femoral Fracture in Mice: Potential Mechanisms and Age-Related Effects [PhD thesis]. Davis, University of California; 2019.