A cellular solid model for modulus reduction due to resorption of trabeculae in bone

Vajjhala, S.; Kraynik, A. M.; Gibson, L. J.

Affiliations

¹Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

²Sandia National Laboratories, Albuquerque, NM 87185-0834

Abstract

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.

Links

DOI: 10.1115/1.1289996

PubMed: 11091953

WoS: 000167111200008

History

Received: 2000-01-23

Revised: 2000-05-12

Cited Works (9)

Year	Entry
1997	Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. 2nd ed. Cambridge, UK: Cambridge University Press; 1997. Cambridge Solid State Science Series.
1997	Silva MJ, Gibson LJ. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. Int J Mech Sci. May 1997;39(5):549-563.
1995	van Rietbergen B, Weinans H, Huiskes R, Odgaard A. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech. January 1995;28(1):69-81.
1997	Silva MJ, Keaveny TM, Hayes WC. Load sharing between the shell and centrum in the lumbar vertebral body. Spine. January 1997;22(2):140-150.
1997	Silva MJ, Gibson LJ. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone. 1997;21(2):191-199.
1995	Lotz JC, Cheal EJ, Hayes WC. Stress distributions within the proximal femur during gait and falls: implications for osteoporotic fracture. Osteoporos Int. July 1995;5(3):252-261.
1982	Gibson LJ, Ashby MF. The mechanics of three-dimensional cellular materialsthe mechanics of three-dimensional cellular materials. Proc R Soc Lon Ser-A. July 8, 1982;382(1782):43-59.
1999	Rho J-Y, Roy ME II, Tsui TY, Pharr GM. Elastic properties of microstructural components of human bone tissue as measured by nanoindentation. J Biomed Mater Res. 1999;A45(1):48-54.
1985	McBroom RJ, Hayes WC, Edwards WT, Goldberg RP, White AA III. Prediction of vertebral body compressive fracture using quantitative computed tomography. J Bone Joint Surg. 1985;67A(8):1206-1214.

Cited By (22)

Year	Entry
2004	Hellmich C, Ulm F-J, Dormieux L. Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? arguments from a multiscale approach. Biomech Model Mechanobiol. June 2004;2(4):219-238.
2002	Guo XE, Kim CH. Mechanical consequence of trabecular bone loss and its treatment: a three-dimensional model simulation. Bone. February 2002;30(2):404-411.
2002	Jaasma MJ, Bayraktar HH, Niebur GL, Keaveny TM. Biomechanical effects of intraspecimen variations in tissue modulus for trabecular bone. J Biomech. 2002;35(2):237-246.
2005	Gibson LJ. Biomechanics of cellular solids. J Biomech. 2005;38(3):377-399.
2008	Harrison NM, McDonnell PF, O’Mahoney DC, Kennedy OD, O’Brien FJ, McHugh PE. Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties. J Biomech. August 7, 2008;41(11):2589-2596.
2001	Arthur Moore TL, Gibson LJ. Modeling modulus reduction in bovine trabecular bone damaged in compressio. J Biomech Eng. December 2001;123(6):613-622.
2002	Makiyama AM, Vajjhala S, Gibson LJ. Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low density trabecular bone. J Biomech Eng. October 2002;124(4):512-520.
2004	Moore TLA, O’Brien FJ, Gibson LJ. Creep does not contribute to fatigue in bovine trabecular bone. J Biomech Eng. June 2004;126(3):321-329.
2009	Dendorfer S, Maier HJ, Hammer J. Fatigue damage in cancellous bone: an experimental approach from continuum to micro scale. J Mech Behav Biomed Mater. January 2009;2(1):113-119.
2022	Youssefian S, Bressner JA, Osanov M, Guest JK, Zbijewski WB, Levin AS. Sensitivity of the stress field of the proximal femur predicted by CT-based FE analysis to modeling uncertainties. J Orthop Res. May 2022;40(5):1163-1173.
2020	Smith SM, Angielczyk KD. Deciphering an extreme morphology: bone microarchitecture of the hero shrew backbone (Soricidae: Scutisorex). Proc R Soc B. May 13, 2020;287(1926):20200457.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
2003	Kim CH. In Vivo Trabecular Bone Response to Mechanical Loading and Parathyroid Hormone Stimulation [PhD thesis]. Columbia University; 2003.
2012	Hamed E. Multiscale Modeling of Elastic Moduli and Strength of Bone [PhD thesis]. University of Illinois at Urbana-Champaign; 2012.
2009	Moesen M. Modeling of the Geometry and Mechanical Behavior of Bone Scaffolds [PhD thesis]. Leuven, Belgium: Katholieke Universiteit Leuven; June 2009.
2001	Arthur Moore TL. Microdamage Accumulation in Bovine Trabecular Bone [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 2001.
2017	Wang J. Trabecular Topology: Computational Structural Design Inspired by Bone Remodeling [Master's thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 2017.
2005	Chung S. Bone Image Analysis: Quantifying Topological Change in Bone Under Uniform Erosion [PhD thesis]. Stony Brook, NY: Stony Brook University; December 2005.
2001	Boyd SK. Microstructural Bone Adaptation in an Experimental Model of Osteoarthritis [PhD thesis]. Calgary, AB: University of Calgary; January 2001.
2007	Ruffoni D. Modeling of Material and Architectural Quality of Trabecular Bone [PhD thesis]. Liège, Belgique: Université de Liège; September 2007.
2022	Blázquez Carmona P. Mechanobiology of Bone Regeneration: Distraction Osteogenesis and Tissue Engineering [PhD thesis]. Universidad de Sevilla; 2022.
2013	Mecke D. Probabilistic Analysis of the Microstructure of Human Trabecular Bone With High and Low Volume Fractions [Master's thesis]. San Antionio, TX: University of Texas at San Antonio; December 2013.