Review Article

Biomechanics and Mechanobiology of Trabecular Bone: A Review

[+] Author and Article Information
Ramin Oftadeh

Center for Advanced Orthopaedic Studies,
Department of Orthopaedic Surgery,
Beth Israel Deaconess Medical Center,
Harvard Medical School,
Boston, MA 02215
Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115

Miguel Perez-Viloria, Juan C. Villa-Camacho

Center for Advanced Orthopaedic Studies,
Department of Orthopaedic Surgery,
Beth Israel Deaconess Medical Center,
Harvard Medical School,
Boston, MA 02215

Ashkan Vaziri

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115

Ara Nazarian

Center for Advanced Orthopaedic Studies,
Department of Orthopaedic Surgery,
Beth Israel Deaconess Medical Center,
Harvard Medical School,
Boston, MA 02215
e-mail: anazaria@bidmc.harvard.edu

1These authors have contributed equally to this work.

2Corresponding author.

Manuscript received August 5, 2014; final manuscript received November 17, 2014; accepted manuscript posted November 20, 2014; published online December 10, 2014. Assoc. Editor: Blaine A. Christiansen.

J Biomech Eng 137(1), 010802 (Jan 01, 2015) (15 pages) Paper No: BIO-14-1365; doi: 10.1115/1.4029176 History: Received August 05, 2014; Revised November 17, 2014; Accepted November 20, 2014; Online December 10, 2014

Trabecular bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. Studying the mechanical properties of trabecular bone is important, since trabecular bone is the main load bearing bone in vertebral bodies and also transfers the load from joints to the compact bone of the cortex of long bones. This review article highlights the high dependency of the mechanical properties of trabecular bone on species, age, anatomic site, loading direction, and size of the sample under consideration. In recent years, high resolution micro finite element methods have been extensively used to specifically address the mechanical properties of the trabecular bone and provide unique tools to interpret and model the mechanical testing experiments. The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabecular bone microstructure and macrostructure and corresponding mechanical properties such as elastic properties and strength.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Bayraktar, H. H., Morgan, E. F., Niebur, G. L., Morris, G. E., Wong, E. K., and Keaveny, T. M., 2004, “Comparison of the Elastic and Yield Properties of Human Femoral Trabecular and Cortical Bone Tissue,” J. Biomech., 37(1), pp. 27–35. [CrossRef] [PubMed]
Chevalier, Y., Pahr, D., and Zysset, P. K., 2009, “The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body,” ASME J. Biomech. Eng., 131(11), p. 111003. [CrossRef]
Verhulp, E., Van Rietbergen, B., Müller, R., and Huiskes, R., 2008, “Micro-Finite Element Simulation of Trabecular-Bone Post-Yield Behaviour—Effects of Material Model, Element Size and Type,” Comput. Methods Biomech. Biomed. Eng., 11(4), pp. 389–395. [CrossRef]
Vanderoost, J., Jaecques, S. V., Van der Perre, G., Boonen, S., D'hooge, J., Lauriks, W., and van Lenthe, G. H., 2011, “Fast and Accurate Specimen-Specific Simulation of Trabecular Bone Elastic Modulus Using Novel Beam—Shell Finite Element Models,” J. Biomech., 44(8), pp. 1566–1572. [CrossRef] [PubMed]
Hamed, E., Jasiuk, I., Yoo, A., Lee, Y., and Liszka, T., 2012, “Multi-Scale Modelling of Elastic Moduli of Trabecular Bone,” J. R. Soc., Interface, 9(72), pp. 1654–1673. [CrossRef]
Stauber, M., Rapillard, L., van Lenthe, G. H., Zysset, P., and Müller, R., 2006, “Importance of Individual Rods and Plates in the Assessment of Bone Quality and Their Contribution to Bone Stiffness,” J. Bone Miner. Res., 21(4), pp. 586–595. [CrossRef] [PubMed]
Stauber, M., and Müller, R., 2006, “Volumetric Spatial Decomposition of Trabecular Bone Into Rods and Plates—A New Method for Local Bone Morphometry,” Bone, 38(4), pp. 475–484. [CrossRef] [PubMed]
Liu, X. S., Sajda, P., Saha, P. K., Wehrli, F. W., and Guo, X. E., 2006, “Quantification of the Roles of Trabecular Microarchitecture and Trabecular Type in Determining the Elastic Modulus of Human Trabecular Bone,” J. Bone Miner. Res., 21(10), pp. 1608–1617. [CrossRef] [PubMed]
Parfitt, A. M., 2001, “The Bone Remodeling Compartment: A Circulatory Function for Bone Lining Cells,” J Bone Miner. Res., 16(9), pp. 1583–1585. [CrossRef] [PubMed]
Parfitt, A. M., 2002, “Targeted and Nontargeted Bone Remodeling: Relationship to Basic Multicellular Unit Origination and Progression,” Bone, 30(1), pp. 5–7. [CrossRef] [PubMed]
Canalis, E., 2005, “The Fate of Circulating Osteoblasts,” N. Engl. J. Med., 352(19), pp. 2014–2016. [CrossRef] [PubMed]
Harada, S., and Rodan, G. A., 2003, “Control of Osteoblast Function and Regulation of Bone Mass,” Nature, 423, pp. 349–355. [CrossRef] [PubMed]
Barragan-Adjemian, C., Nicolella, D., Dusevich, V., Dallas, M. R., Eick, J. D., and Bonewald, L. F., 2006, “Mechanism by Which MLO-A5 Late Osteoblasts/Early Osteocytes Mineralize in Culture: Similarities With Mineralization of Lamellar Bone,” Calcif. Tissue Int., 79(5), pp. 340–353. [CrossRef] [PubMed]
Karsenty, G., and Wagner, E. F., 2002, “Reaching a Genetic and Molecular Understanding of Skeletal Development,” Dev. Cell, 2(4), pp. 389–406. [CrossRef] [PubMed]
Franz-Odendaal, T. A., Hall, B. K., and Witten, P. E., 2006, Buried Alive: How Osteoblasts Become Osteocytes, Developmental Dynamics, Vol. 235, American Association of Anatomists, 235, pp. 176–190.
Kamioka, H., Honjo, T., and Takano-Yamamoto, T., 2001, “A Three-Dimensional Distribution of Osteocyte Processes Revealed by the Combination of Confocal Laser Scanning Microscopy and Differential Interference Contrast Microscopy,” Bone, 28(2), pp. 145–149. [CrossRef] [PubMed]
Sugawara, Y., Kamioka, H., Honjo, T., Tezuka, K., and Takano-Yamamoto, T., 2005, “Three-Dimensional Reconstruction of Chick Calvarial Osteocytes and Their Cell Processes Using Confocal Microscopy,” Bone, 36(5), pp. 877–883. [CrossRef] [PubMed]
Han, Y., Cowin, S. C., Schaffler, M. B., and Weinbaum, S., 2004, “Mechanotransduction and Strain Amplification in Osteocyte Cell Processes,” Proc. Natl. Acad. Sci. U. S. A., 101(47), pp. 16689–16694. [CrossRef] [PubMed]
Lanyon, L. E., 1993, “Osteocytes, Strain Detection, Bone Modeling and Remodeling,” Calcif. Tissue Int., 53(Suppl 1), pp. S102–106 [Discussion S106–107]. [CrossRef] [PubMed]
Tatsumi, S., Ishii, K., Amizuka, N., Li, M., Kobayashi, T., Kohno, K., Ito, M., Takeshita, S., and Ikeda, K., 2007, “Targeted Ablation of Osteocytes Induces Osteoporosis With Defective Mechanotransduction,” Cell Metab., 5(6), pp. 464–475. [CrossRef] [PubMed]
Dallas, S. L., Prideaux, M., and Bonewald, L. F., 2013, “The Osteocyte: An Endocrine Cell and More,” Endocr. Rev., 34(5), pp. 658–690. [CrossRef] [PubMed]
Burr, D. B., Robling, A. G., and Turner, C. H., 2002, “Effects of Biomechanical Stress on Bones in Animals,” Bone, 30(5), pp. 781–786. [CrossRef] [PubMed]
Ehrlich, P. J., Noble, B. S., Jessop, H. L., Stevens, H. Y., Mosley, J. R., and Lanyon, L. E., 2002, “The Effect of in Vivo Mechanical Loading on Estrogen Receptor Alpha Expression in Rat Ulnar Osteocytes,” J. Bone Miner. Res., 17(9), pp. 1646–1655. [CrossRef] [PubMed]
Klein-Nulend, J., Bakker, A. D., Bacabac, R. G., Vatsa, A., and Weinbaum, S., 2013, “Mechanosensation and Transduction in Osteocytes,” Bone, 54(2), pp. 182–190. [CrossRef] [PubMed]
Vatsa, A., Breuls, R. G., Semeins, C. M., Salmon, P. L., Smit, T. H., and Klein-Nulend, J. 2008, “Osteocyte Morphology in Fibula and Calvaria—Is There a Role for Mechanosensing?,” Bone, 43(3), pp. 452–458. [CrossRef] [PubMed]
Vatsa, A., Semeins, C. M., Smit, T. H., and Klein-Nulend, J., 2008, “Paxillin Localisation in Osteocytes—Is it Determined by the Direction of Loading?,” Biochem. Biophys. Res. Commun., 377(4), pp. 1019–1024. [CrossRef] [PubMed]
Pavalko, F. M., Norvell, S. M., Burr, D. B., Turner, C. H., Duncan, R. L., and Bidwell, J. P., 2003, “A Model for Mechanotransduction in Bone Cells: The Load-Bearing Mechanosomes,” J. Cell. Biochem., 88(1), pp. 104–112. [CrossRef] [PubMed]
You, J., Yellowley, C. E., Donahue, H. J., Zhang, Y., Chen, Q., and Jacobs, C. R., 2000, “Substrate Deformation Levels Associated With Routine Physical Activity Are Less Stimulatory to Bone Cells Relative to Loading-Induced Oscillatory Fluid Flow,” ASME J. Biomech. Eng., 122(4), pp. 387–393. [CrossRef]
Weinbaum, S., Cowin, S. C., and Zeng, Y., 1994, “A Model for the Excitation of Osteocytes by Mechanical Loading-Induced Bone Fluid Shear Stresses,” J. Biomech., 27(3), pp. 339–360. [CrossRef] [PubMed]
Cowin, S. C., Weinbaum, S., and Zeng, Y., 1995, “A Case for Bone Canaliculi as the Anatomical Site of Strain Generated Potentials,” J. Biomech., 28(11), pp. 1281–1297. [CrossRef] [PubMed]
Hung, C. T., Allen, F. D., Pollack, S. R., and Brighton, C. T., 1996, “Intracellular Ca2+ Stores and Extracellular Ca2+ Are Required in the Real-Time Ca2+ Response of Bone Cells Experiencing Fluid Flow,” J. Biomech., 29(11), pp. 1411–1417. [CrossRef] [PubMed]
Hung, C. T., Pollack, S. R., Reilly, T. M., and Brighton, C. T., 1995, “Real-Time Calcium Response of Cultured Bone Cells to Fluid Flow,” Clin. orthop. Relat. Res., 313, pp. 256–269. [PubMed]
Lu, X. L., Huo, B., Park, M., and Guo, X. E., 2012, ““Calcium Response in Osteocytic Networks Under Steady And Oscillatory Fluid Flow,” Bone, 51(3), pp. 466–473. [CrossRef] [PubMed]
Zhang, D., Weinbaum, S., and Cowin, S. C., 1998, “Electrical Signal Transmission in a Bone Cell Network: The Influence of a Discrete Gap Junction,” Ann. Biomed. Eng., 26(4), pp. 644–659. [CrossRef] [PubMed]
Fritton, S. P., and Weinbaum, S., 2009, “Fluid and Solute Transport in Bone: Flow-Induced Mechanotransduction,” Annu. Rev. Fluid Mech., 41, pp. 347–374. [CrossRef] [PubMed]
Owan, I., Burr, D. B., Turner, C. H., Qiu, J., Tu, Y., Onyia, J. E., and Duncan, R. L., 1997, “Mechanotransduction in Bone: Osteoblasts Are More Responsive to Fluid Forces Than Mechanical Strain,” Am. J. Physiol., 273, pp. C810–815. [PubMed]
Smalt, R., Mitchell, F. T., Howard, R. L., and Chambers, T. J., 1997, “Induction of NO and Prostaglandin E2 in Osteoblasts by Wall-Shear Stress But Not Mechanical Strain,” Am. J. Physiol., 273, pp. E751–758. [PubMed]
Burr, D. B., Milgrom, C., Fyhrie, D., Forwood, M., Nyska, M., Finestone, A., Hoshaw, S., Saiag, E., and Simkin, A., 1996, “In Vivo Measurement of Human Tibial Strains During Vigorous Activity,” Bone, 18(5), pp. 405–410. [CrossRef] [PubMed]
Fritton, S. P., McLeod, K. J., and Rubin, C. T., 2000, “Quantifying the Strain History of Bone: Spatial Uniformity and Self-Similarity of Low-Magnitude Strains,” J. Biomech., 33(3), pp. 317–325. [CrossRef] [PubMed]
You, L., Cowin, S. C., Schaffler, M. B., and Weinbaum, S., 2001, “A Model for Strain Amplification in the Actin Cytoskeleton of Osteocytes Due to Fluid Drag on Pericellular Matrix,” J. Biomech., 34, pp. 1375–1386. [CrossRef] [PubMed]
McNamara, L. M., Majeska, R. J., Weinbaum, S., Friedrich, V., and Schaffler, M. B., 2009, “Attachment of Osteocyte Cell Processes to the Bone Matrix,” Anat. Rec., 292(3), pp. 355–363. [CrossRef]
Wang, Y., McNamara, L. M., Schaffler, M. B., and Weinbaum, S., 2007, “A Model for the Role of Integrins in Flow Induced Mechanotransduction in Osteocytes,” Proc. Natl. Acad. Sci. U. S. A., 104(4), pp. 15941–15946. [CrossRef] [PubMed]
Santos, A., Bakker, A. D., and Klein-Nulend, J., 2009, “The Role of Osteocytes in Bone Mechanotransduction,” Osteoporosis Int., 20(6), pp. 1027–1031. [CrossRef]
Adachi, T., Aonuma, Y., Tanaka, M., Hojo, M., Takano-Yamamoto, T., and Kamioka, H., 2009, “Calcium Response in Single Osteocytes to Locally Applied Mechanical Stimulus: Differences in Cell Process and Cell Body,” J. Biomech., 42(12), pp. 1989–1995. [CrossRef] [PubMed]
Thi, M. M., Suadicani, S. O., Schaffler, M. B., Weinbaum, S., and Spray, D. C., 2013, “Mechanosensory Responses of Osteocytes to Physiological Forces Occur Along Processes and Not Cell Body and Require AlphaVbeta3 Integrin,” Proc. Natl. Acad. Sci. U. S. A., 110(52), pp. 21012–21017. [CrossRef] [PubMed]
Nicolella, D. P., Feng, J. Q., Moravits, D. E., Bonivitch, A. R., Wang, Y., Dusecich, V., Yao, W., Lane, N., and Bonewald, L. F., 2008, “Effects of Nanomechanical Bone Tissue Properties on Bone Tissue Strain: Implications for Osteocyte Mechanotransduction,” J. Musculoskeletal Neuronal Interact., 8(4), pp. 330–331.
Malone, A. M., Anderson, C. T., Tummala, P., Kwon, R. Y., Johnston, T. R., Stearns, T., and Jacobs, C. R., 2007, “Primary Cilia Mediate Mechanosensing in Bone Cells by a Calcium-Independent Mechanism,” Proc. Natl. Acad. Sci. U. S. A., 104(33), pp. 13325–13330. [CrossRef] [PubMed]
Xiao, Z., Zhang, S., Mahlios, J., Zhou, G., Magenheimer, B. S., Guo, D., Dallas, S. L., Maser, R., Calvet, J. P., Bonewald, L., and Quarles, L. D., 2006, “Cilia-Like Structures and Polycystin-1 in Osteoblasts/Osteocytes and Associated Abnormalities in Skeletogenesis and Runx2 Expression,” J. Biol. Chem., 281, pp. 30884–30895. [CrossRef] [PubMed]
Bonewald, L. F., 2011, “The Amazing Osteocyte,” J. Bone Miner. Res., 26(2), pp. 229–238. [CrossRef] [PubMed]
Gardinier, J. D., Townend, C. W., Jen, K. P., Wu, Q., Duncan, R. L., and Wang, L., 2010, “In Situ Permeability Measurement of the Mammalian Lacunar–Canalicular System,” Bone, 46(4), pp. 1075–1081. [CrossRef] [PubMed]
Kamioka, H., Miki, Y., Sumitani, K., Tagami, K., Terai, K., Hosoi, K., and Kawata, T., 1995, “Extracellular Calcium Causes the Release of Calcium From Intracellular Stores in Chick Osteocytes,” Biochem. Biophys. Res. Commun., 212(2), pp. 692–696. [CrossRef] [PubMed]
Hung, C. T., Allen, F. D., Pollack, S. R., and Brighton, C. T., 1996, “What is the Role of the Convective Current Density in the Real-Time Calcium Response of Cultured Bone Cells to Fluid Flow?” J. Biomech., 29(11), pp. 1403–1409. [CrossRef] [PubMed]
Klein-Nulend, J., van der Plas, A., Semeins, C. M., Ajubi, N. E., Frangos, J. A., Nijweide, P. J., and Burger, E. H., 1995, “Sensitivity of Osteocytes to Biomechanical Stress In Vitro,” FASEB J., 9(5), pp. 441–445. [PubMed]
Bakker, A. D., Soejima, K., Klein-Nulend, J., and Burger, E. H., 2001, “The Production of Nitric Oxide and Prostaglandin E(2) by Primary Bone Cells is Shear Stress Dependent,” J. Biomech, 34(5), pp. 671–677. [CrossRef] [PubMed]
Bakker, A. D., Silva, V. C., Krishnan, R., Bacabac, R. G., Blaauboer, M. E., Lin, Y. C., Marcantonio, R. A., Cirelli, J. A., and Klein-Nulend, J., 2009, “Tumor Necrosis Factor Alpha and Interleukin-1beta Modulate Calcium and Nitric Oxide Signaling in Mechanically Stimulated Osteocytes,” Arthritis Rheum., 60(11), pp. 3336–3345. [CrossRef] [PubMed]
Tan, S. D., Bakker, A. D., Semeins, C. M., Kuijpers-Jagtman, A. M., and Klein-Nulend, J., 2008, “Inhibition of Osteocyte Apoptosis by Fluid Flow is Mediated by Nitric Oxide,” Biochem. Biophys. Res. Commun., 369(4), pp. 1150–1154. [CrossRef] [PubMed]
Xia, X., Batra, N., Shi, Q., Bonewald, L. F., Sprague, E., and Jiang, J. X., 2010, “Prostaglandin Promotion of Osteocyte Gap Junction Function Through Transcriptional Regulation of Connexin 43 by Glycogen Synthase Kinase 3/Beta-Catenin Signaling,” Mol. Cell. Biol., 30(24), pp. 206–219. [CrossRef] [PubMed]
Kitase, Y., Barragan, L., Qing, H., Kondoh, S., Jiang, J. X., Johnson, M. L., and Bonewald, L. F., 2010, “Mechanical Induction of PGE2 in Osteocytes Blocks Glucocorticoid-Induced Apoptosis Through Both the Beta-Catenin and PKA Pathways,” J. Bone Miner. Res., 25(12), pp. 2657–2668. [CrossRef] [PubMed]
Krishnan, V., Bryant, H. U., and Macdougald, O. A., 2006, “Regulation of Bone Mass by Wnt Signaling,” J. Clin. Invest., 116(5), pp. 1202–1209. [CrossRef] [PubMed]
Canalis, E., Giustina, A., and Bilezikian, J. P., 2007, “Mechanisms of Anabolic Therapies for Osteoporosis,” N. Engl. J. Med., 357(9), pp. 905–916. [CrossRef] [PubMed]
Gong, Y., Slee, R. B., Fukai, N., Rawadi, G., Roman-Roman, S., Reginato, A. M., Wang, H., Cundy, T., Glorieux, F. H., Lev, D., Zacharin, M., Oexle, K., Marcelino, J., Suwairi, W., Heeger, S., Sabatakos, G., Apte, S., Adkins, W. N., Allgrove, J., Arslan-Kirchner, M., Batch, J. A., Beighton, P., Black, G. C., Boles, R. G., Boon, L. M., Borrone, C., Brunner, H. G., Carle, G. F., Dallapiccola, B., De Paepe, A., Floege, B., Halfhide, M. L., Hall, B., Hennekam, R. C., Hirose, T., Jans, A., Juppner, H., Kim, C. A., Keppler-Noreuil, K., Kohlschuetter, A., LaCombe, D., Lambert, M., Lemyre, E., Letteboer, T., Peltonen, L., Ramesar, R. S., Romanengo, M., Somer, H., Steichen-Gersdorf, E., Steinmann, B., Sullivan, B., Superti-Furga, A., Swoboda, W., van den Boogaard, M. J., Van Hul, W., Vikkula, M., Votruba, M., Zabel, B., Garcia, T., Baron, R., Olsen, B. R., and Warman, M. L., 2001, “LDL Receptor-Related Protein 5 (LRP5) Affects Bone Accrual and Eye Development,” Cell, 107(4), pp. 513–523. [CrossRef] [PubMed]
Babij, P., Zhao, W., Small, C., Kharode, Y., Yaworsky, P. J., Bouxsein, M. L., Reddy, P. S., Bodine, P. V., Robinson, J. A., Bhat, B., Marzolf, J., Moran, R. A., and Bex, F., 2003, “High Bone Mass in Mice Expressing a Mutant LRP5 Gene,” J. Bone Miner. Res., 18(6), pp. 960–974. [CrossRef] [PubMed]
Boyden, L. M., Mao, J., Belsky, J., Mitzner, L., Farhi, A., Mitnick, M. A., Wu, D., Insogna, K., and Lifton, R. P., 2002, “High Bone Density Due to a Mutation in LDL-Receptor-Related Protein 5,” N. Engl. J. Med., 346, pp. 1513–1521. [CrossRef] [PubMed]
Dyson, E., and Whitehouse, W., 1968, “Composition of Trabecular Bone in Children and Its Relation to Radiation Dosimetry,” Nature, 217, pp. 576–578. [CrossRef] [PubMed]
Gong, J., Arnold, J., and Cohn, S., 1964, “Composition of Trabecular and Cortical Bone,” Anat. Rec., 149(3), pp. 325–331. [CrossRef] [PubMed]
Jee, W., 1983, “The Skeletal Tissues,” Histol. Cell Tissue Biol., 5, pp. 206–254.
Fritsch, A., and Hellmich, C., 2007, “‘Universal’ Microstructural Patterns in Cortical and Trabecular, Extracellular and Extravascular Bone Materials: Micromechanics-Based Prediction of Anisotropic Elasticity,” J. Theor. Biol., 244(4), pp. 597–620. [CrossRef] [PubMed]
McNamara, L., Van der Linden, J., Weinans, H., and Prendergast, P., 2006, “Stress-Concentrating Effect of Resorption Lacunae in Trabecular Bone,” J. Biomech., 39(4), pp. 734–741. [CrossRef] [PubMed]
Runkle, J., and Pugh, J., 1975, “The Micro-Mechanics of Cancellous Bone. II. Determination of the Elastic Modulus of Individual Trabeculae by a Buckling Analysis,” Bull. Hosp. Jt. Dis., 36(1), pp. 2–10.
Townsend, P. R., Rose, R. M., and Radin, E. L., 1975, “Buckling Studies of Single Human Trabeculae,” J. Biomech., 8(3-4), pp. 199–201. [CrossRef] [PubMed]
Hoffler, C. E., Guo, X. E., Zysset, P. K., and Goldstein, S. A., 2005, “An Application of Nanoindentation Technique to Measure Bone Tissue Lamellae Properties,” ASME J. Biomech. Eng., 127(7), pp. 1046–1053. [CrossRef]
Rho, J.-Y., Tsui, T. Y., and Pharr, G. M., 1997, “Elastic Properties of Human Cortical and Trabecular Lamellar Bone Measured by Nanoindentation,” Biomaterials, 18(20), pp. 1325–1330. [CrossRef] [PubMed]
Zysset, P., Guo, X., Hoffler, C., Moore, K., and Goldstein, S., 1998, “Mechanical Properties of Human Trabecular Bone Lamellae Quantified by Nanoindentation,” Technol. Health Care, 6(5-6), pp. 429–432. [CrossRef] [PubMed]
Zysset, P. K., Edward Guo, X., Edward Hoffler, C., Moore, K. E., and Goldstein, S. A., 1999, “Elastic Modulus and Hardness of Cortical and Trabecular Bone Lamellae Measured by Nanoindentation in the Human Femur,” J. Biomech., 32(10), pp. 1005–1012. [CrossRef] [PubMed]
Turner, C. H., Rho, J., Takano, Y., Tsui, T. Y., and Pharr, G. M., 1999, “The Elastic Properties of Trabecular and Cortical Bone Tissues Are Similar: Results From Two Microscopic Measurement Techniques,” J. Biomech., 32(4), pp. 437–441. [CrossRef] [PubMed]
Ko, C.-C., Douglas, W. H., and Cheng, Y.-S., 1995, “Intrinsic Mechanical Competence of Cortical and Trabecular Bone Measured by Nanoindentation and Microindentation Probes,” BED, 29, pp. 415–415.
Roy, M., Rho, J.-Y., Tsui, T. Y., and Pharr, G. M., 1996, “Variation of Young's Modulus and Hardness in Human Lumbar Vertebrae Measured by Nanoindentation,” BED, 33, pp. 385–386.
Fan, Z., Swadener, J., Rho, J., Roy, M., and Pharr, G., 2002, “Anisotropic Properties of Human Tibial Cortical Bone as Measured by Nanoindentation,” J. Orthop. Res., 20(4), pp. 806–810. [CrossRef] [PubMed]
Rho, J. Y., Roy, M. E., Tsui, T. Y., and Pharr, G. M., 1999, “Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation,” J. Biomed. Mater. Res., 45(1), pp. 48–54. [CrossRef] [PubMed]
Rho, J., Zioupos, P., Currey, J., and Pharr, G., 2002, “Microstructural Elasticity and Regional Heterogeneity in Human Femoral Bone of Various Ages Examined by Nano-Indentation,” J. Biomech., 35(2), pp. 189–198. [CrossRef] [PubMed]
Rho, J. Y., Ashman, R. B., and Turner, C. H., 1993, “Young's Modulus of Trabecular and Cortical Bone Material: Ultrasonic and Microtensile Measurements,” J. Biomech., 26(2), pp. 111–119. [CrossRef] [PubMed]
Ryan, S. D., and Williams, J. L., 1989, “Tensile Testing of Rodlike Trabeculae Excised From Bovine Femoral Bone,” J. Biomech., 22(4), pp. 351–355. [CrossRef] [PubMed]
Choi, K., Kuhn, J. L., Ciarelli, M. J., and Goldstein, S. A., 1990, “The Elastic Moduli of Human Subchondral, Trabecular, and Cortical Bone Tissue and the Size-Dependency of Cortical Bone Modulus,” J. Biomech., 23(11), pp. 1103–1113. [CrossRef] [PubMed]
Kuhn, J. L., Goldstein, S. A., Choi, R., London, M., Feldkamp, L., and Matthews, L. S., 1989, “Comparison of the Trabecular and Cortical Tissue Moduli From Human Iliac Crests,” J. Orthop. Res., 7(6), pp. 876–884. [CrossRef] [PubMed]
Choi, K., and Goldstein, S. A., 1992, “A Comparison of the Fatigue Behavior of Human Trabecular and Cortical Bone Tissue,” J. Biomech., 25(12), pp. 1371–1381. [CrossRef] [PubMed]
Nicholson, P., Cheng, X., Lowet, G., Boonen, S., Davie, M., Dequeker, J., and Van der Perre, G., 1997, “Structural and Material Mechanical Properties of Human Vertebral Cancellous Bone,” Med. Eng. Phys., 19(8), pp. 729–737. [CrossRef] [PubMed]
Shieh, S.-J., Zimmerman, M., and Langrana, N., 1995, “The Application of Scanning Acoustic Microscopy in a Bone Remodeling Study,” ASME J. Biomech. Eng., 117(3), pp. 286–292. [CrossRef]
Ladd, A. J., Kinney, J. H., Haupt, D. L., and Goldstein, S. A., 1998, “Finite-Element Modeling of Trabecular Bone: Comparison With Mechanical Testing and Determination of Tissue Modulus,” J. Orthop. Res., 16(5), pp. 622–628. [CrossRef] [PubMed]
Hou, F. J., Lang, S. M., Hoshaw, S. J., Reimann, D. A., and Fyhrie, D. P., 1998, “Human Vertebral Body Apparent and Hard Tissue Stiffness,” J. Biomech., 31(11), pp. 1009–1015. [CrossRef] [PubMed]
Jensen, K., Mosekilde, L., and Mosekilde, L., 1990, “A Model of Vertebral Trabecular Bone Architecture and Its Mechanical Properties,” Bone, 11(6), pp. 417–423. [CrossRef] [PubMed]
Hodgskinson, R., Currey, J., and Evans, G., 1989, “Hardness, an Indicator of the Mechanical Competence of Cancellous Bone,” J. Orthop. Res., 7(5), pp. 754–758. [CrossRef] [PubMed]
Cyganik, Ł., Binkowski, M., Kokot, G., Rusin, T., Popik, P., Bolechała, F., Nowak, R., Wróbel, Z., and John, A., 2014, “Prediction of Young's Modulus of Trabeculae in Microscale Using Macro-Scale’s Relationships Between Bone Density and Mechanical Properties,” J. Mech. Behav. Biomed. Mater., 36, pp. 120–134. [CrossRef] [PubMed]
Gillard, F., Boardman, R., Mavrogordato, M., Hollis, D., Sinclair, I., Pierron, F., and Browne, M., 2014, “The Application of Digital Volume Correlation (DVC) to Study the Microstructural Behaviour of Trabecular Bone During Compression,” J. Mech. Behav. Biomed. Mater., 29, pp. 480–499. [CrossRef] [PubMed]
Timoshenko, S., 1983, History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures, Courier Dover Publications, Mineola, NY.
Haiat, G., Padilla, F., Svrcekova, M., Chevalier, Y., Pahr, D., Peyrin, F., Laugier, P., and Zysset, P., 2009, “Relationship Between Ultrasonic Parameters and Apparent Trabecular Bone Elastic Modulus: A Numerical Approach,” J. Biomech., 42(13), pp. 2033–2039. [CrossRef] [PubMed]
Ashman, R. B., and Rho, J. Y., 1988, “Elastic Modulus of Trabecular Bone Material,” J. Biomech., 21(3), pp. 177–181. [CrossRef] [PubMed]
Brennan, O., Kennedy, O. D., Lee, T. C., Rackard, S. M., and O’Brien, F. J., 2009, “Biomechanical Properties Across Trabeculae From the Proximal Femur of Normal and Ovariectomised Sheep,” J. Biomech., 42(4), pp. 498–503. [CrossRef] [PubMed]
Niebur, G. L., Feldstein, M. J., Yuen, J. C., Chen, T. J., and Keaveny, T. M., 2000, “High-Resolution Finite Element Models With Tissue Strength Asymmetry Accurately Predict Failure of Trabecular Bone,” J. Biomech., 33(12), pp. 1575–1583. [CrossRef] [PubMed]
Verhulp, E., van Rietbergen, B., Müller, R., and Huiskes, R., 2008, “Indirect Determination of Trabecular Bone Effective Tissue Failure Properties Using Micro-Finite Element Simulations,” J. Biomech., 41(7), pp. 1479–1485. [CrossRef] [PubMed]
Ciarelli, M., Goldstein, S., Kuhn, J., Cody, D., and Brown, M., 1991, “Evaluation of Orthogonal Mechanical Properties and Density of Human Trabecular Bone From the Major Metaphyseal Regions With Materials Testing and Computed Tomography,” J. Orthop. Res., 9(5), pp. 674–682. [CrossRef] [PubMed]
Hodgskinson, R., and Currey, J., 1993, “Separate Effects of Osteoporosis and Density on the Strength and Stiffness of Human Cancellous Bone,” Clin. Biomech., 8(5), pp. 262–268. [CrossRef]
Keaveny, T. M., Guo, X. E., Wachtel, E. F., McMahon, T. A., and Hayes, W. C., 1994, “Trabecular Bone Exhibits Fully Linear Elastic Behavior and Yields at Low Strains,” J. Biomech., 27(9), pp. 1127–1136. [CrossRef] [PubMed]
Goldstein, S. A., Wilson, D. L., Sonstegard, D. A., and Matthews, L. S., 1983, “The Mechanical Properties of Human Tibial Trabecular Bone as a Function of Metaphyseal Location,” J. Biomech., 16(12), pp. 965–969. [CrossRef] [PubMed]
Brown, T. D., and Ferguson, A. B., 1980, “Mechanical Property Distributions in the Cancellous Bone of the Human Proximal Femur,” Acta Orthop., 51(1–6), pp. 429–437. [CrossRef]
Renders, G., Mulder, L., Langenbach, G., Van Ruijven, L., and Van Eijden, T., 2008, “Biomechanical Effect of Mineral Heterogeneity in Trabecular Bone,” J. Biomech., 41(13), pp. 2793–2798. [CrossRef] [PubMed]
Mosekilde, L., Mosekilde, L., and Danielsen, C., 1987, “Biomechanical Competence of Vertebral Trabecular Bone in Relation to Ash Density and Age in Normal Individuals,” Bone, 8(2), pp. 79–85. [CrossRef] [PubMed]
Galante, J., Rostoker, W., and Ray, R., 1970, “Physical Properties of Trabecular Bone,” Calcif. Tissue Res., 5(1), pp. 236–246. [CrossRef] [PubMed]
Keaveny, T. M., Pinilla, T. P., Crawford, R. P., Kopperdahl, D. L., and Lou, A., “Systematic and Random Errors in Compression Testing of Trabecular Bone,” J. Orthop. Res., 15(1), pp. 101–110. [CrossRef] [PubMed]
Linde, F., Hvid, I., and Madsen, F., 1992, “The Effect of Specimen Geometry on the Mechanical Behaviour of Trabecular Bone Specimens,” J. Biomech., 25(4), pp. 359–368. [CrossRef] [PubMed]
Jacobs, C., Davis, B., Rieger, C., Francis, J., Saad, M., and Fyhrie, D., 1999, “The Impact of Boundary Conditions and Mesh Size on the Accuracy of Cancellous Bone Tissue Modulus Determination Using Large-Scale Finite-Element Modeling,” J. Biomech., 32(11), pp. 1159–1164. [CrossRef] [PubMed]
Cowin, S. C., 1985, “The Relationship Between The Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147. [CrossRef]
Zysset, P., and Curnier, A., 1995, “An Alternative Model for Anisotropic Elasticity Based on Fabric Tensors,” Mech. Mater., 21(4), pp. 243–250. [CrossRef]
Shi, X., Wang, X., and Niebur, G. L., 2009, “Effects of Loading Orientation on the Morphology of the Predicted Yielded Regions in Trabecular Bone,” Ann. Biomed. Eng., 37(2), pp. 354–362. [CrossRef] [PubMed]
Öhman, C., Baleani, M., Perilli, E., Dall’Ara, E., Tassani, S., Baruffaldi, F., and Viceconti, M., 2007, “Mechanical Testing of Cancellous Bone From the Femoral Head: Experimental Errors Due to Off-Axis Measurements,” J. Biomech., 40(11), pp. 2426–2433. [CrossRef] [PubMed]
Morgan, E. F., Bayraktar, H. H., and Keaveny, T. M., 2003, “Trabecular Bone Modulus–Density Relationships Depend on Anatomic Site,” J. Biomech., 36(5), pp. 897–904. [CrossRef] [PubMed]
Morgan, E. F., and Keaveny, T. M., 2001, “Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site,” J. Biomech., 34(5), pp. 569–577. [CrossRef] [PubMed]
Nazarian, A., Muller, J., Zurakowski, D., Müller, R., and Snyder, B. D., 2007, “Densitometric, Morphometric and Mechanical Distributions in the Human Proximal Femur,” J. Biomech., 40(1), pp. 2573–2579. [CrossRef] [PubMed]
Harrison, N. M., and McHugh, P. E., 2010, “Comparison of Trabecular Bone Behavior in Core and Whole Bone Samples Using High-Resolution Modeling of a Vertebral Body,” Biomech. Model. Mechanobiol., 9(4), pp. 469–480. [CrossRef] [PubMed]
Ün, K., Bevill, G., and Keaveny, T. M., 2006, “The Effects of Side-Artifacts on the Elastic Modulus of Trabecular Bone,” J. Biomech., 39(11), pp. 1955–1963. [CrossRef] [PubMed]
Day, J., Ding, M., Van Der Linden, J., Hvid, I., Sumner, D., and Weinans, H., 2001, “A Decreased Subchondral Trabecular Bone Tissue Elastic Modulus is Associated With Pre-Arthritic Cartilage Damage,” J. Orthop. Res., 19(5), pp. 914–918. [CrossRef] [PubMed]
Ashman, R., Rho, J., and Turner, C., 1989, “Anatomical Variation of Orthotropic Elastic Moduli of the Proximal Human Tibia,” J. Biomech., 22(8-9), pp. 895–900. [CrossRef] [PubMed]
Røhl, L., Larsen, E., Linde, F., Odgaard, A., and Jørgensen, J., 1991, “Tensile and Compressive Properties of Cancellous Bone,” J. Biomech., 24(12), pp. 1143–1149. [CrossRef] [PubMed]
Linde, F., Hvid, I., and Jensen, N. C.,1985, “Material Properties of Cancellous Bone in Repetitive Axial Loading,” Eng. Med., 14, pp. 173–177. [CrossRef] [PubMed]
Linde, F., and Hvid, I., 1987, “Stiffness Behaviour of Trabecular Bone Specimens,” J. Biomech., 20(1), pp. 83–89. [CrossRef] [PubMed]
Turner, C. H., Cowin, S. C., Rho, J. Y., Ashman, R. B., and Rice, J. C., 1990, “The Fabric Dependence of the Orthotropic Elastic Constants of Cancellous Bone,” J. Biomech., 23(6), pp. 549–561. [CrossRef] [PubMed]
Hernandez, C., Beaupré, G., Keller, T., and Carter, D., 2001, “The Influence of Bone Volume Fraction and Ash Fraction on Bone Strength and Modulus,” Bone, 29(1), pp. 74–78. [CrossRef] [PubMed]
Martin, R., and Ishida, J., 1989, “The Relative Effects of Collagen Fiber Orientation, Porosity, Density, and Mineralization on Bone Strength,” J. Biomech., 22(5), pp. 419–426. [CrossRef] [PubMed]
Ciarelli, T., Fyhrie, D., Schaffler, M., and Goldstein, S., 2000, “Variations in Three-Dimensional Cancellous Bone Architecture of the Proximal Femur in Female Hip Fractures and in Controls,” J. Bone Miner. Res., 15(1), pp. 32–40. [CrossRef] [PubMed]
Cory, E., Nazarian, A., Entezari, V., Vartanians, V., Müller, R., and Snyder, B. D., 2010, “Compressive Axial Mechanical Properties of Rat Bone as Functions of Bone Volume Fraction, Apparent Density and Micro-CT Based Mineral Density,” J. Biomech., 43(5), pp. 953–960. [CrossRef] [PubMed]
Goulet, R. W., Goldstein, S. A., Ciarelli, M. J., Kuhn, J. L., Brown, M., and Feldkamp, L., 1994, “The Relationship Between the Structural and Orthogonal Compressive Properties of Trabecular Bone,” J. Biomech., 27(4), pp. 375–389. [CrossRef] [PubMed]
Keller, T. S., 1994, “Predicting the Compressive Mechanical Behavior of Bone,” J. Biomech., 27(9), pp. 1159–1168. [CrossRef] [PubMed]
Hodgskinson, R., and Currey, J., 1992, “Young's Modulus, Density and Material Properties in Cancellous Bone Over a Large Density Range,” J. Mater. Sci.: Mater. Med., 3(5), pp. 377–381. [CrossRef]
Ulrich, D., Van Rietbergen, B., Laib, A., and Ruegsegger, P., 1999, “The Ability of Three-Dimensional Structural Indices to Reflect Mechanical Aspects of Trabecular Bone,” Bone, 25(1), pp. 55–60. [CrossRef] [PubMed]
Kabel, J., Van Rietbergen, B., Odgaard, A., and Huiskes, R., 1999, “Constitutive Relationships of Fabric, Density, and Elastic Properties in Cancellous Bone Architecture,” Bone, 25(4), pp. 481–486. [CrossRef] [PubMed]
Rüegsegger, P., Koller, B., and Müller, R., 1996, “A Microtomographic System for the Nondestructive Evaluation of Bone Architecture,” Calcif. Tissue Int., 58(1), pp. 24–29. [CrossRef] [PubMed]
Hipp, J. A., Jansujwicz, A., Simmons, C. A., and Snyder, B. D., 1996, “Trabecular Bone Morphology From Micro-Magnetic Resonance Imaging,” J. Bone Miner. Res., 11(2), pp. 286–292. [CrossRef] [PubMed]
Ladd, A. J., and Kinney, J. H., 1998, “Numerical Errors and Uncertainties in Finite-Element Modeling of Trabecular Bone,” J. Biomech., 31(10), pp. 941–945. [CrossRef] [PubMed]
Ulrich, D., Van Rietbergen, B., Weinans, H., and Rüegsegger, P., 1998, “Finite Element Analysis of Trabecular Bone Structure: A Comparison of Image-Based Meshing Techniques,” J. Biomech., 31(12), pp. 1187–1192. [CrossRef] [PubMed]
Müller, R., and Rüegsegger, P., 1995, “Three-Dimensional Finite Element Modelling of Non-Invasively Assessed Trabecular Bone Structures,” Med. Eng. Phys., 17(2), pp. 126–133. [CrossRef] [PubMed]
Cowin, S., and Mehrabadi, M., 1989, “Identification of the Elastic Symmetry of Bone and Other Materials,” J. Biomech., 22(6-7), pp. 503–515. [CrossRef] [PubMed]
Hildebrand, T., Laib, A., Müller, R., Dequeker, J., and Rüegsegger, P., 1999, “Direct Three-Dimensional Morphometric Analysis of Human Cancellous Bone: Microstructural Data From Spine, Femur, Iliac Crest, and Calcaneus,” J. Bone Miner. Res., 14(7), pp. 1167–1174. [CrossRef] [PubMed]
Kabel, J., Odgaard, A., Van Rietbergen, B., and Huiskes, R., 1999, “Connectivity and the Elastic Properties of Cancellous Bone,” Bone, 24(2), pp. 115–120. [CrossRef] [PubMed]
Kabel, J., van Rietbergen, B., Dalstra, M., Odgaard, A., and Huiskes, R., 1999, “The Role of an Effective Isotropic Tissue Modulus in the Elastic Properties of Cancellous Bone,” J. Biomech., 32(7), pp. 673–680. [CrossRef] [PubMed]
Van Rietbergen, B., Odgaard, A., Kabel, J., and Huiskes, R., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657. [CrossRef] [PubMed]
Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M., and Huiskes, R., 1997, “Fabric and Elastic Principal Directions of Cancellous Bone are Closely Related,” J. Biomech., 30(5), pp. 487–495. [CrossRef] [PubMed]
Arbenz, P., van Lenthe, G. H., Mennel, U., Müller, R., and Sala, M., 2008, “A Scalable Multi-Level Preconditioner for Matrix-Free μ-Finite Element Analysis of Human Bone Structures,” Int. J. Numer. Methods Eng., 73(7), pp. 927–947. [CrossRef]
Podshivalov, L., Fischer, A., and Bar-Yoseph, P., 2011, “3D Hierarchical Geometric Modeling and Multiscale FE Analysis as a Base for Individualized Medical Diagnosis of Bone Structure,” Bone, 48(4), pp. 693–703. [CrossRef] [PubMed]
Podshivalov, L., Fischer, A., and Bar-Yoseph, P., 2011, “Multiscale FE Method for Analysis of Bone Micro-Structures,” J. Mech. Behav. Biomed. Mater., 4(6), pp. 888–899. [CrossRef] [PubMed]
Wang, H., Liu, X. S., Zhou, B., Wang, J., Ji, B., Huang, Y., Hwang, K.-C., and Guo, X. E., 2013, “Accuracy of Individual Trabecula Segmentation Based Plate and Rod Finite Element Models in Idealized Trabecular Bone Microstructure,” ASME J. Biomech. Eng., 135(4), p. 044502. [CrossRef]
Helgason, B., Perilli, E., Schileo, E., Taddei, F., Brynjólfsson, S., and Viceconti, M., 2008, “Mathematical Relationships Between Bone Density and Mechanical Properties: A Literature Review,” Clin. Biomech., 23(2), pp. 135–146. [CrossRef]
Cheal, E., Snyder, B., Nunamaker, D., and Hayes, W., 1987, “Trabecular Bone Remodeling Around Smooth and Porous Implants in an Equine Patellar Model,” J. Biomech., 20(11-12), pp. 1121–1134. [CrossRef] [PubMed]
Fyhrie, D., and Carter, D., 1990, “Femoral Head Apparent Density Distribution Predicted From Bone Stresses,” J. Biomech., 23(1), pp. 1–10. [CrossRef] [PubMed]
Lotz, J., Cheal, E., and Hayes, W., 1991, “Fracture Prediction for the Proximal Femur Using Finite Element Models: Part I—Linear Analysis,” ASME J. Biomech. Eng., 113(4), pp. 353–360. [CrossRef]
Gibson, L. J., 1985, “The Mechanical Behaviour of Cancellous Bone,” J. Biomech., 18(5), pp. 317–328. [CrossRef] [PubMed]
Silva, M. J., and Gibson, L. J., 1997, “The Effects of Non-Periodic Microstructure and Defects on the Compressive Strength of Two-Dimensional Cellular Solids,” Int. J. Mech. Sci., 39(5), pp. 549–563. [CrossRef]
Yeh, O., and Keaveny, T., 1999, “Biomechanical Effects of Intraspecimen Variations in Trabecular Architecture: A Three-Dimensional Finite Element Study,” Bone, 25(2), pp. 223–228. [CrossRef] [PubMed]
Fyhrie, D. P., and Hou, F. J., 1995, “Prediction of Human Vertebral Cancellous Bone Strength Using Non-Linear, Anatomically Accurate, Large-Scale, Finite Element Analysis,” BED, 29, pp. 301–301.
Van Rietbergen, B., Ulrich, D., Pistoia, W., Huiskes, R., and Rüegsegger, P., 1998, “Prediction of Trabecular Bone Failure Parameters Using a Tissue Failure Criterion,” Transactions of the Annual Meeting-Orthopaedic Research Society, Orthopaedic Research Scoiety, pp. 550–550.
Niebur, G. L., Hsia, A. C., Chen, T. J., and Keaveny, T., 1999, “Simulation of Trabecular Bone Yield Using Nonlinear Finite Element Analysis,” BED, 43, pp. 175–176.
Keyak, J., Rossi, S., Jones, K., Les, C., and Skinner, H., 2001, “Prediction of Fracture Location in the Proximal Femur Using Finite Element Models,” Med. Eng. Phys., 23(9), pp. 657–664. [CrossRef] [PubMed]
Fenech, C., and Keaveny, T., 1999, “A Cellular Solid Criterion for Predicting the Axial-Shear Failure Properties of Bovine Trabecular Bone,” ASME J. Biomech. Eng., 121(4), pp. 414–422. [CrossRef]
Keyak, J. H., and Rossi, S. A., 2000, “Prediction of Femoral Fracture Load Using Finite Element Models: An Examination of Stress-and Strain-Based Failure Theories,” J. Biomech., 33(2), pp. 209–214. [CrossRef] [PubMed]
Gibson, L. J., and Ashby, M. F., 1999, Cellular Solids: Structure and Properties, Cambridge University Press, New York.
Triantafillou, T., and Gibson, L., 1990, “Multiaxial Failure Criteria for Brittle Foams,” Int. J. Mech. Sci., 32(6), pp. 479–496. [CrossRef]
Keaveny, T., Wachtel, E., Zadesky, S., and Arramon, Y., 1999, “Application of the Tsai–Wu Quadratic Multiaxial Failure Criterion to Bovine Trabecular Bone,” ASME J. Biomech. Eng., 121(1), pp. 99–107. [CrossRef]
Keaveny, T. M., Wachtel, E. F., Ford, C. M., and Hayes, W. C., 1994, “Differences Between the Tensile and Compressive Strengths of Bovine Tibial Trabecular Bone Depend on Modulus,” J. Biomech., 27(9), pp. 1137–1146. [CrossRef] [PubMed]
Nazarian, A., Stauber, M., Zurakowski, D., Snyder, B. D., and R.Müller, 2006, “The Interaction of Microstructure and Volume Fraction in Predicting Failure in Cancellous Bone,” Bone, 39(6), pp. 1196–1202. [CrossRef] [PubMed]
Lotz, J. C., Gerhart, T. N., and Hayes, W. C., 1990, “Mechanical Properties of Trabecular Bone From the Proximal Femur: A Quantitative CT Study,” J. Comput. Assisted Tomogr., 14(1), pp. 107–114. [CrossRef]
McCalden, R. W., and McGeough, J. A., 1997, “Age-Related Changes in the Compressive Strength of Cancellous Bone. The Relative Importance of Changes in Density and Trabecular Architecture,” J. Bone Jt. Surg., 79(3), pp. 421–427.
Ding, M., Dalstra, M., Danielsen, C. C., Kabel, J., Hvid, I., and Linde, F., 1997, “Age Variations in the Properties of Human Tibial Trabecular Bone,” J. Bone Jt. Surg., 79(6), pp. 995–1002. [CrossRef]
Ford, C. M., and Keaveny, T. M., 1996, “The Dependence of Shear Failure Properties of Trabecular Bone on Apparent Density and Trabecular Orientation,” J. Biomech., 29(10), pp. 1309–1317. [CrossRef] [PubMed]
Tassani, S., Öhman, C., Baleani, M., Baruffaldi, F., and Viceconti, M., 2010, “Anisotropy and Inhomogeneity of the Trabecular Structure can Describe the Mechanical Strength of Osteoarthritic Cancellous Bone,” J. Biomech., 43(6), pp. 1160–1166. [CrossRef] [PubMed]
Rice, J., Cowin, S., and Bowman, J., 1988, “On the Dependence of the Elasticity and Strength of Cancellous Bone on Apparent Density,” J. Biomech., 21(2), pp. 155–168. [CrossRef] [PubMed]
Sanyal, A., Gupta, A., Bayraktar, H. H., Kwon, R. Y., and Keaveny, T. M., 2012, “Shear Strength Behavior of Human Trabecular Bone,” J. Biomech., 45(15), pp. 2513–2519. [CrossRef] [PubMed]
Perilli, E., Baleani, M., Öhman, C., Fognani, R., Baruffaldi, F., and Viceconti, M., 2008, “Dependence of Mechanical Compressive Strength on Local Variations in Microarchitecture in Cancellous Bone of Proximal Human Femur,” J. Biomech., 41(2), pp. 438–446. [CrossRef] [PubMed]
Kopperdahl, D. L., and Keaveny, T. M., 1998, “Yield Strain Behavior of Trabecular Bone,” J. Biomech., 31(7), pp. 601–608. [CrossRef] [PubMed]
Silva, M. J., Keaveny, T. M., and Hayes, W. C., 1998, “Computed Tomography-Based Finite Element Analysis Predicts Failure Loads and Fracture Patterns for Vertebral Sections,” J. Orthop. Res., 16(3), pp. 300–308. [CrossRef] [PubMed]
Rennick, J. A., Nazarian, A., Entezari, V., Kimbaris, J., Tseng, A., Masoudi, A., Nayeb-Hashemi, H., Vaziri, A., and Snyder, B. D., 2013, “Finite Element Analysis and Computed Tomography Based Structural Rigidity Analysis of Rat Tibia With Simulated Lytic Defects,” J. Biomech., 46(5), pp. 2701–2709. [CrossRef] [PubMed]
Turner, C., 1989, “Yield Behavior of Bovine Cancellous Bone,” ASME J. Biomech. Eng., 111(4), pp. 256–260. [CrossRef]
Burr, D. B., Forwood, M. R., Fyhrie, D. P., Martin, R. B., Schaffler, M. B., and Turner, C. H., 1997, “Bone Microdamage and Skeletal Fragility in Osteoporotic and Stress Fractures,” J. Bone Miner. Res., 12(1), pp. 6–15. [CrossRef] [PubMed]
Isaksson, H., Nagao, S., MaŁkiewicz, M., Julkunen, P., Nowak, R., and Jurvelin, J. S., 2010, “Precision of Nanoindentation Protocols for Measurement of Viscoelasticity in Cortical and Trabecular Bone,” J. Biomech., 43(12), pp. 2410–2417. [CrossRef] [PubMed]
Keaveny, T. M., Wachtel, E. F., and Kopperdahl, D. L., 1999, “Mechanical Behavior of Human Trabecular Bone After Overloading,” J. Orthop. Res., 17(3), pp. 346–353. [CrossRef] [PubMed]
Pugh, J., Rose, R., and Radin, E., 1973, “A Possible Mechanism of Wolff's Law: Trabecular Microfractures,” Arch. Physiol. Biochem., 81(1), pp. 27–40. [CrossRef]
Benaissa, R., Uhthoff, H. K., and Mercier, P., 1989, “Repair of Trabecular Fatigue Fractures Cadaver Studies of the Upper Femur,” Acta Orthop., 60(5), pp. 585–589. [CrossRef]
Zysset, P., and Curnier, A., 1996, “A 3D Damage Model for Trabecular Bone Based on Fabric Tensors,” J. Biomech., 29(12), pp. 1549–1558. [CrossRef] [PubMed]
Fondrk, M., Bahniuk, E., Davy, D., and Michaels, C., 1988, “Some Viscoplastic Characteristics of Bovine and Human Cortical Bone,” J. Biomech., 21(8), pp. 623–630. [CrossRef] [PubMed]
Kopperdahl, D. L., Pearlman, J. L., and Keaveny, T. M., 2000, “Biomechanical Consequences of an Isolated Overload on the Human Vertebral Body,” J. Orthop. Res., 18(5), pp. 685–690. [CrossRef] [PubMed]
Vashishth, D., Koontz, J., Qiu, S., Lundin-Cannon, D., Yeni, Y., Schaffler, M., and Fyhrie, D., 2000, “In Vivo Diffuse Damage in Human Vertebral Trabecular Bone,” Bone, 26(2), pp. 147–152. [CrossRef] [PubMed]
Haddock, S. M., Yeh, O. C., Mummaneni, P. V., Rosenberg, W. S., and Keaveny, T. M., 2004, “Similarity in the Fatigue Behavior of Trabecular Bone Across Site and Species,” J. Biomech., 37(2), pp. 181–187. [CrossRef] [PubMed]
Bowman, S., Guo, X., Cheng, D., Keaveny, T., Gibson, L., Hayes, W., and McMahon, T., 1998, “Creep Contributes to the Fatigue Behavior of Bovine Trabecular Bone,” ASME J. Biomech. Eng., 120(5), pp. 647–654. [CrossRef]
Bowman, S. M., Keaveny, T. M., Gibson, L. J., Hayes, W. C., and McMahon, T. A., 1994, “Compressive Creep Behavior of Bovine Trabecular Bone,” J. Biomech., 27(3), pp. 301–310. [CrossRef] [PubMed]
Dendorfer, S., Maier, H., and Hammer, J., 2009, “Fatigue Damage in Cancellous Bone: An Experimental Approach From Continuum to Micro Scale,” J. Mech. Behav. Biomed. Mater., 2(1), pp. 113–119. [CrossRef] [PubMed]
Kosmopoulos, V., Schizas, C., and Keller, T. S., 2008, “Modeling the Onset and Propagation of Trabecular Bone Microdamage During Low-Cycle Fatigue,” J. Biomech., 41(3), pp. 515–522. [CrossRef] [PubMed]
Homminga, J., McCreadie, B., Ciarelli, T., Weinans, H., Goldstein, S., and Huiskes, R., 2002, “Cancellous Bone Mechanical Properties From Normals and Patients With Hip Fractures Differ on the Structure Level, Not on the Bone Hard Tissue Level,” Bone, 30(5), pp. 759–764. [CrossRef] [PubMed]
Chevalier, Y., Pahr, D., Allmer, H., Charlebois, M., and Zysset, P., 2007, “Validation of a Voxel-Based FE Method for Prediction of the Uniaxial Apparent Modulus of Human Trabecular Bone Using Macroscopic Mechanical Tests and Nanoindentation,” J. Biomech., 40(15), pp. 3333–3340. [CrossRef] [PubMed]
Hoffler, C., Moore, K., Kozloff, K., Zysset, P., Brown, M., and Goldstein, S., 2000, “Heterogeneity of Bone Lamellar-Level Elastic Moduli,” Bone, 26(6), pp. 603–609. [CrossRef] [PubMed]
Kaneko, T. S., Bell, J. S., Pejcic, M. R., Tehranzadeh, J., and Keyak, J. H., 2004, “Mechanical Properties, Density and Quantitative CT Scan Data of Trabecular Bone With and Without Metastases,” J. Biomech., 37(4), pp. 523–530. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

An illustration of the hierarchical nature of trabecular bone

Grahic Jump Location
Fig. 2

An illustration of bone cell population

Grahic Jump Location
Fig. 3

Strain-amplification model illustrating the osteocyte process in cross section and longitudinal section. Actin filaments span the process, which is attached to the canalicular wall via transverse elements. Applied loading results in interstitial fluid flow through the pericellular matrix, producing a drag force on the tethering fibers.

Grahic Jump Location
Fig. 4

Illustration of an integrin-based strain-amplification model

Grahic Jump Location
Fig. 5

(a) Scanning electronmicroscopy image of atrabeculum. (b) Indent locations across the width of a trabeculum. (c) Tissue Young modulus of trabecular bone using nano-indentation from skeletally mature sheep after undergoing overiectomy (OVX). (From Reference 97 with permission.)

Grahic Jump Location
Fig. 8

Spatial decomposition of trabecular bone. The initial binary image that served as input for our algorithm is shown in panel (a). A skeletonization and optimization algorithm is applied to get a homotopic shape preserving skeleton as shown in panel (b). This skeleton is then point-classified, thus arc-, surface-, border-, and intersection-points are shown in different colors. (c) This point-classified skeleton is then spatially decomposed by removing the intersection points. (d) A two-way multicolor dilation algorithm was applied to find the volumetric extend of each element, yielding in the final spatially decomposed structure. (From Reference 7 with permission.)

Grahic Jump Location
Fig. 7

Schematic flowchart of computing multiscale material properties: (a) representative elementary volume (RVE) homogenization for estimation of the effective material properties of the bone model at all intermediate levels; (b) a correlation between the porosity of the geometrical models and their respective effective material properties; (c) inverse local material properties model as a function of porosity; and (d) computational model verification. (From Reference 147 with permission.)

Grahic Jump Location
Fig. 6

(a) The layout of the cored specimens (S1–S7) demonstrated on a proximal femur image. Three-dimensional visualization of the average (b) modulus (E) with the upper and lower limits of data at each site; and (c) bone volume fraction (BV/TV) distribution of human proximal femur. In (a), sites S1, S4, S6, and S7 form a loop or belt from the femoral head, through the neck and onto the trochanteric region, where the applied load (in a relatively uniform magnitude) traverses through the proximal femur and disburses into the cortical shaft. It is possible that the loads resultant from normal daily activities are mostly translated though this loop, whereas sites S2 and S3 encounter the higher loads applied to the proximal femur for higher impact activities. (From Reference 117 with permission.)

Grahic Jump Location
Fig. 9

Failure occurs at subregions with the lowest BV/TV values. Subregions number 1, 2, 3, and 4 with the lowest BV/TV values here coincide with the four regions that fail based on the visual data provided by the time-lapsed mechanical testing. (From Reference 167 with permission.)

Grahic Jump Location
Fig. 10

Reductions in secant modulus and accumulation of strain with increasing number of load cycles characterized the cyclic behavior of trabecular bone. Failure was defined as the cycle before which a specimen could no longer sustain the prescribed normalized stress, as indicated by a rapid increase in strain upon the subsequent loading cycle. Creep strain was defined by translation along the X-axis (ck), and damage strain was defined by the difference of the hysteresis loop strains (dk + d1). Total strain was the sum (ck + dk). (From Reference 189 with permission.)



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