The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

Choi, K.; Kuhn, J. L.; Ciarelli, M. J.; Goldstein, S. A.

Year	Entry
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
2011	Ferguson VL, Olesiak SE. Nanoindentation of bone. In: Oyen ML, ed. Handbook of Nanoindentation With Biological Applications. Singapore: Pan Stanford Publishing Pte. Ltd; 2011:185-237.
1993	Hollister SJ, Riemer BA. Digital image based finite element analysis for bone microstructure using conjugate gradient and Gaussian filter techniques. In: Wilson JN, Wilson DC, eds. Mathematical Methods in Medical Imaging II. SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation; July 11-16, 1993; San Diego, CA.95-106. Proceedings of the SPIE; vol 2035.
1994	Linde F. Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Dan Med Bull. April 1994;41(2):119-138.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1996	van Rietbergen B. Mechanical Behavior and Adaptation of Trabecular Bone in Relation to Bone Morphology [PhD thesis]. Nijmegen, Netherlands: Catholic University of Nijmegen; 1996.
2011	Yue N, Shin J, Untaroiu CD. Blunt injury response of occupant lower extremity during automotive crashes: a finite element study. In: Proceedings of the 39th International Workshop on Human Subjects for Biomechanical Research. 2011.
2010	Tomasch E, Kirschbichler S, Sinz W, Steffan H, Darok M, Dimai H-P, Patsch J. Methodology to predict thresholds for loading corridors of human ribs. In: Proceedings of the 2010 International IRCOBI Conference on the Biomechanics of Impact. September 15-17, 2010; Hannover, Germany.285-288.
2011	Yue N, Shin J, Untaroiu CD. Development and validation of an occupant lower limb finite element model. In: Proceedings of the SAE World Congress & Exhibition. April 12-14, 2011; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2011-11-1128.
2018	Wu D, Isaksson P, Ferguson SJ, Persson C. Young’s modulus of trabecular bone at the tissue level: a review. Acta Biomater. September 15, 2018;78:1.
2000	Fyhrie DP, Hoshaw SJ, Hamid MS, Hou FJ. Shear stress distribution in the trabeculae of human vertebral bone. Annals Biomed Eng. October 2000;28(10):1194-1199.
1997	Rho J-Y, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997;18(20):1325-1330.
2003	Taboas JM, Maddox RD, Krebsbach PH, Hollister SJ. Indirect solid free form fab.rication of local and global porous, biomimetic and composite 3d polymer-ceramic scaffolds. Biomaterials. January 2003;24(1):181-194.
2011	Cox LGE, van Rietbergen B, van Donkelaar CC, Ito K. Analysis of bone architecture sensitivity for changes in mechanical loading, cellular activity, mechanotransduction, and tissue properties. Biomech Model Mechanobiol. January 2011;10(5):701-712.
1993	Turner CH, Burr DB. Basic biomechanical measurements of bone: a tutorial. Bone. 1993;14(4):595-608.
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.
1998	Wang XD, Masilamani NS, Mabrey JD, Alder ME, Agrawal CM. Changes in the fracture toughness of bone may not be reflected in its mineral density, porosity, and tensile properties. Bone. July 1998;23(1):67-72.
2000	Hoffler CE, Moore KE, Kozloff K, Zysset PK, Brown MB, Goldstein SA. Heterogeneity of bone lamellar-level elastic moduli. Bone. June 2000;26(6):603-609.
2002	Hengsberger S, Kulik A, Zysset P. Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions. Bone. 2002;30(1):178-184.
2002	Homminga J, McCreadie BR, Ciarelli TE, Weinans H, Goldstein SA, Huiskes R. Cancellous bone mechanical properties from normals and patients with hip fractures differ on the structure level, not on the bone hard tissue level. Bone. May 2002;30(5):759-764.
2005	Hernandez CJ, Tang SY, Baumbach BM, Hwu PB, Sakkee AN, van der Ham F, DeGroot J, Bank RA, Keaveny TM. Trabecular microfracture and the influence of pyridinium and non-enzymatic glycation-mediated collagen cross-links. Bone. December 2005;37(6):825-832.
2006	McNamara LM, Ederveen AGH, Lyons CG, Price C, Schaffler MB, Weinans H, Prendergast PJ. Strength of cancellous bone trabecular tissue from normal, ovariectomized and drug-treated rats over the course of ageing. Bone. August 2006;39(2):392-400.
2006	McCreadie BR, Morris MD, Chen T-c, Rao DS, Finney WF, Widjaja E, Goldstein SA. Bone tissue compositional differences in women with and without osteoporotic fracture. Bone. December 2006;39(6):1190-1195.
2009	Bevill G, Eswaran SK, Farahmand F, Keaveny TM. The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties. Bone. April 2009;44(4):573-578.
2009	Busse B, Hahn M, Soltau M, Zustin J, Püschel K, Duda GN, Amling M. Increased calcium content and inhomogeneity of mineralization render bone toughness in osteoporosis: mineralization, morphology and biomechanics of human single trabeculae. Bone. December 2009;45(6):1034-1043.
1993	Goldstein SA, Goulet R, McCubbrey D. Measurement and significance of three-dimensional architecture to the mechanical integrity of trabecular bone. Calcif Tiss Int. February 1993;53(suppl 1):S127-S133.
2007	Wu L. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures. Clin Biomech (Bristol, Avon). 2007;22(2):221-229.
2011	Johnston JD, Kontulainen SA, Masri BA, Wilson DR. Predicting subchondral bone stiffness using a depth-specific CT topographic mapping technique in normal and osteoarthritic proximal tibiae. Clin Biomech (Bristol, Avon). December 2011;26(10):1012-1018.
2011	Donnelly E. Methods for assessing bone quality: a review. Clin Orthop Relat Res. August 2011;469:2128-2138.
1994	Soslowsky LJ, An CH, Johnston SP, Carpenter JE. Geometric and mechanical properties of the coracoacromial ligament and their relationship to rotator cuff diseas. Clin Orthop Relat Res. July 1994;304:10-17.
2001	Hengsberger S, Kulik A, Zysset P. A combined atomic force microscopy and nanoindentation technique to investigate the elastic properties of bone structural units. Eur Cell Mater. January–June 2001;1:12-17.
1997	Guo XE, Goldstein SA. Is trabecular bone tissue different from cortical bone tissue? Forma. 1997;12(3-4):185-196.
1991	Martin RB. Determinants of the mechanical properties of bones. J Biomech. 1991;24(suppl 1):79-88.
1991	Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. Application of homogenization theory to the study of trabecular bone mechanics. J Biomech. 1991;24(9):825-839.
1992	Hogan HA. Micromechanics modeling of Haversian cortical bone properties. J Biomech. May 1992;25(5):549-556.
1992	Choi K, Goldstein SA. A comparison of the fatigue behavior of human trabecular and cortical bone tissue. J Biomech. 1992;25(12):1371-1381.
1993	Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. February 1993;26(2):111-119.
1994	Zhu M, Keller TS, Spengler DM. Effects of specimen load-bearing and free surface layers on the compressive mechanical properties of cellular materials. J Biomech. 1994;27(1):57-66.
1994	Hollister SJ, Brennan JM, Kikuchi N. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stres. J Biomech. 1994;27(4):433-444.
1994	Prendergast P, Taylor D. Prediction of bone adaptation using damage accumulation. J Biomech. August 1994;27(8):1067-1076.
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. 1995;28(1):69-81.
1997	Prendergast PJ, Huiskes R, Søballe K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech. June 1997;30(6):539-548.
1997	Jepsen KJ, Schaffler MB, Kuhn JL, Goulet RW, Bonadio J, Goldstein SA. Type I collagen mutation alters the strength and fatigue behavior of Mov13 cortical tissue. J Biomech. November–December 1997;30(11-12):1141-1147.
1998	Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. July 1998;31(7):601-608.
1998	Hou FJ, Lang SM, Hoshaw SJ, Reimann DA, Fyhrie DP. Human vertebral body apparent and hard tissue stiffness. J Biomech. November 1998;31(11):1009-1015.
1999	Van Rietbergen B, Müller R, Ulrich D, Rüegsegger P, Huiskes R. Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions. J Biomech. February 1999;32(2):165-173.
1999	Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.
1999	Liu D, Weiner S, Wagner HD. Anisotropic mechanical properties of lamellar bone using miniature cantilever bending specimens. J Biomech. July 1999;32(7):647-654.
1999	Kabel J, van Rietbergen B, Dalstra M, Odgaard A, Huiskes R. The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. J Biomech. 1999;32(7):673-680.
1999	Ulrich D, van Rietbergen B, Laib A, Rüegsegger P. Load transfer analysis of the distal radius from in-vivo high-resolution CT-imaging. J Biomech. August 1999;32(8):821-828.
1999	Jacobs CR, Davis BR, Rieger CJ, Francis JJ, Saad M, Fyhrie DP. 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. November 1999;32(11):1159-1164.
2000	Braidotti P, Bemporad E, D'Alessio T, Sciuto SA, Stagni L. Tensile experiments and sem fractography on bovine subchondral bone. J Biomech. September 2000;33(9):1153-1157.
2001	van der Linden JC, Birkenhäger-Frenkel DH, Verhaar JAN, Weinans H. Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution. J Biomech. December 2001;34(12):1573-1580.
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.
2004	Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.
2004	Bourne BC, van der Meulen MCH. Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation. J Biomech. 2004;37(5):613-621.
2004	Silva MJ, Brodt MD, Fan Z, Rho J-Y. Nanoindentation and whole-bone bending estimates of material properties in bones from the senescence accelerated mouse SAMP6. J Biomech. November 2004;37(11):1639-1646.
2006	McNamara LM, Van der Linden JC, Weinans H, Prendergast PJ. Stress-concentrating effect of resorption lacunae in trabecular bone. J Biomech. 2006;39(4):734-741.
2007	Mulder L, van Ruijven LJ, Koolstra JH, van Eijden TMGJ. Biomechanical consequences of developmental changes in trabecular architecture and mineralization of the pig mandibular condyle. J Biomech. 2007;40(7):1575-1582.
2009	Brennan O, Kennedy OD, Lee TC, Rackard SM, O'Brien FJ. Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep. J Biomech. March 11, 2009;42(4):498-503.
2011	Brennan O, Kennedy OD, Lee TC, Rackard SM, O’Brien FJ, McNamara LM. The effects of estrogen deficiency and bisphosphonate treatment on tissue mineralisation and stiffness in an ovine model of osteoporosis. J Biomech. February 3, 2011;44(3):386-390.
2011	Szabó ME, Taylor M, Thurner PJ. Mechanical properties of single bovine trabeculae are unaffected by strain rate. J Biomech. March 15, 2011;44(5):962-967.
2020	Alonso MG, Bertolino G, Yawny A. Mechanobiological based long bone growth model for the design of limb deformities correction devices. J Biomech. August 26, 2020;109:109905.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
1998	Zysset PK, Goulet RW, Hollister SJ. A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng. October 1998;120(5):640-646.
1999	Kopperdahl DL, Roberts AD, Keaveny TM. Localized damage in vertebral bone is most detrimental in regions of high strain energy density. J Biomech Eng. December 1999;121(6):622-628.
2005	Hoffler CE, Guo XE, Zysset PK, Goldstein SA. An application of nanoindentation technique to measure bone tissue lamellae properties. J Biomech Eng. January 2005;127(7):1046-1053.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
2001	Swadener JG, Rho J, Pharr GM. Effects of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone. J Biomed Mater Res. October 2001;57(1):108-112.
1999	Roy ME, Rho J-Y, Tsui TY, Evans ND, Pharr GM. Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone. J Biomed Mater Res. February 1999;A44(2):191-197.
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.
1998	Swartz SM, Parker A, Huo C. Theoretical and empirical scaling patterns and topological homology in bone trabeculae. J Exp Biol. February 1998;201(4):573-590.
2000	Lucchinetti E, Thomann D, Danuser G. Micromechanical testing of bone trabeculae: potentials and limitations. J Mater Sci. December 2000;35(24):6057-6064.
2011	Jungmann R, Szabo ME, Schitter G, Tang RY-S, Vashishth D, Hansma PK, Thurner PJ. Local strain and damage mapping in single trabeculae during three-point bending tests. J Mech Behav Biomed Mater. May 2011;4(4):523-534.
2011	Szabó ME, Zekonyte J, Katsamenis OL, Taylor M, Thurner PJ. Similar damage initiation but different failure behavior in trabecular and cortical bone tissue. J Mech Behav Biomed Mater. November 2011;4(8):1787-1796.
2012	Vaughan TJ, McCarthy CT, McNamara LM. A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone. J Mech Behav Biomed Mater. August 2012;12:50-62.
2019	Asgari M, Abi-Rafeh J, Hendy GN, Pasini D. Material anisotropy and elasticity of cortical and trabecular bone in the adult mouse femur via AFM indentation. J Mech Behav Biomed Mater. May 2019;93:81-92.
2020	Martig S, Hitchens PL, Lee PVS, Whitton RC. The relationship between microstructure, stiffness and compressive fatigue life of equine subchondral bone. J Mech Behav Biomed Mater. January 2020;101:103439.
2020	Gastaldi D, Baleani M, Fognani R, Airaghi F, Bonanni L, Vena P. An experimental procedure to perform mechanical characterization of small-sized bone specimens from thin femoral cortical wall. J Mech Behav Biomed Mater. December 2020;112:104046.
1994	Mente PL, Lewis JL. Elastic modulus of calcified cartilage is an order of magnitude less than that of subchondral bone. J Orthop Res. September 1994;12(5):637-647.
1994	Les CM, Keyak JH, Stover SM, Taylor KT, Kaneps AJ. Estimation of material properties in the equine metacarpus with use of quantitative computed tomography. J Orthop Res. November 1994;12(6):822-833.
1995	Mullender MG, Huiskes R. Proposal for the regulatory mechanism of Wolff's law. J Orthop Res. July 1995;13(4):503-512.
1998	Ladd AJC, Kinney JH, Haupt DL, Goldstein SA. Finite‐element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus. J Orthop Res. September 1998;16(5):622-628.
2000	Guo XE, Goldstein SA. Vertebral trabecular bone microscopic tissue elastic modulus and hardness do not change in ovariectomized rats. J Orthop Res. March 2000;18(2):333-336.
2001	Day JS, Ding M, van der Linden JC, Hvid I, Sumner DR, Weinans H. A decreased subchondral trabecular bone tissue elastic modulus is associated with pre‐arthritic cartilage damage. J Orthop Res. September 2001;19(5):914-918.
1999	Weiner S, Traub W, Wagner HD. Lamellar bone: structure–function relations. J Struct Biol. June 1999;126(3):241-255.
1998	Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.
2008	Gupta HS, Zioupos P. Fracture of bone tissue: the ‘hows’ and the ‘whys’. Med Eng Phys. December 2008;30(10):1209-1226.
2004	Burr DB. Anatomy and physiology of the mineralized tissues: role in the pathogenesis of osteoarthrosis. Osteoarthritis Cartilage. 2004;12(suppl):S20-S30.
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.
2006	Imai K, Ohnishi I, Bessho M, Nakamura K. Nonlinear finite element model predicts vertebral bone strength and fracture site. Spine. July 15, 2006;31(16):1789-1794.
2001	Birnbaum K, Sindelar R, Gärtner JR, Wirtz DC. Material properties of trabecular bone structures. Surg Radiol Anat. 2001;23(6):399-407.
2010	Campbell SE. Nanoindentation of Bio- and Geo-Mineralized Composites: Contribution of Microstructure and Composition [PhD thesis]. University of Colorado; 2010.
2007	Cole JH. The Role of Architecture and Tissue Properties in the Structural Integrity of Human Vertebral Cancellous Bone [PhD thesis]. Ithaca, NY: Cornell University; May 2007.
2015	Goff M. The Role of Micro and Ultra-Structure in Microdamage Accumulation in Cancellous Bone [PhD thesis]. Ithaca, NY: Cornell University; August 2015.
2005	Cook RB. Non-Invasively Assessed Skeletal Bone Status and Its Relationship to the Biomechanical Properties and Condition of Cancellous Bone [PhD thesis]. Cranfield, UK: Cranfield University; December 18, 2005.
2011	Donaldson FE. On Incorporating Bone Microstructure in Macro-Finite-Element Models [PhD thesis]. Edinburgh, UK: University of Edinburgh; March 2011.
2002	Hengsberger S. Mechanical Characterization of Bone from the Tissue Down to the Lamellar Level by Means of Nanoindentation [PhD thesis]. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne; 2002.
2006	Garcia D. Elastic Plastic Damage Laws for Cortical Bone [PhD thesis]. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne; 2006.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Erasmus University Rotterdam; 2005.
1993	Guo X-DE. Fatigue of Trabecular Bone [PhD thesis]. Cambridge, MA: Harvard University; 1993.
2010	Feng L. Multi-Scale Characterization of Swine Femoral Cortical Bone and Long Bone Defect Repair by Regeneration [PhD thesis]. University of Illinois at Urbana-Champaign; 2010.
2012	Hamed E. Multiscale Modeling of Elastic Moduli and Strength of Bone [PhD thesis]. University of Illinois at Urbana-Champaign; 2012.
2002	Follet H. Caractérisation Biomécanique Et Modélisation 3D Par Imagerie X Et IRM Haute Résolution De L’os Spongieux Humain: Evaluation Du Risque Fracturaire [PhD thesis]. Institut national des sciences appliquées de Lyon (INSA Lyon); 2002.
2019	Du J. Mechanical Adaptation of Human Trabecular Bone: Experimental and Computational Study [PhD thesis]. Loughborough University; 2019.
2019	Ilas DC. The Role of Mesenchymal Stem Cells and Osteocytes in Subchondral Bone Changes in Hip Osteoarthritis [PhD thesis]. University of Leeds; May 2019.
2007	Akhtar R. Micromechanical Behaviour of Bone [PhD thesis]. University of Manchester; 2007.
2014	Jameson JR. Characterization of Bone Material Properties and Microstructure in Osteogenesis Imperfecta/brittle Bone Disease [PhD thesis]. Marquette University; December 2014.
1996	Ford CM. Failure of the Human Proximal Femur: Material and Structural Perspectives [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; September 1996.
1996	Silva MJ. Predicting the Failure Behavior of the Human Vertebral Body [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1996.
2015	Oftadeh R. Hierarchical Analysis and Multiscale Modelling of Cellular Structures: From Meta Materials to Bone Structure [PhD thesis]. Northeastern University; December 2015.
2020	O’Sullivan LM. Time-Sequence of Biomechanical Adaption in Trabecular Tissue During Estrogen Deficiency [PhD thesis]. National University of Ireland Galway; March 2020.
2012	Jimenez Palomar I. Mechanical Properties of Bone At the Sub-lamellar Level [PhD thesis]. London, England: Queen Mary University of London; September 2012.
2005	Buie HR. Use of Finite Element Method Modelling and Rapid Prototyping to Study the Effect of Trabecular Bone Architecture on Apparent Mechanical Properties [Master's thesis]. Kingston, ON: Queen's University; November 2005.
2008	Crookshank MCM. Optimizing Fracture Management: Correlating the Physical and Mechanical Properties of Bone to Computed Tomography to Generate an Estimate of Bone Quality [Master's thesis]. Queen's University; January 2008.
2010	Engbretson AC. Determining the Modulus of Intact Bovine Vertebral Cancellous Bone Tissue: Development and Validation of a Protocol [Master's thesis]. Kingston, ON: Queen’s University; August 25, 2010.
2013	Morton JJ. An Investigation of Rat Vertebra Failure Behaviour Under Uniaxial Compression Through Time-Lapsed Micro-CT Imaging [Master's thesis]. Kingston, ON: Queen's University; 2013.
2013	Toal VR. The Mechanics of Microdamage and Microfracture in Trabecular Bone [PhD thesis]. Brisbane, Australia: Queensland University of Technology; September 2013.
2001	Tanck EJM. Mechanical Regulation of Bone Development [PhD thesis]. Nijmegen, Netherlands: Katholieke Universiteit Nijmegen; June 2001.
2006	Whitty M. Development of a Physiological Three Dimensional Finite Element Model of a Human Tibia [Master's thesis]. Kingston, ON: Royal Military College of Canada; May 2006.
2001	Kim DG. Micromechanical Analysis of Bone At a Bone-Implant Interface [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; April 2001.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Dallas, TX: Southern Methodist University. Tong W, advisor; August 3, 2011.
2004	McNamara LM. Biomechanical Origins of Osteoporosis [PhD thesis]. Trinity College Dublin; March 2004.
2006	Verhulp E. Analyses of Trabecular Bone Failure [PhD thesis]. Eindhoven, The Netherlands: Eindhoven University of Technology; 2006.
2021	Frank M. Mechanical Characterization of Individual Trabeculae [PhD thesis]. Vienna University of Technology; February 2021.
2010	Johnston JD. Development of a Non-Invasive Imaging Technique for Characterizing Subchondral Bone Density and Stiffness [PhD thesis]. Vancouver, BC: University of British Columbia; December 2010.
2002	Wohl GR. Bone Mechanics in Transplanted Osteochondral Grafts [PhD thesis]. Calgary, AB: University of Calgary; September 2002.
1998	Kopperdahl DL. Structural Consequences of Damage on the Mechanical Behavior of the Human Vertebral Body [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1998.
2003	Bayraktar HH. Multiaxial Strength and Micromechanics of Human Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2003.
2004	Kazakia GJ. Development, Analysis, and Imaging of a Tissue Engineered Trabecular Bone Substitute [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2004.
2008	Bevill GR. Micromechanical Modeling of Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2008.
2013	Wang Y-K. Multi-Level Micromechanical Modeling of Bone Tissues [PhD thesis]. Los Angeles, CA: Los Angeles, University of California; 2013.
2014	Su W-iA. Biomechanics of Osteochondral Graft Insertion: Cartilage Damage and Protection Strategies [PhD thesis]. San Diego (UCSD), University of California; 2014.
1991	Choi K. The Micro Mechanical Properties of Bone Tissue [PhD thesis]. University of Michigan; 1991.
1991	Hollister SJ. Homogenization Analysis of Trabecular Bone and Prediction Ofbone Ingrowth Using Topology Optimization [PhD thesis]. Ann Arbor, MI: University of Michigan; 1991.
1993	McCubbrey DA. The Macroscopic Architectural Properties of Vertebral Trabecular Bone and Their Relation to Whole Vertebral Failure Loads [PhD thesis]. University of Michigan; 1993.
1994	Jepsen KJ. Characterization of the Hierarchical Composite Properties of Cortical Bone: A Transgenic Approach [PhD thesis]. Ann Arbor, MI: University of Michigan; 1994.
1995	Guldberg RE. Mechanical Adaptation of Trabecular Bone Formation in Vivo [PhD thesis]. Ann Arbor, MI: University of Michigan; 1995.
1995	Tseng K-F. Investigating the Structure-Function Relationships of Long Bone: An Approach Using Growth Hormone Mouse Models [PhD thesis]. University of Michigan; 1995.
1998	Ciarelli TE. Architectural and Material Contributions to Fracture of the Spine and Proximal Femur [PhD thesis]. University of Michigan; 1998.
2000	Borodkin JL. The Influence of Interface Micromechanics on the Biological Fixation of Porous-Coated Implants [PhD thesis]. University of Michigan; 2000.
2000	McCreadie BR. Structural and Material Changes in Osteoporosis: Their Impact on the Mechanical Environment of the Osteocyte [PhD thesis]. Ann Arbor, MI: University of Michigan; 2000.
2006	Jongpaiboonkit L. Calcium Phosphate Scaffolds for Bone Tissue Engineering and Self-Association PEG-PLLA Diblock Copolymer for Controlled Drug Delivery System [PhD thesis]. University of Michigan; 2006.
2006	Seong W-J. Relationships Between the Physical Properties of Human Jawbone and the Initial Stability of Dental Implant, and Their Dependency on Anatomical Regions of Jawbone [PhD thesis]. University of Minnesota; April 2006.
2019	Martig S. Compressive Fatigue Life and Micromorphology of Equine Metacarpal Subchondral Bone [PhD thesis]. University of Melbourne; June 2019.
2012	Barkaoui A. Modélisation multiéchelle du comportement mécano-biologique de l’os humain: De l’ultrastructure au remodelage osseux [PhD thesis]. University of Orleans; 2012.
2010	Wald MJ. Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2010.
2013	Amini M. Stiffness of the Proximal Tibial Bone in Normal and Osteoarthritic Conditions: A Parametric Finite Element Simulation Study [Master's thesis]. University of Saskatchewan; January 2013.
2019	Yue N. A Numerical Investigation of Biomechanical Response and Injury of Occupant Lower Extremities in Automotive Frontal Impact Scenario [Master's thesis]. Charlottesville, VA: University of Virginia; December 2019.
2018	Khor F. Computational Modeling of Hard Tissue Response and Fracture in the Lower Cervical Spine Under Compression Including Age Effects [Master's thesis]. Waterloo, ON: University of Waterloo; 2018.
2011	Burkhart TA. Biomechanics of the Upper Extremity in Response to Dynamic Impact Loading Indicative of a Forward Fall: An Experimental and Numerical Investigation [PhD thesis]. University of Windsor; 2011.
2001	Zhang N. Investigation of Bone Mechanical Properties At the Microscopic Level Using Ultrasonic Methods and Numerical Simulation [PhD thesis]. Detroit, MI: Wayne State University; 2001.
2019	Knowles NK. Improving Material Mapping in Glenohumeral Finite Element Models: A Multi-Level Evaluation [PhD thesis]. University of Western Ontario; 2019.
2020	Hamandi FMRA. Hierarchical Structure, Properties and Bone Mechanics At Macro, Micro, and Nano Levels [PhD thesis]. Dayton, OH: Wright State University; 2020.

Year	Entry
1970	Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.
1988	Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.
1982	Williams JL, Lewis JL. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. J Biomech Eng. February 1982;104(1):50-56.
1975	Runkle JC, Pugh J. The micro-mechanics of cancellous bone, II: determination of the elastic modulus of individual trabeculae by a buckling analysis. Bull Hosp Joint Dis. April 1975;36(1):2-10.
1984	Brown TD, Vrahas MS. The apparent elastic modulus of the juxtarticular subchondral bone of the femoral head. J Orthop Res. 1984;2(1):32-38.
1967	Ascenzi A, Bonucci E. The tensile properties of single osteons. Acta Anat. 1967;158(4):375-386.
1960	Frost HM. Presence of microscopic cracks in vivo in bone. Henry Ford Hosp Med Bull. 1960;8(1):25-35.
1952	Dempster WT, Liddicoat RT. Compact bone as a non-isotropic material. Am J Anat. 1952;91(3):331-362.
1975	Townsend PR, Rose RM, Radin EL. Buckling studies of single human trabeculae. J Biomech. July 1975;8(3-4):199-200.
1968	Ascenzi A, Bonucci E. The compressive properties of single osteons. Anat Rec. July 1968;161(3):377-392.
1989	Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS. Comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res. November 1989;7(6):876-884.
1965	Sedlin ED. A rheologic model for cortical bone: a study of physical properties of human femoral samples. Acta Orthop Scand. 1965;(suppl 83):1-77.
1964	Gong JK, Arnold JS, Cohn SH. Composition of trabecular and cortical bone. Anat Rec. 1964;149(3):325-331.
1951	Evans FG, Lebow M. Regional differences in some of the physical properties of the human femur. J Appl Physiol. 1951;3(9):563-572.
1973	Simkin A, Robin G. The mechanical testing of bone in bending. J Biomech. 1973;6(1):31-39.
1974	Reilly DT, Burstein AH. The mechanical properties of cortical bone. J Bone Joint Surg. 1974;56A(5):1001-1022.
1989	Hodgskinson R, Currey JD, Evans GP. Hardness, an indicator of the mechanical competence of cancellous bone. J Orthop Res. September 1989;7(5):754-758.
1988	Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.
1974	Reilly DT, Burstein AH, Frankel VH. The elastic modulus for bone. J Biomech. May 1974;7(3):271-275.
1975	Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.
1970	Timoshenko SP, Goodier JN. Theory of Elasticity. 3rd ed. New York, NY: McGraw-Hill Book Co; 1970.
1975	Currey JD, Butler G. The mechanical properties of bone tissue in children. J Bone Joint Surg. September 1975;57A(6):810-814.
1989	Martin RB, Ishida J. The relative effects of collagen fiber orientation, porosity, density, and mineralization on bone strength. J Biomech. 1989;22(5):419-426.
1966	Sedlin‌ ED, Hirsch C. Factors affecting the determination of the physical properties of femoral cortical bone. Acta Orthop Scand. 1966;37(1):29-48.
1972	Burstein AH, Currey JD, Frankel VH, Reilly DT. The ultimate properties of bone tissue: the effects of yielding. J Biomech. January 1972;5(1):35-44.
1966	Weaver JK. The microscopic hardness of bone. J Bone Joint Surg. March 1966;48A(2):273-288.
1989	Ryan SD, Williams JL. Tensile testing of rodlike trabeculae excised from bovine femoral bone. J Biomech. 1989;22(4):351-355.