Elastic constants of cancellous bone

van Rietbergen, Bert; Huiskes, Rik

Year	Entry
1990	Snyder BD, Hayes WC. Multiaxial structure-property relations in trabecular bone. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:31-59.
1986	Cowin SC, Van Buskirk WC. Thermodynamic restrictions on the elastic constants of bone. J Biomech. 1986;19(1):85-87.
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.
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.
1996	Rüegsegger P, Koller B, Müller R. A microtomographic system for the nondestructive evaluation of bone architecture. Calcif Tiss Int. 1996;58(1):24-29.
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.
1990	Odgaard A, Andersen K, Melsen F, Gundersen HJG. A direct method for fast three-dimensional serial reconstruction. J Microsc (Oxford). September 1990;159(pt 3):335-342.
1995	Zysset PK, Curnier A. An alternative model for anisotropic elasticity based on fabric tensors. Mech Mater. November 1995;21(4):243-250.
1983	Stone JL, Beaupre GS, Hayes WC. Multiaxial strength characteristics of trabecular bone. J Biomech. 1983;16(9):743-752.
1985	Kaplan SJ, Hayes WC, Stone JL, Beaupré GS. Tensile strength of bovine trabecular bone. J Biomech. 1985;18(9):723-727.
1999	Kabel J, van Rietbergen B, Odgaard A, Huiskes R. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone. October 1999;25(4):481-486.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1997	Keaveny TM, Pinilla TP, Crawford RP, Kopperdahl DL, Lou A. Systematic and random errors in compression testing of trabecular bone [published correction appears in J Orthop Res. 1995;17(1):151]. J Orthop Res. 1997;15(1):101-110.
1994	Keaveny TM, Guo XE, Wachtel EF, McMahon TA, Hayes WC. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. J Biomech. 1994;27(9):1127-1136.
1994	Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech. April 1994;27(4):375-389.
1983	Bensusan JS, Davy DT, Heiple KG, Verdin KG. Tensile, compressive and torsional testing of cancellous bone. In: Transacation of the 29th Annual Meeting of the Orthopaedic Research Society. March 8-10, 1983; Anaheim, CA.132.
1980	Zilch H, Rohlmann A, Bergmann G, Kölbel R. Material properties of femoral cancellous bone in axial loading, II: time dependent properties. Arch Orthop Trauma Surg. December 1980;97(4):257-262.
1988	Turner CH, Cowin SC. Errors induced by off-axis measurement of the elastic properties of bone. J Biomech Eng. August 1988;110(3):213-215.
1989	Turner CH. Yield behavior of bovine cancellous bone [published correction appears in J Biomech Eng. 1989;111(4):335]. J Biomech Eng. August 1989;111(3):256-260.
1989	Ashman RB, Rho JY, Turner CH. Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J Biomech. 1989;22(8-9):895-900.
1993	Hodgskinson R, Currey JD. Separate effects of osteoporosis and density on the strength and stiffness of human cancellous bone. Clin Biomech (Bristol, Avon). September 1993;8(5):262-268.
1973	Pugh JW, Rose RM, Radin EL. Elastic and viscoelastic properties of trabecular bone: dependence on structure. J Biomech. 1973;6(5):475-485.
1998	Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech. December 1998;31(12):1187-1192.
1977	Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg. 1977;59A(7):954-962.
1997	Odgaard A, Kabel J, van Rietbergen B, Dalstra M, Huiskes R. Fabric and elastic principal directions of cancellous bone are closely related. J Biomech. 1997;30(5):487-495.
1991	Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB. 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. May 1991;9(5):674-682.
1997	Cowin SC, Yang G. Averaging anisotropic elastic constant data. J Elast. February 1997;46(2):151-180.
1989	Linde F, Hvid I, Pongsoipetch B. Energy absorptive properties of human trabecular bone specimens during axial compression. J Orthop Res. May 1989;7(3):432-439.
1994	Keller TS. Predicting the compressive mechanical behavior of bone. J Biomech. September 1994;27(9):1159-1168.
1990	Hodgskinson R, Currey JD. The effect of variation in structure on the Young's modulus of cancellous bone: a comparison of human and non-human material. Proc Inst Mech Eng Part H-J Eng Med. 1990;204(2):115-121.
1987	Linde F, Hvid I. Stiffness behaviour of trabecular bone specimens. J Biomech. 1987;20(1):83-89.
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.
1985	Linde F, Hvid I, Jensen NC. Material properties of cancellous bone in repetitive axial loading. Eng Med. October 1985;14(4):173-177.
1994	Frey P, Sarter B, Gautherie M. Fully automatic mesh generation for 3‐D domains based upon voxel sets. Int J Num Meth Eng. August 30, 1994;37(16):2735-2753.
1994	Keaveny TM, Wachtel EF, Ford CM, Hayes WC. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J Biomech. 1994;27(9):1137-1146.
1996	Mullender MG, Huiskes R, Versleyen H, Buma P. Osteocyte density and histomorphometric parameters in cancellous bone of the proximal femur in five mammalian species. J Orthop Res. November 1996;14(6):972-979.
1999	Ulrich D, van Rietbergen B, Laib A, Rüegsegger P. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone. 1999;25(1):55-60.
1990	Choi K, Kuhn JL, Ciarelli MJ, Goldstein SA. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J Biomech. 1990;23(11):1103-1113.
1983	Goldstein SA, Wilson DL, Sonstegard DA, Matthews LS. The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J Biomech. 1983;16(12):965-969.
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.
1990	Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech. 1990;23(6):549-561.
1974	Reilly DT, Burstein AH. The mechanical properties of cortical bone. J Bone Joint Surg. 1974;56A(5):1001-1022.
1994	Bonse U, Busch F, Günnewig O, Beckmann F, Pahl R, Delling G, Hahn M, Graeff W. 3D computed X-ray tomography of human cancellous bone at 8 μm spatial and 10⁻⁴ energy resolution. Bone Miner. April 1994;25(1):25-38.
1991	Røhl L, Larsen E, Linde F, Odgaard A, Jørgensen J. Tensile and compressive properties of cancellous bone. J Biomech. 1991;24(12):1143-1149.
1994	Bowman SM, Keaveny TM, Gibson LJ, Hayes WC, McMahon TA. Compressive creep behavior of bovine trabecular bone. J Biomech. March 1994;27(3):301-310.
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.
1988	Harrigan TP, Jasty M, Mann RW, Harris WH. Limitations of the continuum assumption in cancellous bone. J Biomech. 1988;21(4):269-275.
1998	Ladd AJC, Kinney JH. Numerical errors and uncertainties in finite-element modeling of trabecular bone. J Biomech. October 1998;31(10):941-945.
1996	van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech. December 1996;29(12):1653-1657.
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.
1980	Carter DR, Schwab GH, Spengler DM. Tensile fracture of cancellous bone. Acta Orthop Scand. 1980;51(5):733-741.
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.
1989	Feldkamp LA, Goldstein SA, Parfitt MA, Jesion G, Kleerekoper M. The direct examination of three‐dimensional bone architecture in vitro by computed tomography. J Bone Miner Res. 1989;4(1):3-11.
1999	Hildebrand T, Laib A, Müller R, Dequeker J, Rüegsegger P. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res. July 1999;14(7):1167-1174.
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.
1993	Keaveny TM, Borchers RE, Gibson LJ, Hayes WC. Theoretical analysis of the experimental artifact in trabecular bone compressive modulus [published correction appears in J Biomech. 1993;26(9):1143]. J Biomech. April–May 1993;26(4-5):599-607.
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.
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.
1998	Van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Relationships between bone morphology and bone elastic properties can be accurately quantified using high‐resolution computer reconstructions. J Orthop Res. January 1998;16(1):23-28.
1993	Odgaard A, Gundersen HJG. Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone. March–April 1993;14(2):173-182.
1996	Hipp JA, Jansujwicz A, Simmons CA, Snyder BD. Trabecular bone morphology from micro-magnetic resonance imaging. J Bone Miner Res. February 1996;11(2):286-292.
1991	Odgaard A, Linde F. The underestimation of Young's modulus in compressive testing of cancellous bone specimens. J Biomech. 1991;24(8):691-698.
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.
1994	Linde F. Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Dan Med Bull. April 1994;41(2):119-138.
1992	Hodgskinson R, Currey JD. Young's modulus, density and material properties in cancellous bone over a large density range. J Mater Sci Mater Med. September 1992;3(5):377-381.
1985	Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137-147.
1999	Kabel J, Odgaard A, van Rietbergen B, Huiskes R. Connectivity and the elastic properties of cancellous bone. Bone. 1999;24(2):115-120.
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.
1991	Linde F, Nørgaard P, Hvid I, Odgaard A, Søballe K. Mechanical properties of trabecular bone: dependency on strain rate. J Biomech. 1991;24(9):803-809.
1992	Linde F, Hvid I, Madsen F. The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens. J Biomech. 1992;25(4):359-368.
1993	Linde F, Sørensen HCF. The effect of different storage methods on the mechanical properties of trabecular bone. J Biomech. 1993;26(10):1249-1252.
1997	Keaveny TM. Mechanistic approaches to analysis of trabecular bone. Forma. 1997;12(3-4):267-275.
1963	Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids. September 1963;11(5):357-372.
1997	Beck JD, Canfield BL, Haddock SM, Chen TJH, Kothari M, Keaveny TM. Three-dimensional imaging of trabecular bone using the computer numerically controlled milling technique. Bone. 1997;21(3):281-287.
1989	Cowin SC, Mehrabadi MM. Identification of the elastic symmetry of bone and other materials. J Biomech. 1989;22(6-7):503-515.
1993	Keaveny TM, Borchers RE, Gibson L, Hayes WC. Trabecular bone modulus and strength can depend on specimen geometry. J Biomech. August 1993;26(8):991-995.

Year	Entry
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
2003	Lin ASP, Barrows TH, Cartmell SH, Guldberg RE. Microarchitectural and mechanical characterization of oriented porous polymer scaffolds. Biomaterials. February 2003;24(3):481-489.
2003	Kowalczyk P. Elastic properties of cancellous bone derived from finite element models of parameterized microstructure cells. J Biomech. July 2003;36(7):961-972.
2011	Coelho PG, Fernandes PR, Rodrigues HC. Multiscale modeling of bone tissue with surface and permeability control. J Biomech. January 11, 2011;44(2):321-329.
2011	Cherkaev E, Bonifasi-Lista C. Characterization of structure and properties of bone by spectral measure method. J Biomech. January 11, 2011;44(2):345-351.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
2007	Liu XS. High-Resolution Image Based Micro-Mechanical Modeling of Trabecular Bone [PhD thesis]. Columbia University; 2007.
2004	Samuel SP. Fluid/solid Interactions in Cancellous Bone [PhD thesis]. Cleveland State University; August 2004.
2023	Moshage SG. Non-Invasive Determinants of Juvenile Equine Bone Strength for Assessing Exercise Interventions [PhD thesis]. University of Illinois at Urbana-Champaign; 2023.
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]. Queen's University; November 2005.
2011	Kristensen E. The Role of Growth Hormone in the Development of Bone Microarchitecture, Craniofacial Shape and Bone Strength [PhD thesis]. Calgary, AB: University of Calgary; February 2011.
2012	Evdokimenko E. Investigation Into Mechanical Properties of Bone and Its Main Constituents [PhD thesis]. San Diego (UCSD), University of California; 2012.
2012	Mengoni M. On the Development of an Integrated Bone Remodeling Law for Orthodontic Tooth Movements Models Using the Finite Element Method [PhD thesis]. Liège, Belgique: Université de Liège; June 2012.
2002	Hwang I-K. Biomechanical Analysis of Wrist Impact Loading During Fall Arrests: Experimental and Computer Simulation Study [PhD thesis]. University of Wisconsin – Milwaukee; December 2002.
2009	García-Rodríguez S. Mechanical Behavior of Trabecular Bone [PhD thesis]. University of Wisconsin – Madison; 2009.