Effects of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone

Swadener, J. G.; Rho, Jae‐Young; Pharr, G. M.

Affiliations

¹Metals and Ceramics Division, Oak Ridge National Laboratory, P.O. Box 2008, MS-6093,Oak Ridge, Tennessee 37831-6093

²Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200

³Department of Biomedical Engineering, University of Memphis, Memphis, Tennessee 38152-6582

Abstract and keywords

Many biological materials are known to be anisotropic. In particular, microstructural components of biological materials may grow in a preferred direction, giving rise to anisotropy in the microstructure. Nanoindentation has been shown to be an effective technique for determining the mechanical properties of microstructures as small as a few microns. However, the effects of anisotropy on the properties measured by nanoindentation have not been fully addressed. This study presents a method to account for the effects of anisotropy on elastic properties measured by nanoindentation. This method is used to correlate elastic properties determined from earlier nanoindentation experiments and from earlier ultrasonic velocity measurements in human tibial cortical bone. Also presented is a procedure to determine anisotropic elastic moduli from indentation measurements in multiple directions.

Keywords: anisotropy; cortical bone; elastic modulus; nanoindentation; ultrasonic velocity

Links

DOI: 10.1002/1097-4636(200110)57:1<108::AID-JBM1148>3.0.CO;2-6

PubMed: 11416856

WoS: 000169842900015

History

Received: 2000-7-24

Revised: 2001-01-24

Accepted: 2001-03-22

Cited Works (20)

Year	Entry
1988	Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.
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.
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.
1967	Ascenzi A, Bonucci E. The tensile properties of single osteons. Acta Anat. 1967;158(4):375-386.
1999	Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.
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.
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.
2001	Swadener JG, Pharr GM. Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution. Philos Mag. February 2001;81A(2):447-466.
1974	Reilly DT, Burstein AH, Frankel VH. The elastic modulus for bone. J Biomech. May 1974;7(3):271-275.
1999	Rho J-Y, Pharr GM. Effects of drying on the mechanical properties of bovine femur measured by nanoindentation. J Mater Sci Mater Med. 1999;10(8):485-488.
1992	Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res. 1992;7(6):1564-1583.
1989	Mente PL, Lewis JL. Experimental method for the measurement of the elastic modulus of trabecular bone tissue. J Orthop Res. 1989;7(3):456-461.
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.
1996	Rho J-Y. An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone. Ultrasonics. December 1996;34(8):777-783.
1990	Ascenzi A, Baschieri P, Benvenuti A. The bending properties of single osteons. J Biomech. 1990;23(8):763-771.
1989	Ryan SD, Williams JL. Tensile testing of rodlike trabeculae excised from bovine femoral bone. J Biomech. 1989;22(4):351-355.
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.
1994	Ascenzi A, Baschieri P, Benvenuti A. The torsional properties of single selected osteons. J Biomech. July 1994;27(7):875-884.

Cited By (41)

Year	Entry
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.
2008	Lau A, Oyen ML, Kent RW, Murakami D, Torigaki T. Indentation stiffness of aging human costal cartilage. Acta Biomater. 2008;4(1):97-103.
2011	Novitskaya E, Chen P-Y, Lee S, Castro-Ceseña A, Hirata G, Lubarda VA, McKittrick J. Anisotropy in the compressive mechanical properties of bovine cortical bone and the mineral and protein constituents. Acta Biomater. August 2011;7(8):3170-3177.
2008	Yoon YJ, Cowin SC. The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol. February 2008;7(1):1-11.
2008	Nikolov S, Raabe D. Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization. Biophys J. June 2008;94(11):4220-4232.
2009	Budyn É, Hoc T. Analysis of micro fracture in human Haversian cortical bone under transverse tension using extended physical imaging. Int J Num Meth Eng. 2009;82(8):940-965.
2006	Hofmann T, Heyroth F, Meinhard H, Fränzel W, Raum K. Assessment of composition and anisotropic elastic properties of secondary osteon lamellae. J Biomech. 2006;39(12):2282-2294.
2008	Oyen ML, Ferguson VL, Bembey AK, Bushby AJ, Boyde A. Composite bounds on the elastic modulus of bone. J Biomech. August 7, 2008;41(11):2585-2588.
2012	Feng L, Chittenden M, Schirer J, Dickinson M, Jasiuk I. Mechanical properties of porcine femoral cortical bone measured by nanoindentation. J Biomech. June 26, 2012;45(10):1775-1782.
2005	Akkus O. Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model. J Biomech Eng. June 2005;127(3):383-390.
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.
2009	Franzoso G, Zysset PK. Elastic anisotropy of human cortical bone secondary osteons measured by nanoindentation. J Biomech Eng. February 2009;131(2):021001.
2010	Carnelli D, Gastaldi D, Sassi V, Contro R, Ortiz C, Vena P. A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue. J Biomech Eng. August 2010;132(8):081008.
2008	Mulder L, Koolstra JH, den Toonder JMJ, van Eijden TMGJ. Relationship between tissue stiffness and degree of mineralization of developing trabecular bone. J Biomed Mater Res. February 2008;A84(2):508-515.
2009	Espinoza Orías AA, Deuerling JM, Landrigan MD, Renaud JE, Roeder RK. Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur. J Mech Behav Biomed Mater. July 2009;2(3):255-263.
2012	Pathak S, Vachhani SJ, Jepsen KJ, Goldman HM, Kalidindi SR. Assessment of lamellar level properties in mouse bone utilizing a novel spherical nanoindentation data analysis method. J Mech Behav Biomed Mater. September 2012;13:102-117.
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	Remache D, Semaan M, Rossi JM, Pithioux M, Milan J. Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone. J Mech Behav Biomed Mater. January 2020;101:103426.
2002	Fan Z, Swadener JG, Rho JY, Roy ME, Pharr GM. Anisotropic properties of human tibial cortical bone as measured by nanoindentation. J Orthop Res. July 2002;20(4):806-810.
2005	Gupta HS, Schratter S, Tesch W, Roschger P, Berzlanovich A, Schoeberl T, Klaushofer K, Fratzl P. Two different correlations between nanoindentation modulus and mineral content in the bone–cartilage interface. J Struct Biol. February 2005;149(2):138-148.
2006	Bembey AK, Oyen ML, Bushby AJ, Boyde A. Viscoelastic properties of bone as a function of hydration state determined by nanoindentation. Philos Mag. November 21–December 11, 2006;86(33-35):5691-5703.
2010	Campbell SE. Nanoindentation of Bio- and Geo-Mineralized Composites: Contribution of Microstructure and Composition [PhD thesis]. University of Colorado; 2010.
2013	Paietta RC. Microscale Material Properties of Bone and the Mineralized Tissues of the Intervertebral Disc-Vertebral Body Interface [PhD thesis]. Boulder, CO: University of Colorado; 2013.
2017	Wahlquist JA. Zonal Articular Cartilage Possesses Complex Mechanical Behavior Spanning Multiple Length Scales: Dependence on Chemical Heterogeneity, Anisotropy, and Microstructure [PhD thesis]. Boulder, CO: University of Colorado; 2017.
2017	Yu Y. Contributions of Anisotropic and Heterogeneous Tissue Modulus to Apparent Trabecular Bone Mechanical Properties [PhD thesis]. New York, NY: Columbia University; 2017.
2005	Yoon YJ. Estimates of Bone Elastic Constants At Sequential Hierarchical Levels [PhD thesis]. New York, NY: The City University of New York; 2005.
2018	Li Q. Role of Meniscus Micromechanics in Joint Function and Osteoarthritis [PhD thesis]. Drexel University; December 2018.
2014	Carretta R. Post-Yield Mechanics and Material Composition of Single Trabeculae: A Combined Experimental and Modelling Approach [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2014.
2022	Peruzzi CRP. Nanoscale Deformation Mechanisms and Yield Prediction of Lamellar Bone [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2022.
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.
2010	Killian ML. The Influence of Traumatic Impaction and Pathological Loading on Knee Menisci [PhD thesis]. Houghton, MI: Michigan Technological University; 2010.
2011	Wu Z. Measures of Bone Quality and Their Relationship to Bone Mechanical Properties [PhD thesis]. University of Notre Dame; December 2011.
2020	Karali A. Multi-Scale Evaluation of Bone Combining Indentation, in Situ XCT Mechanics and Digital Volume Correlation [PhD thesis]. Portsmouth, England: University of Portsmouth; 2020.
2024	Davis SL. Using High Resolution X-Ray Computed Tomography and Digital Volume Correlation to Assess Full-Field 3d Strain Distribution Patterns in Osteoarthritic Cartilage [PhD thesis]. Portsmouth, England: University of Portsmouth; 2024.
2009	Ferreri SL. Anti-Catabolic Role of Ultrasonic Mechanical Perturbation in Prevention of Bone Loss and Turnover in OVX Rat Model: A Combined Empirical, Nanomechanical and Micro-Numerical Simulation Approach [PhD thesis]. Stony Brook, NY: Stony Brook University; August 2009.
2006	Soares Silva LDM. Nanoindentation Study and Quantitative Backscattered Electron Imaging of Human Cortical Bone [Master's thesis]. Vancouver, BC: University of British Columbia; 2006.
2013	Wang Y-K. Multi-Level Micromechanical Modeling of Bone Tissues [PhD thesis]. Los Angeles, CA: Los Angeles, University of California; 2013.
2012	Evdokimenko E. Investigation Into Mechanical Properties of Bone and Its Main Constituents [PhD thesis]. San Diego (UCSD), University of California; 2012.
2005	Oyen ML. Ultrastructural Characterization of Time-Dependent, Inhomogeneous Materials and Tissues [PhD thesis]. Minneapolis, MN: University of Minnesota; June 2005.
2009	Potter RS. Age Effects on the Material and Mechanical Properties of Bone At the Osteocyte Lacuna [Master's thesis]. San Antionio, TX: University of Texas at San Antonio; December 2009.
2011	Islam A. Mechanistic Model of Nanoscratch Test to Determine the in Situ Toughness of Bone [Master's thesis]. San Antionio, TX: University of Texas at San Antonio; May 2011.