Material anisotropy and elasticity of cortical and trabecular bone in the adult mouse femur via AFM indentation

Asgari, Meisam<sup>1</sup>; Abi-Rafeh, Jad<sup>2</sup>; Hendy, Geoffrey N.<sup>3</sup>; Pasini, Damiano<sup>1</sup>

Affiliations

¹Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, Canada H3A 0C3

²Department of Medicine, McGill University, Montreal, QC, Canada H4A 3J1

³Metabolic Disorders and Complications, McGill University Health Centre Research Institute, Departments of Medicine, Physiology, and Human Genetics, McGill University, Montreal, QC, Canada H4A 3J1

Abstract and keywords

This paper investigates the elastic properties of bone tissue in the adult mouse femur through Atomic Force Microscopy (AFM) indentation with the goal of understanding its microstructure and underlying mechanics at the nano length scale. Both trabecular and cortical bone types are studied. In particular, we examined the elasticity of cortical bone and individual trabeculae in the longitudinal and transverse directions of the samples. For cortical bone, the elastic modulus in the longitudinal direction was found to be 10–15% higher than that in the transverse direction; for trabecular bone, this difference was 42%. For the trabeculae, this value was found to be in a lower range (0.92 ± 0.22 GPa). As per the transverse elastic modulus, an average of 1.58 ± 0.36 GPa was measured for cortical bone, and 0.55 ± 0.21 GPa for trabecular bone. The anisotropy ratio was within the range of 1.2–1.5 for cortical bone and 1.7–2 for trabecular bone. While the elastic modulus of cortical bone varied along the length of the femur with up to 30% variation, no significant differences were observed within each transverse section. The effect of indentation frequency (1–500 Hz) on the longitudinal elastic moduli was also investigated for cortical and trabecular bone, with results showing a correlation between indentation frequency and elastic modulus.

Statement of significance: This study examines the adult mouse femur with a twofold aim: to investigate the anisotropy and inhomogeneity of cortical and trabecular bone tissues and to elucidate their elastic behavior at the nanometer length scale. The elastic moduli of cortical bone and individual trabecula are measured in the longitudinal and transverse cross-sections via AFM indentation at selected locations and in specific directions of the adult mouse femur. The results provide insights into the relationship between mechanical properties and structural morphology of cortical and trabecular bone tissue.

Keywords: AFM indentation; Elastic modulus; Cortical bone; Trabecular bone; Bone anisotropy; Bone heterogeneity; Bone viscoelasticity

Links

DOI: 10.1016/j.jmbbm.2019.01.024

PubMed: 30776678

WoS: 000464482900010

History

Received: 2018-09-27

Revised: 2019-01-28

Accepted: 2019-01-30

Online: 2019-01-31

Cited Works (55)

Year	Entry
1987	Lees S. Considerations regarding the structure of the mammalian mineralized osteoid from viewpoint of the generalized packing model. Connect Tissue Res. 1987;16(4):281-303.
1974	Reilly DT, Burstein AH, Frankel VH. The elastic modulus for bone. J Biomech. May 1974;7(3):271-275.
2006	Buehler MJ. Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc Natl Acad Sci USA. August 15, 2006;103(33):12285-12290.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1988	Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.
2000	Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R. Critical evaluation of known bone material properties to realize anisotropic fe-simulation of the proximal femur. J Biomech. October 2000;33(10):1325-1330.
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
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.
2015	Katsamenis OL, Jenkins T, Thurner PJ. Toughness and damage susceptibility in human cortical bone is proportional to mechanical inhomogeneity at the osteonal-level. Bone. July 2015;76:158-168.
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.
2007	Buehler MJ. Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization. Nanotechnology. July 25, 2007;18(9):295102.
2008	Sharir A, Barak MM, Shahar R. Whole bone mechanics and mechanical testing. Vet J. July 2008;177(1):8-17.
1991	Martin RB. Determinants of the mechanical properties of bones. J Biomech. 1991;24(suppl 1):79-88.
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.
2001	Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001;3:307-333.
2003	Ferguson VL, Ayers RA, Bateman TA, Simske SJ. Bone development and age-related bone loss in male C57BL/6J mice. Bone. March 2003;32(3):387-398.
1999	Weiner S, Traub W, Wagner HD. Lamellar bone: structure–function relations. J Struct Biol. June 1999;126(3):241-255.
1998	Weiner S, Wagner HD. The material bone: structure-mechanical function relations. Ann Rev Mater Sci. August 1998;28:271-298.
2003	Hengsberger S, Enstroem J, Peyrin F, Zysset P. How is the indentation modulus of bone tissue related to its macroscopic elastic response? a validation study. J Biomech. October 2003;36(10):1503-1509.
2011	Donnelly E. Methods for assessing bone quality: a review. Clin Orthop Relat Res. August 2011;469:2128-2138.
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.
2014	Reznikov N, Shahar R, Weiner S. Bone hierarchical structure in three dimensions. Acta Biomater. September 2014;10(8):3815-3826.
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.
1999	Rho JY, Zioupos P, Currey JD, Pharr GM. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone. September 1999;25(3):295-300.
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	Choi K, Goldstein SA. A comparison of the fatigue behavior of human trabecular and cortical bone tissue. J Biomech. 1992;25(12):1371-1381.
2001	Thompson JB, Kindt JH, Drake B, Hansma HG, Morse DE, Hansma PK. Bone indentation recovery time correlates with bond reforming time. Nature. December 13, 2001;414(6865):773-776.
2004	Fratzl P, Gupta HS, Paschalis EP, Roschger P. Structure and mechanical quality of the collagen–mineral nano-composite in bone. J Mater Chem. 2004;14(14):2115-2123.
2007	Beaupied H, Lespessailles E, Benhamou C-L. Evaluation of macrostructural bone biomechanics. Joint Bone Spine. May 2007;74(3):233-239.
1993	Turner CH, Burr DB. Basic biomechanical measurements of bone: a tutorial. Bone. 1993;14(4):595-608.
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.
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.
2015	Reznikov N, Chase H, Brumfeld V, Shahar R, Weiner S. The 3D structure of the collagen fibril network in human trabecular bone: relation to trabecular organization. Bone. February 2015;71:189-195.
2010	Hamed E, Lee Y, Jasiuk I. Multiscale modeling of elastic properties of cortical bone. Acta Mech. August 2010;213(1):131-154.
2005	Schriefer JL, Robling AG, Warden SJ, Fournier AJ, Mason JJ, Turner CH. A comparison of mechanical properties derived from multiple skeletal sites in mice. J Biomech. March 2005;38(3):467-475.
1993	Sasaki N, Nakayama Y, Yoshikawa M, Enyo A. Stress relaxation function of bone and bone collagen. J Biomech. December 1993;26(12):1369-1376.
2001	Eppell SJ, Tong W, Katz JL, Kuhn L, Glimcher MJ. Shape and size of isolated bone mineralites measured using atomic force microscopy. J Orthop Res. November 2001;19(6):1027-1034.
1991	Woo SL-Y, Hollis JM, Adams DJ, Lyon RM, Takai S. Tensile properties of the human femur-anterior cruciate ligament-tibia complex: the effects of specimen age and orientation. Am J Sports Med. 1991;19(3):217-225.
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.
1996	McKee MD, Nanci A. Osteopontin at mineralized tissue interfaces in bone, teeth, and osseointegrated implants: ultrastructural distribution and implications for mineralized tissue formation, turnover, and repair. Microsc Res Tech. February 1996;33(2):141-164.
1993	Katz JL, Meunier A. Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae. J Biomech Eng. November 1993;115(4B):543-548.
2000	Garner E, Lakes R, Lee T, Swan C, Brand R. Viscoelastic dissipation in compact bone: implications for stress-induced fluid flow in bone. J Biomech Eng. April 2000;122(2):166-172.
2007	Olszta MJ, Cheng X, Jee SS, Kumar R, Kim Y-Y, Kaufman MJ, Douglas EP, Gower LB. Bone structure and formation: a new perspective. Mater Sci Eng R Rep. November 28, 2007;58(3-5):77-116.
2017	Schwiedrzik J, Taylor A, Casari D, Wolfram U, Zysset P, Michler J. Nanoscale deformation mechanisms and yield properties of hydrated bone extracellular matrix. Acta Biomater. September 15, 2017;60:302.
2006	Donnelly E, Baker SP, Boskey AL, van der Meulen MC. Effects of surface roughness and maximum load on the mechanical properties of cancellous bone measured by nanoindentation. J Biomed Mater Res. May 2006;A77(2):426-435.
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	Xu J, Rho JY, Mishra SR, Fan Z. Atomic force microscopy and nanoindentation characterization of human lamellar bone prepared by microtome sectioning and mechanical polishing technique. J Biomed Mater Res. December 1, 2003;A67(3):719-726.
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.
2001	Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001.
2005	Hansma PK, Fantner GE, Kindt JH, Thurner PJ, Schitter G, Turner PJ, Udwin SF, Finch MM. Sacrificial bonds in the interfibrillar matrix of bone. J Musculoskel Neuron Interact. October–December 2005;5(4):313-315.
2004	Hassenkam T, Fantner G, Cutroni J, Weaver J, Morse D, Hansma P. High-resolution AFM imaging of intact and fractured trabecular bone. Bone. July 2004;35(1):4-10.
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.
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.

Cited By (2)

Year	Entry
2020	Chen X, Hughes R, Mullin N, Hawkins RJ, Holen I, Brown NJ, Hobbs JK. Mechanical heterogeneity in the bone microenvironment as characterized by atomic force microscopy. Biophys J. August 4, 2020;119(3):502-513.
2019	Nobakhti S. Multiscale Characteristics of Bone Toughness [PhD thesis]. Northeastern University; July 2019.