Minimizing specimen length in elastic testing of end-constrained cancellous bone

wbldb

Lievers, W. B.^1,2; Waldman, S. D.^1,2,3; Pilkey, A. K.^1,2

Minimizing specimen length in elastic testing of end-constrained cancellous bone

J Mech Behav Biomed Mater. January 2010;3(1):22-30

©2009 Elsevier Ltd. All rights reserved.

Affiliations

¹Department of Mechanical and Materials Engineering, Queen’s University, Kingston, Ontario, Canada, K7L 3N6

²Human Mobility Research Centre, Queen’s University, Kingston, Ontario, Canada, K7L 3N6

³Department of Chemical Engineering, Queen’s University, Kingston, Ontario, Canada, K7L 3N6
Abstract

End-constraint is needed when performing tensile and compressive testing of cancellous bone so that frictional and structural end-effects are minimized and the mechanical properties are not underestimated. Since many end-constrained testing techniques are limited to certain sites and species by the large specimen sizes required, reductions in overall specimen length would be advantageous. The following study examines the effect of specimen gauge length and aspect ratio on the elastic tensile testing of cancellous bone from the bovine femoral condyle. Three different nominal gauge lengths (10, 16, 22 mm) were examined at two different diameters (5.1, 10.7 mm) which bound the range typically used for cancellous bone testing. No effect of gauge length or aspect ratio was observed, but evidence of a diameter effect was noted. Three-dimensional finite element method (FEM) models confirmed the experimental observations and demonstrated that an overestimation of modulus begins to occur for specimens shorter than 10 mm.
Links

DOI: 10.1016/j.jmbbm.2009.02.001

PubMed: 19878899

WoS: 000271958100004
History

Received: 2008-03-6

Revised: 2009-02-6

Accepted: 2009-02-24

Online: 2009-03-5

Cited Works (38)

Year	Entry
1992	Lakes RS. Saint-Venant end effects for materials with negative Poisson's ratios. J Appl Mech. 1992;59(4):744-746.
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.
1987	Ashman RB, Corin JD, Turner CH. Elastic properties of cancellous bone: measurement by an ultrasonic technique. J Biomech. 1987;20(10):979-986.
2006	Stoppie N, Pattijn V, Cleynenbreugel T, Wevers M, Vander Sloten J, Ignace N. Structural and radiological parameters for the characterization of jawbone. Clin Oral Implants Res. 2006;17(2):124-133.
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.
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.
1991	Allard RN, Ashman RB. A comparison between cancellous bone compressive moduli determined from surface strain and total specimen deflection. In: Transacation of the 37th Annual Meeting of the Orthopaedic Research Society. March 4-7, 1991; Anaheim, CA.151.
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.
2008	Perilli E, Baleani M, Öhman C, Fognani R, Baruffaldi F, Viceconti M. Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur. J Biomech. 2008;41(2):438-446.
2004	Nazarian A, Müller R. Time-lapsed microstructural imaging of bone failure behavior. J Biomech. 2004;37(1):55-65.
2001	Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001;3:307-333.
2006	Nazarian A, Stauber M, Zurakowski D, Snyder BD, Müller R. The interaction of microstructure and volume fraction in predicting failure in cancellous bone. Bone. December 2006;39(6):1196-1202.
1982	Horgan CO. Saint-Venant end effects in composites. J Compos Mater. 1982;16(5):411-422.
2007	Lievers WB, Lee V, Arsenault SM, Waldman SD, Pilkey AK. Specimen size effect in the volumetric shrinkage of cancellous bone measured at two levels of dehydration. J Biomech. 2007;40(9):1903-1909.
1962	Bates RG. Revised standard values for pH measurements from 0 to 95°c. J Res Natl Bur Stand. 1962;66(2):179-184.
2006	Ün K, Bevill G, Keaveny TM. The effects of side-artifacts on the elastic modulus of trabecular bone. J Biomech. 2006;39(11):1955-1963.
2005	Nazarian A, Stauber M, Müller R. Design and implementation of a novel mechanical testing system for cellular solids. J Biomed Mater Res. 2005;B73(2):400-411.
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.
1989	Linde F, Hvid I. The effect of constraint on the mechanical behaviour of trabecular bone specimens. J Biomech. 1989;22(5):485-490.
1945	Cook M, Larke EC. Resistance of copper and copper alloys to homogeneous deformation in compression. J Inst Metals. 1945;71(12):371-390.
1989	Odgaard A, Hvid I, Linde F. Compressive axial strain distributions in cancellous bone specimens. J Biomech. 1989;22(8-9):829-835.
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.
2001	Banse X, Devogelaer JP, Munting E, Delloye C, Cornu O, Grynpas M. Inhomogeneity of human vertebral cancellous bone: systematic density and structure patterns inside the vertebral body. Bone. 2001;28(5):563-571.
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.
2001	Onck PR, Andrews EW, Gibson LJ. Size effects in ductile cellular solids, I: modeling. Int J Mech Sci. 2001;43(3):681-699.
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.
1999	Borrelli A, Patria MC. Saint-Venant's Principle for a piezoelectric body. SIAM J Appl Math. 1999;59(3):1098-1111.
1988	Harrigan TP, Jasty M, Mann RW, Harris WH. Limitations of the continuum assumption in cancellous bone. J Biomech. 1988;21(4):269-275.
1980	Carter DR, Schwab GH, Spengler DM. Tensile fracture of cancellous bone. Acta Orthop Scand. 1980;51(5):733-741.
2007	Bevill G, Easley SK, Keaveny TM. Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site. J Biomech. 2007;40(15):3381-3388.
1976	Arridge RGC, Folkes MJ. Effect of sample geometry on the measurement of mechanical properties of anisotropic materials. Polymer. 1976;17(6):495-500.
1985	Kaplan SJ, Hayes WC, Stone JL, Beaupré GS. Tensile strength of bovine trabecular bone. J Biomech. 1985;18(9):723-727.
2008	Helgason B, Perilli E, Schileo E, Taddei F, Brynjólfsson S, Viceconti M. Mathematical relationships between bone density and mechanical properties: a literature review. Clin Biomech (Bristol, Avon). 2008;23(2):135-146.
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.
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.
1992	Stephen NG, Wang MZ. Decay rates for the hollow circular cylinder. J Appl Mech. 1992;59(4):747-753.
2001	Andrews EW, Gioux G, Onck P, Gibson LJ. Size effects in ductile cellular solids, II: experimental results. Int J Mech Sci. 2001;43(3):701-713.
1965	Toupin RA. Saint-Venant's principle. Arch Ration Mech Anal. 1965;18(2):83-96.

Cited By (30)

Year	Entry
2018	Bian T, Zhao K, Meng Q, Jiao H, Tang Y, Luo J. Preparation and properties of calcium phosphate cement/small intestinal submucosa composite scaffold mimicking bone components and Haversian microstructure. Mater Lett. February 1, 2018;212:73-77.
2019	Bidhendi AJ, Geitmann A. Methods to quantify primary plant cell wall mechanics. J Exp Bot. 2019;70(14):3615-3648.
2013	Olszewski H, Wojnicz W, Wittbrodt E. Method of skeletal system modelling. Arch Mech Engng. September 2013;60(3):335-346.
2015	Oroszlány Á, Nagy P, Kovács JG. Compressive properties of commercially available PVC foams intended for use as mechanical models for human cancellous bone. Acta Polytech Hung. 2015;12(2):89-101.
2013	Shang-cheng W, Dong-mei W, Fang W, Qiu-gen W, Chun-hui W, Shan-guang C. Tensile and compressive mechanical property of human bone tissue [in Chinese]. Ch J Tissue Eng Res. 2013;17(7):1180-1184.
2013	Wojnicz W, Olszewski H, Wittbrodt E. Chosen aspects of skeletal system modeling: numerical solid and shell models of femur part. In: Pietraszkiewicz W, Górski J, eds. Shell Structures: Theory and Applications. Vol 3. CRC Press; 2013:359-362.
2016	Wojnicz W, Olszewski H, Lipiński K, Wittbrodt E. Numerical model of femur part. In: Awrejcewicz J, ed. Dynamical Systems: Modelling: Łódź, Poland, December 7–10, 2015. Springer International Publishing; 2016:421-435. Springer Proceedings in Mathematics & Statistics; vol 181.
2011	Lomakin J, Huber PA, Eichler C, Arakane Y, Kramer KJ, Beeman RW, Kanost MR, Gehrke SH. Mechanical properties of the beetle elytron, a biological composite material. Biomacromolecules. 2011;12(2):321-335.
2010	Lievers WB, Petryshyn AC, Poljsak AS, Waldman SD, Pilkey AK. Specimen diameter and "side artifacts" in cancellous bone evaluated using end-constrained elastic tension. Bone. August 2010;47(2):371-377.
2020	Silva-Henao JD, Rueda Esteban RJ, Marañon-Leon A, Casas-Rodríguez JP. Post-yield mechanical properties of bovine trabecular bone: relationships with bone volume fraction and strain rate. Eng Fract Mech. June 15, 2020;232:107053.
2013	Horgan CO. End effects in mechanical testing of biomaterials. J Biomech. March 15, 2013;46(5):1040-1041.
2014	Yamada S, Tadano S, Fukuda S. Nanostructure and elastic modulus of single trabecula in bovine cancellous bone. J Biomech. November 7, 2014;47(14):3482-3487.
2018	Enns-Bray WS, Ferguson SJ, Helgason B. Strain rate dependency of bovine trabecular bone under impact loading at sideways fall velocity. J Biomech. June 2018;75:46-52.
2014	Aiyangar AK, Vivanco J, Au AG, Anderson PA, Smith EL, Ploeg H-L. Dependence of anisotropy of human lumbar vertebral trabecular bone on quantitative computed tomography-based apparent density. J Biomech Eng. September 2014;136(9):091003.
2021	Bennison MBL, Pilkey AK, Lievers WB. Misalignment error in cancellous bone apparent elastic modulus depends on bone volume fraction and degree of anisotropy. J Biomech Eng. February 2021;143(2):021005.
2021	Ma Z, Qiang Z, Zeng K, Xiao J, Zhou L, Zu L, Zhao H, Ren L. Prediction of cross section fracture path of cortical bone through nanoindentation array. J Mech Behav Biomed Mater. April 2021;116:104303.
2022	Knowles NK, Kusins J, Columbus MP, Athwal GS, Ferreira LM. Experimental DVC validation of heterogeneous micro finite element models applied to subchondral trabecular bone of the humeral head. J Orthop Res. September 2022;40(9):2039-2047.
2019	Bian T, Zhao K, Meng Q, Tang Y, Jiao H, Luo J. The construction and performance of multi-level hierarchical hydroxyapatite (HA)/collagen composite implant based on biomimetic bone Haversian motif. Mater Des. January 15, 2019;162:60-69.
2010	Lievers WB, Poljsak AS, Waldman SD, Pilkey AK. Effects of dehydration-induced structural and material changes on the apparent modulus of cancellous bone. Med Eng Phys. 2010;32(8):921-925.
2010	Cristofolini L, Schileo E, Juszczyk M, Taddei F, Martelli S, Viceconti M. Mechanical testing of bones: the positive synergy of finite–element models and in vitro experiments. Philos Trans R Soc A-Math Phys Eng Sci. June 13, 2010;368(1920):2725-2763.
2011	Guérard S, Chevalier Y, Moreschi H, Defontaine M, Callé S, Mitton D. Young’s modulus repeatability assessment using cycling compression loading on cancellous bone. Proc Inst Mech Eng Part H-J Eng Med. November 2011;225(11):1113-1117.
2013	Vivanco J, Garcia S, Ploeg HL, Alvarez G, Cullen D, Smith EL. Apparent elastic modulus of ex vivo trabecular bovine bone increases with dynamic loading. Proc Inst Mech Eng Part H-J Eng Med. August 2013;227(8):904-912.
2020	Bennison MBL. The Role of Cancellous Bone Architecture in Misalignment and Side Effect Errors [Master's thesis]. Sudbury, ON: Laurentian University; 2020.
2009	Lievers WB. Effects of Geometric and Material Property Changes on the Apparent Elastic Properties of Cancellous Bone [PhD thesis]. Queen's University; April 2009.
2010	Engbretson AC. Determining the Modulus of Intact Bovine Vertebral Cancellous Bone Tissue: Development and Validation of a Protocol [Master's thesis]. Queen's University; August 25, 2010.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Southern Methodist University; August 3, 2011.
2020	Amromanoh OA. An Experimental Study of the Effect of Bone Inorganic-Organic Composition on the Mechanical Properties [Master's thesis]. Winnipeg, MB: University of Manitoba; April 2020.
2019	Knowles NK. Improving Material Mapping in Glenohumeral Finite Element Models: A Multi-Level Evaluation [PhD thesis]. University of Western Ontario; 2019.
2011	Aiyangar AK. Physical and Computational Modeling of Subsidence of Anterior Interbody Fusion Devices [PhD thesis]. University of Wisconsin – Madison; 2011.
2011	Vivanco Morales JF. Investigation of Fabrication and Environmental Effects on Bioceramic Bone Scaffolds [PhD thesis]. University of Wisconsin – Madison; 2011.