Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties

wbldb

Harrison, Noel M.^1,2; McDonnell, Pat F.^1,2; O’Mahoney, Denis C.¹; Kennedy, Oran D.^3,4; O’Brien, Fergal J.^3,4; McHugh, Peter E.^1,2

Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties

J Biomech. August 7, 2008;41(11):2589-2596

©2008 Elsevier Ltd. All rights reserved.

Affiliations

¹National Centre for Biomedical Engineering Science, National University of Ireland, Galway, Ireland

²Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, Ireland

³Department of Anatomy, Royal College of Surgeons in Ireland, Dublin, Ireland

⁴Trinity Centre for Bioengineering, Trinity College, Dublin 2, Ireland
Abstract and keywords

High-resolution voxel-based finite element software, such as FEEBE developed at the NCBES, is widely used for studying trabecular bone at the micro-scale. A new approach to determine heterogeneous bone tissue material properties for computational models was proposed in this study. The specimen-specific range of tissue moduli across strut width was determined from nanoindentation testing. This range was mapped directly using linear interpolation to that specimen's micro-computed tomography (μCT) grey value range as input material properties for finite element analysis. The method was applied to cuboid trabecular bone samples taken from eight, 4-year-old (skeletally mature) ovine L5 vertebrae. Before undergoing experimental uniaxial compression tests, the samples were μCT scanned and 30 μm resolution finite element models were generated. The linear elastic finite element models were compressed to 1% strain. This material property assignment method for computational models accurately reproduced the experimentally determined apparent modulus and concentrations of stress at locations of failure.

Keywords: Trabecular; Cancellous; Voxel; Vertebra; Nanoindentation; Grey values; μCT
Links

DOI: 10.1016/j.jbiomech.2008.05.014

PubMed: 18602110

WoS: 000259129000034
History

Accepted: 2008-05-13

Cited Works (53)

Year	Entry
2001	Homminga J, Huiskes R, Van Rietbergen B, Rüegsegger P, Weinans H. Introduction and evaluation of a gray-value voxel conversion technique. J Biomech. April 2001;34(4):513-517.
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
2005	Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech. 2005;38(4):707-716.
2004	Taddei F, Pancanti A, Viceconti M. An improved method for the automatic mapping of computed tomography numbers onto finite element models. Med Eng Phys. 2004;26(1):61-69.
1988	Cann CE. Quantitative CT for determination of bone mineral density: a review. Radiology. February 1988;166(2):509-522.
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.
1999	Kabel J, Odgaard A, van Rietbergen B, Huiskes R. Connectivity and the elastic properties of cancellous bone. Bone. 1999;24(2):115-120.
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.
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.
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.
2007	van Ruijven LJ, Mulder L, van Eijden TMGJ. Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone. J Biomech. 2007;40(6):1211-1218.
2001	Morgan EF, Yeh OC, Chang WC, Keaveny TM. Nonlinear behavior of trabecular bone at small strains. J Biomech Eng. February 2001;123(1):1-9.
2002	Kopperdahl DL, Morgan EF, Keaveny TM. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. J Orthop Res. July 2002;20(4):801-805.
1998	Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. July 1998;31(7):601-608.
1980	Rohlmann A, Zilch H, Bergmann G, Kölbel R. Material properties of femoral cancellous bone in axial loading, I: time independent properties. Arch Orthop Trauma Surg. September 1980;97(2):95-102.
2000	Vajjhala S, Kraynik AM, Gibson LJ. A cellular solid model for modulus reduction due to resorption of trabeculae in bone. J Biomech Eng. October 2000;122(5):511-515.
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.
1985	Beaupre GS, Hayes WC. Finite element analysis of a three-dimensional open-celled model for trabecular bone. J Biomech Eng. August 1985;107(3):249-256.
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.
1994	Keller TS. Predicting the compressive mechanical behavior of bone. J Biomech. September 1994;27(9):1159-1168.
2001	Pistoia W, van Rietbergen B, Laib A, Rüegsegger P. High-resolution three-dimensional-pqct images can be an adequate basis for in-vivo μfe analysis of bone. J Biomech Eng. October 2001;123(2):176-183.
2003	Ferguson VL, Bushby AJ, Boyde A. Nanomechanical properties and mineral concentration in articular calcified cartilage and subchondral bone. J Anat. August 2003;203(2):191-202.
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.
1989	Linde F, Hvid I. The effect of constraint on the mechanical behaviour of trabecular bone specimens. J Biomech. 1989;22(5):485-490.
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.
2002	Hara T, Tanck E, Homminga J, Huiskes R. The influence of microcomputed tomography threshold variations on the assessment of structural and mechanical trabecular bone properties. Bone. July 2002;31(1):107-109.
1983	Parfitt AM, Mathews CH, Villanueva AR, Kleerekoper M, Frame B, Rao DS. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis: implications for the microanatomic and cellular mechanisms of bone loss. J Clin Invest. October 1983;72(4):1396-1409.
2001	Yeni YN, Fyhrie DP. Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions. J Biomech. December 2001;34(12):1649-1654.
1999	Camacho NP, Rinnerthaler S, Paschalis EP, Mendelsohn R, Boskey AL, Fratzl P. Complementary information on bone ultrastructure from scanning small angle X-ray scattering and Fourier-transform infrared microspectroscopy. Bone. September 1999;25(3):287-293.
1998	Zannoni C, Mantovani R, Viceconti M. Material properties assignment to finite element models of bone structures: a new method. Med Eng Phys. December 1998;20(10):735-740.
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.
1988	Harrigan TP, Jasty M, Mann RW, Harris WH. Limitations of the continuum assumption in cancellous bone. J Biomech. 1988;21(4):269-275.
2002	van Rietbergen B, Majumdar S, Newitt D, MacDonald B. High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment. Clin Biomech (Bristol, Avon). February 2002;17(2):81-88.
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.
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.
1984	Currey JD. Effects of differences in mineralization on the mechanical properties of bone. Philos Trans R Soc Lond B Biol Sci. February 13, 1984;304(1121):509-518.
1998	Guldberg RE, Hollister SJ, Charras GT. The accuracy of digital image-based finite element models. J Biomech Eng. 1998;120(2):289-295.
1990	Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study. J Comput Assist Tomogr. January–February 1990;14(1):107-114.
1999	Niebur GL, Yuen JC, Hsia AC, Keaveny TM. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng. December 1999;121(6):629-635.
2006	Akhtar R, Eichhorn SJ, Mummer PM. Microstructure-based finite element modelling and characterisation of bovine trabecular bone. J Bionic Eng. 2006;3(1):3-9.
1990	Jensen KS, Mosekilde L, Mosekilde L. A model of vertebral trabecular bone architecture and its mechanical properties. Bone. 1990;11(6):417-423.
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	Majumdar S, Kothari M, Augat P, Newitt DC, Link TM, Lin JC, Lang T, Lu Y, Genant HK. High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties. Bone. May 1998;22(5):445-454.
2003	Morgan EF, Bayraktar HH, Keaveny TM. Trabecular bone modulus–density relationships depend on anatomic site. J Biomech. July 2003;36(7):897-904.
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.
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.
1995	Rho JY, Hobatho MC, Ashman RB. Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys. July 1995;17(5):347-355.
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. May 2004;37(5):613-621.
1973	Hounsfield GN. Computerized transverse axial scanning (tomography), I: description of system. Br J Radiol. 1973;46:1016-1022.
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.
1999	Yeh OC, Keaveny TM. Biomechanical effects of intraspecimen variations in trabecular architecture: a three-dimensional finite element study. Bone. August 1999;25(2):223-228.
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.

Cited By (37)

Year	Entry
2019	Cichański A, Nowicki K. Trabecular bone microstructural FEM analysis for out-of plane resolution change. In: Arkusz K, Będziński R, Klekiel T, Piszczatowski S, eds. Biomechanics in Medicine and Biology. Proceedings of the International Conference of the Polish Society of Biomechanics; September 5-7, 2018; Zielona Góra, Poland. Cham: Springer; 2019:210-218. Advances in Intelligent Systems and Computing; vol 831.
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.
2009	Shi X, Wang X, Niebur GL. Effects of loading orientation on the morphology of the predicted yielded regions in trabecular bone. Ann Biomed Eng. 2009;37(2):354-362.
2019	Knowles NK, Ip K, Ferreira LM. The effect of material heterogeneity, element type, and down-sampling on trabecular stiffness in micro finite element models. Ann Biomed Eng. February 2019;47(2):615-623.
2010	Harrison NM, McHugh PE. Comparison of trabecular bone behavior in core and whole bone samples using high-resolution modeling of a vertebral body. Biomech Model Mechanobiol. 2010;9(4):469-480.
2013	Harrison NM, McDonnell P, Mullins L, Wilson N, O’Mahoney D, McHugh PE. Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach. Biomech Model Mechanobiol. April 2013;12(2):225-241.
2010	Shi X, Liu XS, Wang X, Guo XE, Niebur GL. Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone. Bone. May 2010;46(5):1260-1266.
2012	Gross T, Pahr DH, Peyrin F, Zysset PK. Mineral heterogeneity has a minor influence on the apparent elastic properties of human cancellous bone: SRμCT-based finite element study. Comput Methods Biomech Biomed Eng. November 2012;15(11):1137-1144.
2020	Januddi F, Harun MN, Syahrom A, Bakri A, Alkbir MFM. Effect of including periodic boundary condition on the fatigue behaviour of cancellous bone. Int J Integr Eng. 2020;12(5):70-80.
2009	Mc Donnell P, Harrison N, Liebschner MAK, Mc Hugh PE. Simulation of vertebral trabecular bone loss using voxel finite element analysis. J Biomech. 2009;42(16):2789-2796.
2010	Lee T, Garlapati RR, Lam K, Lee PVS, Chung Y-S, Choi JB, Vincent TBC, De SD. Fast tool for evaluation of iliac crest tissue elastic properties using the reduced-basis methods. J Biomech Eng. November 2010;132(12):121009.
2010	Liu XS, Zhang XH, Sekhon KK, Adams MF, McMahon DJ, Bilezikian JP, Shane E, Guo XE. High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone. J Bone Miner Res. April 2010;25(4):746-756.
2012	Kelly N, McGarry JP. Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue. J Mech Behav Biomed Mater. May 2012;9:184-197.
2013	Depalle B, Chapurlat R, Walter-Le-Berre H, Bou-Saïd B, Follet H. Finite element dependence of stress evaluation for human trabecular bone. J Mech Behav Biomed Mater. February 2013;18:200-212.
2019	Knowles NK, Langohr GDG, Faieghi M, Nelson A, Ferreira LM. Development of a validated glenoid trabecular density-modulus relationship. J Mech Behav Biomed Mater. February 2019;90:140-145.
2020	Huo SH, Jiang C, Cui X, Liu GR. A high-fidelity 3D S-FEM stress analysis of a highly heterogeneous swine skull. Med Biol Eng Comput. March 2020;58(3):625-641.
2021	Bennison MBL, Pilkey AK, Lievers WB. Evaluating a theoretical and an empirical model of “side effects” in cancellous bone. Med Eng Phys. August 2021;94:8-15.
2011	Genc KO. The Effects of Altered Gravity Environments on the Mechanobiology of Bone: From Bedrest to Spaceflight [PhD thesis]. Cleveland, OH: Case Western Reserve University; August 2011.
2016	Wang J. Plate-Rod Microstructural Modeling for Accurate and Fast Assessment of Bone Strength [PhD thesis]. Columbia University; 2016.
2017	Yu Y. Contributions of Anisotropic and Heterogeneous Tissue Modulus to Apparent Trabecular Bone Mechanical Properties [PhD thesis]. Columbia University; 2017.
2012	Hamed E. Multiscale Modeling of Elastic Moduli and Strength of Bone [PhD thesis]. University of Illinois at Urbana-Champaign; 2012.
2019	Du J. Mechanical Adaptation of Human Trabecular Bone: Experimental and Computational Study [PhD thesis]. Loughborough University; 2019.
2013	Pino W. Computational Modeling of Trabecular Bone in Lower Extremity Injuries Due to Impact [Master's thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 2013.
2010	Shi X. Effects of Architecture on Microdamage Susceptibility in Trabecular Bone [PhD thesis]. University of Notre Dame; April 2010.
2012	Kelly N. An Experimental and Computational Investigation of the Inelastic Behaviour of Trabecular Bone [PhD thesis]. Galway, Ireland: National University of Ireland Galway; September 2012.
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.
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.
2018	Driver MG. Finite Element Analysis of Cortical Shell Contributions to Apparent Stiffness and the Effect of Vascular Apertures in Rat Vertebrae Under Uniaxial Compression [Master's thesis]. Queen's University; December 2018.
2022	Beloglowka K. Ex Vivo Mechanical Testing and FEA Modelling of Bovine Trabecular Bone [Master's thesis]. Queen's University; September 2022.
2016	Chen Y. Verification and Validation of MicroCT-Based Finite Element Models of Bone Tissue Biomechanics [PhD thesis]. Sheffield, UK: University of Sheffield; July 2016.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Southern Methodist University; August 3, 2011.
2014	Gross T. Development and Application of 3d CT Image-Based Micro and Macro Finite Element Models for Human Bones and Orthopedic Implant Systems [PhD thesis]. Vienna University of Technology; 2014.
2012	Wilkerson LT. Finite Element Analysis of Cancellous Bone [Master's thesis]. University of Kentucky; 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.
2020	Belda González R. Mechanical and Morphometric Characterization of Cancellous Bone [PhD thesis]. Universität Politècnica de València; March 2020.
2024	Benais R. Computational Modeling of Trabecular Bone Indentation and Development of a New Test Method to Perform Unconstrained Load-Induced Subsidence of an Intervertebral Body Fusion Device [Master's thesis]. University of Waterloo; 2024.
2019	Knowles NK. Improving Material Mapping in Glenohumeral Finite Element Models: A Multi-Level Evaluation [PhD thesis]. University of Western Ontario; 2019.