Connectivity and the elastic properties of cancellous bone

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Kabel, J.¹; Odgaard, A.¹; van Rietbergen, B.²; Huiskes, R.²

Connectivity and the elastic properties of cancellous bone

Bone. 1999;24(2):115-120

Affiliations

¹Orthopaedic Research Laboratory, Department of Orthopaedic Surgery, Aarhus University Hospital, Aarhus, Denmark

²Orthopaedic Research Laboratory, Institute of Orthopaedics, University of Nijmegen, Nijmegen, The Netherlands
Abstract

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14–91 years and a wide range of trabecular architecture was found. Each specimen was three-dimensionally reconstructed with a voxel size of either 20 or 25 μm. Using the detailed three-dimensional reconstructions as input for microstructural finite-element models, the complete elastic properties of the trabecular architecture were obtained and maximum and mean stiffness could be calculated. Volume fraction and true three-dimensional architectural measurements of connectivity density and surface density were determined. Connectivity density was determined in an unbiased manner by the Euler number, which is a topological property. Using multiple regression analysis it was found that volume fraction explained by far the greatest part (84%–94%) of the variation in both mean and maximum stiffness. When connectivity density and surface density were included, the correlations increased marginally to 89%–95%. Noticeably negative regression coefficients were found for connectivity density. The results suggest that, in normal cancellous bone, the connectivity density has very limited value for assessment of elastic properties by morphological variables, but if a relation exists then stiffness decreases with increasing connectivity.
Links

DOI: 10.1016/S8756-3282(98)00164-1

PubMed: 9951779

WoS: 000078231800007
History

Received: 1998-03-26

Revised: 1998-10-2

Accepted: 1998-10-23

Online: 1999-01-21

Cited Works (32)

Year	Entry
1986	Garrahan NJ, Mellish RWE, Compston JE. A new method for the two-dimensional analysis of bone structure in human iliac crest biopsies. J Microsc (Oxford). June 1986;142(3):341-349.
1990	Hodgskinson R, Currey JD. Effects of structural variation on Young's modulus of non-human cancellous bone. Proc Inst Mech Eng Part H-J Eng Med. 1990;204(1):43-52.
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.
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	Kleerekoper M, Villanueva AR, Stanciu J, Rao DS, Parfitt AM. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tiss Int. 1985;37(6):594-597.
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.
1994	Compston JE. Connectivity of cancellous bone: assessment and mechanical implications. Bone. September–October 1994;15(5):463-466.
1993	Gundersen HJG, Boyce RW, Nyengaard JR, Odgaard A. The connEulor: unbiased estimation of connectivity using physical disectors under projection. Bone. May–June 1993;14(3):217-222.
1996	Ford CM, Keaveny TM, Hayes WC. The effect of impact direction on the structural capacity of the proximal femur during falls. J Bone Miner Res. March 1996;11(3):377-383.
1987	Mosekilde L, Mosekilde L, Danielsen CC. Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone. 1987;8(2):79-85.
1992	Hahn M, Vogel M, Pompesius-Kempa M, Delling G. Trabecular bone pattern factor: a new parameter for simple quantification of bone microarchitecture. Bone. 1992;13(4):327-330.
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.
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.
1995	Boyce RW, Ebert DC, Youngs TA, Paddock CL, Mosekilde L, Stevens ML, Gundersen HJG. Unbiased estimation of vertebral trabecular connectivity in calcium-restricted ovariectomized minipigs. Bone. June 1995;16(6):637-642.
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.
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.
1995	Kinney JH, Lane NE, Haupt DL. In vivo, three‐dimensional microscopy of trabecular bone. J Bone Miner Res. February 1995;10(2):264-270.
1987	Parfitt AM. Trabecular bone architecture in the pathogenesis and prevention of fracture. Am J Med. January 26, 1987;82(suppl 1B):68-72.
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.
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.
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.
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.
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.
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.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1994	Odgaard A, Andersen K, Ullerup R, Frich LH, Melsen F. Three-dimensional reconstruction of entire vertebral bodies. Bone. May–June 1994;15(3):335-342.
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.
1993	Recker RR. Architecture and vertebral fracture. Calcif Tiss Int. 1993;53(suppl 1):S139-S142.
1969	Currey JD. The mechanical consequences of variation in the mineral content of bone. J Biomech. March 1969;2(1):1-11.
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.

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Year	Entry
2019	Colabella L, Cisilino AP, Fachinotti V, Kowalczyk P. Multiscale design of elastic solids with biomimetic cancellous bone cellular microstructures. Struct Multidiscip Optim. August 2019;60(2):639-661.
2001	van Rietbergen B, Huiskes R. Elastic constants of cancellous bone. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:15-1–15-24.
2012	Nikodem A. Correlations between structural and mechanical properties of human trabecular femur bone. Acta Bioeng Biomech. 2012;14(2):37-46.
2002	Banse X. When density fails to predict bone strength. Acta Orthop Scand. 2002;73(2)(suppl 303):2-57.
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.
2000	Day JS, Ding M, Odgaard A, Sumner DR, Hvid I, Weinans H. Parallel plate model for trabecular bone exhibits volume fraction-dependent bias. Bone. November 2000;27(5):715-720.
2001	Tanck E, Homminga J, van Lenthe GH, Huiskes R. Increase in bone volume fraction precedes architectural adaptation in growing bone. Bone. June 2001;28(6):650-654.
2002	Thomsen JS, Ebbesen EN, Mosekilde L. Predicting human vertebral bone strength by vertebral static histomorphometry. Bone. March 2002;30(3):502-508.
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.
2002	Pothuaud L, Van Rietbergen B, Mosekilde L, Beuf O, Levitz P, Benhamou CL, Majumdar S. Combination of topological parameters and bone volume fraction better predicts the mechanical properties of trabecular bone. J Biomech. August 2002;35(8):1091-1099.
2003	Zysset PK. A review of morphology–elasticity relationships in human trabecular bone: theories and experiments. J Biomech. October 2003;36(10):1469-1485.
2008	Harrison NM, McDonnell PF, O’Mahoney DC, Kennedy OD, O’Brien FJ, McHugh PE. 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.
2011	Golden KM, Murphy NB, Cherkaev E. Spectral analysis and connectivity of porous microstructures in bone. J Biomech. 2011;44(2):337-344.
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.
2012	Hazrati Marangalou J, Ito K, van Rietbergen B. A new approach to determine the accuracy of morphology–elasticity relationships in continuum FE analyses of human proximal femur. J Biomech. November 15, 2012;45(15):2884-2892.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
2002	Ding M, Odgaard A, Danielsen CC, Hvid I. Mutual associations among microstructural, physical and mechanical properties of human cancellous bone. J Bone Joint Surg. August 2002;84B(6):900-907.
2001	Dempster DW, Cosman F, Kurland ES, Zhou H, Nieves J, Woelfert L, Shane E, Plavetić K, Müller R, Bilezikian J, Lindsay R. Effects of daily treatment with parathyroid hormone on bone microarchitecture and turnover in patients with osteoporosis: a paired biopsy study. J Bone Miner Res. October 2001;16(10):1846-1853.
2006	Liu XS, Sajda P, Saha PK, Wehrli FW, Guo XE. Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone. J Bone Miner Res. October 2006;21(10):1608-1617.
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.
2015	Maquer G, Musy SN, Wandel J, Gross T, Zysset PK. Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables. J Bone Miner Res. June 2015;30(6):1000-1008.
2019	Saers JPP, Ryan TM, Stock JT. Trabecular bone structure scales allometrically in the foot of four human groups. J Hum Evol. October 2019;135:102654.
2020	Acciaioli A, Falco L, Balean M. Measurement of apparent mechanical properties of trabecular bone tissue: accuracy and limitation of digital image correlation technique. J Mech Behav Biomed Mater. March 2020;103:103542.
2020	Colabella L, Cisilino A, Fachinotti V, Capiel C, Kowalczyk P. Multiscale design of artificial bones with biomimetic elastic microstructures. J Mech Behav Biomed Mater. August 2020;108:103748.
2002	Ding M, Odgaard A, Linde F, Hvid I. Age-related variations in the microstructure of human tibial cancellous bone. J Orthop Res. May 2002;20(3):615-621.
2001	Roschger P, Grabner BM, Rinnerthaler S, Tesch W, Kneissel M, Berzlanovich A, Klaushofer K, Fratzl P. Structural development of the mineralized tissue in the human L4 vertebral body. J Struct Biol. November 2001;136(2):126-136.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
2017	Saers JPP. Ontogeny and Functional Adaptation of Trabecular Bone in the Human Foot [PhD thesis]. Cambridge, UK: University of Cambridge; July 2017.
2003	Bredbenner TL. Damage Modeling of Vertebral Trabecular Bone [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 2003.
2007	Liu XS. High-Resolution Image Based Micro-Mechanical Modeling of Trabecular Bone [PhD thesis]. Columbia University; 2007.
2010	Zhang XH. High Resolution Imaging Based Patient Specific Biomechanical Assessment of Bone Quality [PhD thesis]. Columbia University; 2010.
2007	Cole JH. The Role of Architecture and Tissue Properties in the Structural Integrity of Human Vertebral Cancellous Bone [PhD thesis]. Ithaca, NY: Cornell University; May 2007.
2004	İnceoğlu S. Failure of Pedicle Screw-Bone Interface: Biomechanics of Pedicle Screw Insertion and Pullout [PhD thesis]. Cleveland State University; December 2004.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Erasmus University Rotterdam; 2005.
2002	Follet H. Caractérisation Biomécanique Et Modélisation 3D Par Imagerie X Et IRM Haute Résolution De L’os Spongieux Humain: Evaluation Du Risque Fracturaire [PhD thesis]. Institut national des sciences appliquées de Lyon (INSA Lyon); 2002.
2009	Moesen M. Modeling of the Geometry and Mechanical Behavior of Bone Scaffolds [PhD thesis]. Katholieke Universiteit Leuven; June 2009.
2020	Bennison MBL. The Role of Cancellous Bone Architecture in Misalignment and Side Effect Errors [Master's thesis]. Sudbury, ON: Laurentian University; 2020.
2014	Holub O. Biomechanics of Spinal Metastases [PhD thesis]. University of Leeds; April 2014.
2015	Oftadeh R. Hierarchical Analysis and Multiscale Modelling of Cellular Structures: From Meta Materials to Bone Structure [PhD thesis]. Northeastern University; December 2015.
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.
2001	Tanck EJM. Mechanical Regulation of Bone Development [PhD thesis]. Nijmegen, Netherlands: Katholieke Universiteit Nijmegen; June 2001.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Southern Methodist University; August 3, 2011.
2009	Varga P. Prediction of Distal Radius Fracture Load Using HR-PQCT-Based Finite Element Analysis [PhD thesis]. Vienna University of Technology; December 2009.
2000	Niebur GL. A Computational Investigation of Multiaxial Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2000.
2021	Shaffer SK. High-Speed Exercise and Fetlock Kinematics Affect the Development of Stress-Reactions in Racehorse Proximal Sesamoid Bones [PhD thesis]. Davis, University of California; 2021.
2013	Iori G. Micro-FEM Models Based on Micro-CT Reconstructions for the in Vitro Characterization of the Elastic Properties of Trabecular Bone Tissue [Master's thesis]. University of Bologna; 2013.
2010	Wald MJ. Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2010.
2020	Belda González R. Mechanical and Morphometric Characterization of Cancellous Bone [PhD thesis]. Universität Politècnica de València; March 2020.
2013	Pratt I. In Vivo Imaging of Cortical Porosity by Synchrotron Phase Contrast Micro Computed Tomography [Master's thesis]. University of Saskatchewan; August 2013.
2016	Andronowski JM. Evaluating Differential Nuclear DNA Yield Rates Among Human Bone Tissue Types: A Synchrotron Micro-CT Approach [PhD thesis]. Knoxville, University of Tennessee; May 2016.
2022	Xiao P. Medical Image-Based AI Techniques in Prediction of Trabecular Bone Microarchitecture and Mechanical Properties [PhD thesis]. San Antionio, TX: University of Texas at San Antonio; December 2022.