Identification of the elastic symmetry of bone and other materials

Cowin, S. C.<sup>1</sup>; Mehrabadi, M. M.<sup>2</sup>

Affiliations

¹Department of Biomedical and Mechanical Engineering, Tulane University, New Orleans, LA 70118, U.S.A.

Abstract

A simplified classification scheme for the elastic symmetries of a solid is applied to the identification of the elastic symmetry of a material by three different methods—visual, stereological and numerical algorithm. Each method is illustrated with an application to bone tissues, but the methods apply to all materials.

Links

DOI: 10.1016/0021-9290(89)90001-8

PubMed: 2681216

WoS: A1989CA09200001

History

Received: 1988-08-15

Cited Works (9)

Year	Entry
1984	Harrigan TP, Mann RW. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci. March 1984;19(3):761-767.
1974	Whitehouse WJ. The quantitative morphology of anisotropic trabecular bone. J Microsc (Oxford). July 1974;101:153-168.
1984	Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.
1987	Kuhn JL. Trabecular Bone Structure and Mechanical Properties [PhD thesis]. University of Michigan; 1987.
1986	Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.
1985	Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137-147.
1974	Whitehouse WJ, Dyson ED. Scanning electron microscope studies of trabecular bone in the proximal end of the human femur. J Anat. 1974;118(pt 3):417-444.
1981	Van Buskirk WC, Cowin SC, Ward RN. Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone. J Biomech Eng. May 1981;103(2):67-72.
1987	Katz JL, Meunier A. The elastic anisotropy of bone. J Biomech. 1987;20(11-12):1063-1070.

Cited By (49)

Year	Entry
2007	Cowin SC, Doty SB. Modeling material symmetry. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:139-167.
2007	Cowin SC, Doty SB. Modeling material microstructure. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:225-245.
2007	Cowin SC, Doty SB. Bone tissue. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:341-384.
2007	Cowin SC, Doty SB. Bone tissue adaptation. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:385-424.
1994	Linde F. Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Dan Med Bull. April 1994;41(2):119-138.
1996	van Rietbergen B. Mechanical Behavior and Adaptation of Trabecular Bone in Relation to Bone Morphology [PhD thesis]. Nijmegen, Netherlands: Catholic University of Nijmegen; 1996.
1991	Weinans HH. Mechanically Induced Bone Adaptations Around Orthopaedic Implants [PhD thesis]. Nijmegen, The Netherlands: Katholieke Universiteit te Nijmegen; 1991.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
2020	Janc K, Tarasiuk J, Lipinski P, Bonnet A-S, Wronski S. Assessment of mechanical properties of bone trabeculae as an inverse problem of heterogeneous material modeling. Arch Mech. 2020;72(5):385-414.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
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.
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.
1991	Martin RB. Determinants of the mechanical properties of bones. J Biomech. 1991;24(suppl 1):79-88.
1992	Gross TS, McLeod KJ, Rubin CT. Characterizing bone strain distributions in vivo using three triple rosette strain gages. J Biomech. September 1992;25(9):1081-1087.
1994	Deligianni DD, Maris A, Missirlis YF. Stress relaxation behaviour of trabecular bone specimens. J Biomech. December 1994;27(12):1469-1476.
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.
2010	Tassani S, Öhman C, Baleani M, Baruffaldi F, Viceconti M. Anisotropy and inhomogeneity of the trabecular structure can describe the mechanical strength of osteoarthritic cancellous bone. J Biomech. April 19, 2010;43(6):1160-1166.
2011	Tassani S, Öhman C, Baruffaldi F, Baleani M, Viceconti M. Volume to density relation in adult human bone tissue. J Biomech. 2011;44(1):103-108.
2013	Hazrati Marangalou J, Ito K, Cataldi M, Taddei F, van Rietbergen B. A novel approach to estimate trabecular bone anisotropy using a database approach. J Biomech. September 27, 2013;46(14):2356-2362.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
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.
2000	Nafei A, Kabel J, Odgaard A, Linde F, Hvid I. Properties of growing trabecular ovine bone, II: architectural and mechanical properties. J Bone Joint Surg. August 2000;82B(6):921-927.
1996	Hipp JA, Jansujwicz A, Simmons CA, Snyder BD. Trabecular bone morphology from micro-magnetic resonance imaging. J Bone Miner Res. February 1996;11(2):286-292.
1997	Gross TS, Edwards JL, Mcleod KJ, Rubin CT. Strain gradients correlate with sites of periosteal bone formation. J Bone Miner Res. June 1997;12(6):982-988.
2012	Souzanchi MF, Palacio-Mancheno P, Borisov YA, Cardoso L, Cowin SC. Microarchitecture and bone quality in the human calcaneus: local variations of fabric anisotropy. J Bone Miner Res. December 2012;27(12):2562-2572.
2000	Lucchinetti E, Thomann D, Danuser G. Micromechanical testing of bone trabeculae: potentials and limitations. J Mater Sci. December 2000;35(24):6057-6064.
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.
2008	Natali AN, Carniel EL, Pavan PG. Constitutive modelling of inelastic behaviour of cortical bone. Med Eng Phys. September 2008;30(7):905-912.
1995	Zioupos P, Currey JD, Mirza MS, Barton DC. Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses. Philos Trans R Soc Lond B Biol Sci. March 29, 1995;347(1322):383-396.
2021	Kolesnikov G. Damage function of a quasi-brittle material, damage rate, acceleration and jerk during uniaxial compression: model and application to analysis of trabecular bone tissue destruction. Symmetry. October 2021;13(10):1759.
1998	Majumdar S. A review of magnetic resonance (MR) imaging of trabecular bone micro-architecture: contribution to the prediction of biomechanical properties and fracture prevalence. Technol Health Care. 1998;6(5-6):321-327.
2003	Bredbenner TL. Damage Modeling of Vertebral Trabecular Bone [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 2003.
2005	Yoon YJ. Estimates of Bone Elastic Constants At Sequential Hierarchical Levels [PhD thesis]. New York, NY: The City University of New York; 2005.
2013	Souzanchi MF. The Effect of Microarchitecture and Fabric Anisotropy of Trabecular Bone on Its Mechanical Behavior [PhD thesis]. New York, NY: The City University of New York; 2013.
2011	Donaldson FE. On Incorporating Bone Microstructure in Macro-Finite-Element Models [PhD thesis]. Edinburgh, UK: University of Edinburgh; March 2011.
1994	Zysset P. A Constitutive Law for Trabecular Bone [PhD thesis]. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne; 1994.
2007	Voide R. Functional Phenotyping of Bone: A Hierarchical Assessment of Bone Failure Characteristics [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2007.
2008	Nazarian A. Relative Interaction of Material and Structure in Normal and Pathologic Bone [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2008.
2015	Oftadeh R. Hierarchical Analysis and Multiscale Modelling of Cellular Structures: From Meta Materials to Bone Structure [PhD thesis]. Northeastern University; December 2015.
2005	Espinoza Orias AA. The Relationship Between the Mechanical Anisotropy of Human Cortical Bone Tissue and Its Microstructure [PhD thesis]. University of Notre Dame; April 2005.
2001	Lin W. Development of Quantitative Ultrasound to Determine the Physical Properties of Bone [PhD thesis]. Stony Brook, NY: State University of New York at Stony Brook; May 2001.
1994	Fritton SP. Computational Simulation of Trabecular Bone Adaptation [PhD thesis]. Tulane University; January 1994.
1994	Oden ZM. Computational Prediction of Functional Adaptation in Canine Radii [PhD thesis]. Tulane University; 1994.
2007	MacNeil JAM. Clinical Assessment of Bone Quality [PhD thesis]. Calgary, AB: University of Calgary; June 2007.
2000	Niebur GL. A Computational Investigation of Multiaxial Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: University of California; 2000.
2003	Bayraktar HH. Multiaxial Strength and Micromechanics of Human Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2003.
2003	Fox JC. Biomechanics of the Proximal Femur: Role of Bone Distribution and Architecture [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2003.
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.
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.