Ultrasonic wave propagation in human cortical bone, I: theoretical considerations for hexagonal symmetry

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Yoon, Hyo Sub¹; Katz, J. Lawrence¹

Ultrasonic wave propagation in human cortical bone, I: theoretical considerations for hexagonal symmetry

J Biomech. 1976;9(6):407-412

Affiliations

¹Laboratory for Crystallographic Biophysics, Department of Physics, Rensselaer Polytechnic Institute, Troy, N.Y. 12181, U.S.A.
Abstract

From the theory of wave propagation in an anisotropic elastic medium are derived the basic equations relating the five independent second-order elastic stiffness constants (fourth-rank tensor) to the ultrasonic wave speeds in a hexagonal medium, with special emphasis on determining the microtextural symmetry of human cortical bone. In addition, the three pure mode directions of high symmetry in a hexagonal medium are explicitly shown. Finally, expressions relating the ‘technical moduli’ such as Young's modulus, shear modulus and bulk modulus to the elastic compliances are presented for the most general case (triclinic symmetry) and then are specialized for the hexagonal system.
Links

DOI: 10.1016/0021-9290(76)90118-4

PubMed: 932054

WoS: A1976BV06800006
History

Received: 1975-07-25

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Cited By (30)

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1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
2012	Parnell WJ, Vu MB, Grimal Q, Naili S. Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone. Biomech Model Mechanobiol. July 2012;11(6):883-901.
1995	Turner CH, Chandran A, Pidaparti RMV. The anisotropy of osteonal bone and its ultrastructural implications. Bone. July 1995;17(1):85-89.
1984	Katz JL, Yoon HS, Lipson S, Maharidge R, Meunier A, Christel P. The effects of remodeling on the elastic properties of bone. Calcif Tiss Int. 1984;36(suppl 1):S31-S36.
1976	Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, II: measurements of elastic properties and microhardness. J Biomech. 1976;9(7):459-464.
1979	Lakes RS, Katz JL, Sternstein SS. Viscoelastic properties of wet cortical bone, I: torsional and biaxial studies. J Biomech. 1979;12(9):657-678.
1980	Gottesman T, Hashin Z. Analysis of viscoelastic behaviour of bones on the basis of microstructure. J Biomech. 1980;13(2):89-96.
1984	Lipson SF, Katz JL. The relationship between elastic properties and microstructure of bovine cortical bone. J Biomech. 1984;17(4):231-240.
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	Katz JL, Meunier A. The elastic anisotropy of bone. J Biomech. 1987;20(11-12):1063-1070.
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2005	Yoon YJ. Estimates of Bone Elastic Constants At Sequential Hierarchical Levels [PhD thesis]. New York, NY: The City University of New York; 2005.
2011	Donaldson FE. On Incorporating Bone Microstructure in Macro-Finite-Element Models [PhD thesis]. Edinburgh, UK: University of Edinburgh; March 2011.
1988	Lotz JC. Hip Fracture Risk Predictions by X-Ray Computed Tomography [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; August 1988.
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.
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2001	Kim DG. Micromechanical Analysis of Bone At a Bone-Implant Interface [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; April 2001.
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.
1982	Ashman RB. Ultrasonic Determination of the Elastic Properties of Cortical Bone: Techniques and Limitations [PhD thesis]. Tulane University; 1982.
2018	Khor F. Computational Modeling of Hard Tissue Response and Fracture in the Lower Cervical Spine Under Compression Including Age Effects [Master's thesis]. University of Waterloo; 2018.
2013	Faingold A. Bone Elementary Units: Mechanical Properties and Structure [PhD thesis]. Weizmann Institute of Science; February 2013.