Femoral head apparent density distribution predicted from bone stresses

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Fyhrie, D. P.¹; Carter, D. R.^1,2

Femoral head apparent density distribution predicted from bone stresses

J Biomech. 1990;23(1):1-10

©1990 Pergamon Press plc

Affiliations

¹Veterans Administration RR & D Center 640/153, 3801 Miranda Ave. Palo Alto, CA 94304, U.S.A.

²Department of Mechanical Engineering, Stanford University, Stanford CA 94305. U.S.A.
Abstract

A new theory relating bone morphology to applied stress is used to predict the apparent density distribution in the femoral head and neck. Cancellous bone is modeled as a self-optimizing material and cortical bone as a saturated (maximum possible bone density) response to stresses in the bone tissue. Three different approaches are implemented relating bone apparent density to: (1) the von Mises stress, (2) the strain energy density in the mineralized tissue and (3) a defined closed effective stress (spherical stress). An iterative nonlinear three-dimensional finite element model is used to predict the apparent density distribution in the femoral head and neck for each of the three approaches. It is shown that the von Mises stress (an open effective stress) cannot accurately predict bone apparent density. It is shown that strain energy density and the defined closed effective stress can predict apparent density and that they give predictions consistent with the observed density pattern in the femoral head and neck.
Links

DOI: 10.1016/0021-9290(90)90363-8

PubMed: 2307686

WoS: A1990CQ50200001
History

Revised: 1987-02-23

Cited Works (16)

Year	Entry
1976	Cowin SC, Hegedus DH. Bone remodeling, I: theory of adaptive elasticity. J Elast. 1976;6(3):313-326.
1964	Gong JK, Arnold JS, Cohn SH. Composition of trabecular and cortical bone. Anat Rec. 1964;149(3):325-331.
1981	Firoozbakhsh K, Cowin SC. An analytical model of Pauwels’ functional adaptation mechanism in bone. J Biomech Eng. November 1981;103(4):246-252.
1981	Rushfeldt PD, Mann RW, Harris WH. Improved techniques for measuringin vitro the geometry and pressure distribution in the human acetabulum, II: instrumented endoprosthesis measurement of articular surface pressure distribution. J Biomech. 1981;14(5):315-323.
1972	Kummer BKF. Biomechanics of bone: mechanical properties, functional structure, functional adaptation. In: Fung YC, Perrone N, Anliker M, eds. Biomechanics: Its Foundations and Objectives. Symposium on Biomechanics, its Foundations and Objectives; July 29-31, 1970. Englewood Cliff, NJ: Inc., Prentice-Hall International; 1972:237-271.
1986	Fyhrie DP, Carter DR. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 1986;4(3):304-317.
1984	Röhrle H, Scholten R, Sigolotto C, Sollbach W, Kellner H. Joint forces in the human pelvis-leg skeleton during walking. J Biomech. 1984;17(6):409-424.
1983	Brown TD, Shaw DT. In vitro contact stress distributions in the natural human hip. J Biomech. 1983;16(6):373-384.
1984	Hart RT, Davy DT, Heiple KG. A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. J Biomech Eng. November 1984;106(4):342-350.
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.
1981	Huiskes R, Janssen JD, Slooff TJ. A detailed comparison of experimental and theoretical stress-analyses of a human femur. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:211-234.
1981	Cowin SC, Firoozbakhsh K. Bone remodeling of diaphysial surfaces under constant load: theoretical predictions. J Biomech. 1981;14(7):471-484.
1985	Cowin SC, Hart RT, Balser JR, Kohn DH. Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients. J Biomech. 1985;18(9):665-684.
1980	Brown TD, Ferguson AB Jr. Mechanical property distributions in the cancellous bone of the human proximal femur. Acta Orthop Scand. 1980;51(1):429-437.
1987	Carter DR, Fyhrie DP, Whalen RT. Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. J Biomech. 1987;20(8):785-794.
1981	Roesler H. Some historical remarks on the theory of cancellous bone structure (Wolff's Law). In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:27-42.

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1991	Weinans HH. Mechanically Induced Bone Adaptations Around Orthopaedic Implants [PhD thesis]. Nijmegen, The Netherlands: Katholieke Universiteit te Nijmegen; 1991.
2001	Keaveny TM. Strength of trabecular bone. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:16-1–16-42.
1990	Goldstein SA, Hollister SJ, Kuhn JL, Kikuchi N. The mechanical and remodeling properties of trabecular bone. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:61-81.
1996	Biewener AA, Fazzalari NL, Konieczynski DD, Baudinette RV. Adaptive changes in trabecular architecture in relation to functional strain patterns and disuse. Bone. July 1996;19(1):1-8.
1998	Fazzalari NL, Forwood MR, Manthey BA, Smith K, Kolesik P. Three-dimensional confocal images of microdamage in cancellous bone. Bone. October 1998;23(4):373-378.
1991	Carter DR, Wong M, Orr TE. Musculoskeletal ontogeny, phylogeny, and functional adaptation. J Biomech. 1991;24(suppl 1):3-16.
1991	Goldstein SA, Matthews LS, Kuhn JL, Hollister SJ. Trabecular bone remodeling: an experimental model. J Biomech. 1991;24(suppl 1):135-150.
1992	Weinans H, Huiskes R, Grootenboer HJ. The behavior of adaptive bone-remodeling simulation models. J Biomech. December 1992;25(12):1425-1441.
1997	Turner CH, Annet V, Pidaparti RMV. A uniform strain criterion for trabecular bone adaptation: do continuum-level strain gradients drive adaptation? J Biomech. June 1997;30(6):555-563.
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1993	Weinans H, Huiskes R, Van Rietbergen B, Sumner DR, Turner TM, Galante JO. Adaptive bone remodeling around bonded noncemented total hip arthroplasty: a comparison between animal experiments and computer simulation. J Orthop Res. July 1993;11(4):500-513.
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.
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