Estimation of in Situ Elastic Properties of Biphasic Cartilage Based on a Transversely Isotropic Hypo-Elastic Model

[+] Author and Article Information
J. J. Garcia, N. J. Altiero, R. C. Haut

Department of Materials Science and Mechanics, College of Engineering and Orthopædic Biomechanics Laboratories, College of Osteopathic Medicine, Michigan State University, East Lansing, MI 48824

J Biomech Eng 122(1), 1-8 (Sep 01, 1999) (8 pages) doi:10.1115/1.429622 History: Received August 03, 1998; Revised September 01, 1999
Copyright © 2000 by ASME
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Mow,  V. C., Kuei,  S. C., Lai,  W. M., and Armstrong,  C. G., 1980, “Biphasic creep and stress relaxation of articular cartilage: Theory and experiment,” ASME J. Biomech. Eng., 102, pp. 73–84.
Mow,  V. C., Gibbs,  M. C., Lai,  W. M., Zhu,  W. B., and Athanasiou,  K. A., 1989, “Biphasic indentation of articular cartilage—II. A numerical algorithm and an experimental study,” J. Biomech., 22, pp. 853–861.
Jurvelin,  J., Saamanen,  A., Arokoski,  J., Helminen,  H. J., Kiviranta,  I., and Tammi,  M., 1988, “Biomechanical properties of the canine knee articular cartilage as related to matrix proteoglycans and collagen,” J. Engineering in Medicine, 17, pp. 157–162.
Jurvelin,  J. S., Buschmann,  M. D., and Hunziker,  E. B., 1997, “Optical and mechanical determination of Poisson’s ratio of adult bovine humeral cartilage,” J. Biomech., 30, pp. 235–241.
Cohen,  B., Gardner,  T. R., and Ateshian,  G. A., 1993, “The influence of transverse isotropy on cartilage indentation behavior. A study on the human humeral head,” Trans. Orthop. Res. Soc., 18, p. 185.
Garcia, J. J., Altiero, N. J., and Haut, R. C., 1998a, “A method to determine material properties of biphasic cartilage based on a transversely isotropic model,” Proc. 8th Injury Prevention Through Biomechanics Symposium, Wayne State University, pp. 145–156.
Atkinson,  P. J., and Haut,  R. C., 1995, “Subfracture insult to the human cadaver patellofemoral joint produces occult injury,” J. Orthop. Res., 13, pp. 936–944.
Haut,  R. C., Ide,  T. M., and DeCamp,  C. E., 1995, “Mechanical responses of the rabbit patello-femoral joint to blunt impact,” ASME J. Biomech. Eng., 117, pp. 402–408.
Newberry,  W., Zukosky,  D., and Haut,  R. C., 1997, “Subfracture insult to a knee joint causes alterations in bone and in the functional stiffness of overlying cartilage,” J. Orthop. Res., 15, pp. 450–455.
Athanasiou,  K. A., Rosenwasser,  M. P., Buckwalter,  J. A., Molinin,  T. I., and Mow,  V. C., 1991, “Interspecies comparison of in situ intrinsic mechanical properties of distal femoral cartilage,” J. Orthop. Res., 9, pp. 330–340.
Holmes,  M. H., 1986, “Finite deformation of soft tissue: Analysis of a mixture model in uni-axial compression,” ASME J. Biomech. Eng., 108, pp. 372–381.
Kwan,  M. K., Lai,  W. M., and Mow,  V. C., 1990, “A finite deformation theory for cartilage and other soft hydrated connective tissues—I. Equilibrium results,” J. Biomech., 23, pp. 145–155.
Holmes,  M. H., and Mow,  V. C., 1990, “The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration,” J. Biomech., 23, pp. 1145–1156.
Almeida, E. S., Spilker, R. L., and Holmes M. H., 1995, “A transversely isotropic constitutive law for the solid matrix of articular cartilage,” Adv. in Bioengineering, ASME BED-Vol. 29, pp. 161–162.
Ateshian,  G. A., Warden,  W. H., Kim,  J. J., Grelsamer,  R. P., and Mow,  V. C., 1997, “Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments,” J. Biomech., 30, pp. 1157–1164.
Almeida,  E. S., and Spilker,  R. L., 1997, “Mixed and penalty finite element models for the nonlinear behavior of biphasic soft tissues in finite deformation: Part II—Nonlinear examples,” Comput. Meth. Biomech. Biomed. Eng., 1, pp. 151–170.
Truesdell,  C., 1955, “Hypo-elasticity,” J. Rational Mechanics and Analysis, 4, pp. 83–133.
Noll,  W., 1955, “On the continuity of the solid and fluid states,” J. Rational Mechanics and Analysis, 4, pp. 3–81.
Xiao,  H., Bruhns,  O. T., and Meyers,  A., 1997, “Hypo-elasticity model based upon the logarithmic stress rate,” J. Elast., 47, pp. 51–68.
Bernstein,  B., 1960, “Hypo-elasticity and elasticity,” Arch. Ration. Mech. Anal., 6, pp. 90–104.
Eberhardt,  A. W., Keer,  L. M., Lewis,  J. L., and Vithoontien,  V., 1990, “An analytical model of joint contact,” ASME J. Biomech. Eng., 112, pp. 407–413.
Garcia,  J. J., Altiero,  N. J., and Haut,  R. C., 1998b, “An approach for the stress analysis of transversely isotropic biphasic cartilage under impact load,” ASME J. Biomech. Eng., 120, pp. 608–613.
Hayes,  W. C., Keer,  L. M., Herrman,  G., and Mockros,  L. F., 1972, “A mathematical analysis for indentation tests of articular cartilage,” J. Biomech., 5, pp. 541–555.
MARC Analysis Research Corporation, 1992, “MARC reference library. Volume D: User subroutines and special routines,” Palo Alto, CA.
Kelkar, R., and Ateshian, G. A., 1995, “Contact creep response between a rigid impermeable cylinder and a biphasic cartilage layer using integral transforms,” Proc. 1995 Bioengineering Conference, ASME BED-Vol. 29, pp. 313–314.
Soltz, M. A., and Ateshian, G. A., 1997, “Experimental measurement of cartilage interstitial fluid pressurization under confined compression stress-relaxation,” Adv. in Bioengineering, ASME BED-Vol. 36, pp. 159–160.
Armstrong,  C. G., Lai,  W. M., and Mow,  V. C., 1986, “An analysis of the unconfined compression of articular cartilage,” ASME J. Biomech. Eng., 106, pp. 165–173.
Mow,  V. C., Holmes,  M. H., and Lai,  W. M., 1984, “Fluid transport and mechanical properties of articular cartilage: a review,” J. Biomech., 17, pp. 377–394.
Li, X., 1994, “A criterion to predict damage in articular cartilage due to blunt impact,” Ph.D. Dissertation, Michigan State University.
Anderson,  D. D., Brown,  T. D., Yang,  K. H., and Radin,  E. L., 1990, “A dynamic finite element analysis of impulsive loading of the extension-splinted rabbit knee,” ASME J. Biomech. Eng., 112, pp. 119–128.
Anderson,  D., Brown,  T., and Radin,  E., 1991, “Stress wave effects in a finite element analysis of an impulsively loaded articular joint,” Part H, J. Engineering in Medicine, 205, pp. 27–34.
Suh,  J.-K., and Bai,  S., 1998, “Finite element formulation of a biphasic poroviscoelastic model of articular cartilage,” ASME J. Biomech. Eng., 120, pp. 195–201.


Grahic Jump Location
Stress-stretch curves from the uniaxial solution with a constant coefficient a1=0.8 and different values for the coefficient n (0.020▴, 0.067▪, and 0.113♦): (a) equilibrium, (b) rapid loading. No differences are visible in the rapid loading curves. All curves have the same slope in the undeformed configuration.
Grahic Jump Location
Stress-stretch curves from the uniaxial solution with a constant coefficient n=0.113 and different values for the coefficient a1 (0.8♦, 2.0▪, 3.0♦). All curves have the same slope in the undeformed configuration.
Grahic Jump Location
Experimental force-stretch ratio curves obtained with the spherical indentor of 2 mm diameter showing the responses for rapid loading and equilibrium
Grahic Jump Location
Comparison of stress and lateral displacement between the hypo-elastic and hyperelastic solutions for uniaxial loading
Grahic Jump Location
Experimental values of Poisson’s ratio for cartilage determined by indentation with a flat, nonporous indentor assuming infinitesimal deformation of an isotropic, elastic solid phase
Grahic Jump Location
Uniaxial stress-stretch curves obtained using the average properties from this study for rabbit retro-patellar cartilage. Observe the substantial contribution of water pressure to total stress in the rapid loading response.



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