Polymer Dynamics as a Mechanistic Model for the Flow-Independent Viscoelasticity of Cartilage

[+] Author and Article Information
D. P. Fyhrie

Bone and Joint Center, Department of Orthopaedic Surgery, Henry Ford Health System, Detroit, MI 48202

J. R. Barone

USDA/ARS/ANRI/EQL, Bldg. 012, Rm. 1-3, BARC-West, 10300 Baltimore Ave., Beltsville, MD 20705

J Biomech Eng 125(5), 578-584 (Oct 09, 2003) (7 pages) doi:10.1115/1.1610019 History: Received February 05, 2002; Revised May 12, 2003; Online October 09, 2003
Copyright © 2003 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 in compression—Theory and Experiments,” J. Biomech. Eng., 102, pp. 73–84.
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.
Mak,  A. F., 1986, “The apparent viscoelastic behavior of articular cartilage—The Contributions From the Intrinsic Matrix Viscoelasticity and Interstitial Fluid Flows,” J. Biomech. Eng., 108, pp. 123–130.
DiSilvestro,  M. R., Zhu,  Q., Wong,  M., Jurvelin,  J. S., and Suh,  J. K., 2001, “Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: I—Simultaneous Prediction of Reaction Force and Lateral Displacement,” J. Biomech. Eng., 123, pp. 191–197.
DiSilvestro,  M. R., Zhu,  Q., and Suh,  J. K., 2001, “Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: II—Effect of Variable Strain Rates,” J. Biomech. Eng., 123, pp. 198–200.
Lai,  W. M., Hou,  I. S., and Mow,  V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” J. Biomech. Eng., 113, pp. 245–258.
Huang,  C. Y., Mow,  V. C., and Ateshian,  G. A., 2001, “The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage,” J. Biomech. Eng., 123, pp. 410–417.
Buckwalter,  J. A., 1998, “Articular Cartilage: Injuries and Potential for Healing,” J. Orthop. Sports Phys. Ther., 28, pp. 192–202.
Buckwalter,  J. A., and Mankin,  H. J., 1998, “Articular Cartilage Repair and Transplantation,” Arthritis Rheum., 41, pp. 1331–1342.
Buckwalter,  J. A., and Mankin,  H. J., 1998, “Articular Cartilage: Degeneration and Osteoarthritis, Repair, Regeneration, and Transplantation,” Instr Course Lect, 47, pp. 487–504.
Buckwalter,  J. A., and Mankin,  H. J., 1998, “Articular Cartilage: Tissue Design and Chondrocyte-Matrix Interactions,” Instr Course Lect, 47, pp. 477–486.
Harper,  G. S., Comper,  W. D., and Preston,  B. N., 1984, “Dissipative Structures in Proteoglycan Solutions,” J. Biol. Chem., 259, pp. 10582–10589.
Comper,  W. D., Williams,  R. P., and Zamparo,  O., 1990, “Water Transport in Extracellular Matrices,” Connect. Tissue Res., 25, pp. 89–102.
Buschmann,  M. D., and Grodzinsky,  A. J., 1995, “A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics,” J. Biomech. Eng., 117, pp. 179–192.
Garcia,  A. M., Frank,  E. H., Grimshaw,  P. E., and Grodzinsky,  A. J., 1996, “Contributions of Fluid Convection and Electrical Migration to Transport in Cartilage: Relevance to Loading,” Arch. Biochem. Biophys., 333, pp. 317–325.
Brown,  T. D., and Singerman,  R. J., 1986, “Experimental Determination of the Linear Biphasic Constitutive Coefficients of Human Fetal Proximal Femoral Chondroepiphysis,” J. Biomech., 19, pp. 597–605.
DiSilvestro,  M. R., and Suh,  J. K., 2001, “A Cross-Validation of the Biphasic Poroviscoelastic Model of Articular Cartilage in Unconfined Compression, Indentation, and Confined Compression,” J. Biomech., 34, pp. 519–525.
de Gennes, P. G., 1984, “Scaling Concepts in Polymer Physics,” Cornell University Press.
de Gennes, P. G., 1990, Introduction to Polymer Dynamics, Cambridge University Press, Cambridge, MA.
de Gennes, P. G. 1997, Soft Interfaces: The 1994 Dirac Memorial Lecture, Cambridge University Press, New York, NY.
Doi, M., and Edwards, S. F., 1986, “The Theory of Polymer Dynamics,” Clarendon Press, Oxford.
Edwards,  S. F., 1992, “The Edwards Model,” International Journal of Modern Physics, B, Condensed Matter Physics, Statistical Physics, Applied Physics, 6, pp. 1563–1594.
Grosberg, A. I., Khokhlov, A. R., and Grosberg, A. I., 1994, The Statistical Physics of Macromolecules, Springer-Verlag, Heidelberg.
Grosberg, A. Y., and Khokhlov, A. R., 1997, Giant Molecules, Academic Press, San Diego, CA.
Neville, A. C., 1993, Biology of Fibrous Composites: Development Beyond the Cell Membrane, Cambridge University Press, Cambridge.
Einstein, A., 1956, Investigations on the Theory of the Brownian Movement, Dover Publications, New York, NY.
Ferry, J. D., 1980, Viscoelastic Properties of Polymers, John Wiley & Sons, Inc.
Bird, R. B., Armstrong, R. C., and Hassager, O., 1977, Dynamics of Polymeric Liquids, John Wiley & Sons, Inc.
Soltz,  M. A., and Ateshian,  G. A., 1998, “Experimental Verification and Theoretical Prediction of Cartilage Interstitial Fluid Pressurization at an Impermeable Contact Interface in Confined Compression,” J. Biomech., 31, pp. 927–934.
Cussler, E. L., 1997, Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, New York, NY.


Grahic Jump Location
A two-dimensional sketch of a polymer molecule (solid) of length L in a network of obstacles that create a confining tube (dotted lines)
Grahic Jump Location
Discrete relaxation spectrum of the reptation relaxation function with τd=1 s and p<203. The complete relaxation spectrum has an infinite number of small components that converge to (0,0).
Grahic Jump Location
(a) Strain history for data from Huang, et al. and DiSilvestro, et al.; (b) possible stress responses: dashed line is nonsteady state, solid line reaches steady state (note: neither is an equilibrium state); (c) strain rate history for data from Huang, et al. and DiSilvestro, et al.
Grahic Jump Location
Normalized average errors for different amounts of data fit by the polymer reptation relaxation function. One set of cartilage stress relaxation data showed existence of a best-fit time at approximately 0.5 s (minimal average error) and the other had a plateau of accuracy between approximately 2 and 20 s. The results for the latter data set do not rule out the possibility of an unresolved minimum for t<1 s. On the figure, the small numbers next to the curves are representative numbers of data points that were fit. Results from less than 21 data points are not appropriate for testing the usefulness of the fitted model.
Grahic Jump Location
Fit of the polymer reptation relaxation function to the stress relaxation data of 7 for the best-fit time (50 data points, τd=11.02 s,σ0=0.6178 MPa). The reptation function was increasingly poor at representing the data as the fitted time was increased or decreased.
Grahic Jump Location
Fit of the polymer reptation relaxation function to the stress data of 4 for 201 data points (20.1 s of data, τd=99.06 s,σ0=0.0747 MPa). The data were equally well fit for periods of 2 to 20 s, but were increasingly poorly fit for longer times.



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