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TECHNICAL PAPERS

A Microstructural Model of Elastostatic Properties of Articular Cartilage in Confined Compression

[+] Author and Article Information
Predrag Bursać, C. Victoria McGrath, Solomon R. Eisenberg, Dimitrije Stamenović

Department of Biomedical Engineering, Boston University, Boston, MA 02215

J Biomech Eng 122(4), 347-353 (Mar 30, 2000) (7 pages) doi:10.1115/1.1286561 History: Received April 22, 1999; Revised March 30, 2000
Copyright © 2000 by ASME
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References

Maroudas,  A., and Bannon,  C., 1981, “Measurement of Swelling Pressure in Cartilage and Comparison With the Osmotic Pressure of Constituent Proteoglycans,” Biorheology, 18, pp. 619–632.
Grodzinsky,  A. J., 1983, “Electromechanical and Physiological Properties of Connective Tissues,” CRC Crit. Rev. Biomed. Eng., 9, pp. 133–199.
Maroudas,  A., Mizrahi,  J., Haim,  E. B., and Ziv,  I., 1987, “Swelling Pressure in Cartilage,” Adv. Microcirc., 13, pp. 203–212.
Mizrahi, J., Maroudas, A., and Benaim, E., 1990, “Unconfined Compression for Studying Cartilage Creep,” Methods in Cartilage Research, Maroudas, A., and Kuettner, K., eds., Academic Press, London, pp. 293–298.
Khalsa,  P. S., and Eisenberg,  S. R., 1997, “Compressive Behavior of Articular Cartilage Is Not Completely Explained by Proteoglycan Osmotic Pressure,” J. Biomech., 30, pp. 589–594.
Bursać,  P., Obitz,  T. W., Eisenberg,  S. R., and Stamenović,  D., 1999, “Confined and Unconfined Stress Relaxation of Cartilage: Appropriateness of a Transversely Isotropic Analysis,” J. Biomech., 32, pp. 1125–1130.
Farquhar,  T., Dawson,  P. R., and Torzilli,  P. A., 1990, “A Microstructural Model for the Anisotropic Drained Stiffness of Articular Cartilage,” ASME J. Biomech. Eng., 112, pp. 414–425.
Mow,  V. C., Ratcliffe,  A., and Poole,  A. R., 1992, “Cartilage and Diarthrodial Joints as Paradigms for Hierarchical Materials and Structures,” Biomaterials, 13, pp. 67–97.
Schwartz, M. H., 1993, “A Microstructural Model for the Mechanical Response of Articular Cartilage,” Ph.D. Thesis, University of Minnesota, Minneapolis, MN.
Schwartz,  M. H., Leo,  P. H., and Lewis,  J. L., 1994, “A Microstructural Model for the Elastic Response of Articular Cartilage,” J. Biomech., 27, pp. 865–873.
Buschmann,  M. D., and Grodzinsky,  A. J., 1995, “A Molecular Model of Proteoglycans Associated Electrostatic Forces in Cartilage Mechanics,” ASME J. Biomech. Eng., 117, pp. 179–172.
Soulhat,  J., Buschmann,  M. D., and Shirazi-Adl,  A., 1997, “A Nonhomogeneous Composite Model of Articular Cartilage: Development and Validation in Unconfined Compression,” Trans. Annual Meeting of the Orthopaedic Research Society, 22, p. 822.
Soulhat,  J., Buschmann,  M. D., and Shirazi-Adl,  A., 1998, “Non-linear Cartilage Mechanics in Unconfined Compression,” Trans. Annual Meeting of the Orthopaedic Research Society, 23, p. 226.
Abé, H., Hayashi, K., and Sato, M., eds., 1996, Data Book on the Mechanical Properties of Living Cells, Tissues and Organs, Springer, Tokyo, p. 220.
Setton,  L. A., Tohyama,  H., and Mow,  V. C., 1998, “Swelling and Curling Behaviors of Articular Cartilage,” ASME J. Biomech. Eng., 120, pp. 355–361.
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Figures

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Confined compression of the hexagonal model (a) and of the triangular model (b); F is compressing force, w is model width, and h is model height
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Tensile stress–strain curve of pig tendon. Solid circles are measured data points, open circles are extrapolated data points. Redrawn from Abé et al.14.
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Axial (solid line) and lateral (dotted line) stress–strain curves predicted by the triangular model for bath concentration cb of: (a) 0.50, (b) 0.15, (c) 0.05, and (d) 0.01 M NaCl. Note that units for two-dimensional stress are N/m.
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Equilibrium axial (circles) and lateral (triangles) stress–strain curves obtained from confined compression test on calf cartilage for bath concentration cb of: (a) 0.50, (b) 0.15, (c) 0.05 and (d) 0.01 M NaCl. Symbols are data points; lines are linear regressions.
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Aggregate modulus HA, lateral modulus λ, and shear modulus μ as a function of saline bath concentration cb predicted by the triangular model (a) and obtained from experimental data (b). Note that units for two-dimensional elastic moduli are N/m.
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Average fiber tension versus hydration relationship predicted by the triangular model for fiber Young’s modulus Ef of 0.35, 0.62, and 1.66 GPa. Hydration is calculated as (A−Af)/Af, where A is the total area of the network (A=w×h) and Af is the area subtended by the fibers. Results correspond to physiological bath concentration cb=0.15 M NaCl.
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Compressive modulus (dσy/dε) calculated from the triangular model (solid line) and compressive modulus (dp/dε) calculated from the two-dimensional swelling pressure (p) (dashed line) versus compressive strain (ε). dσy/dε includes the contributions of both the collagen network and PGs, whereas dp/dε includes only the contribution of PGs. Results correspond to p calculated for physiological bath concentration cb=0.15 M NaCl.

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