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TECHNICAL BRIEF

The Asymmetry of Transient Response in Compression Versus Release for Cartilage in Unconfined Compression

[+] Author and Article Information
L. P. Li

Biosyntech Inc., 475 Armand-Frappier Blvd., Park of Science and High Technology, Laval, Canada H7V 4B3

M. D. Buschmann

Institute of Biomedical Engineering, Ecole Polytechnique of Montreal, CanadaDepartment of Chemical Engineering, Ecole Polytechnique of Montreal, Canada

A. Shirazi-Adl

Institute of Biomedical Engineering, Ecole Polytechnique of Montreal, CanadaDepartment of Mechanical Engineering, Ecole Polytechnique of Montreal, Canada

J Biomech Eng 123(5), 519-522 (Apr 17, 2001) (4 pages) doi:10.1115/1.1388295 History: Received August 29, 2000; Revised April 17, 2001
Copyright © 2001 by ASME
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References

Li,  L. P., Soulhat,  J., Buschmann,  M. D., and Shirazi-Adl,  A., 1999, “Nonlinear Analysis of Cartilage in Unconfined Ramp Compression Using a Fibril Reinforced Poroelastic Model,” Clin. Biomech., 14, pp. 673–682.
Li,  L. P., Buschmann,  M. D., and Shirazi-Adl,  A., 2000, “A Fibril Reinforced Nonhomogenous Poroelastic Model for Articular Cartilage: Inhomogeneous Responses in Unconfined Compression,” J. Biomech., 33, pp. 1533–1541.
Soulhat,  J., Buschmann,  M. D., and Shirazi-Adl,  A., 1999, “A Fibril-Network Reinforced Biphasic Model of Cartilage in Unconfined Compression,” ASME J. Biomech. Eng., 121, pp. 340–347.
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,” ASME J. Biomech. Eng., 102, pp. 73–84.
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.
Spilker,  R. L., Suh,  J. K., and Mow,  V. C., 1990, “Effects of Friction on the Unconfined Compressive Response of Articular Cartilage: A Finite Element Analysis,” ASME J. Biomech. Eng. 112, pp. 138–146.
Buschmann,  M. D., Soulhat,  J., Shirazi-Adl,  A., Jurvelin,  J. S., and Hunziker,  E. B., 1998, “Confined Compression of Articular Cartilage: Linearity in Ramp and Sinusoidal Tests and the Importance of Interdigitation and Incomplete Confinement,” J. Biomech., 31, pp. 171–178.
Fortin,  M., Soulhat,  J., Shirazi-Adl,  A., Hunziker,  E. B., and Buschmann,  M. D., 2000, “Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model,” ASME J. Biomech. Eng., 122, pp. 1–6.
Lai,  W. M., and Mow,  V. C., 1980, “Drag Induced Compression of Articular Cartilage During a Permeation Experiment,” Biorheology, 17, pp. 111–123.
Li,  L. P., Shirazi-Adl,  A., and Buschmann,  M. D., 1999, “The Asymmetry of Compression vs. Release for Articular Cartilage in Unconfined Compression Can Be Described by a Nonlinear Poroelastic Model,” Trans. Annu. Meet. — Orthop. Res. Soc., 24, p. 160.

Figures

Grahic Jump Location
Load variations for the test versus model, being normalized by the value at t=0 (with 100 μm compression). The inset shows the sequence of ramp compression/relaxation and release/relaxation steps considered; every ramp is applied in 5 seconds. A 100 μm compression has been previously applied and equilibrium has been reached before t=0. The further compression (or loading) phases i, ii and iii and the release (or unloading) phases a, b, and c are of interest in the present study (solid lines in the inset, shaded in the load-time variation); they have the same reference compression magnitude, i.e., start loading/unloading from 100 μm compression. The load determined by the model always returns to the reference value (fine dotted horizontal line) at the reference compression magnitude, while there is a small downshift for the experimental data (possibly indicating property change with time in a room temperature). The material parameters adopted are: Em=0.26 MPa, vm=0.42,Efε=3000,Ef0=3 MPa, k0=1.5×10−3mm4/Ns,M=0, and the initial void ratio 3.6.
Grahic Jump Location
Radial strains at r=7/15R, showing the effect of the fibril stiffening with its strain. For both cases, Ef=0 when εf<0. When the fibril stiffening is considered, it is the case shown in Fig. 1. When the fibril stiffening is neglected, the constant Ef is taken to be 8 MPa (i.e., Efε=0,Ef0=8) so that the radial strain at t=0(4.24‰) is close to that of the compared case (3.89‰); the permeability k0=2.2×10−3 mm4/Ns, while other parameters are the same as for the compared case. For convenience of comparison, the strains are normalized respectively by the corresponding values at t=0. The markers “×” identify the curve tips of the shorter peaks.
Grahic Jump Location
Pore pressure or compressive axial stress of the nonfibrillar matrix at r=7/15R for the same cases demonstrated in Fig. 2. The variation of the axial stress for the case of no fibril stiffening (not shown) is even smaller than for the case of fibril stiffening. (The sum of the pore pressure and the axial stress makes the total stress.)
Grahic Jump Location
Pore pressures at r=7/15R extracted by the finite and small deformation theories, respectively, when the fibril stiffening with its strain is considered. The material parameters used are the same for both cases, as shown in the caption of Fig. 1. The markers “×” identify the curve tips of the shorter peaks.

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