A Special Theory of Biphasic Mixtures and Experimental Results for Human Annulus Fibrosus Tested in Confined Compression

[+] Author and Article Information
Stephen M. Klisch

Department of Mechanical Engineering, University of California, Berkeley, CA

Jeffrey C. Lotz

Orthopædic Bioengineering Laboratory, Department of Orthopædic Surgery, University of California, San Francisco, CA 94143

J Biomech Eng 122(2), 180-188 (Nov 30, 1999) (9 pages) doi:10.1115/1.429640 History: Received October 13, 1998; Revised November 30, 1999
Copyright © 2000 by ASME
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Grahic Jump Location
Schematic of experimental design. The specimen is supported between a rigid platen at X3=0, a fixed porous platen at X3=h, and a rigid confining chamber on its periphery. The displacement is applied to the rigid platen. The junction between the rigid platen and the specimen (i.e., X3=0) is chosen as a “stationary” reference plane. Thus, the displacements are zero at X3=0 and are prescribed at X3=h.
Grahic Jump Location
Protocol for obtaining cylindrical axial and radial test specimens from an intact intervertebral disc. A lateral block of the disc was removed and 2-mm-thick axial and radial slices were cut from the block. A cylindrical test specimen was punched from each slice using the internal confining chamber.
Grahic Jump Location
Experimental data measured for the solid stress at X3=h (surface stress) versus time for four consecutive stress-relaxation cycles during test 1A.
Grahic Jump Location
Theoretical curve-fit using Eqs. (19), (23), (25), (26) to the experimental data representing the equilibrium solid stress versus the measured equilibrium stretch λ3 for test 1A. Circles=experimental points, line=theoretical fit. The material constants were α0=0.074 MPa,β=0.658, and Q=0.027 MPa, and the R2 value was 1.000. With Q=0, the R2 value was 1.000 (not shown).
Grahic Jump Location
Optimized numerical solution to Eq. (21) to achieve a best-fit regression to the experimental data measured for the solid stress at X3=h (surface stress) versus time for the first two stress-relaxation cycles for test 1A. Circles=experimental points, line=theoretical fit. The material constants were k0=0.0061 mm4/N-s and M=9.5 and the R2 value was 0.989. With Q=0, the R2 value was 0.991 (not shown).
Grahic Jump Location
Plot of equilibrium aggregate modulus HA0 versus initial water content ϕ0f. A nonlinear power law relationship HA0=0.008(ϕ0f)−13.1 MPa best describes the curve, R2=0.49. This dependence was significant (p<0.001).
Grahic Jump Location
Plot of initial permeability constant k0 versus initial water content ϕ0f. A nonlinear power law relationship k0=0.1156(ϕ0f)15.41 mm4/N-s best describes the curve, R2=0.38. This dependence was significant (p<0.001).



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