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TECHNICAL PAPERS

Direction-Dependent Constriction Flow in a Poroelastic Solid: The Intervertebral Disc Valve

[+] Author and Article Information
D. C. Ayotte

AO ASIF Research Institute, Clavadelerstrasse, CH-7270 Davos Platz, SwitzerlandDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

K. Ito, S. M. Perren, S. Tepic

AO ASIF Research Institute, Clavadelerstrasse, CH-7270 Davos Platz, Switzerland

J Biomech Eng 122(6), 587-593 (Aug 10, 2000) (7 pages) doi:10.1115/1.1319658 History: Received October 06, 1999; Revised August 10, 2000
Copyright © 2000 by ASME
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References

Adams,  M. A., McNally,  D. S., and Dolan,  P., 1996, “‘Stress’ Distributions Inside Intervertebral Discs: The Effects of Age and Degeneration,” J. Bone Joint Surg. Br., 78, pp. 965–972.
McNally,  D. S., and Adams,  M., 1992, “Internal Intervertebral Disc Mechanics as Revealed by Stress Profilometry,” Spine, 17, pp. 66–73.
Urban,  J. P. G., and McMullin,  J. F., 1988, “Swelling Pressure of the Lumbar Intervertebral Discs: Influence of Age, Spinal Level, Composition and Degeneration,” Spine, 13, pp. 179–187.
Nachemson,  A., and Elfstroem,  G., 1970, “Intravital Dynamic Pressure Measurements in Lumbar Discs,” Scand. J. Rehabil. Med., S1, pp. 5–40.
Wilke,  H. J., Neef,  P., Caimi,  M., Hoogland,  T., and Claes,  L. E., 1999, “New in Vivo Measurements of Pressures in the Intervertebral Disc in Daily Life,” Spine, 24, pp. 755–762.
Urban,  J. P. G., 1987, “Factors Influencing the Fluid Content of Intervertebral Discs,” Adv. Microcirc., 13, pp. 160–170.
Ayotte,  D., Tepic,  S., and Ito,  K., 1999, “Fluid Flow in the Intervertebral Disc and Its Relation to Disc Degeneration,” J. Bone Joint Surg. Br., 81, p. 67.
Setton,  L. A., Zhu,  W., Weinbaum,  M., Ratcliff,  A., and Mow,  V. C., 1993, “Compressive Properties of the Cartilaginous End-Plate of the Baboon Lumbar Spine.” J. Orthop. Res., 11, pp. 228–239.
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.
Bernick,  S., and Cailliet,  R., 1982, “Vertebral End-Plate Changes With Aging of Human Vertebrae,” Spine, 7, pp. 97–102.
Roberts,  S., Menage,  J., and Eisenstein,  S. M., 1993, “The Cartilage End-Plate and Intervertebral Disc in Scoliosis: Calcification and Other Sequelae,” J. Orthop. Res., 5, pp. 747–757.
Nachemson,  A., Lewin,  T., Maroudas,  A., and Freeman,  M. A. R., 1970, “In Vitro Diffusion of Dye Through the End-Plates and the Annulus Fibrosus of Human Lumbar Inter-Vertebral Discs,” Acta Orthop. Scand., 41, pp. 589–607.
Gibson, L. J., and Ashby, M. F., 1988, Cellular Solids: Structure and Properties, Pergamon Press, New York.
Happel, J., and Brenner, H., 1983, Low Reynolds Number Hydrodynamics, Martinus Nijhoff, Den Hague.
Buschmann,  M., Soulha,  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.
Ayotte, D., Tepic, S., and Ito, K., 2000, “Direction-Dependent Resistance to Flow in the Endplate of the Intervertebral Disc: An Ex Vivo Study,” J. Orthop. Res., submitted.
Cassidy,  J. J., Hiltner,  A., and Baer,  E., 1990, “The Response of the Hierarchical Structure of the Intervertebral Disc to Uniaxial Compression,” J. Mat. Med., 1, pp. 69–80.
Maroudas,  A., Stockwell,  R., Nachemson,  A., and Urban,  J., 1975, “Factors Involved in the Nutrition of the Human Lumbar Intervertebral Disc: Cellularity and Diffusion of Glucose in Vitro,” J. Anat., 120, pp. 113–130.
Urban,  J. P. G., Holm,  S., Maroudas,  A., and Nachemson,  A., 1977, “Nutrition of the Intervertebral Disc, An in Vivo Study of Solute Transport,” Clin. Orthop., 129, pp. 101–114.
Urban,  J., Holm,  S., and Maroudas,  A., 1978, “Diffusion of Small Solutes Into the Intervertebral Disc: An in Vivo Study,” Biorheology, 15, pp. 203–223.
Ogata,  K., and Whiteside,  L. A., 1981, “Nutritional Pathways of the Intervertebral Disc, An Experimental Study Using Hydrogen Washout Technique,” Spine, 6, pp. 211–216.
Maroudas, A., 1980, “Physical Chemistry of Articular Cartilage and the Intervertebral Disc,” The Joints and Synovial Fluid, Sokoloff, L., ed., Academic Press, New York, pp. 240–293.

Figures

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Scanning electron micrographs of the surface of the bony endplate underlying the cartilage endplate in the intervertebral disc: (a) human (surface); (b) sheep (cross section embedded in resin; back-scattered electron imaging technique). The deposit on the surface in (a) is most likely calcified cartilage. The micrograph of (b) shows the channeling of the marrow contact holes (MCH) from the surface of the bony endplate into the trabecular spaces (TB) of the vertebral body.
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Permeability test assembly of the physical model. All dimensions in mm.
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Axisymmetric finite element mesh. The axis of symmetry is on the left side; the mesh was refined toward the constriction hole on the bottom left, the radius of which is made up of four elements corresponding to 4 mm.
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Schematic diagram of the iteration technique used in the paired finite element model. Fd is the element drag force (N), u is the average element velocity (m/s), V is the element volume (m3),viscdyn is the fluid dynamic viscosity (m2/s), and Kinf is the element absolute permeability (m5/kg).
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Material property curves of the physical model foam: (a) the change in absolute permeability (K) with applied strain (legend is applied pressure in bar); (b) the stress–strain curve.
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Physical model constriction flow results showing a scatter plot of the average imbibition resistance (Rim) versus the average exudation resistance (Rex) with increasing applied pressure (from 0.04 bar to 2.5 bar). With increasing pressure Rim only increased modestly, whereas Rex rose considerably.
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Finite element model results for exudation at a typical applied pressure of 0.39 bar (detail at the constriction hole): (a) velocity distribution (m/s) of the “PORO” model; (b) corresponding volumetric strain of the “SOLID” model.
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Finite element model results for imbibition at a typical applied pressure of 0.39 bar (detail at the constriction hole): (a) velocity distribution (m/s) of the “PORO” model; (b) corresponding volumetric strain of the “SOLID” model.
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Validation of the finite element model results against the physical model results: (a) average exudation resistance (Rex) and imbibition resistance (Rim) versus applied pressure (the physical model resistances are presented as a mean value of three measurements taken at each applied pressure); (b) the resistance ratio (Rex/Rim) versus applied pressure.
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Results of the finite element simulation of cartilage endplate calcification at an applied pressure of 0.39 bar. The change in average exudation resistance (Rex), average imbibition resistance (Rim) and the resistance ratio (Rex/Rim) with respect to the constriction hole radius were determined for a constant cross-sectional area of the foam.

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