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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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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