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TECHNICAL PAPERS: Bone/Orthopedic

Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering

[+] Author and Article Information
Robert L. Mauck, Clark T. Hung

Department of Biomedical Engineering

Gerard A. Ateshian

Departments of Mechanical and Biomedical Engineering, Columbia University, New York, NY 10027

J Biomech Eng 125(5), 602-614 (Oct 09, 2003) (13 pages) doi:10.1115/1.1611512 History: Received September 19, 2002; Revised April 21, 2003; Online October 09, 2003
Copyright © 2003 by ASME
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Figures

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Schematic of dynamic unconfined compression of gel construct between frictionless impermeable platens in a bathing solution containing an excess of solute
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Solute concentration, c⁁f(r⁁,t⁁), at select time points for the case Rg=100,Rd=0.1, (a) in the absence of dynamic loading (ε0=0), and (b) when ε0=−0.20 and f⁁=1000
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Average solute concentration normalized by the external bath concentration, c⁁avgf(t⁁)/κfc⁁f*, as a function of time, for various choices of governing parameters (Rg=1,Rd=1,ε0=−0.20 and f⁁=1000;Rg=1,Rd=1,ε0=0;Rg=1,Rd=1,ε0=−0.20 and f⁁=10)
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Average solute concentration normalized by the external bath concentration, c⁁avgf(t⁁)/κfc⁁f*, as a function of time, for various choices of governing parameters (Rg=100,Rd=0.1,ε0=−0.20, and f⁁=0;Rg=100,Rd=0.1,ε0=−0.20, and f⁁=10;Rg=100,Rd=0.1,ε0=−0.20, and f⁁=100)
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For Rd=0.1, 0.5, and 1.0, ε0=−0.20, (a) steady-state value of c⁁avgf(t⁁)/κfc⁁f* (averaged over a loading cycle) as t⁁→∞, and (b) time t⁁e when c⁁avgf(t⁁e)/κfc⁁f*=1−e−1, as a function of Rg and f⁁. In the absence of dynamic loading, c⁁avgf(∞)/κfc⁁f*=1 and t⁁e=0.111 for all values of Rg and Rd.
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For Rd=0.1, Rg=100, and f⁁=100, (a) transient value of c⁁avgf(t⁁)/κfc⁁f* versus t⁁ with increasing strain magnitude (ε0=0 to −0.20) and (b) steady-state values of c⁁avgf(t⁁)/κfc⁁f* (averaged over a loading cycle) as t⁁→∞ and time t⁁e when c⁁avgf(t⁁e)/c⁁f*=1−e−1, as a function of ε0. Dashed line indicates loading-free condition.
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Solute molar flux relative to solid phase, c⁁f(v⁁rf−v⁁rs), at r⁁=1 over the first five loading cycles for the case Rg=100,Rd=1, in the absence of dynamic loading (ε0=0), and when ε0=−0.20,f⁁=1000, and Rd=1 or Rd=0.1. Vertical dashed line at t⁁=0 indicates asymptote to infinity. Inset shows solute molar flux relative to the solid phase at very early times of loading (t⁁<5.0×10−7) under the above conditions.
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(a) Radial displacement u⁁r(r⁁=1,t⁁) and (b) axial load W⁁(t⁁) over time with Rd=0.1,Rg=100, in the absence of dynamic loading (f⁁=0)

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