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TECHNICAL PAPERS: Soft Tissue

Analysis of the Dynamic Permeation Experiment with Implication to Cartilaginous Tissue Engineering

[+] Author and Article Information
W. Y. Gu

Tissue Biomechanics Laboratory, Department of Biomedical Engineering, University of Miami, Coral Gables, FL

D. N. Sun

Department of Biomedical Engineering and Orthopaedic Surgery, School of Medicine, Johns Hopkins University, Baltimore, MD

W. M. Lai

Columbia University, New York, NY

V. C. Mow

Chair, Department of Biomedical Engineering, Columbia University, New York, NY

J Biomech Eng 126(4), 485-491 (Sep 27, 2004) (7 pages) doi:10.1115/1.1785806 History: Received March 17, 2003; Revised December 31, 2003; Online September 27, 2004
Copyright © 2004 by ASME
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References

Figures

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(a) A schematic representation of the permeation problem under consideration. (b) The pressure difference across the tissue. Only one cycle is drawn here. (c) The normalized displacement at the top boundary (z=h) as a function of time for loading frequency (f) of 0.01 Hz. After 4 to 5 cycles, it is seen that a steadily periodic response is achieved. This motion of the solid matrix is due to the drag of fluid permeation.
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(a) The time variation of the normalized water volume flux distribution throughout the tissue during the 8th pressure cycle (f=0.01 Hz). The water volume flux is defined as Jww(vw−vs) and normalized by D+/h (=1 μm/s). Steady downward streaming of fluid is seen near the top of the specimen (z/h>0.6), and oscillatory efflux is seen at the lower platen (z/h=0). (b) The time variation of the normalized water volume flux distribution throughout the tissue during the 8th pressure differential cycle (f=0.01 Hz). At the downstream boundary (z/h=1), the cation efflux may be positive (into the tissue) or negative (out of the tissue). The cation flux distribution is normalized by 10−4 mol/m2 s. (c) The time variation of axial strain distribution throughout the tissue during the 8th pressure differential cycle (f=0.01 Hz). Oscillatory compressive strain is seen at the lower portion of the tissue, while steady compression is seen in the top portion. (d) The variation of cation concentration distribution throughout the tissue during 8th pressure differential cycle (f=0.01 Hz). (e) The electrical potential distributions inside the tissue relative to the bottom of the tissue during 8th cycle (f=0.01 Hz). Note that the electrical potential may change polarity in time and space.
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(a) The length of the boundary layer vs. the frequency. The parameter values are the same as those in the case with typical cartilage parameter values (see Table 1) except the frequency. The length of the strain boundary layer, δ, is defined as the distance from the supporting boundary (x=0) where maximum strain variation occurs to the point where 1/e(e is the basis of natural logarithm) of the maximum strain variation occurs. (b) The ratios of the maximum positive and negative fluxes (at the supporting boundary) in the dynamic case over the corresponding constant fluxes in the static case. The parameter values are the same as those in the standard case except the frequency. Note that all are calculated from data at the 8th cycle.
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(a) The time-averaged water flux over a period of the 8th cycle vs. different DC offsets of the applied pressure. (b) The averaged cation flux in a period vs. different DC offsets of the applied pressure. The frequency is a parameter.
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(a) The potential response on a pair of Ag/AgCl electrodes placed in solutions across the tissue during the 7th and 8th cycles (f=0.01 Hz). The bottom electrode is taken to be ground. Steadily periodic potential responses are observed when the steadily mechanical responses are obtained. (b) The magnitude of the potential response measured by Ag/AgCl electrodes at the 8th cycle vs. tissue FCD with tissue stiffness as a parameter.

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