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TECHNICAL PAPERS: Fluids/Heat/Transport

An Electrodiffusion-Filtration Model for Effects of Endothelial Surface Glycocalyx on Microvessel Permeability to Macromolecules

[+] Author and Article Information
Bin Chen, Bingmei M. Fu

Department of Mechanical Engineering, University of Nevada–Las Vegas, Las Vegas, NV 89154

J Biomech Eng 126(5), 614-624 (Nov 23, 2004) (11 pages) doi:10.1115/1.1800571 History: Received March 12, 2004; Revised May 03, 2004; Online November 23, 2004
Copyright © 2004 by ASME
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References

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Figures

Grahic Jump Location
(a) Plane view of junction-orifice-fiber entrance layer model of interendothelial cleft. At the entrance of cleft on the luminal side, the surface glycocalyx is represented by a periodic square array of cylindrical fibers. a, radius of these fibers; Δ, gap spacing between fibers; Lf, thickness of the glycocalyx layer. The charge density in the glycocalyx layer is Cm.Ci(x) and Ci(x) (x=−Lf,0) are the concentrations of charged ions/molecules from the fiber side and from the lumen/cleft side, respectively, at the interfaces between the fiber layer and the lumen/cleft entrance. E(x) and E(x) (x=−Lf,0) are the corresponding electrical potentials at the interfaces. Junction strands with periodic openings lie parallel to the luminal front. 2D, spacing between adjacent breaks in a junction strand; L1 and L3, distances between the junction strand and luminal and tissue fronts, respectively; Ljun, junction strand thickness. (b) Three-dimensional sketch of single periodic unit of width 2D showing a large orifice of width 2d and height 2B, and a narrow slit of width 2bs in junction strand (modified from 4).
Grahic Jump Location
(a) Ratio of apparent hydraulic conductivity when the surface glycocalyx layer is negatively charged to that when this layer is neutral, Lp/Lp no charge, as a function of the charge density Cm of the fiber layer. Solid line shows the model prediction when Lf=100 nm and 2B=20 nm under the normal condition. Dotted line is the case when Lf=100 nm and 2B=40 nm for the increased permeability state. (b) Ratio of apparent hydraulic conductivity when the surface glycocalyx layer is negatively charged to that when this layer is absent, Lp/Lp no fiber as a function of the fiber layer thickness Lf when the charge density Cm=0 mEq/l (solid line), Cm=25 mEq/l (dashed line), 50 mEq/l (dotted line), 75 mEq/l (dashed–dotted–dashed line) and 100 mEq/l (dashed–dotted–dotted–dotted–dashed line).
Grahic Jump Location
Apparent permeability of α-lactalbumin as a function of the hydrostatic pressure in the microvessel lumen under various conditions. Symbols are experimental data and lines are model predictions. Squares, triangles, and circles represent the permeability data measured in venular microvessels in frog mesentery when the perfusate was Ringer and frog plasma, Ringer and albumin (BSA), and Ringer alone, respectively (data from 3). The solid line shows the model prediction when the charge of surface glycocalyx layer is present. The dashed line shows the results when the charge is absent. The dotted line is the case when the surface glycocalyx layer is absent. The dashed–dotted–dotted–dotted–dashed line is the case when the fiber layer is removed and the cleft height is increased from 20 to 27 nm. The dashed–dotted–dashed line is the case when the cleft height 2B is increased to 30 nm and the surface glycocalyx layer is partially removed (Lf=20 nm).
Grahic Jump Location
Apparent permeability of albumin as a function of the hydrostatic pressure in the microvessel lumen under various conditions. The lines with symbols are experimental data 16 and the lines without symbols are model predictions. The solid lines with triangles represent the permeability data measured in three individual perfused microvessels when the perfusate was Ringer-BSA (control). The regression line for these three control experiments is plotted as the short dashed line with triangles. The short dashed line without triangles is the model prediction. The solid line without symbols shows the model prediction when the charge on the surface glycocalyx layer is present. When the cleft width 2B is increased to 2.5-fold of its control, the long dashed line is the model prediction for the case of the glycocalyx layer without the charge and the dashed–dotted–dashed line is for the case of with charge.
Grahic Jump Location
Ratio of apparent permeability of charged solutes to diffusive permeability of a neutral solute with the same size (P/Pd neutral) as a function of the hydrostatic pressure in the microvessel lumen. Solid line is for positively charged ribonuclease (+3), dotted line for negatively charged α-lactalbumin (−11) and dashed line for the neutral solute. All solutes have the same radius of 2.01 nm.
Grahic Jump Location
Apparent permeability of α-lactalbumin as a function of the hydrostatic pressure in the microvessel lumen when the perfusate is protein free solution (Ringer-only). Circles are experimental data 3. Lines are model predictions. Six cases with different ultrastructural parameters are considered: 1a) Lf=0, 2D=1000 nm (solid line) and 1b) Lf=20 nm, 2D=780 nm (dotted line); 2a) Lf=0,2d=600 nm (long dashed line) and 2b) Lf=20 nm,2d=1170 nm (short dashed line); 3a) Lf=0,2B=27 nm (dashed–dotted–dotted–dotted–dashed line) and 3b) Lf=20 nm,2B=30 nm (dashed–dotted–dashed line). The hydraulic conductivity Lp of each case is ∼fivefold of that for the control when the perfusate is Ringer-BSA.
Grahic Jump Location
Apparent permeability of solute as a function of the charge density Cm in the glycocalyx at constant hydrostatic pressures of 0 (solid line), 15 (dashed line), and 30 (dashed–dotted–dashed line) cm H2O. (a) α-lactalbumin (radius=2.01 nm, net charge=−11), dotted line is for net charge=−19; (b) albumin (radius=3.5 nm, net charge=−19).

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