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TECHNICAL PAPERS: Modeling

A Model for Mechanics of Primary Lymphatic Valves

[+] Author and Article Information
Ernesto Mendoza, Geert W. Schmid-Schönbein

Department of Bioengineering, The Whitaker Institute for Biomedical Engineering, University of California San Diego, La Jolla, CA 92093-0412

J Biomech Eng 125(3), 407-414 (Jun 10, 2003) (8 pages) doi:10.1115/1.1568128 History: Received September 01, 2002; Revised December 01, 2002; Online June 10, 2003
Copyright © 2003 by ASME
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References

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Figures

Grahic Jump Location
Schematic of the cross-section of a junction between two endothelial cell extensions in the wall of an initial lymphatic. The top of the cell represents the lymphatic lumen, the bottom adjacent connective tissue to which the cells are attached by anchoring filaments. The left cell (Cell #1) is assumed to be attached by anchoring filaments in all regions except in the domain from location x=0 until x=L+ΔL, in which it is free to bend into the lumen of the lymphatic. Its deflection into the lumen is w(x). L is the length of the unattached region but without overlap with the extension of cell #2, ΔL is the length of the region with overlap between the two cell extensions. The extension of the right cell (Cell #2) is assumed to be attached everywhere in this diagram by anchoring filaments. p(x) is the fluid pressure through the fluid gap between the two cell extensions with p(L)=pT and p(L+ΔL)=pL.
Grahic Jump Location
Scanning electron micrographs of initial lymphatics in rat cremaster muscle as viewed in inclined sections through the muscle tissue. Panel A: Overview of initial lymphatic channel (LY) located in proximity of arteriolar and venular microvessels (V). The blood vessels and lymphatic channel are sandwiched between several muscle layers (SKM). Note the continuous and highly attenuated endothelium of the partially compressed initial lymphatic. Panel B: Higher magnification views of the inner lumen of initial lymphatics. The specimen was fixed during rest without lymphatic pumping. Note the smooth lymphatic lining without significant openings between lymphatic endothelial cells. Panels C to E: Examples of the inner lumen of initial lymphatics of muscle specimen fixed during active lymph pumping. Note the presence of open gaps in the endothelium (arrows). In some gaps the underlying connective tissue fibers are visible (Panel C). The length of the bar is 30 μm in panel A, 5 μm in panels B to E.
Grahic Jump Location
(A) Top Panel: Cell #1 deflection, w(x), for the case of unattached cell extension L=1 μm and cell overlap ΔL=2 μm and transendothelial fluid pressure ΔP=pT−pL=10 dyn/cm2. (A) Bottom Panel: The fluid pressure drop Δp(x) along the fluid gap from x=L to x=L+ΔL. (B) Relationship between volumetric flowrate Q (equation 8) and the transendothelial pressure drop ΔP=pT−pL. Note the flow rate is equal to zero at negative transendothelial pressure drops, confirming the valve action of the model.
Grahic Jump Location
Cell deflection w(x) for multiple values of the transendothelial pressure drop ΔP (1 dyn/cm2 , 2.5 dyn/cm2 , 5 dyn/cm2 , 10 dyn/cm2 ).
Grahic Jump Location
Cell deflections w(x) for (A) different lengths of the region without overlap L and (B) overlap regions with length ΔL (see Figure 1). The transendothelial fluid pressure ΔP=pT−pL=10 dyn/cm2 is constant in this case.
Grahic Jump Location
The volumetric flow rate Q, normalized by its value Q10, at a transendothelial pressure of 10 dyn/cm2 (7.59 10−15 cm3/sec at ΔL=0.5 μm; 7.51 10−15 cm3/sec at ΔL=1 μm; 7.50 10−15 cm3/sec at ΔL=1.5 μm) as a function of the transendothelial pressure ΔP=pT−pL.
Grahic Jump Location
Schematic diagram of the combined action of primary and secondary lymphatic valves during expansion and compression of a lymphatic channel.

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