Skip to main content Accessibility help
Hostname: page-component-55597f9d44-mzfmx Total loading time: 0.69 Render date: 2022-08-09T23:29:55.040Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

Published online by Cambridge University Press:  25 April 2008

Department of Physics, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
Department of Physics, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
Department of Physics, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan


A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity Lp, defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6 nm radius and 8 nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Adamson, R. H. 1990 Permeability of frog mesenteric capillaries after partial pronase digestion of the endothelial glycocalyx. J. Physiol. 428, 113.CrossRefGoogle ScholarPubMed
Adamson, R. H. & Clough, G. 1992 Plasma proteins modify the endothelial cell glycocalyx of frog mesenteric microvessel. J. Physiol. 445, 473486.CrossRefGoogle Scholar
Adamson, R. H. & Michel, C. C. 1993 Pathways through the intercellular clefts of frog mesenteric capillaries. J. Physiol. 466, 303327.Google ScholarPubMed
Adamson, R. H., Lenz, J. F., Zhang, X., Adamson, G. N., Weinbaum, S. & Curry, F. E. 2004 Oncotic pressures opposing filtration across non-fenestrated rat microvessles. J. Physiol. 557, 889907.CrossRefGoogle Scholar
Babuska, I. & Suri, M. 1994 The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev. 36, 578632.CrossRefGoogle Scholar
van den Berg, B. M., Vink, H. & Spaan, J. A. E. 2003 The endothelial glycocalyx protects against myocardial edema. Circ. Res. 92, 592594.CrossRefGoogle ScholarPubMed
van den Berg, B. M., Nieuwdorp, M., Stroes, E. S. G. & Vink, H. 2006 Glycocalyx and endothelial (dys) function: from mice to men. Pharmacol. Rep. 58, Suppl. 7580.Google ScholarPubMed
Boggon, T. J., Murray, J., Chappuis-Flament, S., Wong, E., Gumbiner, B. M. & Shapiro, L. 2002 C-cadherin ectodomain structure and implications for cell adhesion mechanisms. Science 296, 13081313.CrossRefGoogle ScholarPubMed
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid in a dense swarm of particles. Appl. Sci. Res. A 1, 2734.CrossRefGoogle Scholar
Bundgaard, M. 1984 The three-dimensional organization of tight junctions in a capillary endothelium revealed by serial-section electron micrscopy. J. Ultrastruct. Res. 88, 117.CrossRefGoogle Scholar
Curry, F. E. & Michel, C. C. 1980 A fibre matrix model of capillary permeability. Microvasc. Res. 20, 9699.CrossRefGoogle ScholarPubMed
Damiano, E. R. & Stace, T. M. 2002 A mechano-electrochemical model of radial deformation of the capillary glycocalyx. Biophys. J. 82, 11531175.CrossRefGoogle ScholarPubMed
Damiano, E. R., Duling, B. R., Ley, K. & Skalak, T. C. 1996 Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer. J. Fluid Mech. 314, 163189.CrossRefGoogle Scholar
Damiano, E. R., Long, D. S. & Smith, M. L. 2004 Estimation of viscosity profiles using velocimetry data from parallel flows of linearly viscous fluids. J. Fluid Mech. 512, 119.CrossRefGoogle Scholar
Feng, J. & Weinbaum, S. 2000 Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans. J. Fluid Mech. 422, 281317.CrossRefGoogle Scholar
Feng, J., Ganatos, P. & Weinbaum, S. 1998 Motion of a sphere near planar confining boundaries in a Brinkman medium. J. Fluid Mech. 375, 265296.CrossRefGoogle Scholar
Fu, B. M., Weinbaum, S., Tsay, R. Y. & Curry, F. E. 1994 A junction–orifice–fibre entrance layer model for capillary permeability: application to frog mesenteric capillaries. Trans. ASME J. Biomech. Engng 116, 502513.CrossRefGoogle ScholarPubMed
Han, Y., Weinbaum, S., Spaan, J. A. E. & Vink, H. 2006 Large-deformation analysis of the elastic recoil of fibre layers in a Brinkman medium with application to the endothelial glycocalyx. J. Fluid Mech. 554, 217235.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1973 In Low Reynolds Number Hydrodynamics, 2nd edn, p. 393. Martinus Nijhoff.Google Scholar
Hasimoto, H. 1958 On the flow of a viscous fluid past a thin screen at small Reynolds numbers. J. Phys. Soc. Japan 13, 633639.CrossRefGoogle Scholar
Henry, C. B. S. & Duling, B. R. 1999 Permeation of the luminal capillary glycocalyx is determined by hyaluronan. Am. J. Physiol. 277, H508H514.Google ScholarPubMed
Henry, C. B. S. & Duling, B. R. 2000 TNF-α increases entry of macromolecules into luminal endothelial cell glycocalyx. Am. J. Physiol. 279, H2815H2823.Google ScholarPubMed
Hu, X. & Weinbaum, S. 1999 A new view of Starling's hypothesis at the microstructural level. Microvasc. Res. 58, 281304.CrossRefGoogle ScholarPubMed
Hu, X., Adamson, R. H., Liu, B., Curry, F. E. & Weinbaum, S. 2000 Starling forces that oppose filtration after tissue oncotic pressure is increased. Am. J. Physiol. Heart Circ. Physiol. 279, H1724H1736.CrossRefGoogle ScholarPubMed
Intaglietta, M. & de Plomb, E. P. 1973 Fluid exchange in tunnel and tube capillaries. Microvasc. Res. 6, 153168.CrossRefGoogle ScholarPubMed
Karniadakis, G. E. & Sherwin, S. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.CrossRefGoogle Scholar
Levick, J. R. 1987 Flow through interstitium and other fibrous matrices. Q. J. Exp. Physiol. 72, 409437.CrossRefGoogle ScholarPubMed
Lipowsky, H. 1995 Shear stress in the circulation. In Flow-Dependent Regulation of Vascular Function (ed. Bevan, J. A., Kaley, G. & Rubanyi, G. M.), pp. 2845 Oxford University Press.CrossRefGoogle Scholar
Long, D. S., Smith, M. L., Pries, A. R., Ley, K. & Damiano, E. R. 2004 Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution. Proc. Natl Acad. Sci. 101, 10 06010 065.CrossRefGoogle ScholarPubMed
Luft, J. H. 1966 Fine structure of capillary and endocapillary layer as revealed by ruthenium red. Fed. Proc. 25, 17731783.Google Scholar
Mason, J. C., Curry, F. E. & Michel, C. C. 1977 The effect of proteins on the filtration coefficient of individually perfused frog mesenteric capillaries. Microvasc. Res. 13, 185204.CrossRefGoogle Scholar
Michel, C. C. 1997 Starling: the formulation of his hypothesis of microvascular fluid exchange and its significance after 100 years. Exp. Physiol. 82, 130.CrossRefGoogle ScholarPubMed
Michel, C. C. & Curry, F. E. 1999 Microvascular permeability. Physiol. Rev. 79, 703761.CrossRefGoogle ScholarPubMed
Pahakis, M. Y., Kosky, J. R., Dull, R. O. & Tarbell, J. M. 2007 The role of endothelial glycocalyx components in mechanotransduction of fluid shear stress. Biochem. Biophys. Res. Commun. 355, 228233.CrossRefGoogle ScholarPubMed
Phillips, C. G., Parker, K. H. & Wang, W. 1994 A model for flow through discontinuities in the tight junction of the endothelial intercellular cleft. Bull. Math. Biol. 56, 723741.CrossRefGoogle ScholarPubMed
Pries, A. R., Secomb, T. W. & Gaehtgens, P. 2000 The endothelial surface layer. Pflugers Arch–Eur. J. Physiol. 440, 653666.CrossRefGoogle ScholarPubMed
Priezjev, N. V. & Troian, S. M. 2006 Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions. J. Fluid Mech. 554, 2546.CrossRefGoogle Scholar
Sangani, A. S. & Acrivos, A. 1982 Slow flow past periodic arrays of cylinders with application to heat transfer. Intl J. Multiphase Flow 8, 193206.CrossRefGoogle Scholar
Schulze, C. & Firth, J. A. 1992 The interendothelial junction in myocardial capillaries: evidence for the existence of regularly spaced, cleft-spanning structures. J. Cell Sci. 101, 647655.Google ScholarPubMed
Shapiro, L., Fannon, A. M., Kwong, P. D., Thompson, A., Lehmann, M. S., Grubel, G., Legrand, J. F., Als-Nielsen, J., Colman, D. R. & Hendrickson, W. A. 1995 Structural basis of cell-cell adhesion by cadherins. Nature 374, 327337.CrossRefGoogle ScholarPubMed
Smith, M. L., Long, D. S., Damiano, E. R. & Ley, K. 2003 Near-wall μ-PIV reveals a hydrodynamically relevant endothelial surface layer in venules in vivo. Biophys. J. 85, 637645.CrossRefGoogle Scholar
Sparrow, E. M. & Loeffler, A. L. jr 1959 Longitudinal laminar flow between cylinders arranged in regular array. AIChE J. 5, 325330.CrossRefGoogle Scholar
Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. 2001 Quasi-periodic substructure in the microvessel endothelial glycocalyx: a possible explanation for molecular filtering? J. Struct. Biol. 136, 239255.CrossRefGoogle ScholarPubMed
Starling, E. H. 1896 On the absorption of fluids from the convective tissue spaces. J. Physiol. 19, 312326.CrossRefGoogle Scholar
Sugihara-Seki, M. 1996 The motion of an ellipsoid in tube flow at low Reynolds numbers. J. Fluid Mech. 324, 287308.CrossRefGoogle Scholar
Sugihara-Seki, M. 2004 Motion of a sphere in a cylindrical tube filled with a Brinkman medium. Fluid Dyn. Res. 34, 5976.CrossRefGoogle Scholar
Sugihara-Seki, M. 2006 Transport of spheres suspended in the fluid flowing between hexagonally arranged cylinders. J. Fluid Mech. 551, 309321.CrossRefGoogle Scholar
Thi, M. M., Tarbell, J. M., Weinbaum, S. & Spray, D. C. 2004 The role of the glycocalyx in reorganization of the actin cytoskeleton under fluid shear stress: A ‘bumper-car’ model. Proc. Natl Acad. Sci. 101, 16 48316 488.CrossRefGoogle ScholarPubMed
Truskey, G. A., Yuan, F. & Katz, D. F. 2004 In Transport Phenomena in Biological Systems. Pearson.Google Scholar
Tsay, R. & Weinbaum, S. 1991 Viscous flow in a channel with periodic cross-bridging fibres: exact solutions and Brinkman approximation. J. Fluid Mech. 226, 125148.CrossRefGoogle Scholar
Tsay, R., Weinbaum, S. & Pfeffer, R. 1989 A new model for capillary filtration based on recent electron microscopic studies of endothelial junctions. Chem. Engng Commun 82, 67102.CrossRefGoogle Scholar
Vink, H. & Duling, B. R. 1996 Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries. Circ. Res. 79, 581589.CrossRefGoogle ScholarPubMed
Vink, H. & Duling, B. R. 2000 Capillary endothelial surface layer selectively reduces plasma solute distribution volume. Am. J. Physiol. 278, H285H289.Google ScholarPubMed
Weinbaum, S. 1998 1997 Whitaker distinguished lecture: Models to solve mysteries in biomechanics at the cellular level; a new view of fibre matrix layers. Ann. Biomed. Engng 26, 627643.CrossRefGoogle Scholar
Weinbaum, S., Tsay, R. & Curry, F. E. 1992 A three-dimensional junction–pore–matrix model for capillary permeability. Microvasc. Res. 44, 85111.CrossRefGoogle ScholarPubMed
Weinbaum, S., Zhang, X., Han, Y., Vink, H. & Cowin, S. C. 2003 Mechanotransduction and flow across the endothelial glycocalyx. Proc. Natl Acad. Sci. 100, 79887995.CrossRefGoogle ScholarPubMed
Weinbaum, S., Tarbell, J. M. & Damiano, E. R. 2007 The structure and function of the endothelial glycocalyx layer. Annu. Rev. Biomed. Engng 9, 121167.CrossRefGoogle ScholarPubMed
Zeng, Y. & Weinbaum, S. 1994 Stokes flow through periodic orifices in a channel. J. Fluid Mech. 263, 207226.CrossRefGoogle Scholar
Zhang, X., Curry, F. & Weinbaum, S. 2006 Mechanism of osmotic flow in a periodic fibre array. Am. J. Physiol. 290, H844H852.Google Scholar
Zhang, X., Adamson, R. H., Curry, F. E. & Weinbaum, S. 2006 A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle. Am. J. Physiol. 291, H2950H2964.Google ScholarPubMed
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *