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

Journal of Fluid Mechanics

Volumn 601, Issue , 2008, Pages 229-252

  Sugihara Seki, M ^a   Akinaga, T ^a   Itano, T ^a  

^a KANSAI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ENDOTHELIAL CELLS; FLOW RATE; HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; PRESSURE DROP; STEADY FLOW;

BRINKMAN EQUATION; INTERCELLULAR CLEFT; MICROVESSEL WALL;

HYDRODYNAMICS;

ENDOTHELIAL CELLS; FLOW RATE; HYDRAULIC CONDUCTIVITY; HYDRODYNAMICS; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; PRESSURE DROP; STEADY FLOW;

DARCY LAW; FLUID FLOW; HYDRAULIC CONDUCTIVITY; NUMERICAL MODEL; PERMEABILITY; STEADY FLOW; THREE-DIMENSIONAL FLOW; WALL;

RATTUS;

EID: 42449098934     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008000530     Document Type: Article

References (60)

1. ADAMSON, R. H. 1990 Permeability of frog mesenteric capillaries after partial pronase digestion of the endothelial glycocalyx. J. Physiol. 428, 1-13.
2. ADAMSON, R. H. & CLOUGH, G. 1992 Plasma proteins modify the endothelial cell glycocalyx of frog mesenteric microvessel. J. Physiol. 445, 473-486.
3. ADAMSON, R. H. & MICHEL, C. C. 1993 Pathways through the intercellular clefts of frog mesenteric capillaries. J. Physiol. 466, 303-327.
4. 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, 889-907.
5. BABUSKA, I. & SURI, M. 1994 The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev. 36 578-632.
6. VAN DEN BERG, B. M., VINK, H. & SPAAN, J. A. E. 2003 The endothelial glycocalyx protects against myocardial edema. Circ. Res. 92, 592-594.
7. 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. 75-80.
8. 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, 1308-1313.
9. 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, 27-34.
10. BUNDGAARD, M. 1984 The three-dimensional organization of tight junctions in a capillary endothelium revealed by serial-section electron micrscopy. J. Ultrastruct. Res. 88, 1-17.
11. CURRY, F. E. & MICHEL, C. C. 1980 A fibre matrix model of capillary permeability. Microvasc. Res. 20, 96-99.
12. DAMIANO, E. R. & STACE, T. M. 2002 A mechano-electrochemical model of radial deformation of the capillary glycocalyx. Biophys. J. 82, 1153-1175.
13. 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, 163-189.
14. 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, 1-19.
15. 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, 281-317.
16. FENG, J., GANATOS, P. & WEINBAUM, S. 1998 Motion of a sphere near planar confining boundaries in a Brinkman medium. J. Fluid Mech. 375, 265-296.
17. 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, 502-513.
18. 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, 217-235.
19. HAPPEL, J. & BRENNER, H. 1973 In Low Reynolds Number Hydrodynamics, 2nd edn, p. 393. Martinus Nijhoff.
20. HASIMOTO, H. 1958 On the flow of a viscous fluid past a thin screen at small Reynolds numbers. J. Phys. Soc. Japan 13, 633-639.
21. HENRY, C. B. S. & DULING, B. R. 1999 Permeation of the luminal capillary glycocalyx is determined by hyaluronan. Am. J. Physiol. 277, H508-H514.
22. HENRY, C. B. S. & DULING, B. R. 2000 TNF-α increases entry of macromolecules into luminal endothelial cell glycocalyx. Am. J. Physiol. 279, H2815-H2823.
23. HU, X. & WEINBAUM, S. 1999 A new view of Starling's hypothesis at the microstructural level. Microvasc. Res. 58, 281-304.
24. 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, H1724-H1736.
25. INTAGLIETTA, M. & DE PLOMB, E. P. 1973 Fluid exchange in tunnel and tube capillaries. Microvasc. Res. 6, 153-168.
26. KARNIADAKIS, G. E. & SHERWIN, S. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.
27. LEVICK, J. R. 1987 Flow through interstitium and other fibrous matrices. Q. J. Exp. Physiol. 72, 409-437.
28. LIPOWSKY, H. 1995 Shear stress in the circulation. In Flow-Dependent Regulation of Vascular Function (ed. J. A. Bevan, G. Kaley & G. M. Rubanyi), pp. 28-45 Oxford University Press.
29. 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, 10 060-10 065.
30. LUFT, J. H. 1966 Fine structure of capillary and endocapillary layer as revealed by ruthenium red. Fed. Proc. 25, 1773-1783.
31. 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, 185-204.
32. MICHEL, C. C. 1997 Starling: The formulation of his hypothesis of microvascular fluid exchange and its significance after 100 years. Exp. Physiol. 82, 1-30.
33. MICHEL, C. C. & CURRY, F. E. 1999 Microvascular permeability. Physiol. Rev. 79, 703-761.
34. 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, 228-233.
35. 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, 723-741.
36. PRIES, A. R., SECOMB, T. W. & GAEHTGENS, P. 2000 The endothelial surface layer. Pflugers Arch Eur. J. Physiol. 440, 653-666.
37. 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, 25-46.
38. SANGANI, A. S. & ACRIVOS, A. 1982 Slow flow past periodic arrays of cylinders with application to heat transfer. Intl J. Multiphase Flow 8, 193-206.
39. 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, 647-655.
40. 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, 327-337.
41. 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, 637-645.
42. SPARROW, E. M. & LOEFFLER, JR A. L. 1959 Longitudinal laminar flow between cylinders arranged in regular array. AIChE J. 5, 325-330.
43. 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, 239-255.
44. STARLING, E. H. 1896 On the absorption of fluids from the convective tissue spaces. J. Physiol. 19, 312-326.
45. SUGIHARA-SEKI, M. 1996 The motion of an ellipsoid in tube flow at low Reynolds numbers. J. Fluid Mech. 324, 287-308.
46. SUGIHARA-SEKI, M. 2004 Motion of a sphere in a cylindrical tube filled with a Brinkman medium. Fluid Dyn. Res. 34, 59-76.
47. SUGIHARA-SEKI, M. 2006 Transport of spheres suspended in the fluid flowing between hexagonally arranged cylinders. J. Fluid Mech. 551, 309-321.
48. 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, 16 483-16 488.
49. TRUSKEY, G. A., YUAN, F. & KATZ, D. F. 2004 In Transport Phenomena in Biological Systems. Pearson.
50. TSAY, R. & WEINBAUM, S. 1991 Viscous flow in a channel with periodic cross-bridging fibres: Exact solutions and Brinkman approximation. J. Fluid Mech. 226, 125-148.
51. 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, 67-102.
52. VINK, H. & DULING, B. R. 1996 Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries. Circ. Res. 79, 581-589.
53. VINK, H. & DULING, B. R. 2000 Capillary endothelial surface layer selectively reduces plasma solute distribution volume. Am. J. Physiol. 278, H285-H289.
54. 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, 627-643.
55. WEINBAUM, S., TSAY, R. & CURRY, F. E. 1992 A three-dimensional junction-pore-matrix model for capillary permeability. Microvasc. Res. 44, 85-111.
56. WEINBAUM, S., ZHANG, X., HAN, Y., VINK, H. & COWIN, S. C. 2003 Mechanotransduction and flow across the endothelial glycocalyx. Proc. Natl Acad. Sci. 100, 7988-7995.
57. WEINBAUM, S., TARBELL, J. M. & DAMIANO, E. R. 2007 The structure and function of the endothelial glycocalyx layer. Annu. Rev. Biomed. Engng 9, 121-167.
58. ZENG, Y. & WEINBAUM, S. 1994 Stokes flow through periodic orifices in a channel. J. Fluid Mech. 263, 207-226.
59. ZHANG, X., CURRY, F. & WEINBAUM, S. 2006 Mechanism of osmotic flow in a periodic fibre array. Am. J. Physiol. 290, H844-H852.
60. 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, H2950-H2964.