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Effect of endothelial glycocalyx layer redistribution upon microvessel poroelastohydrodynamics. (English) Zbl 1422.76212

Summary: The endothelial glycocalyx layer (EGL) is a macromolecular layer that lines the inner surface of blood vessels. It is believed to serve a number of physiological functions in the microvasculature, including protection of the vessel walls from potentially harmful levels of fluid shear, as a molecular sieve that acts to regulate transendothelial mass transport, and as a transducer of mechanical stress from the vessel lumen. To best fulfil some of its roles, it has been suggested that the EGL redistributes, so that it is thickest at the cell-cell junctions. It has also been suggested that the majority of mechanotransduction occurs through the solid phase of the EGL, rather than via its fluid phase. The difficulties associated with measuring the distribution of the EGL in vivo make these hypotheses difficult to confirm experimentally. Consequently, to gauge the impact of EGL redistribution from a theoretical standpoint, we compute the flow through a porous-lined microvessel, the endothelial surface of which has been informed by confocal microscopy images of a postcapillary venule. Following earlier studies, we model the poroelastohydrodynamics of the EGL using biphasic mixture theory, taking advantage of a recently developed boundary integral representation of these equations to solve the coupled poroelastohydrodynamics using the boundary element method. However, the low permeabilities of the EGL mean that viscous effects are confined to thin layers, thereby also enabling an asymptotic treatment of the dynamics in this limit. In this asymptotic regime, we also consider a two-layer Stokes flow model for the lumen flow to approximate the effect of red blood cells within the lumen. We demonstrate that redistribution of the EGL can have a substantial impact upon microvessel haemodynamics. We also confirm that the bulk of the mechanical stress is indeed carried through the solid phase of the EGL.

MSC:

76Z05 Physiological flows
92C30 Physiology (general)

Software:

BEMLIB; spatstat; PETSc
Full Text: DOI

References:

[1] Adamson, R. H.; Lenz, J. F.; Zhang, X.; Adamson, G. N.; Weinbaum, S.; Curry, F. E., Oncotic pressures opposing filtration across non-fenestrated rat microvessels, J. Physiol., 557, 3, 889-907, (2004) · doi:10.1113/jphysiol.2003.058255
[2] Baddeley, A.2010 Analysing spatial point patterns in R. Tech. Rep., CSIRO, Version 4.1. Available at www.csiro.au/resources/pf16h.html.
[3] Baddeley, A.; Turner, R., spatstat: an R package for analyzing spatial point patterns, J. Stat. Softw., 12, 6, 1-42, (2005) · doi:10.18637/jss.v012.i06
[4] Baddeley, A.; Turner, R.; Mateu, J.; Bevan, A., Hybrids of Gibbs point process models and their implementation, J. Stat. Softw., 55, 11, 1-43, (2013) · doi:10.18637/jss.v055.i11
[5] Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W. D., Kaushik, D., Knepley, M. G.et al.2014aPETSc users manual. In Tech. Rep., Argonne National Laboratory,; ANL-95/11 - Revision 3.5.
[6] Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W. D., Kaushik, D., Knepley, M. G.et al. 2014b PETSc Web page. http://www.mcs.anl.gov/petsc.
[7] Balay, S., Gropp, W. D., Mcinnes, L. C. & Smith, B. F.1997Efficient management of parallelism in object oriented numerical software libraries. In Modern Software Tools in Scientific Computing (ed. Arge, E., Bruaset, A. M. & Langtangen, H. P.), pp. 163-202. Birkhäuser. doi:10.1007/978-1-4612-1986-6_8 · Zbl 0882.65154
[8] Barbee, K. A.; Davies, P. F.; Lal, R., Shear stress-induced reorganization of the surface topography of living endothelial cells imaged by atomic force microscopy, Circulat. Res., 74, 1, 163-171, (1994) · doi:10.1161/01.RES.74.1.163
[9] Barry, S. I.; Parkerf, K. H.; Aldis, G. K., Fluid flow over a thin deformable porous layer, Z. Angew. Math. Phys., 42, 633-648, (1991) · Zbl 0733.76076 · doi:10.1007/BF00944763
[10] Van Den Berg, B. M.; Spaan, J. A. E.; Rolf, T. M.; Vink, H., Atherogenic region and diet diminish glycocalyx dimension and increase intima-to-media ratios at murine carotid artery bifurcation, Am. J. Physiol. Heart Circ. Physiol., 290, 2, H915-H920, (2006) · doi:10.1152/ajpheart.00051.2005
[11] Brown, R.2007 Fitellipse: least squares ellipse fitting. Available at http://www.mathworks.com/matlabcentral/fileexchange/15125-fitellipse-m, last checked: 18.02.2011.
[12] Clough, G.; Michel, C. C., Quantitative comparisons of hydraulic permeability and endothelial intercellular cleft dimensions in single frog capillaries, J. Physiol., 405, 563-576, (1998) · doi:10.1113/jphysiol.1988.sp017348
[13] Colom, B.; Bodkin, J. V.; Beyrau, M.; Woodfin, A.; Ody, C.; Rourke, C.; Chavakis, T.; Brohi, K.; Imhof, B. A.; Nourshargh, S., Leukotriene b4-neutrophil elastase axis drives neutrophil reverse transendothelial cell migration in vivo, Immunity, 42, 6, 1075-1086, (2015) · doi:10.1016/j.immuni.2015.05.010
[14] Curry, F. E.; Adamson, R. H., Endothelial glycocalyx: permeability barrier and mechanosensor, Ann. Biomed. Engng., 40, 4, 828-839, (2012) · doi:10.1007/s10439-011-0429-8
[15] Dabagh, M.; Jalali, P.; Butler, P. J.; Tarbell, J. M., Shear-induced force transmission in a multicomponent, multicell model of the endothelium, J. R. Soc. Interface, 11, 98, (2014) · doi:10.1098/rsif.2014.0431
[16] Damiano, E. R., The effect of the endothelial-cell glycocalyx on the motion of red blood cells through capillaries, Microvasc. Res., 55, 1, 77-91, (1998) · doi:10.1006/mvre.1997.2052
[17] Damiano, E. R.; Duling, B. R.; Ley, K.; Skalak, T. C., Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer, J. Fluid Mech., 314, 163-189, (1996) · Zbl 0879.76100 · doi:10.1017/S0022112096000274
[18] Damiano, E. R.; Long, D. S.; El-Khatib, F. H.; Stace, T. M., On the motion of a sphere in a Stokes flow parallel to a Brinkman half-space, J. Fluid Mech., 500, 75-101, (2004) · Zbl 1065.76047 · doi:10.1017/S0022112003006566
[19] Damiano, E. R.; Stace, T. M., Flow and deformation of the capillary glycocalyx in the wake of a leukocyte, Phys. Fluids, 17, 3, (2005) · Zbl 1187.76113 · doi:10.1063/1.1863278
[20] Drew, D. A., Mathematical modelling of two-phase flow, Annu. Rev. Fluid Mech., 15, 2, 261-291, (1983) · Zbl 0569.76104 · doi:10.1146/annurev.fl.15.010183.001401
[21] Ebong, E. E.; Macaluso, F. P.; Spray, D. C.; Tarbell, J. M., Imaging the endothelial glycocalyx in vitro by rapid freezing/freeze substitution transmission electron microscopy, Arterioscler. Thromb. Vasc. Biol., 31, 8, 1908-1915, (2011) · doi:10.1161/ATVBAHA.111.225268
[22] Ehlers, W.; Bluhm, J., Porous Media: Theory, Experiments and Numerical Applications, (2002), Springer · Zbl 1001.00011 · doi:10.1007/978-3-662-04999-0
[23] Engwirda, D.2009 MESH2d - Automatic Mesh Generation. Available at http://www.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-automatic-mesh-generation, last checked: 01.03.2014.
[24] Feng, J.; Ganatos, P.; Weinbaum, S., Motion of a sphere near planar confining boundaries in a Brinkman medium, J. Fluid Mech., 375, 265-296, (1998) · Zbl 0930.76091 · doi:10.1017/S002211209800278X
[25] Feng, J.; Weinbaum, S., Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans, J. Fluid Mech., 422, 281-317, (2000) · Zbl 0988.76022 · doi:10.1017/S0022112000001725
[26] Florian, J. A.; Kosky, J. R.; Ainslie, K.; Pang, Z.; Dull, R. O.; Tarbell, J. M., Heparan sulfate proteoglycan is a mechanosensor on endothelial cells, Circulat. Res., 93, e136-e142, (2003) · doi:10.1161/01.RES.0000101744.47866.D5
[27] Gambaruto, A. M., Computational haemodynamics of small vessels using the moving particle semi-implicit (MPS) method, J. Comput. Phys., 302, 68-96, (2015) · Zbl 1349.76937 · doi:10.1016/j.jcp.2015.08.039
[28] Gouverneur, M.; Berg, B.; Nieuwdorp, M.; Stroes, E.; Vink, H., Vasculoprotective properties of the endothelial glycocalyx: effects of fluid shear stress, J. Internal Med., 259, 4, 393-400, (2006) · doi:10.1111/j.1365-2796.2006.01625.x
[29] Guiggiani, M.; Gigante, A., A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method, Trans. ASME J. Appl. Mech., 57, 4, 906-915, (1990) · Zbl 0735.73084 · doi:10.1115/1.2897660
[30] Han, Y.; Weinbaum, S.; Spaan, J. A. E.; Vimk, H., 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, (2006) · Zbl 1156.76318 · doi:10.1017/S0022112005007779
[31] Hariprasad, D. S.; Secomb, T. W., Motion of red blood cells near microvessel walls: effects of a porous layer, J. Fluid Mech., 705, 195-212, (2012) · Zbl 1250.76192 · doi:10.1017/jfm.2012.102
[32] Holcombe, S.2011 Growbubbles – maximum radius packing. Available at http://www.mathworks.com/matlabcentral/fileexchange/33213-growbubbles-maximum-radius-packing, last checked: 12.05.2015.
[33] Hu, X.; Adamson, R. H.; Liu, B.; Curry, F. E.; Weinbaum, S., Starling forces that oppose filtration after tissue oncotic pressure is increased, Am. J. Physiol. Heart Circ. Physiol., 279, 4, H1724-H1736, (2000)
[34] Hu, X.; Weinbaum, S., A new view of Starling’s hypothesis at the microstructural level, Microvasc. Res., 58, 3, 281-304, (1999) · doi:10.1006/mvre.1999.2177
[35] Illian, J.; Penttinen, A.; Stoyan, H.; Stoyan, D., Statistical Analysis and Modelling of Spatial Point Patterns, (2008), Wiley · Zbl 1197.62135
[36] Johnson, S. G.2013 Cubature (multi-dimensional integration). Available at http://ab-initio.mit.edu/wiki/index.php/Cubature, last checked: 05.10.2014.
[37] Kim, S.; Kong, R. L.; Popel, A. S.; Intaglietta, M.; Johnson, P. C., Temporal and spatial variations of cell-free layer width in arterioles, Am. J. Physiol. Heart Circ. Physiol., 293, 3, H1526-H1535, (2007) · doi:10.1152/ajpheart.01090.2006
[38] Kolev, N., Multiphase Flow Dynamics, vol. 1: Fundamentals, (2002), Springer · Zbl 1016.76001
[39] Levick, J. R.; Michel, C. C., Microvascular fluid exchange and the revised Starling principle, Cardiovasc. Res., 87, 2, 198-210, (2010) · doi:10.1093/cvr/cvq062
[40] Ley, K.2008The microcirculation in inflammation. In Microcirculation, 2nd edn. (ed. Tuma, R. F., Durn, W. N. & L., K.), chap. 9, pp. 387-448. Academic. doi:10.1016/B978-0-12-374530-9.00011-5
[41] Long, D. S.; Smith, M. L.; Pries, A. R.; Ley, K.; Damiano, E. R., Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution, Proc. Natl Acad. Sci. USA, 101, 27, 10060-10065, (2004) · doi:10.1073/pnas.0402937101
[42] Michel, C. C., Starling: the formulation of his hypothesis of microvascular fluid exchange and its significance after 100 years, Expl. Physiol., 82, 1, 1-30, (1997) · doi:10.1113/expphysiol.1997.sp004000
[43] Nerem, R. M.; Levesque, M. J.; Cornhill, J. F., Vascular endothelial morphology as an indicator of the pattern of blood flow, J. Biomech. Engng, 103, 3, 172-176, (1981) · doi:10.1115/1.3138275
[44] Nieuwdorp, M.; Van Haeften, T. W.; Gouverneur, M. C. L. G.; Mooij, H. L.; Van Lieshout, M. H. P.; Levi, M.; Meijers, J. C. M.; Holleman, F.; Hoekstra, J. B. L.; Vink, H., Loss of endothelial glycocalyx during acute hyperglycemia coincides with endothelial dysfunction and coagulation activation in vivo, Diabetes, 55, 2, 480-486, (2006) · doi:10.2337/diabetes.55.02.06.db05-1103
[45] Perrin, R. M.; Harper, S. J.; Bates, D. O., A role for the endothelial glycocalyx in regulating microvascular permeability in diabetes mellitus, Cell Biochem. Biophys., 49, 2, 65-72, (2007) · doi:10.1007/s12013-007-0041-6
[46] Peskin, C. S.1972 Flow patterns around heart valves: a digital computer method for solving the equations of motion. PhD thesis, Albert Einstein College of Medicine.
[47] Pozrikidis, C., Boundary Integral and Singularity Methods for Linearized Viscous Flow, (1992), Cambridge University Press · Zbl 0772.76005 · doi:10.1017/CBO9780511624124
[48] Pozrikidis, C., A Practical Guide to Boundary Element Methods with the Software Library BEMLIB, (2002), Chapman & Hall/CRC · Zbl 1019.65097 · doi:10.1201/9781420035254
[49] Pries, A. R.; Secomb, T. W.; Gessner, T.; Sperandio, M. B.; Gross, J. F.; Gaehtgens, P., Resistance to blood flow in microvessels in vivo, Circulat. Res., 75, 904-915, (1994) · doi:10.1161/01.RES.75.5.904
[50] Secomb, T. W.; Hsu, R.; Pries, A. R., A model for red blood cell motion in glycocalyx-lined capillaries, Am. J. Physiol. Heart Circ. Physiol., 274, 3, H1016-H1022, (1998)
[51] Secomb, T. W.; Hsu, R.; Pries, A. R., Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity, Am. J. Physiol. Heart Circ. Physiol., 281, 2, H629-H636, (2001)
[52] Sharan, M.; Popel, A. S., A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall, Biorheology, 38, 415-428, (2001)
[53] Smith, M. L.; Long, D. S.; Damiano, E. R.; Ley, K., Near-wall-PIV reveals a hydrodynamically relevant endothelial surface layer in venules in vivo, Biophys. J., 85, 1, 637-645, (2003) · doi:10.1016/S0006-3495(03)74507-X
[54] Squire, J. M.; Chew, M.; Nneji, G.; Neal, C.; Barry, J.; Michel, C., Quasi-periodic substructure in the microvessel endothelial glycocalyx: a possible explanation for molecular filtering?, J. Struct. Biol., 136, 3, 239-255, (2001) · doi:10.1006/jsbi.2002.4441
[55] Sumets, P. P.; Cater, J. E.; Long, D. S.; Clarke, R. J., A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx, Proc. R. Soc. Lond. A, 471, 2179, (2015) · Zbl 1371.76176
[56] Tarbell, J. M.; Shi, Z.-D., Effect of the glycocalyx layer on transmission of interstitial flow shear stress to embedded cells, Biomech. Model. Mechanobiol., 12, 1, 111-121, (2013) · doi:10.1007/s10237-012-0385-8
[57] Tarbell, J. M., Simon, S. I. & Curry, F.-R. E.2014Mechanosensing at the vascular interface. Annu. Rev. Biomed. Engng16 (1), 505-532; pMID: 24905872. doi:10.1146/annurev-bioeng-071813-104908
[58] Thi, M. M.; Tarbell, J. M.; Weinbaum, S.; Spray, D. C., The role of the glycocalyx in reorganization of the actin cytoskeleton under fluid shear stress: a bumper-car model, Proc. Natl Acad. Sci. USA, 101, 47, 16483-16488, (2004) · doi:10.1073/pnas.0407474101
[59] Vincent, P. E.; Sherwin, S. J.; Weinberg, P. D., Viscous flow over outflow slits covered by an anisotropic Brinkman medium: a model of flow above interendothelial cell clefts, Phys. Fluids, 20, 6, (2008) · Zbl 1182.76803 · doi:10.1063/1.2938761
[60] Vincent, P. E.; Sherwin, S. J.; Weinberg, P. D., The effect of a spatially heterogeneous transmural water flux on concentration polarization of low density lipoprotein in arteries, Biophys. J., 96, 8, 3102-3115, (2009) · doi:10.1016/j.bpj.2009.01.022
[61] Vincent, P. E.; Sherwin, S. J.; Weinberg, P. D., The effect of the endothelial glycocalyx layer on concentration polarisation of low density lipoprotein in arteries, J. Theor. Biol., 265, 1, 1-17, (2010) · Zbl 1406.92163 · doi:10.1016/j.jtbi.2010.04.015
[62] Vink, H.; Constantinescu, A. A.; Spaan, J. A. E., Oxidized lipoproteins degrade the endothelial surface layer: implications for platelet – endothelial cell adhesion, Circulation, 101, 13, 1500-1502, (2000) · doi:10.1161/01.CIR.101.13.1500
[63] Vink, H.; Duling, B. R., Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries, Circulat. Res., 79, 3, 581-589, (1996) · doi:10.1161/01.RES.79.3.581
[64] Wang, W.; Parker, K. H., The effect of deformable porous surface layers on the motion of a sphere in a narrow cylindrical tube, J. Fluid Mech., 283, 287-305, (1995) · Zbl 0839.76089 · doi:10.1017/S0022112095002321
[65] Wei, H. H.; Waters, S. L.; Liu, S. Q.; Grotberg, J. B., Flow in a wavy-walled channel lined with a poroelastic layer, J. Fluid Mech., 492, 23-45, (2003) · Zbl 1063.76689 · doi:10.1017/S0022112003005378
[66] Weinbaum, S., 1997 Whitaker distinguished lecture: models to solve mysteries in biomechanics at the cellular level; a new view of fiber matrix layers, Ann. Biomed. Engng, 26, 627-643, (1998) · doi:10.1114/1.134
[67] Weinbaum, S., Tarbell, J. M. & Damiano, E. R.2007The structure and function of the endothelial glycocalyx layer. Annu. Rev. Biomed. Engng9 (1), 121-167; pMID: 17373886. doi:10.1146/annurev.bioeng.9.060906.151959
[68] Weinbaum, S.; Zhang, X.; Yuefeng Han, H. V.; Cowin, S., Mechanotransduction and flow across the endothelial glycocalyx, Proc. Natl Acad. Sci., 100, 13, 7988-7995, (2003) · doi:10.1073/pnas.1332808100
[69] Woodfin, A.; Voisin, M.-B.; Beyrau, M.; Colom, B.; Caille, D.; Diapouli, F.-M.; Nash, G. B.; Chavakis, T.; Albelda, S. M.; Rainger, G. E., The junctional adhesion molecule jam-c regulates polarized transendothelial migration of neutrophils in vivo, Nat. Immunol., 12, 8, 761-769, (2011) · doi:10.1038/ni.2062
[70] Yao, Y.; Rabodzey, A.; Dewey, C. F., Glycocalyx modulates the motility and proliferative response of vascular endothelium to fluid shear stress, Am. J. Physiol. Heart Circ. Physiol., 293, 2, H1023-H1030, (2007) · doi:10.1152/ajpheart.00162.2007
[71] Yen, W.-Y.; Cai, B.; Zeng, M.; Tarbell, J. M.; Fu, B. M., Quantification of the endothelial surface glycocalyx on rat and mouse blood vessels, Microvasc. Res., 83, 3, 337-346, (2012) · doi:10.1016/j.mvr.2012.02.005
[72] Zhao, Y.; Chien, S.; Weinbaum, S., Dynamic contact forces on leukocyte microvilli and their penetration of the endothelial glycocalyx, Biophys. J., 80, 3, 1124-1140, (2001) · doi:10.1016/S0006-3495(01)76090-0
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