Skip to main content
SpringerLink
Log in

Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

The effect of red blood cells and the undulation of the endothelium on the shear stress in the microvasculature is studied numerically using the lattice Boltzmann–immersed boundary method. The results demonstrate a significant effect of both the undulation of the endothelium and red blood cells on wall shear stress. Our results also reveal that morphological alterations of red blood cells, as occur in certain pathologies, can significantly affect the values of wall shear stress. The resulting fluctuations in wall shear stress greatly exceed the nominal values, emphasizing the importance of the particulate nature of blood as well as a more realistic description of vessel wall geometry in the study of hemodynamic forces. We find that within the channel widths investigated, which correspond to those found in the microvasculature, the inverse minimum distance normalized to the channel width between the red blood cell and the wall is predictive of the maximum wall shear stress observed in straight channels with a flowing red blood cell. We find that the maximum wall shear stress varies several factors more over a range of capillary numbers (dimensionless number relating strength of flow to membrane elasticity) and reduced areas (measure of deflation of the red blood cell) than the minimum wall shear stress. We see that waviness reduces variation in minimum and maximum shear stresses among different capillary and reduced areas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Aarts PAMM, Heethaar RM, Sixma JJ (1984) Red blood cell deformability influences platelets-vessel wall interaction in flowing blood. Blood 64(6):1228–1233

    Google Scholar 

  • Bagchi P (2007) Mesoscale simulation of blood flow in small vessels. Biophys J 92(6):1858–1877

    Article  Google Scholar 

  • Barabino GA, McIntire LV, Eskin SG, Sears DA, Udden M (1987) Endothelial cell interactions with sickle cell, sickle trait, mechanically injured, and normal erythrocytes under controlled flow. Blood 70(1):152–157

    Google Scholar 

  • Barakat AI (1999) Responsiveness of vascular endothelium to shear stress: potential role of ion channels and cellular cytoskeleton (review). Int J Mol Med 4:323–332

    Google Scholar 

  • Barbee KA, Davies PF, Lal R (1994) Shear stress-induced reorganization of the surface topography of living endothelial cells imaged by atomic force microscopy. Cardiovasc Res 74:163–171

    Google Scholar 

  • Barbee KA, Mundel T, Lal R, Davies PF (1995) Subcellular distribution of shear stress at the surface of flow-aligned and nonaligned endothelial monolayers. Am J Physiol Heart Circ Physiol 268(4):H1765–H1772

    Article  Google Scholar 

  • Baskurt OK (2012) Red blood cell mechanical stability. In: 2012 world congress on engineering and technology, Oct 2012, pp 8–10

  • Bouzidi M, Firdaouss M, Lallemand P (2001) Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys Fluids 13(11):3452–3459

    Article  MATH  Google Scholar 

  • Chtcheglova LA, Wildling L, Waschke J, Drenckhahn D, Afm PH (2010) AFM functional imaging on vascular endothelial cells. J Mol Recognit 23(6):589

    Article  Google Scholar 

  • Culver JC, Dickinson ME (2010) The effects of hemodynamic force on embryonic development. Microcirculation 17(3):164–178

    Article  Google Scholar 

  • Davies PF (1995) Flow-mediated endothelial mechanotransduction. Physiol Rev 75(3):519–560

    Article  Google Scholar 

  • Diez-Silva M, Dao M, Han J, Lim C-T, Suresh S (2010) Shape and biomechanical characteristics of human red blood cells in health and disease. MRS Bull/Mater Res Soc 35(5):382–388

    Article  Google Scholar 

  • Dondorp AM, Pongponratn E, White NJ (2004) Reduced microcirculatory flow in severe falciparum malaria: pathophysiology and electron-microscopic pathology. Acta Trop 89(3):309–317

    Article  Google Scholar 

  • Fedosov DA, Caswell B, Suresh S, Karniadakis GE (2011a) Quantifying the biophysical characteristics of Plasmodium-falciparum-parasitized red blood cells in microcirculation. Proc Natl Acad Sci 108(1):35–39

    Article  Google Scholar 

  • Fedosov DA, Caswell B, Karniadakis GE (2011b) Wall shear stress-based model for adhesive dynamics of red blood cells in malaria. Biophys J 100(9):2084–2093

    Article  Google Scholar 

  • Freund JB, Vermot J (2014) The wall-stress footprint of blood cells flowing in microvessels. Biophys J 106(3):752–762

    Article  Google Scholar 

  • García-Cardeña G, Slegtenhorst BR (2016) Hemodynamic control of endothelial cell fates in development. Ann Rev Cell Dev Biol 6(32):633–648

    Article  Google Scholar 

  • Ghigliotti G, Selmi H, El Asmi L, Misbah C (2012) Why and how does collective red blood cells motion occur in the blood microcirculation? Phys Fluids 24:10

    Article  MATH  Google Scholar 

  • Hahn C, Schwartz MA (2009) Mechanotransduction in vascular physiology and atherogenesis. Nat Rev Mol Cell Biol 10(1):53–62

    Article  Google Scholar 

  • Kaoui B, Harting J, Misbah C (2011) Two-dimensional vesicle dynamics under shear flow: effect of confinement. Phys Rev E Stat Nonlinear Soft Matter Phys 83:6

    Article  Google Scholar 

  • Kroll MH, David HJ, McIntire LV, Schafer AI, Moake JL (1996) Platelets and shear stress. Blood 88(5):1525–1542

    Google Scholar 

  • Krüger T, Varnik F, Raabe D (2009) Shear stress in lattice Boltzmann simulations. Phys Rev E 79(4):1–15

    Article  Google Scholar 

  • Namgung B, Ong PK, Johnson PC, Kim S (2011) Effect of cell-free layer variation on arteriolar wall shear stress. Ann Biomed Eng 39(1):359–366

    Article  Google Scholar 

  • Oberleithner H, Ludwig T, Riethmüller C, Hillebrand U, Albermann L, Schäfer C, Shahin V, Schillers H (2004) Human endothelium: target for aldosterone. Hypertension 43(5):952–956

    Article  Google Scholar 

  • Oulaid O, Zhang J (2015) Temporal and spatial variations of wall shear stress in the entrance region of microvessels. J Biomech Eng 137(6):061008

    Article  Google Scholar 

  • Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517

    Article  MathSciNet  MATH  Google Scholar 

  • Pontrelli G, König CS, Halliday I, Spencer TJ, Collins MW, Long Q, Succi S (2011) Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile. Med Eng Phys 33(7):832–839

    Article  Google Scholar 

  • Roman BL, Pekkan K (2015) Mechanotransduction in embryonic vascular development. Biomech Model Mechanobiol 11(8):1149–1168

    Article  Google Scholar 

  • Rorai C, Touchard A, Zhu L, Brandt L (2015) Motion of an elastic capsule in a constricted microchannel. Eur Phys J E Soft Matter 38(5):134

    Article  Google Scholar 

  • Satcher RL, Bussolari SR, Gimbrone MA Jr, Dewey CF Jr (1992) The distribution of fluid forces on model arterial endothelium using computational fluid dynamics. J Biomech Eng 114:309–316

    Article  Google Scholar 

  • Shen Z, Farutin A, Thiébaud M, Misbah C (2017) Interaction and rheology of vesicle suspensions in confined shear flow. Phys Rev Fluids 2(10):103101

    Article  Google Scholar 

  • Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Tahiri N, Biben T, Ez-Zahraouy H, Benyoussef A, Misbah C (2013) On the problem of slipper shapes of red blood cells in the microvasculature. Microvasc Res 85:40–45

    Article  Google Scholar 

  • Tsubota KI, Wada S (2010) Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell. Phys Rev E Stat Nonlinear Soft Matter Phys 81:1

    Article  Google Scholar 

  • Tsubota K, Wada S, Yamaguchi T (2006) Particle method for computer simulation of red blood cell motion in blood flow. Comput Methods Programs Biomed 83(2):139–146

    Article  Google Scholar 

  • Uzarski JS, Scott EW, Mcfetridge PS (2013) Adaptation of endothelial cells to physiologically-modeled, variable shear stress. PLoS ONE 8:2

    Article  Google Scholar 

  • Vlahovska PM, Podgorski T, Misbah C (2009) Vesicles and red blood cells in flow: from individual dynamics to rheology. C R Phys 10(8):775–789

    Article  Google Scholar 

  • Vlahovska PM, Barthes-Biesel D, Misbah C (2013) Flow dynamics of red blood cells and their biomimetic counterparts. C R Phys 14(6):451–458

    Article  Google Scholar 

  • Wu T, Feng JJ (2013) Simulation of malaria-infected red blood cells in microfluidic channels: passage and blockage. Biomicrofluidics 7(4):1–18

    Article  MathSciNet  Google Scholar 

  • Xiong W, Zhang J (2010) Shear stress variation induced by red blood cell motion in microvessel. Ann Biomed Eng 38(8):2649–2659

    Article  Google Scholar 

  • Xu Z, Zheng Y, Wang X, Shehata N, Wang C, Sun Y (2018) Stiffness increase of red blood cells during storage. Microsyst Nanoeng 4:17103 March 2017

    Article  Google Scholar 

  • Ye T, Phan-Thien N, Khoo B, Lim CT (2014) Numerical modelling of a healthy/malaria-infected erythrocyte in shear flow using dissipative particle dynamics method. J Appl Phys 115:224701

    Article  Google Scholar 

  • Ye T, Phan-Thien N, Lim CT (2015) Particle-based simulations of red blood cells: a review. J Biomech 49(11):2255–2266

    Article  Google Scholar 

  • Yin X, Zhang J (2012) Cell-free layer and wall shear stress variation in microvessels. Biorheology 49(4):261–270

    Google Scholar 

  • Zhang J, Johnson PC, Popel AS (2007) An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Phys Biol 4(4):285–295

    Article  Google Scholar 

Download references

Acknowledgements

Brenna Hogan is supported by a doctoral fellowship from Ecole Polytechnique. This research is funded in part by a permanent endowment in Cardiovascular Cellular Engineering from the AXA Research Fund, the Centre National d’Etudes Spatiales (CNES), and the French–German university program (Living Fluids, Grant CFDA-Q1-14).

Author information

Authors and Affiliations

  1. Hydrodynamics Laboratory (LadHyX), École Polytechnique, Palaiseau, France

    Brenna Hogan & Abdul I. Barakat

  2. Laboratoire Interdisciplinaire de Physique (LiPhy), Université Joseph Fourier, Saint-Martin-d’Hères, France

    Hengdi Zhang & Chaouqi Misbah

  3. Laboratoire Ondes et Matière d’Aquitaine (LOMA), Université de Bordeaux, Talence, France

    Zaiyi Shen

Authors
  1. Brenna Hogan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zaiyi Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hengdi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chaouqi Misbah
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Abdul I. Barakat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdul I. Barakat.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hogan, B., Shen, Z., Zhang, H. et al. Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation. Biomech Model Mechanobiol 18, 1095–1109 (2019). https://doi.org/10.1007/s10237-019-01130-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-019-01130-8

Keywords

Search

Navigation