Effects of red blood cell aggregation on the blood flow in a symmetrical stenosed microvessel

  • L. L. XiaoEmail author
  • C. S. Lin
  • S. Chen
  • Y. Liu
  • B. M. Fu
  • W. W. Yan
Original Paper


In order to figure out whether red blood cell (RBC) aggregation is beneficial or deleterious for the blood flow through a stenosis, fluid mechanics of a microvascular stenosis was examined through simulating the dynamics of deformable red blood cells suspended in plasma using dissipative particle dynamics. The spatial variation in time-averaged cell-free layer (CFL) thickness and velocity profiles indicated that the blood flow exhibits asymmetry along the flow direction. The RBC accumulation occurs upstream the stenosis, leading to a thinner CFL and reduced flow velocity. Therefore, the emergence of stenosis produces an increased blood flow resistance. In addition, an enhanced Fahraeus–Lindqvist effect was observed in the presence of the stenosis. Finally, the effect of RBC aggregation combined with decreased stenosis on the blood flow was investigated. The findings showed that when the RBC clusters pass through the stenosis with a throat comparable to the RBC core in diameter, the blood flow resistance decreases with increasing intercellular interaction strength. But if the RBC core is larger and even several times than the throat, the blood flow resistance increases largely under strong RBC aggregation, which may contribute to the mechanism of the microthrombus formation.


Stenosed microvessel Dissipative particle dynamics RBC core CFL RBC aggregation 



This work is supported by the National Natural Science Foundation of China (Grant No. 11872283), the National Natural Science Foundation of China (Grant No. 11872062), Shanghai Science and Technology Talent Program (19YF1417400) and the Starting Research Fund from Shanghai University of Engineering Science (E3-0501-18-01024). The grants are gratefully acknowledged.


  1. Alizadehrad D, Imai Y, Nakaaki K, Ishikawa T, Yamaguchi T (2012) Parallel simulation of cellular flow in microvessels using a particle method. J Biomech Sci Eng 7:57–71. CrossRefGoogle Scholar
  2. Bacher C, Schrack L, Gekle S (2017) Clustering of microscopic particles in constricted blood flow. Phys Rev Fluids 2:013102. CrossRefGoogle Scholar
  3. Bacher C, Kihm A, Schrack L, Kaestner L, Laschke MW, Wagner C, Gekle S (2018) Antimargination of microparticles and platelets in the vicinity of branching vessels. Biophys J 115:411–425. CrossRefGoogle Scholar
  4. Bagchi P, Johnson PC, Popel AS (2005) Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J Biomech Eng-T ASME 127:1070–1080CrossRefGoogle Scholar
  5. Baskurt OK, Meiselman HJ (2007) Hemodynamic effects of red blood cell aggregation. Indian J Exp Biol 45:25–31Google Scholar
  6. Bishop JJ, Popel AS, Intaglietta M, Johnson PC (2001) Effects of erythrocyte aggregation and venous network geometry on red blood cell axial migration. Am J Physiol Heart Circ Physiol 281:H939–950. CrossRefGoogle Scholar
  7. Bryngelson SH, Freund JB (2016) Capsule-train stability. Phys Rev Fluids 1:033201. CrossRefGoogle Scholar
  8. Bryngelson SH, Freund JB (2018) Global stability of flowing red blood cell trains. Phys Rev Fluids 3:073101. CrossRefGoogle Scholar
  9. Chien S, Usami S, Taylor HM, Lundberg JL, Gregersen MI (1966) Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. J Appl Physiol 21:81–87CrossRefGoogle Scholar
  10. Clark LR, Berman SE, Rivera-Rivera LA, Hoscheidt SM (2017) Macrovascular and microvascular cerebral blood flow in adults at risk for Alzheimer’s disease. Alzheimers Dement Diagn Assess Dis Monit 7:48–55Google Scholar
  11. Cokelet GR, Goldsmith HL (1991) Decreased hydrodynamic resistance in the two-phase flow of blood through small vertical tubes at low flow rates. Circ Res 68:1–17CrossRefGoogle Scholar
  12. Doddi SK, Bagchi P (2009) Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys Rev E 79:046318CrossRefGoogle Scholar
  13. Ernst FD (1988) Microcirculation and hemorheology. Munchen Med Wochen 130:863–866Google Scholar
  14. Espanol P (1995) Hydrodynamics from dissipative particle dynamics. Phys Rev E 52:1734–1742MathSciNetCrossRefGoogle Scholar
  15. Evans E, Rawicz W, Smith BA (2013) Back to the future: mechanics and thermodynamics of lipid biomembranes. Faraday Discuss 161:591–611. CrossRefGoogle Scholar
  16. Fedosov DA (2010) Multiscale modeling of blood flow and soft matter. Dissertation, Brown UniversityGoogle Scholar
  17. Fedosov DA, Caswell B, Karniadakis GE (2010a) Systematic coarse-graining of spectrin-level red blood cell models. Comput Method Appl M 199:1937–1948MathSciNetCrossRefzbMATHGoogle Scholar
  18. Fedosov DA, Caswell B, Popel AS, Karniadakis GE (2010b) Blood flow and cell-free layer in microvessels. Microcirculation 17:615–628CrossRefGoogle Scholar
  19. Fedosov DA, Pan WX, Caswell B, Gompper G, Karniadakis GE (2011) Predicting human blood viscosity in silico. Proc Natl Acad Sci USA 108:11772–11777CrossRefGoogle Scholar
  20. Fujiwara H et al (2009) Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel. J Biomech 42:838CrossRefGoogle Scholar
  21. Gao C, Zhang P, Marom G, Deng YF, Bluestein D (2017) Reducing the effects of compressibility in DPD-based blood flow simulations through severe stenotic microchannels. J Comput Phys 335:812–827. MathSciNetCrossRefGoogle Scholar
  22. Groot RD, Warren PB (1997) Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107:4423–4435CrossRefGoogle Scholar
  23. Ha H, Lee SJ (2013) Hemodynamic features and platelet aggregation in a stenosed microchannel. Microvasc Res 90:96–105. CrossRefGoogle Scholar
  24. Hoogerbrugge PJ, Koelman JMVA (1992) Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys Lett 19:155–160CrossRefGoogle Scholar
  25. Hu RQ, Li F, Lv JQ, He Y, Lu DT, Yamada T, Ono N (2015) Microfluidic analysis of pressure drop and flow behavior in hypertensive micro vessels. Biomed Microdevices 17:60. CrossRefGoogle Scholar
  26. Isfahani AHG, Freund JB (2012) Forces on a wall-bound leukocyte in a small vessel due to red cells in the blood stream. Biophys J 103:1604–1615CrossRefGoogle Scholar
  27. Kaliviotis E, Dusting J, Sherwood JM, Balabani S (2016) Quantifying local characteristics of velocity, aggregation and hematocrit of human erythrocytes in a microchannel flow. Clin Hemorheol Microcirc 63:123–148. CrossRefGoogle Scholar
  28. Kaliviotis E, Sherwood JM, Balabani S (2017) Partitioning of red blood cell aggregates in bifurcating microscale flows. Sci Rep 7:44563. CrossRefGoogle Scholar
  29. Kang M, Ji HS, Kim KC (2008) In-vitro investigation of RBCs’ flow characteristics and hemodynamic feature through a microchannel with a micro-stenosis. Int J Biol Biomed Eng 2:1–8Google Scholar
  30. Labazi H, Trask AJ (2017) Coronary microvascular disease as an early culprit in the pathophysiology of diabetes and metabolic syndrome. Pharmacol Res 123:114–121. CrossRefGoogle Scholar
  31. Lee K, Danilina AV, Kinnunen M, Priezzhev AV, Meglinski I (2016) Probing the red blood cells aggregating force with optical tweezers. IEEE J Sel Top Quantum Electron 22:7000106Google Scholar
  32. Li X, Peng Z, Lei H, Dao M, Karniadakis GE (2014) Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Philos Trans Ser A Math Phys Eng Sci 372:20130389. MathSciNetCrossRefzbMATHGoogle Scholar
  33. Liu YL, Zhang L, Wang XD, Liu WK (2004) Coupling of Navier–Stokes equations with protein molecular dynamics and its application to hemodynamics. Int J Numer Meth Fl 46:1237–1252MathSciNetCrossRefzbMATHGoogle Scholar
  34. Maeda N, Suzuki Y, Tanaka S, Tateishi N (1996) Erythrocyte flow and elasticity of microvessels evaluated by marginal cell-free layer and flow resistance. Am J Physiol Heart Circ Physiol 271:H2454–H2461CrossRefGoogle Scholar
  35. Pivkin IV, Karniadakis GE (2008) Accurate coarse-grained modeling of red blood cells. Phys Rev Lett 101:118105CrossRefGoogle Scholar
  36. Polwaththe-Gallage HN, Saha SC, Sauret E, Flower R, Senadeera W, Gu YT (2016) SPH-DEM approach to numerically simulate the deformation of three-dimensional RBCs in non-uniform capillaries. Biomed Eng Online 15:349–370. CrossRefGoogle Scholar
  37. Pries AR, Secomb TW (2005) Microvascular blood viscosity in vivo and the endothelial surface layer. Am J Physiol Heart C 289:H2657–H2664CrossRefGoogle Scholar
  38. Pries AR, Neuhaus D, Gaehtgens P (1992) Blood-viscosity in tube flow—dependence on diameter and hematocrit. Am J Physiol 263:H1770–H1778Google Scholar
  39. Rampling MW, Meiselman HJ, Neu B, Baskurt OK (2004) Influence of cell-specific factors on red blood cell aggregation. Biorheology 41:91–112Google Scholar
  40. Reinke W, Gaehtgens P, Johnson PC (1987) Blood-viscosity in small tubes—effect of shear rate, aggregation, and sedimentation. Am J Physiol 253:H540–H547Google Scholar
  41. Sherwood JM, Holmes D, Kaliviotis E, Balabani S (2014a) Spatial distributions of red blood cells significantly alter local haemodynamics. PLoS ONE 9:e100473. CrossRefGoogle Scholar
  42. Sherwood JM, Kaliviotis E, Dusting J, Balabani S (2014b) Hematocrit, viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel. Biomech Model Mech 13:259–273. CrossRefGoogle Scholar
  43. Soutani M, Suzuki Y, Tateishi N, Maeda N (1995) Quantitative evaluation of flow dynamics of erythrocytes in microvessels: influence of erythrocyte aggregation. Am J Physiol Heart Circ Physiol 268:H1959–H1965. CrossRefGoogle Scholar
  44. Steffen P, Verdier C, Wagner C (2013) Quantification of depletion-induced adhesion of red blood cells. Phys Rev Lett 110:018102CrossRefGoogle Scholar
  45. Vahidkhah K (2015) Three-dimensional computational simulation of multiscale multiphysics cellular/particualte process in microcirculatory blood flow. Dissertation, The State of New JerseyGoogle Scholar
  46. Vahidkhah K, Balogh P, Bagchi P (2016) Flow of red blood cells in stenosed microvessels. Sci Rep 6:28194CrossRefGoogle Scholar
  47. Xiao L (2016) Numerical simulation of flow behaviors of cells in microvessels using dissipative particle dynamics. Dissertation, The Hong Kong Polytechnic UniversityGoogle Scholar
  48. Xiao LL, Liu Y, Chen S, Fu BM (2016a) Numerical simulation of a single cell passing through a narrow slit. Biomech Model Mechanobiol 15:1655–1667. CrossRefGoogle Scholar
  49. Xiao LL, Liu Y, Chen S, Fu BM (2016b) Simulation of deformation and aggregation of two red blood cells in a stenosed microvessel by dissipative particle dynamics. Cell Biochem Biophys 74:513–525. CrossRefGoogle Scholar
  50. Xu D, Kaliviotis E, Munjiza A, Avital E, Ji C, Williams J (2013) Large scale simulation of red blood cell aggregation in shear flows. J Biomech 46:1810–1817. CrossRefGoogle Scholar
  51. Yazdani A, Karniadakis GE (2016) Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction. Soft Matter 12:4339–4351. CrossRefGoogle Scholar
  52. Yazdani A, Li H, Humphrey JD, Karniadakis GE (2017) A general shear-dependent model for thrombus formation. PLoS Comput Biol 13:e1005291. CrossRefGoogle Scholar
  53. Ye T, Phan-Thien N, Khoo BC, Lim CT (2014) Dissipative particle dynamics simulations of deformation and aggregation of healthy and diseased red blood cells in a tube flow. Phys Fluids 26:111902CrossRefGoogle Scholar
  54. Zhang JF, Johnson PC, Popel AS (2009) Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc Res 77:265–272CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Automotive EngineeringShanghai University of Engineering ScienceShanghaiChina
  2. 2.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina
  3. 3.Department of Mechanical EngineeringThe Hong Kong Polytechnic UniversityHong KongChina
  4. 4.Department of Biomedical EngineeringThe City College of the City University of New YorkNew YorkUSA
  5. 5.College of Metrology and Measurement EngineeringChina Jiliang UniversityHangzhouChina

Personalised recommendations