Rheologica Acta

, Volume 55, Issue 6, pp 433–449 | Cite as

Dynamic and rheological properties of soft biological cell suspensions

  • Alireza Yazdani
  • Xuejin Li
  • George Em KarniadakisEmail author
Original Contribution


Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.


Blood Dynamics Rheology Red blood cell Vesicle Capsule 



We acknowledge support from the National Institutes of Health (NIH) grants U01HL114476 and U01HL116323. A.Y. acknowledges TACC/STAMPEDE resources through XSEDE grant (TG-DMS140007), and X.L. acknowledges ALCF through INCITE program for providing computational resources that have lead to the unpublished research results reported within this paper.


  1. Abkarian M, Faivre M, Viallat A (2007) Swinging of red blood cells under shear flow. Phys Rev Lett 98:188, 302CrossRefGoogle Scholar
  2. Aingaran M, Zhang R, Law SKY, Peng ZL, Undisz A, Meyer E, Diez-Silva M, Burke TA, Spielmann T, Lim CT, Suresh S, Dao M, Marti M (2012) Host cell deformability is linked to transmission in the human malaria parasite plasmodium falciparum. Cell Microbiol 14:983–993CrossRefGoogle Scholar
  3. AlMomani T, Udaykumar H, Marshall J, Chandran K (2008) Micro-scale dynamic simulation of erythrocyte–platelet interaction in blood flow. Ann Biomed Eng 36(6):905–920CrossRefGoogle Scholar
  4. Apostolidis AJ, Beris AN (2014) Modeling of the blood rheology in steady-state shear flows. J Rheol 58:607–633CrossRefGoogle Scholar
  5. Apostolidis AJ, Armstrong MJ, Beris AN (2015) Modeling of human blood rheology in transient shear flows. J Rheol 59:275–298CrossRefGoogle Scholar
  6. Atzberger PJ, Kramer PR, Peskin CS (2007) A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. J Comput Phys 224:1255–1292CrossRefGoogle Scholar
  7. Bagchi P, Kalluri RM (2009) Dynamics of nonspherical capsules in shear flow. Phys Rev E 80:016307CrossRefGoogle Scholar
  8. Bagchi P, Kalluri RM (2010) Rheology of a dilute suspension of liquid-filled elastic capsules. Phys Rev E 81:056320CrossRefGoogle Scholar
  9. Bagchi P, Yazdani A (2012) Analysis of membrane tank-tread of nonspherical capsules and red blood cells. Eur Phys J E 35:103CrossRefGoogle Scholar
  10. Barabino GA, Platt MO, Kaul DK (2010) Sickle cell biomechanics. Annu Rev Biomed Eng 12:345–367CrossRefGoogle Scholar
  11. Barthes-Biesel D (2010) Capsule motion is flow: deformation and membrane buckling. C R Phys 10:764–774CrossRefGoogle Scholar
  12. Barthes-Biesel D (2011) Modeling the motion of capsules in flow. Curr Opin Colloid Interface Sci 16:3–12CrossRefGoogle Scholar
  13. Barthes-Biesel D, Rallison J (1981) The time-dependent deformation of a capsule freely suspended in a linear shear flow. J Fluid Mech 113:251–267CrossRefGoogle Scholar
  14. Baskurt O, Meiselman H (2003) Blood rheology and hemodynamics. Semin Thromb Hemost 29:435–450CrossRefGoogle Scholar
  15. Batchelor G (1970) The stress system in a suspension of force-free particles. J Fluid Mech 41:545–570CrossRefGoogle Scholar
  16. Biben T, Farutin A, Misbah C (2011) Three-dimensional vesicles under shear flow: numerical study of dynamics and phase diagram. Phys Rev E 83:031921CrossRefGoogle Scholar
  17. Boal DH, Seifert U, Zilker A (1992) Dual network model for red blood cell membranes. Phys Rev Lett 69:3405–3408CrossRefGoogle Scholar
  18. Bow H, Pivkin IV, Diez-Silva M, Goldfless SJ, Dao M, Niles JC, Suresh S, Han J (2011) A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11:1065–1073CrossRefGoogle Scholar
  19. Breyiannis G, Pozrikidis C (2000) Simple shear flow of suspensions of elastic capsules. Theor Comput Fluid Dyn 13:327–347CrossRefGoogle Scholar
  20. Casson N (1992) Rheology of disperse systems. Pergamon Press, New York, pp 84–104Google Scholar
  21. Chiang EY, Frenette PS (2005) Sickle cell vaso-occlusion. Hematol Oncol Clin N Am 19:771–784CrossRefGoogle Scholar
  22. 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 21:81–87Google Scholar
  23. Chien S, Usami S, Bertles JF (1970) Abnormal rheology of oxygenated blood in sickle cell anemia. J Clin Invest 49:623–634CrossRefGoogle Scholar
  24. Clausen JR, Reasor DA, Aidun CK (2011) The rheology and microstructure of concentrated non-colloidal suspensions of deformable capsules. J Fluid Mech 685:202–234CrossRefGoogle Scholar
  25. Cordasco D, Bagchi P (2014) Intermittency and synchronized motion of red blood cell dynamics in shear flow. J Fluid Mech 759:472–488CrossRefGoogle Scholar
  26. Cordasco D, Yazdani A, Bagchi P (2014) Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys Fluids 26:041902CrossRefGoogle Scholar
  27. Coupier G, Kaoui B, Podgorski T, Misbah C (2008) Noninertial lateral migration of vesicles in bounded poiseuille flow. Phys Fluids 20:111702CrossRefGoogle Scholar
  28. Coupier G, Farutin A, Minetti C, Podgorski T, Misbah C (2012) Shape diagram of vesicles in poiseuille flow. Phys Rev Lett 108:178106CrossRefGoogle Scholar
  29. Crowl L, Fogelson AL (2011) Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions. J Fluid Mech 676:348–375CrossRefGoogle Scholar
  30. Danker G, Misbah C (2007) Rheology of a dilute suspension of vesicles. Phys Rev Lett 98:088104CrossRefGoogle Scholar
  31. Danker G, Vlahovska PM, Misbah C (2009) Vesicles in poiseuille flow. Phys Rev Lett 102:148102CrossRefGoogle Scholar
  32. Deng MG, Li XJ, Liang HJ, Caswell B, Karniadakis GE (2012) Simulation and modeling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres. J Fluid Mech 711:192–211CrossRefGoogle Scholar
  33. Deschamps J, Kantsler V, Segre E, Steinberg V (2009a) Dynamics of a vesicle in general flow. Proc Natl Acad Sci USA 106:11444–11447CrossRefGoogle Scholar
  34. Deschamps J, Kantsler V, Steinberg V (2009b) Phase diagram of single vesicle dynamical states in shear flow. Phys Rev Lett 102:118105CrossRefGoogle Scholar
  35. Diez-Silva M, Dao M, Han J, Lim CT, Suresh S (2010) Shape and biomechanical characteristics of human red blood cells in health and disease. MRS Bull 35:382–388CrossRefGoogle Scholar
  36. Dimitrakopoulos P (2012) Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: effects of the constitutive law and membrane modeling. Phys Rev E 85:041917CrossRefGoogle Scholar
  37. Discher DE, Boal DH, Boey SK (1998) Simulations of the erythrocyte cytoskeleton at large deformation. ii. micropipette aspiration. Biophys J 75:1584–1597CrossRefGoogle Scholar
  38. Discher DE, Eisenberg A (2002) Polymer vesicles. Science 297:967–973CrossRefGoogle Scholar
  39. Doddi SK, Bagchi P (2008) Lateral migration of a capsule in a plane poiseuille flow in a channel. Int J Multiphase Flow 34:966–986CrossRefGoogle Scholar
  40. Doddi SK, Bagchi P (2009) Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys Rev E 79:046318CrossRefGoogle Scholar
  41. Dondorp AM, Pongponratn E, White NJ (2004) Reduced microcirculatory flow in severe falciparum malaria: pathophysiology and electron-microscopic pathology. Acta Trop 89:309–317CrossRefGoogle Scholar
  42. Dou Q, Ferrone FA (1993) Simulated formation of polymer domains in sickle hemoglobin. Biophys J 65:2068–2077CrossRefGoogle Scholar
  43. Dupin M, Halliday I, Care CM, Munn LL (2008) Lattice Boltzmann modeling of blood cell dynamics. Int J Comput Fluid Dyn 22:481–492CrossRefGoogle Scholar
  44. Dupire J, Socol M, Viallat A (2012) Full dynamics of a red blood cell in shear flow. Proc Natl Acad Sci USA 109:20808–20813CrossRefGoogle Scholar
  45. Eckstein EC, Belgacem F (1991) Model of platelet transport in flowing blood with drift and diffusion terms. Biophys J 60:53–69CrossRefGoogle Scholar
  46. Fai TG, Griffith BE, Mori Y, Peskin CS (2013) Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers i: numerical method and results. SIAM J Sci Comput 35:B1132–B1161CrossRefGoogle Scholar
  47. Fåhræus R, Lindqvist T (1931) The viscosity of the blood in narrow capillary tubes. Am J Physiol 96:562–568Google Scholar
  48. Fedosov DA, Caswell B, Karniadakis GE (2010) A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J 98:2215–2225CrossRefGoogle Scholar
  49. 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 USA 108:35–39CrossRefGoogle Scholar
  50. Fedosov DA, Lei H, Caswell B, Suresh S, Karniadakis GE (2011b) Multiscale modeling of red blood cell mechanics and blood flow in malaria. PLoS Comput Biol 7:e1002270CrossRefGoogle Scholar
  51. Fedosov DA, Pan WX, Caswell B, Gompper G, Karniadakis GE (2011c) Predicting human blood viscosity in silico. Proc Natl Acad Sci USA 108:11772–11777CrossRefGoogle Scholar
  52. Fedosov DA, Fornleitner J, Gompper G (2012) Margination of white blood cells in microcapillary flow. Phys Rev Lett 108:028104CrossRefGoogle Scholar
  53. Fedosov DA, Peltomäki M, Gompper G (2014a) Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft matter 10:4258–4267CrossRefGoogle Scholar
  54. Fedosov DA, Dao M, Karniadakis GE, Suresh S (2014b) Computational biorheology of human blood flow in health and disease. Ann Biomed Eng 42:368–387CrossRefGoogle Scholar
  55. Fischer TM, Stohr-Lissen M, Schmid-Schonbein H (1978) The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202:894–896CrossRefGoogle Scholar
  56. Freund JB (2007) Leukocyte margination in a model microvessel. Phys Fluids 19:023301CrossRefGoogle Scholar
  57. Freund JB (2014) Numerical simulation of flowing blood cells. Ann Rev Fluid Mech 46:67–95CrossRefGoogle Scholar
  58. Fung YC (1993) Biomechanics: Mechanical properties of living tissues, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  59. Gross M, Krüger T, Varnik F (2014) Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects. Soft Matter 10:4360–4372CrossRefGoogle Scholar
  60. Hanasaki I, Walther JH, Kawano S, Koumoutsakos P (2010) Coarse-grained molecular dynamics simulations of shear-induced instabilities of lipid bilayer membranes in water. Phys Rev E 82:051602CrossRefGoogle Scholar
  61. Hao W, Xu Z, Liu C, Lin G (2015) A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. J Comput Phys 280:345–362CrossRefGoogle Scholar
  62. Hochmuth R, Worthy P, Evans E (1979) Red cell extensional recovery and the determination of membrane viscosity. Biophy J 26:101–114CrossRefGoogle Scholar
  63. Hosseini SM, Feng JJ (2012) How malaria parasites reduce the deformability of infected RBC. Biophy J 103:1–10CrossRefGoogle Scholar
  64. Imai Y, Nakaaki K, Kondo H, Ishikawa T, Lim CT, Yamaguchi T (2010) Modeling of hemodynamics arising from malaria infection. J Biomech 43:1386–1393CrossRefGoogle Scholar
  65. Imai Y, Kondo H, Ishikawa T, Lim CT, Yamaguchi T (2011) Margination of red blood cells infected by plasmodium falciparum in a microvessel. J Biomech 44:1553–1558CrossRefGoogle Scholar
  66. Kantsler V, Steinberg V (2005) Orientation and dynamics of a vesicle in tank-treading motion in shear flow. Phys Rev Lett 95:258101CrossRefGoogle Scholar
  67. Kantsler V, Steinberg V (2006) Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. Phys Rev Lett 96:036001CrossRefGoogle Scholar
  68. Kaul DK, Xue H (1991) Rate of deoxygenation and rheologic behavior of blood in sickle cell anemia. Blood 77:1353–1361Google Scholar
  69. Keller SR, Skalak R (1982) The algorithm is based on an idealized ellipsoidal model of the tank-treading cell. J Fluid Mech 120:27–47CrossRefGoogle Scholar
  70. Kotsalis EM, Hanasaki I, Walther JH, Koumoutsakos P (2010) Non-periodic Molecular Dynamics simulations of coarse grained lipid bilayer in water. Comput Math Appl 59:2370–2373CrossRefGoogle Scholar
  71. Kraus M, Wintz W, Seifert U, Lipowsky R (1996) Fluid vesicles in shear flow. Phys Rev Lett 77:3685CrossRefGoogle Scholar
  72. Kumar A, Graham MD (2012a) Accelerated boundary integral method for multiphase flow in non-periodic geometries. J Comput Phys 231:6682–6713CrossRefGoogle Scholar
  73. Kumar A, Graham MD (2012b) Mechanism of margination in confined flows of blood and other multicomponent suspensions. Phys Rev Lett 109:108102CrossRefGoogle Scholar
  74. Lac E, Barthes-Biesel D, Pelekasis N, Tsamopoulos J (2004) Spherical capsules in three-dimensional unbounded stokes flows: effect of the membrane constitutive law and onset of buckling. J Fluid Mech 516:303–334CrossRefGoogle Scholar
  75. Lehoux S, Castier Y, Tedgui A (2006) Molecular mechanisms of the vascular responses to haemodynamic forces. J Intern Med 259:381–392CrossRefGoogle Scholar
  76. Lei H, Karniadakis G (2013) Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations. Proc Natl Acad Sci USA 110:11326–11330CrossRefGoogle Scholar
  77. Lei H, Karniadakis GE (2012) Quantifying the rheological and hemodynamic characteristics of sickle cell anemia. Biophys J 102:185–194CrossRefGoogle Scholar
  78. Li H, Lykotrafitis G (2011) A coarse-grain molecular dynamics model for sickle hemoglobin fibers. J Mech Behav Biomed Mater 4:162–173CrossRefGoogle Scholar
  79. Li H, Ha V, Lykotrafitis G (2012a) Modeling sickle hemoglobin fibers as one chain of coarse-grained particles. J Biomech 45:1947–1951CrossRefGoogle Scholar
  80. Li H, Lykotrafitis G (2012b) Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane. Biophys J 102:75–84CrossRefGoogle Scholar
  81. Li H, Lykotrafitis G (2014a) Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network. Biophys J 107:642–653CrossRefGoogle Scholar
  82. Li J, Dao M, Lim CT, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 88:3707–3719CrossRefGoogle Scholar
  83. Li J, Lykotrafitis G, Dao M, Suresh S (2007) Cytoskeletal dynamics of human erythrocyte. Proc Natl Acad Sci USA 104:4937–4942CrossRefGoogle Scholar
  84. Li XJ, Pivkin IV, Liang HJ, Karniadakis GE (2009) Shape transformations of membrane vesicles from amphiphilic triblock copolymers: a dissipative particle dynamics simulation study. Macromolecules 42:3195–3200CrossRefGoogle Scholar
  85. Li XJ, Caswell B, Karniadakis GE (2012c) Effect of chain chirality on the self-assembly of sickle hemoglobin. Biophys J 103:1130–1140CrossRefGoogle Scholar
  86. Li XJ, Popel AS, Karniadakis GE (2012d) Blood-plasma separation in y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study. Phys Biol 9:026010CrossRefGoogle Scholar
  87. Li XJ (2013a) Shape transformations of bilayer vesicles from amphiphilic block copolymers: a dissipative particle dynamics simulation study. Soft Matter 9:11663–11670CrossRefGoogle Scholar
  88. Li XJ, Vlahovska PV, Karniadakis GE (2013b) Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter 9:28–37CrossRefGoogle Scholar
  89. Li XJ, Peng ZL, Lei H, Dao M, Karniadakis GE (2014b) Probing red blood cell mechanics, rheology and dynamics with a two-component multiscale model. Phil Trans R Soc A 372:20130389CrossRefGoogle Scholar
  90. Li XJ, Tang Y-H, Liang HJ, Karniadakis GE (2014c) Large-scale dissipative particle dynamics simulations of self-assembled amphiphilic systems. Chem Commun 50:8306–8308CrossRefGoogle Scholar
  91. Lipowsky R (1991) The conformation of membranes. Nature 349:475–481CrossRefGoogle Scholar
  92. Liu SC, Derick LH, Zhai S, Palek J (1991) Uncoupling of the spectrin-based skeleton from the lipid bilayer in sickled red cells. Science 252:574–576CrossRefGoogle Scholar
  93. McWhirter JL, Noguchi H, Gompper G (2009) Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc Natl Acad Sci USA 106:6039–6043CrossRefGoogle Scholar
  94. McWhirter JL, Noguchi H, Gompper G (2011) Deformation and clustering of red blood cells in microcapillary flows. Soft Matter 7:10967–10977CrossRefGoogle Scholar
  95. Merrill EW, Gilliland ER, Cokelet G, Shin H, Britten A, Wells RE (1963) Rheology of human blood near and at zero flow. Biophys J 3:199–213CrossRefGoogle Scholar
  96. Misbah C (2006) Vacillating breathing and tumbling of vesicles under shear flow. Phys Rev Lett 96:028104CrossRefGoogle Scholar
  97. Mujumdar A, Beris AN, Metzner AB (2002) Transient phenomena in thixotropic systems. J Nonnewton Fluid Mech 102:157–178CrossRefGoogle Scholar
  98. Narsimhan V, Zhao H, Shaqfeh ES (2013) Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded couette flow at zero reynolds number. Phys Fluids 25:061901CrossRefGoogle Scholar
  99. Noguchi H, Gompper G (2004) Fluid vesicles with viscous membranes in shear flow. Phys Rev Lett 93:258102CrossRefGoogle Scholar
  100. Noguchi H, Gompper G (2005a) Dynamics of fluid vesicles in shear flow: Effect of membrane viscosity and thermal fluctuations. Phys Rev E 72:011901CrossRefGoogle Scholar
  101. Noguchi H, Gompper G (2005b) Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc Natl Acad Sci USA 102:14159–14164CrossRefGoogle Scholar
  102. Noguchi H, Gompper G (2007) Swinging and tumbling of fluid vesicles in shear flow. Phys Rev Lett 98:128103CrossRefGoogle Scholar
  103. Pan TW, Wang T (2009) Dynamical simulation of red blood cell rheology in microvessels. Int J Numer Anal Mod 6:455–473Google Scholar
  104. Pan W, Caswell B, Karniadakis GE (2010) A low-dimensional model for the red blood cell. Soft Matter 6:4366–4376CrossRefGoogle Scholar
  105. Park YK, Diez-Silva M, Popescu G, Lykotrafitis G, Choi W, Feld MS, Suresh S (2008) Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum. Proc Natl Acad Sci USA 105:13730–13735CrossRefGoogle Scholar
  106. Park YK, Best CA, Auth T, Gov NS, Safran SA, Popescu G, Suresh S, Feld MS (2010) Metabolic remodeling of the human red blood cell membrane. Proc Natl Acad Sci USA 107:1289–1294CrossRefGoogle Scholar
  107. Peskin CS (2002) The immersed boundary method. Acta numerica 11:479–517CrossRefGoogle Scholar
  108. Peng Z, Asaro RJ, Zhu Q (2010) Multiscale simulation of erythrocyte membranes. Phys Rev E 81:031904CrossRefGoogle Scholar
  109. Peng Z, Li XJ, Pivkin IV, Dao M, Karniadakis GE, Suresh S (2013) Lipid–bilayer and cytoskeletal interactions in a red blood cell. Proc Natl Acad Sci USA 110:13356–13361CrossRefGoogle Scholar
  110. Peng Z, Mashayekh A, Zhu Q (2014) Erythrocyte responses in low-shear-rate flows: effects of non-biconcave stress-free state in the cytoskeleton. J Fluid Mech 742:96–118CrossRefGoogle Scholar
  111. Peng Z, Salehyar S, Zhu Q (2015) Stability of the tank treading modes of erythrocytes and its dependence on cytoskeleton reference states. journal of fluid mechanics. J Fluid Mech 771:449–467CrossRefGoogle Scholar
  112. Pietzsch J (2004) Mind the membrane. Horizon Symposia: Living Frontier. Nature Publishing GroupGoogle Scholar
  113. Pivkin IV, Karniadakis GE (2008) Accurate coarse-grained modeling of red blood cells. Phys Rev Lett 101:118105CrossRefGoogle Scholar
  114. Pozrikidis C (2003) Modeling and simulation of capsules and biological cells. CRC PressGoogle Scholar
  115. Puig-de-Morales-Marinkovic M, Turner KT, Butler JP, Fredberg JJ, Suresh S (2007) Viscoelasticity of the human red blood cell. Am J Physiol Cell Physiol 293:C597–C605CrossRefGoogle Scholar
  116. Qin Z, Durand LG, Allard L, Cloutier G (1998) Effects of a sudden flow reduction on red blood cell rouleau formation and orientation using rf backscattered power. Ultrasound Med Biol 24:503–511CrossRefGoogle Scholar
  117. Quinn DJ, Pivkin IV, Wong SK, Chiam KH, Dao M, Karniadakis GE, Suresh S (2011) Combined simulation and experimental study of large deformation of red blood cells in microfluidic systems. Ann Biomed Eng 39:1041–1050CrossRefGoogle Scholar
  118. Ramanujan S, Pozrikidis C (1998) Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J Fluid Mech 361:117–143CrossRefGoogle Scholar
  119. Reasor Jr DA, Mehrabadi M, Ku DN, Aidun CK (2013) Determination of critical parameters in platelet margination. Ann Biomed Eng 41:238–249CrossRefGoogle Scholar
  120. Rehage H, Husmann M, Walter A (2002) From two-dimensional model networks to microcapsules. Rheol Acta 41:292–306CrossRefGoogle Scholar
  121. Ryman BE, Tyrrell DA (1979) Liposomes—methodology and applications. Front Biol 48:549–74Google Scholar
  122. Samsel RW, Perelson AS (1982) Kinetics of rouleau formation. i. a mass action approach with geometric features. Biophys J 37:493–514CrossRefGoogle Scholar
  123. Secomb T, Styp-Rekowska B, Pries AR (2007) Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann Biomed Eng 35:755CrossRefGoogle Scholar
  124. Shi L, Pan TW, Glowinski R (2014) Three-dimensional numerical simulation of red blood cell motion in poiseuille flows. Int J Numer Meth Fl 76(7):397–415CrossRefGoogle Scholar
  125. Singh RK, Li X, Sarkar K (2014) Lateral migration of a capsule in plane shear near a wall. J Fluid Mech 739:421–443CrossRefGoogle Scholar
  126. Skalak R, Tozeren A, Zarda R, Chien S (1973) Strain energy function of red blood cell membranes. Biophys J 13:245–264CrossRefGoogle Scholar
  127. Skalak R, Keller SR, Secomb TW (1981) Mechanics of blood flow. J Biomech Eng 103:102–115CrossRefGoogle Scholar
  128. Spann AP, Zhao H, Shaqfeh ES (2014) Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow. Phys Fluids 26:031902CrossRefGoogle Scholar
  129. Sui Y, Low H, Chew Y, Roy P (2008) Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow. Phys Rev E 77:016310CrossRefGoogle Scholar
  130. Sun C, Migliorini C, Munn LL (2003) Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. Biophys J 85:208–222CrossRefGoogle Scholar
  131. Tilles AW, Eckstein EC (1987) The near-wall excess of platelet-sized particles in blood flow: its dependence on hematocrit and wall shear rate. Microvasc Res 33:211–223CrossRefGoogle Scholar
  132. Tokarev A, Butylin A, Ermakova E, Shnol E, Panasenko G, Ataullakhanov F (2011) Finite platelet size could be responsible for platelet margination effect. Biophys J 101:1835–1843CrossRefGoogle Scholar
  133. Vahidkhah K, Bagchi P (2015) Microparticle shape effects on margination, near-wall dynamics and adhesion in a three-dimensional simulation of red blood cell suspension. Soft Matter 11:2097–2109CrossRefGoogle Scholar
  134. Vahidkhah K, Diamond SL, Bagchi P (2014) Platelet dynamics in three-dimensional simulation of whole blood. Biophys J 106:2529–2540CrossRefGoogle Scholar
  135. Veerapaneni SK, Rahimian A, Biros G, Zorin D (2011a) A fast algorithm for simulating vesicle flows in three dimensions. J Comput Phys 230:5610–5634CrossRefGoogle Scholar
  136. Veerapaneni SK, Young YN, Vlahovska PM, Blawzdziewicz J (2011b) Dynamics of a compound vesicle in shear flow. Phys Rev Lett 106:158103CrossRefGoogle Scholar
  137. Vitkova V, Mader MA, Polack B, Misbah C, Podgorski T (2008) Micro-macro link in rheology of erythrocyte and vesicle suspensions. Biophys J 95:L33–L35CrossRefGoogle Scholar
  138. Winkler RG, Fedosov DA, Gompper G (2014) Dynamical and rheological properties of soft colloid suspensions. Curr Opin Colloid Interface Sci 19:594–610CrossRefGoogle Scholar
  139. Woldhuis B, Tangelder G, Slaaf DW, Reneman RS (1992) Concentration profile of blood platelets differs in arterioles and venules. Am J Physiol Heart Circ Physiol 262:H1217–H1223Google Scholar
  140. Wu TH, Feng JJ (2013) Simulation of malaria-infected red blood cells in microfluidic channels: passage and blockage. Biomicrofluidics 7:044115CrossRefGoogle Scholar
  141. Yazdani A, Bagchi P (2012) Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method. Phys Rev E 85:056308CrossRefGoogle Scholar
  142. Yazdani A, Bagchi P (2013) Influence of membrane viscosity on capsule dynamics in shear flow. J Fluid Mech 718:569–595CrossRefGoogle Scholar
  143. Yazdani AZ, Bagchi P (2011) Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow. Phys Rev E 84:026314CrossRefGoogle Scholar
  144. Ye T, Phan-Thien N, Khoo BC, Lim CT (2014) Numerical modelling of a healthy/malaria-infected erythrocyte in shear flow using dissipative particle dynamics method. J Appl Phys 115 :224701CrossRefGoogle Scholar
  145. Zhao H, Isfahani AH, Olson LN, Freund JB (2010) A spectral boundary integral method for flowing blood cells. J Comput Phys 229:3726–3744CrossRefGoogle Scholar
  146. Zhao H, Shaqfeh ES (2011a) The dynamics of a vesicle in simple shear flow. J Fluid Mech 674:578–604CrossRefGoogle Scholar
  147. Zhao H, Shaqfeh ES (2011b) Shear-induced platelet margination in a microchannel. Phys Rev E 83:061924CrossRefGoogle Scholar
  148. Zhao H, Shaqfeh ES (2013) The dynamics of a non-dilute vesicle suspension in a simple shear flow. J Fluid Mech 725:709–731CrossRefGoogle Scholar
  149. Zhao H, Spann AP, Shaqfeh ES (2011) The dynamics of a vesicle in a wall-bound shear flow. Phys Fluids 23:121901CrossRefGoogle Scholar
  150. Ou-Yang Z-C, Helfrich W (1989) Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys Rev A 39:5280CrossRefGoogle Scholar
  151. Zhu L, Brandt L (2014) The motion of a deforming capsule through a corner. arXiv preprint arXiv:14090155
  152. Zupancic Valant A, Ziberna L, Papaharilaou Y, Anayiotos A, Georgiou G (2011) The influence of temperature on rheological properties of blood mixtures with different volume expander—implications in numerical arterial hemodynamics simulations. Rheol Acta 50:389–402CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Alireza Yazdani
    • 1
  • Xuejin Li
    • 1
  • George Em Karniadakis
    • 1
    Email author
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Personalised recommendations