A review of numerical methods for red blood cell flow simulation

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 18, Issue 2, 2015, Pages 130-140

  Ju, Meongkeun ^a   Ye, Swe Soe ^a   Namgung, Bumseok ^a   Cho, Seungkwan ^a   Low, Hong Tong ^a   Leo, Hwa Liang ^a   Kim, Sangho ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

blood rheology; haemodynamics; RBC aggregation modelling; RBC deformation modelling

Indexed keywords

CELLS; DEFORMATION; HEMODYNAMICS; NUMERICAL METHODS; TURBULENT FLOW;

BLOOD RHEOLOGY; BOUNDARY INTEGRAL METHODS; FLUID MODELLING; HAEMODYNAMICS; IMMERSED BOUNDARY METHODS; MULTIPHASE FLUIDS; SIMULATION TECHNIQUE; STRUCTURE INTERACTIONS;

BLOOD;

ALGORITHM; ARTICLE; BIOMECHANICS; BIOMEDICAL ENGINEERING; BLOOD RHEOLOGY; COMPUTER SIMULATION; ERYTHROCYTE AGGREGATION; ERYTHROCYTE KINETICS; EXPERIMENTAL MODEL; HEMODYNAMICS; MATHEMATICAL MODEL; MEMBRANE MODEL; MICROCIRCULATION; THERMAL ANALYSIS; VISCOELASTICITY; BIOLOGICAL MODEL; CYTOLOGY; ERYTHROCYTE; ERYTHROCYTE DEFORMABILITY; ERYTHROCYTE MEMBRANE; HUMAN; MATHEMATICAL COMPUTING; PHYSIOLOGY;

COMPUTER SIMULATION; ERYTHROCYTE DEFORMABILITY; ERYTHROCYTE MEMBRANE; ERYTHROCYTES; HEMORHEOLOGY; HUMANS; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 84908053478     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255842.2013.783574     Document Type: Article

References (74)

1. ArmstrongJK, MeiselmanHJ, FisherTC. 1999. Evidence against macromolecular “bridging” as the mechanism of red blood cell aggregation induced by nonionic polymers. Biorheology. 36(5–6):433–437.
2. BagchiP. 2007. Mesoscale simulation of blood flow in small vessels. Biophys J. 92(6):1858–1877.
3. BagchiP, JohnsonPC, PopelAS. 2005. Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J Biomech Eng-Trans ASME. 127(7):1070–1080.
4. Barthes-BieselD, DiazA, DheninE. 2002. Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J Fluid Mech. 460:211–222.
5. BaumlerH, DonathE, KrabiA, KnippelW, BuddeA, KiesewetterH. 1996. Electrophoresis of human red blood cells and platelets. Evidence for depletion of dextran. Biorheology. 33(4–5):333–351.
6. BaumlerH, NeuB, DonathE, KiesewetterH. 1999. Basic phenomena of red blood cell rouleaux formation. Biorheology. 36(5–6):439–442.
7. BeardDA, BassingthwaighteJB. 2001. Modeling advection and diffusion of oxygen in complex vascular networks. Ann Biomed Eng. 29(4):298–310.
8. Ben AmiR, BarshteinG, ZeltserD, GoldbergY, ShapiraI, RothA, KerenG, MillerH, ProchorovV, EldorA, et al., 2001. Parameters of red blood cell aggregation as correlates of the inflammatory state. Am J Physiol-Heart C. 280(5):H1982–H1988.
9. BrochardF, LennonJF. 1975. Frequency spectrum of flicker phenomenon in erythrocytes. J Phys-Paris. 36(11):1035–1047.
10. BrooksDE. 1973. Effect of neutral polymers on electrokinetic potential of cells and other charged-particles. IV. Electrostatic effects in dextran-mediated cellular interactions. J Colloid Interf Sci. 43(3):714–726.
11. BrowiczT. 1890. Further observation of motion phenomena on red blood cells in pathological states. Zbl med Wissen. 28:625–627.
12. ChenXW, JaronD, BarbeeKA, BuerkDG. 2006. The influence of radial RBC distribution, blood velocity profiles, and glycocalyx on coupled NO/O-2 transport. J Appl Physiol. 100(2):482–492.
13. ChienS, JanKM. 1973. Ultrastructural basis of mechanism of rouleaux formation. Microvasc Res. 5(2):155–166.
14. ChienS, SimchonS, AbbottRE, JanKM. 1977. Surface adsorption of dextrans on human red-cell membrane. J Colloid Interf Sci. 62(3):461–470.
15. ChungB, JohnsonPC, PopelAS. 2007. Application of Chimera grid to modelling cell motion and aggregation in a narrow tube. Int J Numer Meth Fl. 53(1):105–128.
16. DaoM, LiJ, SureshS. 2006. Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mat Sci Eng C-Bio S. 26(8):1232–1244.
17. DemboM, TorneyDC, SaxmanK, HammerD. 1988. The reaction-limited kinetics of membrane-to-surface adhesion and detachment. P R Soc B-Bio. 234(1274):55–83.
18. DeonikarP, KavdiaM. 2010. A computational model for nitric oxide, nitrite and nitrate biotransport in the microcirculation: effect of reduced nitric oxide consumption by red blood cells and blood velocity. Microvasc Res. 80(3):464–476.
19. DischerDE, BoalDH, BoeySK. 1998. Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration. Biophys J. 75(3):1584–1597.
20. DupinMM, HallidayI, CareCM, AlboulL, MunnLL. 2007. Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys Rev E. 75(6):066707.
21. DzwinelW, BoryczkoK, YuenDA. 2003. A discrete-particle model of blood dynamics in capillary vessels. J Colloid Interf Sci. 258(1):163–173.
22. EggletonCD, PopelAS. 1998. Large deformation of red blood cell ghosts in a simple shear flow. Phys Fluids. 10(8):1834–1845.
23. EvansEA, SkalakR. 1980. Mechanics and thermodynamics of biomembranes. Boca Raton, FL: CRC Press.
24. FedosovAE. 2010. Multiscale modeling of blood flow and soft matter. USA: PhD. Brown.
25. FedosovDA, CaswellB, KarniadakisGE. 2010. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J. 98(10):2215–2225.
26. FrancoisM, ShyyW. 2003. Computations of drop dynamics with the immersed boundary method, part 2: drop impact and heat transfer. Numer Heat Tr B-Fund. 44(2):119–143.
27. FungYC. 1993. Biomechanics: mechanical properties of living tissues. 2nd ed. New York: Springer-Verlag.
28. HochmuthRM, MohandasN. 1972. Uniaxial loading of red-cell membrane. J Biomech. 5(5):501–509.
29. HoogerbruggePJ, KoelmanJMVA. 1992. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys Lett. 19(3):155–160.
30. JanoschekF, ToschiF, HartingJ. 2010. Simplified particulate model for coarse-grained hemodynamics simulations. Phys Rev E. 82(5):056710.
31. KimS, PopelAS, IntagliettaM, JohnsonPC. 2006. Effect of erythrocyte aggregation at normal human levels on functional capillary density in rat spinotrapezius muscle. Am J Physiol-Heart C. 290(3):H941–H947.
32. KounovNB, PetrovVG. 1999. Determination of erythrocyte aggregation. Math Biosci. 157(1–2):345–356.
33. LiJ, DaoM, LimCT, SureshS. 2005. Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J. 88(5):3707–3719.
34. LiuYL, ZhangL, WangXD, LiuWK. 2004. Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics. Int J Numer Meth Fl. 46(12):1237–1252.
35. MacMeccanRM, ClausenJR, NeitzelGP, AidunCK. 2009. Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method. J Fluid Mech. 618:13–39.
36. MaedaN. 1996. Erythrocyte rheology in microcirculation. Jpn J Physiol. 46(1):1–14.
37. MalevanetsA, KapralR. 1999. Mesoscopic model for solvent dynamics. J Chem Phys. 110(17):8605–8613.
38. MarkoJF, SiggiaED. 1995. Stretching DNA. Macromolecules. 28(26):8759–8770.
39. MchedlishviliG, MaedaN. 2001. Blood flow structure related to red cell flow: a determinant of blood fluidity in narrow microvessels. Jpn J Physiol. 51(1):19–30.
40. MelchionnaS. 2011. A model for red blood cells in simulations of large-scale blood flows. Macromol Theory Simul. 20(7):548–561.
41. MohandasN, ClarkMR, JacobsMS, ShohetSB. 1980. Analysis of factors regulating erythrocyte deformability. J Clin Invest. 66(3):563–573.
42. N'driNA, ShyyW, Tran-Soy-TayR. 2003. Computational modeling of cell adhesion and movement using a continuum-kinetics approach. Biophys J. 85(4):2273–2286.
43. NeuB, MeiselmanHJ. 2002. Depletion-mediated red blood cell aggregation in polymer solutions. Biophys J. 83(5):2482–2490.
44. NoguchiH, GompperG. 2005. Shape transitions of fluid vesicles and red blood cells in capillary flows. P Natl Acad Sci USA. 102(40):14159–14164.
45. OngPK, JainS, KimS. 2011. Temporal variations of the cell-free layer width may enhance NO bioavailability in small arterioles: effects of erythrocyte aggregation. Microvasc Res. 81(3):303–312.
46. PanWX, FedosovDA, CaswellB, KarniadakisGE. 2011. Predicting dynamics and rheology of blood flow: a comparative study of multiscale and low-dimensional models of red blood cells. Microvasc Res. 82(2):163–170.
47. ParpartAK, HoffmanJF. 1956. Flicker in erythrocytes – Vibratory movements in the cytoplasm. J Cell Compar Physl. 47(2):295–303.
48. PeskinCS. 1977. Numerical-analysis of blood-flow in heart. J Comput Phys. 25(3):220–252.
49. PivkinIV, KarniadakisGE. 2008. Accurate coarse-grained modeling of red blood cells. Phys Rev Lett. 101(11):118105.
50. PopelAS, JohnsonPC. 2005. Microcirculation and hemorheology. Ann Rev Fluid Mech. 37:43–69.
51. PopescuG, ParkY, DasariRR, BadizadeganK, FeldMS. 2007. Coherence properties of red blood cell membrane motions. Phys Rev E. 76(3):031902.
52. PozrikidisC. 1992. Boundary integral and singularity methods for linearized viscous flow. Cambridge: Cambridge University Press.
53. PozrikidisC. 2001. Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J Fluid Mech. 440:269–291.
54. PozrikidisC. 2003. Numerical simulation of the flow-induced deformation of red blood cells. Ann Biomed Eng. 31(10):1194–1205.
55. PriesAR, NeuhausD, GaehtgensP. 1992. Blood-viscosity in tube flow - Dependence on diameter and hematocrit. Am J Physiol. 263(6):H1770–H1778.
56. Puig-De-Morales-MarinkovicM, TurnerKT, ButlerJP, FredbergJJ, SureshS. 2007. Viscoelasticity of the human red blood cell. Am J Physiol-Cell Ph. 293(2):C597–C605.
57. RamanujanS, PozrikidisC. 1998. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J Fluid Mech. 361:117–143.
58. RamplingMW, MeiselmanHJ, NeuB, BaskurtOK. 2004. Influence of cell-specific factors on red blood cell aggregation. Biorheology. 41(2):91–112.
59. SecombTW, Styp-RekowskaB, PriesAR. 2007. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann Biomed Eng. 35(5):755–765.
60. StoltzJF, SinghM, RihaP. 1999. Hemorheology in practice. Amsterdam: IOS Press.
61. StreyH, PetersonM. 1995. Measurement of erythrocyte-membrane elasticity by flicker eigenmode decomposition. Biophys J. 69(2):478–488.
62. SuiY, ChewYT, RoyP, LowHT. 2007. A hybrid immersed-boundary and multi-block lattice Boltzmann method for simulating fluid and moving-boundaries interactions. Int J Numer Meth Fl. 53(11):1727–1754.
63. SvetinaS, ZiherlP. 2008. Morphology of small aggregates of red blood cells. Bioelectrochemistry. 73(2):84–91.
64. TryggvasonG, BunnerB, EsmaeeliA, JuricD, Al-RawahiN, TauberW, HanJ, NasS, JanYJ. 2001. A front-tracking method for the computations of multiphase flow. J Comput Phys. 169(2):708–759.
65. TsubotaK, WadaS, YamaguchiT. 2006a. Particle method for computer simulation of red blood cell motion in blood flow. Comput Meth Prog Bio. 83(2):139–146.
66. TsubotaK, WadaS, YamaguchiT. 2006b. Simulation study on effects of hematocrit on blood flow properties using particle method. J Biomech Sci Eng. 1(1):159–170.
67. UdaykumarHS, KanHC, ShyyW, TranSonTayR. 1997. Multiphase dynamics in arbitrary geometries on fixed Cartesian grids. J Comput Phys. 137(2):366–405.
68. UlkerP, SatiL, Celik-OzenciC, MeiselmanHJ, BaskurtOK. 2009. Mechanical stimulation of nitric oxide synthesizing mechanisms in erythrocytes. Biorheology. 46(2):121–132.
69. ZhangJF, JohnsonPC, PopelAS. 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.
70. ZhangJF, JohnsonPC, PopelAS. 2008. Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. J Biomech. 41(1):47–55.
71. ZhangJF, JohnsonPC, PopelAS. 2009. Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc Res. 77(3):265–272.
72. ZhongcanOY, HelfrichW. 1989. Bending energy of vesicle membranes – General expressions for the 1st, 2nd, and 3rd variation of the shape energy and applications to spheres and cylinders. Phys Rev A. 39(10):5280–5288.
73. ZhuC. 1991. A thermodynamic and biomechanical theory of cell-adhesion.1. General formulism. J Theoret Biol. 150(1):27–50.
74. ZiherlP, SvetinaS. 2005. Nonaxisymmetric phospholipid vesicles: rackets, boomerangs, and starfish. Europhys Lett. 70(5):690–696.