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Rheological characterization of cellular blood in shear

Published online by Cambridge University Press:  10 June 2013

D. A. Reasor Jr
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30322, USA
J. R. Clausen
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30322, USA
C. K. Aidun*
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30322, USA Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA 30322, USA
*
Email address for correspondence: cyrus.aidun@me.gatech.edu

Abstract

A hybrid lattice-Boltzmann spectrin-link (LB–SL) method is used to simulate dense suspensions of red blood cells (RBCs) for investigating rheological properties of blood. RBC membranes are modelled using a coarse-grained SL method and are filled with a viscous Newtonian fluid solution with viscosity five times that of the suspending fluid. Relative viscosities, normal stress differences, and particle pressures are reported for a range of capillary numbers at a physiologically realistic haematocrit value of approximately 42.5 %. Viscosity shear thinning is demonstrated for shear rates ranging from 14 to 440  s−1 and is shown to be affected by the orientation and bending modulus of RBCs. The particle-phase pressure undergoes a change in sign from positive to negative as the shear rate is increased. The particle-phase normal stress tensor values show that there is a transition from compressive to tensile states in the flow direction as the shear rate is increased. The normal stress differences are notably different from those recently reported for deformable capsule suspensions using a similar methodology, which suggests that the bending stiffness and the biconcave shape of RBCs affect the rheology of blood.

Type
Papers
Copyright
©2013 Cambridge University Press 

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References

Aidun, C. K. & Clausen, J. R. 2010 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439472.Google Scholar
Aidun, C. K. & Lu, Y. 1995 Lattice Boltzmann simulation of solid particles suspended in fluid. J. Statist. Phys. 81 (1–2), 4961.Google Scholar
Aidun, C. K., Lu, Y. & Ding, E.-J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287311.CrossRefGoogle Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545570.Google Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (3), 511525.Google Scholar
Bishop, N. W. M. & Sherratt, F. 2000 Finite Element Based Fatique Calculations. NAFEMS: The International Association for the Engineering Analysis Community.CrossRefGoogle Scholar
Bustamante, C., Bryant, Z. & Smith, S. B. 2003 Ten years of tension: single-molecule DNA mechanics. Nature 421, 423427.Google Scholar
Casson, N. 1959 A flow equation for pigment oil suspensions of the printing ink type. In Rheology of Dispersed Systems (ed. Mill, C. C.), pp. 84102. Pergamon.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329364.CrossRefGoogle Scholar
Chien, S. 1970 Shear dependence of effective cell volume as a determinant of blood viscosity. Science 977978.Google Scholar
Clausen, J. R. 2010 The effect of particle deformation on the rheology of noncollodial suspensions. PhD thesis, Georgia Institute of Technology.Google Scholar
Clausen, J. R. & Aidun, C. K. 2010 Capsule dynamics and rheology in shear flow: particle pressure and normal stress. Phys. Fluids 22, 123302.CrossRefGoogle Scholar
Clausen, J. R., Reasor, D. A. & Aidun, C. K. 2010 Parallel performance of a Lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture. Comput. Phys. Commun. 181, 10131020.Google Scholar
Clausen, J. R., Reasor, D. A. & Aidun, C. K. 2011 The rheology and microstructure of concentrated noncolloidal suspensions of deformable capsules. J. Fluid Mech. 685, 202234.Google Scholar
Cokelet, G. R. 1980 Rheology and hemodynamics. Annu. Rev. Physiol. 42, 311324.Google Scholar
Cokelet, G. R. & Meiselman, H. J. 1968 Rheological comparison of hemoglobiin solutions and erythocyte suspensions. Science 162 (3850), 275277.CrossRefGoogle Scholar
Dao, M., Li, J. & Suresh, S. 2006 Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mater. Sci. Engng C 26, 12321244.Google Scholar
Deboeuf, A., Gauthier, G., Martin, G., Yurkovetsky, J. & Morris, J. F. 2009 Particle pressure in a sheared suspension: a bridge from osmosis to granular dilatancy. Phys. Rev. Lett. 102 (10), 108301.Google Scholar
Dupin, M. M., Halliday, I., Care, C. M., Alboul, L. & Munn, L. L. 2007 Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys. Rev. E 75, 066707.CrossRefGoogle ScholarPubMed
Fedosov, D. A., Caswell, B. & Karniadakis, G. E. 2009 Coarse-grained red blood cell model with accurate mechanical properties, rheology and dynamics. In 31st Intl Conference of IEEE EMBS, pp. 42664269. Minneapolis.Google Scholar
Fedosov, D. A., Caswell, B. & Karniadakis, G. E. 2010a A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys. J. 98, 22152225.CrossRefGoogle ScholarPubMed
Fedosov, D. A., Caswell, B. & Karniadakis, G. E. 2010b Systematic coarse-graining of spectrin-level red blood cell models. Comput. Meth. Appl. Mech. Engng 199, 19371948.CrossRefGoogle ScholarPubMed
Fedosov, D. A., Caswell, B., Popel, A. S. & Karniadakis, G. E. 2010c Blood flow and cell-free layer in microvessels. Microcirculation 17, 615628.Google Scholar
Fedosov, D. A., Pan, W., Caswell, B., Gompper, G. & Karniadakis, G. E. 2011 Predicting human blood viscosity in silico. Proc. Natl Acad. Sci. 108 (29), 1177211777.Google Scholar
Forsyth, A. M., Wan, J., Owrutsky, P. D., Abkarian, M. & Stone, H. A. 2011 Multiscale approach to link red blood cell dynamics, shear viscosity, and ATP release. Proc. Natl Acad. Sci. 108 (27), 1098610991.Google Scholar
Fung, Y. C. 1993 Biomechanics: Mechanical Properties of Living Tissues, 2nd edn. Springer.Google Scholar
Fung, Y. C. 1996 Biomechanics: Circulation, 2nd edn. Springer.Google Scholar
Harkness, J. & Whittington, R. 1970 Blood-plasma viscosity: an approximate temperature-invariant arising from generalized concepts. Biorheology 6 (3), 169187.CrossRefGoogle ScholarPubMed
Haynes, R. H. 1961 The rheology of blood. Trans. Soc. Rheol. 5, 85101.Google Scholar
Hochmuth, R. M. & Waugh, R. E. 1987 Erythroctye membrane elasticity and viscosity. Annu. Rev. Physiol. 49, 209219.Google Scholar
Hwang, W. & Waugh, R. 1997 Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. Biophys. J. 72, 26692678.Google Scholar
Junk, M., Klar, A. & Luo, L.-S. 2005 Asymptotic analysis of the lattice Boltzmann equation. J. Comput. Phys. 210 (2), 676704.Google Scholar
Junk, M. & Yong, W.-A. 2003 Rigorous Navier–Stokes limit of the lattice Boltzmann equation. Asymptot. Anal. 35 (2), 165185.Google Scholar
Kennedy, M. R., Pozrikidis, C. & Skalak, R. 1994 Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Comput. Fluids 23 (2), 251278.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. J. Rheol. 3 (1), 137152.Google Scholar
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C 5, 19211928.Google Scholar
Li, J., Dao, M., Lim, C. T. & Suresh, S. 2005 Spectrin-level mdeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys. J. 88, 37073719.Google Scholar
MacMeccan, R. M. 2007 Mechanistic effects of erythrocytes on platelet deposition in coronary thrombosis. PhD thesis, Georgia Institute of Technology.Google Scholar
MacMeccan, R. M., Clausen, J. R., Neitzel, G. P. & Aidun, C. K. 2009 Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method. J. Fluid Mech. 618, 1339.Google Scholar
Madi, A., Hecht, I., Bransburg-Zabary, S., Merbl, Y., Pick, A., Zucker-Toledano, M., Quintana, F. J., Tauber, A. I., Cohen, I. R. & Ben-Jacob, E. 2009 Organization of the autoantibody repertoire in healthy newborns and adults revealed by system level informatics of antigen microarray data. Proc. Natl Acad. Sci. 106 (34), 1448414489.Google Scholar
Marko, J. F. & Siggia, E. D. 1995 Stretching DNA. Macromolecules 28, 87598770.Google Scholar
McWhirter, J. L., Noguchi, H. & Gompper, G. 2009 Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc. Natl Acad. Sci. 106 (15), 60396043.Google Scholar
Merrill, E. W. 1969 Rheology of blood. Phys. Rev. 49 (4), 863888.Google Scholar
Merrill, E., Cokelet, G., Britten, A. & Wells, R. 1963 Non-Newtonian rheology of human blood-effect of fibrinogen deduced by ‘subtraction’. Circulat. Res. 13 (1), 4855.Google Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43 (5), 12131237.Google Scholar
Morris, J. F. & Brady, J. F. 1998 Pressure-driven flow of a suspension: buoyancy effects. Intl J. Multiphase Flow 24 (1), 105130.Google Scholar
Nott, P. R. & Brady, J. F. 1994 Pressure-driven suspension flow: simulation and theory. J. Fluid Mech. 275, 157199.CrossRefGoogle Scholar
Pivkin, I. V. & Karniadakis, G. E. 2008 Accurate coarse-grained modeling of red blood cells. Phys. Rev. Lett. 101, 118105.Google Scholar
Popel, A. S. & Johnson, P. C. 2005 Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37, 4369.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 2003 Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Engng 31, 11941205.Google Scholar
Pries, A. R., Neuhaus, D. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Physiol. Heart Circ. Physiol. 263, H1770H1778.Google Scholar
Reasor, D. A. 2011 Numerical simulation of cellular blood flow. PhD thesis, Georgia Institute of Technology.Google Scholar
Reasor, D. A., Clausen, J. R. & Aidun, C. K. 2012 Coupling the lattice-Boltzmann and spectrin-link methods for the direct numerical simulation of cellular blood flow. Intl J. Numer. Meth. Fluids 68, 767781.Google Scholar
Reasor, D. A., Mehrabadi, M., Ku, D. N. & Aidun, C. K. 2013 Determination of critical parameters in platelet margination. Ann. Biomed. Engng 41 (2), 238249.Google Scholar
Schmid-Schönbein, H. 1969 Fluid drop-like transition of erythrocytes under shear. Science 165, 288291.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.Google Scholar
Sugihara-Seki, M. & Fu, B. M. 2005 Blood flow and permeability in microvessels. Fluid Dyn. Res. 37, 82132.Google Scholar
Tao, R. & Huang, K. 2011 Reducing blood viscosity with magnetic fields. Phys. Rev. E 84, 011905.Google Scholar
Tsubota, K. & Wada, S. 2010 Elastic force of red blood cell membrane during tank-treading motion: consideration of the membrane’s natural state. Intl J. Mech. Sci. 52, 356364.Google Scholar
Wagner, A. J. & Pagonabarraga, I. 2002 Lees–Edwards boundary conditions for Lattice Boltzmann. J. Statist. Phys. 107 (1), 521537.CrossRefGoogle Scholar
Wells, R. E. 1961 The variability of blood viscosity. Am. J. Med. 31 (4), 505509.Google Scholar
Wu, J. & Aidun, C. K. 2009 Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force. Intl J. Numer. Meth. Fluids 62 (7), 765783.Google Scholar
Yazdani, A. Z. K. & 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, 026314.Google Scholar