Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-17T09:19:08.339Z Has data issue: false hasContentIssue false

Dynamics of a large population of red blood cells under shear flow

Published online by Cambridge University Press:  07 February 2019

C. Minetti
Affiliation:
Service de chimie physique EP, Université libre de Bruxelles, 50, avenue Frankin-Roosevelt, CP16/62, B-1050 Brussels, Belgium
V. Audemar
Affiliation:
Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
T. Podgorski
Affiliation:
Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
G. Coupier*
Affiliation:
Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
*
Email address for correspondence: [email protected]

Abstract

An exhaustive description of the dynamics under shear flow of a large number of red blood cells in a dilute regime is proposed, which highlights and takes into account the dispersion in cell properties within a given blood sample. Physiological suspending fluid viscosity is considered, a configuration surprisingly seldom considered in experimental studies, as well as a more viscous fluid that is a reference in the literature. Stable and unstable flipping motions well described by Jeffery orbits or modified Jeffery orbits are identified, as well as transitions to and from tank-treading motion in the more viscous suspending fluid case. Hysteresis loops upon shear rate increase or decrease are highlighted for the transitions between unstable and stable orbits as well as for the transition between flipping and tank-treading. We identify which of the characteristic parameters of motion and of the transition thresholds depend on flow stress only or also on suspending fluid viscosity.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abkarian, M., Faivre, M. & Viallat, A. 2007 Swinging of red blood cells under shear flow. Phys. Rev. Lett. 98, 188302.Google Scholar
Abkarian, M. & Viallat, A. 2005 Dynamics of vesicles in a wall-bounded shear flow. Biophys. J. 89, 10551066.Google Scholar
Anczurowski, E. & Mason, S. G. 1967 The kinetics of flowing dispersions. III. Equilibrium orientations of rods and discs (experimental). J. Colloid Interface Sci. 23, 533546.Google Scholar
Bagchi, P. & Kalluri, R. M. 2009 Dynamics of nonspherical capsules in shear flow. Phys. Rev. E 80, 016307.Google Scholar
Barthès-Biesel, D. 2016 Motion and deformation of elastic capsules and vesicles in flow. Annu. Rev. Fluid Mech. 48 (1), 2552.Google Scholar
Barthès-Biesel, D. & Rallison, J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251267.Google Scholar
Betz, T., Lenz, M., Joanny, J.-F. & Sykes, C. 2009 Atp-dependent mechanics of red blood cells. Proc. Natl Acad. Sci. USA 106, 1532115325.Google Scholar
Biben, T., Farutin, A. & Misbah, C. 2011 Three-dimensional vesicles under shear flow: numerical study of dynamics and phase diagram. Phys. Rev. E 83, 031921.Google Scholar
Bitbol, M. 1986 Red blood cell orientation in orbit c = 0. Biophys. J. 49, 10551068.Google Scholar
Brust, M., Schaefer, C., Doerr, R., Pan, L., Garcia, M., Arratia, P. E. & Wagner, C. 2013 Rheology of human blood plasma: viscoelastic versus newtonian behavior. Phys. Rev. Lett. 110, 078305.Google Scholar
Callens, N., Minetti, C., Coupier, G., Mader, M.-A., Dubois, F., Misbah, C. & Podgorski, T. 2008 Hydrodynamic lift of vesicles under shear flow in microgravity. Europhys. Lett. 83, 24002.Google Scholar
Canham, P. B. & Burton, A. C. 1968 Distribution of size and shape in populations of normal human red cells. Circ. Res. 22, 405422.Google Scholar
Chien, S. 1970 Shear dependence of effective cell volume as a determinant of blood viscosity. Science 168, 977979.Google Scholar
Chien, S. 1987 Red cell deformability and its relevance to blood flow. Annu. Rev. Phys. 49, 177192.Google Scholar
Cordasco, D. & Bagchi, P. 2013 Orbital drift of capsules and red blood cells in shear flow. Phys. Fluids 25, 091902.Google Scholar
Cordasco, D. & Bagchi, P. 2014 Intermittency and synchronized motion of red blood cell dynamics in shear flow. J. Fluid Mech. 759, 472488.Google Scholar
Cordasco, D., Yazdani, A. & Bagchi, P. 2014 Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys. Fluids 26, 041902.Google Scholar
Coupier, G., Kaoui, B., Podgorski, T. & Misbah, C. 2008 Noninertial lateral migration of vesicles in bounded Poiseuille flow. Phys. Fluids 20, 111702.Google Scholar
Danker, G., Biben, T., Podgorski, T., Verdier, C. & Misbah, C. 2007 Dynamics and rheology of a dilute suspension of vesicles: higher-order theory. Phys. Rev. E 76, 041905.Google Scholar
Deschamps, J., Kantsler, V. & Steinberg, V. 2009 Phase diagram of single vesicle dynamical states in shear flow. Phys. Rev. Lett. 102, 118105.Google Scholar
Dobbe, J. G. G., Hardeman, M. R., Streekstra, G. J., Strackee, J., Ince, C. & Grimbergen, C. A. 2002a Analyzing red blood cell-deformability distributions. Blood Cells 28, 373384.Google Scholar
Dobbe, J. G. G., Streekstra, G. J., Hardeman, M. R., Ince, C. & Grimbergen, C. A. 2002b Measurement of the distribution of red blood cell deformability using an automated rheoscope. Cytometry 50, 313325.Google Scholar
Dupire, J., Abkarian, M. & Viallat, A. 2015 A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow. Soft Matt. 11, 83728382.Google Scholar
Dupire, J., Socol, M. & Viallat, A. 2012 Full dynamics of a red blood cell in shear flow. Proc. Natl Acad. Sci. USA 109, 2080820813.Google Scholar
Dupont, C., Delahaye, F., Barthès-Biesel, D. & Salsac, A.-V. 2016 Stable equilibrium configurations of an oblate capsule in shear flow. J. Fluid Mech. 791, 738757.Google Scholar
Dupont, C., Salsac, A.-V. & Barthès-Biesel, D. 2013 Off-plane motion of a prolate capsule in shear flow. J. Fluid Mech. 721, 180198.Google Scholar
Evans, J., Gratzer, W., Mohandas, N., Parker, K. & Sleep, J. 2008 Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of atp dependence. Biophys. J. 94, 41344144.Google Scholar
Farutin, A., Aouane, O. & Misbah, C. 2012 Vesicle dynamics under weak flows: application to large excess area. Phys. Rev. E 85, 061922.Google Scholar
Farutin, A., Biben, T. & Misbah, C. 2010 Analytical progress in the theory of vesicles under linear flow. Phys. Rev. E 81, 061904.Google Scholar
Farutin, A. & Misbah, C. 2012 Squaring, parity breaking, and s tumbling of vesicles under shear flow. Phys. Rev. Lett. 109, 248106.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. USA 108, 1177211777.Google Scholar
Fischer, T. M. & Korzeniewski, R. 2013 Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium. J. Fluid Mech. 736, 351365.Google Scholar
Fischer, T. M. 2007 Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium. Biophys. J. 93, 25532561.Google Scholar
Fischer, T. M., Stöhr-Liesen, M. & Schmidt-Schönbein, H. 1978 The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894896.Google Scholar
Fischer, T. M., Haest, C. W., Stöhr-Liesen, M., Schmid-Schönbein, H. & Skalak, R. 1981 The stress-free shape of the red blood cell membrane. Biophys. J. 34, 409422.Google Scholar
Foessel, E., Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 477486.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. USA 108, 1098610991.Google Scholar
Fung, Y. C. 1993 Biomechanics: Mechanical Properties of Living Tissues. Springer.Google Scholar
Goldsmith, H. L. & Marlow, J. 1972 Flow behaviour of erythrocytes. I. rotation and deformation in dilute suspensions. Proc. R. Soc. Lond. B 182, 351384.Google Scholar
Grandchamp, X., Coupier, G., Srivastav, A., Minetti, C. & Podgorski, T. 2013 Lift and down-gradient shear-induced diffusion in red blood cell suspensions. Phys. Rev. Lett. 110, 108101.Google Scholar
Grau, M., Pauly, S., Ali, J., Walpurgis, K., Thevis, M., Bloch, W. & Suhr, F. 2013 RBC-NOS-dependent S-nitrosylation of cytoskeletal proteins improves RBC deformability. PLoS ONE 8, 110.Google Scholar
de Haas, K. H., Blom, C., van den Ende, D., Duits, M. H. G. & Mellema, J. 1997 Deformation of giant lipid bilayer vesicles in shear flow. Phys. Rev. E 56, 7132.Google Scholar
Hénon, S., Lenormand, G., Richert, A. & Gallet, F. 1999 A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys. J. 76, 11451151.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.Google Scholar
Kantsler, V., Segre, E. & Steinberg, V. 2008 Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow. Europhys. Lett. 82, 58005.Google Scholar
Kantsler, V. & Steinberg, V. 2005 Orientation and dynamics of a vesicle in tank-treading motion in shear flow. Phys. Rev. Lett. 95, 258101.Google Scholar
Kantsler, V. & Steinberg, V. 2006 Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. Phys. Rev. Lett. 96, 036001.Google Scholar
Keller, J. R. & Skalak, R. 1982 Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120, 2747.Google Scholar
Kessler, S., Finken, R. & Seifert, U. 2009 Elastic capsules in shear flow: analytical solutions for constant and time-dependent shear rates. Eur. Phys. J. E 29, 399413.Google Scholar
Laadhari, A., Saramito, P. & Misbah, C. 2012 Vesicle tumbling inhibited by inertia. Phys. Fluids 24, 031901.Google Scholar
Lac, E. & Barthès-Biesel, D. 2005 Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17, 072105.Google Scholar
Lanotte, L., Mauer, J., Mendez, S., Fedosov, D. A., Fromental, J.-M., Claveria, V., Nicoud, F., Gompper, G. & Abkarian, M. 2016 Red cells dynamic morphologies govern blood shear thinning under microcirculatory flow conditions. Proc. Natl Acad. Sci. USA 113, 1328913294.Google Scholar
Lebedev, V. V., Turitsyn, K. S. & Vergeles, S. S. 2007 Dynamics of nearly spherical vesicles in an external flow. Phys. Rev. Lett. 99, 218101.Google Scholar
Levant, M. & Steinberg, V. 2016 Intermediate regime and a phase diagram of red blood cell dynamics in a linear flow. Phys. Rev. E 94, 062412.Google Scholar
Lim, H. W. G., Wortis, M. & Mukhopadhyay, R. 2002 Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: evidence for the bilayer couple hypothesis from membrane mechanics. Proc. Natl Acad. Sci. USA 99, 1676616769.Google Scholar
Linderkamp, O. & Meiselman, H. J. 1982 Geometric, osmotic, and membrane mechanical properties of density-separated human red cells. Blood 59, 11211127.Google Scholar
Linderkamp, O., Wu, P. Y. K. & Meiselman, H. J. 1983 Geometry of neonatal and adult red blood cells. Ped. Res. 17, 250253.Google Scholar
Mader, M.-A., Ez-Zahraouy, H., Misbah, C. & Podgorski, T. 2007 On coupling between the orientation and shape of a vesicle under shear flow. Eur. Phys. J. E 22, 275.Google Scholar
Mader, M.-A., Vitkova, V., Abkarian, M., Viallat, A. & Podgorski, T. 2006 Dynamics of viscous vesicles in shear flow. Eur. Phys. J. E 19, 389.Google Scholar
Mauer, J., Mendez, S., Lanotte, L., Nicoud, F., Abkarian, M., Gompper, G. & Fedosov, D. A. 2018 Flow-induced transitions of red blood cell shapes under shear. Phys. Rev. Lett. 121, 118103.Google Scholar
Mendez, S. & Abkarian, M. 2018 In-plane elasticity controls the full dynamics of red blood cells in shear flow. Phys. Rev. Fluids 3, 101101.Google Scholar
Miccio, L., Memmolo, P., Merola, F., Netti, P. A. & Ferraro, P. 2015 Red blood cell as an adaptive optofluidic microlens. Nat. Comm. 6, 6502.Google Scholar
Mills, J. P., Qie, L., Dao, M., Lim, C. T. & Suresh, S. 2004 Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mol. Cell. Biomech. 1, 169180.Google Scholar
Minetti, C., Podgorski, T., Coupier, G. & Dubois, F. 2014 Fully automated digital holographic processing for monitoring the dynamics of a vesicle suspension under shear flow. Biomed. Opt. Expr. 5, 15541568.Google Scholar
Minetti, C., Vitkova, V., Dubois, F. & Bivas, I. 2016 Digital holographic microscopy as a tool to study the thermal shape fluctuations of lipid vesicles. Opt. Lett. 41, 18331836.Google Scholar
Misbah, C. 2006 Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96, 028104.Google Scholar
Morris, D. R. & Williams, A. R. 1979 The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro. Biochim. Biophys. Acta 550, 288296.Google Scholar
Noguchi, H. & Gompper, G. 2005a Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. Phys. Rev. E 72, 011901.Google Scholar
Noguchi, H. & Gompper, G. 2005b Vesicle dynamics in shear and capillary flows. J. Phys. Cond. Matter 17, S3439.Google Scholar
Noguchi, H. & Gompper, G. 2007 Swinging and tumbling of fluid vesicles in shear flow. Phys. Rev. Lett. 98, 128103.Google Scholar
Olla, P. 1997 The lift on a tank-treading ellipsoidal cell in a shear flow. J. Phys. II France 7, 15331540.Google Scholar
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, 96118.Google Scholar
Pfafferott, C., Nash, G. & Meiselman, H. J. 1985 Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging. Biophys. J. 47, 695704.Google Scholar
Prado, G., Farutin, A., Misbah, C. & Bureau, L. 2015 Viscoelastic transient of confined red blood cells. Biophys. J. 108, 21262136.Google Scholar
Pries, A., Neuhaus, N. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Phys. 20, H1770H1778.Google Scholar
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, 117143.Google Scholar
Rioual, F., Biben, T. & Misbah, C. 2004 Analytical analysis of a vesicle tumbling under a shear flow. Phys. Rev. E 69, 061914.Google Scholar
Rizzo, A., Corsetto, P. G., Montorfano, M. S., Zava, S., Tavella, S., Cancedda, R. & Berra, B. 2012 Effects of long-term space flight on erythrocytes and oxidative stress of rodents. PLoS ONE 7, e3261.Google Scholar
Rodak, B. F., Fritsma, G. A. & Doig, K. 2007 Hematology: Clinical Principles and Applications. Elsevier.Google Scholar
Roman, S., Lorthois, S., Duru, P. & Risso, F. 2012 Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients. Microvasc. Res. 84, 249261.Google Scholar
Roman, S., Merlo, A., Duru, P., Risso, F. & Lorthois, S. 2016 Going beyond 20 μm-sized channels for studying red blood cell phase separation in microfluidic bifurcations. Biomicrofluidics 10, 034103.Google Scholar
Ross, P. D. & Minton, A. P. 1977 Hard quasispherical model for the viscosity of hemoglobin solutions. Biochem. Biophys. Res. Commun. 76, 971976.Google Scholar
Shen, Z., Coupier, G., Kaoui, B., Polack, B., Harting, J., Misbah, C. & Podgorski, T. 2016 Inversion of hematocrit partition at microfluidic bifurcations. Microvasc. Res. 105, 4046.Google Scholar
Simmonds, M. J., Detterich, J. A. & Connes, P. 2014 Nitric oxide, vasodilation and the red blood cell. Biorheology 51, 121134.Google Scholar
Sinha, K. & Graham, M. D. 2015 Dynamics of a single red blood cell in simple shear flow. Phys. Rev. E 92, 042710.Google Scholar
Skotheim, J. M. & Secomb, T. W. 2007 Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. Phys. Rev. Lett. 98, 078301.Google Scholar
Svelc, T. & Svetina, S. 2012 Stress-free state of the red blood cell membrane and the deformation of its skeleton. Cell. Mol. Biol. Lett. 17, 217227.Google Scholar
Vitkova, V., Coupier, G., Mader, M.-A., Kaoui, B., Misbah, C. & Podgorski, T. 2009 Tumbling of viscous vesicles in a linear shear field near a wall. J. Optoelectron. Adv. M. 11, 12181221.Google Scholar
Vitkova, V., Mader, M.-A., Polack, B., Misbah, C. & Podgorski, T. 2008 Micro-macro link in rheology of erythrocyte and vesicle suspensions. Biophys. J. 95, 3335.Google Scholar
Walter, J., Salsac, A.-V. & Barthès-Biesel, D. 2011 Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes. J. Fluid Mech. 676, 318347.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
Zabusky, N. J., Segre, E., Deschamps, J., Kantsler, V. & Steinberg, V. 2011 Dynamics of vesicles in shear and rotational flows: modal dynamics and phase diagram. Phys. Fluids 23, 041905.Google Scholar
Supplementary material: File

Minetti et al. supplementary material

Minetti et al. supplementary material 1

Download Minetti et al. supplementary material(File)
File 535.7 KB