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Reorientation of a single red blood cell during sedimentation

Published online by Cambridge University Press:  29 September 2016

D. Matsunaga ,
Y. Imai ,
C. Wagner  and
T. Ishikawa
D. Matsunaga*
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
Y. Imai
Affiliation:
School of Engineering, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
C. Wagner
Affiliation:
Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
T. Ishikawa
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan Department of Biomedical Engineering, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
*
†Email address for correspondence: [email protected]
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Abstract

The reorientation phenomenon of a single red blood cell during sedimentation is simulated using the boundary element method. The cell settles downwards due to a density difference between the internal and external fluids, and it changes orientation toward a vertical orientation regardless of Bond number or viscosity ratio. The reorientation phenomenon is explained by a shape asymmetry caused by the gravitational driving force, and the shape asymmetry increases almost linearly with the Bond number. When velocities are normalised by the driving force, settling/drifting velocities are weak functions of the Bond number and the viscosity ratio, while the angular velocity of the reorientation drastically changes with these parameters: the angular velocity is smaller for lower Bond number or higher viscosity ratio. As a consequence, trajectories of the sedimentation are also affected by the angular velocity, and blood cells with slower reorientation travel longer distances in the drifting direction. We also explain the mechanism of the reorientation using an asymmetric dumbbell. From the analysis, we show that the magnitude of the angular velocity is explained by two main factors: the shape asymmetry and the instantaneous orientation angle.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 806 , 10 November 2016 , pp. 102 - 128
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Copyright
© 2016 Cambridge University Press 

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References

Baskurt, O., Neu, B. & Meiselman, J. H. 2012 Red Blood Cell Aggregation. CRC Press.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
Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Math. Proc. Camb. 70, 303–310.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2012 Settling of a vesicle in the limit of quasispherical shapes. J. Fluid Mech. 690, 227–261.Google Scholar
Boedec, G., Jaeger, M. & Leonetti, M. 2013 Sedimentation-induced tether on a settling vesicle. Phys. Rev. E 88, 010702.Google Scholar
Boedec, G., Leonetti, M. & Jaeger, M. 2011 3d vesicle dynamics simulations with a linearly triangulated surface. J. Comput. Phys. 230 (4), 1020–1034.Google Scholar
Boltz, H.-H. & Kierfeld, J. 2015 Shapes of sedimenting soft elastic capsules in a viscous fluid. Phys. Rev. E 92, 033003.Google Scholar
Brochard, F. & Lennon, J. F. 1975 Frequency spectrum of the flicker phenomenon in erythroctes. J. Phys. (Paris) 36 (11), 1035–1047.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
Canham, P. B., Jay, A. W. L. & Tilsworth, E. 1971 The rate of sedimentation of individual human red blood cells. J. Cell. Physiol. 78 (3), 319–331.Google Scholar
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, 041917.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 (51), 20808–20813.Google Scholar
Evans, E. & Fung, Y. C. 1972 Improved measurements of the erythrocyte geometry. Microvasc. Res. 4 (4), 335–347.Google Scholar
Foessel, É., Walter, J., Salsac, A.-V. & Barthès-Biesel, 2011 Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 477–486.Google Scholar
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19 (2), 023301.Google Scholar
Gov, N. & Safran, S. A. 2005 Red blood cell shape and fluctuations: cytoskeleton confinement and atp activity. J. Biol. Phys. 31 (3–4), 453–464.Google Scholar
Groom, A. C. & Anderson, J. C. 1972 Measurement of the size distribution of human erythrocytes by a sedimentation method. J. Cell. Physiol. 79 (1), 127–137.CrossRefGoogle ScholarPubMed
Guazzelli, E. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43 (1), 97–116.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1963 Low Reynolds number hydrodynamics with special applications to particulate media. Martinus Nijhoff.Google Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693–703.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 (2), 1145–1151.Google Scholar
Hoffman, J. F. & Inoué, S. 2006 Directly observed reversible shape changes and hemoglobin stratification during centrifugation of human and amphiuma red blood cells. Proc. Natl Acad. Sci. USA 103 (8), 2971–2976.Google Scholar
Huang, Z. H., Abkarian, M. & Viallat, A. 2011 Sedimentation of vesicles: from pear-like shapes to microtether extrusion. New J. Phys. 13 (3), 035026.Google Scholar
Hwang, W. C. & Waugh, R. E. 1997 Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. Biophys. J. 72 (6), 2669–2678.Google Scholar
Jay, A. W. L. & Canham, P. B. 1972 Sedimentation of single human red blood cells. Differences between normal and glutaraldehyde fixed cells. J. Cell. Physiol. 80 (3), 367–372.Google Scholar
Kim, S. & Karrila, J. S. 1991 Microhydrodynamics – Principles and Selected Applications. Dover.Google Scholar
Koh, C. J. & Leal, L. G. 1989 The stability of drop shapes for translation at zero reynolds number through a quiescent fluid. Phys. Fluids A 1 (8), 1309–1313.Google Scholar
Li, L., Manikantan, H., Saintillan, D. & Spagnolie, S. 2013 The sedimentation of flexible filaments. J. Fluid Mech. 735, 705–736.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 (26), 16766–16769.Google Scholar
Matsunaga, D., Imai, Y., Omori, T., Ishikawa, T. & Yamaguchi, T. 2014 A full GPU implementation of a numerical method for simulating capsule suspensions. J. Biomech. Sci. Engng 14, 00039.Google Scholar
Matsunaga, D., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2015 Deformation of a spherical capsule under oscillating shear flow. J. Fluid Mech. 762, 288–301.Google Scholar
Matsunaga, D., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2016 Rheology of a dense suspension of spherical capsules under simple shear flow. J. Fluid Mech. 786, 110–127.Google Scholar
Meyer, M., Desbrun, M., Schröder, P. & Barr, A. 2003 Discrete differential-geometry operators for triangulated 2-manifolds. In Mathematics and Visualization (ed. Hege, H.-C. & Polthier, K.), pp. 35–57. Springer.Google Scholar
Mogami, Y., Ishii, J. & Baba, A. S. 2001 Theoretical and experimental dissection of gravity-dependent mechanical orientation in gravitactic microorganisms. Biol. Bull. 201, 26–33.Google Scholar
Nix, S., Imai, Y., Matsunaga, D., Yamaguchi, T. & Ishikawa, T. 2014 Lateral migration of a spherical capsule near a plane wall in stokes flow. Phys. Rev. E 90, 043009.Google Scholar
Omori, T., Ishikawa, T., Imai, Y. & Yamaguchi, T. 2013 Shear-induced diffusion of red blood cells in a semi-dilute suspension. J. Fluid Mech. 724, 154–174.Google Scholar
Ou-Yang, Z. & 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, 5280–5288.Google Scholar
Peltomaki, M. & Gompper, G. 2013 Sedimentation of single red blood cells. Soft Matt. 9, 8346–8358.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, 96–118.Google Scholar
Pozrikidis, C. 1990 The instability of a moving viscous drop. J. Fluid Mech. 210, 1–21.Google Scholar
Pozrikidis, C. 1992a Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Pozrikidis, C. 1992b The buoyancy-driven motion of a train of viscous drops within a cylindrical tube. J. Fluid Mech. 237, 627–648.Google Scholar
Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297, 123–152.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, 117–143.Google Scholar
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347–388.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
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245–264.Google Scholar
Suárez, I. R., Leidy, C., Téllez, G., Gay, G. & Gonzalez-Mancera, A. 2013 Slow sedimentation and deformability of charged lipid vesicles. PLoS ONE 8 (7), e68309.Google Scholar
Sui, Y., Chew, Y. T., Roy, P. & Low, H. T. 2008 A hybrid method to study flow-induced deformation of three-dimensional capsules. J. Comput. Phys. 227 (12), 6351–6371.Google Scholar
The Japanese Society for Laboratory Hematology 2003 Blood Test Standard, 2nd edn. Ishiyaku (in Japanese).Google Scholar
Tsubota, K., Wada, S. & Liu, H. 2014 Elastic behavior of a red blood cell with the membrane’s nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion. Biomech. Model. Mechan. 13 (4), 735–746.Google Scholar
Turlier, H., Fedosov, D. A., Audoly, B., Auth, T., Gov, N. S., Sykes, C., Joanny, J. F., Gompper, G. & Betz, T. 2016 Equilibrium physics breakdown reveals the active nature of red blood cell flickering. Nat. Phys. 12 (5), 513–519.Google Scholar
Veerapaneni, S. K., Gueyffier, D., Zorin, D. & Biros, G. 2009 A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D. J. Comput. Phys. 228 (7), 2334–2353.Google Scholar
Walter, J., Salsac, A.-V., Barthès-Biesel, D. & Le Tallec, P. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Int. J. Numer. Meth. Eng. 83 (7), 829–850.Google Scholar
Westergren, A. 1921 Studies of the suspension stability of the blood in pulmonary tuberculosis. Acta Med. Scand. 54 (1), 247–282.Google Scholar

Matsunaga et al. supplementary movie

Sedimentation of a single red blood cell under Bond number Bo=2.5×101 and viscosity ratio (a) λ=1.0 and (b) λ=5.0. The initial orientation angle is Θ0=π/4, and the animation shows up to non-dimensional time (aΔρg)t/μ =300. Note that camera is also settling with the cell.

Download Matsunaga et al. supplementary movie(Video)
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