Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

References

• Abkarian M, Faivre M, Viallat A. 2007. Swinging of red blood cells under shear flow. Phys Rev Lett. 98(18):188302. doi:10.1103/PhysRevLett.98.188302.
   PubMed Web of Science ®Google Scholar
• Bagchi P. 2010. Front-tracking methods for capsules, vesicles and blood cells. In: Pozrikidis C, editor. Computational hydrodynamics of capsules and biological cells, Chapter 5 New York (NY): CRC Press; p. 149–182.
   Google Scholar
• Bronzino JD. 2000. The biomedical engineering handbook. 2nd ed.. Boca Raton, FL: CRC Press.
   Google Scholar
• Dodson, III, WR, Dimitrakopoulos P. 2010. Tank-treading of erythrocytes in strong shear flows via a nonstiff cytoskeleton-based continuum computational modeling. Biophys J. 99:2906C2916.
   Web of Science ®Google Scholar
• Eggleton CD, Popel AS. 1998. Large deformation of red blood cell ghosts in a simple shear flow. Phys Fluids. 10(8):1834–1845. doi:10.1063/1.869703.
   PubMed Web of Science ®Google Scholar
• Evans EA, Fung YC. 1972. Improved measurements of the erythrocyte geometry. Microvasc Res. 4(4):335–347. doi:10.1016/0026-2862(72)90069-6.
   PubMed Web of Science ®Google Scholar
• Fedosov DA, Caswell B, Karniadakis GE. 2010. Dissipative particle dynamics modeling of red blood. In: Pozrikidis C, editor. Computational hydrodynamics of capsules and biological cells, Chapter 6. New York (NY): CRC Press; p. 183–218.
   Google Scholar
• Fedosov DA, Noguchi H, Gompper G. 2014. Multiscale modeling of blood flow: from single cells to blood rheology. Biomech Model Mechanobiol. 13(2):239–258. doi:10.1007/s10237-013-0497-9.
   PubMed Web of Science ®Google Scholar
• Fischer TM. 2007. Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium. Biophy J. 93(7):2553–2561. doi:10.1529/biophysj.107.104505.
   PubMed Web of Science ®Google Scholar
• Fischer TM, Korzeniewski R. 2011. Effects of shear rate and suspending medium viscosity on elongation of red cells tank-treading in shear flow. Cytom A. 79A(11):946–951. doi:10.1002/cyto.a.21126.
   Web of Science ®Google Scholar
• 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(4370):894–896. doi:10.1126/science.715448.
   PubMed Web of Science ®Google Scholar
• Guo Z, Zheng C, Shi B. 2002. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys Rev E. 65(4):046308. doi:10.1103/PhysRevE.65.046308.
   Web of Science ®Google Scholar
• Helfrich W. 1973. Elastic properties of lipid bilayers: theory and possible experiments. Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie. 28:693–703.
   Google Scholar
• Kim Y, Kim K, Park Y. 2012. Measurement techniques for red blood cell deformability: recent advances. In: Moschandreou T, editor. Blood cell – an overview of studies in hematology, chapter 10. Rijeka, Croatia: InTech.
   Google Scholar
• Kruger T. 2012. Computer simulation study of collective phenomena in dense suspensions of red blood cells under shear. Springer.
   Google Scholar
• Keller SR, Skalak R. 1982. Motion of a tank-treading ellipsoidal particle in a shear flow. J Fluid Mech. 120(1):27–47. doi:10.1017/S0022112082002651.
   Web of Science ®Google Scholar
• Krüger T, Varnik F, Raabe D. 2011. Efficient and accurate Simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice boltzmann finite element method. Comput Math Appl. 61(12):3485–3505. doi:10.1016/j.camwa.2010.03.057.
   Web of Science ®Google Scholar
• Lac E, Barthès-Biesel D, Pelekasis NA, Tsamopoulos J. 1999. Spherical capsules in three-dimensional unbounded stokes flows: Effect of the membrane constitutive law and onset of buckling. J Fluid Mech. 516:303–334. doi:10.1017/S002211200400062X.
   Web of Science ®Google Scholar
• Le G, Zhang J. 2009. Boundary slip from the immersed boundary lattice Boltzmann models. Phys Rev E. 79(2):026701. doi:10.1103/PhysRevE.79.026701.
   Google Scholar
• McClain BL, Finkelstein IJ, Fayer MD. 2004. Vibrational echo experiments on red blood cells: Comparison of the dynamics of cytoplasmic and aqueous hemoglobin. Chem Phys Lett. 392(4-6):324–329. doi:10.1016/j.cplett.2004.05.080.
   Web of Science ®Google Scholar
• Noguchi H, Gompper G. 2004. Fluid vesicles with viscous membranes in shear flow. Phys Rev Lett. 93(25):258102. doi:10.1103/PhysRevLett.93.258102.
   PubMed Web of Science ®Google Scholar
• Noguchi H, Gompper G. 2005. Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc Natl Acad Sci USA. 102(40):14159–14164. doi:10.1073/pnas.0504243102.
   PubMed Web of Science ®Google Scholar
• Oishi M, Utsubo K, Kinoshita H, Fujii T, Oshima M. 2012. Continuous and simultaneous measurement of the tank-treading motion of red blood cells and the surrounding flow using translational confocal micro-particle image velocimetry (micro-PIV) with sub-micron resolution. Meas Sci Technol. 23(3):035301. doi:10.1088/0957-0233/23/3/035301.
   Google Scholar
• Peskin CS. 1977. Numerical analysis of blood flow in the heart. J Comput Phys. 25(3):220–252. doi:10.1016/0021-9991(77)90100-0.
   Web of Science ®Google Scholar
• Pozrikidis C. 2010. Computational hydrodynamics of capsules and biological cells. New York (NY): CRC Press.
   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. doi:10.1017/S0022112098008714.
   Web of Science ®Google Scholar
• Secomb TW, Styp-Rekowska BS, Pries AR. 2007. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann Biomed Eng. 35(5):755–765. doi:10.1007/s10439-007-9275-0.
   PubMed Web of Science ®Google Scholar
• Skalak R, Tozeren A, Zarda RP, Chien S. 1973. Strain energy function of red blood cell membranes. Biophys J. 13(3):245–264. doi:10.1016/S0006-3495(73)85983-1.
   PubMed Web of Science ®Google Scholar
• Skotheim JM, Secomb TW. 2007. Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. Phys Rev Lett. 98(7):078301. doi:10.1103/PhysRevLett.98.078301.
   PubMed Web of Science ®Google Scholar
• Succi S. 2001. The Lattice Boltzmann equation. Oxford: Oxford University Press.
   Google Scholar
• Sui Y, Chew YT, Roy P, Low HT. 2008. A hybrid method to study flow-induced deformation of three-dimensional capsules. J Comput Phys. 227(12):6351–6371. doi:10.1016/j.jcp.2008.03.017.
   Web of Science ®Google Scholar
• Tran-Son-Tay R, Sutera SP, Rao PR. 1984. Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion. Biophys J. 46(1):65–72. doi:10.1016/S0006-3495(84)83999-5.
   PubMed Web of Science ®Google Scholar
• Zhang J. 2011. Lattice Boltzmann method for microfluidics: models and applications. Microfluid Nanofluid. 10(1):1–28. doi:10.1007/s10404-010-0624-1.
   Web of Science ®Google Scholar
• Zhang J. 2011. Effect of suspending viscosity on red blood cell dynamics and blood flows in microvessels. Microcirculation. 18(7):562–573. doi:10.1111/j.1549-8719.2011.00116.x.
   PubMed Web of Science ®Google Scholar
• Zhang J, Johnson PC, Popel AS. 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. doi:10.1088/1478-3975/4/4/005.
   PubMed Web of Science ®Google Scholar
• Zhang J, Johnson PC, Popel AS. 2008. Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. J Biomech. 41(1):47–55. doi:10.1016/j.jbiomech.2007.07.020.
   PubMed Web of Science ®Google Scholar
• Zhang J, Johnson PC, Popel AS. 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. doi:10.1016/j.mvr.2009.01.010.
   PubMed Web of Science ®Google Scholar