Dynamic Response of a Red Blood Cell in Shear Flow

Document Type : Research Article

Authors

Department of Mechanical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

Three-dimensional simulation of a red blood cell deformation in a shear flow is
performed using immersed boundary lattice Boltzmann method for the fluid flow simulation, as well as
finite element method for membrane deformation. Immersed boundary method has been used to model
interaction between fluid and membrane of the red blood cell. Red blood cell is modeled as a biconcave
discoid capsule containing fluid with an elastic membrane. Computations are performed at relatively
small and large shear rates in order to study the dynamic behavior of red blood cell, especially tumbling
and swinging modes of its motion. A rigid-body-like motion with the constant-amplitude oscillation
of deformation parameter and continuous rotation is observed for red blood cell at its tumbling mode.
However, at a relatively large shear rate, red blood cell follows a periodic gradual deformation and
elongation with a final ellipsoidal shape. The effect of different initial orientations of red blood cell is
also investigated in the present paper. Results show that the dynamic response of red blood cell is not
sensitive to this parameter.

Highlights

[1] H. Schmid-Schönbein, R. Wells, Fluid Drop-Like Transition of Erythrocytes under Shear, Science, 165(3890) (1969) 288-291.

[2] H.L. Goldsmith, J. Marlow, Flow Behaviour of Erythrocytes. I. Rotation and Deformation in Dilute Suspensions, Proceedings of the Royal Society of London. Series B. Biological Sciences, 182(1068) (1972) 351-384.

[3] T.M. Fischer, M. Stohr-Lissen, H. Schmid-Schonbein, The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow, Science, 202(4370) (1978) 894-896.

[4] R. Tran-Son-Tay, S.P. Sutera, P.R. Rao, Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion, Biophysical Journal, 46(1) (1984) 65-72.

[5] C. Pfafferott, G.B. Nash, H.J. Meiselman, Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging, Biophysical Journal, 47(5) (1985) 695-704.

[6] M. Abkarian, M. Faivre, A. Viallat, Swinging of Red Blood Cells under Shear Flow, Physical Review Letters, 98(18) (2007) 188302.

[7] J. Dupire, M. Socol, A. Viallat, Full dynamics of a red blood cell in shear flow, Proceedings of the National Academy of Sciences, 109(51) (2012) 20808-20813.

[8] S. Ramanujan, C. Pozrikidis, Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, Journal of Fluid Mechanics, 361 (1998) 117-143.

[9] E. Lac, Barth, Egrave, D. S-Biesel, N.A. Pelekasis, J. Tsamopoulos, Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling, Journal of Fluid Mechanics, 516 (2004) 303-334.

[10] C.D. Eggleton, A.S. Popel, Large deformation of red blood cell ghosts in a simple shear flow, Physics of Fluids, 10(8) (1998) 1834-1845.

[11] X. Li, K. Sarkar, Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane, Journal of Computational Physics, 227(10) (2008) 4998-5018.

[12] S.K. Doddi, P. Bagchi, Three-dimensional computational modeling of multiple deformable cells flowing in microvessels, Physical Review E, 79(4) (2009) 046318.

[13] Y. Sui, Y.T. Chew, P. Roy, H.T. Low, A hybrid method to study flow-induced deformation of three-dimensional capsules, Journal of Computational Physics, 227(12) (2008) 6351-6371.

[14] T. Kruger, F. Varnik, D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Computers and Mathematics with Applications, 61(12) (2011) 3485- 3505.

[15] Z. Hashemi, M. Rahnama, S. Jafari, Lattice Boltzmann simulation of three-dimensional capsule deformation in a shear flow with different membrane constitutive laws, Scientia Iranica. Transaction B, Mechanical Engineering, 22(5) (2015) 1877.

[16] G. Breyiannis, C. Pozrikidis, Simple Shear Flow of Suspensions of Elastic Capsules, Theoretical and Computational Fluid Dynamics, 13(5) (2000) 327- 347.

[17] P. Bagchi, P.C. Johnson, A.S. Popel, Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow, Journal of Biomechanical Engineering, 127(7) (2005) 1070-1080.

[18] Y. Sui, Y.T. Chew, P. Roy, X.B. Chen, H.T. Low, Transient deformation of elastic capsules in shear flow: Effect of membrane bending stiffness, Physical Review E, 75(6) (2007) 066301.

[19] A. Viallat, M. Abkarian, Red blood cell: from its mechanics to its motion in shear flow, International journal of laboratory hematology, 36(3) (2014) 237- 243.

[20] Z. Hashemi, M. Rahnama, Numerical simulation of transient dynamic behavior of healthy and hardened red blood cells in microcapillary flow, International journal for numerical methods in biomedical engineering, 32(11) (2016) e02763.

[21] Z. Hashemi, M. Rahnama, S. Jafari, Lattice Boltzmann simulation of healthy and defective red blood cell settling in blood plasma, Journal of biomechanical engineering, 138(5) (2016) 051002.

[22] Y. Sui, X. Chen, Y. Chew, P. Roy, H. Low, Numerical simulation of capsule deformation in simple shear flow, Computers & Fluids, 39(2) (2010) 242-250.

[23] Y. Sui, Y. Chew, P. Roy, Y. Cheng, H. Low, Dynamic motion of red blood cells in simple shear flow, Physics of Fluids, 20(11) (2008) 112106.

[24] R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain Energy Function of Red Blood Cell Membranes, Biophysical Journal, 13(3) (1973) 245-264.

[25] L.-S. Luo, Lattice-gas automata and lattice boltzmann equations for two-dimensional hydrodynamics, Ph.D. thesis, Georgia Institute of Technology, (1993).

[26] E. Evans, Y.-C. Fung, Improved measurements of the erythrocyte geometry, Microvascular Research, 4(4) (1972) 335-347.

[27] J. Charrier, S. Shrivastava, R. Wu, Free and constrained inflation of elastic membranes in relation to thermoforming-non-axisymmetric problems, The Journal of Strain Analysis for Engineering Design, 24(2) (1989) 55-74.

[28] S. Shrivastava, J. Tang, Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming, The Journal of Strain Analysis for Engineering Design, 28(1) (1993) 31-51.

[29] C.S. Peskin, The immersed boundary method, Acta numerica, 11 (2002) 479-517.

Keywords

References

[1] H. Schmid-Schönbein, R. Wells, Fluid Drop-Like Transition of Erythrocytes under Shear, Science, 165(3890) (1969) 288-291.
[2] H.L. Goldsmith, J. Marlow, Flow Behaviour of Erythrocytes. I. Rotation and Deformation in Dilute Suspensions, Proceedings of the Royal Society of London. Series B. Biological Sciences, 182(1068) (1972) 351-384.
[3] T.M. Fischer, M. Stohr-Lissen, H. Schmid-Schonbein, The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow, Science, 202(4370) (1978) 894-896.
[4] R. Tran-Son-Tay, S.P. Sutera, P.R. Rao, Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion, Biophysical Journal, 46(1) (1984) 65-72.
[5] C. Pfafferott, G.B. Nash, H.J. Meiselman, Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging, Biophysical Journal, 47(5) (1985) 695-704.
[6] M. Abkarian, M. Faivre, A. Viallat, Swinging of Red Blood Cells under Shear Flow, Physical Review Letters, 98(18) (2007) 188302.
[7] J. Dupire, M. Socol, A. Viallat, Full dynamics of a red blood cell in shear flow, Proceedings of the National Academy of Sciences, 109(51) (2012) 20808-20813.
[8] S. Ramanujan, C. Pozrikidis, Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, Journal of Fluid Mechanics, 361 (1998) 117-143.
[9] E. Lac, Barth, Egrave, D. S-Biesel, N.A. Pelekasis, J. Tsamopoulos, Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling, Journal of Fluid Mechanics, 516 (2004) 303-334.
[10] C.D. Eggleton, A.S. Popel, Large deformation of red blood cell ghosts in a simple shear flow, Physics of Fluids, 10(8) (1998) 1834-1845.
[11] X. Li, K. Sarkar, Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane, Journal of Computational Physics, 227(10) (2008) 4998-5018.
[12] S.K. Doddi, P. Bagchi, Three-dimensional computational modeling of multiple deformable cells flowing in microvessels, Physical Review E, 79(4) (2009) 046318.
[13] Y. Sui, Y.T. Chew, P. Roy, H.T. Low, A hybrid method to study flow-induced deformation of three-dimensional capsules, Journal of Computational Physics, 227(12) (2008) 6351-6371.
[14] T. Kruger, F. Varnik, D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Computers and Mathematics with Applications, 61(12) (2011) 3485- 3505.
[15] Z. Hashemi, M. Rahnama, S. Jafari, Lattice Boltzmann simulation of three-dimensional capsule deformation in a shear flow with different membrane constitutive laws, Scientia Iranica. Transaction B, Mechanical Engineering, 22(5) (2015) 1877.
[16] G. Breyiannis, C. Pozrikidis, Simple Shear Flow of Suspensions of Elastic Capsules, Theoretical and Computational Fluid Dynamics, 13(5) (2000) 327- 347.
[17] P. Bagchi, P.C. Johnson, A.S. Popel, Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow, Journal of Biomechanical Engineering, 127(7) (2005) 1070-1080.
[18] Y. Sui, Y.T. Chew, P. Roy, X.B. Chen, H.T. Low, Transient deformation of elastic capsules in shear flow: Effect of membrane bending stiffness, Physical Review E, 75(6) (2007) 066301.
[19] A. Viallat, M. Abkarian, Red blood cell: from its mechanics to its motion in shear flow, International journal of laboratory hematology, 36(3) (2014) 237- 243.
[20] Z. Hashemi, M. Rahnama, Numerical simulation of transient dynamic behavior of healthy and hardened red blood cells in microcapillary flow, International journal for numerical methods in biomedical engineering, 32(11) (2016) e02763.
[21] Z. Hashemi, M. Rahnama, S. Jafari, Lattice Boltzmann simulation of healthy and defective red blood cell settling in blood plasma, Journal of biomechanical engineering, 138(5) (2016) 051002.
[22] Y. Sui, X. Chen, Y. Chew, P. Roy, H. Low, Numerical simulation of capsule deformation in simple shear flow, Computers & Fluids, 39(2) (2010) 242-250.
[23] Y. Sui, Y. Chew, P. Roy, Y. Cheng, H. Low, Dynamic motion of red blood cells in simple shear flow, Physics of Fluids, 20(11) (2008) 112106.
[24] R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain Energy Function of Red Blood Cell Membranes, Biophysical Journal, 13(3) (1973) 245-264.
[25] L.-S. Luo, Lattice-gas automata and lattice boltzmann equations for two-dimensional hydrodynamics, Ph.D. thesis, Georgia Institute of Technology, (1993).
[26] E. Evans, Y.-C. Fung, Improved measurements of the erythrocyte geometry, Microvascular Research, 4(4) (1972) 335-347.
[27] J. Charrier, S. Shrivastava, R. Wu, Free and constrained inflation of elastic membranes in relation to thermoforming-non-axisymmetric problems, The Journal of Strain Analysis for Engineering Design, 24(2) (1989) 55-74.
[28] S. Shrivastava, J. Tang, Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming, The Journal of Strain Analysis for Engineering Design, 28(1) (1993) 31-51.
[29] C.S. Peskin, The immersed boundary method, Acta numerica, 11 (2002) 479-517.
AUT Journal of Mechanical Engineering
Volume 1, Issue 2
December 2017
Pages 233-242

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