Skip to main content
SpringerLink
Log in

A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

Red blood cells (RBCs) are the most common type of blood cells in the blood and 99 % of the blood cells are RBCs. During the circulation of blood in the cardiovascular network, RBCs squeeze through the tiny blood vessels (capillaries). They exhibit various types of motions and deformed shapes, when flowing through these capillaries with diameters varying between 5 and 10 µm. RBCs occupy about 45 % of the whole blood volume and the interaction between the RBCs directly influences on the motion and the deformation of the RBCs. However, most of the previous numerical studies have explored the motion and deformation of a single RBC when the interaction between RBCs has been neglected. In this study, motion and deformation of two 2D (two-dimensional) RBCs in capillaries are comprehensively explored using a coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM) model. In order to clearly model the interactions between RBCs, only two RBCs are considered in this study even though blood with RBCs is continuously flowing through the blood vessels. A spring network based on the DEM is employed to model the viscoelastic membrane of the RBC while the inside and outside fluid of RBC is modelled by SPH. The effect of the initial distance between two RBCs, membrane bending stiffness (K b ) of one RBC and undeformed diameter of one RBC on the motion and deformation of both RBCs in a uniform capillary is studied. Finally, the deformation behavior of two RBCs in a stenosed capillary is also examined. Simulation results reveal that the interaction between RBCs has significant influence on their motion and deformation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  • Bayliss, L.: The axial drift of the red cells when blood flows in a narrow tube. J. Physiol 149(3), 593–613 (1959). doi:10.1113/jphysiol.1959.sp006363

    Article  MathSciNet  Google Scholar 

  • Cooke, B.M., Mohandas, N., Coppel, R.L.: The malaria-infected red blood cell: structural and functional changes. Adv. Parasitol. 50, 1–86 (2001). doi:10.1016/S0065-308X(01)50029-9

    Article  Google Scholar 

  • Dupire, J., Socol, M., Viallat, A.: Full dynamics of a red blood cell in shear flow. Proc. Natl. Acad. Sci. 109(51), 20808–20813 (2012). doi:10.1073/pnas.1210236109

    Article  Google Scholar 

  • Fåhræus R, Lindqvist T.: The viscosity of the blood in narrow capillary tubes. Am. J. Physiol. Legacy Cont. 96(3):562–568. http://ajplegacy.physiology.org/content/96/3/562

  • Fedosov, D.A., Lei, H., Caswell, B., Suresh, S., Karniadakis, G.E.: Multiscale modeling of red blood cell mechanics and blood flow in malaria. PLoS Comput. Biol. 7(12), e1002270 (2011). doi:10.1371/journal.pcbi.1002270

    Article  MathSciNet  Google Scholar 

  • Frcitas, R.A.: Exploratory design in medical nanotechnology: a mechanical artificial red cell. Artif. Cells Blood Substit. Biotechnol. 26(4), 411–430 (1998). doi:10.3109/10731199809117682

    Article  Google Scholar 

  • Hou, H.W., Li, Q., Lee, G., Kumar, A., Ong, C., Lim, C.T.: Deformability study of breast cancer cells using microfluidics. Biomed. Microdevices 11(3), 557–564 (2009). doi:10.1007/s10544-008-9262-8

    Article  Google Scholar 

  • Jiang, X.M., Wang, T., Xing, Z.W.: Simulation Study of Hemodynamics of Red Blood Cells in Stenotic Microvessels. Adv. Mater. Res. 647, 321–324 (2013). doi:10.4028/www.scientific.net/AMR.647.321

    Article  Google Scholar 

  • Kaoui, B., Harting, J., Misbah, C.: Two-dimensional vesicle dynamics under shear flow: effect of confinement. Phys. Rev. E 83(6), 066319 (2011). doi:10.1103/PhysRevE.83.066319

    Article  Google Scholar 

  • Le, D.-V., White, J., Peraire, J., Lim, K., Khoo, B.: An implicit immersed boundary method for three-dimensional fluid–membrane interactions. J. Comput. Phys. 228(22), 8427–8445 (2009). doi: 10.1016/j.jcp.2009.08.018

  • Liu, G.R., Liu, M.: Smoothed particle hydrodynamics: a meshfree particle method. World Scientific Publishing Company Incorporated, (2003)

  • Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997). doi:10.1006/jcph.1997.5776

  • Nagayama, K., Honda, K.: 3D Particle Simulations of Deformation of Red Blood Cells in Micro-Capillary Vessel. (2012)

  • Pan, T.W., Wang, T.: Dynamical simulation of red blood cell rheology in microvessels. Int. J. Numer Anal Model. 6, 455-473 (2009). http://www.math.ualberta.ca/ijnam/Volume-6-2009/No-3-09/2009-03-07.pdf

  • Polwaththe-Gallage, H.-N., Saha, S.C., Sauret, E., Flower, R., Gu, Y.: Numerical Investigation of Motion and Deformation of a Single Red Blood Cell in a Stenosed Capillary. Int. J. Comput. Methods, 1540003 (2015)

  • Polwaththe-Gallage, H.N., Gu, Y., Saha, S.C., Senadeera, W., Oloyede, A.: (2012) Numerical simulation of red blood cells’ motion : a review. Paper presented at the 4th International Conference on Computational Methods (ICCM: Crowne Plaza. Gold Coast, QLD (2012)

    Google Scholar 

  • Polwaththe-Gallage, H.N., Saha, S.C., Gu, Y.: Deformation of a single red blood cell in a microvessel. ANZIAM J. 55, C64–C79 (2014). http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/7828

  • Pozrikidis, C.: Axisymmetric motion of a file of red blood cells through capillaries. Phys. Fluids. (1994-present) 17(3), 031503 (2005). doi:10.1063/1.1830484

    Article  MathSciNet  MATH  Google Scholar 

  • Pries, A., Secomb, T., Gaehtgens, P.: Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res. 32(4), 654–667 (1996). doi:10.1016/S0008-6363(96)00065-X

    Article  Google Scholar 

  • Secomb, T.: Flow-dependent rheological properties of blood in capillaries. Microvasc. Res. 34(1), 46–58 (1987)

    Article  Google Scholar 

  • Shi, L., Pan, T.W., Glowinski, R.: Deformation of a single red blood cell in bounded Poiseuille flows. Phys. Rev. E 85(1), 016307 (2012). doi:10.1103/PhysRevE.85.016307

    Article  Google Scholar 

  • Shi, X., Lin, G., Zou, J., Fedosov, D.A.: A lattice Boltzmann fictitious domain method for modeling red blood cell deformation and multiple-cell hydrodynamic interactions in flow. Int. J. Numer. Meth. Fluids 72(8), 895–911 (2013). doi:10.1002/fld.3764

    Article  MathSciNet  Google Scholar 

  • Shvartsman, L.D., Fine, I.: Optical transmission of blood: effect of erythrocyte aggregation. Biomedical Engineering, IEEE Transactions on 50(8), 1026–1033 (2003). doi:10.1109/TBME.2003.814532

    Article  Google Scholar 

  • Sun, C., Munn, L.L.: Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis. Biophys. J. 88(3), 1635–1645 (2005). doi:10.1529/biophysj.104.051151

    Article  Google Scholar 

  • Suresh, S., Spatz, J., Mills, J.P., Micoulet, A., Dao, M., Lim, C.T., Beil, M., Seufferlein, T.: Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomater. 1(1), 15–30 (2005). doi:10.1016/j.actbio.2004.09.001

    Article  Google Scholar 

  • Tsubota, K.-I., Wada, S., Yamaguchi, T.: Simulation study on effects of hematocrit on blood flow properties using particle method. J. Biomech. Sci. Eng. 1(1), 159–170 (2006). doi:10.1299/jbse.1.159

    Article  Google Scholar 

  • Ye, T., Phan-Thien, N., Khoo, B.C., Lim, C.T.: Dissipative particle dynamics simulations of deformation and aggregation of healthy and diseased red blood cells in a tube flow. Phys. Fluids (1994-present) 26(11), 111902 (2014). doi:10.1063/1.4900952

    Article  Google Scholar 

Download references

Acknowledgments

Support provided by the ARC Future Fellowship Grant (FT100100172), ARC Discovery grant (DP150100828) and the High Performance Computer (HPC) resources in Queensland University of Technology (QUT) are gratefully acknowledged. The fourth author acknowledge that the Australian Governments fully fund the Australian Red Cross Blood Service for the provision of blood products and services to the Australian community.

Author information

Authors and Affiliations

  1. School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD, 4001, Australia

    Hasitha-Nayanajith Polwaththe-Gallage, Suvash C. Saha, Emilie Sauret & Yuantong Gu

  2. Research Program Leader, Research and Development, Australian Red Cross Blood Service, Kelvin Grove, QLD, 4059, Australia

    Robert Flower

Authors
  1. Hasitha-Nayanajith Polwaththe-Gallage
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suvash C. Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emilie Sauret
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert Flower
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuantong Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuantong Gu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polwaththe-Gallage, HN., Saha, S.C., Sauret, E. et al. A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries. Int J Mech Mater Des 12, 477–494 (2016). https://doi.org/10.1007/s10999-015-9328-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-015-9328-8

Keywords

Search

Navigation