Skip to main content

Study of the Partitioning of Red Blood Cells Through Asymmetric Bifurcating Microchannels

Abstract

Purpose

The heterogeneous distribution of red blood cells (RBCs) in the microcirculatory system is a complicated phenomenon because many factors influence how they are partitioned at microvascular bifurcations. In this study, we investigated the RBC partitioning mechanism by fabricating an in vitro experimental apparatus.

Methods

The apparatus comprised a bifurcating, microfluidic channel, and the flow rate through the channels can be controlled readily over a wide range. The division turning point at which an RBC trajectory changes from one bifurcation to the other was identified via particle-tracking velocimetry on individual RBCs.

Results

The experimental results were close to the theoretical predictions and numerical simulations. The hematocrit variation before and after bifurcation was quantitatively estimated by image analysis and compared to the prediction based on Pries’ empirical model. The Zweifach–Fung effect was enhanced in the smaller fractional flow, increasing the RBC flux bias. Moreover, a cell-free layer with axial symmetry was formed in the parent channel, and an asymmetric cell-free layer was formed immediately after bifurcation.

Conclusions

These obtained results will help clarify the RBC partitioning mechanism at microvascular bifurcations.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Goldsmith, H. L. (1986). The microcirculatory society Eugene M. Landis award lecture: The microrheology of human blood. Microvascular Research,31(2), 121–142.

    Google Scholar 

  2. Fung, Y. C. (1997). Biomechanics: Circulation (2nd ed.). New York: Springer.

    Google Scholar 

  3. Popel, A. C. (2005). Microcirculation and hemorheology. Annual Review of Fluid Mechanics,37, 43–69.

    MathSciNet  MATH  Google Scholar 

  4. Chien, S., Tvetenstrand, C. D., Epstein, M. A., & Schmid-Schonbein, G. W. (1985). Model studies on distributions of blood cells at microvascular bifurcations. American Journal of Physiology-Heart and Circulatory Physiology,248(4), 568–576.

    Google Scholar 

  5. Fenton, B. M., Carr, R. T., & Cokelet, G. R. (1985). Nonuniform red cell distribution in 20 to 100 μm bifurcations. Microvascular Research,29(1), 103–126.

    Google Scholar 

  6. Ditchfield, R., & Olbricht, W. L. (1996). Effects of particle concentration on the partitioning of suspensions at small divergent bifurcations. Journal of Biomechanical Engineering,118(3), 287–294.

    Google Scholar 

  7. Roberts, B. W., & Olbricht, W. L. (2003). Flow-induced particulate separations. AIChE Journal,49, 2842–2849.

    Google Scholar 

  8. Roberts, B. W., & Olbricht, W. L. (2006). The distribution of freely suspended particles at microfluidic bifurcations. AIChE Journal,52(1), 199–206.

    Google Scholar 

  9. Doyeux, V., Podgorski, T., Peponas, S., Ismail, M., & Coupier, G. (2011). Spheres in the vicinity of a bifurcation: Elucidating the Zweifach-Fung effect. Journal of Fluid Mechanics,674, 359–388.

    MathSciNet  MATH  Google Scholar 

  10. Schmid-Schonbein, G. W., Skalak, R., Usami, S., & Chien, S. (1980). Cell distribution in capillary networks. Microvascular Research,19(1), 18–44.

    Google Scholar 

  11. Mchedlishvili, G., & Varazashvili, M. (1982). Flow conditions of red cells and plasma in microvascular bifurcations. Biorheology,19(5), 613–620.

    Google Scholar 

  12. Carr, R. T., & Wickham, L. L. (1991). Influence of vessel diameter on red cell distribution at microvascular bifurcations. Microvascular Research,41(2), 184–196.

    Google Scholar 

  13. Pries, A. R., Ley, K., Claassen, M., & Gaehtgens, P. (1989). Red cell distribution at microvascular bifurcations. Microvascular Research,38(1), 81–101.

    Google Scholar 

  14. Pries, A. R., Secomb, T. W., Gaehtgens, P., & Gross, J. F. (1990). Blood flow in microvascular networks. Experiments and simulation. Circulation research,67(4), 826–834.

    Google Scholar 

  15. Ishikawa, T., Fujiwara, H., Matsuki, N., Yoshimoto, T., Imai, Y., Ueno, H., et al. (2011). Asymmetry of blood flow and cancer cell adhesion in a microchannel with symmetric bifurcation and confluence. Biomedical Microdevices,13, 159–167.

    Google Scholar 

  16. Leble, V., Lima, R., Dias, R., Fernandes, C., Ishikawa, T., Imai, Y., et al. (2011). Asymmetry of red blood cell motions in a microchannel with a diverging and converging bifurcation. Biomicrofluidics,5, 044120.

    Google Scholar 

  17. Sherwood, J. M., Kaliviotis, E., Dusting, J., & Balabani, S. (2012). The effect of red blood cell aggregation on velocity and cell-depleted layer characteristics of blood in a bifurcating microchannel. Biomicrofluidics,6(2), 024119.

    Google Scholar 

  18. Sherwood, J. M., Kaliviotis, E., Dusting, J., & Balabani, S. (2014). Hematocrit, viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel. Biomechanics and Modeling in Mechanobiology,13(2), 259–273.

    Google Scholar 

  19. Sherwood, J. M., Holmes, D., Kaliviotis, E., & Balabani, S. (2014). Spatial distributions of red blood cells significantly alter local hemodynamics. PLoS ONE,9, e100473.

    Google Scholar 

  20. Kaliviotis, E., Sherwood, J. M., & Balabani, S. (2017). Partitioning of red blood cell aggregates in bifurcating microscale flows. Scientific Reports,7, 44563.

    Google Scholar 

  21. Kaliviotis, E., Sherwood, J. M., & Balabani, S. (2018). Local viscosity distribution in bifurcating microfluidic blood flows. Physics of Fluids,30(3), 030706.

    Google Scholar 

  22. Clavica, F., Homsy, A., Jeandupeux, L., & Obrist, D. (2016). Red blood cell phase separation in symmetric and asymmetric microchannel networks: Effect of capillary dilation and inflow velocity. Scientific Reports,6, 36763.

    Google Scholar 

  23. Roman, S., Merlo, A., Duru, P., Risso, F., & Lorthois, S. (2016). Going beyond 20 μ m-sized channels for studying red blood cell phase separation in microfluidic bifurcations. Biomicrofluidics,10(3), 034103.

    Google Scholar 

  24. Shen, Z., Coupier, G., Kaoui, B., Polack, B., Harting, J., Misbah, C., et al. (2016). Inversion of hematocrit partition at microfluidic bifurcations. Microvascular Research,105, 40–46.

    Google Scholar 

  25. Kodama, Y., Aoki, H., Yamagata, Y., & Tsubota, K. (2019). In vitro analysis of blood flow in a microvascular network with realistic geometry. Journal of Biomechanics,88, 88–94.

    Google Scholar 

  26. Li, X., Popel, A. S., & Karniadakis, G. E. (2012). Blood–plasma separation in y-shaped bifurcating microfluidic channels: A dissipative particle dynamics simulation study. Physical Biology,9(2), 026010.

    Google Scholar 

  27. Hyakutake, T., & Nagai, S. (2015). Numerical simulation of red blood cell distributions in three-dimensional microvascular bifurcations. Microvascular Research,97, 115–123.

    Google Scholar 

  28. Lykov, K., Li, X., Lei, H., Pivkin, I. V., & Karniadakis, G. E. (2015). Inflow/outflow boundary conditions for particle-based blood flow simulations: Application to arterial bifurcations and trees. PLoS Computational Biology,11(8), e1004410.

    Google Scholar 

  29. Wang, Z., Sui, Y., Salsac, A. V., Barthès-Biesel, D., & Wang, W. (2016). Motion of a spherical capsule in branched tube flow with finite inertia. Journal of Fluid Mechanics,806, 603–626.

    MathSciNet  MATH  Google Scholar 

  30. Balogh, P., & Bagchi, P. (2017). A computational approach to modeling cellular-scale blood flow in complex geometry. Journal of Computational Physics,334, 280–307.

    MathSciNet  Google Scholar 

  31. Balogh, P., & Bagchi, P. (2017). Direct numerical simulation of cellular-scale blood flow in 3D microvascular networks. Biophysical Journal,113, 2815–2826.

    Google Scholar 

  32. Balogh, P., & Bagchi, P. (2018). Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks. Physics of Fluids,30(5), 051902.

    Google Scholar 

  33. Ye, T., Peng, L., & Li, Y. (2018). Three-dimensional motion and deformation of a red blood cell in bifurcated microvessels. Journal of Applied Physics,123(6), 064701.

    Google Scholar 

  34. White, F. M. (1991). Viscous fluid flow (2nd ed.). New York: McGraw-Hill Inc.

    Google Scholar 

  35. McNamara, G. R., & Zanetti, G. (1988). Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters,61(20), 2332.

    Google Scholar 

  36. Succi, S. (2001). The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford: Oxford University Press.

    MATH  Google Scholar 

  37. Peskin, C. S. (1977). Numerical analysis of blood flow in the heart. Journal of Computational Physics,25(3), 220–252.

    MathSciNet  MATH  Google Scholar 

  38. Zhang, J., Johnson, P. C., & Popel, A. S. (2007). An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Physical Biology,4, 285–295.

    Google Scholar 

  39. Crowl, L. M., & Fogelson, A. L. (2010). Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. International Journal for Numerical Methods in Biomedical Engineering,26(3–4), 471–487.

    MathSciNet  MATH  Google Scholar 

  40. Inamuro, T. (2012). Lattice Boltzmann methods for moving boundary flows. Fluid Dynamics Research,44(2), 024001.

    MathSciNet  MATH  Google Scholar 

  41. Guo, Z., Zheng, C., & Shi, B. (2002). Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E,65(4), 046308.

    MATH  Google Scholar 

  42. Evans, E. A., & Fung, Y. C. (1972). Improved measurements of the erythrocyte geometry. Microvascular Research,4, 335–347.

    Google Scholar 

  43. Krüger, T. (2012). Computer simulation study of collective phenomena in dense suspensions of red blood cells under shear. Berlin: Springer.

    Google Scholar 

  44. Oulaid, O., Saad, A. K. W., Aires, P. S., & Zhang, J. (2016). Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows. Computer Methods in Biomechanics and Biomedical Engineering,19(6), 648–662.

    Google Scholar 

  45. Waugh, R. E., & Hochmuth, R. M. (2006). Chapter 60: Mechanics and deformability of hematocytes. In J. D. Bronzino (Ed.), Biomedical engineering fundamentals (3rd ed.). Boca Raton, FL: CRC Press.

    Google Scholar 

Download references

Acknowledgements

This research was supported by a Grant-in-Aid for Scientific Research (C) (No. 18K12052) from the Japan Society for the Promotion of Science, funding from the Japan Keirin Association, and Takahashi Industrial and Economic Research Founding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Toru Hyakutake.

Ethics declarations

Conflict of interest

The authors confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yamamoto, K., Abe, H., Miyoshi, C. et al. Study of the Partitioning of Red Blood Cells Through Asymmetric Bifurcating Microchannels. J. Med. Biol. Eng. 40, 53–61 (2020). https://doi.org/10.1007/s40846-019-00492-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40846-019-00492-9

Keywords

  • Red blood cell
  • Bifurcating channel
  • Cell-free layer
  • Image analysis