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.
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References
Goldsmith, H. L. (1986). The microcirculatory society Eugene M. Landis award lecture: The microrheology of human blood. Microvascular Research,31(2), 121–142.
Fung, Y. C. (1997). Biomechanics: Circulation (2nd ed.). New York: Springer.
Popel, A. C. (2005). Microcirculation and hemorheology. Annual Review of Fluid Mechanics,37, 43–69.
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.
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.
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.
Roberts, B. W., & Olbricht, W. L. (2003). Flow-induced particulate separations. AIChE Journal,49, 2842–2849.
Roberts, B. W., & Olbricht, W. L. (2006). The distribution of freely suspended particles at microfluidic bifurcations. AIChE Journal,52(1), 199–206.
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.
Schmid-Schonbein, G. W., Skalak, R., Usami, S., & Chien, S. (1980). Cell distribution in capillary networks. Microvascular Research,19(1), 18–44.
Mchedlishvili, G., & Varazashvili, M. (1982). Flow conditions of red cells and plasma in microvascular bifurcations. Biorheology,19(5), 613–620.
Carr, R. T., & Wickham, L. L. (1991). Influence of vessel diameter on red cell distribution at microvascular bifurcations. Microvascular Research,41(2), 184–196.
Pries, A. R., Ley, K., Claassen, M., & Gaehtgens, P. (1989). Red cell distribution at microvascular bifurcations. Microvascular Research,38(1), 81–101.
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.
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.
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.
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.
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.
Sherwood, J. M., Holmes, D., Kaliviotis, E., & Balabani, S. (2014). Spatial distributions of red blood cells significantly alter local hemodynamics. PLoS ONE,9, e100473.
Kaliviotis, E., Sherwood, J. M., & Balabani, S. (2017). Partitioning of red blood cell aggregates in bifurcating microscale flows. Scientific Reports,7, 44563.
Kaliviotis, E., Sherwood, J. M., & Balabani, S. (2018). Local viscosity distribution in bifurcating microfluidic blood flows. Physics of Fluids,30(3), 030706.
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.
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.
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.
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.
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.
Hyakutake, T., & Nagai, S. (2015). Numerical simulation of red blood cell distributions in three-dimensional microvascular bifurcations. Microvascular Research,97, 115–123.
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.
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.
Balogh, P., & Bagchi, P. (2017). A computational approach to modeling cellular-scale blood flow in complex geometry. Journal of Computational Physics,334, 280–307.
Balogh, P., & Bagchi, P. (2017). Direct numerical simulation of cellular-scale blood flow in 3D microvascular networks. Biophysical Journal,113, 2815–2826.
Balogh, P., & Bagchi, P. (2018). Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks. Physics of Fluids,30(5), 051902.
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.
White, F. M. (1991). Viscous fluid flow (2nd ed.). New York: McGraw-Hill Inc.
McNamara, G. R., & Zanetti, G. (1988). Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters,61(20), 2332.
Succi, S. (2001). The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford: Oxford University Press.
Peskin, C. S. (1977). Numerical analysis of blood flow in the heart. Journal of Computational Physics,25(3), 220–252.
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.
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.
Inamuro, T. (2012). Lattice Boltzmann methods for moving boundary flows. Fluid Dynamics Research,44(2), 024001.
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.
Evans, E. A., & Fung, Y. C. (1972). Improved measurements of the erythrocyte geometry. Microvascular Research,4, 335–347.
Krüger, T. (2012). Computer simulation study of collective phenomena in dense suspensions of red blood cells under shear. Berlin: Springer.
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.
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.
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.
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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
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DOI: https://doi.org/10.1007/s40846-019-00492-9