Characterization of Blood Flow in Capillaries by Numerical Simulation

Tong Wang, Zhongwen Xing

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DOI: 10.4236/jmp.2010.16049                

Abstract

This paper presents a numerical investigation of the axisymmetric, pressure driven motion of single file erythrocyte (i.e., red blood cell) suspensions flowing in capillaries of diameter 8-11 µm. Our study success-fully recreates several important in vivo hemodynamic and hemorheological properties of microscopic blood flow, such as parachute shape of the cells, blunt velocity profile, and the Fahraeus effect, and they have been shown to have strong dependence on cell deformability, hematocrit and vessel size.

Keywords

Numerical Simulation, Blood Flow Dynamics, Red Blood Cell, Capillary, Rheology

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. Pozrikidis, “Modeling and Simulation of Capsules and Biological Cells,” Chapman and Hall, London, 2003.
[2]	T. W. Secomb, R. Skalak, N. ?zkaya and J. F. Gross, “Flow of Axisymmetric Red Blood Cells in Narrow Cap-illaries,” Journal of Fluid Mechanics, Vol. 163, February 1986, pp. 405-423.
[3]	N. Maeda, “Erythrocyte Rheology in Microcirculation,” The Japanese Journal of Physiology, Vol. 46, 1996, pp. 1-14.
[4]	H. Vink and B. R. Duling, “Identification of Distinct Luminal Domains for Macromolecules, Erythrocytes, and Leukocytes within Mammalian Capillaries,” Circulation Research, Vol. 79, September 1996, pp. 581-598.
[5]	R. Fahraeus, “The Suspension Stability of the Blood,” Physiological Reviews, Vol. 9, April 1929, pp. 241-274.
[6]	S. P. Sutera, V. Seshadri, P. A. Croce, and R. M. Ho-chmuth, “Capillary Blood Flow : II. Deformable Model Cells in Tube Flow,” Microvascular Research, Vol. 2, October 1970, pp. 420-433.
[7]	K. Tsubota, S. Wada, and T. Yamaguchi, “Simulation Study on Effects of Hematocrit on Blood Flow Properties Using Particle Method,” Journal of Biomechanical Sci-ence and Engineering, Vol.1, 2006, pp.159-170.
[8]	C. Pozrikidis, “Axisymmetric Motion of a File of Red Blood Cells through Capillaries,” Physics of Fluids, Vol. 17, March 2005, pp. 1-14.
[9]	J. Zhang, P. Johnson, and A. Popel, “An Immersed Boundary Lattice Boltzmann Approach to Simulate De-formable Liquid Capsules and its Application to Micro-scopic Blood Flows,” Physical Biology, Vol. 4, Decem-ber 2007, 285-295.
[10]	T. Wang, T.-W. Pan, Z.W. Xing and R. Glowinski, “Nu-merical Simulation of Rheology of Red Blood Cell Rouleaux in Microchannels,” Physical Review E, Vol. 79, April 200, pp. 1-11.
[11]	T.-W. Pan and T. Wang, “Dynamical Simulation of Red Blood Cell Rheology in Microvessels,” International Journal of Numerical Analysis & Modeling, Vol. 6, 2009, pp. 455-473.
[12]	J. C. Hansen, R. Skalak, S. Chien and A. Hoger, “Influ-ence of Network Topology on the Elasticity of the Red Blood Cell Membrane skeleton,” Biophysical Journal, Vol. 72, May 1997, pp. 2369-2381.
[13]	C. S. Peskin, “Numerical Analysis of Blood Flow in the Heart,” Journal of Computational Physics, Vol. 25, No-vember 1977, pp. 220-252.
[14]	P. Bagchi, “Mesoscale Simulation of Blood Flow in Small Vessels”, Biophysical Journal, vol. 92, March 2007, pp. 1858-1877.
[15]	C. Eggleton and A. Popel, “Large Deformation of Red Blood Cell Ghosts in a Simple Shear Flow,” Physics of Fluids, Vol. 10, August 1998, pp. 1834-1845.
[16]	Y. Liu and W. K. Liu, “Rheology of Red Blood Cell Ag-gregation by Computer Simulation,” Journal of Compu-tational Physics, Vol. 220, December 2006, pp. 139-154.
[17]	Y. Suzuki, N. Tateishi, M. Soutani, and N. Maeda, “Deformation of Erythrocytes in Microvessels and Glass Capillaries: Effects of Erythrocyte Deformability,” Microcirculation, Vol. 3, March 1996, pp. 49-57.
[18]	K. H. Albrecht, P. Gaehtgens, A. Pries and M. Heuser, “The Fahraeus Effect in Narrow Capillaries (i.d. 3.3 to 11.0 μm),” Microvascular Research, Vol. 18, September 1979, pp. 33-47.
[19]	R. T. Yen and Y. C. Fung, “Inversion of Fahraeus Effect and Effect of Mainstream Flow on Capillary Hematocrit,” Journal of Applied Physiology, Vol. 42, April 1977, pp. 578-586.
[20]	S. Wada and R. Kobayashi, “Numerical Simulation of Various Shape Changes of a Swollen Red Blood Cell by Decrease of Its Volume,” Transactions of the Japan So-ciety Mechanical Engineering (Series A), vol. 69, January 2003, pp.14-21.