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Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions

Published online by Cambridge University Press:  11 April 2011

L. CROWL  and
A. L. FOGELSON
L. CROWL*
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
A. L. FOGELSON
Affiliation:
Department of Mathematics and Department of Bioengineering, 155 South 1400 East, University of Utah, Salt Lake City, UT 84112, USA
*
†Email address for correspondence: [email protected]
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Abstract

The concentration of platelets near the blood vessel wall is important because platelets survey the condition of the vessel wall and respond to injuries to it. Under arterial flow conditions, platelets are non-uniformly distributed across the vessel lumen and have a high concentration within a few microns of the vessel wall. This is believed to be a consequence of the complex motion of red blood cells which constitute a large fraction of the blood's volume. We use a novel lattice Boltzmann-immersed boundary method to simulate, in two dimensions, the motion of dense red blood cell suspensions and their effect on platelet-sized particles. We track the development of a red blood cell-free layer near the wall and the later development of the platelet near-wall excess. We find that the latter develops more quickly at high wall shear rates and that the magnitude of the excess and its proximity to the wall are dependent on haematocrit. Treating the simulation data as if it were generated by a drift–diffusion process, we find that the effective lateral platelet diffusivity depends strongly on lateral position; it has a magnitude of order of 10−6 cm2 s−1 over much of the lumen but drops to almost zero close to the wall. This large effective diffusivity over the core of the lumen combined with reduced space for platelets in this region because of the inward migration of red blood cells largely but not completely accounts for the observed platelet-concentration profiles. We present evidence for a highly localized red blood cell-induced platelet drift at the edge of the red cell-free layer and suggest a physical mechanism that may generate it.

JFM classification

Biological Fluid Dynamics: Blood flow Biological Fluid Dynamics: Capsule/cell dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 348 - 375
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Bagchi, P. 2007 Mesoscale simulation of blood flow in small vessels. Biophys. J. 92, 1858–1877.CrossRefGoogle ScholarPubMed
Barthes-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222.CrossRefGoogle Scholar
Chan, P. C.-H. & Leal, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92, 131–170.CrossRefGoogle Scholar
Climent, E. & Maxey, M. R. 2003 Numerical simulations of random suspensions at finite Reynolds numbers. Intl J. Multiphase Flow 29 (4), 579–601.CrossRefGoogle Scholar
Crowl, L. & Fogelson, A. L. 2010 Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Intl J. Numer. Meth. Biomed. Engng 26 (3–4), 471–487.CrossRefGoogle ScholarPubMed
Dupin, M. M., Halliday, I., Care, C. M., Alboul, L. & Munn, L. L. 2007 Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys. Rev. E 75, 066707-1-17.CrossRefGoogle ScholarPubMed
Eckstein, E. C. & Belgacem, F. 1991 Model of platelet transport in flowing blood with drift and diffusion terms. Biophys. J. 60, 53–69.Google Scholar
Eckstein, E. C., Tilles, A. W. & Millero, F. J. III 1988 Conditions for the occurrence of large near-wall excesses of small particles during blood flow. Microvasc. Res. 36, 31–39.CrossRefGoogle ScholarPubMed
Eggleton, C. D. & Popel, A. S. 1998 Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10 (8), 1834–1845.CrossRefGoogle Scholar
Fischer, T. M., Stohr-Lissen, M. & Schmid-Schonbein, H. 1978 The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894–896.CrossRefGoogle ScholarPubMed
Fogelson, A. L. & Guy, R. D. 2008 Immersed-boundary-type models of intravascular platelet aggregation. Comput. Meth. Appl. Mech. Engng 197, 2087–2104.CrossRefGoogle Scholar
Fogelson, A., Kuharsky, A. & Yu, H. 2003 Computational modeling of blood clotting: coagulation and three-dimensional platelet aggregation. In Polymer and Cell Dynamics: Multicsale Modeling and Numerical Simulations (ed. Alt, W., Chaplain, M., Griebel, M. & Lenz, J.), pp. 145–154. Birkhaeuser-Verlag.CrossRefGoogle Scholar
Gardiner, C. W. 2004 Handbook of Stochastic Method for Physics, Chemistry, and the Natural Sciences. Springer.CrossRefGoogle Scholar
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall. Part II. Couette flow. Chem. Engng Sci. 22, 653–660.CrossRefGoogle Scholar
Goldsmith, H. 1971 Red cell motions and wall interactions in tube flow. Fed. Proc. 30 (5), 1578–1588.Google Scholar
Goldsmith, H. L. & Marlow, J. 1972 Flow behavior of erythrocytes. Part I. Rotation and deformation in dilute suspensions. Proc. R. Soc. Lond. B 182 (1068), 351–384.Google Scholar
Guo, Z., Zheng, C. & Shi, B. 2002 Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 1–6.CrossRefGoogle ScholarPubMed
He, X., Zou, Q., Luo, L. & Dembo, M. 1997 Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann [BGK] model. J. Stat. Phys. 87 (1/2), 115–136.Google Scholar
Hu, H. H. & Joseph, D. D. 1999 Lift on a sphere near a plane wall in a second order fluid. J. Non-Newtonian Fluid Mech. 88, 173–184.Google Scholar
Koleski, J. F. & Eckstein, E. C. 1991 Near wall concentration profiles of 1.0 and 2.5 μm beads during flow of blood suspensions. Trans. Am. Soc. Artif. Intern. Organs 37, 9–12.Google Scholar
Ladd, A. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104 (5/6), 1191–1251.Google Scholar
MacMeccan, R. M., Clausen, J. R., Neitzel, G. P. & Aidun, C. K. 2009 Simulating deformable particle suspensions using a coupled lattice-boltzmann and finite-element method. J. Fluid Mech. 618, 13–39.Google Scholar
McLaughlin, J. B. 1993 The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 246, 249–265.CrossRefGoogle Scholar
Nguyen, N. Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations. Phys. Rev. E 66 (4), 046708[1–12].CrossRefGoogle ScholarPubMed
Pan, T. W., Joseph, D. D., Bai, R., Glowinski, R. & Sarin, V. 2002 Fluidization of 1204 spheres: Simulation and experiment. J. Fluid Mech. 451, 169–191.CrossRefGoogle Scholar
Peskin, C. 2002 The Immersed Boundary method. Acta Numerica 11, 1–39.Google Scholar
Pozrikidis, C. 2001 Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech. 440, 269–291.Google Scholar
Qian, H., Sheetz, M. P. & Elson, E. L. 1991 Single particle tracking: Analysis of diffusion and flow in two-dimensional systems. Biophys. J. 60, 910–921.CrossRefGoogle ScholarPubMed
Savitzky, A. & Golay, M. J. E. 1964 Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639.CrossRefGoogle Scholar
Skalak, R., Tozeren, A., Zarda, R. & Chein, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245–264.Google Scholar
Sui, Y., Chew, Y. T. & Low, H. T. 2007 A lattice Boltzmann study on the large deformation of red blood cells in shear flow. Intl J. Mod. Phys. C 18 (6), 993–1011.CrossRefGoogle Scholar
Tangelder, G. J., Teirlinck, H. C. & Slaaf, D. W., Reneman, R. S. 1985 Distribution of blood platelets flowing in arterioles. Am. J. Physiol. Heart Circ. 248 (3), H318–H323.CrossRefGoogle ScholarPubMed
Tilles, A. W. & Eckstein, E. C. 1987 The near-wall excess of platelet-sized particles in blood flow: Its dependence on hematocrit and wall shear rate. Microvasc. Res. 33, 211–223.CrossRefGoogle ScholarPubMed
Turitto, V. T., Benis, A. M. & Leonard, E. F. 1972 Platelet diffusion in flowing blood. Ind. Engng Chem. Fundamen. 11 (2), 216–223.Google Scholar
Vikhansky, A. 2003 A new modification of the immersed boundary method for fluid-solid flows: moderate Reynolds numbers. J. Comput. Phys. 191, 328–339.Google Scholar
Wohl, P. R. & Rubinow, S. L. 1974 The transverse force on a drop in an unbounded parabolix flow. J. Fluid Mech. 62, 185–207.Google Scholar
Woldhuis, B., Tangelder, G. J., Slaaf, D. W. & Reneman, R. S. 1992 Concentration profile of blood platelets differs in arterioles and venules. Am. J. Physiol. Heart Circ. 262 (4), H1217–H1223.CrossRefGoogle ScholarPubMed
Yeh, C., Calvez, A. C. & Eckstein, E. C. 1994 An estimated shape function for drift in a platelet-transport model. Biophys. J. 67, 1706–1716.CrossRefGoogle Scholar