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Micro-scale Dynamic Simulation of Erythrocyte–Platelet Interaction in Blood Flow

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Abstract

Platelet activation, adhesion, and aggregation on the blood vessel and implants result in the formation of mural thrombi. Platelet dynamics in blood flow is influenced by the far more numerous erythrocytes (RBCs). This is particularly the case in the smaller blood vessels (arterioles) and in constricted regions of blood flow (such as in valve leakage and hinge regions) where the dimensions of formed elements of blood become comparable with that of the flow geometry. In such regions, models to predict platelet motion, activation, aggregation and adhesion must account for platelet–RBC interactions. This paper studies platelet–RBC interactions in shear flows by performing simulations of micro-scale dynamics using a computational fluid dynamics (CFD) model. A level-set sharp-interface immersed boundary method is employed in the computations in which RBC and platelet boundaries are tracked on a two-dimensional Cartesian grid. The RBCs are assumed to have an elliptical shape and to deform elastically under fluid forces while the platelets are assumed to behave as rigid particles of circular shape. Forces and torques between colliding blood cells are modeled using an extension of the soft-sphere model for elliptical particles. RBCs and platelets are transported under the forces and torques induced by fluid flow and cell–cell and cell–platelet collisions. The simulations show that platelet migration toward the wall is enhanced with increasing hematocrit, in agreement with past experimental observations. This margination is seen to occur due to hydrodynamic forces rather than collisional forces or volumetric exclusion effects. The effect of fluid shear forces on the platelets increases exponentially as a function of hematocrit for the range of parameters covered in this study. The micro-scale analysis can be potentially employed to obtain a deterministic relationship between fluid forces and platelet activation and aggregation in blood flow past cardiovascular implants.

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References

  1. Aarts P. A., et al. Fluid shear as a possible mechanism for platelet diffusivity in flowing blood. J. Biomech. 19(10):799–805, 1986

    Article  PubMed  CAS  Google Scholar 

  2. Aarts P. A., et al. Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arteriosclerosis 8(6):819–824, 1988

    PubMed  CAS  Google Scholar 

  3. Alkhamis T. M., R. L. Beissinger, J. R. Chedian. Effect of red blood cells on platelet adhesion and aggregation in low-stress shear flow. ASAIO Trans. 33(3):636–642, 1987

    PubMed  CAS  Google Scholar 

  4. Barthes-Biesel D., H. Sgaier. Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in a shear flow. J. Fluid Mech. 160:119–135, 1985

    Article  Google Scholar 

  5. Blackshear P. L., K. W. Bartlet, R. J. Forstrom. Fluid dynamic factors affecting particle capture and retention. Ann. NY Acad. Sci. 283:270–279, 1977

    Article  Google Scholar 

  6. Brown C., et al. Morphological, biochemical, and functional changes in human platelets subjected to shear stress. J. Lab. Clin. Med. 86(3):462–471 (1975)

    PubMed  Google Scholar 

  7. Cadroy Y., S. R. Hanson. Effects of red blood cell concentration on hemostasis and thrombus formation in a primate model. Blood 75(11):2185–2193, 1990

    PubMed  CAS  Google Scholar 

  8. Chow T. W., et al. Shear stress-induced Von Willebrand factor binding to platelet glycoprotein Ib initiates calcium influx associated with aggregation. Blood 80(1):113–120, 1992

    PubMed  CAS  Google Scholar 

  9. Cohen H., R. G. Muncaster. The Theory of Pseudo-Rigid Bodies. New York: Springer-Verlag, 1988

    Google Scholar 

  10. Crowe C., M. Sommwerfeld, Y. Tsuji. Multiphase Flows with Droplets and Particles. Boca Raton, FL: CRC Press, 1998

    Google Scholar 

  11. Dulinska I., et al. Stiffness of normal and pathological erythrocytes studied by means of atomic force microscopy. J. Biochem. Biophys. Methods 66(1–3):1–11, 2006

    Article  PubMed  CAS  Google Scholar 

  12. Eckstein E. C., J. F. Koleski, C. M. Waters. Concentration profiles of 1 and 2.5 micrometer beads during blood flow: hematocrit effects. Trans. Am. Soc. Art. Int. Org. 35:188–190, 1989

    CAS  Google Scholar 

  13. Einstein A. Eine Neue Bestimmung Der Molekuldimensionen. Annelen der Physik. 19:289–306, 1906

    Article  CAS  Google Scholar 

  14. Fogelson A. L. A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting. Appl. Math. 52:1089–1110, 1980

    Google Scholar 

  15. Goldsmith H. L., V. T. Turitto. Rheological aspects of thrombosis and haemostasis: basic principles and applications. Icth-report – subcommittee on rheology of the international committee on thrombosis and haemostasis. Thromb. Haemost. 55(3):415–435, 1986

    PubMed  CAS  Google Scholar 

  16. Haga J. H., A. J. Beaudon, J. G. White, J. Strony. Quantification of the passive mechanical properties of the resting platelets. Ann. Biomed. Eng. 29:268–277, 1998

    Article  Google Scholar 

  17. Harrison P. Platelet function analysis. Blood Rev. 19(2):111–123, 2005

    Article  PubMed  Google Scholar 

  18. Hellums J. D. 1993 Whitaker lecture: biorheology in thrombosis research. Ann. Biomed. Eng. 22(5):445–455, 1994

    Article  PubMed  CAS  Google Scholar 

  19. Holme P. A., et al. Shear-induced platelet activation and platelet microparticle formation at blood flow conditions as in arteries with a severe stenosis. Arterioscler. Thromb. Vasc. Biol. 17(4):646–653, 1997

    PubMed  CAS  Google Scholar 

  20. Huang P. Y., J. D. Hellums. Aggregation and disaggregation kinetics of human blood platelets: part I. Development and validation of a population balance method. Biophys. J. 65(1):334–343, 1993

    PubMed  CAS  Google Scholar 

  21. Joist J. H., J. E. Bauman, S. P. Sutera. Platelet adhesion and aggregation in pulsatile shear flow: effects of red blood cells. Thromb. Res. 92(6 Suppl 2):S47–S52, 1998

    PubMed  CAS  Google Scholar 

  22. Keller S. R., R. Skalak. Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120:27–47, 1982

    Article  Google Scholar 

  23. Konstantopoulos K., et al. Shear-induced platelet aggregation in normal subjects and stroke patients. Thromb. Haemost. 74(5):1329–1334, 1995

    PubMed  CAS  Google Scholar 

  24. Marella S., S. Krishnan, H. Liu, H. S. Udaykumar. Sharp interface Cartesian grid method I: an easily implemented technique for 3d moving boundary computations. J. Comput. Phys. 210(1):1–31, 2005

    Article  Google Scholar 

  25. Marella S. V., H. S. Udaykumar. Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components. Phys. Fluids 16:244–264, 2004

    Article  CAS  Google Scholar 

  26. Miyazaki Y., et al. High shear stress can initiate both platelet aggregation and shedding of procoagulant containing microparticles. Blood 88(9):3456–3464, 1996

    PubMed  CAS  Google Scholar 

  27. Peerschke E. I., et al. Ex vivo evaluation of erythrocytosis-enhanced platelet thrombus formation using the cone and plate(let) analyzer: effect of platelet antagonists. Br. J. Haematol. 127(2):195–203, 2004

    Article  PubMed  CAS  Google Scholar 

  28. Ramstack J. M., L. Zuckerman, L. F. Mockros. Shear-induced activation of platelets. J. Biomech. 12(2):113–125, 1979

    Article  PubMed  CAS  Google Scholar 

  29. Rand R. P., E. Lacombe, H. E. Hunt, W. H. Austin. Viscosity of normal human blood under normothermic and hypotherimic conditions. J. Appl. Physiol. 19:117–122, 1964

    PubMed  CAS  Google Scholar 

  30. Reimers R. C., S. P. Sutera, J. H. Joist. Potentiation by red blood cells of shear-induced platelet aggregation: relative importance of chemical and physical mechanisms. Blood 64(6):1200–1206, 1984

    PubMed  CAS  Google Scholar 

  31. Sethian J. A. Evolution, implementation, and application of levelset and fast marching methods for advancing fronts. J. Comp. Phys. 169:503–555, 2001

    Article  CAS  Google Scholar 

  32. Shankaran H., P. Alexandridis, S. Neelamegham. Aspects of hydrodynamic shear regulating shear-induced platelet activation and self-association of Von Willebrand factor in suspension. Blood 101(7):2637–2645, 2003

    Article  PubMed  CAS  Google Scholar 

  33. Snabre P., P. Mills. Rheology of concentrated suspensions of viscoelastic particles. Colloids Surf. A Physiochem. Eng. Asp. 152:79–88, 1999

    Article  CAS  Google Scholar 

  34. Sorensen E. N., et al. Computational simulation of platelet deposition and activation: I. Model development and properties. Ann. Biomed. Eng. 27(4):436–448, 1999

    Article  PubMed  CAS  Google Scholar 

  35. Sorensen E. N., et al. Computational simulation of platelet deposition and activation: Ii. Results for poiseuille flow over collagen. Ann. Biomed. Eng. 27(4):449–458, 1999

    Article  PubMed  CAS  Google Scholar 

  36. Sussman M., E. Fatemi. An efficient, interface-preserving levelset redistancing algorithm and its applications to interface incompressible fluid flow. SIAM J. Sci. Comput. 20:1165–1191, 1999

    Article  Google Scholar 

  37. Sussman M., E. Fatemi, P. Smereka, S. Osher. An improved levelset methods for incompressible two-phase flows. Comput. Fluids 27:663–680, 1998

    Article  CAS  Google Scholar 

  38. Tilles A. W., E. C. Eckstein. The near-wall excess of platelet-sized particles in blood flow: its dependence on hematocrit and wall shear rate. Microvasc. Res. 33(2):211–223, 1987

    Article  PubMed  CAS  Google Scholar 

  39. Turitto V. T., H. J. Weiss. Red blood cells: their dual role in thrombus formation. Science 207(4430):541–543, 1980

    Article  PubMed  CAS  Google Scholar 

  40. Turrito V. T., A. M. Benis, E. F. Leonard. Platelet diffusion in flowing blood. Ind. Eng. Chem. Fundam. 11:216–233, 1972

    Article  Google Scholar 

  41. Wang N.-T., A. L. Fogelson. Computational methods for continuum models of platelet aggregation. J. Comp. Phys. 151:649–675, 1999

    Article  Google Scholar 

  42. Waters C. M., E. C. Eckstein. Concentration profiles of platelet-sized latex beads for conditions relevant to hollow-fiber hemodialyzers. Artif. Organs 14(1):7–13, 1990

    Article  PubMed  CAS  Google Scholar 

  43. Wootton D. M., D. N. Ku. Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Eng. 1:299–329, 1999

    Article  PubMed  CAS  Google Scholar 

  44. Wu K. K. Platelet activation mechanisms and markers in arterial thrombosis. J. Intern. Med. 239(1):17–34, 1996

    Article  PubMed  CAS  Google Scholar 

  45. Yeh C., A. C. Calvez, E. C. Eckstein. An estimated shape function for drift in a platelet-transport model. Biophys. J. 67(3):1252–1259, 1994

    PubMed  CAS  Google Scholar 

  46. Yeh C., E. C. Eckstein. Transient lateral transport of platelet-sized particles in flowing blood suspensions. Biophys. J. 66(5):1706–1716, 1994

    Article  PubMed  CAS  Google Scholar 

  47. Zang Y., R. L. Street, J. R. Koseff. A non-staggered grid, fractional step method for time dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comp. Phys. 114:18–33, 1994

    Article  Google Scholar 

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Acknowledgments

Partial support of this work by a scholarship from Hashemite University, Zarqa, Jordan (T.A.), and from the Iowa Department of Economic Development is gratefully acknowledged.

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  1. T. AlMomani

    Present address: Department of Biomedical Engineering, Hashemite University, Zarqa, Jordan

Authors and Affiliations

  1. Department of Biomedical Engineering, 1402 SC, College of Engineering, University of Iowa, Iowa City, IA , 52242-1527, USA

    T. AlMomani & K. B. Chandran

  2. Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, IA, USA

    H. S. Udaykumar

  3. IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA, USA

    H. S. Udaykumar & K. B. Chandran

  4. School of Engineering, University of Vermont, Burlington, VT, USA

    J. S. Marshall

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  1. T. AlMomani
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Correspondence to K. B. Chandran.

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AlMomani, T., Udaykumar, H.S., Marshall, J.S. et al. Micro-scale Dynamic Simulation of Erythrocyte–Platelet Interaction in Blood Flow. Ann Biomed Eng 36, 905–920 (2008). https://doi.org/10.1007/s10439-008-9478-z

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