Annals of Biomedical Engineering

, Volume 34, Issue 6, pp 958–970 | Cite as

Near-Wall Deposition Probability of Blood Elements as A New Hemodynamic Wall Parameter

  • Min-Cheol Kim
  • Jin Hyun Nam
  • Chong-Sun Lee
Original Paper

The present study was performed to investigate deposition probability of blood particles on the vessel walls. To track dynamics of movement and adhesion of blood particles in the near wall region, two models such as the particle rolling model (PR-model) and the near wall force model (NWF-model) were employed in the present study. Simulations of the present models for the pre-activated platelets in the stagnated point flow chamber and for the pre-activated monocytes in the stenotic perfusion tube resulted in significant correlations with the experimental data. The proposed near wall deposition probability (NWDP) index exhibited good fits with the experimental data of the stagnation point flow chamber for the platelet. As for the monocyte, the NWDP index exhibited the best fit with the experimental data of the stenotic tube. The new hemodynamic index, NWDP, is different from the wall shear stress (WSS)-based hemodynamic parameters, such as MWSS (Mean Wall Shear Stress), AWSS (Amplitude of Wall Shear Stress), and OSI (Oscillatory Shear Index) in that it locates regions of both the high and low WSS. The proposed NWDP index needs to be tested and compared in real geometries for its effectiveness in locating regions of lesion-prone sites.


NWDP (Near-wall deposition probability) Particle deposition model Platelet Monocyte Particle trajectory Computer simulation Hemodynamics 



ratio of correction factors c 1 and c 2 in NWDP index


area (m2)


contact area of the particle on the wall (m2)


constant in Eq. (8)


constant in Eq. (8)


correction factor of t m to fit with actual movement of the particle


correction factor of t a to fit with actual adhesion of the particle


diameter (m)


particle diameter (m)


distance from the horizontal plate in a stagnation flow chamber (m)


distance from the center of the particle to the wall surface (m)


spatial coordinate in the radial direction (m)


particle radius (m)


radius (m)


time (s)


time scale for the adhesion of a particle (s)


time scale for the movement of a particle (s)


pulse period (s)


average velocity (ms−1)


relative coordinate in the wall normal direction (m)


spatial coordinate in the axial direction (m)


diameter based Reynolds number (Ud/v)

\( \alpha \)

Wormersley number \( (R\sqrt {\omega /\nu }) \)

\( \Re \)

correlation coefficient

\( \nu \)

kinematic viscosity \( ({{\eta/\rho }}) \) (m2 s−1)

\( \eta \)

dynamic viscosity (kg m−1 s−1)

\( \rho \)

fluid density (kg m−3)

\( \rho _p \)

particle density (kg m−3)

\( \omega \)

angular velocity \( ({{{2\pi}/T}}) \) (s−1)









This work was conducted with the supports of Korean Ministry of Health and Welfare, 02-PJ3-PG3-31403-0004.


  1. 1.
    Affeld, K., A. J. Reininger, J. Gadischke, K. Grunert, S. Schmidt, and F. Thiele. Fluid mechanics of the stagnation point flow chamber and its platelet deposition. Artificial Organs 19:597–602, 1995.PubMedCrossRefGoogle Scholar
  2. 2.
    Alevriadou, B. R., J. M. Moake, N. A. Turner, Z. M. Ruggeri, et al. Real Time Analysis Shear-Dependant Thrombus Formation and Its blockade by Inhibitor of Von Willebrand Factor Binding to Platelets. Blood 5:1263–1276, 1993.Google Scholar
  3. 3.
    Barber, K. M., A. Pinero, and G. A. Truskey. Effect of recirculating flow on U-937 cell adhesion to human umbilical vein endothelial cells. Am. J. Physiol. 275:591–598, 1998.Google Scholar
  4. 4.
    Bombeli, T., B. R. Schwarz, and J. M. Harlan. Adhesion of activated platelets to Endotherial cells: Evidence for a GPIIbIIIa-dependent Bridging Mechanism and Novel Roles for Endotherial Intercellular Adhesion Molecular 1 (ICAM-1), αvβ3 Integrin and GPIbα. J. Exp. Med. 187:329–339, 1997.CrossRefGoogle Scholar
  5. 5.
    Bonnefoy, A., Q. Liu, C. Legrand, and M. M. Frojmonvic. Efficiency of Platelet Adhesion to fibrinogen Depends on both Cell Activation and Flow. Biophy. J. 78:2834–2843, 2000.Google Scholar
  6. 6.
    Brenner, H. The slow motion of a sphere through a viscous fluid toward a plane surface. Chem. Eng. Sci. 16:242–251, 1961.CrossRefGoogle Scholar
  7. 7.
    Buchanan, J. R., Jr., C. Kleinstreuer, and J. K. Comer. Rheologycal effects on pulsatile hemodynamics in a stenosed tube. Com. Fluids 29:695–724, 2000.CrossRefGoogle Scholar
  8. 8.
    Burger, P. C., and D. D. Wagner. Platelet P-selectin facilitates atherosclerosis lesion development. Blood 101:2661–2666, 2003.PubMedCrossRefGoogle Scholar
  9. 9.
    Cherukat, P., and J. B. McLaughlin. The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263:1–18, 1994.CrossRefGoogle Scholar
  10. 10.
    Ehrlich, L. W., and M. H. Friedman. Particle path and stasis in unsteady flow through a bifurcation. J. Biomech.10:561–568, 1977.PubMedCrossRefGoogle Scholar
  11. 11.
    Evasgelista, V., S. Manarini, S. Rotondo, N. Marterlli et al. Platelet/Polymorphonuclear Leukocyte Interaction in Dynamic Conditions: Evidence of Adhesion Cascade and Cross Talk Between P-Selectin and β2 Integrin CD11b/CD18. Blood 88:4183–4194, 1996.Google Scholar
  12. 12.
    Faxén, H. Die Bewegung einer starren Kugel Längs der Achse eines mit zaher Flüsigkeit fefüllten Rohres. Arkiv Mat. Astron. Fys. 17:1–28, 1923.Google Scholar
  13. 13.
    Fukagata, K., S. Zarhrai, F. H. Bark, and S. Kondo. Influence of the near-wall drag correction in a Lagrangina simulation of particulate turbulent channel flow. Proceedings of the First Symposium on Turbulence and Shear Flow Phenomena, Santa Barbara, 259–264, 1999.Google Scholar
  14. 14.
    Gonzales, R. S., and T. M. Wick. Hemodynamics modulation of monocytic cell adherence to vascular endothelium. Ann. Biomed. Eng. 24:382–393, 1996.PubMedCrossRefGoogle Scholar
  15. 15.
    Hinds, M. T., Y. J. Park, S. A. Jones, D. P. Giddens, and B. R. Alevriadou. Local hemodynamics affect monocytic cell adhesion to a three-dimensional flow model coated with E-selectin. J. Biomech. 34:95–103, 2001.PubMedCrossRefGoogle Scholar
  16. 16.
    Hyun, S., C. Kleinstreuer, and J. P. Archie. Computational particle-hemodynamics analysis and geometric reconstruction after carotid endarterectomy. Comp. Bio. Med. 31:365–384, 2001.CrossRefGoogle Scholar
  17. 17.
    Karino, T., and H. L. Goldsmith. Flow behavior of blood cells and rigid spheres in an annular vortex. Philosoph. Trans. Roy. Soc. Lond.: Series B 279:413–445, 1977.CrossRefGoogle Scholar
  18. 18.
    Karino, T., and H. L. Goldsmith. Adhesion of human platelets to collagen on the walls distal to a tubular expansion. Microvasc. Res. 17:238–262, 1979.PubMedCrossRefGoogle Scholar
  19. 19.
    Li, N., H. Hu, M. Lindqvist, E. Wikström-Jonsson, A. H. Goodall, and P. Hjemdahl. Platelet-Leukocyte Cross talk in Whole Blood. Arterioscler Thromb Vasc Biol. 20:2702–2708, 2000.PubMedGoogle Scholar
  20. 20.
    Libby, P. Inflammation in atherosclerosis. Nature 420:868–874, 2000.CrossRefGoogle Scholar
  21. 21.
    Longest, P. W. Computational Analysis of Transient Particle Hemodynamics with Application to Femoral Bypass Graft Designs. Ph.D. Theses, Mechanical and Aerospace Engineering Department, North Carolina State University, Raleigh, NC, 2002.Google Scholar
  22. 22.
    Longest, P. W., and C. Kleinstreuer. Numerical simulation of wall shear stress conditions and platelet localization in realistic end-to-side arterial anastomoses. ASME J. Biomech. Eng. 125:671–681, 2003a.CrossRefGoogle Scholar
  23. 23.
    Longest, P. W., and C. Kleinstreuer. Comparison of blood particle deposition models for non-parallel flow domains. J. Biomech. 36:421–430, 2003b.CrossRefGoogle Scholar
  24. 24.
    Lusis, A. J.. Atherosclerosis. Nature 407:233–241, 2000.PubMedCrossRefGoogle Scholar
  25. 25.
    McLaughlin, J. B. The lift on a small sphere in wakk-bounded linear shear flows. J. Fluid Mech. 226:249–265, 1993.CrossRefGoogle Scholar
  26. 26.
    Pritchard, W. F., P. F. Davies, Z. Derafshi, D. C. Polacek, R. Tsao, R. O. Dull, S. A. Jones, and D. P. Giddens. Effect of wall shear stress and fluid recirculation of the localization of circulating monocytes in a theree-dimensional flow model. J. Biomech. 28:1459–1469, 1995.PubMedCrossRefGoogle Scholar
  27. 27.
    Rinker, K. D., V. Prabhakar, and G. A. Truskey. Effect of Contact Time and Force on Monocyte Adhesion to Vascular Endothelium. Biophy. J. 80:1722–2732, 2001.CrossRefGoogle Scholar
  28. 28.
    Tambasco, M., D. A. Steinman. Path-Dependent Hemodynamics of the Stenosed Carotid Bifurcation. Ann. Biomed. Eng. 31:1054–1065, 2003.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulKorea
  2. 2.School of Mechanical & Automotive EngineeringKookmin UniversitySeoulKorea
  3. 3.Department of Mechanical and Control EngineeringHandong Global UniversityPohangKorea
  4. 4.Professor of Department of Mechanical and Control EngineeringCE2-104, Handong Global University, Heunghae-eup, Buk-guPohangSeoulKorea

Personalised recommendations