Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1991 Jul;60(1):53–69. doi: 10.1016/S0006-3495(91)82030-6

Model of platelet transport in flowing blood with drift and diffusion terms.

E C Eckstein 1, F Belgacem 1
PMCID: PMC1260038  PMID: 1883945

Abstract

A drift term is added to the convective diffusion equation for platelet transport so that situations with near-wall excesses of platelets can be described. The mathematical relationship between the drift and the fully developed, steady-state platelet concentration profile is shown and a functional form of the drift that leads to concentration profiles similar to experimentally determined profiles is provided. The transport equation is numerically integrated to determine concentration profiles in the developing region of a tube flow. With the approximate drift function and typical values of augmented diffusion constant, the calculated concentration profiles have near-wall excesses that mimic experimental results, thus implying the extended equation is a valid description of rheological events. Stochastic differential equations that are equivalent to the convective diffusion transport equation are shown, and simulations with them are used to illustrate the impact of the drift term on platelet concentration profiles during deposition in a tube flow.

Full text

PDF
53

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Aarts P. A., Steendijk P., Sixma J. J., Heethaar R. M. Fluid shear as a possible mechanism for platelet diffusivity in flowing blood. J Biomech. 1986;19(10):799–805. doi: 10.1016/0021-9290(86)90130-2. [DOI] [PubMed] [Google Scholar]
  2. Aarts P. A., van den Broek S. A., Prins G. W., Kuiken G. D., Sixma J. J., Heethaar R. M. Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arteriosclerosis. 1988 Nov-Dec;8(6):819–824. doi: 10.1161/01.atv.8.6.819. [DOI] [PubMed] [Google Scholar]
  3. Beck M. R., Jr, Eckstein E. C. Preliminary report on platelet concentration in capillary tube flows of whole blood. Biorheology. 1980;17(5-6):455–464. [PubMed] [Google Scholar]
  4. Bilsker D. L., Waters C. M., Kippenhan J. S., Eckstein E. C. A freeze-capture method for the study of platelet-sized particle distributions. Biorheology. 1989;26(6):1031–1040. doi: 10.3233/bir-1989-26606. [DOI] [PubMed] [Google Scholar]
  5. Bugliarello G., Sevilla J. Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes. Biorheology. 1970 Aug;7(2):85–107. doi: 10.3233/bir-1970-7202. [DOI] [PubMed] [Google Scholar]
  6. Carr R. T. Estimation of hematocrit profile symmetry recovery length downstream from a bifurcation. Biorheology. 1989;26(5):907–920. [PubMed] [Google Scholar]
  7. Corattiyl V., Eckstein E. C. Regional platelet concentration in blood flow through capillary tubes. Microvasc Res. 1986 Sep;32(2):261–270. doi: 10.1016/0026-2862(86)90061-0. [DOI] [PubMed] [Google Scholar]
  8. Eckstein E. C., Koleski J. F., Waters C. M. Concentration profiles of 1 and 2.5 microns beads during blood flow. Hematocrit effects. ASAIO Trans. 1989 Jul-Sep;35(3):188–190. [PubMed] [Google Scholar]
  9. Eckstein E. C. Rheophoresis--a broader concept of platelet dispersivity. Biorheology. 1982;19(6):717–724. doi: 10.3233/bir-1982-19605. [DOI] [PubMed] [Google Scholar]
  10. Eckstein E. C., Tilles A. W., Millero F. J., 3rd Conditions for the occurrence of large near-wall excesses of small particles during blood flow. Microvasc Res. 1988 Jul;36(1):31–39. doi: 10.1016/0026-2862(88)90036-2. [DOI] [PubMed] [Google Scholar]
  11. Folie B. J., McIntire L. V. Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow. Biophys J. 1989 Dec;56(6):1121–1141. doi: 10.1016/S0006-3495(89)82760-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Friedman L. I., Liem H., Grabowski E. F., Leonard E. F., McCord C. W. Inconsequentiality of surface properties for initial platelet adhesion. Trans Am Soc Artif Intern Organs. 1970;16:63–73. [PubMed] [Google Scholar]
  13. Goldsmith H. L. Red cell motions and wall interactions in tube flow. Fed Proc. 1971 Sep-Oct;30(5):1578–1590. [PubMed] [Google Scholar]
  14. Goldsmith H. L., Turitto V. T. 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. 1986 Jun 30;55(3):415–435. [PubMed] [Google Scholar]
  15. Hubbell J. A., McIntire L. V. Visualization and analysis of mural thrombogenesis on collagen, polyurethane and nylon. Biomaterials. 1986 Sep;7(5):354–363. doi: 10.1016/0142-9612(86)90006-2. [DOI] [PubMed] [Google Scholar]
  16. Keller K. H. Effect of fluid shear on mass transport in flowing blood. Fed Proc. 1971 Sep-Oct;30(5):1591–1599. [PubMed] [Google Scholar]
  17. Palmer A. A. Platelet and leucocyte skimming. Bibl Anat. 1967;9:300–303. [PubMed] [Google Scholar]
  18. Perkkiö J., Hokkanen J., Keskinen R. Theoretical model of phase separation of erythrocytes, platelets, and plasma at branches. Med Phys. 1986 Nov-Dec;13(6):882–886. doi: 10.1118/1.595813. [DOI] [PubMed] [Google Scholar]
  19. Perkkiö J., Wurzinger L. J., Schmid-Schönbein H. Plasma and platelet skimming at T-junctions. Thromb Res. 1987 Mar 1;45(5):517–526. doi: 10.1016/0049-3848(87)90314-8. [DOI] [PubMed] [Google Scholar]
  20. Popel A. S. Theory of oxygen transport to tissue. Crit Rev Biomed Eng. 1989;17(3):257–321. [PMC free article] [PubMed] [Google Scholar]
  21. Sakariassen K. S., Baumgartner H. R. Axial dependence of platelet-collagen interactions in flowing blood. Upstream thrombus growth impairs downstream platelet adhesion. Arteriosclerosis. 1989 Jan-Feb;9(1):33–42. doi: 10.1161/01.atv.9.1.33. [DOI] [PubMed] [Google Scholar]
  22. Tangelder G. J., Slaaf D. W., Tierlinck H. C., Alewijnse R., Reneman R. S. Localization within a thin optical section of fluorescent blood platelets flowing in a microvessel. Microvasc Res. 1982 Mar;23(2):214–230. doi: 10.1016/0026-2862(82)90066-8. [DOI] [PubMed] [Google Scholar]
  23. Tilles A. W., Eckstein E. C. The near-wall excess of platelet-sized particles in blood flow: its dependence on hematocrit and wall shear rate. Microvasc Res. 1987 Mar;33(2):211–223. doi: 10.1016/0026-2862(87)90018-5. [DOI] [PubMed] [Google Scholar]
  24. Waters C. M., Eckstein E. C. Concentration profiles of platelet-sized latex beads for conditions relevant to hollow-fiber hemodialyzers. Artif Organs. 1990 Feb;14(1):7–13. doi: 10.1111/j.1525-1594.1990.tb01586.x. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES