Effect of Eddy Length Scale on Mechanical Loading of Blood Cells in Turbulent Flow

  • Patrick N. Dooley
  • Nathan J. QuinlanEmail author


Non-physiological turbulent blood flow is known to occur in and near implanted cardiovascular devices, but its effects on blood are poorly understood. The objective of this work is to investigate the effect of turbulent eddy length scale on blood cell damage, and in particular to test the hypothesis that only eddies similar in size to blood cells can cause damage. The microscale flow near a red blood cell (RBC) in an idealized turbulent eddy is modeled computationally using an immersed boundary method. The model is validated for the special case of a tank-treading RBC. In comparisons between turbulent flow fields, based on Kolmogorov theory, the model predicts that damage due to the smallest eddies is almost independent of the Kolmogorov length scale. The model predicts that within a given flow field, however, eddies of sub-cellular scale are less damaging than larger eddies. Eddy decay time and the turbulent energy spectral density are highlighted as important factors. The results suggest that Kolmogorov scale is not an adequate predictor of flow-induced blood trauma, and highlights the need for deeper understanding of the microscale structure of turbulent blood flow.


Turbulent blood flow Thrombosis Hemolysis Red blood cell Immersed boundary method 



Patrick N. Dooley gratefully acknowledges the support of the Irish Research Council for Science, Engineering and Technology, funded by the National Development Plan.


  1. 1.
    Bagchi, P., P. C. Johnson, and A. S. Popel. Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J. Biomech. Eng. 127:1070–1080, 2005.CrossRefPubMedGoogle Scholar
  2. 2.
    Baldwin, J. T., S. Deutsch, H. L. Petrie, and J. M. Tarbell. Determination of principal Reynolds stresses in pulsatile flows after elliptical filtering of discrete velocity measurements. J. Biomech. Eng. 115:396–403, 1993.CrossRefPubMedGoogle Scholar
  3. 3.
    Bernard, P. S., and J. M. Wallace. Turbulent Flow Analysis, Measurement, and Prediction. Hoboken, NJ: John Wiley & Sons, 2002.Google Scholar
  4. 4.
    Bradshaw, P. An Introduction to Turbulence and Its Measurement. Oxford: Pergamon Press, 1971.Google Scholar
  5. 5.
    Chen, S., G. Doolen, J. R. Herring, R. H. Kraichnan, S. A. Orzag, and Z. Su She. Far-dissipation range of turbulence. Phys. Rev. Lett. 70:3051–3054, 1993.CrossRefPubMedGoogle Scholar
  6. 6.
    Dasi, L. P., L. Ge., and H. A. Simon. Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta. Phys. Fluids 19:067105, 2007.CrossRefGoogle Scholar
  7. 7.
    Davidson, P. A. Turbulence: An Introduction for Scientists and Engineers. Oxford: Oxford University Press, 2004.Google Scholar
  8. 8.
    Ellis, J. T., T. M. Wick, and A. P. Yoganathan. Prosthesis-induced hemolysis: mechanisms and quantification of shear stress. J. Heart Valve Dis. 7:376–386, 1998.PubMedGoogle Scholar
  9. 9.
    Evans, E. A., and P. L. La Celle. Intrinsic material properties of the erythrocyte membrane indicated by mechanical analysis of deformation. Blood 45:29–43, 1975.PubMedGoogle Scholar
  10. 10.
    Evans, E. A., R. Waugh, and L. Melnik. Elastic area compressibility modulus of red cell membrane. Biophys. J. 16:585–595, 1976.CrossRefPubMedGoogle Scholar
  11. 11.
    Fischer, T. M. Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium. Biophys. J. 93:2553–2561, 2007.CrossRefPubMedGoogle Scholar
  12. 12.
    Fischer, T. M., M. Stöhr-Liesen, and H. Schmid-Schönbein. The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202:894–896, 1978.CrossRefPubMedGoogle Scholar
  13. 13.
    Ge, L., L. Dasi, F. Sotiropoulos, and A. J. Yoganathan. Characterization of hemodynamic forces induced by mechanical heart valves: Reynolds vs. viscous stresses. Ann. Biomed. Eng. 36:276–297, 2008.CrossRefPubMedGoogle Scholar
  14. 14.
    Grigioni, M., P. Caprari, A. Tarzia, and G. D’Avenio. Prosthetic heart valves’ mechanical loading of red blood cells in patients with hereditary membrane defects. J. Biomech. 38:1557–1565, 2005.CrossRefPubMedGoogle Scholar
  15. 15.
    Hellums, J. D., and C. H. Brown. Blood cell damage by mechanical forces. In: Cardiovascular Flow Dynamics and Measurements, edited by N. H. C. Hwang and N. A. Normann. Baltimore: University Park Press, 1977.Google Scholar
  16. 16.
    Hochmuth, R. M., and R. E. Waugh. Erythrocyte membrane elasticity and viscosity. Annu. Rev. Physiol. 49:209–219, 1987.CrossRefPubMedGoogle Scholar
  17. 17.
    Jones, S. A. A relationship between Reynolds stresses and viscous dissipation: implications to red cell damage. Ann. Biomed. Eng. 23:21–28, 1995.CrossRefPubMedGoogle Scholar
  18. 18.
    Kameneva, M. V., G. W. Burgreen, K. Kono, B. Repko, J. F. Antaki, and M. Umezu. Effects of turbulent stresses upon mechanical hemolysis: experimental and computational analysis. Am. Soc. Artif. Intern. Organs J. 50:418–423, 2004.Google Scholar
  19. 19.
    Leverett, L. B., J. D. Hellums, C. P. Alfrey, and E. C. Lynch. Red blood cell damage by shear stress. Biophys. J. 12:257–273, 1972.CrossRefPubMedGoogle Scholar
  20. 20.
    Liu, J. S., P. C. Lu, and S. H. Chu. Turbulence characteristics downstream of bileaflet aortic valve prostheses. J. Biomech. Eng. 122:118–124, 2000.CrossRefPubMedGoogle Scholar
  21. 21.
    Lokhandwalla, M., and B. Sturtevant. Mechanical haemolysis in shock wave lithotripsy (SWL): I. Analysis of cell deformation due to SWL flow-fields. Phys. Med. Biol. 46:413–437, 2001.CrossRefPubMedGoogle Scholar
  22. 22.
    Lu, P. C., H. C. Lai, and J. S. Liu. A reevaluation and discussion on the threshold limit for hemolysis in a turbulent shear flow. J. Biomech. 34:1361–1364, 2001.CrossRefPubMedGoogle Scholar
  23. 23.
    Martínez, D. O., S. Chen, G. D. Doolen, R. J. Kraichnan, L. P. Wang, and Y. Zhou. Energy spectrum in the dissipation range of fluid turbulence. J. Plasma Phys. 57:195–201, 1997.CrossRefGoogle Scholar
  24. 24.
    Nobach, H., E. Müller, and C. Tropea. Efficient estimation of power spectral density from laser Doppler anemometer data. Exp. Fluid 24:499–509, 1998.CrossRefGoogle Scholar
  25. 25.
    OpenCFD Limited, OpenFoam 1.4,, 2007.
  26. 26.
    Peskin, C. S., Numerical analysis of blood flow in the heart. J. Comput. Phys. 25:220–252, 1977.CrossRefGoogle Scholar
  27. 27.
    Quinlan, J., and P. Dooley. Models of flow-induced loading on blood cells in laminar and turbulent flow, with application to cardiovascular device flow. Ann. Biomed. Eng. 35:1347–1356, 2007.CrossRefPubMedGoogle Scholar
  28. 28.
    Rand, R. P., and A. C. Burton. Mechanical properties of the red cell membrane: I. Membrane stiffness and intracellular pressure. Biophys. J. 4:115–135, 1964.CrossRefPubMedGoogle Scholar
  29. 29.
    Saddoughi, S. G., and V. Veeravalli. Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268:333–372, 1994.CrossRefGoogle Scholar
  30. 30.
    Sallam, A. M., and N. H. C. Hwang. Human red blood cells in a turbulent shear flow: contribution of Reynolds shear stresses. Biorheology 21:783–797, 1984.PubMedGoogle Scholar
  31. 31.
    Sutera, S. P., and J. H. Joist. Haematological effects of turbulent blood flow. In: Thrombosis, Embolism and Bleeding, edited by E. C. Butchart and E. Bodnar. London: ICR Publishers, 1992.Google Scholar
  32. 32.
    Tran-Son-Tay, R., S. P. Sutera, G. I. Zahalak, and P. R. Rao. Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow. Biophys. J. 51:915–924, 1987.CrossRefPubMedGoogle Scholar
  33. 33.
    Travis, B. R., H. L. Leo, P. A. Shah, D. H. Frakes, and A. P. Yoganathan. An analysis of turbulent shear stresses in leakage flow through a bileaflet mechanical prostheses. J. Biomech. Eng. 124:155–165, 2002.CrossRefPubMedGoogle Scholar
  34. 34.
    Unverdi, S. O., and G. Tryggvason. A front-tracking method for viscous incompressible multi-fluid flows. J. Comput. Phys. 100:25–37, 1997.CrossRefGoogle Scholar
  35. 35.
    Williams, A. R., D. E. Hughes, and W. L. Nyborg. Hemolysis near a transversely oscillating wire. Science 169:871–873, 1970.CrossRefPubMedGoogle Scholar
  36. 36.
    Yoganathan, A. P., T. M. Wick, and H. Reul. Influence of flow characteristics of prosthetic valves on thrombus formation. In: Thrombosis, Embolism and Bleeding, edited by E. C. Butchart and E. Bodnar. London: ICR Publishers, 1992.Google Scholar

Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  1. 1.National Centre for Biomedical Engineering Science and Department of Mechanical and Biomedical EngineeringNational University of IrelandGalwayIreland

Personalised recommendations