Biomechanics and Modeling in Mechanobiology

, Volume 4, Issue 4, pp 249–260

A novel formulation for blood trauma prediction by a modified power-law mathematical model

  • Mauro Grigioni
  • Umberto Morbiducci
  • Giuseppe D’Avenio
  • Giacomo Di Benedetto
  • Costantino Del Gaudio
Original paper


With the increasing use of artificial organs, blood damage has been raising ever more clinical concern. Blood trauma is in fact a major complication resulting from the implantation of medical devices and the use of life support apparatuses. Red blood cells damage predictive models furnish critical information on both the design and the evaluation of artificial organs, because their correct usage and implementation are thought to provide clear and rational guidance for the improvement of safety and efficacy. The currently adopted power-law shear-induced haemolysis prediction model lacks sensitivity with respect to the cumulative effect of previously applied stress magnitudes. An alternative model is proposed where a mechanical quantity was defined, able to describe the blood damage sustained by red cells under unsteady stress conditions, taking into account the load history. The proposed formulation predicted the same trend as the available experimental data. The obtained results have to be considered a preliminary validation of the basic hypothesis of this modified red blood cell damage prediction model. To date, the necessity to design further experiments to validate the proposed damage function clashes with the limitations inherent to current systems to get the time-varying shear stress completely under control.


Red blood cells damage Mathematical model Blood trauma prediction Mechanical haemolysis Time-varying shear stress 


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  1. Apel J, Paul R, Klaus S, Siess T, Reul H (2001)Assessment of haemolysis related quantities in a microaxial blood pump by computational fluid dynamics. Artif Organs 5:341–347CrossRefGoogle Scholar
  2. Baldwin JT, Deutsch S, Geselowitz DB, Tarbell JM (1994) LDA Measurements of Mean Velocity and Reynolds Stress Fields within an Artificial Heart Ventricle. TRANS ASME- J Biomechanical Engineering 116:190–200Google Scholar
  3. Barbaro V, Grigioni M, Daniele C, D’Avenio G (1998) Principal stress analysis in LDA measurement of the flow field downstream of 19-mm Sorin Bicarbon heart valve. Technol Health Care 6(4):259–270PubMedGoogle Scholar
  4. Blackshear PL (1972a) Mechanical haemolysis in flowing blood. In: Fung YC (eds). Biomechanics Its foundation and objectives Englewood Cliffs. Prentice Hall Inc., NJGoogle Scholar
  5. Blackshear PL (1972b) Haemolysis at prosthetic surfaces. In: Hair MR (eds) Chemistry of biosurfaces. Marcel Dekker, New YorkGoogle Scholar
  6. Blackshear PL, Blackshear GL (1987) Mechanical haemolysis. In: Skalak R, Chien S (eds) Handbook of bioengineering. McGraw-Hill, NewYorkGoogle Scholar
  7. Blackshear PL, Dorman FD, Steinbach JH (1965) Some mechanical effects that influence haemolysis. Trans Am Soc Artif Intern Organs 11:112PubMedGoogle Scholar
  8. Bludszuweit C (1995) Three-dimensional numerical prediction of stress loading of blood particles in a centrifugal pump. Artif Organs 19(7):590–596PubMedGoogle Scholar
  9. Bludszuweit C (1995) Model for a general mechanical blood damage prediction. Artif Organs 19(7):583–589PubMedGoogle Scholar
  10. Bodnar E (1996) Editorial: the Medtronic Parallel™ valve and the lessons learned. J Heart Valve Dis 5:572–573PubMedGoogle Scholar
  11. Burgreen GW, Antaki JF, Wu ZJ, Holmes AJ (2001) Computational fluid dynamics as a development tool for rotary blood pumps. Artif Organs 25(5):336–340CrossRefPubMedGoogle Scholar
  12. Chan WK, Wong YW, Ding Y, Chua LP, Yu SC (2002) Numerical investigation of the effect of blade geometry on blood trauma in a centrifugal blood pump. Artif Organs 26(9):785–793CrossRefPubMedGoogle Scholar
  13. De Wachter D, Verdonck P (2002) Numerical calculation of haemolysis levels in peripheral hemodialysis cannulas. Artif Organs 26(7):576–582CrossRefPubMedGoogle Scholar
  14. Ellis JT, Wick TM, Yoganathan AP (1998) Prosthesis-induced haemolysis: mechanisms and quantification of shear stress. J Heart Valve Dis 7:376–386PubMedGoogle Scholar
  15. Giersiepen M, Wurzinger LJ, Opitz R, Reul H (1990) Estimation of shear stress related blood damage in heart valve prostheses: in vitro comparison of 25 aortic valves. Int J Artif Organs 13(5):300–306PubMedGoogle Scholar
  16. Goubergrits L, Affeld K (2004) Numerical estimation of blood damage in artificial organs. Artif Organs 28(5):499–507CrossRefPubMedGoogle Scholar
  17. Grigioni M, Daniele C, D’Avenio G, Barbaro V (1999) A discussion on the threshold limit for haemolysis related to Reynolds shear stress. J Biomech 32(10):1107–1112CrossRefPubMedGoogle Scholar
  18. Grigioni M, Daniele C, Morbiducci U, Di Benedetto G, D’Avenio G, Barbaro V (2002) Mechanical blood trauma potential in vascular access devices: a comparison of case studies. Int J Artif Organs 25(9):882–891PubMedGoogle Scholar
  19. Grigioni M, Daniele C, Morbiducci U, D’Avenio G, Di Benedetto G, Barbaro V (2004) The power-law mathematical model for blood damage prediction: analytical developments and physical inconsistencies. Artif Organs 28(5):467–475CrossRefPubMedGoogle Scholar
  20. Hansen JC, Skalak R, Chien S, Hoger A (1996) An elastic network model based on the structure of the red blood cell membrane skeleton. Biophys J 70(1):146–166PubMedCrossRefGoogle Scholar
  21. Kameneva MV, Marad PF, Brugger JM, Repko BM, Wang JH, Moran J, Borovetz HS (2002) In vitro evaluation of haemolysis and sublethal blood trauma in a novel subcutaneous vascular access system for hemodialysis. ASAIO Journal 48(1):34–38CrossRefPubMedGoogle Scholar
  22. Kameneva MV, Burgreen GW, Kono K, Repko B, Antaki JF, Umezu M (2004) Effects of turbulent stresses on mechanical hemolysis: experimental and computational analysis. ASAIO J 50:418–423CrossRefPubMedGoogle Scholar
  23. Klaus S, Korfer S, Mottaghy K, Reul H, Glasmacher B (2002) In vitro blood damage by high shear flow: human versus porcine blood. Int J Artif Organs 25(4):306–312PubMedGoogle Scholar
  24. Klaus S, Korfer S, Mottaghy K, Reul H, Glasmacher B (2003) Blood traumatization by time varying high shear stresses: investigations with a new model system. Int J Artif Organs 26(7):635Google Scholar
  25. Kuypers FA (1998) Red cell membrane damage. J Heart Valve Dis 7(4):387–395PubMedGoogle Scholar
  26. Leverett LB, Hellums JD, Alfrey CP, Lynch BC (1972) Red blood cell damage by shear stress. Biophysical Journal 12:257–273PubMedGoogle Scholar
  27. Lim WL, Chew YT, Chew TC, Low HT (2001) Pulsatile flow studies of a porcine bioprosthetic aortic valve in vitro: PIV measurements and shear-induced blood damage. J Biomech 34:1417–1427CrossRefPubMedGoogle Scholar
  28. Lu PC, Lai HC, Liu JS (2001) A reevaluation and discussion on the threshold limit for haemolysis in a turbulent shear flow. J Biomech 34(10):1361–1364CrossRefPubMedGoogle Scholar
  29. Maraj R, Jacobs LE, Ioli A, Kotler MN (1998) Evaluation of haemolysis in patients with prosthetic heart valves. Clin Cardiol 21:387–92PubMedGoogle Scholar
  30. Mohandas N, Clark MR, Jacobs MS, Shohet SB (1980) Analysis of factors regulating erythrocyte deformability. J Clin Invest 66(3): 563–573PubMedGoogle Scholar
  31. Mohandas N, Chasis JA, Shohet SB (1983) The influence of membrane skeleton on red cell deformability, membrane material properties, and shape. Semin Hematol 20(3):225–242PubMedGoogle Scholar
  32. Paul R, Apel J, Klaus S, Schugner F, Schwindke P, Reul H (2003) Shear stress related blood damage in laminar couette flow. Artif Organs 27(6):517–529CrossRefPubMedGoogle Scholar
  33. Richardson E (1975) Applications of a theoretical model for haemolysis in shear flow. Biorheology 12:27–37PubMedGoogle Scholar
  34. Sallam AM, Hwang NHC (1984) Human red blood cell haemolysis in a turbulent shear flow: contribution of Reynolds shear stresses. Biorheology 21:783–797PubMedGoogle Scholar
  35. Schima H, Wieselthaler G (1995) Mechanically induced blood trauma: are the relevant questions already solved, or is it still an important field to be investigated? Artif Organs 19(7):563–564PubMedGoogle Scholar
  36. Schima H, Muller MR, Tsangaris S, Gheiseder G, Schlusche C, Losert U, Thoma H, Wolner E (1993) Mechanical blood traumatization by tubing and throttles in in vitro pump tests: experimental results and implications for haemolysis theory. Artif Organs 17(3):164–170PubMedCrossRefGoogle Scholar
  37. Song X, Throckmorton AL, Wood HG, Antaki JF, Olsen DB (2003) Computational fluid dynamics prediction of blood damage in a centrifugal pump. Artif Organs 27(10):938–941CrossRefPubMedGoogle Scholar
  38. Steegers A, Paul R, Reul H, Rau G (1999) Leakage flow at mechanical heart valve prostheses: improved washout or increased blood damage?. J Heart Valve Dis 8(3):312–323PubMedGoogle Scholar
  39. Yano T, Sekine K, Mitoh A, Mitamura Y, Okamoto E, Kim DW, Nishimura I, Murabayashi S, Yozu R (2003) An estimation method of haemolysis within an axial flow blood pump by computational fluid dynamics analysis. Artif Organs 27(10):920–925CrossRefPubMedGoogle Scholar
  40. Yeleswarapu KK, Antaki JF, Kameneva MV, Rajagopal KR (1995) A mathematical model for shear-induced haemolysis. Artif Organs 19(7):576–582PubMedGoogle Scholar
  41. Yobobori T (1968) An interdisciplinary approach to fracture and strenght of solids. Wolters-Noordhoff Scientific Publications Ltd, GroningenGoogle Scholar
  42. Zimmer R, Steegers A, Paul R, Affeld K, Reul H (2000) Velocities, shear stresses and blood damage potential of the leakage jets of the Medtronic Parallel bileaflet valve. Int J Artif Organs 23:41–48PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Mauro Grigioni
    • 1
  • Umberto Morbiducci
    • 1
    • 2
  • Giuseppe D’Avenio
    • 1
  • Giacomo Di Benedetto
    • 1
  • Costantino Del Gaudio
    • 1
  1. 1.Cardiovascular Bioengineering Unit, Technology and Health DepartmentIstituto Superiore di SanitàRomeItaly
  2. 2.Department of MechanicsUniversità Politecnica delle MarcheAnconaItaly

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