Abstract
While the power-law model has been used widely to predict hemolysis numerically, it has a few inherent limitations that may result in inaccurate prediction. As an alternative, the viscoelastic model is a strain-based model derived using the mechanical properties of the red blood cell and erythrocyte. The model assumes two different time scales that lead to modified exponential trends versus the exposure time. As a zero-dimensional model, the viscoelastic model is not applicable to a complex multi-dimensional problem. In the present study, it is extended to a form based on partial differential equations for multi-dimensional hemodynamic flows such as cannulas and blood pumps. The extended method is revised further to comply with a physical constraint. When evaluated using experimental data and relative hemolysis indices, the extended viscoelastic model does not show a clear advantage over the power-law model for cannula problems with relatively short residence times. In contrast, the viscoelastic model shows improved agreement with experimental data consistently for flows inside blood pumps with relatively long residence times. Considering that the viscoelastic model was targeted originally at improving prediction at a long residence time, the present results are consistent with a previous study. As a result, it is implied that the extended viscoelastic model is useful for specific applications such as blood pumps compared to the previous methods.
Similar content being viewed by others
References
M. E. Debakey, The odyssey of the artificial heart, Artificial Organs, 24 (6) (2000) 405–411.
T. Thom, H. Nancy, R. Wayne, R. John and M. Teri, Heart disease and stroke statistics-2006 update: A report from the American heart association statistics committee and stroke statistics subcommittee, Circulation, 113 (6) (2006) e85–e151.
M. Behbahani et al., A review of computational fluid dynamics analysis of blood pumps, European Journal of Applied Mathematics, 20 (4) (2009) 363–397.
E. F. Bernstein, P. L. Blackshear Jr. and K. H. Keller, Factors influencing erythrocyte destruction in artificial organs, The American Journal of Surgery, 114 (1) (1967) 126–138.
C. Crexells, N. Aerichide, Y. Bonny, G. Lepage and L. Campeau, Factors influencing hemolysis in valve prosthesis, American Heart Journal, 84 (2) 161–170.
L. B. Leverett, J. D. Hellums, C. P. Alfrey and E. C. Lynch, Red blood cell damage by shear stress, Biophysical Journal, 12 (3) (1972) 257–273.
D. Arora, M. Behr and M. Pasquali, A tensor-based measure for estimating blood damage, Artificial Organs, 28 (11) (2004) 1002–1015.
M. Behr and M. Pasquali, Hemolysis estimation in a centrifugal blood pump using a tensor-based measure, Artificial Organs, 30 (7) (2006) 539–547.
Y. Chen and M. K. Sharp, A strain-based flow-induced hemolysis prediction model calibrated by in vitro erythrocyte deformation measurements, Artificial Organs, 35 (2) (2011) 145–156.
M. Giersiepen, J. L. Wurzinger, R. Opitz and H. Reul, Estimation of shear stress-related blood damage in heart valve prostheses-in vitro comparison of 25 aortic valves, The International Journal of Artificial Organs, 13 (5) (1990) 300–306.
L. Goubergrits and K. Affeld, Numerical estimation of blood damage in artificial organs, Artificial Organs, 28 (5) (2004) 499–507.
M. Grigioni, C. Daniele, U. Morbiducci, G. D’Avenio, G. Di Benedetto and V. Barbaro, The power-law mathematical model for blood damage prediction: Analytical developments and physical inconsistencies, Artificial Organs, 28 (5) (2004) 467–475.
M. Grigioni, U. Morbiducci, G. D’Avenio, G. Di Benedetto and C. Del Gaudio, A novel formulation for blood trauma prediction by a modified power-law mathematical model, Biomechanics and Modeling in Mechanobiology, 4 (4) (2005) 249–260.
W. L. Lim, Y. T. Chew, T. C. Chew and H. T. Low, Pulsatile flow studies of a porcine bioprosthetic aortic valve in vitro: PIV measurements and shear-induced blood damage, Journal of Biomechanics, 34 (11) (2001) 1417–1427.
R. Paul, J. Apel, S. Klaus, F. Schügner, P. Schwindke and H. Reul, Shear stress related blood damage in laminar Couette flow, Artificial Organs, 27 (6) (2003) 517–529.
G. Heuser and R. Optiz, A couette viscometer for short time shearing of blood, Biorheology, 17 (1–2) (1980) 17–24.
G. Arwatz and A. J. Smits, A viscoelastic model of shear-induced hemolysis in laminar flow, Biorheology, 50 (1–2) (2013) 45–55.
R. P. Rand, Mechanical properties of the red cell membrane, Biophysical Journal, 4 (2) (1964) 303–316.
J. Wan, A. M. Forsyth and H. A. Stone, Red blood cell dynamics: From cell deformation to ATP release, Integrative Biology (2011) 972–981.
A. Garon and M. I. Farinas, Fast three-dimensional numerical hemolysis approximation, Artificial Organs, 28 (11) (2004) 1016–1025.
M. Esmaily-Moghadam, T. Y. Hsia and A. L. Marsden, A non-discrete method for computation of residence time in fluid mechanics simulations, Physics of Fluids, 25 (11) (2013) 110802.
M. I. Farinas, A. Garon, D. Lacasse and D. N’dri, Asymptotically consistent numerical approximation of hemolysis, Journal of Biomechanical Engineering, 128 (5) (2006) 688–696.
D. S. De Wachter, P. R. Verdonck, J. Y. De Vos and R. O. Hombrouckx, Blood trauma in plastic haemodialysis cannulae, International Journal of Artificial Organs, 20 (7) (1997) 366–370.
M. E. Taskin, K. H. Fraser, T. Zhang, C. Wu, B. P. Griffith and Z. J. Wu, Evaluation of Eulerian and Lagrangian models for hemolysis estimation, ASAIO Journal, 58 (4) (2012) 363–372.
T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu, A new k-∈ eddy viscosity model for high reynolds number turbulent flows, Computers and Fluids, 24 (3) (1995) 227–238.
J. Mohara, K. Kawahito, Y. Misawa and K. Fuse, Evaluation of platelet damage in two different centrifugal pumps based on measurements of α-granule packing proteins, Artificial Organs, 22 (5) (1998) 371–374.
Y. Takami et al., Hemolytic characteristics of a pivot bearing supported Gyro centrifugal pump (C1E3) simulating various clinical applications, Artificial Organs, 20 (9) (1996) 1042–1049.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Hyoung-gwon Choi
Seung Hun Lee received the B.S. and M.S. degrees in Mechanical Engineering from Sogang University, Korea in 2016 and 2018. His research interests include problems of mass transfer in medical devices.
Youngmoon Cho received the B.S. degree in Mechanical Engineering from Sogang University, Korea in 2015.
Seongwon Kang received the B.S. and M.S. degrees in Mechanical Engineering from Seoul National University, Korea in 1997 and 1999, and Ph.D. degree in Mechanical Engineering from Stanford University, USA in 2008.
Nahmkeon Hur received the B.S. and M.S. degrees in Mechanical Engineering from Seoul National University, Korea in 1979 and 1981, and Ph.D. degree in Mechanical Engineering from Stevens Institute of Technology, USA in 1988.
Wonjung Kim received the B.S. and M.S. degrees in Mechanical Engineering from Seoul National University, Korea in 2006 and 2009, and Ph.D. degree in Mechanical Engineering from Massachusetts Institute of Technology, USA in 2013.
Rights and permissions
About this article
Cite this article
Lee, S., Cho, Y., Kang, S. et al. Evaluation of an extended viscoelastic model to predict hemolysis in cannulas and blood pumps. J Mech Sci Technol 33, 2181–2188 (2019). https://doi.org/10.1007/s12206-019-0420-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-019-0420-0