On the representation of effective stress for computing hemolysis

  • P. WuEmail author
  • Q. Gao
  • P.-L. Hsu
Original Paper


Hemolysis is a major concern in blood-circulating devices, which arises due to hydrodynamic loading on red blood cells from ambient flow environment. Hemolysis estimation models have often been used to aid hemocompatibility design. The preponderance of hemolysis models was formulated on the basis of laminar flows. However, flows in blood-circulating devices are rather complex and can be laminar, transitional or turbulent. It is an extrapolation to apply these models to turbulent flows. For the commonly used power-law models, effective stress has often been represented using Reynolds stresses for estimating hemolysis in turbulent flows. This practice tends to overpredict hemolysis. This study focused on the representation of effective stress in power-law models. Through arithmetic manipulations from Navier–Stokes equation, we showed that effective stress can be represented in terms of energy dissipation, which can be readily obtained from CFD simulations. Three cases were tested, including a capillary tube, the FDA benchmark cases of nozzle model and blood pump. The results showed that the representation of effective stress in terms of energy dissipation greatly improved the prediction of hemolysis for a wide range of flow conditions. The improvement increases as Reynolds number increases; the overprediction of hemolysis was reduced by up to two orders of magnitude.


Hemolysis Blood damage Scalar stress Energy dissipation Reynolds stress CFD 



The authors also would like to acknowledge the coordinated support from Natural Science Foundation of China (Grant No. 51406127); Natural Science Foundation of Jiangsu Province (Grant No. BK20140344). Insightful comments by the reviewers are also acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Artificial Organ Technology Lab, Bio-manufacturing Research Centre, School of Mechanical and Electric EngineeringSoochow UniversitySuzhouChina
  2. 2.Institute of Fluid MechanicsZhejiang UniversityHangzhouChina

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