Development of multi-phase models of blood flow for medium-sized vessels with stenosis

The purpose of the work was to develop two-phase non-Newtonian blood models for medium-sized vessels with stenosis using power law and Herschel-Bulkley models.

The blood flow was simulated in 3D models of blood vessels with 60% stenosis. The Ansys Fluent software was applied to implement the two-phase non-Newtonian blood models. In the present paper, the mixture model was selected to model the two phases of blood: plasma and red blood cells.

Simulations were carried out for four blood models: a) single-phase non-Newtonian, b) two-phase non-Newtonian, c) two-phase Herschel-Bulkley with yield stress 0 mPa, and d) two-phase Herschel-Bulkley with yield stress 10 mPa for blood plasma, while flow took place in vessel with stenosis 60%. Presentation of results in this paper shows that stenosis can substantially affect blood flow in the artery, causing variations of velocity and wall shear stress. Thus, the results in the present paper are maximum values of blood velocity and wall shear stress, profiles and distributions of blood velocity and wall shear stress computed for single- and two-phase blood models for medium-sized vessels with stenosis.

For the two-phase blood models the influence of initial velocity on blood flow in the stenosis zone is not observed, the velocity profiles are symmetric and parabolic. Contrary, for the single phase non-Newtonian blood model, the velocity profile is flat in the stenosis zone and distribution of velocity is disturbed just behind the stenosis zone. The shapes of wall shear stress profiles for two-phase blood models are similar and symmetric in the center of stenosis. The biggest differences in maximum values of velocities and wall shear stress are observed between single phase non-Newtonian power law and Herschel-Bulkley blood models. The comparison of the obtained results with the literature indicates that the two-phase Herschel-Bulkley model is the most suitable for describing flow in medium-sized vessels with stenosis.