Theoretical model of blood rheology including hemolysis

Authors:

• Krystian Jędrzejczak,
• Łukasz Makowski,
• Wojciech Orciuch

Abstract

Mathematical modeling of blood flow in the in vivo environment is a complex issue due to the non-newtonian rheology of blood and the occurrence of hemolysis. As part of this work, a simulation in the ANSYS Fluent software was performed for a model blood vessel with atherosclerotic changes. The blood rheological model based on the work of Buyevich-Kapbsov and the population balance of red cell agglomerates size coupled with hemolysis model was used to create a two-parameter model taking into account the change of the size of blood agglomerates and blood hemolysis in a transient flow. The population balance was solved using the Direct Quadrature Methods of Moments (DQMOM), that takes into account the agglomeration of red blood cells and their breakage under the shear and turbulent stresses and also hemolysis of red cells. The effective volume fraction changed due to the variable shape factor depending on the size of the agglomerate. Local size distribution of agglomerates direct influences blood rheology and flow. The theoretical model was implemented in Computational Fluid Dynamics (CFD) code and the simulation was carried out in a conventional blood vessel with cholesterol deposits with the pulsative flow reflecting the typical heart rate. The rheological parameters of blood and the percentage of blood hemolysis were discussed in comparison with the experimental data of hemolysis depending on the shear rate in the in vitro environment.