Numerical modelling of Newtonian and non-Newtonian representation of blood in a distal end-to-side vascular bypass graft anastomosis

The proliferation of disease at the bed of the distal junction of an end-to-side anastomosis is attributed to abnormal wall shear stress (WSS) distribution. WSS is proportional to the viscosity and shear rate of the flowing fluid. Blood is characterised by a shear rate dependent viscosity. Various constitutive equations have been developed to represent the shear rate dependence of blood viscosity: Newtonian, Carreau, Power law, Carreau-Yasuda, Bi-exponential, Cross, Modified Cross, Herschel-Bulkley, etc. In the femoral artery, the instantaneous shear rate varies from 1-1200 s^-1 over a cardiac cycle. An idealised, 45° rigid, 6 mm diameter, end-to-side femoral anastomosis was modelled on a Computational Fluid Dynamic software package Fluent 6.0. A steady flow of 0.15 and 0.01 m/s was applied to the inlet to model high and low wall shear rate environments respectively. Blood was modelled using the various constitutive equations. The resulting WSS distribution on the bed of the artery was then obtained. At high shear rates there was no significant difference between WSS distribution. At low shear rates there were qualitative differences of up to 300%. In conclusion, the choice of blood constitutive equation has to be based on the particular situation under study e.g. flow rate, steady/unsteady flow, and geometry.