Numerical implementation of viscoelastic blood flow in a simplified arterial geometry

The influence of the non-Newtonian stress–strain relation of blood on the oscillatory shear index (OSI) and mean wall shear stress (WSS) are described. The unsteady linear 1D momentum equation is solved for a viscoelastic fluid, with six elements of the Maxwell type and one dashpot element connected in parallel. Anovel numerical algorithm is described which uses the upwind finite difference method to solve the equation of momentum. Results obtained by using a finite difference approach show significantly higher values of OSI when blood is assumed to be a viscoelastic fluid compared with those of simplified Newtonian fluid model. The calculation of OSI in human normal conditions for the Newtonian fluid differs in 12% (if α = 0.02) from the results obtained from using the viscoelastic model.