On the uncertainty quantification of blood flow viscosity models

The blood viscosity uncertainty is investigated in an idealized portal-vein flow and its effect is propagated in the 3D Navier-Stokes equations and quantified on the quantities of interest, such as wall shear, pressure and mass flow split. The variability of the random blood viscosity is investigated in detail assuming that the true blood viscosity is given in the range covered by four Carreau blood viscosity model variants. Three different characterizations of the associated Probability Density Functions (PDFs) were considered: (i) a single blood Carreau model with random parameters that covers the variability range under consideration; (ii) the assumption that there is equal probability of sampling each of the four different Carreau model variants; and (iii) the assumption of a bi-linear composition of the four Carreau models affected by random coefficients. These assumptions result in different inlet blood viscosity PDFs that were propagated in the Navier-Stokes solution with the application of a non-intrusive stochastic collocation method based on the generalized polynomial chaos expansion. The stochastic simulations have quantified the uncertainty of random viscosity model parameters on the interested flow parameters wall shear stress and pressure for two Reynolds numbers: Re=212 and Re=21. The results include error bars of these variables and hierarchy impact of the random variables on the solution.