Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

With growing focus on patient specific studies, little attempt has yet been ade to quantify the modelling uncertainty. Here uncertainty in both geometry definition obtained from in vivo MRI scans and mathematical models for blood are considered for a peripheral bypass graft. The approximate error bounds in computed measures are quantified from the flow field in steady state simulations with rigid walls assumption.

A brief outline of the medical image filtering and segmentation procedures is given, as well as virtual model reconstruction and surface smoothing. Diversities in these methods lead to variants of the virtual model definition, where the mean differences are within a pixel size. The blood is described here by either a Newtonian or a non-Newtonian Carreau constitutive model.

The impact of the uncertainty is considered with respect to clinically relevant data such as wall shear stress. This parameter is locally very sensitive to the surface definition, however variability in the topology has an effect on the core flow field and measures to study the flow structures are detailed and comparison performed. Integrated effect of the Lagrangian dynamics of the flow are presented in the form of stir mixing, which also has a strong clinical relevance.