The geometrical multiscale modelling in hemodynamics and hemorheology

The complexity of the cardiovascular system makes it unfeasible to perform 3D simulations in large vascular regions. Thus, truncated 3D regions of interest must be considered, originating artificial sections. Commonly these simulations are carried out neglecting the remaining cardiovascular system. However there is a strong relation between local and global hemodynamics that must be taken into account in order to perform realistic simulations. The global circulation can be approximated through reduced (1D and 0D) models. The reduced models have lower accuracy and complexity, yet they provide the useful information to be coupled to the 3D model. On the other hand, experimental results demonstrate that blood can exhibit non-Newtonian characteristics such as shear-thinning viscosity, viscoelasticity or yield stress, which should be captured by the mathematical model. We address both issues of the geometrical multiscale modelling of the cardiovascular system and blood rheology. We describe the different models, including 3D generalized Newtonian fluids and fluid-structure interaction. We also focus on the coupling between them, detailing 1D-3D, 0D-3D and 1D-0D couplings. Several numerical results are presented to illustrate the geometrical multiscale approach.