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.
