A 3D/1D geometrical multiscale model of cerebral vasculature

Geometrical multiscale modeling is a strategy advocated in computational hemodynamics for representing in a single numerical model dynamics that involve different space scales. This approach is particularly useful to describe complex networks such as the circle of Willis in the cerebral vasculature. A multiscale model of the cerebral circulation is presented where a one-dimensional (1D) description of the circle of Willis, relying on the one-dimensional Euler equations, is coupled to a fully three-dimensional model of a carotid artery, based on the solution of the incompressible Navier-Stokes equations. Even if vascular compliance is often not relevant to the meaningfulness of three-dimensional (3D) results by themselves, it is crucial in the multiscale model, since it is the driving mechanism of pressure-wave propagation. Unfortunately, 3D simulations in compliant domains still demand computational costs significantly higher than in the rigid case. Appropriate matching conditions between the two models have been devised to concentrate the effects of the compliance at the interfaces and to obtain reliable results still solving a 3D problem on rigid vessels.