Numerical simulation of blood flows through a porous interface

Mathematical models and computational methods are gaining much attention in medicine and biology.  This highlight paper represents an excellent example in which advanced mathematical methods are applied to the study of a problem of medical and engineering relevance; i.e., the treatment of cerebral aneurysms. In particular, the authors apply mathematical homogenization to develop a model of blood flow through a sieve of metallic wires, which is applied in practice to prevent the rupture of aneurysms. This yields in the governing equations of blood flow a new term accounting for the sieve. An ad-hoc stabilized finite element discretization is then proposed and analyzed.  Numerical experiments show that the computational method correctly captures the behavior of the sieve. This approach is used for the comparison of different treatment configurations in the frame of realistic models of cerebral aneurysms. 

Alfio Quarteroni,
Associate Editor

Numerical simulation of blood flows through a porous interface
Miguel A. Fernandez, Jean-Frédéric Gerbeau and Vincent Martin
ESAIM: M2AN 42 (2008) 961-990