  In this work we study the hemodynamics in a stented artery connected either
to a collateral artery or to an aneurysmal sac. The blood flow is driven by the
pressure drop. Our aim is to characterize the flow-rate and the pressure in the
contiguous zone to the main artery: using boundary layer theory we construct a
homogenized first order approximation with respect to epsilon, the size of the
stent's wires. This provides an explicit expression of the velocity profile
through and along the stent. The profile depends only on the input/output
pressure data of the problem and some homogenized constant quantities: it is
explicit. In the collateral artery this gives the flow-rate. In the case of the
aneurysm, it shows that : (i) the zeroth order term of the pressure in the sac
equals the averaged pressure along the stent in the main artery, (ii) the
presence of the stent inverses the rotation of the vortex. Extending the tools
set up in [Bonnetier et al, Adv. Math. Fluids, 2009, Milisic, Meth. Apl. Ann.,
2009] we prove rigorously that our asymptotic approximation is first order
accurate with respect to . We derive then new implicit interface conditions
that our approximation formally satisfies, generalizing our analysis to other
possible geometrical configurations. In the last part we provide numerical
results that illustrate and validate the theoretical approach.
