Model reduction approaches for simulation of cardiovascular stents and pulmonary valve

The talk focuses on two particular approaches to reduce complexity of cardiovascular devices modeling, a key issue to achieve realistic
simulations in clinically relevant time. First, I will discuss a (Chorin-Temam) projection scheme for an incompressible fluid through a thin porous interface, modelled as a surface resistance term in the Navier-Stokes equations. The approach can be used as a reduced model of multilayer stents (thin-wired tubular devices) and pulmonary
valves. A finite element formulation will be described, which, treating the interface conditions with a Nitsche penalization method,
yields unconditional stability for any non-negative value of the interface resistance.
As next, a geometrical-based model order reduction for the simulation of the pulmonary artery will be described, motivated by pre-operative studies of artificial valve implantation. Given a set of patient geometries, we created an atlas (i.e. a representative template of the patient set), extracting then a reduced basis (POD) of the fluid numerical solution on this domain. By considering the patient geometries as small deformations of the atlas, the pre-computed POD basis will be mapped on individual meshes, allowing fast
patient-specific simulations to investigate rest/exercise flow conditions and different artificial valve properties.