Wiass Institute Berlin
Numerical simulations of the cardiovascular system, including the modeling of medical devices, entails physical, mathematical and geometrical complexities. Model order reduction, i.e. problem-specific approaches aimed at reducing the complexity of a mathematical model, approaches to reduce complexity is a key issue to achieve realistic simulations in a reasonable time. First, we will discuss a numerical scheme for an incompressible fluid through a thin porous interface, modelled as a surface resistance term in the incompressible Navier-Stokes equations. The approach can be used as a reduced model of multilayer "stents" (thin-wired tubular devices) and pulmonary valves.?As next, a geometrical-based model order reduction for the simulation of the pulmonary artery will be described. Given a set of patient geometries, we created an "atlas" (i.e. a representative template of the patient set), extracting then a basis of the fluid numerical solution on this domain. By considering the patient geometries as small deformations of the atlas, this pre-computed basis will be mapped on individual meshes, allowing fast patient-specific simulations.