Reduced order modeling for finite element simulation of the cardiovascular system
Campus de Cuenca
Monday September 23, 2013

Alfonso Caiazzo

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.