A data assimilation approach for non-Newtonian blood flow simulations in 3D geometries

Blood flow simulations can play an important role in medical training and diagnostic predictions associated to several pathologies of the cardiovascular system. The main challenge, at the present stage, is to obtain reliable numerical simulations in the particular districts of the cardiovascular system that we are interested in. Here, we propose a Data Assimilation procedure, in the form of a non linear optimal control problem of Dirichlet type, to reconstruct the blood flow profile from known data, available in certain parts of the computational domain. This method will allow us to obtain the boundary conditions, not fully determined by the physics of the model, in order to recover more accurate simulations. To solve the control problem we propose a Discretize then Optimize (DO) approach, based on a stabilized finite element method. Numerical simulations on 3D geometries are performed to validate this procedure. In particular, we consider some idealized geometries of interest, and real geometries such as a saccular aneurysm and a bypass. We assume blood as an homogeneous fluid with non-Newtonian inelastic shear-thinning behavior. The results show that, even in the presence of noisy data, accuracy can be improved using the optimal control approach.