The recent  progress in the technology of medical devices, in particular in medical imaging techniques, allows us to consider patient-specific blood flow  simulations. To this end, known data can be included into the numerical simulations by using Data Assimilation techniques based on a variational approach.In this direction, we will present a nonlinear optimal control problem to reconstruct a blood flow profile by assuming the knowledge of partial velocity measurements. In order to illustrate  this methodology, we present  numerical results, based on a discretize then optimize approach, which indicates its robustness  with respect to different geometries and measured data. Blood flow in real vessels will also be considered, including the discussion of a particular clinical case. Finally, we discuss the possibility of using similar approaches to a different problem, where the  original real vessel is reconstructed, rather than just the velocity profile.

Blood flow; Optimal Control