Methods for assimilating blood velocity measures in hemodynamics simulations: Preliminary results

New measurement devices and techniques in biomedical images provide medical doctors with a huge amount of data on blood flow and vascular morphologies. These data are crucial for performing (and validating) individualbased simulations of hemodynamics (see e.g. [1]). Availability of velocity measures inside a region of interest poses problems that are new to the community of computational hemodynamics and however well known in other engineering fields. In particular, integration of data (measures) and numerical simulations has been an issue of utmost relevance in the prediction of fluid geophysics phenomena and, in particular, weather forecast. In computational hemodynamics a mathematically sound assimilation of data and numerical simulations is needed, on one hand for improving reliability of numerical results, on the other one for filtering noise and measurements errors. In this paper we consider and compare some possible methods for integrating numerical simulations and velocity measures in some internal points of the computational domain. Preliminary numerical results for a 2D Stokes problem are presented both for noise free and noisy data, investigating convergence rate and noise sensitivity