New devices for medical imaging and measurements provide a formidable data
set that can be used for validating accuracy of numerical simulations of
blood flow. A different approach consists of merging these data with
numerical simulations. This is anticipated to improve the accuracy of
computations thanks to patient-specific measures as well as the quality of
(noisy) measurements thanks to the mathematical models implemented in the
numerical solvers. The outcome of this Data Assimilation (DA) process is
therefore a more reliable estimation of the hemodynamics of a specific
patient. Reliability is becoming a fundamental concern in computational
hemodynamics as soon as scientific computing is progressively accepted as a
tool for supporting decision making in clinical routine.
DA is a well established approach in meteorology and geophysics, while it
is still in its infancy in hemodynamics. Different methodologies can be
pursued, either based on classical stochastic estimation techniques (Kalman
filter) or on variational approaches. In this talk, we will present two
examples of variational DA for both assimilating available blood velocity
measures into an incompressible Navier-Stokes simulation and for estimating
the compliance of a vascular tissue by solving an inverse fluid-structure
interaction problem.
In collaboration with: M. D'Elia (Emory University), M. Perego (Florida
State University), C. Vergara (University of Bergamo).