Biomedical Engineering Reference
In-Depth Information
12
Applications of variational data assimilation in
computational hemodynamics
Marta D'Elia, Lucia Mirabella, Tiziano Passerini, Mauro Perego, Marina
Piccinelli, Christian Vergara, and Alessandro Veneziani
Abstract.
The development of new technologies for acquiring measures and images
in order to investigate cardiovascular diseases raises new challenges in scientific
computing. These data can be in fact merged with the numerical simulations for
improving the accuracy and reliability of the computational tools. Assimilation of
measured data and numerical models is well established in meteorology, whilst it is
relatively new in computational hemodynamics. Different approaches are possible
for the mathematical setting of this problem. Among them, we follow here a vari-
ational formulation, based on the minimization of the mismatch between data and
numerical results by acting on a suitable set of control variables. Several modelling
and methodological problems related to this strategy are open, such as the analysis
of the impact of the noise affecting the data, and the design of effective numerical
solvers. In this chapter we present three examples where a mathematically sound
(variational) assimilation of data can significantly improve the reliability of the nu-
merical models.
Accuracy
and
reliability
of computational models are increasingly
important features in view of the progressive adoption of numerical tools in the de-
Marta D'Elia, Tiziano Passerini, Marina Piccinelli, Alessandro Veneziani ( )
Department of Mathematics and Computer Science, Emory University, 400 Dowman Dr, 30322,
Atlanta GA, USA
e-mail:
marta,tiziano,marina,ale
@mathcs.emory.edu
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}
Lucia Mirabella
W.H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology,
315 Ferst Dr., 30332 Atlanta GA, USA
e-mail: lucia.mirabella@bme.gatech.edu
Mauro Perego
Department of Scientific Computing, Florida State University, Tallahassee FL, USA
e-mail: mperego@fsu.edu
Christian Vergara
Department of Information Engineering and Mathematical Methods, University of Bergamo, Italy
e-mail: christian.vergara@unibg.it
