Applications of variational data assimilation in computational hemodynamics
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
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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 variational 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 numerical 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 Lucia Mirabella W.H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, 315 Ferst Dr., 30332 Atlanta GA, USA e-mail: [email protected] Mauro Perego Department of Scientific Computing, Florida State University, Tallahassee FL, USA e-mail: [email protected] Christian Vergara Department of Information Engineering and Mathematical Methods, University of Bergamo, Italy e-mail: [email protected]
Ambrosi D., Quarteroni A., Rozza G. (Eds.): Modeling of Physiological Flows. DOI 10.1007/978-88-470-1935-5 12, © Springer-Verlag Italia 2012
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sign of new therapies and, more in general, in the decision making process of medical doctors.
12.1 Introduction In the last 20 years mathematical and numerical models have been progressively used as a tool for supporting medical research in the cardiovascular science. In silico experiments can provide remarkable insights into a physio-pathological process completing more traditional in vitro and in vivo investigations. Numerical models have been playing the role of “individual based” simulators, able to furnish a dynamical representation of the biology of a specific patient as a support to the prognostic activity. At the same time, the need for quantitative responses for diagnostic purposes has strongly stimulated the design of new methods and instruments for measurements and im
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