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Modeling of Physiological Flows pp 363–394Cite as

Applications of variational data assimilation in computational hemodynamics

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Part of the book series: MS&A — Modeling, Simulation and Applications ((MS&A,volume 5))

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 modeling 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 design of new therapies and, more in general, in the decision making process of medical doctors.

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Notes

  1. 1.

    Notice that we use the word “sites” for the location of measurements, as opposed to the word “nodes” for points where velocities are computed. We do not assume at this level particular positions for the sites, even though in the applications it is reasonable to assume that they are located on planes transverse to the blood stream.

  2. 2.

    The post-processing in this case is trivially the identity application.

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Acknowledgements

Marina Piccinelli and Alessandro Veneziani thank Emory University Research Committee for the support of the Project “Image based numerical fluid structure interactions simulations in computational hemodynamics”. Tiziano Passerini is supported by the NIH Grant 5R01HL070531-08 “Biology, Biomechanics and Atherosclerosis”. The research of C. Vergara has been (partially) supported by the ERC Advanced Grant N.227058 MATHCARD. The authors wish to thank Marijn Brummer (Emory Children’s Healthcare of Atlanta), Eldad Haber (University of British Columbia, Canada), Robert Taylor (Emory School of Medicine), Michelle Consolini (Emory School of Medicine), Michele Benzi (Emory University), Max Gunzburger (Florida State University), George E. Karniadakis (Brown University).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, 400 Dowman Dr, 30322, Atlanta, GA, USA

    Marta D’Elia, Tiziano Passerini, Marina Piccinelli & Alessandro Veneziani

  2. W.H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, 315 Ferst Dr., 30332, Atlanta, GA, USA

    Lucia Mirabella

  3. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA

    Mauro Perego

  4. Department of Information Engineering and Mathematical Methods, University of Bergamo, Bergamo, Italy

    Christian Vergara

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  1. Marta D’Elia
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  2. Lucia Mirabella
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  7. Alessandro Veneziani
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Correspondence to Alessandro Veneziani .

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  1. MOX - Department of Mathematics, Politecnico di Milano, Italy

    Davide Ambrosi  & Alfio Quarteroni  & 

  2. Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Laussane, Switzerland

    Alfio Quarteroni  & Gianluigi Rozza  & 

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D’Elia, M. et al. (2012). Applications of variational data assimilation in computational hemodynamics. In: Ambrosi, D., Quarteroni, A., Rozza, G. (eds) Modeling of Physiological Flows. MS&A — Modeling, Simulation and Applications, vol 5. Springer, Milano. https://doi.org/10.1007/978-88-470-1935-5_12

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