Applications of variational data assimilation in computational hemodynamics

  • Marta D’Elia
  • Lucia Mirabella
  • Tiziano Passerini
  • Mauro Perego
  • Marina Piccinelli
  • Christian Vergara
  • Alessandro Veneziani
Part of the MS&A — Modeling, Simulation and Applications book series (MS&A, volume 5)


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.


Wall Shear Stress Data Assimilation Bicuspid Aortic Valve Tikhonov Regularization Arbitrary Lagrangian Eulerian 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Marta D’Elia
    • 1
  • Lucia Mirabella
    • 2
  • Tiziano Passerini
    • 1
  • Mauro Perego
    • 3
  • Marina Piccinelli
    • 1
  • Christian Vergara
    • 4
  • Alessandro Veneziani
    • 1
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.W.H. Coulter Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA
  4. 4.Department of Information Engineering and Mathematical MethodsUniversity of BergamoBergamoItaly

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