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Boundary Control Problems in Hemodynamics

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Trends in Biomathematics: Modeling, Optimization and Computational Problems

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Abstract

Blood flow simulations can be improved by integrating known data into the numerical modeling approach. Data Assimilation techniques based on a variational formulation play an important role in this issue. We propose a non-linear optimal control problem to reconstruct the blood flow profile from partial observations of known data in different geometries. Blood flow is assumed to behave as a homogeneous fluid with non-Newtonian inelastic shear-thinning behavior or, to simplify, blood flow is governed by the Navier-Stokes equations. Using a Discretize then Optimize (DO) approach, we solve a non-linear optimal control problem and present numerical results that indicate its robustness with respect to different idealized geometries and measured data. Blood flow in real vessels will also be considered, including the discussion of particular clinical cases.

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Acknowledgements

This work was partially supported by FCT—Fundação para a Ciência e a Tecnologia through the project UID/Multi/04621/2013 of the CEMAT—Center for Computational and Stochastic Mathematics, IST, ULisboa—Portugal, project EXCL/MAT-NAN/0114/2012, and the grant SFRH/BPD/109574/2015.

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Authors and Affiliations

  1. Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Adélia Sequeira & Jorge Tiago

  2. Escola Superior de Tecnologia do Barreiro, Instituto Politécnico de Setúbal, Lavradio, Portugal

    Telma Guerra

Authors
  1. Adélia Sequeira
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  2. Jorge Tiago
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  3. Telma Guerra
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Correspondence to Adélia Sequeira .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Brazil, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Sequeira, A., Tiago, J., Guerra, T. (2018). Boundary Control Problems in Hemodynamics. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_3

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