Boundary Control Problems in Hemodynamics

Adélia Sequeira (), Jorge Tiago () and Telma Guerra ()
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Adélia Sequeira: Instituto Superior Técnico, Universidade de Lisboa, Department of Mathematics and CEMAT
Jorge Tiago: Instituto Superior Técnico, Universidade de Lisboa, Department of Mathematics and CEMAT
Telma Guerra: Instituto Politécnico de Setúbal, Escola Superior de Tecnologia do Barreiro

A chapter in Trends in Biomathematics: Modeling, Optimization and Computational Problems, 2018, pp 27-48 from Springer

Abstract: 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.

Keywords: Fluid Control Problem; Blood Flow Simulation; Present Numerical Results; Ground Truth Solution; Carreau Viscosity Model (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-91092-5_3

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DOI: 10.1007/978-3-319-91092-5_3

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