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Patient-specific Blood Flow Simulations: Setting DirichletBoundary Conditions for Minimal Error with Respect to Measured Data

Published online by Cambridge University Press:  31 July 2014

J. Tiago ,
A. Gambaruto  and
A. Sequeira
J. Tiago*
Affiliation:
Departamento de Matemática and CEMAT/IST Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
A. Gambaruto
Affiliation:
Computer Applications in Science & Engineering (CASE), Barcelona Supercomputing Center Nexus I - Campus Nord UPC, C/ Jordi Girona 2, 3a. Planta, 08034 Barcelona, Spain
A. Sequeira
Affiliation:
Departamento de Matemática and CEMAT/IST Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
*
⋆Corresponding author. E-mail: jftiago@math.ist.utl.pt
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Abstract

We present a fully automatic approach to recover boundary conditions and locations of thevessel wall, given a crude initial guess and some velocity cross-sections, which can becorrupted by noise. This paper contributes to the body of work regarding patient-specificnumerical simulations of blood flow, where the computational domain and boundaryconditions have an implicit uncertainty and error, that derives from acquiring andprocessing clinical data in the form of medical images. The tools described in this paperfit well in the current approach of performing patient-specific simulations, where areasonable segmentation of the medical images is used to form the computational domain,and boundary conditions are obtained as velocity cross-sections from phase-contrastmagnetic resonance imaging. The only additional requirement in the proposed methods is toobtain additional velocity cross-section measurements throughout the domain. The toolsdeveloped around optimal control theory, would then minimize a user defined cost functionto fit the observations, while solving the incompressible Navier-Stokes equations.Examples include two-dimensional idealized geometries and an anatomically realisticsaccular geometry description.

Keywords

boundary controlerror minimizationpatient-specificcomputational hemodynamicsdomain uncertaintyboundary condition uncertainty
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 6: Blood flows , 2014 , pp. 98 - 116
Copyright
© EDP Sciences, 2014

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