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Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Published online by Cambridge University Press:  17 June 2013

Toni Lassila ,
Andrea Manzoni ,
Alfio Quarteroni  and
Gianluigi Rozza
Toni Lassila
Affiliation:
Modelling and Scientific Computing, Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland.. toni.lassila@epfl.ch; alfio.quarteroni@epfl.ch
Andrea Manzoni
Affiliation:
Now at SISSA MathLab, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy.; andrea.manzoni@sissa.it; gianluigi.rozza@sissa.it
Alfio Quarteroni
Affiliation:
Modelling and Scientific Computing, Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland.. toni.lassila@epfl.ch; alfio.quarteroni@epfl.ch MOX, Modellistica e Calcolo Scientifico, Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.; alfio.quarteroni@polimi.it
Gianluigi Rozza
Affiliation:
Now at SISSA MathLab, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy.; andrea.manzoni@sissa.it; gianluigi.rozza@sissa.it
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Abstract

We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes equations in 2D to identify an anastomosis angle and a cuffed shape that are robust with respect to a possible range of residual flows. We also consider a reduced order modelling framework based on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model reduction or the robust framework.

Keywords

Optimal controlshape optimizationarterial bypass graftsuncertaintyworst-case designreduced order modellingNavier-Stokes equations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 1107 - 1131
Copyright
© EDP Sciences, SMAI, 2013

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