Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1107-1131.

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.

DOI : 10.1051/m2an/2012059
Classification : 35Q93, 49Q10, 76D05
Mots-clés : optimal control, shape optimization, arterial bypass grafts, uncertainty, worst-case design, reduced order modelling, Navier-Stokes equations 
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Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi. Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty. ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1107-1131. doi : 10.1051/m2an/2012059. http://archive.numdam.org/articles/10.1051/m2an/2012059/

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