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.

@ARTICLE{LassilaManzoniQuarteroniRozza2013,
author = {Lassila, T. and Manzoni, A. and Quarteroni, A. and Rozza, G.},
title = {Boundary control and shape optimization for the robust design of
bypass anastomoses under uncertainty},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
year = {2013},
volume = {47},
pages = {1107--1131},
number = {4},
doi = {10.1051/m2an/2012059},
}