We review the optimal design of an arterial bypass graft following either a (i) boundaryoptimal control approach, or a (ii) shape optimization formulation. The main focus isquantifying and treating the uncertainty in the residual flow when the hosting artery isnot completely occluded, for which the worst-case in terms of recirculation effects isinferred to correspond to a strong orifice flow through near-complete occlusion.Aworst-case optimal control approach is applied to the steady Navier-Stokes equations in 2Dto identify an anastomosis angle and a cuffed shape that are robust with respect to apossible range of residual flows. We also consider a reduced order modelling frameworkbased on reduced basis methods in order to make the robust design problem computationallyfeasible. The results obtained in 2D are compared with simulations in a 3D geometry butwithout model reduction or the robust framework.
