Optimization, Control and Shape Design of an Arterial Bypass
Friday 21st May 2004
We present multi-level geometrical approaches in the study of aortocoronaric bypass anastomoses configurations. The theory of optimal control based on adjoint formulation is appliedin order to optimize the shape of the incoming branch of the bypass (the toe) into the coronary. At this level two possibile options are available in shape design: one implements local boundary variations in computational domain, the other is based on a linearized design in a suitable reference domain through the theory of small perturbations. At a coarser level, reduced basis methodologies based on parametrized partial differential equations are developed to provide (a) a sensitivity analysis for geometrical quantities of interest in bypass configurations and (b) rapid and reliable prediction of integral functional outputs. The aims is (i) to provide design indications for arterial surgery in the perspective of future development for prosthetic bypasses, (ii) to develop multi-level numerical methods for optimization and shape design by optimal control, and (iii) to provide an input-output relationship led by models with lower complexity and computational costs. We have numerically investigated a reduced model based on Stokes equations a vorticity cost functional (to be minimized) in the down-field zone of by-pass. In local shape design procedure a Taylor like patch has been found. A feedback procedure with Navier-Stokes fluid model is proposed based on the analysis of wall shear stress and its related indexes of interest.