Real time reduced basis techniques for arterial bypass geometries

AbstractThe reduced basis method on parametrized domains is applied to approximate blood flow through an arterial bypass.The aim is to provide (a) a sensitivity analysis for relevant geometrical quantities in bypass configurations and (b) rapidand reliable prediction of integral functional outputs (such as fluid mechanics indexes). The goal of this investigation is(i) to achieve design indications for arterial surgery in the perspective of future development for prosthetic bypasses, (ii)to develop numerical methods for optimization and design in biomechanics, and (iii) to provide an input–outputrelationship led by models with lower complexity and computational costs than the complete solution of fluid dynamicsequations by a classical finite element method.Keywords: Design of improved biomechanical devices; Parametrized PDEs; Generalized Stokes problem; Reducedbasis methods; Arterial bypass optimization, Haemodynamics.1. Design and optimization in arterial bypassconfigurationsWhen a coronary artery is affected by a stenosis, theheart muscle cannot be properly oxygenated throughblood. Aorto-coronaric anastomosis restores the oxygenamount through a bypass surgery downstream anocclusion. At present, different kinds and shapes ofaorto-coronaric bypasses are available and, conse-quently, different surgery procedures can be devised toset up a bypass. Numerical simulation of physiologicalflows allows better understanding of phenomenainvolved in coronary diseases (see [1]) and a potentialreduction of surgical and post-surgical failures. It mayalso suggest new means in bypass surgical procedures aswell as with less invasive methods to devise improvedbypass configuration (see [2] and [3]). Efficient schemesfor reduced-basis techniques [4] applied to parametrizedpartial differential equations (P