On the comparison between topological and surface sensitivities for bio-fluid dynamics applications

Nasal Breathing Difficulties (NBD) consist of pathologies which are difficult to diagnose, heal and affect a high percentage of the population; the only way to treat these diseases is, most of the times, by surgery but the success rate is not very high since many patients have no relief from it. This should be attributed to the variety of the nose’s functions, which is far more complex than a simple duct to connect the environment to the lungs. CFD is emerging as an innovative approach to study these problems systematically; in this contribution the target is to use a method based on adjoint equations to get senstivity maps whose purpose is to provide surgeons with more informations on which are the regions, inside the nose, to focus on. This work focuses only on the reduction of the pressure drop across the nose, therefore a single objective function is used. Three different frameworks, with two formulations of the continuous adjoint equation method, are compared: in two cases topological sensitivities were used while in the latter the surface sensitivity was evaluated.