Fluid-structure interactions in the human upper airway — large-displacement biomechanics

Abstract

Obstructive breathing disorders, such as sleep apnoea and snoring, interfere with normal respiration and sleep, reducing brain-oxygen saturation and are linked with hypertension and heart failure. The mechanics of the human upper airway are characterised by the interaction of the low-stiffness structures, being the soft palate and throat sidewalls, with the air flow producing soft-tissue vibrations that may lead to airway closure. In order to investigate this dynamical system we employ a cantilevered flexible plate (soft-palate) immersed in a two-dimensional channel (pharynx) flow. For this canonical analogue, we take the next step towards biomechanical realism by modelling finite-amplitude motions of the flexible plate and incorporating finite thickness in its structure. The structural model makes use of a geometrically nonlinear formulation of the solid mechanics. Viscous flow is modelled at Reynolds numbers giving unsteady laminar flow. The fully-coupled fluid-structure interaction (FSI) model is developed using the open-source finite-element library oomph-lib. We begin with a validation study of the structural mechanics through examining the effects of finite amplitude and finite thickness on the in-vacuo modes. Thereafter, we use the FSI model to illustrate both stable and unstable motions of the plate.This paper demonstrates the versatility of the new modelling approach and its suitability for characterising the dependence of the plate’s stability on the system parameters.