Interaction between steady flow and individualised compliant segments: application to upper airways

To describe upper airway obstruction in patients with sleep apnea syndrome, the steady state solutions of a simple model of local pharyngeal obstruction were studied. Importantly, the present model embodies a series of two individualised elements, each having its own compliance, which enables the consideration, from a conceptual point of view, of local differences in anatomical and physiological properties between pharyngeal regions. The evolution of inspiratory flow and area variations were predicted using the transmural pressure at the downstream element as the controlled variable. Derivation and normalisation of fundamental governing equations, written for non-viscous and viscous fluids, reveal very different kinds of behaviour, depending on values of the speed index defined from the local distensibility, or its modulation by a friction factor for viscous fluid. The two-element model is able to describe a considerably rich mechanical behaviour, including the occurrence of critical conditions when area becomes very high or small, i.e. when the distensibility-dependent speed index at the upstream element tends toward unity. In spite of its simplicity, not only does the present model describe steady state behaviours that resemble the well-known phenomenon of choking in an elastic tube, but the viscous fluid conditions also reveal (i) an area evolution following a typical doubly folded shape, (ii) the occurrence of a close succession maximum and minimum flows which can be seen as a physiological 'flow plateau'. It is concluded that the concept of interaction behind the two-element model must be considered as soon as flow interacts in a compliant structure characterised by anatomical and/or functional singularities.