On the stability of the upper airways system

Simple models for upper pharyngeal obstruction, describing the sleep apnea syndrome are proposed. Stability is discussed, of two and three individualized elements, with and without elastic connections, interacting with the steady flow. Considering the flow as the controlling parameter, critical steady state flows are located and their post-critical behavior is discussed for various models. It is pointed out that non-linear constitutive elastic laws are necessary contrary to the linear ones introduced by Fodil (1998) [15]. Finally the three element model will be presented and studied with non-linear constitutive relations and side connections. Applications of the theory will be performed and discussion for the three models will be presented. It is pointed out that the sleep apnea syndrome is due to the instability of the upper pharyngeal region.