| The deflection of a Y-shaped membrane under a uniform static pressure load is analyzed as a suitable structural component for a model of forced expiration, flow limitation and wheezing, as occur in obstructive airway diseases. First a linear model is analyzed using the Rayleigh-Ritz finite element method. The predicted deformation increases monotonically with transmural pressure. The linear restrictions are then removed and a nonlinear, finite strain, finite deformation model is developed.; The predicted tube law is qualitatively the same at various cross-sections of the trachea, and is insensitive to the magnitude and shape assumed for the resting area. The predicted wave speed shows an initial raise, followed by a sustained fall as collapse progresses. Maximal flow rate computed for parameters relevant to the human trachea is 12 lps, which is of the same order as the observed value 6--10 lps. |
