Airway collapse and reopening due to mechanical ventilation exerts mechanical stress on airway walls and injures surfactant-compromised lungs. The reopening of a collapsed airway was modeled experimentally and computationally by the progression of a semi-infinite bubble in a narrow fluid-occluded channel. The extent of injury caused by bubble progression to pulmonary epithelial cells lining the channel was evaluated. Counterintuitively, cell damage increased with decreasing opening velocity. The presence of pulmonary surfactant, Infasurf, completely abated the injury. These results support the hypotheses that mechanical stresses associated with airway reopening injure pulmonary epithelial cells and that pulmonary surfactant protects the epithelium from this injury. Computational simulations identified the magnitudes of components of the stress cycle associated with airway reopening (shear stress, pressure, shear stress gradient, or pressure gradient) that may be injurious to the epithelial cells. By comparing these magnitudes to the observed damage, we conclude that the steep pressure gradient near the bubble front was the most likely cause of the observed cellular damage.

We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lung's thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances.Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system.We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.

We performed a theoretical investigation of the progression of a finger of air through a liquid-filled flexible-walled channel - an initial model of pulmonary airway reopening. Positive pressure, Pb* drives the bubble forward, and separates flexible walls that are modelled as membranes under tension, T, supported by linearly elastic springs with elasticity K. The gap width between the walls under stress-free conditions is 2H, and the liquid has constant surface tension, γ, and viscosity, μ. Three parameters define the state of the system: Ca = μU/γ is a dimensionless velocity that represents the ratio of viscous to capillary stresses; η = T/γ is the wall tension to surface tension ratio, and γ = KH2/γ is the wall elastance parameter. We examined steady-state solutions as a function of these parameters using lubrication analysis and the boundary element method.These studies showed multiple-branch behaviour in the Pb-Ca relationship, where Pb = Pb*/(γ/H) is the dimensionless bubble pressure. Low Ca flows (Ca [Lt ] min (1, (Γ3/η)1/2)) are dominated by the coupling of surface tension and elastic stresses. In this regime, Pb decreases as Ca increases owing to a reduction in the downstream resistance to flow, caused by the shortening of the section connecting the open end of the channel to the fully collapsed region. High Ca behaviour (max (1, (γ3/η)1/2) [Lt ] Ca [Lt ] η) is dominated by the balance between fluid viscous and longitudinal wall tension forces, resulting in a monotonically increasing Pb–Ca relationship. Increasing η or decreasing Γ reduces the Ca associated with the transition from one branch to the other. Low Ca streamlines show closed vortices at the bubble tip, which disappear with increasing Ca.Start-up yield pressures are predicted to range from 1 [les ] Pyield*/(γ/L*) [les ] 2, which is less than the minimum pressure for steady-state reopening, Pmin/(γ/L*), where L* is the upstream channel width. Since Pyield* < Pmin*, the theory implies that low Ca reopening may be unsteady, a behaviour that has been observed experimentally. Our results are consistent with experimental observations showing that Pb* in highly compliant channels scales with γ/L*. In contrast, we find that wall shear stress scales with γ/H. These results imply that wall shear and normal stresses during reopening are potentially very large and may be physiologically significant.

Summary A single‐server system with stationary compound Poisson input and general independent service times, the latter being subject to random interruptions of independently but otherwise arbitrarily distributed durations, is studied. For a variety of service‐interruption interactions (including the preemptive‐repeat) the distributions of busy period duration, of queue length, and of waiting time are characterized by transforms and by moments. Applications are made to priority scheduling problems.

This paper describes a method for obtaining numerical information concerning the time-dependent behavior of stochastic processes such as those arising in queuing theory. The method leads to an approximate inverse of the Laplace transform. Examples are given of applications to transforms with known inverses, and the evolution of expected waiting time at a simple single-server queue is illustrated, both when there is a stationary solution and in the saturated case.