Donald P. Gaver

A Theoretical Model Study of the Influence of Fluid Stresses on a Cell Adhering to a Microchannel Wall

We predict the amplification of mechanical stress, force, and torque on an adherent cell due to flow within a narrow microchannel. We model this system as a semicircular bulge on a microchannel wall, with pressure-driven flow. This two-dimensional model is solved computationally by the boundary element method. Algebraic expressions are developed by using forms suggested by lubrication theory that can be used simply and accurately to predict the fluid stress, force, and torque based upon the fluid viscosity, muoffhannel height, H, cell size, R, and flow rate per unit width, Q2-d. This study shows that even for the smallest cells (gamma = R/H << 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a cell-free system. Increased flow resistance and fluid stress amplification occur with bigger cells (gamma > 0.25), because of constraints by the channel wall. In these cases we find that the shear stress amplification is proportional to Q2-d(1-gamma)-2, and the force and torque are proportional to Q2-d(1-gamma2)-5/2. Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of approximately 10% for flow in channels and thus are useful for the analysis of cells in flow chambers. For cell adhesion in tubes, the approximations are accurate to approximately 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these constrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.

Droplet spreading on a thin viscous film

We investigated experimentally the flows induced by a localized surfactant (oleic acid) on thin glycerol films. The oleic acid creates surface-tension gradients, which drive convention on the surface and within the film. Qualitative descriptions of the Lagrangian flow field were provided by flow-visualization experiments. Quantitative measurements of surface flows were conducted using dyed glycerol markers, where the initial motion of these markers is used to define the position of the timedependent ‘ convection front ’. The flow characteristics were found to depend largely upon the magnitude of a gravitational parameter, G, representing the ratio of gravitational to surface-tension gradient (Marangoni) forces. Small G (G 0. For this reason, surface markers may not be used to measure accurately the position of the droplet’s leading edge. Finally, simulations of the Lagrangian flows conducted using the theory of Gaver & Grotberg (1990) compare favourably with these experimental results in the limit of dilute surfactant concentrations, and thus experimental verification of that theory is provided by this work. The results of this study may be useful for understanding the behaviour of the lung’s thin-film lining after an aerosol droplet of insoluble exogenous surfactant lands upon its surface.

The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube

We have utilized a computational model of semi-infinite air bubble progression in a surfactant-doped, fluid-filled rigid capillary to investigate the continual interfacial expansion dynamics that occur during the opening of collapsed pulmonary airways. This model simulates mixed-kinetic conditions with nonlinear surfactant equations of state similar to those of pulmonary surfactant. Several dimensionless parameters govern the system responses: the capillary number ( Ca ) that relates viscous to surface tension forces; the elasticity number ( El ), a measure of the ability of surfactant to modify the surface tension; the bulk Peclet number ( Pe ), relating bulk convection rates to diffusion rates; the adsorption and desorption Stanton numbers ( St a and St d ) that relate the adsorption/desorption rates to surface convective rates; and finally the adsorption depth (λ), a dimensionless bulk surfactant concentration parameter. We investigated this model by performing detailed parameter variation studies at fixed and variable equilibrium concentrations. We find that the surfactant properties can strongly influence the interfacial pressure drop through modification of the surface tension and the creation of Marangoni stresses that influence the viscous stresses along the interface. In addition, these studies demonstrate that, depending upon the range of parameters, either film thickening or film thinning responses are possible. In particular, we find that when Pe [Gt ]1 (as with pulmonary surfactant) or when sorption rates are low, concentration profiles can substantially differ from near-equilibrium approximations and can result in film thinning. These responses may influence stresses on epithelial cells that line pulmonary airways and the stability of these airways, and may be important to the delivery of exogenous surfactant to deep regions of the lung.

Biomechanics of liquid–epithelium interactions in pulmonary airways

The delicate structure of the lung epithelium makes it susceptible to surface tension induced injury. For example, the cyclic reopening of collapsed and/or fluid-filled airways during the ventilation of injured lungs generates hydrodynamic forces that further damage the epithelium and exacerbate lung injury. The interactions responsible for epithelial injury during airway reopening are fundamentally multiscale, since air-liquid interfacial dynamics affect global lung mechanics, while surface tension forces operate at the molecular and cellular scales. This article will review the current state-of-knowledge regarding the effect of surface tension forces on (a) the mechanics of airway reopening and (b) epithelial cell injury. Due to the complex nature of the liquid-epithelium system, a combination of computational and experimental techniques are being used to elucidate the mechanisms of surface-tension induced lung injury. Continued research is leading to an integrated understanding of the biomechanical and biological interactions responsible for cellular injury during airway reopening. This information may lead to novel therapies that minimize ventilation induced lung injury.

The influence of surfactant on two-phase flow in a flexible-walled channel under bulk equilibrium conditions

A preliminary model of pulmonary airway reopening is developed that includes the physicochemical influence of surfactant under bulk-equilibrium conditions. The airway is modeled following Gaver et al. [J. Fluid. Mech. 319, 25–65 (1996)] as a flexible-walled channel, where walls are membranes under longitudinal tension T, and supported with elasticity E with a stress-free separation distance 2H. The lining fluid has viscosity μ and surface tension γ*. Airway reopening occurs when a semi-infinite bubble of air with pressure Pb* progresses steadily at velocity U and separates the walls. Surfactant exists in the lining fluid (C*) and at the air–liquid interface (Γ*). Bulk equilibrium is assumed (C*=C0) and the kinetic transfer of surfactant between the bulk and interface occurs with a rate k. The equilibrium relationship between Γ* and C* is based upon Henry’s isotherm (Γeq=KC0). The surface tension equation of state, a relationship between γ* and Γ*, is assumed to be linear near Γeq. Marangoni stresses devel...

The steady propagation of a bubble in a flexible-walled channel: Asymptotic and computational models

The steady motion at zero Reynolds number of a semi-infinite bubble through a fluid-filled, flexible-walled channel, a model for the reopening of a collapsed lung airway, is described using asymptotic and numerical methods. The channel walls are membranes that are supported by external springs and are held under large longitudinal tension. An asymptotic analysis is presented under the assumption that membrane slopes are uniformly small. Near the bubble tip, the flow is equivalent to that of a semi-infinite bubble in a weakly tapered channel. Key features of this two-dimensional flow are matched to long-wavelength approximations describing the remainder of the solution domain. The analysis is valid for a wide range of bubble speeds, and it takes a particularly simple form when the bubble peels apart the channel walls as it advances. Predictions of bubble pressure as a function of bubble speed are validated by comparison with existing computations, new boundary-element simulations describing bubble motion in a channel with one rigid and one deformable wall, and experiments.

Unsteady bubble propagation in a flexible channel: Predictions of a viscous stick-slip instability

We investigate the unsteady motion of a long bubble advancing under either prescribed pressure p(b) or prescribed volume flux q(b) into a fluid-filled flexible-walled channel at zero Reynolds number, an idealized model for the reopening of a liquid-lined lung airway. The channel walls are held under longitudinal tension and are supported by external springs; the bubble moves with speed U. Provided p(b) exceeds a critical pressure p(crit) the system exhibits two types of steady motion. At low speeds, the bubble acts like a piston, slowly pushing a column of fluid ahead of itself, and U decreases with increasing p(b). At high speeds, the bubble rapidly peels the channel walls apart and U increases with increasing p(b.) Using two independent time-dependent simulation techniques (a two-dimensional boundary-element method and a one-dimensional asymptotic approximation), we show that with prescribed p(b) > p(crit), peeling motion is stable and the steady pushing solution is unstable; for p(b) > p(crit) the system ultimately exhibits unsteady pushing behaviour for which U continually diminishes with time. When q(b) is prescribed, peeling motion (with large q(b)) is again stable, but pushing motion (with small q(b)) loses stability at long times to a novel instability leading to spontaneous relaxation oscillations of increasing amplitude and period, for which the bubble switches abruptly between slow unsteady pushing and rapid quasi-steady peeling. This stick-slip motion is characterized using a third-order lumped-parameter model which in turn is reduced to a nonlinear map. Implications for the inflation of occluded lung airways are discussed.

In situ enhancement of pulmonary surfactant function using temporary flow reversal

Acute respiratory distress syndrome is a pulmonary disease with a mortality rate of ∼40% and 75,000 deaths annually in the United States. Mechanical ventilation restores airway patency and gas transport but leads to ventilator-induced lung injury. Furthermore, surfactant replacement therapy is ineffective due to surfactant delivery difficulties and deactivation by vascular proteins leaking into the airspace. Here, we demonstrated that surfactant function can be substantially improved (up to 50%) in situ in an in vitro pulmonary airway model using unconventional flows that incorporate a short-term retraction of the air-liquid interface, leading to a net decrease in cellular damage. Computational fluid dynamic simulations provided insights into this method and demonstrated the physicochemical hydrodynamic foundation for the improved surfactant microscale transport and mobility. This study may provide a starting point for developing novel ventilation waveforms to improve surfactant function in edematous airways.

Biofluid mechanics of the pulmonary system

Presents an overview of leading areas of discovery in biofluid mechanics related to the pulmonary system, with particular reference to the airways. Areas briefly reviewed include airway gas dynamics, impedance studies, collapsible-tube studies, and airway liquid studies. Emphasis is placed on promising further directions, such as analysis of interacting fluid-mechanical or fluid-structure phenomena, multi-scale modeling across widely varying length and time scales, and integration of advanced simulations into respiratory investigation and pulmonary medicine.

The Pulsatile Propagation of a Finger of Air Within a Fluid-Occluded Cylindrical Tube.

We computationally investigate the unsteady pulsatile propagation of a finger of air through a liquid-filled cylindrical rigid tube using a combined boundary element method and lubrication theory approach. The flow-field is governed by the dimensionless parameters Ca(Q)(t) = Ca(M) + Ca(Omega) sin(Omegat) = muQ*(t*)/piR(2)gamma, Omega = muomegaR/gamma and A = 2Ca(Omega)/Omega. Here, Ca(Q)(t) consists of both mean (Ca(M)) and oscillatory (Ca(Omega)) components. It is shown that the behavior of this system is appropriately described by steady-state responses until the onset of reverse flow, wherein the system operates in the unsteady regime (Ca(Omega) > Ca(M)). When flows in this regime are considered, converging and diverging stagnation points move dynamically throughout the cycle and may temporarily separate from the interface at high Omega. We have also found that for Ca(Omega) < 10Ca(M) the bubble tip pressure drop DeltaP(tip) may be estimated accurately from the pressure measured downstream of the bubble tip when corrections for the pressure drop due to Poiseuille flow are applied. The normal stress gradient at the tube wall ( partial differentialtau(n)/ partial differentialz) is discussed in detail, as this is believed to be the primary factor in airway epithelial cell damage (Bilek et al 2003). In the unsteady regime we find that local film-thinning produces high partial differentialtau(n)/ partial differentialz at low Ca(Omega). Film thickening at moderate Ca(Omega) in the unsteady regime protects the tube wall from the large gradients near the bubble tip, therefore reducing partial differentialtau(n)/ partial differentialz. We find that the stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be of interest to our field of study, pulmonary airway reopening.