Using a theoretical model, we studied spreading of a bolus of insoluble surfactant deposited on a thin liquid layer of a model airway. Applications include instillation of exogenous surfactant as a treatment for neonatal respiratory distress syndrome, the use of surfactant carriers to deliver drugs via the lung, and the movement of liquid along the airway tree due to naturally occurring gradients of surface tension. The time-dependent governing equations were solved numerically for longitudinal axisymmetric surfactant spreading. We examined the influences of the resident liquid layer (thickness, viscosity, endogenous surfactant, airway radius), of the bolus (volume and surfactant content), and of gravity. The gradient in surface tension drives the flow toward the region of higher surface tension, ultimately creating a shocklike wave of nearly twice the initial lining thickness. Pressure gradients due to interfacial curvature (capillarity) have little effect on the rate of surfactant spread. The presence of an endogenous resident surfactant greatly augments the rate of spreading while inhibiting development of the shock. In all cases studied, the effect of circumferential curvature was negligible, indicating that the liquid layer can be treated as if it were spreading over a flat surface. Our results reveal that the surfactant spreads as time to the one-third power. Accordingly, a surfactant deposited in the trachea of a neonate would spread to the periphery in approximately 12 s.

The present study characterizes the dynamic interfacial properties of calf lung surfactant (CLS) and samples reconstituted in a stepwise fashion from phospholipid (PL), hydrophobic apoprotein (HA), surfactant apoprotein A (SP-A), and neutral lipid fractions. Dipalmitoylphosphatidylcholine (DPPC), the major PL component of surfactant, was examined for comparison. Surface tension was measured over a range of oscillation frequencies (1-100 cycles/min) and bulk phase concentrations (0.01-1 mg/ml) by using a pulsating bubble surfactometer. Distinct differences in behavior were seen between samples. These differences were interpreted by using a previously validated model of surfactant adsorption kinetics that describes function in terms of 1) adsorption rate coefficient (k1), 2) desorption rate coefficient (k2), 3) minimum equilibrium surface tension (gamma*), 4) minimum surface tension at film collapse (gammamin), and 5) change in surface tension with interfacial area for gamma < gamma* (m2). Results show that DPPC and PL have k1 and k2 values several orders of magnitude lower than CLS. PL had a gammamin of 19-20 dyn/cm, significantly greater than CLS (nearly zero). Addition of the HA to PL restored dynamic interfacial behavior to nearly that of CLS. However, m2 remained at a reduced level. Addition of the SP-A to PL + HA restored m2 to a level similar to that of CLS. No further improvement in function occurred with the addition of the neutral lipid. These results support prior studies that show addition of HA to the PL markedly increases adsorption and film stability. However, SP-A is required to completely normalize dynamic behavior.

A model is presented of surfactant replacement therapy. An instilled bolus is pushed into the lungs on the first inspiration, coating the airways with a layer of surfactant and depositing some in the alveoli. Layer thickness depends on the capillary number (muU/gamma, where mu, U, and gamma are bolus viscosity, advancing meniscus velocity, and surface tension, respectively). Larger capillary number leads to thicker layers, reducing alveolar delivery. Subsequently, surface tension gradients sweep surfactant into alveoli not receiving surfactant during the first inspiration. The effects on spreading of sorption kinetics, bolus viscosity, initial layer thickness, initial penetration of surfactant, gravity, and shear stress are examined. Sorption nearly eliminates surface tension gradients in central airways but produces a sharp transition at the leading edge of the exogenous layer. Local thinning of the liquid layer results, trapping 95% of the surfactant in the airways. Gravity and ventilation augment transport somewhat. Transport to the periphery takes 4-170 s for the leading edge but considerably longer for the bulk of the surfactant. The model demonstrates how the various physical parameters governing surfactant distribution might alter the response to surfactant replacement therapy.

Measurements of surface tension in the lung have shown that a time-mean gradient exists with the potential to generate clearance flows toward the mouth in the thin liquid layer that lines the airways. A model is developed to explore this phenomenon in the simple case of a membrane with linear variation in strain along its length, coupled with the unique properties of pulmonary surfactant. The evolution equations are solved numerically for liquid layer thickness and surfactant concentration during a single oscillatory cycle, and the net volume exchanged is computed. The parameters governing the flow are shown to be time scales for viscous effects, tau(v), surface diffusion, tau(DS), surfactant adsorption, tau(A), surfactant desorption, tau(D), oscillation, tau(o), and the average membrane strain epsilon. The volume pumped toward the less compliant end on the initial cycle is maximized when tau(o)/tau(v) approximately O(1) and is relatively insensitive to tau(DS). Rapid adsorption generally augments liquid transport for tau(o)/tau(D) < O(1). Pumping drops precipitously if tau(o)/tau(D) > O(1). Effects of strain amplitude are reported as well. For parameter values approximating those in the lung, pumping rates are near optimal; the mean surface velocity is approximately 0.05 mm/sec, compared with 0.2 mm/sec produced by the action of cilia on the mucus layer. This mechanism might therefore be important in assisting clearance from the lung or maintaining a liquid layer over alveolar facets.

The method of surfactant instillation into the lungs for treatment of neonatal respiratory distress syndrome is an important attribute of delivery, and it may determine the overall efficacy of treatment. Previous studies primarily focused on the rate at which the bolus is instilled. These findings show that rapid injections lead to a more homogenous distribution, whereas slow infusions drain into the dependent lung with respect to gravity, resulting in a heterogeneous deposition. These results suggest that it is beneficial to form a meniscus, from which a more homogenous dispersal can proceed. The objective of the present study was to develop a functional criterion for meniscus formation during bolus injection. An in vitro experiment was used to examine the clinical setting of surfactant instillation. The physical variables examined were the bolus viscosity (mu) and density (rho), gravity (g), injection rate (Q), orientation of the trachea with respect to gravity (theta), tracheal size (D), surface tension (gamma), and catheter size (d). All quantities were varied, except gravity and catheter size. Experimental results show that a meniscus will form when NSt > 0. 004Re2/3, where NSt is Stokes number and Re is Reynolds number, NSt = muQ/D4rhogsintheta, a ratio of viscous effects to gravitational effects, and Re = rhoQD/d2mu, a ratio of inertial effects to viscous effects. Rapid injections, high viscosity, and small inclination with respect to gravity promote meniscus formation. These results can be used to refine the guidelines for administration of surfactant replacement therapy.