Spreading of exogenous surfactant in an airway

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.