Model for a pump that drives circulation of pleural fluid

Abstract

Physical and mathematical models were used to study a mechanism that could maintain the layer of pleural fluid that covers the surface of the lung. The pleural space was modeled as a thin layer of viscous fluid lying between a membrane carrying tension (T), representing the lung, and a rigid wall, representing the chest wall. Flow of the fluid was driven by sliding between the membrane and wall. The physical model consisted of a cylindrical balloon with strings stretched along its surface. When the balloon was inflated inside a vertical circular cylinder containing a viscous fluid, the strings formed narrow vertical channels between broad regions in which the balloon pressed against the outer cylinder. The channels simulated the pleural space in the regions of lobar margins. Oscillatory rotation of the outer cylinder maintained a lubricating layer of fluid between the balloon and the cylinder. The thickness of the fluid layer (h), measured by fluorescence videomicroscopy, was larger for larger fluid viscosity (mu), larger sliding velocity (U), and smaller pressure difference (delta P) between the layer and the channel. A mathematical model of the flow in a horizontal section was analyzed, and numerical solutions were obtained for parameter values of mu, U, delta P, and T that matched those of the physical model. The computed results agreed reasonably well with the experimental results. Scaling laws yield the prediction that h is approximately (T/delta P)(microU/T)2/3. For physiological values of the parameters, the predicted value of h is approximately 10(-3) cm, in good agreement with the observed thickness of the pleural space.