Pulmonary Edema, Reabsorption, and Clearance

We present a 2D flow model of the alveolar interstitium as a long, thin rectangle, 0≤x≤L, -d≤y’≤d where d/L<<1. The capillary membrane at y’=-d follows a Starling equation with k_c the hydraulic conductivity. The alveolar membrane at y’=d also employs a Starling equation with k_A the hydraulic conductivity, but we include an additional velocity term, -v_ab, for active fluid reabsorption. Interstitial pressures are imposed at the ends, p_i = p_iB at x=0,L. Lubrication theory is applied to the capillary blood flow while the alveolus has a static liquid lining with surface tension, σ. The interstitium is treated as a porous media using the Brinkman equation and the coupled system solved with Fourier series. The resulting flow can be from the alveoli to the capillary (clearance), from the capillary to the alveoli (pulmonary edema), or both. Fluid originating from both capillary and alveolus exits the ends to the lymphatics. Model predictions correlate well with clinical criteria of pulmonary edema and therapies such as reducing σ, positive end expiratory pressure (PEEP) for the alveolar gas, and reducing blood pressure. There is good correlation to animal experiments that measure pulmonary lymphatic flows which increase linearly with blood pressure, but only account for ~10% of edema recovery flows with ~90% crossing directly to the capillary. v_ab increases reabsorption flow rates in the central region and shifts streamlines in the end regions to enhance alveolar fluid exit. Wall shear stress levels on the membranes are found to be in the biologically stimulating range.