The alveolar edema equation

Pulmonary edema is excessive liquid accumulation in the alveolar air spaces and interstitium. This reduces gas exchange leading to increased morbidity and mortality. Clearance of pulmonary edema fluid relies on reabsorption into the alveolar interstitium and then either to the alveolar capillaries or to the lung lymphatics. How it reaches the lymphatics has been a puzzle since 1896. Our 2D model of an interstitial strip resolves that puzzle. We also show that alveolar interstitial pressures differ from values used in traditional medical textbooks. Our approach employs detailed fluid mechanical analysis of the alveolar capillary blood flow, interstitial fluid flow, and the alveolar liquid layer with gas interface and surface tension effects. The governing equations are coupled by Starling equations at both the capillary and alveolar membranes. Traditional approaches only consider the capillary Starling equation. Approximately 80% of the strip is 1D flow directly across the interstitium for either edema or clearance. There, we derive simple equations, usable by physiologists and clinicians, which predict the interstitial fluid pressure and the cross-flow rates (edema or alveolar-capillary clearance). Contrary to conventional tenets, the cross-flow rate magnitude is controlled by the alveolar membrane filtration coefficient, not the capillary membrane. Finally, we derive the critical capillary blood pressure leading to pulmonary edema, i.e., the alveolar edema equation. The latter matches well with clinical data on edema from high blood pressure or ARDS. It can be used to personalize PEEP therapy to prevent edema prophylactically or clear it.