Flow mechanisms of the air-blood barrier

The air-blood barrier protects the lung from blood/serum entering the air spaces, i.e., from "drowning in your own fluids". Failure leads to pulmonary edema, a regularly fatal complication during the Covid-19 pandemic which claimed 7 million lives worldwide. Finding no mathematical models for the underlying fluid mechanics, we created the first. Governing flow equations for alveolar capillary, interstitium, and alveolus are coupled by crossflows at the capillary and epithelial membranes and end-exit flows to the lymphatics. Case examples include normal/recovery, cardiogenic pulmonary edema, acute respiratory distress syndrome, effects of positive end expiratory pressure, and a wide range of parameter values for permeability of the membranes and interstitial matrix. Previously unknown membrane fluid shear stresses calculate to values that affect cell function in many systems. We add active epithelial reabsorption which has two effects: shifting streamlines to favor alveolar-lymphatic clearance and adding to the direct alveolar-capillary clearance. Simple algebraic equations are derived for the interstitial fluid pressure, pi, membrane crossflow velocities and the critical capillary pressure, pcrit, above which edema occurs. For validation, the pcrit predictions fit clinical definitions and flow calculations of lymphatic vs capillary clearance match animal experimental data. For decades the value of pi has been imposed as an input, whereas we calculate the value as an output. They don't agree. Since the space is too small for measurements, the ability to calculate pi and pcrit offers new insights, questions long-held beliefs, and opens applications from physiological studies to personalized clinical care.