A Computational Model of Pulmonary Edema

The study of pulmonary edema has lacked a robust mechanistic model which can be used to interpret data, sort diagnoses, promote personalization of interventions, and monitor therapeutic responses. To address this need, we present a 2D flow model of an interalveolar septum with finite length, scaled as 0≤X≤1. Lubrication theory is applied to the capillary blood flow while the alveolus has a static liquid lining. The interstitium between is treated as a porous media, both Darcy and Brinkman approaches. We impose Starling equations at the capillary and alveolar membranes. They relate the cross-membrane fluid velocity from differences of fluid and osmotic pressures and the membrane hydraulic conductivity, k_c and k_A, respectively. The resulting flow can be from the alveoli to the capillary (clearance), or from the capillary to the alveoli (pulmonary edema), crossing the interstitium either way. Generally, there are two interstitial flow regimes: a central region which is quasi-one dimensional and end boundary layers which have rapid changes in pressures, shear stresses, and velocities. Importantly, fluid exits the interstitial ends, X=0,1, to the lymphatics, resolving a lung mystery since 1896. In addition to exploring various diseases and therapies, we also derive analytical solutions in the central region which can be used by clinicians and investigators to calculate alveolar interstitial pressure, cross flow and the critical blood pressure leading to edema. The simplest form depends on the ratio k_A / k_c <<1.