A mathematical model to predict protein wash out kinetics during whole-lung lavage in autoimmune pulmonary alveolar proteinosis

Whole-lung lavage (WLL) remains the standard therapy for pulmonary alveolar proteinosis (PAP), a process in which accumulated surfactants are washed out of the lung with 0.5-2.0 l of saline aliquots for 10-30 wash cycles. The method has been established empirically. In contrast, the kinetics of protein transfer into the lavage fluid has not been fully evaluated either theoretically or practically. Seventeen lungs from patients with autoimmune PAP underwent WLL. We made accurate timetables for each stage of WLL, namely, instilling, retaining, draining, and preparing. Subsequently, we measured the volumes of both instilled saline and drained lavage fluid, as well as the concentrations of proteins in the drained lavage fluid. We also proposed a mathematical model of protein transfer into the lavage fluid in which time is a single variable as the protein moves in response to the simple diffusion. The measured concentrations of IgG, transferrin, albumin, and β₂-microglobulin closely matched the corresponding theoretical values calculated through differential equations. Coefficients for transfer of β₂-microglobulin from the blood to the lavage fluid were two orders of magnitude higher than those of IgG, transferrin, and albumin. Simulations using the mathematical model showed that the cumulative amount of eliminated protein was not affected by the duration of each cycle but dependent mostly on the total time of lavage and partially on the volume instilled. Although physicians have paid little attention to the transfer of substances from the lung to lavage fluid, WLL seems to be a procedure that follows a diffusion-based mathematical model.