Modeling diffusion limitation of gas exchange in lungs containing perfluorocarbon

We reported changes in alveolar-arterial PO2 gradient, ventilation-perfusion heterogeneity, and arterial-alveolar PCO2 gradient during partial liquid ventilation (PLV) in healthy piglets (E. A. Mates, P. Tarczy-Hornoch, J. Hildebrandt, J. C. Jackson, and M. P. Hlastala. In: Oxygen Transport to Tissue XVII, edited by C. Ince. New York: Plenum, 1996, vol. 388, p. 585-597). Here we develop two mathematical models to predict transient and steady-state (SS) gas exchange conditions during PLV and to estimate the contribution of diffusion limitation to SS arterial-alveolar differences. In the simplest model, perfluorocarbon is represented as a uniform flat stirred layer and, in a more complex model, as an unstirred spherical layer in a ventilated terminal alveolar sac. Time-dependent solutions of both models show that SS is established for various inert and respiratory gases within 5-150 s. In fluid-filled unventilated terminal units, all times to SS increased sometimes by hours, e.g., SF6 exceeded 4 h. SS solutions for the ventilated spherical model predicted minor end-capillary disequilibrium of inert gases and significant disequilibrium of respiratory gases, which could explain a large portion of the arterial-alveolar PCO2 gradient measured during PLV (14). We conclude that, during PLV, diffusion gradients for gases are generally small, except for CO2.