A Mathematical Model of Alveolar Gas Exchange in Partial Liquid Ventilation

Abstract

In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Pe´clet number in air ventilation is Pe∼0.01, whereas in PLV it is Pe∼20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments PC-Pg are found to exist. Because Pe≫1, temporal phase differences are found to exist between PC-Pg and the ventilatory cycle that cannot be adequately described by existing non-convective models of gas exchange in PLV. The mass transfer rate is nearly constant throughout the breath when Pe≫1, but when Pe≪1 nearly 100% of the transport occurs during inspiration. A range of respiratory rates (RR), including those relevant to high frequency oscillation (HFO)+PLV, tidal volumes VT and perfusion rates are studied to determine the effect of heterogeneous distributions of ventilation and perfusion on gas exchange. The largest changes in PCO2 and PCCO2 occur at normal and low perfusion rates respectively as RR and VT are varied. At a given ventilation rate, a low RR-high VT combination results in higher PCO2, lower PCCO2 and lower PC-Pg than a high RR-low VT one.