Pressure, flow, and density relationships in airway models during constant-flow ventilation

Adequate CO₂ elimination and normal arterial PCO₂ levels can be maintained in dogs during apnea by delivering a continuous flow of inspired gas at high flow rate (1-3 l·min^-1·kg^-1) through the tubes placed in the main-stem bronchi. However, during constant-flow ventilation (CFV) the mean alveolar pressure is increased, causing increased lung volume despite low pressures in the trachea. We hypothesized that the increased dynamic alveolar pressures during CFV were due to momentum transfer from the high-velocity jet stream to resident gas in the lung. To test this, we simulated CFV in straight tubes and in a branched airway model to determine whether changes in gas flow rate (V̇), gas density (ρ), and tube diameter (D) altered the pressure difference (ΔP) between alveoli and airway opening in a manner consistent with that predicted by conservation of momentum. Momentum analysis predicts that ΔP should vary with V̇², whereas measurements yielded a dependence of branched tubes and V̇^1.69 in branched tubes and V̇^1.9 straight tubes. Substitution of heliox (80% He-20% O₂) for air significantly reduced lung hyperinflation during CFV. As predicted by momentum transfer, ΔP varied with ρ^1.0. Momentum analysis also predicts that ΔP should vary with D^-2.0, whereas measurements indicated a dependence on D^-202. The influence of V̇ and ρ on depth of penetration of the jet down the airway was explored in a straight tube model by varying the flow rate and gas used. The influence of geometry on penetration was measured by changing the ratio of jet-to-airway tube diameters. Depth of penetration of the jet was largely independent of V̇ and ρ but increased as the airway D increased, reaching a maximum depth at a jet-to-airway D ratio near 0.2. We conclude that momentum exchange between the incoming jet and the resident gas can explain the relationship between ΔP and V̇ or ρ and can also explain why airway geometry influences the depth of penetration of bulk flow during CFV. Accordingly, these results explain lung hyperinflation and inhomogeneities of alveolar pressures during CFV and suggest approaches to optimize lung gas exchange during CFV.