Theoretical validation of the respiratory benefits of helium-oxygen mixtures

A theoretical analysis of convective gas transport validates the clinically demonstrated advantage of using helium-oxygen mixtures in treating patients with respiratory problems. Previous studies have attributed that advantage to the ability of helium-oxygen to stay laminar at higher velocities than nitrogen-oxygen. The present work shows that helium-oxygen does not need to be laminar to provide higher flow rates and that its benefits persist under turbulent conditions. The analysis is applied to steady flow through the lungs and through a circular airway obstruction. A simplified model of the lungs gives pressure-flow relations that show a significant increase in oxygen flow rate when nitrogen is substituted by helium. A similar improvement is found for flow through an obstruction. For a given pressure difference across the lungs or across an obstruction, the turbulent flow rate of oxygen increases by approximately 50% when nitrogen is replaced by helium in a mixture containing 20% oxygen.