Steady Expiratory Flow-Pressure Relationship in a Model of the Human Bronchial Tree

Static pressure differences across a human bronchial tree model were obtained for steady expiratory flows of several gases producing Reynolds numbers (Re₁) in the bronchus carrying the entire flow (first bronchus) between 150 and 50,000. The model was constructed from an air-dried lung and was complete to bronchi about 2 mm in diameter. Dimensionless static pressure plotted against Re₁ consolidated the data on a single curve, phenomenologically described by an equation of the form: ΔP_s/ΔPd₁ = A + B Re₁ where ΔPd₁ is a pressure drop for Poiseuille flow. Velocity profile measurements at two sites along the first bronchus for laminar and turbulent flows indicate a dependence on the latter and distance from the first junction. Loss in total pressure was computed and may result from both frictional dissipation and changes in momentum flux associated with development of velocity profiles near the junctions. An average loss in total pressure within a single bronchus was calculated after making several simplifying assumptions, and this result may be useful in modeling both the resistance of the entire bronchial tree and the more complex phenomenon of maximal expiratory flow.