A model of transient oscillatory pressure-flow relationships of canine airways

In a previous paper (27) we developed a lumped parameter model of canine pulmonary airway mechanics featuring airway wall elasticity, gas inertance, and laminar and turbulent gas flow. The model accurately accounted for the steady-state pressure-flow data we obtained during sinusoidal cycling of the lung following a period of apnea. In the present paper, we extend the model to account for the transient decrease in the amplitude of the trans-airway pressure swings that we observed immediately following the apnea, which we have shown to be due to a vagally mediated bronchodilatation reflex. The extended model accounts for this transient in terms of a sudden change in airway smooth muscle tone acting on the viscoelastic properties of the airway wall and tissues mechanically coupled to it. Consequently, this model is able to temporarily store a volume of gas in the conducting airway tree as its volume changes cyclically with that of the whole lung. This means that the flow entering the airway tree from the trachea at any instant (V) is not precisely equal to that entering the alveoli (Valv) even when the gas is considered incompressible. We found that assuming V to be equal to Valv can lead to errors in estimating respiratory tissue impedance of as much as 10%. However, tissue hysteresivity remained almost unaffected, suggesting that the hysteretic properties of respiratory system tissues and airway wall are well matched.