The prediction of pressure drop and variation of resistance within the human bronchial airways

Abstract

Pressure drop and distribution of resistance within the lower airways on inspiration are predicted, from the theory developed earlier, for a wide range of flow rates using a symmetrical rigid model of the anatomy of the bronchial tree based upon data from lungs fixed at 75 % TLC. The resistance depends upon flow rate, the major part being in the trachea and larger bronchi. Airways beyond generation 10 (diameter approximately 0.5 mm) contribute less than 10% to lower AWR. The overall pressure drops obtained are in close agreement with experimental observations.The relationship between pressure and flow is given by ΔP = K(ρμ) 1 2 V ̇ V 3 2 where K is a constant depending only on lung anatomy. This relationship is non-linear and concave to the pressure axis. The non-linearity may not be apparent at flow rates below 2 L/sec.Theequation allows prediction of the effect of gas mixtures on airway resistance, where results again agree with most experimental values available, and overcomes the difficulties associated with theuse of Rohrer's equation. The relation between AWR and lung volume is examined. Assuming the airways are all equally compliant thin-walled elastic tubes, the expected hyperbolic relation between lung volume and AWR is obtained. This agrees closely with recent measurements of lower airway resistance in atropinised subjects.