A non-linear theory of the distribution of pulmonary ventilation

Abstract

A theory for the distribution of ventilation in a two compartment model of the lung is developed, neglecting inertial forces but allowing resistance and compliance to vary with lung volume and resistance to vary with flow rate, all in a non-linear manner. Numerical solutions to the basic equation are found for the distribution of inspired gas between the upper and lower lobes of erect human lungs. Results are presented to show how a bolus of labelled gas inspired at various volumes and flow rates would be distributed. The theory predicts the preferential distribution of the bolus to the lower lobes, if inspired slowly, because these lobes are more compliant than the upper as a result of the gradient of pleural pressure. With increasing inspiratory flow rate more of the inspired bolus is distributed to the upper lobes. Reversal, where ventilation per alveolus in the upper and lower lobes is equal after a given inspired volume occurs at approximately 2 litres/sec when the inspired volume is 400 ml. Above this flow there is a preferential distribution of gas to the upper lobes. This reversal is a direct result of the volume-dependence of resistance, the more expanded upper airways having a lower resistance. The computations are made for a wide range of physiological and anatomical parameters, so that the influence of various factors, such as overall lung volume, airway resistance, and pressure-volume relations, on the distribution of inspired gas, can be explored. The flow rate at which reversal occurs is influenced to some extent by all parameters but is most sensitive to changes in lung volume. The results are in good agreement with recent experiments on the distribution of gas using boli of radio-active Xenon and external counters at the chest wall. It is stressed that the theory can readily be extended to calculate the distribution of ventilation in situations other than uniform inspiration, for example during cyclic breathing at various frequencies, if the appropriate anatomical and physiological variables for expiration can be determined.