A simple model of VA/Q distribution for analysis of inert gas elimination data

A general procedure for fitting compartments models of alveolar ventilation-perfusion ratio (VA/Q) distribution to inert gas elimination data is described. The method can be applied to any model consisting of a number of compartments ventilated and perfused in parallel, each compartment of the model having a fixed predetermined VA/Q ratio. The number of compartments and their VA/Q ratios required for adequately fitting real data have been examined. A 13-compartment model consisting of a shunt, a dead space, and 11 compartments equally spaced on a logarithmic scale from VA/Q of 0.01 to 100 was found to be suitable. The fitting procedure and the 13-compartment model form the basis of a method of analysis of inert gas elimination data. Essentially the method consists of calculating a sample of 30 distributions compatible with the data analyzed taking into account experimental errors in the inert gas measurements. From this sample, the averages and standard deviations of the flows to 13 zones on the VA/Q scale are estimated. The averages are estimates of the true flows to these zones, and the standard deviations give an indication of the range of flows compatible with the data. The method has some advantages over both the enforced-smoothing approach and the Monte Carlo linear programming scheme of Evans and Wagner (J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 42: 889-898, 1977).