Graphical analysis of multiple inert gas elimination data

Abstract

A plot of measured retention-excretion ratios [(Ri/Ei)obs] vs. reciprocal solubility (1/lambda i) for selected inert gases allows quick detection of shunt and ventilation-perfusion (V/Q) inhomogeneity in the lung. We derive simple rules for constructing a smooth R/E function from the data, using a multicompartmental model of the lung. If mixed venous inert gas measurements are available, the values [lambda i(1-Ri)/Ei]obs for the infused gases can be used to estimate the overall VT/QT ratio and provide an additional test of the consistency of the data. For any set of equilibrium compartments ventilated and perfused in parallel, we show that d(R/E)/d(1/lambda) cannot be negative, nor can d2(R/E)/d(1/lambda)2 be greater than zero. A rectilinear R/E function implies a narrow distribution of V/Q among the gas exchange compartments, whereas a downward-concave curve implies a broader distribution. The shunt perfusion and dead-space ventilation can be estimated from the asymptotes of the R/E function. The range of V/Q for the gas exchange compartments can also be bracketed if a well-defined region of curvature is present in the graph. Finally, from the R/E vs. 1/lambda graph and (if mixed venous data are available) from the lambda(1-R)/E values, we can determine quickly whether the data deserve the detailed numerical analysis outlined in our companion paper.