Spectral analysis of inert gas elimination data: resolution limits

A new method of analyzing inert gas data for recovery of the pulmonary ventilation-perfusion ration (VA/Q) distribution is proposed. It is shown that the conventional inert gas elimination equation takes the form of a convolution integral, and the relationship between VA/Q distribution and inert gas elimination resembles that of a noncausal low-pass filter with infinite zero-frequency gain. With the use of this formulation, characteristic features of VA/Q distribution may be represented in the frequency domain in terms of the corresponding energy spectrum. It is shown that the lack of resolution associated with finite data samples and measurement error is caused by distortions in the high-frequency contents of the resulting VA/Q distribution. With six inert gases, the technique cannot resolve a log SD less than 0.21 decade and a modal separation less than 0.87 decade. In the presence of measurement error, the degree of resolution is even less. It is suggested that for maximum resolution the number of discrete and duplicate data samples should be chosen so that the resulting noise and sampling cutoff frequencies are approximately equal.