Relationships among ventilation-perfusion distribution, multiple inert gas methodology and metabolic blood-gas tensions.

The retention equations upon which the Multiple Inert Gas Method is based are derived from basic principles using elementary algebra. It is shown that widely disparate distributions produce indistinguishable sets of retentions. The limits of resolution of perfused compartments in the VA/Q distribution obtainable by the use of the multiple inert gas method are explored mathematically, and determined to be at most shunt and two alveolar compartments ("tripartite" distribution). Every continuous distribution studied produced retentions indistinguishable from those of its unique "matching" tripartite distribution. When a distribution is minimally specified, it is unique. Any additional specification (increased resolution--more compartments) of the distribution results in the existence of an infinitude of possible distributions characterized by indistinguishable sets of retention values. No further increase in resolution results from the use of more tracers. When sets of retention values were extracted from published multiple inert gas method continuous distributions, and compared with the published "measured" retention sets, substantial differences were found. This illustrates the potential errors incurred in the practical, in vivo application of the multiple inert gas method. In preliminary studies, the tripartite distribution could be determined with at least comparable accuracy by blood-gas (oxygen, carbon dioxide) measurements.