To the Editor:--Story's letter raises interesting questions about the alveolar gas equations. Essentially, these indicate the alveolar partial pressures of oxygen and carbon dioxide in terms of barometric pressure, uptake (or output), and alveolar ventilation. They are simply based on conservation of mass.
Alveolar gas equations exist in many versions for different purposes: some versions are accurate, some less accurate, and some only approximate. Accurate versions are required for determination of alveolar PO2in the calculation of venous admixture, for example. Perhaps the most satisfactory version for the anesthesiologist is that of Filley, MacIntosh, and Wright, which does not require inert gases, such as nitrous oxide, to be in equilibrium.
Some approximate versions give a clearer indication of the quantitative relevance of clinically important variables and so are a valuable teaching aid. For this purpose, I favor the following:(Equation 1, Equation 2). The first is accurate if expired minute volume is used to calculate VA, the second is only approximate. Nevertheless, it is quite adequate as a basis for consideration of problems of gas exchange in such situations as high altitude, malignant hyperpyrexia, or ventilatory failure.
These versions of the “universal” alveolar air equation make it quite clear that PAO2is not really a function of PACOsub 2 as Story explains, even though some versions of the alveolar gas equation give this impression. However, if inspired concentrations and respiratory exchange ratio remain constant, then changes in alveolar ventilation alter PAO2and PACO2in different directions, the magnitude of the changes being related to the respiratory exchange ratio. Therefore, it is a case of post hoc rather than propter hoc.
It should be stressed that V with dotCO2and V with dotO2in these equations are output and uptake, respectively, and not production and consumption, as Story states. In the case of oxygen, uptake and consumption seldom differ greatly. However, for carbon dioxide, output may differ greatly from production in an unsteady state. This has considerable clinical relevance. Patients seldom die in a steady state.
Alveolar air equations are at their simplest when FIOsub 2 = 1.0. Then:Equation 3and no corrections are required. An opening parenthesis is missing from Story's Equation 1immediately before PB. This may have caused confusion.
John F. Nunn, M.D., D.Sc., Ph.D., F.R.C.S., F.R.C.A., The Stocks, 3 Russell Road, Moor Park, Northwood, Middlesex, United Kingdom HA6 2LJ.
(Accepted for publication July 1, 1996.)