In view of uncertainties about the best way to estimate mean alveolar gases in patients with ventilation-perfusion inequalities, three different methods were evaluated on 54 patients. 1) O2 and CO2 were recorded by mass spectrometer on an O2 (x)-CO2 (y) diagram. The coordinates at the intersect of the expiratory record with the mixed expired R line (RE) ives the mean alveolar values (PAo2 and PAco2. 2)pa'co2 was calculated with the Bohr equation using a predicted anatomic dead space and PA'o2 was derived with the alveolar equation. 3) End-tidal (ET) P02 were averaged over 1 min at rest in steady state. Mean RET calculated from 3 was identical with RE. Mean values for PAco2, PA'CO2. and PETco2 differed by less that 1 Torr, but the variance was least with the end-tidal method. There was a highly significant correlation between delta aAPco2 using PETco2 and VD/VT, better than with either of the other methods. The end-tidal measurement appears to give the best approximation of mean alveolar gas in pulmonary patients.
Lipschitz continuity and Gateaux differentiability of the best approximation operator in vector-valued Chebyshev approximation