Extracorporeal CO₂ Removal and the Alveolar Gas Equation

To the Editor:

As the use of venovenous extracorporeal membrane oxygenation and extracorporeal CO₂ removal (ECCO₂R) increases to support patients with acute respiratory distress syndrome, an understanding of the physiology of gas exchange and the ramifications for ultraprotective lung ventilation becomes more critical for proper management. In the review “Mechanical Ventilation for Acute Respiratory Distress Syndrome during Extracorporeal Life Support” (1), the authors incorrectly applied a simplified version of the alveolar gas equation (AGE), which led to an unfounded warning that ECCO₂R could lead to a “marked decrease in Pa_O2.”

The simplified AGE is as follows:

$$\begin{array}{l}{\text{Pa}}_{\text{O}2}={\text{Fi}}_{\text{O}2}\times \left({\text{P}}_{\text{atm}}\mathrm{-}{\text{P}}_{\text{H}2\text{O}}\right)\mathrm{\hspace{0.17em}-\hspace{0.17em}}{\text{ P}}_{\text{CO}2}\text{/RER}\\ \end{array}$$

Importantly, the simplified AGE assumes a fixed volume of alveolar gas. However, during ECCO₂R, the volume of CO₂ entering the alveolus ($\dot{\mathrm{V}}$co₂) is much less than the amount of oxygen leaving the alveolus ($\dot{\mathrm{V}}$o₂). The difference in these volumes results in passive inflow of fresh gas into the alveolus. Under normal physiologic conditions, this effect is small and can be ignored (hence the common use of the simplified AGE); however, with large changes in the respiratory exchange ratio (RER), the error introduced on calculated Pa_O2 is substantial. To account for the influx of fresh gas, the full AGE, detailed in the appendix of West’s Respiratory Physiology primer (2) and skipped by generations of medical students, contains an additional term (highlighted in bold):

$${\text{Pa}}_{\mathrm{O2}}={\text{Fi}}_{\mathrm{O2}}\times \left({\text{P}}_{\text{atm}}\mathrm{-}{\text{P}}_{\text{H}2\text{O}}\right)\mathrm{-}{\text{ P}}_{\text{CO}2}\text{/RER }+{\mathbf{FI}}_{\mathbf{O2}}\mathbf{ \times P}{\mathbf{a}}_{\mathbf{CO2}}\mathbf{\times }\left(\mathbf{1-RER}\right)\mathbf{/RER}$$

The impact of varying amounts of CO₂ removal with ECCO₂R on Pa_O2 calculated by both the simplified AGE and the full AGE is shown in Figure 1. The reduction in Pa_O2 is fairly slight when using the full AGE, even with the (unrealistic) assumption of zero oxygen flux across the membrane oxygenator (the effect of which would be to increase RER and further blunt the already small impact on Pa_O2). Therefore, this mechanism (altered RER) should not be invoked as a cause of deteriorating Pa_O2 after initiation of ECCO₂R therapy.

Figure 1.

The Pa_O2 was calculated using the simplified alveolar gas equation (dashed lines) and the full equation (solid lines) at four different levels of Fi_O2 (0.4, 0.5, 0.6, and 0.7) and across a range (from 0 to 100 ml) of CO₂ elimination via ECCO₂R. Baseline respiratory exchange ratio = 0.8. Note that the simplified equation shows a significant reduction in Pa_O2 as CO₂ elimination via ECCO₂R increases, whereas the full equation remains relatively stable. ECCO₂R = extracorporeal CO₂ removal.