To the Editor:
In July of 2013, Mark Siobal and colleagues wrote a paper on volumetric capnography in Respiratory Care.1 In a subsequent letter to the Editor,2 I pointed out an error in their Figure 8. In that figure, the quantity VDalv is represented as the shaded areas between the volume curve and the CO2 axis. Although the vertical axis is labeled simply CO2, there are horizontal lines labeled PaCO2, PACO2, etc, implying that the vertical axis represents pressure. The problem is that if the vertical axis is pressure, then the areas on the graph have the wrong dimensions; they are not volumes. Unfortunately, Mr Siobal failed to heed my advice and, in his most recent paper on the same subject,3 has made the same error 7 more times (Figs. 4, 5, 6, 14, 15, 18, and 19; most of which explicitly label the vertical axis as PCO2 in mm Hg). Figure 6 is particularly egregious because its legend says “From reference 106, with permission.” Checking that reference,4 we see it repeatedly shows the vertical axis labeled as Exhaled FCO2 (carbon dioxide fraction), not PCO2, for volumetric CO2 curves.
Here is the significance of the error. The dimensions of any area on an x-y plot are the dimensions of the vertical axis times the dimensions of the horizontal axis. For example, if the y axis has the dimension of length (L) and the x axis also has the dimension of length, then any area on the graph has the dimensions of length squared (L2). Similarly, if the graph was, say, flow versus time, then the area under the flow curve would have units of volume; flow × time (T) = (volume/time) × time = volume, which has dimensions of length cubed (L3). Now, if a volumetric CO2 graph has its vertical axis labeled as PCO2 (a pressure) and its horizontal axis labeled as volume, then any area has units of pressure × volume = (force/area) × volume = (force/L2) × L3 = force × L, which has dimensions of mass (M) × acceleration × distance, or ML2T−2, representing work, not volume.5
The correct labeling for the volumetric CO2 graph shows the fractional concentration of CO2 on the vertical axis (FCO2 not PCO2).6 Area in units of a fraction times volume yields the units of volume, as required. This was illustrated as early as 1948 in a paper by Fowler,7 where the vertical axis is labeled “CO2 concentration” expressed as a fraction. Fletcher et al4 seem to have written the original article describing volumetric CO2 monitoring. They showed several graphs of volume versus fraction of CO2. Tusman et al8 even state explicitly, “The advantage of using fractions of carbon dioxide compared with partial pressure is that each area represents a volume of carbon dioxide, real or theoretical.”
You may think this issue is a trivial matter, not worth mentioning. But if you are a clinician who is struggling with inconsistencies in the literature, a researcher trying to analyze actual raw data, an educator trying to make a simulation with a spreadsheet, or an engineer trying to design software for a monitor, this kind of error could be quite confusing.
Footnotes
Mr Chatburn has disclosed relationships with IngMar Medical and DeVilbiss/Drive Medical.
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