A Shout Instead of a Whisper: Let's Get the Graphics Right

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 V_Dalv 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 P_aCO2, P_ACO2, 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 P_CO2 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 P_CO2, 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 P_CO2 (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 P_CO2).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.

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