Vd/Vt, how accurate is it really?

My lab stopped inserting A-lines to get arterial blood samples during exercise testing well over 10 years ago. Our decision was partly based on the fact that we didn’t do them often enough to be good at it and partly based on the fact that we didn’t think that we were getting enough extra information from ABG’s to be worth the effort. Since another local hospital (a competitor but part of the same medical school network so we share pulmonary fellows with them) routinely performs level II and level III exercise tests we felt we could refer any patients that really needed ABG’s to the lab there. We don’t regret the decision and don’t feel that it has compromised the quality of our exercise testing.

Because we don’t obtain ABG’s, one of the values we don’t calculate is the deadspace/tidal volume ratio (Vd/Vt). Recently I was reading an article that related Ve-VCO2 to Vd/Vt and I was reminded of some the issues I had with Vd/Vt when I calculated it in the past. We’ve gone through two different exercise test systems since that time so I’m not sure if some of these problems still exist but I thought it would be a good idea to review both the problems and the literature on Vd/Vt to see if I could make some sense of them.

As a reminder, the original Bohr equation for Vd/Vt was:

Original Bohr Equation

The first problem I had run into was that mixed-expired CO2 (PECO2) is routinely calculated from CPET data as:

PECO2 Equation

But it was also reported as a separate value by the test system’s software and the two values did not match.

The second problem was that the test system software reported a non-zero inspired CO2 concentration (PICO2). The PICO2 ranged from 10 mmHg at rest to 6 mmHg at peak exercise and when I reviewed some of the data from that time it is apparent that the PICO2 closely matched the difference between the reported and calculated PECO2.

The test system’s gas analyzers were calibrated using standard physiological gases (21% O2, balance N2 and 5% CO2, 16% O2 balance N2) so I don’t think the elevated PICO2 was an analyzer error or at least not completely. I suspect that this was more likely a software problem having to do with how PICO2 was estimated. In an exercise test systems the gas sampling port is usually located in a manifold between the flow sensor and the mouthpiece. At the beginning of an inhalation the flow sensor, manifold and mouthpiece are filled with exhaled air. This means that during an inhalation a certain amount of exhaled air is sampled until fresh air passes the gas sampling port.

PICO2

PICO2 will therefore be an average of the CO2 concentration in the exhaled air and in the inhaled room air. It will depend on the volume of the flow sensor manifold and the inhaled volume. I can see that the PICO2 should be slightly elevated when the tidal volume is small but when tidal volume increases the PICO2 should decrease proportionally and this did not happen. This leads me to suspect that something was not quite right with the software’s inspiratory gas averaging algorithm.

PECO2 is derived by matching the expiratory flow signal to the time-delayed CO2 signal and integrating the area under the curve. Since:

VCO2 Equation

 it makes sense that the PECO2 derived from the reported VCO2 and Ve differed from the reported PECO2 since the derivation assumes that PICO2 is zero. The question I have at this point (and which cannot be answered since the exercise test system we used at that time was replaced over a dozen years ago) is if PICO2 was falsely elevated then just how accurate was the reported VCO2? A related (and critical) question is which PECO2 should be used to calculate Vd/Vt?

The Bohr equation does not say that PECO2 should be adjusted for PICO2 but an elevated PICO2 in this case is largely an artifact of where it is being measured. If gases were sampled on the far side of the flow sensor instead of the near side PICO2 would probably be zero. Strictly speaking PECO2 is also affected by where it is measured, and the two probably cancel each other out. For this reason I think that deriving PECO2 from VCO2 and VE is probably the most correct approach but that doesn’t mean I’m not left with at least a few doubts.

These problems may well be related to an exercise test system that was developed and sold in the 1990’s but that doesn’t mean that there aren’t other problems associated with calculating Vd/Vt that may not be as well appreciated as they ought to be.

Because alveolar CO2 (PACO2) is difficult to estimate and is also to some extent a dynamic value the modified Bohr equation is used far more commonly:

Modified Bohr Equation

The modified Bohr equation assumes that arterial PCO2 (PaCO2) is equivalent to alveolar PCO2 (PACO2). This is reasonably true in individuals with normal lungs at rest but in individuals with lung disease PACO2 is usually less than PaCO2. This is largely due to V/Q mismatching and gas mixing efficiency. When PACO2 is less than PaCO2 Vd/Vt will be overestimated when the modified Bohr equation is used.

This changes during exercise, however. At rest venous blood is arterialized after only a short distance through the pulmonary capillaries and it is for this reason that there can be a good correlation between PaCO2 and PACO2. At high levels of exercise the amount of carbon dioxide entering the pulmonary capillaries increases dramatically and even though the PaCO2 of the blood exiting the pulmonary capillaries may remain normal the alveolar air becomes dominated by the PCO2 of venous blood. PACO2 under these circumstances can therefore be higher than PaCO2 and Vd/Vt will be underestimated.

In addition, the accuracy of the PaCO2 measurement itself acts as a limit on the overall accuracy of the Vd/Vt calculation. A comparison study using the same ABG sample on several different analyzers showed a standard deviation of +/- 1.5 mm Hg for PCO2. Although this acceptable for clinical purposes an error of +/- 1.5 mmHg leads to a difference of up to +/- 0.03 in Vd/Vt. Since Vd/Vt ranges from about 0.35 at rest to about 0.15 during heavy exercise, the error range is between +/- 9% to +/- 20%.

It’s also not clear to me what level of confidence can be placed on the PECO2 measurement regardless of how it is derived. When exhaled samples were collected in Douglas bags the answer would be the accuracy level of the CO2 analyzer itself (and how sure you were the bag was empty before you started). PECO2 however, is usually derived from a breath-by-breath measurement system that depends on fast gas analyzers and the time-delayed signal from a flow sensor to integrate the CO2 volume of an exhalation. This means that overall PECO2 accuracy is dependent on the accuracy of the flow sensor and integration algorithm as well as the gas analyzer. This does not mean that the PECO2 from a breath-by-breath system is inaccurate just that I don’t know what the possible error level is.

In order to measure mixed expired CO2 one has to be able to collect it and any system designed to do this will add mechanical deadspace to the overall measurement. The fully expanded Bohr equation takes this into consideration:

Machine Deadspace Correction

Machine deadspace is usually taken as its geometrical volume. There are aerodynamic properties to air flow, however, that brings this into question. For example, when gas flow is laminar, the velocity of gas in the center of a tube is much higher than it is around the edges. This means that during an inhalation, before the geometrical volume of gas contained within a flow sensor has actually passed through the flow sensor, room air has already passed completely through the center of the flow sensor and is entering the patient’s airways. Machine deadspace does matter, it’s just not clear there is an exact correlation between “real” dead space and its geometrical volume.

Finally, I hesitate to even bring this up but because PACO2 is technically difficult to measure and PaCO2 is an invasive measurement, end-tidal CO2 (PETCO2) has been proposed numerous times as a substitute value for PaCO2. It has long since been shown that PETCO2 does not match PACO2 or PaCO2 either at rest or during exercise even in patients with normal lungs, let alone those with lung disease. Yes, of course, there are correlations between PETCO2, PACO2 and PaCO2 but these correlations are not exact and they often depend on very limited and specific circumstances so I am not sure why this issue keeps re-surfacing. Hope springs eternal, I guess.

Vd/Vt is used to assess patient ventilatory and circulatory status under a variety of conditions. There are a variety of factors including PICO2 and the level of uncertainty about the measurement of PECO2 and PaCO2 that limit its accuracy. In addition, I think that it is often forgotten that the original Bohr equation used PACO2 and not PaCO2. PACO2 is difficult to measure for a variety of physiological, mechanical and conceptual factors and for this reason I think that it’s become accepted wisdom that PaCO2 is “good enough”. The truth however, is that PaCO2 is a good substitute for PACO2 in only a narrow range of conditions and this is too often ignored. Having said all this, there is probably a lot of clinical relevance to Vd/Vt measurements made using PaCO2 but it really isn’t Vd/Vt that is being measured but something else.

References:

Kampelmacher MJ, van Kesteren RG, Winckers EKA. Instrumental variability of respiratory blood gases among different blood gas analyzers in different laboratories. Eur Respir J 1997; 10: 1341-1344.

Koulouris NG, Latsi P, Dimitroulis J, Jordanoglou B, Gaga M, Jordanoglou J. Noninvasive measurement of mean alveolar carbon dioxide tension and Bohr’s dead space during tidal breathing. Eur Respir J 2001; 17: 1167-1174.

Lewis DA, Sietsema KE, Casaburi R, Sue DY. Inaccuracy of noninvasive estimates of Vd/Vt in clinical exercise testing. Chest 1994; 106: 1476-1480.

Zimmerman MI, Miller A, Brown LK, Bhuptani A, Sloane MF, Teirstein AS. Estimated vs actual values for dead space/tidal volume ratios during incremental exercise in patients for dyspnea. Chest 1994; 106: 131-136.

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