background and general concept
My research project in fellowship was the construction of a mathematical model to convert VBG values into ABG values. The fundamental concept for the model was pretty simple: we can approximate the respiratory quotient (RQ) of tissue in the hand as being constant. This indicates that changes in oxygen content and changes in CO2 content should be proportional:
The initial concept was that by combining a venous blood gas plus a simultaneous measurement of the patient's pulse oximetry, we could back-calculate what the ABG values should be:
In practice, the variation in arterial oxygen saturation was pretty low (most patients were ~88-100% saturated). Consequently, it was possible to approximate the patient's oxygen saturation as 93% without any loss of accuracy. This made things easier, by eliminating the need to obtain a simultaneous pulse oximetry measurement. The final model was:
This model was based on data from four investigators who were kind enough to share their data with me. Importantly, the model appeared to function with data from investigators in several different countries (implying generalizability).
Unfortunately, during the publication process one of these investigators was sent the final manuscript to review it. He was concerned that my model might compete with a commercial model that he was developing – so he withdrew permission for me to use his data. The entire project fell apart and was never published in the medical literature. However, I did post it in the blog here.
Fortunately, Jorg et al. found the model and they have now externally validated it:
Jorg et al: Agreement of pCO2 in venous to arterial blood gas conversion models in undifferentiated emergency patients
These authors performed a prospective evaluation of three different equations for converting VBG values into ABG values. 243 pairs of VBG and ABG values were obtained from undifferentiated emergency department patients who required blood gas analysis (due to respiratory distress in 84% of cases). The median time between venous and arterial sampling was 5 minutes (with an interquartile range of 3-9 minutes).
Three models were used to convert from VBG to ABG values, as shown above. The Zeserson model involves subtracting 5 mm from the venous pCO2 value to approximate the arterial pCO2 value (a simple approach which is commonly advocated in the literature). The Farkas (my) model and the Lemoel model take venous oxygen saturation into account as well.
The Farkas model performed the best, with nearly no bias and a 95% confidence interval of +/- 7 mM:
For all models, accuracy was higher among patients not receiving supplemental oxygen (red dots in graph above). For the Farkas model, among patients not receiving oxygen there was a 95% confidence interval of +/- ~5.5 mm, whereas among patients receiving supplemental oxygen the 95% confidence interval widened to +/- ~9 mm. These differences could reflect differences in sample size (only 71 patients were on oxygen, which could cause a few outliers to affect the overall results). When evaluated in a logistic regression analysis with other potential confounding variables, oxygen supplementation wasn't significantly associated with model accuracy.
These data lead to two questions, which are worth discussion and debate:
(Question #1) Can we just look at the VBG pCO2 and use that to guesstimate the ABG pCO2?
Maybe. In practice, I think a lot of physicians will just look at the VBG pCO2 and guess that the ABG pCO2 is a bit below it (say perhaps ~5 mm lower). This is essentially the same as the Zeserson model.
Using this approach, you're going to be reasonably close to the PaCO2 (generally within a range between 7 mm too low and 13 mm too high). That's not terrible. A seasoned clinician shouldn't be making clinical decisions based on small differences in pCO2. Ideally, clinical decisions such as the need for intubation should be based on gestalt and serial clinical evaluation over time, rather than small increments in pCO2 values.
However, on the other hand, this data suggests that by using a simple equation we can easily do substantially better.
(Question #2) Is VBG with the Farkas equation sufficient to avoid drawing an ABG?
This is a challenging question, since there is no consensus regarding the acceptable precision for blood gas values. In reality, the acceptable precision varies across different clinical scenarios. For example, the precise pCO2 level for a patient with COPD is far less important than the precise pCO2 level of a patient with elevated intracranial pressure.
I'm admittedly biased on this point, but I would argue that the answer is usually yes. This is supported by three arguments:
Argument #1: exact values are generally unimportant
Based on this data, the Farkas equation will get us within +/- 7 mm 95% of the time. I think that's adequate accuracy for most clinical work (with some exceptions, such as elevated intracranial pressure). As discussed above, we shouldn't be making big clinical decisions based on small differences in pCO2.
Argument #2: the equation is probably more accurate than this
Differences between arterial pCO2 and the estimated pCO2 value from VBG analysis come from four sources of error:
- Measurement error involved in the ABG (e.g., air bubbles, analytic error).
- Measurement error involved in the VBG (e.g., air bubbles, analytic error).
- Changes in CO2 values in between drawing the ABG and VBG (as the patient spontaneously breathes).
- Error within the predictive equation that converts VBG to ABG values.
Studies only allow us to evaluate the total of all four sources of error. All of this error is generally attributed to the predictive equation (source #4). Meanwhile, the ABG values are assumed to be completely accurate (they are taken as the gold standard). This assumption will inevitably inflate the amount of error attributed to the predictive equation.
Argument #3: precise ABG values don't exist
Some studies have looked at the variability in pH and pCO2 levels if arterial blood is sampled repeatedly over time in clinically stable patients. These studies show that even in totally stable patients, random fluctuations in pH and pCO2 occur with a standard deviations of ~0.015-0.02 and ~1.5-3 mm, respectively. (Umenda 2008, Sasse 1994, Thorson 1983, Hess 1992) In unstable patients, the variability would probably be substantially greater.
As clinicians, we've all stood at the bedside and watched as a patient's oxygen saturation fluctuates up and down. The same exact thing happens with pH and pCO2 – we just don't think about it.
Given ongoing instability in ABG values over time in clinically unwell patients, the concept that a patient “has” a specific pCO2 value is fundamentally flawed. In reality, the patient's pCO2 value is continually fluctuating over a certain range. Based on data from stable patients, the 95% confidence interval of this range is probably at least +/- 6 mm.
Once we recognize that clinically unwell patients don't actually have a fixed pCO2 level, it becomes obvious that we should accept a small amount of measurement error. Furthermore, if the amount of error involved in estimating the pCO2 level from a VBG falls within the random variation in the pCO2 level over time, that suggests that a corrected VBG value is clinically adequate.
Applying the Farkas equation at the bedside
The most important aspect of the equation is understanding the underlying physiology:
- If the venous oxygen saturation is relatively high (e.g., >80%), then the ABG and VBG values will be very close to one another. This is quite often the case (especially if prolonged tourniquet time or delayed sample processing are avoided). In this situation, the VBG values may simply be utilized clinically without the use of any mathematical correction.
- As the venous saturation decreases, the gap between ABG and VBG values widens. In this situation, mathematical correction may yield more accurate values. However, the practitioner should be aware that if the venous saturation is extremely low, then the estimated ABG values may be somewhat less reliable.
- When interpreting VBG values, the venous oxygen saturation should always be considered. Even if you're not applying mathematical correction equations, the venous oxygen saturation will function as a quality-control metric that indicates how close the ABG and VBG values are.
- It's common to approximate the arterial pCO2 as being 5 mm below the venous pCO2. This approximation has a 95% confidence interval spanning from 13 mm high to 7 mm low. This level of accuracy is often adequate, but not ideal.
- The Farkas equation utilizes venous oxygen saturation to correct for cellular respiration that occurs in the extremity (figure below). Using this equation improved the ability of VBG values to accurately predict arterial CO2 (with a 95% confidence interval of +/- 7 mm).
- Unstable patients who are spontaneously breathing will have ongoing fluctuation in their pCO2 values, likely with a similar degree of variability (the concept that the patient “has” a fixed pCO2 value is a myth). This suggests that estimates of arterial pCO2 from VBG values are sufficiently accurate for most clinical scenarios.
- In practice, it's not necessary to apply this equation to every VBG value. For example, if the venous oxygen saturation is relatively high (>80%), then the ABG and VBG values should be very close.
- In specific scenarios, pCO2 must be very precisely monitored (e.g., neurocritical patients with intracranial pressure crisis). Arterial blood gas may be preferred in these situations.
- Whether VBG values can be utilized to replace ABG values remains a hotly debated topic. Understanding the significance of venous oxygen saturation can add some nuance to the interpretation of VBG results by allowing the practitioner to judge the accuracy of VBG data and apply corrective equations if necessary.
Going further:
- Jorg et al paper (open access).
- PulmCrit: How to convert a VBG into an ABG.
Photo by Saad Ahmad on Unsplash
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I spent a fair bit of time with ABGs and the physiology a few…decades… ago. At that point in time, VBG was anathema. I did look at the differences and had used essentially the Zeserson model (5 mm) as a guestimate at the time; I didn’t derive an equation. Essentially, I assumed a patient with low PaO2 and sat, drawn with a stick vs the normal arterial line, was venous if they didn’t look as bad as their lab value, and reevaluated frequently. I like the work you did on this and I’m glad it was validated and published. The… Read more »
Thanks!! Yeah, VBGs go in and out of style, but the physiology is always the same.
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Hi. Usually oxygen saturation in VBG in hand is quite low- around 10-20%. It is definitely not 80%. Such high values would imply tissue poisoning where no extraction of oxygen may be occuring. The saturation in central line VBG is around 50-60% normally. The value of oxygen saturation depends upon oxygen extraction by peripheral tissues and also the arterial oxygen saturation itself. Has your work been validated in sick patients where these issues may have occured? I am not disagreeing with you. I just wish to know if this equation is applicable to sick patients. I used to subscribe to… Read more »
I think “prediction interval” might be a more correct term than “confidence interval” to refer to a the imprecision of a model’s point prediction for a single patient.
the peripheral O2 sat is frequently surprisingly high, especially in patients who are in vasodilatory shock states and aren’t exercising their hands. look at the graphs I’ve posted here, if you look at the difference in oxygen saturation it’s often relatively low : https://emcrit.org/pulmcrit/vbg-abg/
Thank you for this blog, I really like it and I hope it is useful for everyone.
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