UPDATE: Should We Consider Mathematical Arterialization of VBGs in ED Patients?

A few months back, I wrote about the lack of accuracy in using peripheral venous blood gas to estimate the CO2 of an arterial sample, particularly when the levels are very high1. My continued review of the subject supports the unreliability of such interpretation of peripheral venous values alone. Dr. Rees, a researcher who developed and conducted original research on “mathematical arterialization” of venous blood samples, contacted me with some of the latest work on the subject. His group’s work investigates acid-base mechanics in a broad swath of patient populations (simulation, ICU, outpatient, inpatient, and emergency department) using this mathematical method.

I review their methodology and results below. As a special bonus, Dr. Rees has shared with us a video of him detailing his methodology at a recent conference.

In 2006, Dr. Rees and his colleagues proposed a method for extrapolating the acid base chemistry for arterial blood from peripheral venous blood and a pulse oximeter. The principle of their method comes from mathematically simulating the transport of arterial blood back through the tissue. Their formula relies on two assumptions:

1. A warm, non-ischemic limb should have little to no change in base excess across its tissue.
2. The respiratory quotient (adding oxygen and removing carbon dioxide) over the tissue can only vary between 0.7 and 1.0 (0.7 is aerobic metabolism of fat, and 1.0 is aerobic metabolism of carbohydrates).

They applied their methods to three real patients as well as to several theoretical patient scenarios to demonstrate its use and lay the groundwork for further human trials. They found that their calculated pHa and PCO2a closely matched the measured values in arterial blood (SD 0.002-0.027 and -0.04-0.52kPA, respectively)2.


In 2009, they applied the formula to a group of 40 patients with respiratory disease (22 admitted, 18 outpatient). They adjusted their specimen collection technique to use a standard butterfly needle rather an ABG syringe to better simulate usual venous blood collection techniques. The team found similarly high degrees of correlation between arterial and venous pH and PCO2. They also noted that variation in base excess > 0.2 mmol could theoretically lead to significant errors values, further advising caution in situations of acute changes in peripheral perfusion or acid-base status (such as hypovolemic shock). However, in cases of sepsis, CHF, COPD, MI, PE, the researchers did not actually observe this variation. Aside from changes in perfusion, they also reported that when repeat pulse oximeter readings varied by 4% or more, there were variations in the pH and PCO23.


In 2012, Dr. Rees and his team conducted their largest study, applying their methods to patients in the ED. They divided their samples into 2 groups. Group A consisted of 51 patients who were deemed to be in need of clinical assessment of their acid base status. Group B consisted of 146 patients without clinical need for an arterial sample. In group B, ethical approval to obtain an ABG sample was only given when the venous values were abnormal and it could be considered “clinically reasonable” to obtain the ABG. The purpose of group B was to explore the utility in identifying patients with low pre-test probability who were later found to have abnormal acid base values. Patients with highly variable pulse oximeter readings (>3%) were excluded. The butterfly technique was used to obtain venous samples from the extremity.


The venous values were then “mathematically arterialized” as in the methods described above, and these calculated values were compared to the measured arterial values. Results from this study were:

These results again show high levels of correlation (r-square) between arterial and venous pH and PCO2, within the range of acceptable lab and clinical performance. When comparing “mathematically arterialized” values to the values of measured venous pH and PCO2, they showed an improvement over the use of venous values alone. If the clinicians had relied on measured venous PCO2 alone, the values would have fallen outside of acceptable lab and clinical limits of agreement4.


In conclusion, the mathematical arterialization shows promise in delivering acceptably accurate measurements of arterial pH and pCO2 that are derived from peripheral venous specimens. Software now exists that integrates with existing blood analysis machines and does not require the clinician to manually input values. In the US, this method of deriving arterial values from venous samples is not widely recognized or used. However, its ease, accuracy, and reduced patient suffering are all good reasons to consider implementing mathematical arterialization into our clinical futures. Further research is needed to examine its utility in patients with rapid changes in perfusion or acid-base status.

(Keep scrolling down for the Youtube video!)

Works Cited

1. Chan W. “VBG vs ABG in Hypercarbia.” The Original Kings of County. SUNY Downstate Emergency Medicine Department, 06 Sept. 2016. Web. 05 Jan. 2017.

2. Rees SE, Toftegaard M, et al. “A Method for Calculation of Arterial Acid-base and Blood Gas Status from Measurements in the Peripheral Venous Blood.” Computer Methods and Programs in Biomedicine 81.1 (2006): 18-25. 

3. Rees SE, Hansen A, et al. “Converting Venous Acid-base and Oxygen Status to Arterial in Patients with Lung Disease.” European Respiratory Journal 33.5 (2009): 1141-147.

4. Tygesen G, Matzen H, et al. “Mathematical Arterialization of Venous Blood in Emergency Medicine Patients.” European Journal of Emergency Medicine 19.6 (2012): 363-72. 

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Senior EM Resident at SUNY Downstate / Kings County Hospital, EM/Critical Care Blogger, Medical Student Education Curriculum Co-Chair, has a blackbelt in "keepin' it real"

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