# Winter’s formula and even simpler

Let’s talk about rapid A.B.G. analysis. Just to clarify, I’m talking about arterial blood gases, not the religious rap group “Adopted By Grace” I just discovered existing by googling the phrase “ABG”.

I tend to use Winter’s Formula for analyzing metabolic acidosis: it’s generally simple-enough math I can easily do in my head. To review, Winter’s Formula is used to predict the PaCO2 which should result if there is appropriate respiratory compensation for a metabolic acidosis:

predicted PaCO2 = 1.5 x [HCO3-] + 8.

If the actual measured PaCO2 is lower than predicted, there is a concomitant respiratory alkalosis; if it is higher than predicted there is a concomitant respiratory acidosis.

There are some even EASIER ways to do this calculation however.

SIMPLIFIED WINTER’S FORMULA:
predicted PaCO2 = [HCO3-] + 15. This apparently works for PaCO2 concentrations between 10-40.

There’s also something called:
THE THUMB RULE:

Put your thumb over the first digit of the pH on the ABG. The PaCO2 should be the last two digits. For instance, if the pH is 7.30, then the PaCO2 should be about 30mmHg; if the pH is 7.15 then the PaCO2 should be about 15mmHg, etc.

These are very simplified (and personally, I don’t think it’s that mentally strenuous to go with the more precise Winter’s Formula), but potentially handy when rapid clinical decision-making is necessary (e.g., perhaps a resident giving you ABG results in the middle of the night).

1. I had the values wrong which is why you should go to the paper rather than use your head. The correct pH 7.25 and the pC02 is 28. Winters formula gives you expected pC02 of 32 ± 2 or 30 to 34. Observed pC02 is 28. Rule of 5 finds this 4 away and appropriate. Winters calls it respiratory alkalosis. Should we be addending Winters to ±5?

2. This is a complicated matter. I read a Cleveland Clinic ABG case where the patient had 7.15/23/16. It was an anion gap positive at 21 and the delta gap was 9 and does not suggest any concomitant metabolic alkalosis. The pH is down and the PCO2 is down, so this is an anion gap metabolic acidosis. So far , so good. So next, I apply Winters formula for predicted pC02 with that HCO3: 1.5( 16 ) +8 ±2 = 32±2 so anywhere from 30 to 34 is appropriate respiratory compensation. The observed pC02 is 23; nowhere close to this value and constitutes concomitant respiratory alkalosis. One of the ” wrong” answers was anion gap positive metabolic acidosis with a respiratory alkalosis?! They said this compensation was normal to 23, following some kind of rule of 5?! Well, 32 ain’t within 5 of 23!. The reason for finding ” appropriate compensation ” is to recognize some syndromes such as aspirin toxicity, and also realize when you’re going to have to intubate to support the pH if the patient can’t ventilate properly. Where am I wrong?

3. So I got very perplexed by the above question and spent far too much time googling it.

Dr R.W. Winters was actually a pediatrician who graduated from Yale medical school. He actually did alot of remarkable work with rickets and vitamin D.

The paper that "Winter's formula" comes from is from a 1967 paper in the annals of internal medicine called "The Quantitative Displacement of Acid-Base Equilibrium in Metabolic Acidosis"
http://www.annals.org/content/66/2/312.extract .

What he did, in brief, was take a number of people with clearly identified pure metabolic acidoses, and correlated their bicarbonate values to their CO2 levels. What I find interesting, though, is that most of his patients were kids! The vast majority of them were under the age of 12. I'm not sure I could find any other work confirming the relationship in adults.

I'm sort of skeptical about the use of Winter's formula in identifying "mixed" acid base disorders, especially metabolic acidosis with concomitant respiratory alkalosis. Lets say you had a patient with a pH of 7.1, pCO2 of 20, HCO3 of 10. Winters says that your pCO2 should be 26-30. Great, so what do you do with that information? Do you really want to call it a respiratory alkalosis?

Your pH is still really low, isnt it just appropriate compensation outside of the range of the hundred or so children that Winter's used in his original study? Never made sense to me.

4. so, who was Winter?

5. I am a first year resident in Medicine and find interpretations of ABG really challenging. But You have simplified it. Would appreciate if you have more posts on this topic.

6. Nice review. I agree… it shouldnt be too taxing at this level to use the simple formula.

The only thing I may add is that I like to add a +/- 2 on the end of the formula to the predicted PaCO2 before considering whether or not there is a secondary A-B disorder.

ABG, a religious rap group.. Who knew?!

Cheers