# Abg Case Study Problems

## Introduction

You can solve triple acid-base problems with basic arithmetic and straightforward logic. As an example, let’s work through the following rather classic triple acid-base problem:

An afebrile, atraumatic 26-year-old male with no past medical history is brought to the emergency department because of a three hour history of altered mental status, vomiting and vertigo. The physical examination is positive only for somnolence and tachypnea.

Relevant serum chemistries are:

- Na
^{+}: 143 mEq/L- Cl
^{–}: 100 mEq/L- Serum bicarbonate [HCO
_{3}^{–}]: 16 mEq/L (normal = 24 mEq/L)The arterial blood gas (ABG) reveals:

- pH: 7.50 (normal = 7.40)
- pCO
_{2}: 20 mm Hg (normal = 40 mm Hg)- HCO
_{3}^{–}: 15 mEq/L (normal = 24 mEq/L)What are this patient’s acid-base disorders?

## Step 1: calculate the anion gap

When solving acid-base problems, the first step is *always* to calculate the anion gap:

**Anion gap = [Na ^{+}] – [Cl^{–}] – [HCO_{3}^{–}]**

Note that you don’t need an ABG to calculate the anion gap. In fact, an ABG *can’t* tell you whether there is a high anion gap metabolic acidosis. *Only* the serum electrolytes can tell you that.

So plugging in the numbers from the problem above, the anion gap is = 143 – 100 – 16 = 27.

You know (or *should* know!) that the normal anion gap is 11 so this patient has a high anion gap metabolic acidosis. Congratulations! You solved one third of this triple acid-base disorder problem without lifting a finger and without even looking at the ABG!

Before proceeding to the next step, however, please pay attention to *how high above normal* this patient’s anion gap actually is because you will need this number for the steps that follow. This patient’s anion gap is too high by **16** points. It’s supposed to be 11, but it is 27, so it is too high by **16** points (27-11 = **16**).

Remember the number **16** because you will need it for the next two steps.

## Step 2: see if the serum bicarbonate (HCO_{3}^{–}) is *dropped* in proportion to the degree to which the anion gap *rose*

Recall from the previous step that, in this case, the anion gap is *too high* by **16** points (27-11 = **16**). Therefore, you should expect the serum bicarbonate to be similarly 16 points *below* normal.

A normal serum bicarbonate is 24 mEq/L. (That’s just something you absolutely need to have committed to memory!). In any event, since the patient’s anion gap was *too high* by **16** points, the patient’s bicarbonate should be similarly *low* by 16 points. So you’d expect the serum bicarbonate to be 8 mEq/L (24-**16** = 8).

Here, however, the bicarbonate is 16 mEq/L, which is 8 points *higher* than the expected 8. A higher than expected bicarbonate in a patient with no past medical history suggests a metabolic alkalosis. So this patient also has a metabolic alkalosis on top of his high anion gap metabolic acidosis**.**

Congratulations! So far, you’ve solved two thirds of this patient’s triple acid-base disorder. You know, again without even looking at the ABG (!), that this patient has:

(a) a high anion gap metabolic acidosis (from Step 1); and,

(b) a metabolic alkalosis (from Step 2); and,

(c) another yet-to-be-identified acid-base disturbance (because I told you it was going to be a triple acid-base disorder!).

Let’s go on to Step 3.

## Step 3: look at the arterial blood gas and see if the partial pressure of carbon dioxide (pCO_{2}) is dropping in proportion to the drop in the bicarbonate level

Look back at the ABG above and focus on the pCO_{2. }Notice that the pCO_{2} is *too low* by 20 points. (A normal pCO_{2 }is 40 mm Hg, and this patient’s pCO_{2} is 20 mm Hg. 40-20 = 20.)

Had the respiratory compensation been appropriate, *the pCO _{2} should have dropped by the same number of points as the bicarbonate*. Why? That’s just how it is. (If you’re not convinced, just plug the numbers into Winter’s formula and you’ll get exactly the same result.) In any event, recall that this patient’s serum bicarbonate dropped by only 8 points (it is 16, with normal being 24), so his pCO

_{2}should have dropped by only 8 points as well. Therefore, his pCO

_{2}

*should have been*32 mm Hg (40 – 8 = 32). However, this patient’s pCO

_{2}is lower than the expected 32. It is 20. A too-low pCO

_{2 }

*means*that there is a respiratory alkalosis going on here as well.

We therefore now know that this patient’s triple acid-base disorder is:

(a) high anion gap metabolic acidosis (from Step 1),

(b) metabolic alkalosis (from Step 2); and,

(c) respiratory alkalosis (Step 3).

## Summary

Now that the (rather straightforward!) arithmetic is done, it’s time to look back at the patient history and physical examination to see if your laboratory-based acid-base diagnosis fits the clinical scenario. Recall that this was an afebrile, atraumatic 26-year-old male with no past medical history who presented with altered mental status. This history *alone* suggests a likely toxic ingestion and therefore the possibility of a high anion gap metabolic acidosis. He had been vomiting. That fits with metabolic alkalosis. He was tachypneic on examination. That fits with *respiratory* alkalosis.

And finally, he was altered and vertiginous. That fits with a final clinical diagnosis of **salicylate poisoning **with a characteristic triple acid-base disturbance of (1) **high anion gap metabolic acidosis**, (2) **metabolic alkalosis**, and (3) **respiratory alkalosis**.

Emergency MedicineLaboratory MedicineNephrologyToxicology

Acid-baseHigh anion gap metabolic acidosisRespiratory alkalosisSalicylate poisoningWinter's formula

Mark Yoffe is a practicing internal medicine doctor who writes about medical books and education.

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