A 34-year-old woman with a history of type 1 diabetes mellitus is brought to the emergency… — USMLE Step 2 CK

A $34$ -year-old woman with a history of type $1$ diabetes mellitus is brought to the emergency department due to severe nausea, diffuse abdominal pain, and intractable vomiting for the past $48$ hours. She reports missing her last three doses of insulin because she was unable to tolerate any oral intake. On physical examination, her blood pressure is $98/60\text{ mm Hg}$ , heart rate is $118\text{ /min}$ , and respiratory rate is $22\text{ /min}$ . Her mucous membranes are remarkably dry, and skin turgor is decreased.

Laboratory testing reveals:

Test	Result
Arterial $\text{pH}$	$7.30$
$\text{pCO}_2$	$29\text{ mm Hg}$
$\text{pO}_2$	$95\text{ mm Hg}$
$\text{Na}^+$	$144\text{ mEq/L}$
$\text{K}^+$	$3.2\text{ mEq/L}$
$\text{Cl}^-$	$94\text{ mEq/L}$
$\text{HCO}_3^-$	$14\text{ mEq/L}$
$\text{Glucose}$	$550\text{ mg/dL}$
$\text{BUN}$	$38\text{ mg/dL}$
$\text{Creatinine}$	$1.6\text{ mg/dL}$

Assuming a normal serum anion gap of $12\text{ mEq/L}$ and a normal serum bicarbonate of $24\text{ mEq/L}$ , calculate the patient's delta ratio ( $\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-}$ ) to evaluate for the presence of a mixed acid-base disorder.

Answer: 2.4

Answer

The calculated delta ratio is 2.4.

The patient has a primary high anion gap metabolic acidosis secondary to diabetic ketoacidosis (AG =

36

). In an uncomplicated AGMA, for every

1\text{ mEq/L}

rise in the anion gap, the serum bicarbonate should fall by approximately

1\text{ mEq/L}

, yielding a delta ratio between

1.0

and

2.0

. This patient's delta ratio is

\frac{36-12}{24-14} = 2.4

. A delta ratio greater than

2.0

indicates that the bicarbonate has not dropped as much as expected for the amount of acid present. This means there is a concurrent primary metabolic alkalosis adding bicarbonate to the serum, which in this clinical vignette is driven by profound volume contraction and acid loss from intractable vomiting.

Step-by-Step Solution

Calculate the measured Anion Gap (AG).

\text{AG} = 144 - (94 + 14) = 36\text{ mEq/L}

Establishing the presence of an anion gap metabolic acidosis (AGMA) is the first step in acid-base evaluation.

Calculate the Delta Anion Gap (

\Delta\text{AG}

\Delta\text{AG} = 36 - 12 = 24\text{ mEq/L}

This value represents the excess unmeasured anions contributing to the acidosis.

Calculate the Delta Bicarbonate (

\Delta\text{HCO}_3^-

\Delta\text{HCO}_3^- = 24 - 14 = 10\text{ mEq/L}

This value represents the amount of bicarbonate consumed to buffer the excess acid.

Calculate the Delta Ratio.

\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-} = \frac{24}{10} = 2.4

Comparing the change in anion gap to the change in bicarbonate identifies occult mixed metabolic acid-base disorders.

Key Concept

The delta ratio (

\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-}

) is used to diagnose mixed metabolic acid-base disorders in the setting of a high anion gap metabolic acidosis. A ratio

> 2.0

indicates a concurrent metabolic alkalosis, such as from severe vomiting.

Estimated Time:2m 0s

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