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.

Cevap: 2.4

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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.

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