A 22-year-old man with a history of type 1 diabetes mellitus is brought to the emergency d… — USMLE Step 3

A 22-year-old man with a history of type 1 diabetes mellitus is brought to the emergency department due to altered mental status, nausea, and diffuse abdominal pain. He has not taken his insulin for the past two days. Vital signs show a heart rate of $118/\text{min}$ , blood pressure of $105/65\text{ mmHg}$ , and respiratory rate of $28/\text{min}$ with deep, rapid breaths.

Laboratory results are as follows:

Serum sodium: $142\text{ mEq/L}$
Serum potassium: $4.8\text{ mEq/L}$
Serum chloride: $98\text{ mEq/L}$
Serum bicarbonate: $14\text{ mEq/L}$
Blood urea nitrogen: $32\text{ mg/dL}$
Serum creatinine: $1.4\text{ mg/dL}$
Serum glucose: $520\text{ mg/dL}$

Arterial blood gas (room air):
pH: $7.21$
$pCO_2$ : $24\text{ mmHg}$
$pO_2$ : $98\text{ mmHg}$

Using Winter's formula, what is the mean expected $pCO_2$ (in mmHg) to determine if this patient has an appropriately compensated primary metabolic acidosis?

Cevap: 29 mmHg

Cevap

The mean expected pCO2 is 29 mmHg.

In patients with a primary metabolic acidosis, the physiological response is hyperventilation to reduce

pCO_2

and drive the pH back toward normal. Winter's formula predicts this expected respiratory compensation. The formula is: Expected

pCO_2 = (1.5 \times [\text{HCO}_3^-]) + 8 \pm 2

. Using the patient's serum bicarbonate of

14\text{ mEq/L}

, the mean expected

pCO_2

(1.5 \times 14) + 8 = 29\text{ mmHg}

. Because the patient's actual measured

pCO_2

24\text{ mmHg}

(which is lower than the expected range of

27-31\text{ mmHg}

), he has a concomitant primary respiratory alkalosis, likely secondary to profound anxiety, pain, or early sepsis.

Adım Adım Çözüm

Analyze the arterial blood gas to identify the primary acid-base disorder.

The patient has acidemia (pH 7.21) driven by a low serum bicarbonate (

14\text{ mEq/L}

), confirming a primary metabolic acidosis.

Establishing the primary disturbance dictates which compensation formula should be applied.

Calculate the expected respiratory compensation.

Apply Winter's formula to find the expected

pCO_2

level.

The lungs compensate for metabolic acidosis by increasing ventilation to blow off CO2. Winter's formula determines if this response is appropriate or if a secondary respiratory disorder exists.

Perform the mathematical calculation using the patient's bicarbonate level.

Expected

pCO_2 = 1.5 \times 14 + 8 = 21 + 8 = 29\text{ mmHg}

Plugging the serum bicarbonate into the formula yields the mean expected

pCO_2

Anahtar Kavram

In the setting of a primary metabolic acidosis, Winter's formula (

pCO_2 = 1.5 \times [\text{HCO}_3^-] + 8 \pm 2

) must be used to calculate the expected respiratory compensation and identify concomitant mixed acid-base disorders.

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