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Difficulty: EasyNephrology

A 24-year-old man is brought to the emergency department by his roommate due to increasing lethargy and confusion over the past 12 hours. The patient has a history of type 1 diabetes mellitus and has not taken his insulin for the past week due to financial constraints. Vital signs show a temperature of 37.1∘37.1^\circ C (98.8∘98.8^\circ F), heart rate of 115/min, blood pressure of 105/68 mm Hg, and a respiratory rate of 28/min with deep, rapid breaths.

Laboratory studies reveal:

TestResult
Serum sodium140 mEq/L
Serum potassium4.8 mEq/L
Serum chloride104 mEq/L
Serum bicarbonate12 mEq/L
Blood glucose480 mg/dL

Which of the following arterial pCO2pCO_2 values would best indicate an appropriate, isolated respiratory compensation for this patient's acid-base disturbance?

  1. A
    12 mm Hg
  2. B
    18 mm Hg
  3. 26 mm HgAnswer
  4. D
    34 mm Hg
  5. E
    40 mm Hg

Answer

26 mm Hg
The patient presents with diabetic ketoacidosis, which causes a primary high anion gap metabolic acidosis. To determine if the respiratory compensation (indicated by the patient's deep, rapid Kussmaul respirations) is appropriate and isolated, Winter's formula must be applied: expected pCO2=1.5×[HCO3−]+8±2pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2. With a serum bicarbonate of 1212 mEq/L, the expected pCO2pCO_2 is (1.5×12)+8=18+8=26±2(1.5 \times 12) + 8 = 18 + 8 = 26 \pm 2 mm Hg. Therefore, a value of 2626 mm Hg falls perfectly within this range, indicating an appropriate respiratory compensation without a superimposed secondary acid-base disorder.

Step-by-Step Solution

1
Identify the primary acid-base disturbance.
The patient has a high anion gap metabolic acidosis secondary to diabetic ketoacidosis (Anion gap = 140 - (104 + 12) = 24).
Understanding the primary disorder dictates which compensatory formula must be used.
2
Select the appropriate formula for respiratory compensation in metabolic acidosis.
Winter's formula: Expected pCO2=1.5×[HCO3−]+8±2pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2.
This is the physiological rule governing how the lungs compensate for a primary metabolic acidosis via Kussmaul respirations.
3
Input the patient's bicarbonate level into the formula and calculate.
Expected pCO2=(1.5×12)+8±2=18+8±2=26±2pCO_2 = (1.5 \times 12) + 8 \pm 2 = 18 + 8 \pm 2 = 26 \pm 2 mm Hg.
Performing the calculation determines the precise range (24 to 28 mm Hg) that defines appropriate compensation.

Key Concept

In patients with a primary metabolic acidosis, the appropriate respiratory compensation (hyperventilation) must be calculated using Winter's formula: expected pCO2=1.5×[HCO3−]+8±2pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2.
Estimated Time:1m 0s
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Topics

Nephrology

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