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Difficulty: EasyNephrology

A 22-year-old woman with a history of type 1 diabetes mellitus presents to the emergency department with a 1-day history of nausea, vomiting, and diffuse abdominal pain. She missed several doses of her insulin because she was not feeling well. Her temperature is 37.2∘C37.2^\circ C (99.0∘F99.0^\circ F), blood pressure is 105/65105/65 mmHg, heart rate is 118/min118/min, and respiratory rate is 26/min26/min. Physical examination reveals dry mucous membranes and diffuse abdominal tenderness without rebound or guarding.

Laboratory studies show:
Laboratory StudyResult
Serum sodium140140 mEq/L
Serum potassium4.54.5 mEq/L
Serum chloride104104 mEq/L
Serum bicarbonate1212 mEq/L
Blood glucose450450 mg/dL
Serum creatinine1.21.2 mg/dL

Which of the following is the expected arterial partial pressure of carbon dioxide (pCO2pCO_2) if appropriate respiratory compensation has occurred in this patient?

  1. A
    1212 mmHg
  2. B
    2020 mmHg
  3. 2626 mmHgAnswer
  4. D
    3232 mmHg
  5. E
    4040 mmHg

Answer

The expected arterial pCO2pCO_2 is 2626 mmHg.
The correct expected arterial pCO2pCO_2 is 2626 mmHg. This patient presents with diabetic ketoacidosis, which causes a primary anion gap metabolic acidosis. In the presence of a metabolic acidosis, the physiological response is hyperventilation to decrease arterial pCO2pCO_2 and normalize the blood pH (respiratory compensation). The appropriate degree of respiratory compensation is calculated using Winter's formula: Expected pCO2=1.5×[HCO3−]+8±2pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2. Using the patient's serum bicarbonate of 1212 mEq/L, the expected pCO2=(1.5×12)+8=26±2pCO_2 = (1.5 \times 12) + 8 = 26 \pm 2 mmHg. A measured pCO2pCO_2 within the range of 2424 to 2828 mmHg indicates a simple metabolic acidosis with appropriate compensation.

Step-by-Step Solution

1
Calculate the anion gap and identify the primary acid-base disturbance.
Anion Gap = 140−(104+12)=24140 - (104 + 12) = 24. The patient has an elevated anion gap metabolic acidosis (diabetic ketoacidosis).
Identifying the primary disturbance dictates which compensation formula to use.
2
Apply Winter's formula to determine expected respiratory compensation.
Expected pCO2=(1.5×[HCO3−])+8±2pCO_2 = (1.5 \times [HCO_3^-]) + 8 \pm 2.
Winter's formula predicts the expected pCO2pCO_2 response to a primary metabolic acidosis.
3
Calculate the specific expected value for this patient.
Expected pCO2=(1.5×12)+8=18+8=26pCO_2 = (1.5 \times 12) + 8 = 18 + 8 = 26 (Range: 24−2824 - 28 mmHg).
Plugging in the patient's bicarbonate level of 1212 mEq/L yields the target compensation.

Key Concept

Winter's formula for predicting appropriate respiratory compensation in primary metabolic acidosis
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Topics

Nephrology

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