A 52-year-old woman is evaluated in the emergency department for severe, watery diarrhea over the past five days. She reports feeling profoundly weak. She has no significant past medical history. Her blood pressure is 105/65 mm Hg, pulse is 112/min, and respiratory rate is 22/min. Physical examination shows dry mucous membranes and delayed capillary refill.
Laboratory results:
- Serum sodium: 138 mEq/L
- Serum potassium: 3.2 mEq/L
- Serum chloride: 114 mEq/L
- Serum bicarbonate: 12 mEq/L
- Arterial blood gas (room air): pH 7.24, PaCO2 24 mm Hg, PaO2 96 mm Hg
Using Winter's formula, calculate the patient's expected PaCO2. (Provide the exact median numerical value in mm Hg, excluding the ±2 range)
Answer: 26 mm Hg
Answer
26
In the setting of a primary metabolic acidosis (as seen in this patient with severe diarrhea and a low serum bicarbonate), the lungs compensate by increasing ventilation to blow off . Winter's formula, , is used to determine if the respiratory compensation is appropriate. By plugging in the patient's bicarbonate of 12 mEq/L, the calculation is . The median expected PaCO2 is 26 mm Hg. Since the patient's measured PaCO2 is 24 mm Hg (which falls within the range of 24-28 mm Hg), she has an appropriately compensated simple metabolic acidosis.
Step-by-Step Solution
Key Concept
Calculation of expected respiratory compensation (Winter's formula) in metabolic acidosis