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Difficulty: EasyNephrology

A 32-year-old woman is evaluated in the emergency department for severe, watery diarrhea occurring over the past 5 days after returning from a trip abroad. She reports weakness and dry mouth. Vital signs show a blood pressure of 100/60 mm Hg and a heart rate of 110/min.

Laboratory studies show:
Serum sodium: 140 mEq/L140 \text{ mEq/L}
Serum chloride: 115 mEq/L115 \text{ mEq/L}
Serum bicarbonate: 16 mEq/L16 \text{ mEq/L}
Serum potassium: 3.2 mEq/L3.2 \text{ mEq/L}

Arterial blood gas analysis on room air shows a pH of 7.30.

Assuming appropriate respiratory compensation has occurred, which of the following is the expected arterial partial pressure of carbon dioxide (PaCO2) in this patient?

  1. A
    16 mm Hg16 \text{ mm Hg}
  2. B
    24 mm Hg24 \text{ mm Hg}
  3. 32 mm Hg32 \text{ mm Hg}Answer
  4. D
    40 mm Hg40 \text{ mm Hg}
  5. E
    48 mm Hg48 \text{ mm Hg}

Answer

32 mm Hg32 \text{ mm Hg}
This patient presents with a primary metabolic acidosis due to gastrointestinal bicarbonate losses (severe diarrhea). In the presence of metabolic acidosis, the physiological respiratory compensation is hyperventilation, which decreases the carbon dioxide level. The exact expected PaCO2 can be calculated using Winter's formula: Expected PaCO2=(1.5×[HCO3−])+8±2\text{Expected } PaCO_2 = (1.5 \times [HCO_3^-]) + 8 \pm 2. Using the patient's bicarbonate of 16 mEq/L16 \text{ mEq/L}, the calculation is (1.5×16)+8=24+8=32 mm Hg(1.5 \times 16) + 8 = 24 + 8 = 32 \text{ mm Hg}.

Step-by-Step Solution

1
Identify the primary acid-base disorder based on the provided laboratory values.
The patient has a low pH (7.30) and low bicarbonate (16 mEq/L16 \text{ mEq/L}), indicating a primary metabolic acidosis.
Severe diarrhea causes loss of bicarbonate in the stool, leading to a normal anion gap metabolic acidosis.
2
Select the appropriate formula to calculate respiratory compensation for metabolic acidosis.
Use Winter's formula: Expected PaCO2=(1.5×[HCO3−])+8±2\text{Expected } PaCO_2 = (1.5 \times [HCO_3^-]) + 8 \pm 2.
Winter's formula is the standard physiological calculation to determine if respiratory compensation for metabolic acidosis is adequate.
3
Perform the calculation using the patient's serum bicarbonate level.
(1.5×16)+8=24+8=32 mm Hg(1.5 \times 16) + 8 = 24 + 8 = 32 \text{ mm Hg}.
Inserting the given bicarbonate value of 16 mEq/L16 \text{ mEq/L} yields the precise expected target for PaCO2.

Key Concept

Respiratory compensation in primary metabolic acidosis (Winter's formula)
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Topics

Nephrology

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