A 50-year-old man is evaluated in the neuro-intensive care unit. He was admitted four days… — USMLE Step 2 CK

A 50-year-old man is evaluated in the neuro-intensive care unit. He was admitted four days ago after sustaining a severe closed head injury in a high-speed motor vehicle collision. Over the past 24 hours, the nursing staff reports a dramatic increase in his urine output, totaling 7.5 L of pale, dilute urine. He is currently intubated and sedated. His weight on admission was 72 kg, and his current weight is 70 kg. Vital signs show a blood pressure of 102/64 mm Hg and a heart rate of 118/min. Laboratory studies reveal a serum sodium concentration of 160 mEq/L and a serum osmolality of 330 mOsm/kg $H_2O$ . Urine osmolality is 115 mOsm/kg $H_2O$ . The patient is diagnosed with central diabetes insipidus.

What is this patient's estimated free water deficit in liters?

Answer: 6 L

Answer

The patient has developed severe hypernatremia due to massive free water loss from central diabetes insipidus. To safely correct his sodium levels and formulate an intravenous fluid replacement plan, the free water deficit must be calculated. The standard formula is

FWD = TBW \times (\frac{\text{Measured } Na^+}{140} - 1)

. For a 50-year-old adult male, TBW is estimated as 60% of his current body weight (

0.6 \times 70 \text{ kg} = 42 \text{ L}

). Plugging in the serum sodium of 160 mEq/L yields

42 \times (\frac{160}{140} - 1) = 42 \times \frac{1}{7} = 6

liters.

Step-by-Step Solution

Calculate Total Body Water (TBW)

42 L

TBW for an adult male is approximately 60% (0.6) of his lean body weight. Current weight (70 kg) should be used.

Set up the Free Water Deficit formula

FWD = 42 \times (\frac{160}{140} - 1)

The standard formula requires the TBW and the ratio of the patient's measured serum sodium to the ideal serum sodium (140 mEq/L).

Solve the equation mathematically

42 \times (\frac{20}{140})

simplifies to

42 \times \frac{1}{7}

, which equals exactly 6.

Key Concept

Calculation of Free Water Deficit in Hypernatremia

Estimated Time:1m 30s

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