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Difficulty: HardNephrology

An 82-year-old man with advanced Alzheimer dementia is brought to the emergency department from a skilled nursing facility due to progressive lethargy over the past 3 days. The facility staff report that he has been refusing meals and liquids. On examination, temperature is 37.1°C (98.8°F), blood pressure is 98/60 mm Hg, pulse is 112/min, and respiratory rate is 16/min. The patient appears cachectic with profoundly dry mucous membranes and poor skin turgor. His current weight is 60 kg (132 lb).

Laboratory studies show:
Serum sodium: 168 mEq/L
Serum potassium: 4.1 mEq/L
Serum chloride: 129 mEq/L
Serum bicarbonate: 24 mEq/L
Blood urea nitrogen: 56 mg/dL
Serum creatinine: 1.8 mg/dL

Based on an estimated total body water of 50% of his body weight, what is this patient's calculated free water deficit in liters?

Answer: 6 L

Answer

6
The free water deficit is calculated using the formula: Water Deficit=TBW×(Actual Serum Na+140−1)Water\ Deficit = TBW \times \left(\frac{Actual\ Serum\ Na^+}{140} - 1\right). Given a weight of 6060 kg and an estimated TBW fraction of 50%50\%, the TBW is 3030 L. The actual serum sodium is 168168 mEq/L. Substituting these values into the formula yields: 30×(168140−1)=30×(1.2−1)=30×0.2=630 \times \left(\frac{168}{140} - 1\right) = 30 \times (1.2 - 1) = 30 \times 0.2 = 6 liters. This represents the volume of solute-free water the patient has lost to develop this degree of hypernatremia.

Step-by-Step Solution

1
Calculate the patient's Total Body Water (TBW).
TBW=60×0.50=30TBW = 60 \times 0.50 = 30 L
Free water deficit calculations require an accurate estimate of the patient's baseline TBW, which is typically 50% of lean body weight for elderly men.
2
Set up the free water deficit formula.
Deficit=TBW×(Actual [Na+]Target [Na+]−1)Deficit = TBW \times \left(\frac{Actual\ [Na^+]}{Target\ [Na^+]} - 1\right)
This formula relates the current total body water to the proportional excess of sodium concentration relative to a normal target (140 mEq/L).
3
Substitute the calculated TBW and provided serum sodium values into the formula to find the final deficit.
Deficit=30×(168140−1)=30×(1.2−1)=30×0.2=6Deficit = 30 \times \left(\frac{168}{140} - 1\right) = 30 \times (1.2 - 1) = 30 \times 0.2 = 6 L
This quantifies the exact volume of pure water required to dilute the current total body solute back to a normal serum sodium concentration of 140 mEq/L.

Key Concept

Free water deficit calculation in hypernatremia
Estimated Time:1m 30s
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Topics

Nephrology

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