Free-water deficit in a hypernatremic dog
A 66 lb dog presents with severe dehydration and serum Na of 170 mEq/L. You want to correct gradually to a target of 145 mEq/L. Estimate the free-water deficit. Use total body water = 60 % of body weight.
Hint
Convert lb to kg first. The TBW estimate (60 %) is a fraction of the kg weight. You're estimating how much pure water you'd need to dilute existing sodium down to the target.
Another hint
(1) lb → kg via 2.2 lb/kg. (2) TBW (L) ≈ 0.6 × weight (kg). (3) Free-water deficit (L) ≈ TBW × ((current Na ÷ target Na) − 1). The Na ratio is dimensionless so the answer comes out in liters. Don't forget the safety check on correction rate (no faster than 0.5–1 mEq/L/hr drop).
Show worked answer
-
Convert the patient's weight from lb to kg.
$$\frac{66 \,\cancel{lb}}{2.2 \,\cancel{lb}/kg} = 30 \,kg$$ -
Total body water (TBW) is the fluid compartment we're diluting. For a 30 kg dog, TBW ≈ 0.6 × 30 = 18 L.
$$0.6 \times 30\,kg = 18 \,L$$ -
Free-water deficit (L) ≈ TBW × ((current Na ÷ target Na) − 1). The unit ratios are dimensionless, so the answer comes out in liters.
$$18\,L \times \left(\tfrac{170}{145} - 1\right) = 18 \times 0.1724 \approx 3.1\,L$$ -
That's the free-water deficit alone (volume of pure water needed to bring Na to target). In practice you'd give a hypotonic crystalloid like D5W, 0.45 % NaCl, or maintenance solutions (not pure water), and correct at no faster than 0.5–1 mEq/L/hr to avoid cerebral edema.
-
Sanity check on the correction rate: dropping Na from 170 to 145 is a 25 mEq/L change. At 0.5 mEq/L/hr that needs 50 hours; at 1 mEq/L/hr, 25 hours.
-
Why a hypotonic fluid? You're trying to drop the serum sodium, which means giving fluid with a lower Na concentration than the patient's plasma. Isotonic crystalloids (0.9 % NaCl, LRS) wouldn't move serum Na meaningfully, and hypertonic saline would make it worse. 0.45 % NaCl and D5W are both reasonable choices in dogs; in practice the choice between them depends on whether you also need volume support (0.45 % NaCl) versus pure free water (D5W).
Free-water deficit ≈ 3.1 L. Correct slowly over 25–50 hr (≤ 0.5–1 mEq/L/hr drop in Na) to avoid cerebral edema.