Water-deficit equation: systematic analysis and improvement.

BACKGROUND The water-deficit equation {WD(1) = 0.6 × B(m) × [1 - (140 ÷ Na(+))]; B(m) denotes body mass} is used in medicine and nutrition to estimate the volume (L) of water required to correct dehydration during the initial stages of fluid-replacement therapy. Several equation assumptions may limit its accuracy, but none have been systematically tested. OBJECTIVES We quantified the potential error in WD(1) for the estimation of free water (FW) and total body water (TBW) losses and systematically evaluated its assumptions. DESIGN Thirty-six euhydrated volunteers were dehydrated (2.2-5.8% B(m)) via thermoregulatory sweating. Assumptions within WD(1) were tested by substituting measured euhydrated values for assumed or unknown values. These included the known (premorbid) B(m) (WD(2)), a proposed correction for unknown B(m) (WD(3)), the TBW estimated from body composition (WD(4)), the actual plasma sodium (WD(5)), the substitution of plasma osmolality (Posm) for sodium (WD(6)), and actual Posm (WD(7)). RESULTS Dehydration reduced TBW by 3.49 ± 0.91 L, 57% of which (2.02 ± 0.96 L) was FW loss, and increased plasma sodium from 139 (range: 135-143 mmol/L) to 143 (range: 141-148 mmol/L) mmol/L. Calculations for WD(1) through WD(7) all underestimated TBW loss by 1.5-2.5 L (P < 0.05). WD(1) through WD(5) underestimated FW by 0.5 L to 1.0 L (P < 0.05), but WD(6) and WD(7) estimated FW loss to within 0.06-0.16 L (P > 0.05). CONCLUSIONS WD(1) grossly underestimates TBW and FW losses. Corrections for unknowns and assumptions (WD(2) through WD(5)) improved estimates little. The use of WD(6) = 0.6 × B(m) × [1 - (290 ÷ Posm)] accurately estimates FW but still underestimates TBW losses by >40%.