Water-deficit equation: systematic analysis and improvement

Abstract

Background: The water-deficit equation {WD₁ = 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 WD₁ 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 WD₁ were tested by substituting measured euhydrated values for assumed or unknown values. These included the known (premorbid) B_m (WD₂), a proposed correction for unknown B_m (WD₃), the TBW estimated from body composition (WD₄), the actual plasma sodium (WD₅), the substitution of plasma osmolality (Posm) for sodium (WD₆), and actual Posm (WD₇). 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 WD₁ through WD₇ all underestimated TBW loss by 1.5–2.5 L (P < 0.05). WD₁ through WD₅ underestimated FW by 0.5 L to 1.0 L (P < 0.05), but WD₆ and WD₇ estimated FW loss to within 0.06–0.16 L (P > 0.05). Conclusions: WD₁ grossly underestimates TBW and FW losses. Corrections for unknowns and assumptions (WD₂ through WD₅) improved estimates little. The use of WD₆ = 0.6 × B_m × [1 − (290 ÷ Posm)] accurately estimates FW but still underestimates TBW losses by >40%.