Kidney Week

Abstract: TH-PO0069

The Classic Free Water Deficit Equation Is Inaccurate: A Validated Correction

Session Information

• Fluid, Electrolyte, and Acid-Base Disorders: Clinical Research
  October 22, 2026 | Location: Exhibit Hall A, Convention Center
  Abstract Time: 10:00 AM - 12:00 PM

Category: Fluid, Electrolytes, and Acid-Base Disorders

• 1102 Fluid, Electrolyte, and Acid-Base Disorders: Clinical

Authors

• Reed, Hunter T., University of South Florida, Tampa, Florida, United States

Hunter T. Reed, MD

• Durr, Jacques A., University of South Florida, Tampa, Florida, United States

Jacques A. Durr, MD

• Audi, Akram, University of South Florida, Tampa, Florida, United States

Akram Audi, MD

Background

The classic equation Δw = TBW*([Na]/140 – 1) relating free water deficit to total body water, current and ideal natremia, [Na] and 140 mmol/L, respectively, is erroneous. Correct derivation yields Δw=TBW*(140/[Na]–1). The assumption that TBW = k*wgt is a constant fraction k of weight (k = 0.5 and 0.6 in adult ♀ and ♂) during free water loss is also mistaken, as Δw alters k.

Methods

We performed a method comparison across nine pooled body composition studies to relate measured TBW to monovalent cation space: TBW = a*(Na_e + K_e)/[Na + K]' + b. Using Passing-Bablok (PB) regression and Bland-Altman (BA) plots, we verify this space equals TBW. While this equality is key for deriving Δw, it is not sufficient; rigorous derivation is also required.

Results

The PB regression yielded a slope a = 0.995 CI [0.973–1.017] and y intercept b = 0.086 L CI [-0.621– 0.792] r = 0.981, n = 369 (Fig. 1); BA analysis showed a mean difference between TBWs and these cation spaces of 0.2 ± 5.5 %, confirming they measure the same physiological space. (Fig.1). We expressed TBW = k*(wgt2 - Δw) as a function of current weight, corrected algebraically for Δw, rather than the incorrect formula TBW = k*wgt₂. The classic equation, unlike our version is linear in [Na], a clue to derivation issues. To derive our equations (Fig2, first panel), we eliminated (Na_e + K_e) between states b) and a). We assessed all Δw equations against [Na]₂ and wgt₂ values generated numerically in response to free water losses in a model inspired by a 118 kg ♀ nephrogenic diabetes insipidus patient who presented with [Na]₂ = 177 mmol/L. Only the correct equation recovered the exact Δw values used in data generation (green line seen in Fig. 2, right panel)

Conclusion

Our findings invalidate the classic free water deficit equation that is frequently utilized. On-line applications and electronic resources should be updated to provide a more accurate free water deficit equation.

Funding

• Clinical Revenue Support