Statistical & Clinical Analysis
Adrogué-Madias Formula: Predicted Serum Sodium Change per Liter of IV Infusate
Calculate expected Δ[Na+] = ([Na+ + K+]_infusate - [Na+]_serum) / (TBW + 1) and required 3% hypertonic saline volume (mL) while guarding against osmotic demyelination.
Why dividing by (TBW + 1) accounts for the 1 liter of infused water added to total body water!
Horacio J. Adrogué and Nicolaos E. Madias (2000, New England Journal of Medicine) derived the bedside closed-system mass-balance equation predicting how 1 liter of any IV fluid alters serum sodium [Na+]_s: Δ[Na+]_per_L = ([Na+]_inf + [K+]_inf - [Na+]_s) / (TBW + 1), where Total Body Water TBW = Weight_kg * f_TBW (0.60 adult men, 0.50 adult women/elderly men, 0.45 elderly women)—and where potassium [K+]_inf counts osmotically just like sodium via Edelman exchange!
To prevent Osmotic Demyelination Syndrome (ODS), chronic hyponatremia correction is strictly capped at <= 6–8 mEq/L in 24 hours! In a 70 kg man (f_TBW = 0.60 -> TBW = 42.0 L) with severe symptomatic hyponatremia [Na+]_s = 116 mEq/L receiving 3% NaCl ([Na+]_inf = 513 mEq/L), 1 liter raises [Na+] by +9.23 mEq/L—so achieving a safe +6.0 mEq/L target requires 650 mL (whereas 1 L of 0.9% NaCl at 154 mEq/L raises [Na+] by +0.88 mEq/L)!
| IV Infusate (70 kg, TBW = 42 L, Serum Na = 116 mEq/L) | Δ[Na+] per 1 Liter Infused | Volume for +6 mEq/L Target | ODS Safety Check |
|---|---|---|---|
| 3% Hypertonic NaCl (513 mEq/L, K = 0) | +9.23 mEq/L per L | 650 mL | Never infuse full 1 L blind (> 8 mEq/L)! |
| 0.9% Isotonic NaCl (154 mEq/L, K = 0) | +0.88 mEq/L per L | 6,790 mL (Check ADH/SIADH!) | Note: SIADH high urine Osm can paradoxically lower Na |
| Target 24h Rise > 8 mEq/L or Invalid Weight | Safety Guard | "Exceeds Safe <= 8 mEq/L 24h ODS Cap" | Osmotic Demyelination Guard |
Adrogué-Madias Expected Serum Sodium Change per 1 Liter Infused (mEq/L)
Evaluates ([Na]_inf + [K]_inf - [Na]_serum) / (Weight * f_TBW + 1) from B2:B6.
=IF(OR(B2 < 0, B3 < 0, B4 < 90, B4 > 190, B5 <= 0, B6 < 0.35, B6 > 0.75), "Invalid Hyponatremia Inputs", ROUND((B2 + B3 - B4) / (B5 * B6 + 1), 2))Infusate Volume (mL) for Safe 24-Hour Sodium Rise Target (<= 8 mEq/L Cap)
Computes (Target_Rise / Δ[Na]_per_L) * 1000 mL, blocking unsafe > 8 mEq/L 24-hour correction targets.
=IF(OR(B2 < 0, B3 < 0, B4 < 90, B4 > 190, B5 <= 0, B6 < 0.35, B6 > 0.75), "Invalid Hyponatremia Inputs", IF(OR(B7 <= 0, B7 > 8), "Exceeds Safe <= 8 mEq/L 24h ODS Cap", IF(B2 + B3 <= B4, "Infusate Cannot Raise Serum Na", ROUND((B7 / ((B2 + B3 - B4) / (B5 * B6 + 1))) * 1000, 0))))Try the example
Use the original values or change them to test your understanding.