In clinical settings, particularly in critical care and neurology, calculating the correct infusion rate of hypertonic saline (3% NaCl) is vital for treating symptomatic hyponatremia or managing intracranial pressure. The most widely accepted method for this calculation is the Adrogue-Madias formula.
The Adrogue-Madias Formula
This formula predicts the change in serum sodium concentration resulting from the infusion of one liter of a specific fluid:
Change in Serum Na = (Infusate Na – Serum Na) / (TBW + 1)
Where:
Infusate Na: 513 mEq/L for 3% Saline.
Serum Na: The patient's current measured sodium level.
TBW (Total Body Water): Weight (kg) multiplied by a factor based on age and sex (usually 0.6 for men and 0.5 for women).
Practical Steps for Calculation
Identify the Goal: Determine the target sodium level. Typically, clinicians aim for a rise of 4-6 mEq/L over 24 hours to avoid Osmotic Demyelination Syndrome (ODS).
Calculate TBW: Multiply the patient's weight by their specific constant.
Determine Change per Liter: Use the formula above to see how much 1000ml of 3% saline will raise the patient's sodium.
Calculate Total Volume: Divide the desired total sodium rise (Target – Current) by the "Change per Liter" value.
Calculate Hourly Rate: Divide the Total Volume by the desired timeframe (e.g., 24 hours).
CRITICAL SAFETY NOTE: Rapid correction of chronic hyponatremia can lead to irreversible neurological damage (Osmotic Demyelination Syndrome). Most guidelines suggest not exceeding a correction rate of 8-10 mEq/L in any 24-hour period.
Example Calculation
A 70kg male has a serum sodium of 110 mEq/L. You want to raise it to 116 mEq/L over 24 hours using 3% saline.