# How are fluid deficits calculated in the emergency department (ED) care for hypernatremia?

Updated: Mar 17, 2020
• Author: Zina Semenovskaya, MD; Chief Editor: Romesh Khardori, MD, PhD, FACP  more...
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Traditionally, correction of hypernatremia begins with a calculation of the fluid deficit as shown below. Predicted insensible and other ongoing losses are added to this number and the total is administered over 48 hours. Recheck serum electrolyte levels frequently during therapy. To avoid cerebral edema and associated complications, the serum sodium level should be lowered by no more than 1 mEq/L every hour. In patients with chronic hypernatremia, an even more gradual rate is preferred.

An alternative method to plan the correction of sodium imbalances has been proposed by Adrogue and Madias. They have devised a formula that can be used to calculate the change in serum sodium level after the administration of 1 L of a given infusate. This formula has the advantages of taking into consideration the tonicity of the infusate and encouraging reassessment of the treatment plan with each liter of solution or new set of electrolytes.

Free Water Deficit = Body Weight (kg) X Percentage of Total Body Water (TBW) X ([Serum Na / 140] - 1)

The percentage of TBW should be as follows:

• Young men - 0.6%

• Young women and elderly men - 0.5%

• Elderly women - 0.4%

An example is as follows: A serum sodium level of 155 in a 60-kg young man represents a fluid deficit of 60 X 0.6 X ([155 / 140] - 1) or 3.9 L. With another 900 mL of insensible losses, the patient requires 4.8 L of fluid in the next 48 hours, resulting in an infusion rate of 100 mL/h.

The Adrogue and Madias formula is as follows: Change in Serum Sodium = ([Na] Infused - [Na] serum) / (TBW + 1)

The "1" in the denominator represents the extra liter of infusate added to TBW. When TBW is calculated as above, TBW = Body Weight (kg) X Percent Water

An example is as follows: For the patient above, the expected change can be calculated with D5W or D5 half isotonic sodium chloride solution.

For D5W, Change = (0 - 155) / ([60 X 0.6] + 1) = -4.18 mEq/L

For half isotonic sodium chloride solution, Change = (77 - 155) / ([60 X 0.6] + 1) = -2.1 mEq/L

If D5W is chosen to avoid fluid overload, an infusion rate of 250 mL/h results in a correction just over 1 mEq/h. (Note: This assumes the patient has no other losses during this time. Intrinsic losses make the correction slower [more conservative] than calculated.)