The formula to calculate the free water excess (FWE) is:
\[ FWE = \left( \frac{Na}{Na_{desired}} - 1 \right) \times W \]
Where:
Let's say the current sodium level is 140 mmol/L, the desired sodium level is 135 mmol/L, and the weight of the patient is 70 kg. Using the formula:
\[ FWE = \left( \frac{140}{135} - 1 \right) \times 70 \]
We get:
\[ FWE = \left( 1.037 - 1 \right) \times 70 = 0.037 \times 70 = 2.59 \]
So, the free water excess (\( FWE \)) is 2.59 liters.
Free water excess is a measure used in the medical field to determine the amount of water without solutes that needs to be removed or added to bring a patient’s sodium level to a desired target. It is particularly useful in the management of electrolyte imbalances such as hyponatremia, where the sodium concentration in the blood is abnormally low.
