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.
Definition: This calculator determines the amount of free water required based on various factors.
Formula: \( \text{Free Water Requirement} = \text{Total Water Requirement} - \text{Bound Water} \)
Example: \( \text{Free Water Requirement} = 1000 - 200 \)
Definition: This calculator determines the amount of free water lost over a period.
Formula: \( \text{Free Water Loss} = \text{Initial Free Water} - \text{Remaining Free Water} \)
Example: \( \text{Free Water Loss} = 800 - 500 \)
Definition: This calculator determines the free water deficit in the body.
Formula: \( \text{Free Water Deficit} = \text{Total Body Water} \times \left( \frac{\text{Current Sodium} - \text{Desired Sodium}}{\text{Desired Sodium}} \right) \)
Example: \( \text{Free Water Deficit} = 42 \times \left( \frac{150 - 140}{140} \right) \)
Definition: This equation calculates the free water deficit in the body.
Formula: \( \text{Free Water Deficit} = \text{Total Body Water} \times \left( \frac{\text{Current Sodium} - \text{Desired Sodium}}{\text{Desired Sodium}} \right) \)
Example: \( \text{Free Water Deficit} = 50 \times \left( \frac{155 - 135}{135} \right) \)
