Free Water Deficit in Hypernatremia
Formula for Free Water Deficit in Hypernatremia
| Free Water Deficit (FWD) = TBW x (serum [Na] -140) / 140; TBW = wt (kg) x 0.6 (male) or 0.5 (female). If elderly use, 0.5 (male) and 0.45 (female) |
Note: The FWD does is not constant but will change moving forward. It doesn’t include of ongoing free water losses.
How to Derive the Water Deficit Formula
The Free water deficit is the amount of free water a patient has lost. How do you know how much water a patient has lost?
Much of the water is stored in the intracellular space and we can’t easily measure that. Sodium Concentration becomes a good surrogate for how much free water a patient has lost.
Note, [Na+] is a surrogate for free water, not for volume!
In hypernatremia, the total body sodium (TBS) doesn’t change. Hypernatremia is caused by loss of free water, not a loss of sodium.
[Na+] in serum = TBS ÷ TBW ……………………………….equation 1
That means,
TBS = [Na+] in serum x TBW ……………………………… equation 2
Again, water balance doesn’t affect total body sodium. The total body sodium, at say lab draw #1, when the sodium concentration is high will be the same as in lab draw #2, when the sodium concentration reaches the desired level. To leave from concentration #1 (from lab#1) to the desired sodium concentration in lab #2, you will need to add a certain amount of free water to the patients TBW.
From equation 2 above, we know that the TBS at the high sodium concentration called #1 will be equal to the TBS at the desired lower sodium concentration called #2. The difference is that we would have added X amount of free water to our TBW. And because TBW is weight-based (as shown below), the two TBWs will be different since the patient will weight more after she has received the fluid.
[Na+]high ∗ TBW1 = [Na+]desired ∗ (TBW1 + X)
Where X is the free water deficit. If the desired sodium is 140, rearranging the equation and solving for X gives you:
X = {([Na+]high – 140) ÷ 140 }∗TBW1
Note that the free water deficit, X, is not a static value. What you calculate for X today will not be the same thing tomorrow. X is only valid for that point in time.
Free water deficit doesn’t take into account ongoing water losses. It only tells you what the deficit is right now, it doesn’t tell you what the deficit will be in the future.
The free water clearance is a value that will help tell us to calculate the ongoing water losses.
Estimating the Total Body Water
TBW = Wt (kg) x 0.6 for males
TBW = Wt (kg) x 0.5 for females.
If elderly, use 0.5 for males and 0.45 for females.